[llvm] feat: Scev predicated overflow btc and testing (PR #208581)
Bavly Peter via llvm-commits
llvm-commits at lists.llvm.org
Tue Aug 4 08:11:47 PDT 2026
https://github.com/bavly-bob updated https://github.com/llvm/llvm-project/pull/208581
>From 9d2e6318c6b74e64381955c111ce3f05efe1a55c Mon Sep 17 00:00:00 2001
From: bavly-bob <bavlypeter84 at gmail.com>
Date: Thu, 9 Jul 2026 23:15:49 +0300
Subject: [PATCH 1/3] feat: Scev predicated overflow btc and testing
---
llvm/lib/Analysis/ScalarEvolution.cpp | 22 +++++++--
.../ScalarEvolution/fwrapv-assume-safety.ll | 34 ++++++++++++++
.../LoopVectorize/fwrapv-assume-safety.ll | 45 +++++++++++++++++++
.../Analysis/ScalarEvolutionTest.cpp | 32 +++++++++++++
4 files changed, 130 insertions(+), 3 deletions(-)
create mode 100644 llvm/test/Analysis/ScalarEvolution/fwrapv-assume-safety.ll
create mode 100644 llvm/test/Transforms/LoopVectorize/fwrapv-assume-safety.ll
diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index ea2d72db97fb0..69f0b9c315a30 100644
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -13567,11 +13567,27 @@ ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
Stride = getUMaxExpr(Stride, getOne(Stride->getType()));
}
}
- } else if (!NoWrap) {
+ }else if (!NoWrap) {
// Avoid proven overflow cases: this will ensure that the backedge taken
// count will not generate any unsigned overflow.
- if (canIVOverflowOnLT(RHS, Stride, IsSigned))
- return getCouldNotCompute();
+ if (canIVOverflowOnLT(RHS, Stride, IsSigned)) {
+ if (!AllowPredicates)
+ return getCouldNotCompute();
+
+ unsigned BitWidth = getTypeSizeInBits(RHS->getType());
+ const SCEV *One = getOne(Stride->getType());
+ const SCEV *StrideMinusOne = getMinusSCEV(Stride, One);
+
+ APInt MaxStrideMinusOne = IsSigned ? getSignedRangeMax(StrideMinusOne)
+ : getUnsignedRangeMax(StrideMinusOne);
+ APInt Limit = (IsSigned ? APInt::getSignedMaxValue(BitWidth)
+ : APInt::getMaxValue(BitWidth)) -
+ MaxStrideMinusOne;
+
+ Predicates.push_back(getComparePredicate(
+ IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE, RHS,
+ getConstant(Limit)));
+ }
}
// On all paths just preceeding, we established the following invariant:
diff --git a/llvm/test/Analysis/ScalarEvolution/fwrapv-assume-safety.ll b/llvm/test/Analysis/ScalarEvolution/fwrapv-assume-safety.ll
new file mode 100644
index 0000000000000..f8f7778cda507
--- /dev/null
+++ b/llvm/test/Analysis/ScalarEvolution/fwrapv-assume-safety.ll
@@ -0,0 +1,34 @@
+; RUN: opt < %s -disable-output "-passes=print<scalar-evolution>" 2>&1 | FileCheck %s
+
+; Verify that ScalarEvolution can compute a predicated backedge-taken count
+; for a loop with a non-unit stride (stride = 3) and no 'nsw' flag on the
+; induction variable (e.g. from compilation under -fwrapv).
+; Without the predicate, the backedge-taken count is unpredictable.
+
+define void @fwrapv_stride3(ptr noalias %x, i32 %l, i32 %u) {
+; CHECK-LABEL: Determining loop execution counts for: @fwrapv_stride3
+; CHECK-NEXT: Loop %loop.body: Unpredictable backedge-taken count.
+; CHECK-NEXT: Loop %loop.body: Unpredictable constant max backedge-taken count.
+; CHECK-NEXT: Loop %loop.body: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop.body: Predicated backedge-taken count is
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %u sle) 2147483645
+
+entry:
+ %cmp1 = icmp slt i32 %l, %u
+ br i1 %cmp1, label %loop.body, label %exit
+
+loop.body:
+ %i = phi i32 [ %l, %entry ], [ %i.next, %loop.body ]
+ %idxprom = sext i32 %i to i64
+ %arrayidx = getelementptr inbounds i32, ptr %x, i64 %idxprom
+ %val = load i32, ptr %arrayidx, align 4
+ %inc = add nsw i32 %val, 1
+ store i32 %inc, ptr %arrayidx, align 4
+ %i.next = add i32 %i, 3
+ %cmp = icmp slt i32 %i.next, %u
+ br i1 %cmp, label %loop.body, label %exit
+
+exit:
+ ret void
+}
diff --git a/llvm/test/Transforms/LoopVectorize/fwrapv-assume-safety.ll b/llvm/test/Transforms/LoopVectorize/fwrapv-assume-safety.ll
new file mode 100644
index 0000000000000..6987c4ba66201
--- /dev/null
+++ b/llvm/test/Transforms/LoopVectorize/fwrapv-assume-safety.ll
@@ -0,0 +1,45 @@
+; RUN: opt -passes=loop-vectorize -force-vector-width=4 -force-vector-interleave=1 -S < %s | FileCheck %s
+
+; Verify that a loop with a non-unit stride (stride = 3) and no 'nsw' flag on the
+; induction variable (e.g. from compilation with -fwrapv) can be vectorized
+; by generating a runtime SCEV check to verify the lack of overflow/wrapping.
+
+define void @fwrapv_stride3(ptr noalias %x, i32 %l, i32 %u) {
+; CHECK-LABEL: @fwrapv_stride3(
+; CHECK: vector.scevcheck:
+; CHECK: %ident.check = icmp sgt i32 %u, 2147483645
+; CHECK: %mul = call { i32, i1 } @llvm.umul.with.overflow.i32(i32 3, i32 {{.*}})
+; CHECK: %mul.result = extractvalue { i32, i1 } %mul, 0
+; CHECK: %mul.overflow = extractvalue { i32, i1 } %mul, 1
+; CHECK: [[IDENT:%.*]] = add i32 %l, %mul.result
+; CHECK: [[OVERFLOW:%.*]] = icmp slt i32 [[IDENT]], %l
+; CHECK: [[OVERFLOW2:%.*]] = or i1 [[OVERFLOW]], %mul.overflow
+; CHECK: [[CHECK:%.*]] = or i1 %ident.check, [[OVERFLOW2]]
+; CHECK: br i1 [[CHECK]], label %scalar.ph, label %vector.ph
+; CHECK: vector.body:
+; CHECK: br i1 {{.*}}, label %middle.block, label %vector.body
+; CHECK: scalar.ph:
+; CHECK: [[RESUME_PHI:%.*]] = phi i32
+; CHECK: br label %loop.body
+
+entry:
+ %cmp1 = icmp slt i32 %l, %u
+ br i1 %cmp1, label %loop.body, label %exit
+
+loop.body:
+ %i = phi i32 [ %l, %entry ], [ %i.next, %loop.body ]
+ %idxprom = sext i32 %i to i64
+ %arrayidx = getelementptr inbounds i32, ptr %x, i64 %idxprom
+ %val = load i32, ptr %arrayidx, align 4
+ %inc = add nsw i32 %val, 1
+ store i32 %inc, ptr %arrayidx, align 4
+ %i.next = add i32 %i, 3
+ %cmp = icmp slt i32 %i.next, %u
+ br i1 %cmp, label %loop.body, label %exit, !llvm.loop !0
+
+exit:
+ ret void
+}
+
+!0 = distinct !{!0, !1}
+!1 = !{!"llvm.loop.vectorize.enable", i1 true}
diff --git a/llvm/unittests/Analysis/ScalarEvolutionTest.cpp b/llvm/unittests/Analysis/ScalarEvolutionTest.cpp
index 4bd4463dda787..849a7fec8fe51 100644
--- a/llvm/unittests/Analysis/ScalarEvolutionTest.cpp
+++ b/llvm/unittests/Analysis/ScalarEvolutionTest.cpp
@@ -1495,6 +1495,38 @@ TEST_F(ScalarEvolutionsTest, ImpliedCond) {
});
}
+TEST_F(ScalarEvolutionsTest, PredicatedBackedgeTakenCountForOverflowingStride) {
+ LLVMContext C;
+ SMDiagnostic Err;
+ std::unique_ptr<Module> M = parseAssemblyString(
+ "define void @foo(i32 %n) { "
+ "entry: "
+ " br label %loop "
+ "loop: "
+ " %iv = phi i32 [ 0, %entry ], [ %iv.next, %loop ] "
+ " %iv.next = add i32 %iv, 3 "
+ " %cmp = icmp slt i32 %iv, %n "
+ " br i1 %cmp, label %loop, label %exit "
+ "exit: "
+ " ret void "
+ "}",
+ Err, C);
+
+ ASSERT_TRUE(M && "Could not parse module?");
+ ASSERT_TRUE(!verifyModule(*M) && "Must have been well formed!");
+
+ runWithSE(*M, "foo", [](Function &F, LoopInfo &LI, ScalarEvolution &SE) {
+ const Loop *L = LI.begin() != LI.end() ? *LI.begin() : nullptr;
+ ASSERT_NE(L, nullptr);
+
+ SmallVector<const SCEVPredicate *, 4> Predicates;
+ const SCEV *BTC = SE.getPredicatedBackedgeTakenCount(L, Predicates);
+
+ EXPECT_FALSE(isa<SCEVCouldNotCompute>(BTC));
+ EXPECT_FALSE(Predicates.empty());
+ });
+}
+
TEST_F(ScalarEvolutionsTest, MatchURem) {
LLVMContext C;
SMDiagnostic Err;
>From c726c54a679e176bb2b9104eb5663a797154a313 Mon Sep 17 00:00:00 2001
From: bavly-bob <bavlypeter84 at gmail.com>
Date: Fri, 10 Jul 2026 17:12:07 +0300
Subject: [PATCH 2/3] [ScalarEvolution][test] Update expected test output
---
.../addrec-may-wrap-udiv-canonicalize.ll | 45 +++++++
.../ScalarEvolution/max-trip-count.ll | 23 ++++
.../trip-count-non-unit-stride.ll | 112 ++++++++++++++++++
3 files changed, 180 insertions(+)
diff --git a/llvm/test/Analysis/ScalarEvolution/addrec-may-wrap-udiv-canonicalize.ll b/llvm/test/Analysis/ScalarEvolution/addrec-may-wrap-udiv-canonicalize.ll
index e041c96371762..1132e7478c82a 100644
--- a/llvm/test/Analysis/ScalarEvolution/addrec-may-wrap-udiv-canonicalize.ll
+++ b/llvm/test/Analysis/ScalarEvolution/addrec-may-wrap-udiv-canonicalize.ll
@@ -28,6 +28,15 @@ define void @test_step2_div4(i64 %n) {
; CHECK-NEXT: Loop %loop: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is ((1 + (0 smax %n))<nuw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 4611686018427387903
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is ((1 + (0 smax %n))<nuw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
;
entry:
br label %loop
@@ -78,6 +87,15 @@ define void @test_step3_div6(i64 %n) {
; CHECK-NEXT: Loop %loop: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is ((((-1 * (1 umin (0 smax %n)))<nuw><nsw> + (0 smax %n)) /u 3) + (1 umin (0 smax %n)))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775805
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 3074457345618258602
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775805
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is ((((-1 * (1 umin (0 smax %n)))<nuw><nsw> + (0 smax %n)) /u 3) + (1 umin (0 smax %n)))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775805
;
entry:
br label %loop
@@ -137,6 +155,15 @@ define void @test_step4_div4(i64 %n) {
; CHECK-NEXT: Loop %loop: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is ((3 + (0 smax %n))<nuw> /u 4)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775804
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 2305843009213693951
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775804
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is ((3 + (0 smax %n))<nuw> /u 4)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775804
;
entry:
br label %loop
@@ -219,6 +246,15 @@ define void @test_step2_start_outer_add_rec_step_16(i64 %n, i64 %m) {
; CHECK-NEXT: Loop %loop: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is (({1,+,-16}<%outer.header> + ({0,+,16}<%outer.header> smax %n)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 9223372036854775807
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is (({1,+,-16}<%outer.header> + ({0,+,16}<%outer.header> smax %n)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
; CHECK-NEXT: Loop %outer.header: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %outer.header: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %outer.header: Unpredictable symbolic max backedge-taken count.
@@ -335,6 +371,15 @@ define void @test_step2_div4_start_outer_add_rec_step_2(i64 %n, i64 %m) {
; CHECK-NEXT: Loop %loop: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is (({1,+,-2}<%outer.header> + ({0,+,2}<%outer.header> smax %n)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 9223372036854775807
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is (({1,+,-2}<%outer.header> + ({0,+,2}<%outer.header> smax %n)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 9223372036854775806
; CHECK-NEXT: Loop %outer.header: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %outer.header: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %outer.header: Unpredictable symbolic max backedge-taken count.
diff --git a/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll b/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll
index 501aa963f9294..49051471297d0 100644
--- a/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll
+++ b/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll
@@ -446,6 +446,12 @@ define void @changing_end_bound4(i32 %start, ptr %n_addr, ptr %addr) {
; CHECK-NEXT: Loop %loop: Unpredictable backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i32 1073741823
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 2147483644
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is i32 1073741823
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 2147483644
;
entry:
br label %loop
@@ -573,10 +579,27 @@ define void @max_overflow_me(i8 %n) mustprogress {
; CHECK-NEXT: Loop %loop: <multiple exits> Unpredictable backedge-taken count.
; CHECK-NEXT: exit count for loop: i8 1
; CHECK-NEXT: exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for latch: i8 0
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 65
+; CHECK-EMPTY:
; CHECK-NEXT: Loop %loop: constant max backedge-taken count is i8 1
; CHECK-NEXT: Loop %loop: symbolic max backedge-taken count is i8 1
; CHECK-NEXT: symbolic max exit count for loop: i8 1
; CHECK-NEXT: symbolic max exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for latch: i8 0
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 65
+; CHECK-EMPTY:
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is i8 0
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 65
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i8 0
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 65
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is i8 0
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %n sle) 65
;
entry:
br label %loop
diff --git a/llvm/test/Analysis/ScalarEvolution/trip-count-non-unit-stride.ll b/llvm/test/Analysis/ScalarEvolution/trip-count-non-unit-stride.ll
index b52b4a984296c..ef4d9a3ac43f6 100644
--- a/llvm/test/Analysis/ScalarEvolution/trip-count-non-unit-stride.ll
+++ b/llvm/test/Analysis/ScalarEvolution/trip-count-non-unit-stride.ll
@@ -14,11 +14,39 @@ define void @test_preinc_ult(i64 %len) {
; CHECK-NEXT: Determining loop execution counts for: @test_preinc_ult
; CHECK-NEXT: Loop %loop: <multiple exits> Unpredictable backedge-taken count.
; CHECK-NEXT: exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for loop: ((1 + %len) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
; CHECK-NEXT: exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for latch: ((-1 + (2 umax %len)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
; CHECK-NEXT: symbolic max exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for loop: ((1 + %len) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
; CHECK-NEXT: symbolic max exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for latch: ((-1 + (2 umax %len)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is (((1 + %len) /u 2) umin ((-1 + (2 umax %len)) /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 9223372036854775806
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is (((1 + %len) /u 2) umin ((-1 + (2 umax %len)) /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Compare predicate: %len ule) -2
;
start:
br label %loop
@@ -49,11 +77,39 @@ define void @test_postinc_ult(i64 %len) {
; CHECK-NEXT: Determining loop execution counts for: @test_postinc_ult
; CHECK-NEXT: Loop %loop: <multiple exits> Unpredictable backedge-taken count.
; CHECK-NEXT: exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for loop: ((1 umax %len) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
; CHECK-NEXT: exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for latch: ((-1 + (2 umax %len)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
; CHECK-NEXT: symbolic max exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for loop: ((1 umax %len) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
; CHECK-NEXT: symbolic max exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for latch: ((-1 + (2 umax %len)) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-EMPTY:
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is (((-1 + (2 umax %len)) /u 2) umin ((1 umax %len) /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 9223372036854775806
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is (((-1 + (2 umax %len)) /u 2) umin ((1 umax %len) /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len ule) -2
+; CHECK-NEXT: Compare predicate: %len ule) -2
;
start:
br label %loop
@@ -83,11 +139,39 @@ define void @test_preinc_slt(i64 %len) {
; CHECK-NEXT: Determining loop execution counts for: @test_preinc_slt
; CHECK-NEXT: Loop %loop: <multiple exits> Unpredictable backedge-taken count.
; CHECK-NEXT: exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for loop: ((1 + (0 smax %len))<nuw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
; CHECK-NEXT: exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for latch: ((-1 + (2 smax %len))<nsw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
; CHECK-NEXT: symbolic max exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for loop: ((1 + (0 smax %len))<nuw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
; CHECK-NEXT: symbolic max exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for latch: ((-1 + (2 smax %len))<nsw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is (((1 + (0 smax %len))<nuw> /u 2) umin ((-1 + (2 smax %len))<nsw> /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 4611686018427387902
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is (((1 + (0 smax %len))<nuw> /u 2) umin ((-1 + (2 smax %len))<nsw> /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
;
start:
br label %loop
@@ -118,11 +202,39 @@ define void @test_postinc_slt(i64 %len) {
; CHECK-NEXT: Determining loop execution counts for: @test_postinc_slt
; CHECK-NEXT: Loop %loop: <multiple exits> Unpredictable backedge-taken count.
; CHECK-NEXT: exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for loop: ((1 smax %len) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
; CHECK-NEXT: exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated exit count for latch: ((-1 + (2 smax %len))<nsw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
; CHECK-NEXT: Loop %loop: Unpredictable constant max backedge-taken count.
; CHECK-NEXT: Loop %loop: Unpredictable symbolic max backedge-taken count.
; CHECK-NEXT: symbolic max exit count for loop: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for loop: ((1 smax %len) /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
; CHECK-NEXT: symbolic max exit count for latch: ***COULDNOTCOMPUTE***
+; CHECK-NEXT: predicated symbolic max exit count for latch: ((-1 + (2 smax %len))<nsw> /u 2)
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-EMPTY:
+; CHECK-NEXT: Loop %loop: Predicated backedge-taken count is (((-1 + (2 smax %len))<nsw> /u 2) umin ((1 smax %len) /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated constant max backedge-taken count is i64 4611686018427387902
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Loop %loop: Predicated symbolic max backedge-taken count is (((-1 + (2 smax %len))<nsw> /u 2) umin ((1 smax %len) /u 2))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
+; CHECK-NEXT: Compare predicate: %len sle) 9223372036854775806
;
start:
br label %loop
>From 118d7a4480d69ae1083e0e66bf8f5c11a2487bdf Mon Sep 17 00:00:00 2001
From: bavly-bob <bavlypeter84 at gmail.com>
Date: Thu, 30 Jul 2026 20:45:12 +0300
Subject: [PATCH 3/3] [SCEV] Avoid creating compare predicates before pointer
IV normalization howManyLessThans() can receive pointer-typed induction
variables. Creating a compare predicate before converting the pointer SCEV to
an integer SCEV violates SCEVComparePredicate's type equality invariant. Move
predicate creation after pointer normalization so both operands have matching
integer types.
---
llvm/lib/Analysis/ScalarEvolution.cpp | 33007 ++++++++--------
.../Analysis/ScalarEvolutionTest.cpp | 26 +-
2 files changed, 16520 insertions(+), 16513 deletions(-)
diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index b06bc2512f735..e13f0c5698866 100644
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -1,16500 +1,16507 @@
-//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-//
-// This file contains the implementation of the scalar evolution analysis
-// engine, which is used primarily to analyze expressions involving induction
-// variables in loops.
-//
-// There are several aspects to this library. First is the representation of
-// scalar expressions, which are represented as subclasses of the SCEV class.
-// These classes are used to represent certain types of subexpressions that we
-// can handle. We only create one SCEV of a particular shape, so
-// pointer-comparisons for equality are legal.
-//
-// One important aspect of the SCEV objects is that they are never cyclic, even
-// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
-// the PHI node is one of the idioms that we can represent (e.g., a polynomial
-// recurrence) then we represent it directly as a recurrence node, otherwise we
-// represent it as a SCEVUnknown node.
-//
-// In addition to being able to represent expressions of various types, we also
-// have folders that are used to build the *canonical* representation for a
-// particular expression. These folders are capable of using a variety of
-// rewrite rules to simplify the expressions.
-//
-// Once the folders are defined, we can implement the more interesting
-// higher-level code, such as the code that recognizes PHI nodes of various
-// types, computes the execution count of a loop, etc.
-//
-// TODO: We should use these routines and value representations to implement
-// dependence analysis!
-//
-//===----------------------------------------------------------------------===//
-//
-// There are several good references for the techniques used in this analysis.
-//
-// Chains of recurrences -- a method to expedite the evaluation
-// of closed-form functions
-// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
-//
-// On computational properties of chains of recurrences
-// Eugene V. Zima
-//
-// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
-// Robert A. van Engelen
-//
-// Efficient Symbolic Analysis for Optimizing Compilers
-// Robert A. van Engelen
-//
-// Using the chains of recurrences algebra for data dependence testing and
-// induction variable substitution
-// MS Thesis, Johnie Birch
-//
-//===----------------------------------------------------------------------===//
-
-#include "llvm/Analysis/ScalarEvolution.h"
-#include "llvm/ADT/APInt.h"
-#include "llvm/ADT/ArrayRef.h"
-#include "llvm/ADT/DenseMap.h"
-#include "llvm/ADT/DepthFirstIterator.h"
-#include "llvm/ADT/FoldingSet.h"
-#include "llvm/ADT/STLExtras.h"
-#include "llvm/ADT/ScopeExit.h"
-#include "llvm/ADT/Sequence.h"
-#include "llvm/ADT/SmallPtrSet.h"
-#include "llvm/ADT/SmallVector.h"
-#include "llvm/ADT/Statistic.h"
-#include "llvm/ADT/StringExtras.h"
-#include "llvm/ADT/StringRef.h"
-#include "llvm/Analysis/AssumptionCache.h"
-#include "llvm/Analysis/ConstantFolding.h"
-#include "llvm/Analysis/InstructionSimplify.h"
-#include "llvm/Analysis/LoopInfo.h"
-#include "llvm/Analysis/MemoryBuiltins.h"
-#include "llvm/Analysis/ScalarEvolutionExpressions.h"
-#include "llvm/Analysis/ScalarEvolutionPatternMatch.h"
-#include "llvm/Analysis/TargetLibraryInfo.h"
-#include "llvm/Analysis/ValueTracking.h"
-#include "llvm/Config/llvm-config.h"
-#include "llvm/IR/Argument.h"
-#include "llvm/IR/BasicBlock.h"
-#include "llvm/IR/CFG.h"
-#include "llvm/IR/Constant.h"
-#include "llvm/IR/ConstantRange.h"
-#include "llvm/IR/Constants.h"
-#include "llvm/IR/DataLayout.h"
-#include "llvm/IR/DerivedTypes.h"
-#include "llvm/IR/Dominators.h"
-#include "llvm/IR/Function.h"
-#include "llvm/IR/GlobalAlias.h"
-#include "llvm/IR/GlobalValue.h"
-#include "llvm/IR/InstIterator.h"
-#include "llvm/IR/InstrTypes.h"
-#include "llvm/IR/Instruction.h"
-#include "llvm/IR/Instructions.h"
-#include "llvm/IR/IntrinsicInst.h"
-#include "llvm/IR/Intrinsics.h"
-#include "llvm/IR/LLVMContext.h"
-#include "llvm/IR/Operator.h"
-#include "llvm/IR/PatternMatch.h"
-#include "llvm/IR/Type.h"
-#include "llvm/IR/Use.h"
-#include "llvm/IR/User.h"
-#include "llvm/IR/Value.h"
-#include "llvm/IR/Verifier.h"
-#include "llvm/InitializePasses.h"
-#include "llvm/Pass.h"
-#include "llvm/Support/Casting.h"
-#include "llvm/Support/CommandLine.h"
-#include "llvm/Support/Compiler.h"
-#include "llvm/Support/Debug.h"
-#include "llvm/Support/ErrorHandling.h"
-#include "llvm/Support/InterleavedRange.h"
-#include "llvm/Support/KnownBits.h"
-#include "llvm/Support/SaveAndRestore.h"
-#include "llvm/Support/raw_ostream.h"
-#include <algorithm>
-#include <cassert>
-#include <climits>
-#include <cstdint>
-#include <cstdlib>
-#include <map>
-#include <memory>
-#include <numeric>
-#include <optional>
-#include <tuple>
-#include <utility>
-#include <vector>
-
-using namespace llvm;
-using namespace PatternMatch;
-using namespace SCEVPatternMatch;
-
-#define DEBUG_TYPE "scalar-evolution"
-
-STATISTIC(NumExitCountsComputed,
- "Number of loop exits with predictable exit counts");
-STATISTIC(NumExitCountsNotComputed,
- "Number of loop exits without predictable exit counts");
-STATISTIC(NumBruteForceTripCountsComputed,
- "Number of loops with trip counts computed by force");
-
-#ifdef EXPENSIVE_CHECKS
-bool llvm::VerifySCEV = true;
-#else
-bool llvm::VerifySCEV = false;
-#endif
-
-static cl::opt<unsigned>
- MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
- cl::desc("Maximum number of iterations SCEV will "
- "symbolically execute a constant "
- "derived loop"),
- cl::init(100));
-
-static cl::opt<bool, true> VerifySCEVOpt(
- "verify-scev", cl::Hidden, cl::location(VerifySCEV),
- cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
-static cl::opt<bool> VerifySCEVStrict(
- "verify-scev-strict", cl::Hidden,
- cl::desc("Enable stricter verification with -verify-scev is passed"));
-
-static cl::opt<bool> VerifyIR(
- "scev-verify-ir", cl::Hidden,
- cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
- cl::init(false));
-
-static cl::opt<unsigned> MulOpsInlineThreshold(
- "scev-mulops-inline-threshold", cl::Hidden,
- cl::desc("Threshold for inlining multiplication operands into a SCEV"),
- cl::init(32));
-
-static cl::opt<unsigned> AddOpsInlineThreshold(
- "scev-addops-inline-threshold", cl::Hidden,
- cl::desc("Threshold for inlining addition operands into a SCEV"),
- cl::init(500));
-
-static cl::opt<unsigned> MaxSCEVCompareDepth(
- "scalar-evolution-max-scev-compare-depth", cl::Hidden,
- cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
- cl::init(32));
-
-static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
- "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
- cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
- cl::init(2));
-
-static cl::opt<unsigned> MaxValueCompareDepth(
- "scalar-evolution-max-value-compare-depth", cl::Hidden,
- cl::desc("Maximum depth of recursive value complexity comparisons"),
- cl::init(2));
-
-static cl::opt<unsigned>
- MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
- cl::desc("Maximum depth of recursive arithmetics"),
- cl::init(32));
-
-static cl::opt<unsigned> MaxConstantEvolvingDepth(
- "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
- cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
-
-static cl::opt<unsigned>
- MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
- cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
- cl::init(8));
-
-static cl::opt<unsigned>
- MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
- cl::desc("Max coefficients in AddRec during evolving"),
- cl::init(8));
-
-static cl::opt<unsigned>
- HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
- cl::desc("Size of the expression which is considered huge"),
- cl::init(4096));
-
-static cl::opt<unsigned> RangeIterThreshold(
- "scev-range-iter-threshold", cl::Hidden,
- cl::desc("Threshold for switching to iteratively computing SCEV ranges"),
- cl::init(32));
-
-static cl::opt<unsigned> MaxLoopGuardCollectionDepth(
- "scalar-evolution-max-loop-guard-collection-depth", cl::Hidden,
- cl::desc("Maximum depth for recursive loop guard collection"), cl::init(1));
-
-static cl::opt<bool>
-ClassifyExpressions("scalar-evolution-classify-expressions",
- cl::Hidden, cl::init(true),
- cl::desc("When printing analysis, include information on every instruction"));
-
-static cl::opt<bool> UseExpensiveRangeSharpening(
- "scalar-evolution-use-expensive-range-sharpening", cl::Hidden,
- cl::init(false),
- cl::desc("Use more powerful methods of sharpening expression ranges. May "
- "be costly in terms of compile time"));
-
-static cl::opt<unsigned> MaxPhiSCCAnalysisSize(
- "scalar-evolution-max-scc-analysis-depth", cl::Hidden,
- cl::desc("Maximum amount of nodes to process while searching SCEVUnknown "
- "Phi strongly connected components"),
- cl::init(8));
-
-static cl::opt<bool>
- EnableFiniteLoopControl("scalar-evolution-finite-loop", cl::Hidden,
- cl::desc("Handle <= and >= in finite loops"),
- cl::init(true));
-
-static cl::opt<bool> UseContextForNoWrapFlagInference(
- "scalar-evolution-use-context-for-no-wrap-flag-strenghening", cl::Hidden,
- cl::desc("Infer nuw/nsw flags using context where suitable"),
- cl::init(true));
-
-//===----------------------------------------------------------------------===//
-// SCEV class definitions
-//===----------------------------------------------------------------------===//
-
-void SCEV::computeAndSetCanonical(ScalarEvolution &SE) {
- // Leaf nodes are always their own canonical.
- switch (getSCEVType()) {
- case scConstant:
- case scVScale:
- case scUnknown:
- CanonicalSCEV = this;
- return;
- default:
- break;
- }
-
- // For all other expressions, check whether any immediate operand has a
- // different canonical. Since operands are always created before their parent,
- // their canonical pointers are already set — no recursion needed.
- bool Changed = false;
- SmallVector<SCEVUse, 4> CanonOps;
- for (SCEVUse Op : operands()) {
- CanonOps.push_back(Op->getCanonical());
- Changed |= CanonOps.back() != Op.getPointer();
- }
-
- if (!Changed) {
- CanonicalSCEV = this;
- return;
- }
-
- auto *NAry = dyn_cast<SCEVNAryExpr>(this);
- SCEV::NoWrapFlags Flags = NAry ? NAry->getNoWrapFlags() : SCEV::FlagAnyWrap;
- switch (getSCEVType()) {
- case scPtrToAddr:
- CanonicalSCEV = SE.getPtrToAddrExpr(CanonOps[0]);
- return;
- case scTruncate:
- CanonicalSCEV = SE.getTruncateExpr(CanonOps[0], getType());
- return;
- case scZeroExtend:
- CanonicalSCEV = SE.getZeroExtendExpr(CanonOps[0], getType());
- return;
- case scSignExtend:
- CanonicalSCEV = SE.getSignExtendExpr(CanonOps[0], getType());
- return;
- case scUDivExpr:
- CanonicalSCEV = SE.getUDivExpr(CanonOps[0], CanonOps[1]);
- return;
- case scAddExpr:
- CanonicalSCEV = SE.getAddExpr(CanonOps, Flags);
- return;
- case scMulExpr:
- CanonicalSCEV = SE.getMulExpr(CanonOps, Flags);
- return;
- case scAddRecExpr:
- CanonicalSCEV = SE.getAddRecExpr(
- CanonOps, cast<SCEVAddRecExpr>(this)->getLoop(), Flags);
- return;
- case scSMaxExpr:
- CanonicalSCEV = SE.getSMaxExpr(CanonOps);
- return;
- case scUMaxExpr:
- CanonicalSCEV = SE.getUMaxExpr(CanonOps);
- return;
- case scSMinExpr:
- CanonicalSCEV = SE.getSMinExpr(CanonOps);
- return;
- case scUMinExpr:
- CanonicalSCEV = SE.getUMinExpr(CanonOps);
- return;
- case scSequentialUMinExpr:
- CanonicalSCEV = SE.getUMinExpr(CanonOps, /*Sequential=*/true);
- return;
- default:
- llvm_unreachable("Unknown SCEV type");
- }
-}
-
-//===----------------------------------------------------------------------===//
-// Implementation of the SCEV class.
-//
-
-#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
-LLVM_DUMP_METHOD void SCEV::dump() const {
- print(dbgs());
- dbgs() << '\n';
-}
-#endif
-
-void SCEV::print(raw_ostream &OS) const {
- switch (getSCEVType()) {
- case scConstant:
- cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
- return;
- case scVScale:
- OS << "vscale";
- return;
- case scPtrToAddr: {
- const SCEVCastExpr *PtrCast = cast<SCEVCastExpr>(this);
- const SCEV *Op = PtrCast->getOperand();
- OS << "(ptrtoaddr " << *Op->getType() << " " << *Op << " to "
- << *PtrCast->getType() << ")";
- return;
- }
- case scTruncate: {
- const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
- const SCEV *Op = Trunc->getOperand();
- OS << "(trunc " << *Op->getType() << " " << *Op << " to "
- << *Trunc->getType() << ")";
- return;
- }
- case scZeroExtend: {
- const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
- const SCEV *Op = ZExt->getOperand();
- OS << "(zext " << *Op->getType() << " " << *Op << " to "
- << *ZExt->getType() << ")";
- return;
- }
- case scSignExtend: {
- const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
- const SCEV *Op = SExt->getOperand();
- OS << "(sext " << *Op->getType() << " " << *Op << " to "
- << *SExt->getType() << ")";
- return;
- }
- case scAddRecExpr: {
- const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
- OS << "{" << *AR->getOperand(0);
- for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
- OS << ",+," << *AR->getOperand(i);
- OS << "}<";
- if (AR->hasNoUnsignedWrap())
- OS << "nuw><";
- if (AR->hasNoSignedWrap())
- OS << "nsw><";
- if (AR->hasNoSelfWrap() && !AR->hasNoUnsignedWrap() &&
- !AR->hasNoSignedWrap())
- OS << "nw><";
- AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ">";
- return;
- }
- case scAddExpr:
- case scMulExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr: {
- const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
- const char *OpStr = nullptr;
- switch (NAry->getSCEVType()) {
- case scAddExpr: OpStr = " + "; break;
- case scMulExpr: OpStr = " * "; break;
- case scUMaxExpr: OpStr = " umax "; break;
- case scSMaxExpr: OpStr = " smax "; break;
- case scUMinExpr:
- OpStr = " umin ";
- break;
- case scSMinExpr:
- OpStr = " smin ";
- break;
- case scSequentialUMinExpr:
- OpStr = " umin_seq ";
- break;
- default:
- llvm_unreachable("There are no other nary expression types.");
- }
- OS << "("
- << llvm::interleaved(llvm::make_pointee_range(NAry->operands()), OpStr)
- << ")";
- switch (NAry->getSCEVType()) {
- case scAddExpr:
- case scMulExpr:
- if (NAry->hasNoUnsignedWrap())
- OS << "<nuw>";
- if (NAry->hasNoSignedWrap())
- OS << "<nsw>";
- break;
- default:
- // Nothing to print for other nary expressions.
- break;
- }
- return;
- }
- case scUDivExpr: {
- const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
- OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
- return;
- }
- case scUnknown:
- cast<SCEVUnknown>(this)->getValue()->printAsOperand(OS, false);
- return;
- case scCouldNotCompute:
- OS << "***COULDNOTCOMPUTE***";
- return;
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-ArrayRef<SCEVUse> SCEV::operands() const {
- switch (getSCEVType()) {
- case scConstant:
- case scVScale:
- case scUnknown:
- return {};
- case scPtrToAddr:
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- return cast<SCEVCastExpr>(this)->operands();
- case scAddRecExpr:
- case scAddExpr:
- case scMulExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr:
- return cast<SCEVNAryExpr>(this)->operands();
- case scUDivExpr:
- return cast<SCEVUDivExpr>(this)->operands();
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-bool SCEV::isZero() const { return match(this, m_scev_Zero()); }
-
-bool SCEV::isOne() const { return match(this, m_scev_One()); }
-
-bool SCEV::isAllOnesValue() const { return match(this, m_scev_AllOnes()); }
-
-bool SCEV::isNonConstantNegative() const {
- const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
- if (!Mul) return false;
-
- // If there is a constant factor, it will be first.
- const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
- if (!SC) return false;
-
- // Return true if the value is negative, this matches things like (-42 * V).
- return SC->getAPInt().isNegative();
-}
-
-SCEVCouldNotCompute::SCEVCouldNotCompute()
- : SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0, nullptr) {}
-
-bool SCEVCouldNotCompute::classof(const SCEV *S) {
- return S->getSCEVType() == scCouldNotCompute;
-}
-
-const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
- auto &Entry = ConstantSCEVs[V];
- if (Entry)
- return Entry;
-
- FoldingSetNodeID ID;
- ID.AddInteger(scConstant);
- ID.AddPointer(V);
- void *IP = nullptr;
- if (SCEVConstant *S =
- static_cast<SCEVConstant *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)))
- return Entry = S;
- SCEVConstant *S =
- new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- return Entry = S;
-}
-
-const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
- return getConstant(ConstantInt::get(getContext(), Val));
-}
-
-const SCEV *
-ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
- IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
- // TODO: Avoid implicit trunc?
- // See https://github.com/llvm/llvm-project/issues/112510.
- return getConstant(
- ConstantInt::get(ITy, V, isSigned, /*ImplicitTrunc=*/true));
-}
-
-const SCEV *ScalarEvolution::getVScale(Type *Ty) {
- FoldingSetNodeID ID;
- ID.AddInteger(scVScale);
- ID.AddPointer(Ty);
- void *IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
- return S;
- SCEV *S = new (SCEVAllocator) SCEVVScale(ID.Intern(SCEVAllocator), Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- return S;
-}
-
-const SCEV *ScalarEvolution::getElementCount(Type *Ty, ElementCount EC,
- SCEV::NoWrapFlags Flags) {
- const SCEV *Res = getConstant(Ty, EC.getKnownMinValue());
- if (EC.isScalable())
- Res = getMulExpr(Res, getVScale(Ty), Flags);
- return Res;
-}
-
-SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
- SCEVUse op, Type *ty)
- : SCEV(ID, SCEVTy, computeExpressionSize(op), ty), Op(op) {}
-
-SCEVPtrToAddrExpr::SCEVPtrToAddrExpr(const FoldingSetNodeIDRef ID,
- const SCEV *Op, Type *ITy)
- : SCEVCastExpr(ID, scPtrToAddr, Op, ITy) {
- assert(getOperand()->getType()->isPointerTy() && getType()->isIntegerTy() &&
- "Must be a non-bit-width-changing pointer-to-integer cast!");
-}
-
-SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID,
- SCEVTypes SCEVTy, SCEVUse op,
- Type *ty)
- : SCEVCastExpr(ID, SCEVTy, op, ty) {}
-
-SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, SCEVUse op,
- Type *ty)
- : SCEVIntegralCastExpr(ID, scTruncate, op, ty) {
- assert(getOperand()->getType()->isIntOrPtrTy() && getType()->isIntOrPtrTy() &&
- "Cannot truncate non-integer value!");
-}
-
-SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, SCEVUse op,
- Type *ty)
- : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) {
- assert(getOperand()->getType()->isIntOrPtrTy() && getType()->isIntOrPtrTy() &&
- "Cannot zero extend non-integer value!");
-}
-
-SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, SCEVUse op,
- Type *ty)
- : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) {
- assert(getOperand()->getType()->isIntOrPtrTy() && getType()->isIntOrPtrTy() &&
- "Cannot sign extend non-integer value!");
-}
-
-void SCEVUnknown::deleted() {
- // Clear this SCEVUnknown from various maps.
- SE->forgetMemoizedResults({this});
-
- // Remove this SCEVUnknown from the uniquing map.
- SE->UniqueSCEVs.RemoveNode(this);
-
- // Release the value.
- setValPtr(nullptr);
-}
-
-void SCEVUnknown::allUsesReplacedWith(Value *New) {
- // Clear this SCEVUnknown from various maps.
- SE->forgetMemoizedResults({this});
-
- // Remove this SCEVUnknown from the uniquing map.
- SE->UniqueSCEVs.RemoveNode(this);
-
- // Replace the value pointer in case someone is still using this SCEVUnknown.
- setValPtr(New);
-}
-
-//===----------------------------------------------------------------------===//
-// SCEV Utilities
-//===----------------------------------------------------------------------===//
-
-/// Compare the two values \p LV and \p RV in terms of their "complexity" where
-/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
-/// operands in SCEV expressions.
-static int CompareValueComplexity(const LoopInfo *const LI, Value *LV,
- Value *RV, unsigned Depth) {
- if (Depth > MaxValueCompareDepth)
- return 0;
-
- // Order pointer values after integer values. This helps SCEVExpander form
- // GEPs.
- bool LIsPointer = LV->getType()->isPointerTy(),
- RIsPointer = RV->getType()->isPointerTy();
- if (LIsPointer != RIsPointer)
- return (int)LIsPointer - (int)RIsPointer;
-
- // Compare getValueID values.
- unsigned LID = LV->getValueID(), RID = RV->getValueID();
- if (LID != RID)
- return (int)LID - (int)RID;
-
- // Sort arguments by their position.
- if (const auto *LA = dyn_cast<Argument>(LV)) {
- const auto *RA = cast<Argument>(RV);
- unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
- return (int)LArgNo - (int)RArgNo;
- }
-
- if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
- const auto *RGV = cast<GlobalValue>(RV);
-
- if (auto L = LGV->getLinkage() - RGV->getLinkage())
- return L;
-
- const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
- auto LT = GV->getLinkage();
- return !(GlobalValue::isPrivateLinkage(LT) ||
- GlobalValue::isInternalLinkage(LT));
- };
-
- // Use the names to distinguish the two values, but only if the
- // names are semantically important.
- if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
- return LGV->getName().compare(RGV->getName());
- }
-
- // For instructions, compare their loop depth, and their operand count. This
- // is pretty loose.
- if (const auto *LInst = dyn_cast<Instruction>(LV)) {
- const auto *RInst = cast<Instruction>(RV);
-
- // Compare loop depths.
- const BasicBlock *LParent = LInst->getParent(),
- *RParent = RInst->getParent();
- if (LParent != RParent) {
- unsigned LDepth = LI->getLoopDepth(LParent),
- RDepth = LI->getLoopDepth(RParent);
- if (LDepth != RDepth)
- return (int)LDepth - (int)RDepth;
- }
-
- // Compare the number of operands.
- unsigned LNumOps = LInst->getNumOperands(),
- RNumOps = RInst->getNumOperands();
- if (LNumOps != RNumOps)
- return (int)LNumOps - (int)RNumOps;
-
- for (unsigned Idx : seq(LNumOps)) {
- int Result = CompareValueComplexity(LI, LInst->getOperand(Idx),
- RInst->getOperand(Idx), Depth + 1);
- if (Result != 0)
- return Result;
- }
- }
-
- return 0;
-}
-
-// Return negative, zero, or positive, if LHS is less than, equal to, or greater
-// than RHS, respectively. A three-way result allows recursive comparisons to be
-// more efficient.
-// If the max analysis depth was reached, return std::nullopt, assuming we do
-// not know if they are equivalent for sure.
-static std::optional<int>
-CompareSCEVComplexity(const LoopInfo *const LI, const SCEV *LHS,
- const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) {
- // Fast-path: SCEVs are uniqued so we can do a quick equality check.
- if (LHS == RHS)
- return 0;
-
- // Primarily, sort the SCEVs by their getSCEVType().
- SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
- if (LType != RType)
- return (int)LType - (int)RType;
-
- if (Depth > MaxSCEVCompareDepth)
- return std::nullopt;
-
- // Aside from the getSCEVType() ordering, the particular ordering
- // isn't very important except that it's beneficial to be consistent,
- // so that (a + b) and (b + a) don't end up as different expressions.
- switch (LType) {
- case scUnknown: {
- const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
- const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
-
- int X =
- CompareValueComplexity(LI, LU->getValue(), RU->getValue(), Depth + 1);
- return X;
- }
-
- case scConstant: {
- const SCEVConstant *LC = cast<SCEVConstant>(LHS);
- const SCEVConstant *RC = cast<SCEVConstant>(RHS);
-
- // Compare constant values.
- const APInt &LA = LC->getAPInt();
- const APInt &RA = RC->getAPInt();
- unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
- if (LBitWidth != RBitWidth)
- return (int)LBitWidth - (int)RBitWidth;
- return LA.ult(RA) ? -1 : 1;
- }
-
- case scVScale: {
- const auto *LTy = cast<IntegerType>(cast<SCEVVScale>(LHS)->getType());
- const auto *RTy = cast<IntegerType>(cast<SCEVVScale>(RHS)->getType());
- return LTy->getBitWidth() - RTy->getBitWidth();
- }
-
- case scAddRecExpr: {
- const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
- const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
-
- // There is always a dominance between two recs that are used by one SCEV,
- // so we can safely sort recs by loop header dominance. We require such
- // order in getAddExpr.
- const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
- if (LLoop != RLoop) {
- const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
- assert(LHead != RHead && "Two loops share the same header?");
- if (DT.dominates(LHead, RHead))
- return 1;
- assert(DT.dominates(RHead, LHead) &&
- "No dominance between recurrences used by one SCEV?");
- return -1;
- }
-
- [[fallthrough]];
- }
-
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- case scAddExpr:
- case scMulExpr:
- case scUDivExpr:
- case scSMaxExpr:
- case scUMaxExpr:
- case scSMinExpr:
- case scUMinExpr:
- case scSequentialUMinExpr: {
- ArrayRef<SCEVUse> LOps = LHS->operands();
- ArrayRef<SCEVUse> ROps = RHS->operands();
-
- // Lexicographically compare n-ary-like expressions.
- unsigned LNumOps = LOps.size(), RNumOps = ROps.size();
- if (LNumOps != RNumOps)
- return (int)LNumOps - (int)RNumOps;
-
- for (unsigned i = 0; i != LNumOps; ++i) {
- auto X = CompareSCEVComplexity(LI, LOps[i].getPointer(),
- ROps[i].getPointer(), DT, Depth + 1);
- if (X != 0)
- return X;
- }
- return 0;
- }
-
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-/// Given a list of SCEV objects, order them by their complexity, and group
-/// objects of the same complexity together by value. When this routine is
-/// finished, we know that any duplicates in the vector are consecutive and that
-/// complexity is monotonically increasing.
-///
-/// Note that we go take special precautions to ensure that we get deterministic
-/// results from this routine. In other words, we don't want the results of
-/// this to depend on where the addresses of various SCEV objects happened to
-/// land in memory.
-static void GroupByComplexity(SmallVectorImpl<SCEVUse> &Ops, LoopInfo *LI,
- DominatorTree &DT) {
- if (Ops.size() < 2) return; // Noop
-
- // Whether LHS has provably less complexity than RHS.
- auto IsLessComplex = [&](SCEVUse LHS, SCEVUse RHS) {
- auto Complexity = CompareSCEVComplexity(LI, LHS, RHS, DT);
- return Complexity && *Complexity < 0;
- };
- if (Ops.size() == 2) {
- // This is the common case, which also happens to be trivially simple.
- // Special case it.
- SCEVUse &LHS = Ops[0], &RHS = Ops[1];
- if (IsLessComplex(RHS, LHS))
- std::swap(LHS, RHS);
- return;
- }
-
- // Do the rough sort by complexity.
- llvm::stable_sort(
- Ops, [&](SCEVUse LHS, SCEVUse RHS) { return IsLessComplex(LHS, RHS); });
-
- // Now that we are sorted by complexity, group elements of the same
- // complexity. Note that this is, at worst, N^2, but the vector is likely to
- // be extremely short in practice. Note that we take this approach because we
- // do not want to depend on the addresses of the objects we are grouping.
- for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
- const SCEV *S = Ops[i];
- unsigned Complexity = S->getSCEVType();
-
- // If there are any objects of the same complexity and same value as this
- // one, group them.
- for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
- if (Ops[j] == S) { // Found a duplicate.
- // Move it to immediately after i'th element.
- std::swap(Ops[i+1], Ops[j]);
- ++i; // no need to rescan it.
- if (i == e-2) return; // Done!
- }
- }
- }
-}
-
-/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
-/// least HugeExprThreshold nodes).
-static bool hasHugeExpression(ArrayRef<SCEVUse> Ops) {
- return any_of(Ops, [](const SCEV *S) {
- return S->getExpressionSize() >= HugeExprThreshold;
- });
-}
-
-/// Performs a number of common optimizations on the passed \p Ops. If the
-/// whole expression reduces down to a single operand, it will be returned.
-///
-/// The following optimizations are performed:
-/// * Fold constants using the \p Fold function.
-/// * Remove identity constants satisfying \p IsIdentity.
-/// * If a constant satisfies \p IsAbsorber, return it.
-/// * Sort operands by complexity.
-template <typename FoldT, typename IsIdentityT, typename IsAbsorberT>
-static const SCEV *
-constantFoldAndGroupOps(ScalarEvolution &SE, LoopInfo &LI, DominatorTree &DT,
- SmallVectorImpl<SCEVUse> &Ops, FoldT Fold,
- IsIdentityT IsIdentity, IsAbsorberT IsAbsorber) {
- const SCEVConstant *Folded = nullptr;
- for (unsigned Idx = 0; Idx < Ops.size();) {
- const SCEV *Op = Ops[Idx];
- if (const auto *C = dyn_cast<SCEVConstant>(Op)) {
- if (!Folded)
- Folded = C;
- else
- Folded = cast<SCEVConstant>(
- SE.getConstant(Fold(Folded->getAPInt(), C->getAPInt())));
- Ops.erase(Ops.begin() + Idx);
- continue;
- }
- ++Idx;
- }
-
- if (Ops.empty()) {
- assert(Folded && "Must have folded value");
- return Folded;
- }
-
- if (Folded && IsAbsorber(Folded->getAPInt()))
- return Folded;
-
- GroupByComplexity(Ops, &LI, DT);
- if (Folded && !IsIdentity(Folded->getAPInt()))
- Ops.insert(Ops.begin(), Folded);
-
- return Ops.size() == 1 ? Ops[0] : nullptr;
-}
-
-//===----------------------------------------------------------------------===//
-// Simple SCEV method implementations
-//===----------------------------------------------------------------------===//
-
-/// Compute BC(It, K). The result has width W. Assume, K > 0.
-static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
- ScalarEvolution &SE,
- Type *ResultTy) {
- // Handle the simplest case efficiently.
- if (K == 1)
- return SE.getTruncateOrZeroExtend(It, ResultTy);
-
- // We are using the following formula for BC(It, K):
- //
- // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
- //
- // Suppose, W is the bitwidth of the return value. We must be prepared for
- // overflow. Hence, we must assure that the result of our computation is
- // equal to the accurate one modulo 2^W. Unfortunately, division isn't
- // safe in modular arithmetic.
- //
- // However, this code doesn't use exactly that formula; the formula it uses
- // is something like the following, where T is the number of factors of 2 in
- // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
- // exponentiation:
- //
- // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
- //
- // This formula is trivially equivalent to the previous formula. However,
- // this formula can be implemented much more efficiently. The trick is that
- // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
- // arithmetic. To do exact division in modular arithmetic, all we have
- // to do is multiply by the inverse. Therefore, this step can be done at
- // width W.
- //
- // The next issue is how to safely do the division by 2^T. The way this
- // is done is by doing the multiplication step at a width of at least W + T
- // bits. This way, the bottom W+T bits of the product are accurate. Then,
- // when we perform the division by 2^T (which is equivalent to a right shift
- // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
- // truncated out after the division by 2^T.
- //
- // In comparison to just directly using the first formula, this technique
- // is much more efficient; using the first formula requires W * K bits,
- // but this formula less than W + K bits. Also, the first formula requires
- // a division step, whereas this formula only requires multiplies and shifts.
- //
- // It doesn't matter whether the subtraction step is done in the calculation
- // width or the input iteration count's width; if the subtraction overflows,
- // the result must be zero anyway. We prefer here to do it in the width of
- // the induction variable because it helps a lot for certain cases; CodeGen
- // isn't smart enough to ignore the overflow, which leads to much less
- // efficient code if the width of the subtraction is wider than the native
- // register width.
- //
- // (It's possible to not widen at all by pulling out factors of 2 before
- // the multiplication; for example, K=2 can be calculated as
- // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
- // extra arithmetic, so it's not an obvious win, and it gets
- // much more complicated for K > 3.)
-
- // Protection from insane SCEVs; this bound is conservative,
- // but it probably doesn't matter.
- if (K > 1000)
- return SE.getCouldNotCompute();
-
- unsigned W = SE.getTypeSizeInBits(ResultTy);
-
- // Calculate K! / 2^T and T; we divide out the factors of two before
- // multiplying for calculating K! / 2^T to avoid overflow.
- // Other overflow doesn't matter because we only care about the bottom
- // W bits of the result.
- APInt OddFactorial(W, 1);
- unsigned T = 1;
- for (unsigned i = 3; i <= K; ++i) {
- unsigned TwoFactors = countr_zero(i);
- T += TwoFactors;
- OddFactorial *= (i >> TwoFactors);
- }
-
- // We need at least W + T bits for the multiplication step
- unsigned CalculationBits = W + T;
-
- // Calculate 2^T, at width T+W.
- APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
-
- // Calculate the multiplicative inverse of K! / 2^T;
- // this multiplication factor will perform the exact division by
- // K! / 2^T.
- APInt MultiplyFactor = OddFactorial.multiplicativeInverse();
-
- // Calculate the product, at width T+W
- IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
- CalculationBits);
- const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
- for (unsigned i = 1; i != K; ++i) {
- const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
- Dividend = SE.getMulExpr(Dividend,
- SE.getTruncateOrZeroExtend(S, CalculationTy));
- }
-
- // Divide by 2^T
- const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
-
- // Truncate the result, and divide by K! / 2^T.
-
- return SE.getMulExpr(SE.getConstant(MultiplyFactor),
- SE.getTruncateOrZeroExtend(DivResult, ResultTy));
-}
-
-/// Return the value of this chain of recurrences at the specified iteration
-/// number. We can evaluate this recurrence by multiplying each element in the
-/// chain by the binomial coefficient corresponding to it. In other words, we
-/// can evaluate {A,+,B,+,C,+,D} as:
-///
-/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
-///
-/// where BC(It, k) stands for binomial coefficient.
-const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
- ScalarEvolution &SE) const {
- return evaluateAtIteration(operands(), It, SE);
-}
-
-const SCEV *SCEVAddRecExpr::evaluateAtIteration(ArrayRef<SCEVUse> Operands,
- const SCEV *It,
- ScalarEvolution &SE) {
- assert(Operands.size() > 0);
- const SCEV *Result = Operands[0].getPointer();
- for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
- // The computation is correct in the face of overflow provided that the
- // multiplication is performed _after_ the evaluation of the binomial
- // coefficient.
- const SCEV *Coeff = BinomialCoefficient(It, i, SE, Result->getType());
- if (isa<SCEVCouldNotCompute>(Coeff))
- return Coeff;
-
- Result =
- SE.getAddExpr(Result, SE.getMulExpr(Operands[i].getPointer(), Coeff));
- }
- return Result;
-}
-
-//===----------------------------------------------------------------------===//
-// SCEV Expression folder implementations
-//===----------------------------------------------------------------------===//
-
-/// The SCEVCastSinkingRewriter takes a scalar evolution expression,
-/// which computes a pointer-typed value, and rewrites the whole expression
-/// tree so that *all* the computations are done on integers, and the only
-/// pointer-typed operands in the expression are SCEVUnknown.
-/// The CreatePtrCast callback is invoked to create the actual conversion
-/// (ptrtoint or ptrtoaddr) at the SCEVUnknown leaves.
-class SCEVCastSinkingRewriter
- : public SCEVRewriteVisitor<SCEVCastSinkingRewriter> {
- using Base = SCEVRewriteVisitor<SCEVCastSinkingRewriter>;
- using ConversionFn = function_ref<const SCEV *(const SCEVUnknown *)>;
- Type *TargetTy;
- ConversionFn CreatePtrCast;
-
-public:
- SCEVCastSinkingRewriter(ScalarEvolution &SE, Type *TargetTy,
- ConversionFn CreatePtrCast)
- : Base(SE), TargetTy(TargetTy), CreatePtrCast(std::move(CreatePtrCast)) {}
-
- static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
- Type *TargetTy, ConversionFn CreatePtrCast) {
- SCEVCastSinkingRewriter Rewriter(SE, TargetTy, std::move(CreatePtrCast));
- return Rewriter.visit(Scev);
- }
-
- const SCEV *visit(const SCEV *S) {
- Type *STy = S->getType();
- // If the expression is not pointer-typed, just keep it as-is.
- if (!STy->isPointerTy())
- return S;
- // Else, recursively sink the cast down into it.
- return Base::visit(S);
- }
-
- const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
- // Preserve wrap flags on rewritten SCEVAddExpr, which the default
- // implementation drops.
- SmallVector<SCEVUse, 2> Operands;
- bool Changed = false;
- for (SCEVUse Op : Expr->operands()) {
- Operands.push_back(visit(Op.getPointer()));
- Changed |= Op.getPointer() != Operands.back();
- }
- return !Changed ? Expr : SE.getAddExpr(Operands, Expr->getNoWrapFlags());
- }
-
- const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
- SmallVector<SCEVUse, 2> Operands;
- bool Changed = false;
- for (SCEVUse Op : Expr->operands()) {
- Operands.push_back(visit(Op.getPointer()));
- Changed |= Op.getPointer() != Operands.back();
- }
- return !Changed ? Expr : SE.getMulExpr(Operands, Expr->getNoWrapFlags());
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- assert(Expr->getType()->isPointerTy() &&
- "Should only reach pointer-typed SCEVUnknown's.");
- // Perform some basic constant folding. If the operand of the cast is a
- // null pointer, don't create a cast SCEV expression (that will be left
- // as-is), but produce a zero constant.
- if (isa<ConstantPointerNull>(Expr->getValue()))
- return SE.getZero(TargetTy);
- return CreatePtrCast(Expr);
- }
-};
-
-const SCEV *ScalarEvolution::getPtrToAddrExpr(const SCEV *Op) {
- assert(Op->getType()->isPointerTy() && "Op must be a pointer");
-
- // Treat pointers with unstable representation conservatively, since the
- // address bits may change.
- if (DL.hasUnstableRepresentation(Op->getType()))
- return getCouldNotCompute();
-
- Type *Ty = DL.getAddressType(Op->getType());
-
- // Use the rewriter to sink the cast down to SCEVUnknown leaves.
- // The rewriter handles null pointer constant folding.
- const SCEV *IntOp = SCEVCastSinkingRewriter::rewrite(
- Op, *this, Ty, [this, Ty](const SCEVUnknown *U) {
- FoldingSetNodeID ID;
- ID.AddInteger(scPtrToAddr);
- ID.AddPointer(U);
- ID.AddPointer(Ty);
- void *IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
- return S;
- SCEV *S = new (SCEVAllocator)
- SCEVPtrToAddrExpr(ID.Intern(SCEVAllocator), U, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, U);
- return static_cast<const SCEV *>(S);
- });
- assert(IntOp->getType()->isIntegerTy() &&
- "We must have succeeded in sinking the cast, "
- "and ending up with an integer-typed expression!");
- return IntOp;
-}
-
-const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
- unsigned Depth) {
- assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
- "This is not a truncating conversion!");
- assert(isSCEVable(Ty) &&
- "This is not a conversion to a SCEVable type!");
- assert(!Op->getType()->isPointerTy() && "Can't truncate pointer!");
- Ty = getEffectiveSCEVType(Ty);
-
- FoldingSetNodeID ID;
- ID.AddInteger(scTruncate);
- ID.AddPointer(Op);
- ID.AddPointer(Ty);
- void *IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
-
- // Fold if the operand is constant.
- if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return getConstant(
- cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
-
- // trunc(trunc(x)) --> trunc(x)
- if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
- return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
-
- // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
- if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
- return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
-
- // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
- if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
- return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
-
- if (Depth > MaxCastDepth) {
- SCEV *S =
- new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Op);
- return S;
- }
-
- // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
- // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
- // if after transforming we have at most one truncate, not counting truncates
- // that replace other casts.
- if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
- auto *CommOp = cast<SCEVCommutativeExpr>(Op);
- SmallVector<SCEVUse, 4> Operands;
- unsigned numTruncs = 0;
- for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
- ++i) {
- const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
- if (!isa<SCEVIntegralCastExpr>(CommOp->getOperand(i)) &&
- isa<SCEVTruncateExpr>(S))
- numTruncs++;
- Operands.push_back(S);
- }
- if (numTruncs < 2) {
- if (isa<SCEVAddExpr>(Op))
- return getAddExpr(Operands);
- if (isa<SCEVMulExpr>(Op))
- return getMulExpr(Operands);
- llvm_unreachable("Unexpected SCEV type for Op.");
- }
- // Although we checked in the beginning that ID is not in the cache, it is
- // possible that during recursion and different modification ID was inserted
- // into the cache. So if we find it, just return it.
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
- return S;
- }
-
- // If the input value is a chrec scev, truncate the chrec's operands.
- if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
- SmallVector<SCEVUse, 4> Operands;
- for (const SCEV *Op : AddRec->operands())
- Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
- return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
- }
-
- // Return zero if truncating to known zeros.
- uint32_t MinTrailingZeros = getMinTrailingZeros(Op);
- if (MinTrailingZeros >= getTypeSizeInBits(Ty))
- return getZero(Ty);
-
- // The cast wasn't folded; create an explicit cast node. We can reuse
- // the existing insert position since if we get here, we won't have
- // made any changes which would invalidate it.
- SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
- Op, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Op);
- return S;
-}
-
-// Get the limit of a recurrence such that incrementing by Step cannot cause
-// signed overflow as long as the value of the recurrence within the
-// loop does not exceed this limit before incrementing.
-static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
- ICmpInst::Predicate *Pred,
- ScalarEvolution *SE) {
- unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
- if (SE->isKnownPositive(Step)) {
- *Pred = ICmpInst::ICMP_SLT;
- return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
- SE->getSignedRangeMax(Step));
- }
- if (SE->isKnownNegative(Step)) {
- *Pred = ICmpInst::ICMP_SGT;
- return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
- SE->getSignedRangeMin(Step));
- }
- return nullptr;
-}
-
-// Get the limit of a recurrence such that incrementing by Step cannot cause
-// unsigned overflow as long as the value of the recurrence within the loop does
-// not exceed this limit before incrementing.
-static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
- ICmpInst::Predicate *Pred,
- ScalarEvolution *SE) {
- unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
- *Pred = ICmpInst::ICMP_ULT;
-
- return SE->getConstant(APInt::getMinValue(BitWidth) -
- SE->getUnsignedRangeMax(Step));
-}
-
-namespace {
-
-struct ExtendOpTraitsBase {
- typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
- unsigned);
-};
-
-// Used to make code generic over signed and unsigned overflow.
-template <typename ExtendOp> struct ExtendOpTraits {
- // Members present:
- //
- // static const SCEV::NoWrapFlags WrapType;
- //
- // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
- //
- // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
- // ICmpInst::Predicate *Pred,
- // ScalarEvolution *SE);
-};
-
-template <>
-struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
- static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
-
- static const GetExtendExprTy GetExtendExpr;
-
- static const SCEV *getOverflowLimitForStep(const SCEV *Step,
- ICmpInst::Predicate *Pred,
- ScalarEvolution *SE) {
- return getSignedOverflowLimitForStep(Step, Pred, SE);
- }
-};
-
-const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
- SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
-
-template <>
-struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
- static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
-
- static const GetExtendExprTy GetExtendExpr;
-
- static const SCEV *getOverflowLimitForStep(const SCEV *Step,
- ICmpInst::Predicate *Pred,
- ScalarEvolution *SE) {
- return getUnsignedOverflowLimitForStep(Step, Pred, SE);
- }
-};
-
-const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
- SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
-
-} // end anonymous namespace
-
-// The recurrence AR has been shown to have no signed/unsigned wrap or something
-// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
-// easily prove NSW/NUW for its preincrement or postincrement sibling. This
-// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
-// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
-// expression "Step + sext/zext(PreIncAR)" is congruent with
-// "sext/zext(PostIncAR)"
-template <typename ExtendOpTy>
-static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
- ScalarEvolution *SE, unsigned Depth) {
- auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
- auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
-
- const Loop *L = AR->getLoop();
- const SCEV *Start = AR->getStart();
- const SCEV *Step = AR->getStepRecurrence(*SE);
-
- // Check for a simple looking step prior to loop entry.
- const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
- if (!SA)
- return nullptr;
-
- // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
- // subtraction is expensive. For this purpose, perform a quick and dirty
- // difference, by checking for Step in the operand list. Note, that
- // SA might have repeated ops, like %a + %a + ..., so only remove one.
- SmallVector<SCEVUse, 4> DiffOps(SA->operands());
- for (auto It = DiffOps.begin(); It != DiffOps.end(); ++It)
- if (*It == Step) {
- DiffOps.erase(It);
- break;
- }
-
- if (DiffOps.size() == SA->getNumOperands())
- return nullptr;
-
- // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
- // `Step`:
-
- // 1. NSW/NUW flags on the step increment.
- auto PreStartFlags =
- ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
- const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
- const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
- SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
-
- // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
- // "S+X does not sign/unsign-overflow".
- //
-
- const SCEV *BECount = SE->getBackedgeTakenCount(L);
- if (PreAR && any(PreAR->getNoWrapFlags(WrapType)) &&
- !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
- return PreStart;
-
- // 2. Direct overflow check on the step operation's expression.
- unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
- Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
- const SCEV *OperandExtendedStart =
- SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
- (SE->*GetExtendExpr)(Step, WideTy, Depth));
- if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
- if (PreAR && any(AR->getNoWrapFlags(WrapType))) {
- // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
- // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
- // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
- SE->setNoWrapFlags(const_cast<SCEVAddRecExpr *>(PreAR), WrapType);
- }
- return PreStart;
- }
-
- // 3. Loop precondition.
- ICmpInst::Predicate Pred;
- const SCEV *OverflowLimit =
- ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
-
- if (OverflowLimit &&
- SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
- return PreStart;
-
- return nullptr;
-}
-
-// Get the normalized zero or sign extended expression for this AddRec's Start.
-template <typename ExtendOpTy>
-static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
- ScalarEvolution *SE,
- unsigned Depth) {
- auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
-
- const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
- if (!PreStart)
- return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
-
- return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
- Depth),
- (SE->*GetExtendExpr)(PreStart, Ty, Depth));
-}
-
-// Try to prove away overflow by looking at "nearby" add recurrences. A
-// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
-// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
-//
-// Formally:
-//
-// {S,+,X} == {S-T,+,X} + T
-// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
-//
-// If ({S-T,+,X} + T) does not overflow ... (1)
-//
-// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
-//
-// If {S-T,+,X} does not overflow ... (2)
-//
-// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
-// == {Ext(S-T)+Ext(T),+,Ext(X)}
-//
-// If (S-T)+T does not overflow ... (3)
-//
-// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
-// == {Ext(S),+,Ext(X)} == LHS
-//
-// Thus, if (1), (2) and (3) are true for some T, then
-// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
-//
-// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
-// does not overflow" restricted to the 0th iteration. Therefore we only need
-// to check for (1) and (2).
-//
-// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
-// is `Delta` (defined below).
-template <typename ExtendOpTy>
-bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
- const SCEV *Step,
- const Loop *L) {
- auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
-
- // We restrict `Start` to a constant to prevent SCEV from spending too much
- // time here. It is correct (but more expensive) to continue with a
- // non-constant `Start` and do a general SCEV subtraction to compute
- // `PreStart` below.
- const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
- if (!StartC)
- return false;
-
- APInt StartAI = StartC->getAPInt();
-
- for (unsigned Delta : {-2, -1, 1, 2}) {
- const SCEV *PreStart = getConstant(StartAI - Delta);
-
- FoldingSetNodeID ID;
- ID.AddInteger(scAddRecExpr);
- ID.AddPointer(PreStart);
- ID.AddPointer(Step);
- ID.AddPointer(L);
- void *IP = nullptr;
- const auto *PreAR =
- static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
-
- // Give up if we don't already have the add recurrence we need because
- // actually constructing an add recurrence is relatively expensive.
- if (PreAR && any(PreAR->getNoWrapFlags(WrapType))) { // proves (2)
- const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
- ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
- const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
- DeltaS, &Pred, this);
- if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
- return true;
- }
- }
-
- return false;
-}
-
-// Finds an integer D for an expression (C + x + y + ...) such that the top
-// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
-// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
-// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
-// the (C + x + y + ...) expression is \p WholeAddExpr.
-static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
- const SCEVConstant *ConstantTerm,
- const SCEVAddExpr *WholeAddExpr) {
- const APInt &C = ConstantTerm->getAPInt();
- const unsigned BitWidth = C.getBitWidth();
- // Find number of trailing zeros of (x + y + ...) w/o the C first:
- uint32_t TZ = BitWidth;
- for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
- TZ = std::min(TZ, SE.getMinTrailingZeros(WholeAddExpr->getOperand(I)));
- if (TZ) {
- // Set D to be as many least significant bits of C as possible while still
- // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
- return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
- }
- return APInt(BitWidth, 0);
-}
-
-// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
-// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
-// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
-// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
-static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
- const APInt &ConstantStart,
- const SCEV *Step) {
- const unsigned BitWidth = ConstantStart.getBitWidth();
- const uint32_t TZ = SE.getMinTrailingZeros(Step);
- if (TZ)
- return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
- : ConstantStart;
- return APInt(BitWidth, 0);
-}
-
-static void insertFoldCacheEntry(
- const ScalarEvolution::FoldID &ID, const SCEV *S,
- DenseMap<ScalarEvolution::FoldID, const SCEV *> &FoldCache,
- DenseMap<const SCEV *, SmallVector<ScalarEvolution::FoldID, 2>>
- &FoldCacheUser) {
- auto I = FoldCache.insert({ID, S});
- if (!I.second) {
- // Remove FoldCacheUser entry for ID when replacing an existing FoldCache
- // entry.
- auto &UserIDs = FoldCacheUser[I.first->second];
- assert(count(UserIDs, ID) == 1 && "unexpected duplicates in UserIDs");
- for (unsigned I = 0; I != UserIDs.size(); ++I)
- if (UserIDs[I] == ID) {
- std::swap(UserIDs[I], UserIDs.back());
- break;
- }
- UserIDs.pop_back();
- I.first->second = S;
- }
- FoldCacheUser[S].push_back(ID);
-}
-
-const SCEV *
-ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
- assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
- "This is not an extending conversion!");
- assert(isSCEVable(Ty) &&
- "This is not a conversion to a SCEVable type!");
- assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
- Ty = getEffectiveSCEVType(Ty);
-
- FoldID ID(scZeroExtend, Op, Ty);
- if (const SCEV *S = FoldCache.lookup(ID))
- return S;
-
- const SCEV *S = getZeroExtendExprImpl(Op, Ty, Depth);
- if (!isa<SCEVZeroExtendExpr>(S))
- insertFoldCacheEntry(ID, S, FoldCache, FoldCacheUser);
- return S;
-}
-
-const SCEV *ScalarEvolution::getZeroExtendExprImpl(const SCEV *Op, Type *Ty,
- unsigned Depth) {
- assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
- "This is not an extending conversion!");
- assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!");
- assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
-
- // Fold if the operand is constant.
- if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return getConstant(SC->getAPInt().zext(getTypeSizeInBits(Ty)));
-
- // zext(zext(x)) --> zext(x)
- if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
- return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
-
- // If the operand is an affine AddRec with the no-unsigned-wrap flag, the
- // zero-extension distributes over the recurrence.
- const SCEV *Start, *Step;
- const Loop *L;
- if (Depth <= MaxCastDepth &&
- match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
- const auto *AR = cast<SCEVAddRecExpr>(Op);
- if (AR->hasNoUnsignedWrap()) {
- Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getZeroExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- }
-
- // Before doing any expensive analysis, check to see if we've already
- // computed a SCEV for this Op and Ty.
- FoldingSetNodeID ID;
- ID.AddInteger(scZeroExtend);
- ID.AddPointer(Op);
- ID.AddPointer(Ty);
- void *IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
- if (Depth > MaxCastDepth) {
- SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
- Op, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Op);
- return S;
- }
-
- // zext(trunc(x)) --> zext(x) or x or trunc(x)
- if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
- // It's possible the bits taken off by the truncate were all zero bits. If
- // so, we should be able to simplify this further.
- const SCEV *X = ST->getOperand();
- ConstantRange CR = getUnsignedRange(X);
- unsigned TruncBits = getTypeSizeInBits(ST->getType());
- unsigned NewBits = getTypeSizeInBits(Ty);
- if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
- CR.zextOrTrunc(NewBits)))
- return getTruncateOrZeroExtend(X, Ty, Depth);
- }
-
- // If the input value is a chrec scev, and we can prove that the value
- // did not overflow the old, smaller, value, we can zero extend all of the
- // operands (often constants). This allows analysis of something like
- // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
- if (match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
- const auto *AR = cast<SCEVAddRecExpr>(Op);
- unsigned BitWidth = getTypeSizeInBits(AR->getType());
-
- // The no-unsigned-wrap case is handled before the uniquing lookup above.
-
- // Check whether the backedge-taken count is SCEVCouldNotCompute.
- // Note that this serves two purposes: It filters out loops that are
- // simply not analyzable, and it covers the case where this code is
- // being called from within backedge-taken count analysis, such that
- // attempting to ask for the backedge-taken count would likely result
- // in infinite recursion. In the later case, the analysis code will
- // cope with a conservative value, and it will take care to purge
- // that value once it has finished.
- const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
- if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
- // Manually compute the final value for AR, checking for overflow.
-
- // Check whether the backedge-taken count can be losslessly casted to
- // the addrec's type. The count is always unsigned.
- const SCEV *CastedMaxBECount =
- getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
- const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
- CastedMaxBECount, MaxBECount->getType(), Depth);
- if (MaxBECount == RecastedMaxBECount) {
- Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
- // Check whether Start+Step*MaxBECount has no unsigned overflow.
- const SCEV *ZMul =
- getMulExpr(CastedMaxBECount, Step, SCEV::FlagAnyWrap, Depth + 1);
- const SCEV *ZAdd = getZeroExtendExpr(
- getAddExpr(Start, ZMul, SCEV::FlagAnyWrap, Depth + 1), WideTy,
- Depth + 1);
- const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
- const SCEV *WideMaxBECount =
- getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
- const SCEV *OperandExtendedAdd =
- getAddExpr(WideStart,
- getMulExpr(WideMaxBECount,
- getZeroExtendExpr(Step, WideTy, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1);
- if (ZAdd == OperandExtendedAdd) {
- // Cache knowledge of AR NUW, which is propagated to this AddRec.
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
- // Return the expression with the addrec on the outside.
- Start =
- getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getZeroExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- // Similar to above, only this time treat the step value as signed.
- // This covers loops that count down.
- OperandExtendedAdd =
- getAddExpr(WideStart,
- getMulExpr(WideMaxBECount,
- getSignExtendExpr(Step, WideTy, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1);
- if (ZAdd == OperandExtendedAdd) {
- // Cache knowledge of AR NW, which is propagated to this AddRec.
- // Negative step causes unsigned wrap, but it still can't self-wrap.
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
- // Return the expression with the addrec on the outside.
- Start =
- getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getSignExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- }
- }
-
- // Normally, in the cases we can prove no-overflow via a
- // backedge guarding condition, we can also compute a backedge
- // taken count for the loop. The exceptions are assumptions and
- // guards present in the loop -- SCEV is not great at exploiting
- // these to compute max backedge taken counts, but can still use
- // these to prove lack of overflow. Use this fact to avoid
- // doing extra work that may not pay off.
- if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
- !AC.assumptions().empty()) {
-
- auto NewFlags = proveNoUnsignedWrapViaInduction(AR);
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
- if (AR->hasNoUnsignedWrap()) {
- // Same as nuw case above - duplicated here to avoid a compile time
- // issue. It's not clear that the order of checks does matter, but
- // it's one of two issue possible causes for a change which was
- // reverted. Be conservative for the moment.
- Start =
- getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getZeroExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
-
- // For a negative step, we can extend the operands iff doing so only
- // traverses values in the range zext([0,UINT_MAX]).
- if (isKnownNegative(Step)) {
- const SCEV *N =
- getConstant(APInt::getMaxValue(BitWidth) - getSignedRangeMin(Step));
- if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
- isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
- // Cache knowledge of AR NW, which is propagated to this
- // AddRec. Negative step causes unsigned wrap, but it
- // still can't self-wrap.
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
- // Return the expression with the addrec on the outside.
- Start =
- getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getSignExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- }
- }
-
- // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
- // if D + (C - D + Step * n) could be proven to not unsigned wrap
- // where D maximizes the number of trailing zeros of (C - D + Step * n)
- if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
- const APInt &C = SC->getAPInt();
- const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
- if (D != 0) {
- const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
- const SCEV *SResidual =
- getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
- const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
- return getAddExpr(SZExtD, SZExtR, SCEV::FlagNSW | SCEV::FlagNUW,
- Depth + 1);
- }
- }
-
- if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
- Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getZeroExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- }
-
- // zext(A % B) --> zext(A) % zext(B)
- {
- const SCEV *LHS;
- const SCEV *RHS;
- if (match(Op, m_scev_URem(m_SCEV(LHS), m_SCEV(RHS), *this)))
- return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
- getZeroExtendExpr(RHS, Ty, Depth + 1));
- }
-
- // zext(A / B) --> zext(A) / zext(B).
- if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
- return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
- getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
-
- if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
- // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
- if (SA->hasNoUnsignedWrap()) {
- // If the addition does not unsign overflow then we can, by definition,
- // commute the zero extension with the addition operation.
- SmallVector<SCEVUse, 4> Ops;
- for (SCEVUse Op : SA->operands())
- Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
- return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
- }
-
- const APInt *C, *C2;
- // zext (C + A)<nsw> -> (sext(C) + sext(A))<nsw> if zext (C + A)<nsw> >=s 0.
- // Currently the non-negative check is done manually, as isKnownNonNegative
- // is too expensive.
- if (SA->hasNoSignedWrap() &&
- match(SA, m_scev_Add(m_scev_APInt(C),
- m_scev_SMax(m_scev_APInt(C2), m_SCEV()))) &&
- C->isNegative() && !C->isMinSignedValue() && C2->sge(C->abs())) {
- assert(isKnownNonNegative(SA) && "incorrectly determined non-negative");
- return getAddExpr(getSignExtendExpr(SA->getOperand(0), Ty, Depth + 1),
- getSignExtendExpr(SA->getOperand(1), Ty, Depth + 1),
- SCEV::FlagNSW, Depth + 1);
- }
-
- // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
- // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
- // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
- //
- // Often address arithmetics contain expressions like
- // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
- // This transformation is useful while proving that such expressions are
- // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
- if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
- const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
- if (D != 0) {
- const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
- const SCEV *SResidual =
- getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
- const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
- return getAddExpr(SZExtD, SZExtR, (SCEV::FlagNSW | SCEV::FlagNUW),
- Depth + 1);
- }
- }
- }
-
- if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
- // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
- if (SM->hasNoUnsignedWrap()) {
- // If the multiply does not unsign overflow then we can, by definition,
- // commute the zero extension with the multiply operation.
- SmallVector<SCEVUse, 4> Ops;
- for (SCEVUse Op : SM->operands())
- Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
- return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
- }
-
- // zext(2^K * (trunc X to iN)) to iM ->
- // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
- //
- // Proof:
- //
- // zext(2^K * (trunc X to iN)) to iM
- // = zext((trunc X to iN) << K) to iM
- // = zext((trunc X to i{N-K}) << K)<nuw> to iM
- // (because shl removes the top K bits)
- // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
- // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
- //
- const APInt *C;
- const SCEV *TruncRHS;
- if (match(SM,
- m_scev_Mul(m_scev_APInt(C), m_scev_Trunc(m_SCEV(TruncRHS)))) &&
- C->isPowerOf2()) {
- int NewTruncBits =
- getTypeSizeInBits(SM->getOperand(1)->getType()) - C->logBase2();
- Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
- return getMulExpr(
- getZeroExtendExpr(SM->getOperand(0), Ty),
- getZeroExtendExpr(getTruncateExpr(TruncRHS, NewTruncTy), Ty),
- SCEV::FlagNUW, Depth + 1);
- }
- }
-
- // zext(umin(x, y)) -> umin(zext(x), zext(y))
- // zext(umax(x, y)) -> umax(zext(x), zext(y))
- if (isa<SCEVUMinExpr>(Op) || isa<SCEVUMaxExpr>(Op)) {
- auto *MinMax = cast<SCEVMinMaxExpr>(Op);
- SmallVector<SCEVUse, 4> Operands;
- for (SCEVUse Operand : MinMax->operands())
- Operands.push_back(getZeroExtendExpr(Operand, Ty));
- if (isa<SCEVUMinExpr>(MinMax))
- return getUMinExpr(Operands);
- return getUMaxExpr(Operands);
- }
-
- // zext(umin_seq(x, y)) -> umin_seq(zext(x), zext(y))
- if (auto *MinMax = dyn_cast<SCEVSequentialMinMaxExpr>(Op)) {
- assert(isa<SCEVSequentialUMinExpr>(MinMax) && "Not supported!");
- SmallVector<SCEVUse, 4> Operands;
- for (SCEVUse Operand : MinMax->operands())
- Operands.push_back(getZeroExtendExpr(Operand, Ty));
- return getUMinExpr(Operands, /*Sequential*/ true);
- }
-
- // The cast wasn't folded; create an explicit cast node.
- // Recompute the insert position, as it may have been invalidated.
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
- SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
- Op, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Op);
- return S;
-}
-
-const SCEV *
-ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
- assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
- "This is not an extending conversion!");
- assert(isSCEVable(Ty) &&
- "This is not a conversion to a SCEVable type!");
- assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
- Ty = getEffectiveSCEVType(Ty);
-
- FoldID ID(scSignExtend, Op, Ty);
- if (const SCEV *S = FoldCache.lookup(ID))
- return S;
-
- const SCEV *S = getSignExtendExprImpl(Op, Ty, Depth);
- if (!isa<SCEVSignExtendExpr>(S))
- insertFoldCacheEntry(ID, S, FoldCache, FoldCacheUser);
- return S;
-}
-
-const SCEV *ScalarEvolution::getSignExtendExprImpl(const SCEV *Op, Type *Ty,
- unsigned Depth) {
- assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
- "This is not an extending conversion!");
- assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!");
- assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
- Ty = getEffectiveSCEVType(Ty);
-
- // Fold if the operand is constant.
- if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return getConstant(SC->getAPInt().sext(getTypeSizeInBits(Ty)));
-
- // sext(sext(x)) --> sext(x)
- if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
- return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
-
- // sext(zext(x)) --> zext(x)
- if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
- return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
-
- // If the operand is an affine AddRec with the no-signed-wrap flag, the
- // sign-extension distributes over the recurrence.
- const SCEV *Start, *Step;
- const Loop *L;
- if (Depth <= MaxCastDepth &&
- match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
- const auto *AR = cast<SCEVAddRecExpr>(Op);
- if (AR->hasNoSignedWrap()) {
- Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getSignExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, SCEV::FlagNSW);
- }
- }
-
- // Before doing any expensive analysis, check to see if we've already
- // computed a SCEV for this Op and Ty.
- FoldingSetNodeID ID;
- ID.AddInteger(scSignExtend);
- ID.AddPointer(Op);
- ID.AddPointer(Ty);
- void *IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
- // Limit recursion depth.
- if (Depth > MaxCastDepth) {
- SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
- Op, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Op);
- return S;
- }
-
- // sext(trunc(x)) --> sext(x) or x or trunc(x)
- if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
- // It's possible the bits taken off by the truncate were all sign bits. If
- // so, we should be able to simplify this further.
- const SCEV *X = ST->getOperand();
- ConstantRange CR = getSignedRange(X);
- unsigned TruncBits = getTypeSizeInBits(ST->getType());
- unsigned NewBits = getTypeSizeInBits(Ty);
- if (CR.truncate(TruncBits).signExtend(NewBits).contains(
- CR.sextOrTrunc(NewBits)))
- return getTruncateOrSignExtend(X, Ty, Depth);
- }
-
- if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
- // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
- if (SA->hasNoSignedWrap()) {
- // If the addition does not sign overflow then we can, by definition,
- // commute the sign extension with the addition operation.
- SmallVector<SCEVUse, 4> Ops;
- for (SCEVUse Op : SA->operands())
- Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
- return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
- }
-
- // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
- // if D + (C - D + x + y + ...) could be proven to not signed wrap
- // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
- //
- // For instance, this will bring two seemingly different expressions:
- // 1 + sext(5 + 20 * %x + 24 * %y) and
- // sext(6 + 20 * %x + 24 * %y)
- // to the same form:
- // 2 + sext(4 + 20 * %x + 24 * %y)
- if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
- const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
- if (D != 0) {
- const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
- const SCEV *SResidual =
- getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
- const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
- return getAddExpr(SSExtD, SSExtR, (SCEV::FlagNSW | SCEV::FlagNUW),
- Depth + 1);
- }
- }
- }
- // If the input value is a chrec scev, and we can prove that the value
- // did not overflow the old, smaller, value, we can sign extend all of the
- // operands (often constants). This allows analysis of something like
- // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
- if (match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
- const auto *AR = cast<SCEVAddRecExpr>(Op);
- unsigned BitWidth = getTypeSizeInBits(AR->getType());
-
- // The no-signed-wrap case is handled before the uniquing lookup above.
-
- // Check whether the backedge-taken count is SCEVCouldNotCompute.
- // Note that this serves two purposes: It filters out loops that are
- // simply not analyzable, and it covers the case where this code is
- // being called from within backedge-taken count analysis, such that
- // attempting to ask for the backedge-taken count would likely result
- // in infinite recursion. In the later case, the analysis code will
- // cope with a conservative value, and it will take care to purge
- // that value once it has finished.
- const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
- if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
- // Manually compute the final value for AR, checking for
- // overflow.
-
- // Check whether the backedge-taken count can be losslessly casted to
- // the addrec's type. The count is always unsigned.
- const SCEV *CastedMaxBECount =
- getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
- const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
- CastedMaxBECount, MaxBECount->getType(), Depth);
- if (MaxBECount == RecastedMaxBECount) {
- Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
- // Check whether Start+Step*MaxBECount has no signed overflow.
- const SCEV *SMul =
- getMulExpr(CastedMaxBECount, Step, SCEV::FlagAnyWrap, Depth + 1);
- const SCEV *SAdd = getSignExtendExpr(
- getAddExpr(Start, SMul, SCEV::FlagAnyWrap, Depth + 1), WideTy,
- Depth + 1);
- const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
- const SCEV *WideMaxBECount =
- getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
- const SCEV *OperandExtendedAdd =
- getAddExpr(WideStart,
- getMulExpr(WideMaxBECount,
- getSignExtendExpr(Step, WideTy, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1);
- if (SAdd == OperandExtendedAdd) {
- // Cache knowledge of AR NSW, which is propagated to this AddRec.
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
- // Return the expression with the addrec on the outside.
- Start =
- getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getSignExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- // Similar to above, only this time treat the step value as unsigned.
- // This covers loops that count up with an unsigned step.
- OperandExtendedAdd =
- getAddExpr(WideStart,
- getMulExpr(WideMaxBECount,
- getZeroExtendExpr(Step, WideTy, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1);
- if (SAdd == OperandExtendedAdd) {
- // If AR wraps around then
- //
- // abs(Step) * MaxBECount > unsigned-max(AR->getType())
- // => SAdd != OperandExtendedAdd
- //
- // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
- // (SAdd == OperandExtendedAdd => AR is NW)
-
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
-
- // Return the expression with the addrec on the outside.
- Start =
- getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getZeroExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- }
- }
-
- auto NewFlags = proveNoSignedWrapViaInduction(AR);
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
- if (AR->hasNoSignedWrap()) {
- // Same as nsw case above - duplicated here to avoid a compile time
- // issue. It's not clear that the order of checks does matter, but
- // it's one of two issue possible causes for a change which was
- // reverted. Be conservative for the moment.
- Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getSignExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
-
- // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
- // if D + (C - D + Step * n) could be proven to not signed wrap
- // where D maximizes the number of trailing zeros of (C - D + Step * n)
- if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
- const APInt &C = SC->getAPInt();
- const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
- if (D != 0) {
- const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
- const SCEV *SResidual =
- getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
- const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
- return getAddExpr(SSExtD, SSExtR, (SCEV::FlagNSW | SCEV::FlagNUW),
- Depth + 1);
- }
- }
-
- if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
- Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
- Step = getSignExtendExpr(Step, Ty, Depth + 1);
- return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
- }
- }
-
- // If the input value is provably positive and we could not simplify
- // away the sext build a zext instead.
- if (isKnownNonNegative(Op))
- return getZeroExtendExpr(Op, Ty, Depth + 1);
-
- // sext(smin(x, y)) -> smin(sext(x), sext(y))
- // sext(smax(x, y)) -> smax(sext(x), sext(y))
- if (isa<SCEVSMinExpr>(Op) || isa<SCEVSMaxExpr>(Op)) {
- auto *MinMax = cast<SCEVMinMaxExpr>(Op);
- SmallVector<SCEVUse, 4> Operands;
- for (SCEVUse Operand : MinMax->operands())
- Operands.push_back(getSignExtendExpr(Operand, Ty));
- if (isa<SCEVSMinExpr>(MinMax))
- return getSMinExpr(Operands);
- return getSMaxExpr(Operands);
- }
-
- // The cast wasn't folded; create an explicit cast node.
- // Recompute the insert position, as it may have been invalidated.
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
- SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
- Op, Ty);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Op);
- return S;
-}
-
-const SCEV *ScalarEvolution::getCastExpr(SCEVTypes Kind, const SCEV *Op,
- Type *Ty) {
- switch (Kind) {
- case scTruncate:
- return getTruncateExpr(Op, Ty);
- case scZeroExtend:
- return getZeroExtendExpr(Op, Ty);
- case scSignExtend:
- return getSignExtendExpr(Op, Ty);
- case scPtrToAddr: {
- const SCEV *Expr = getPtrToAddrExpr(Op);
- assert(Expr->getType() == Ty && "requested type must match");
- return Expr;
- }
- default:
- llvm_unreachable("Not a SCEV cast expression!");
- }
-}
-
-/// getAnyExtendExpr - Return a SCEV for the given operand extended with
-/// unspecified bits out to the given type.
-const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
- Type *Ty) {
- assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
- "This is not an extending conversion!");
- assert(isSCEVable(Ty) &&
- "This is not a conversion to a SCEVable type!");
- Ty = getEffectiveSCEVType(Ty);
-
- // Sign-extend negative constants.
- if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- if (SC->getAPInt().isNegative())
- return getSignExtendExpr(Op, Ty);
-
- // Peel off a truncate cast.
- if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
- const SCEV *NewOp = T->getOperand();
- if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
- return getAnyExtendExpr(NewOp, Ty);
- return getTruncateOrNoop(NewOp, Ty);
- }
-
- // Next try a zext cast. If the cast is folded, use it.
- const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
- if (!isa<SCEVZeroExtendExpr>(ZExt))
- return ZExt;
-
- // Next try a sext cast. If the cast is folded, use it.
- const SCEV *SExt = getSignExtendExpr(Op, Ty);
- if (!isa<SCEVSignExtendExpr>(SExt))
- return SExt;
-
- // Force the cast to be folded into the operands of an addrec.
- if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
- SmallVector<SCEVUse, 4> Ops;
- for (const SCEV *Op : AR->operands())
- Ops.push_back(getAnyExtendExpr(Op, Ty));
- return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
- }
-
- // If the expression is obviously signed, use the sext cast value.
- if (isa<SCEVSMaxExpr>(Op))
- return SExt;
-
- // Absent any other information, use the zext cast value.
- return ZExt;
-}
-
-/// Process the given Ops list, which is a list of operands to be added under
-/// the given scale, update the given map. This is a helper function for
-/// getAddRecExpr. As an example of what it does, given a sequence of operands
-/// that would form an add expression like this:
-///
-/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
-///
-/// where A and B are constants, update the map with these values:
-///
-/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
-///
-/// and add 13 + A*B*29 to AccumulatedConstant.
-/// This will allow getAddRecExpr to produce this:
-///
-/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
-///
-/// This form often exposes folding opportunities that are hidden in
-/// the original operand list.
-///
-/// Return true iff it appears that any interesting folding opportunities
-/// may be exposed. This helps getAddRecExpr short-circuit extra work in
-/// the common case where no interesting opportunities are present, and
-/// is also used as a check to avoid infinite recursion.
-static bool CollectAddOperandsWithScales(SmallDenseMap<SCEVUse, APInt, 16> &M,
- SmallVectorImpl<SCEVUse> &NewOps,
- APInt &AccumulatedConstant,
- ArrayRef<SCEVUse> Ops,
- const APInt &Scale,
- ScalarEvolution &SE) {
- bool Interesting = false;
-
- // Iterate over the add operands. They are sorted, with constants first.
- unsigned i = 0;
- while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
- ++i;
- // Pull a buried constant out to the outside.
- if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
- Interesting = true;
- AccumulatedConstant += Scale * C->getAPInt();
- }
-
- // Next comes everything else. We're especially interested in multiplies
- // here, but they're in the middle, so just visit the rest with one loop.
- for (; i != Ops.size(); ++i) {
- const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
- if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
- APInt NewScale =
- Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
- if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
- // A multiplication of a constant with another add; recurse.
- const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
- Interesting |= CollectAddOperandsWithScales(
- M, NewOps, AccumulatedConstant, Add->operands(), NewScale, SE);
- } else {
- // A multiplication of a constant with some other value. Update
- // the map.
- SmallVector<SCEVUse, 4> MulOps(drop_begin(Mul->operands()));
- const SCEV *Key = SE.getMulExpr(MulOps);
- auto Pair = M.insert({Key, NewScale});
- if (Pair.second) {
- NewOps.push_back(Pair.first->first);
- } else {
- Pair.first->second += NewScale;
- // The map already had an entry for this value, which may indicate
- // a folding opportunity.
- Interesting = true;
- }
- }
- } else {
- // An ordinary operand. Update the map.
- auto Pair = M.insert({Ops[i], Scale});
- if (Pair.second) {
- NewOps.push_back(Pair.first->first);
- } else {
- Pair.first->second += Scale;
- // The map already had an entry for this value, which may indicate
- // a folding opportunity.
- Interesting = true;
- }
- }
- }
-
- return Interesting;
-}
-
-bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed,
- const SCEV *LHS, const SCEV *RHS,
- const Instruction *CtxI) {
- const SCEV *(ScalarEvolution::*Operation)(SCEVUse, SCEVUse, SCEV::NoWrapFlags,
- unsigned);
- switch (BinOp) {
- default:
- llvm_unreachable("Unsupported binary op");
- case Instruction::Add:
- Operation = &ScalarEvolution::getAddExpr;
- break;
- case Instruction::Sub:
- Operation = &ScalarEvolution::getMinusSCEV;
- break;
- case Instruction::Mul:
- Operation = &ScalarEvolution::getMulExpr;
- break;
- }
-
- const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) =
- Signed ? &ScalarEvolution::getSignExtendExpr
- : &ScalarEvolution::getZeroExtendExpr;
-
- // Check ext(LHS op RHS) == ext(LHS) op ext(RHS)
- auto *NarrowTy = cast<IntegerType>(LHS->getType());
- auto *WideTy =
- IntegerType::get(NarrowTy->getContext(), NarrowTy->getBitWidth() * 2);
-
- const SCEV *A = (this->*Extension)(
- (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0);
- const SCEV *LHSB = (this->*Extension)(LHS, WideTy, 0);
- const SCEV *RHSB = (this->*Extension)(RHS, WideTy, 0);
- const SCEV *B = (this->*Operation)(LHSB, RHSB, SCEV::FlagAnyWrap, 0);
- if (A == B)
- return true;
- // Can we use context to prove the fact we need?
- if (!CtxI)
- return false;
- // TODO: Support mul.
- if (BinOp == Instruction::Mul)
- return false;
- auto *RHSC = dyn_cast<SCEVConstant>(RHS);
- // TODO: Lift this limitation.
- if (!RHSC)
- return false;
- APInt C = RHSC->getAPInt();
- unsigned NumBits = C.getBitWidth();
- bool IsSub = (BinOp == Instruction::Sub);
- bool IsNegativeConst = (Signed && C.isNegative());
- // Compute the direction and magnitude by which we need to check overflow.
- bool OverflowDown = IsSub ^ IsNegativeConst;
- APInt Magnitude = C;
- if (IsNegativeConst) {
- if (C == APInt::getSignedMinValue(NumBits))
- // TODO: SINT_MIN on inversion gives the same negative value, we don't
- // want to deal with that.
- return false;
- Magnitude = -C;
- }
-
- ICmpInst::Predicate Pred = Signed ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
- if (OverflowDown) {
- // To avoid overflow down, we need to make sure that MIN + Magnitude <= LHS.
- APInt Min = Signed ? APInt::getSignedMinValue(NumBits)
- : APInt::getMinValue(NumBits);
- APInt Limit = Min + Magnitude;
- return isKnownPredicateAt(Pred, getConstant(Limit), LHS, CtxI);
- } else {
- // To avoid overflow up, we need to make sure that LHS <= MAX - Magnitude.
- APInt Max = Signed ? APInt::getSignedMaxValue(NumBits)
- : APInt::getMaxValue(NumBits);
- APInt Limit = Max - Magnitude;
- return isKnownPredicateAt(Pred, LHS, getConstant(Limit), CtxI);
- }
-}
-
-std::optional<SCEV::NoWrapFlags>
-ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp(
- const OverflowingBinaryOperator *OBO) {
- // It cannot be done any better.
- if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap())
- return std::nullopt;
-
- SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap;
-
- if (OBO->hasNoUnsignedWrap())
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- if (OBO->hasNoSignedWrap())
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
-
- bool Deduced = false;
-
- Instruction::BinaryOps Opcode = (Instruction::BinaryOps)OBO->getOpcode();
- const SCEV *LHS = getSCEV(OBO->getOperand(0));
- const SCEV *RHS = getSCEV(OBO->getOperand(1));
-
- bool CanUseNSW = true;
- const APInt *ShiftAmt;
- // Treat `shl %a, C` as `mul %a, 1 << C`.
- if (match(OBO, m_Shl(m_Value(), m_APInt(ShiftAmt)))) {
- unsigned BitWidth = ShiftAmt->getBitWidth();
- if (ShiftAmt->uge(BitWidth))
- return std::nullopt;
- // NSW only transfers if the shift amount is < BitWidth - 1, as INT_MIN * -1
- // overflows.
- CanUseNSW = ShiftAmt->ult(BitWidth - 1);
- Opcode = Instruction::Mul;
- RHS = getConstant(APInt::getOneBitSet(BitWidth, ShiftAmt->getZExtValue()));
- } else if (Opcode != Instruction::Add && Opcode != Instruction::Sub &&
- Opcode != Instruction::Mul) {
- return std::nullopt;
- }
-
- const Instruction *CtxI =
- UseContextForNoWrapFlagInference ? dyn_cast<Instruction>(OBO) : nullptr;
- if (!OBO->hasNoUnsignedWrap() &&
- willNotOverflow(Opcode, /* Signed */ false, LHS, RHS, CtxI)) {
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- Deduced = true;
- }
-
- if (CanUseNSW && !OBO->hasNoSignedWrap() &&
- willNotOverflow(Opcode, /* Signed */ true, LHS, RHS, CtxI)) {
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
- Deduced = true;
- }
-
- if (Deduced)
- return Flags;
- return std::nullopt;
-}
-
-// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
-// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
-// can't-overflow flags for the operation if possible.
-static SCEV::NoWrapFlags StrengthenNoWrapFlags(ScalarEvolution *SE,
- SCEVTypes Type,
- ArrayRef<SCEVUse> Ops,
- SCEV::NoWrapFlags Flags) {
- using namespace std::placeholders;
-
- using OBO = OverflowingBinaryOperator;
-
- bool CanAnalyze =
- Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
- (void)CanAnalyze;
- assert(CanAnalyze && "don't call from other places!");
-
- SCEV::NoWrapFlags SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
- SCEV::NoWrapFlags SignOrUnsignWrap =
- ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
-
- // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
- auto IsKnownNonNegative = [&](SCEVUse U) {
- return SE->isKnownNonNegative(U);
- };
-
- if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
- Flags = ScalarEvolution::setFlags(Flags, SignOrUnsignMask);
-
- SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
-
- if (SignOrUnsignWrap != SignOrUnsignMask &&
- (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
- isa<SCEVConstant>(Ops[0])) {
-
- auto Opcode = [&] {
- switch (Type) {
- case scAddExpr:
- return Instruction::Add;
- case scMulExpr:
- return Instruction::Mul;
- default:
- llvm_unreachable("Unexpected SCEV op.");
- }
- }();
-
- const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
-
- // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
- if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
- auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
- Opcode, C, OBO::NoSignedWrap);
- if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
- }
-
- // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
- if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
- auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
- Opcode, C, OBO::NoUnsignedWrap);
- if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- }
- }
-
- // <0,+,nonnegative><nw> is also nuw
- // TODO: Add corresponding nsw case
- if (Type == scAddRecExpr && ScalarEvolution::hasFlags(Flags, SCEV::FlagNW) &&
- !ScalarEvolution::hasFlags(Flags, SCEV::FlagNUW) && Ops.size() == 2 &&
- Ops[0]->isZero() && IsKnownNonNegative(Ops[1]))
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
-
- // both (udiv X, Y) * Y and Y * (udiv X, Y) are always NUW
- if (Type == scMulExpr && !ScalarEvolution::hasFlags(Flags, SCEV::FlagNUW) &&
- Ops.size() == 2) {
- if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Ops[0]))
- if (UDiv->getOperand(1) == Ops[1])
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Ops[1]))
- if (UDiv->getOperand(1) == Ops[0])
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- }
-
- return Flags;
-}
-
-bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
- return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
-}
-
-/// Get a canonical add expression, or something simpler if possible.
-const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<SCEVUse> &Ops,
- SCEV::NoWrapFlags OrigFlags,
- unsigned Depth) {
- assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
- "only nuw or nsw allowed");
- assert(!Ops.empty() && "Cannot get empty add!");
- if (Ops.size() == 1) return Ops[0];
-#ifndef NDEBUG
- Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
- for (unsigned i = 1, e = Ops.size(); i != e; ++i)
- assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
- "SCEVAddExpr operand types don't match!");
- unsigned NumPtrs = count_if(
- Ops, [](const SCEV *Op) { return Op->getType()->isPointerTy(); });
- assert(NumPtrs <= 1 && "add has at most one pointer operand");
-#endif
-
- const SCEV *Folded = constantFoldAndGroupOps(
- *this, LI, DT, Ops,
- [](const APInt &C1, const APInt &C2) { return C1 + C2; },
- [](const APInt &C) { return C.isZero(); }, // identity
- [](const APInt &C) { return false; }); // absorber
- if (Folded)
- return Folded;
-
- unsigned Idx = isa<SCEVConstant>(Ops[0]) ? 1 : 0;
-
- // Delay expensive flag strengthening until necessary.
- auto ComputeFlags = [this, OrigFlags](ArrayRef<SCEVUse> Ops) {
- return StrengthenNoWrapFlags(this, scAddExpr, Ops, OrigFlags);
- };
-
- // Limit recursion calls depth.
- if (Depth > MaxArithDepth || hasHugeExpression(Ops))
- return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
-
- if (SCEV *S = findExistingSCEVInCache(scAddExpr, Ops)) {
- // Don't strengthen flags if we have no new information.
- SCEVAddExpr *Add = static_cast<SCEVAddExpr *>(S);
- if (Add->getNoWrapFlags(OrigFlags) != OrigFlags)
- Add->setNoWrapFlags(ComputeFlags(Ops));
- return S;
- }
-
- // Okay, check to see if the same value occurs in the operand list more than
- // once. If so, merge them together into an multiply expression. Since we
- // sorted the list, these values are required to be adjacent.
- Type *Ty = Ops[0]->getType();
- bool FoundMatch = false;
- for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
- if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
- // Scan ahead to count how many equal operands there are.
- unsigned Count = 2;
- while (i+Count != e && Ops[i+Count] == Ops[i])
- ++Count;
- // Merge the values into a multiply.
- SCEVUse Scale = getConstant(Ty, Count);
- const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
- if (Ops.size() == Count)
- return Mul;
- Ops[i] = Mul;
- Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
- --i; e -= Count - 1;
- FoundMatch = true;
- }
- if (FoundMatch)
- return getAddExpr(Ops, OrigFlags, Depth + 1);
-
- // Check for truncates. If all the operands are truncated from the same
- // type, see if factoring out the truncate would permit the result to be
- // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
- // if the contents of the resulting outer trunc fold to something simple.
- auto FindTruncSrcType = [&]() -> Type * {
- // We're ultimately looking to fold an addrec of truncs and muls of only
- // constants and truncs, so if we find any other types of SCEV
- // as operands of the addrec then we bail and return nullptr here.
- // Otherwise, we return the type of the operand of a trunc that we find.
- if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
- return T->getOperand()->getType();
- if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
- SCEVUse LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
- if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
- return T->getOperand()->getType();
- }
- return nullptr;
- };
- if (auto *SrcType = FindTruncSrcType()) {
- SmallVector<SCEVUse, 8> LargeOps;
- bool Ok = true;
- // Check all the operands to see if they can be represented in the
- // source type of the truncate.
- for (const SCEV *Op : Ops) {
- if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
- if (T->getOperand()->getType() != SrcType) {
- Ok = false;
- break;
- }
- LargeOps.push_back(T->getOperand());
- } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Op)) {
- LargeOps.push_back(getAnyExtendExpr(C, SrcType));
- } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Op)) {
- SmallVector<SCEVUse, 8> LargeMulOps;
- for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
- if (const SCEVTruncateExpr *T =
- dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
- if (T->getOperand()->getType() != SrcType) {
- Ok = false;
- break;
- }
- LargeMulOps.push_back(T->getOperand());
- } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
- LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
- } else {
- Ok = false;
- break;
- }
- }
- if (Ok)
- LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
- } else {
- Ok = false;
- break;
- }
- }
- if (Ok) {
- // Evaluate the expression in the larger type.
- const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
- // If it folds to something simple, use it. Otherwise, don't.
- if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
- return getTruncateExpr(Fold, Ty);
- }
- }
-
- if (Ops.size() == 2) {
- // Check if we have an expression of the form ((X + C1) - C2), where C1 and
- // C2 can be folded in a way that allows retaining wrapping flags of (X +
- // C1).
- const SCEV *A = Ops[0];
- const SCEV *B = Ops[1];
- auto *AddExpr = dyn_cast<SCEVAddExpr>(B);
- auto *C = dyn_cast<SCEVConstant>(A);
- if (AddExpr && C && isa<SCEVConstant>(AddExpr->getOperand(0))) {
- auto C1 = cast<SCEVConstant>(AddExpr->getOperand(0))->getAPInt();
- auto C2 = C->getAPInt();
- SCEV::NoWrapFlags PreservedFlags = SCEV::FlagAnyWrap;
-
- APInt ConstAdd = C1 + C2;
- auto AddFlags = AddExpr->getNoWrapFlags();
- // Adding a smaller constant is NUW if the original AddExpr was NUW.
- if (ScalarEvolution::hasFlags(AddFlags, SCEV::FlagNUW) &&
- ConstAdd.ule(C1)) {
- PreservedFlags =
- ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNUW);
- }
-
- // Adding a constant with the same sign and small magnitude is NSW, if the
- // original AddExpr was NSW.
- if (ScalarEvolution::hasFlags(AddFlags, SCEV::FlagNSW) &&
- C1.isSignBitSet() == ConstAdd.isSignBitSet() &&
- ConstAdd.abs().ule(C1.abs())) {
- PreservedFlags =
- ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNSW);
- }
-
- if (PreservedFlags != SCEV::FlagAnyWrap) {
- SmallVector<SCEVUse, 4> NewOps(AddExpr->operands());
- NewOps[0] = getConstant(ConstAdd);
- return getAddExpr(NewOps, PreservedFlags);
- }
- }
-
- // Try to push the constant operand into a ZExt: A + zext (-A + B) -> zext
- // (B), if trunc (A) + -A + B does not unsigned-wrap.
- const SCEVAddExpr *InnerAdd;
- if (match(B, m_scev_ZExt(m_scev_Add(InnerAdd)))) {
- const SCEV *NarrowA = getTruncateExpr(A, InnerAdd->getType());
- if (NarrowA == getNegativeSCEV(InnerAdd->getOperand(0)) &&
- getZeroExtendExpr(NarrowA, B->getType()) == A &&
- hasFlags(StrengthenNoWrapFlags(this, scAddExpr, {NarrowA, InnerAdd},
- SCEV::FlagAnyWrap),
- SCEV::FlagNUW)) {
- return getZeroExtendExpr(getAddExpr(NarrowA, InnerAdd), B->getType());
- }
- }
- }
-
- // Canonicalize (-1 * urem X, Y) + X --> (Y * X/Y)
- const SCEV *Y;
- if (Ops.size() == 2 &&
- match(Ops[0],
- m_scev_Mul(m_scev_AllOnes(),
- m_scev_URem(m_scev_Specific(Ops[1]), m_SCEV(Y), *this))))
- return getMulExpr(Y, getUDivExpr(Ops[1], Y));
-
- // Skip past any other cast SCEVs.
- while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
- ++Idx;
-
- // If there are add operands they would be next.
- if (Idx < Ops.size()) {
- bool DeletedAdd = false;
- // If the original flags and all inlined SCEVAddExprs are NUW, use the
- // common NUW flag for expression after inlining. Other flags cannot be
- // preserved, because they may depend on the original order of operations.
- SCEV::NoWrapFlags CommonFlags = maskFlags(OrigFlags, SCEV::FlagNUW);
- while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
- if (Ops.size() > AddOpsInlineThreshold ||
- Add->getNumOperands() > AddOpsInlineThreshold)
- break;
- // If we have an add, expand the add operands onto the end of the operands
- // list.
- Ops.erase(Ops.begin()+Idx);
- append_range(Ops, Add->operands());
- DeletedAdd = true;
- CommonFlags = maskFlags(CommonFlags, Add->getNoWrapFlags());
- }
-
- // If we deleted at least one add, we added operands to the end of the list,
- // and they are not necessarily sorted. Recurse to resort and resimplify
- // any operands we just acquired.
- if (DeletedAdd)
- return getAddExpr(Ops, CommonFlags, Depth + 1);
- }
-
- // Skip over the add expression until we get to a multiply.
- while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
- ++Idx;
-
- // Check to see if there are any folding opportunities present with
- // operands multiplied by constant values.
- if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
- uint64_t BitWidth = getTypeSizeInBits(Ty);
- SmallDenseMap<SCEVUse, APInt, 16> M;
- SmallVector<SCEVUse, 8> NewOps;
- APInt AccumulatedConstant(BitWidth, 0);
- if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
- Ops, APInt(BitWidth, 1), *this)) {
- struct APIntCompare {
- bool operator()(const APInt &LHS, const APInt &RHS) const {
- return LHS.ult(RHS);
- }
- };
-
- // Some interesting folding opportunity is present, so its worthwhile to
- // re-generate the operands list. Group the operands by constant scale,
- // to avoid multiplying by the same constant scale multiple times.
- std::map<APInt, SmallVector<SCEVUse, 4>, APIntCompare> MulOpLists;
- for (const SCEV *NewOp : NewOps)
- MulOpLists[M.find(NewOp)->second].push_back(NewOp);
- // Re-generate the operands list.
- Ops.clear();
- if (AccumulatedConstant != 0)
- Ops.push_back(getConstant(AccumulatedConstant));
- for (auto &MulOp : MulOpLists) {
- if (MulOp.first == 1) {
- Ops.push_back(getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1));
- } else if (MulOp.first != 0) {
- Ops.push_back(getMulExpr(
- getConstant(MulOp.first),
- getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
- SCEV::FlagAnyWrap, Depth + 1));
- }
- }
- if (Ops.empty())
- return getZero(Ty);
- if (Ops.size() == 1)
- return Ops[0];
- return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
- }
- }
-
- // Given a SCEVMulExpr and an operand index, return the product of all
- // operands except the one at OpIdx.
- auto StripFactor = [&](const SCEVMulExpr *M, unsigned OpIdx) -> SCEVUse {
- if (M->getNumOperands() == 2)
- return M->getOperand(OpIdx == 0);
- SmallVector<SCEVUse, 4> Remaining(M->operands().take_front(OpIdx));
- append_range(Remaining, M->operands().drop_front(OpIdx + 1));
- return getMulExpr(Remaining, SCEV::FlagAnyWrap, Depth + 1);
- };
-
- // If we are adding something to a multiply expression, make sure the
- // something is not already an operand of the multiply. If so, merge it into
- // the multiply.
- for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
- const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
- for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
- // Scan all terms to find every occurrence of common factor MulOpSCEV
- // and fold them in one shot:
- // A1*X + A2*X + ... + An*X --> X * (A1 + A2 + ... + An)
- const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
- if (isa<SCEVConstant>(MulOpSCEV))
- continue;
-
- // Cofactors: 1 for bare addends matching MulOpSCEV, or the
- // remaining product for multiply terms containing MulOpSCEV.
- SmallVector<SCEVUse, 4> Cofactors;
- SmallVector<unsigned, 4> DeadIndices;
- for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) {
- if (MulOpSCEV == Ops[AddOp]) {
- // W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
- Cofactors.push_back(getOne(Ty));
- DeadIndices.push_back(AddOp);
- continue;
- }
-
- if (AddOp <= Idx || !isa<SCEVMulExpr>(Ops[AddOp]))
- continue;
-
- const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[AddOp]);
- for (unsigned OMulOp = 0, OE = OtherMul->getNumOperands(); OMulOp != OE;
- ++OMulOp) {
- if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
- // (A*B*C) + (A*D*E) --> A * (B*C + D*E)
- Cofactors.push_back(StripFactor(OtherMul, OMulOp));
- DeadIndices.push_back(AddOp);
- break;
- }
- }
- }
-
- // Fold all collected cofactors with the anchor multiply's cofactor:
- // MulOpSCEV * (Cofactor_1 + ... + Cofactor_n + AnchorCofactor)
- if (!Cofactors.empty()) {
- Cofactors.push_back(StripFactor(Mul, MulOp));
-
- SCEVUse InnerSum = getAddExpr(Cofactors, SCEV::FlagAnyWrap, Depth + 1);
- SCEVUse OuterMul =
- getMulExpr(MulOpSCEV, InnerSum, SCEV::FlagAnyWrap, Depth + 1);
-
- // DeadIndices does not include Idx (the anchor), hence +1.
- if (Ops.size() == DeadIndices.size() + 1)
- return OuterMul;
-
- // Erase Ops[Idx] first, then erase DeadIndices in reverse order.
- // The -1 adjustment accounts for the shift from removing Idx;
- // reverse order means each erasure only shifts later positions,
- // which have already been processed.
- Ops.erase(Ops.begin() + Idx);
- for (unsigned Dead : reverse(DeadIndices))
- Ops.erase(Ops.begin() + (Dead > Idx ? Dead - 1 : Dead));
-
- Ops.push_back(OuterMul);
- return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
- }
- }
- }
-
- // If there are any add recurrences in the operands list, see if any other
- // added values are loop invariant. If so, we can fold them into the
- // recurrence.
- while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
- ++Idx;
-
- // Scan over all recurrences, trying to fold loop invariants into them.
- for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
- // Scan all of the other operands to this add and add them to the vector if
- // they are loop invariant w.r.t. the recurrence.
- SmallVector<SCEVUse, 8> LIOps;
- const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
- const Loop *AddRecLoop = AddRec->getLoop();
- for (unsigned i = 0, e = Ops.size(); i != e; ++i)
- if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
- LIOps.push_back(Ops[i]);
- Ops.erase(Ops.begin()+i);
- --i; --e;
- }
-
- // If we found some loop invariants, fold them into the recurrence.
- if (!LIOps.empty()) {
- // Compute nowrap flags for the addition of the loop-invariant ops and
- // the addrec. Temporarily push it as an operand for that purpose. These
- // flags are valid in the scope of the addrec only.
- LIOps.push_back(AddRec);
- SCEV::NoWrapFlags Flags = ComputeFlags(LIOps);
- LIOps.pop_back();
-
- // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
- LIOps.push_back(AddRec->getStart());
-
- SmallVector<SCEVUse, 4> AddRecOps(AddRec->operands());
-
- // It is not in general safe to propagate flags valid on an add within
- // the addrec scope to one outside it. We must prove that the inner
- // scope is guaranteed to execute if the outer one does to be able to
- // safely propagate. We know the program is undefined if poison is
- // produced on the inner scoped addrec. We also know that *for this use*
- // the outer scoped add can't overflow (because of the flags we just
- // computed for the inner scoped add) without the program being undefined.
- // Proving that entry to the outer scope neccesitates entry to the inner
- // scope, thus proves the program undefined if the flags would be violated
- // in the outer scope.
- SCEV::NoWrapFlags AddFlags = Flags;
- if (AddFlags != SCEV::FlagAnyWrap) {
- auto *DefI = getDefiningScopeBound(LIOps);
- auto *ReachI = &*AddRecLoop->getHeader()->begin();
- if (!isGuaranteedToTransferExecutionTo(DefI, ReachI))
- AddFlags = SCEV::FlagAnyWrap;
- }
- AddRecOps[0] = getAddExpr(LIOps, AddFlags, Depth + 1);
-
- // Build the new addrec. Propagate the NUW and NSW flags if both the
- // outer add and the inner addrec are guaranteed to have no overflow.
- // Always propagate NW.
- Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
- const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
-
- // If all of the other operands were loop invariant, we are done.
- if (Ops.size() == 1) return NewRec;
-
- // Otherwise, add the folded AddRec by the non-invariant parts.
- for (unsigned i = 0;; ++i)
- if (Ops[i] == AddRec) {
- Ops[i] = NewRec;
- break;
- }
- return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
- }
-
- // Okay, if there weren't any loop invariants to be folded, check to see if
- // there are multiple AddRec's with the same loop induction variable being
- // added together. If so, we can fold them.
- for (unsigned OtherIdx = Idx+1;
- OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
- ++OtherIdx) {
- // We expect the AddRecExpr's to be sorted in reverse dominance order,
- // so that the 1st found AddRecExpr is dominated by all others.
- assert(DT.dominates(
- cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
- AddRec->getLoop()->getHeader()) &&
- "AddRecExprs are not sorted in reverse dominance order?");
- if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
- // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
- SmallVector<SCEVUse, 4> AddRecOps(AddRec->operands());
- for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
- ++OtherIdx) {
- const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
- if (OtherAddRec->getLoop() == AddRecLoop) {
- for (unsigned i = 0, e = OtherAddRec->getNumOperands();
- i != e; ++i) {
- if (i >= AddRecOps.size()) {
- append_range(AddRecOps, OtherAddRec->operands().drop_front(i));
- break;
- }
- AddRecOps[i] =
- getAddExpr(AddRecOps[i], OtherAddRec->getOperand(i),
- SCEV::FlagAnyWrap, Depth + 1);
- }
- Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
- }
- }
- // Step size has changed, so we cannot guarantee no self-wraparound.
- Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
- return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
- }
- }
-
- // Otherwise couldn't fold anything into this recurrence. Move onto the
- // next one.
- }
-
- // Okay, it looks like we really DO need an add expr. Check to see if we
- // already have one, otherwise create a new one.
- return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
-}
-
-const SCEV *ScalarEvolution::getOrCreateAddExpr(ArrayRef<SCEVUse> Ops,
- SCEV::NoWrapFlags Flags) {
- FoldingSetNodeID ID;
- ID.AddInteger(scAddExpr);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- void *IP = nullptr;
- SCEVAddExpr *S =
- static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
- if (!S) {
- SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
- llvm::uninitialized_copy(Ops, O);
- S = new (SCEVAllocator)
- SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Ops);
- }
- S->setNoWrapFlags(Flags);
- return S;
-}
-
-const SCEV *ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<SCEVUse> Ops,
- const Loop *L,
- SCEV::NoWrapFlags Flags) {
- FoldingSetNodeID ID;
- ID.AddInteger(scAddRecExpr);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- ID.AddPointer(L);
- void *IP = nullptr;
- SCEVAddRecExpr *S =
- static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
- if (!S) {
- SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
- llvm::uninitialized_copy(Ops, O);
- S = new (SCEVAllocator)
- SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- LoopUsers[L].push_back(S);
- registerUser(S, Ops);
- }
- setNoWrapFlags(S, Flags);
- return S;
-}
-
-const SCEV *ScalarEvolution::getOrCreateMulExpr(ArrayRef<SCEVUse> Ops,
- SCEV::NoWrapFlags Flags) {
- FoldingSetNodeID ID;
- ID.AddInteger(scMulExpr);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- void *IP = nullptr;
- SCEVMulExpr *S =
- static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
- if (!S) {
- SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
- llvm::uninitialized_copy(Ops, O);
- S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
- O, Ops.size());
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Ops);
- }
- S->setNoWrapFlags(Flags);
- return S;
-}
-
-static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
- uint64_t k = i*j;
- if (j > 1 && k / j != i) Overflow = true;
- return k;
-}
-
-/// Compute the result of "n choose k", the binomial coefficient. If an
-/// intermediate computation overflows, Overflow will be set and the return will
-/// be garbage. Overflow is not cleared on absence of overflow.
-static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
- // We use the multiplicative formula:
- // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
- // At each iteration, we take the n-th term of the numeral and divide by the
- // (k-n)th term of the denominator. This division will always produce an
- // integral result, and helps reduce the chance of overflow in the
- // intermediate computations. However, we can still overflow even when the
- // final result would fit.
-
- if (n == 0 || n == k) return 1;
- if (k > n) return 0;
-
- if (k > n/2)
- k = n-k;
-
- uint64_t r = 1;
- for (uint64_t i = 1; i <= k; ++i) {
- r = umul_ov(r, n-(i-1), Overflow);
- r /= i;
- }
- return r;
-}
-
-/// Determine if any of the operands in this SCEV are a constant or if
-/// any of the add or multiply expressions in this SCEV contain a constant.
-static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
- struct FindConstantInAddMulChain {
- bool FoundConstant = false;
-
- bool follow(const SCEV *S) {
- FoundConstant |= isa<SCEVConstant>(S);
- return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
- }
-
- bool isDone() const {
- return FoundConstant;
- }
- };
-
- FindConstantInAddMulChain F;
- SCEVTraversal<FindConstantInAddMulChain> ST(F);
- ST.visitAll(StartExpr);
- return F.FoundConstant;
-}
-
-/// Get a canonical multiply expression, or something simpler if possible.
-const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<SCEVUse> &Ops,
- SCEV::NoWrapFlags OrigFlags,
- unsigned Depth) {
- assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) &&
- "only nuw or nsw allowed");
- assert(!Ops.empty() && "Cannot get empty mul!");
- if (Ops.size() == 1) return Ops[0];
-#ifndef NDEBUG
- Type *ETy = Ops[0]->getType();
- assert(!ETy->isPointerTy());
- for (unsigned i = 1, e = Ops.size(); i != e; ++i)
- assert(Ops[i]->getType() == ETy &&
- "SCEVMulExpr operand types don't match!");
-#endif
-
- const SCEV *Folded = constantFoldAndGroupOps(
- *this, LI, DT, Ops,
- [](const APInt &C1, const APInt &C2) { return C1 * C2; },
- [](const APInt &C) { return C.isOne(); }, // identity
- [](const APInt &C) { return C.isZero(); }); // absorber
- if (Folded)
- return Folded;
-
- // Delay expensive flag strengthening until necessary.
- auto ComputeFlags = [this, OrigFlags](const ArrayRef<SCEVUse> Ops) {
- return StrengthenNoWrapFlags(this, scMulExpr, Ops, OrigFlags);
- };
-
- // Limit recursion calls depth.
- if (Depth > MaxArithDepth || hasHugeExpression(Ops))
- return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
-
- if (SCEV *S = findExistingSCEVInCache(scMulExpr, Ops)) {
- // Don't strengthen flags if we have no new information.
- SCEVMulExpr *Mul = static_cast<SCEVMulExpr *>(S);
- if (Mul->getNoWrapFlags(OrigFlags) != OrigFlags)
- Mul->setNoWrapFlags(ComputeFlags(Ops));
- return S;
- }
-
- if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
- if (Ops.size() == 2) {
- // C1*(C2+V) -> C1*C2 + C1*V
- // If any of Add's ops are Adds or Muls with a constant, apply this
- // transformation as well.
- //
- // TODO: There are some cases where this transformation is not
- // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
- // this transformation should be narrowed down.
- const SCEV *Op0, *Op1;
- if (match(Ops[1], m_scev_Add(m_SCEV(Op0), m_SCEV(Op1))) &&
- containsConstantInAddMulChain(Ops[1])) {
- const SCEV *LHS = getMulExpr(LHSC, Op0, SCEV::FlagAnyWrap, Depth + 1);
- const SCEV *RHS = getMulExpr(LHSC, Op1, SCEV::FlagAnyWrap, Depth + 1);
- return getAddExpr(LHS, RHS, SCEV::FlagAnyWrap, Depth + 1);
- }
-
- if (Ops[0]->isAllOnesValue()) {
- // If we have a mul by -1 of an add, try distributing the -1 among the
- // add operands.
- if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
- SmallVector<SCEVUse, 4> NewOps;
- bool AnyFolded = false;
- for (const SCEV *AddOp : Add->operands()) {
- const SCEV *Mul = getMulExpr(Ops[0], SCEVUse(AddOp),
- SCEV::FlagAnyWrap, Depth + 1);
- if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
- NewOps.push_back(Mul);
- }
- if (AnyFolded)
- return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
- } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
- // Negation preserves a recurrence's no self-wrap property.
- SmallVector<SCEVUse, 4> Operands;
- for (const SCEV *AddRecOp : AddRec->operands())
- Operands.push_back(getMulExpr(Ops[0], SCEVUse(AddRecOp),
- SCEV::FlagAnyWrap, Depth + 1));
- // Let M be the minimum representable signed value. AddRec with nsw
- // multiplied by -1 can have signed overflow if and only if it takes a
- // value of M: M * (-1) would stay M and (M + 1) * (-1) would be the
- // maximum signed value. In all other cases signed overflow is
- // impossible.
- auto FlagsMask = SCEV::FlagNW;
- if (AddRec->hasNoSignedWrap()) {
- auto MinInt =
- APInt::getSignedMinValue(getTypeSizeInBits(AddRec->getType()));
- if (getSignedRangeMin(AddRec) != MinInt)
- FlagsMask = setFlags(FlagsMask, SCEV::FlagNSW);
- }
- return getAddRecExpr(Operands, AddRec->getLoop(),
- AddRec->getNoWrapFlags(FlagsMask));
- }
- }
-
- // Try to push the constant operand into a ZExt: C * zext (A + B) ->
- // zext (C*A + C*B) if trunc (C) * (A + B) does not unsigned-wrap.
- const SCEVAddExpr *InnerAdd;
- if (match(Ops[1], m_scev_ZExt(m_scev_Add(InnerAdd)))) {
- const SCEV *NarrowC = getTruncateExpr(LHSC, InnerAdd->getType());
- if (isa<SCEVConstant>(InnerAdd->getOperand(0)) &&
- getZeroExtendExpr(NarrowC, Ops[1]->getType()) == LHSC &&
- hasFlags(StrengthenNoWrapFlags(this, scMulExpr, {NarrowC, InnerAdd},
- SCEV::FlagAnyWrap),
- SCEV::FlagNUW)) {
- auto *Res = getMulExpr(NarrowC, InnerAdd, SCEV::FlagNUW, Depth + 1);
- return getZeroExtendExpr(Res, Ops[1]->getType(), Depth + 1);
- };
- }
-
- // Try to fold (C1 * D /u C2) -> C1/C2 * D, if C1 and C2 are powers-of-2,
- // D is a multiple of C2, and C1 is a multiple of C2. If C2 is a multiple
- // of C1, fold to (D /u (C2 /u C1)).
- const SCEV *D;
- APInt C1V = LHSC->getAPInt();
- // (C1 * D /u C2) == -1 * -C1 * D /u C2 when C1 != INT_MIN. Don't treat -1
- // as -1 * 1, as it won't enable additional folds.
- if (C1V.isNegative() && !C1V.isMinSignedValue() && !C1V.isAllOnes())
- C1V = C1V.abs();
- const SCEVConstant *C2;
- if (C1V.isPowerOf2() &&
- match(Ops[1], m_scev_UDiv(m_SCEV(D), m_SCEVConstant(C2))) &&
- C2->getAPInt().isPowerOf2() &&
- C1V.logBase2() <= getMinTrailingZeros(D)) {
- const SCEV *NewMul = nullptr;
- if (C1V.uge(C2->getAPInt())) {
- NewMul = getMulExpr(getUDivExpr(getConstant(C1V), C2), D);
- } else if (C2->getAPInt().logBase2() <= getMinTrailingZeros(D)) {
- assert(C1V.ugt(1) && "C1 <= 1 should have been folded earlier");
- NewMul = getUDivExpr(D, getUDivExpr(C2, getConstant(C1V)));
- }
- if (NewMul)
- return C1V == LHSC->getAPInt() ? NewMul : getNegativeSCEV(NewMul);
- }
- }
- }
-
- // Skip over the add expression until we get to a multiply.
- unsigned Idx = 0;
- while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
- ++Idx;
-
- // If there are mul operands inline them all into this expression.
- if (Idx < Ops.size()) {
- bool DeletedMul = false;
- while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
- if (Ops.size() > MulOpsInlineThreshold)
- break;
- // If we have an mul, expand the mul operands onto the end of the
- // operands list.
- Ops.erase(Ops.begin()+Idx);
- append_range(Ops, Mul->operands());
- DeletedMul = true;
- }
-
- // If we deleted at least one mul, we added operands to the end of the
- // list, and they are not necessarily sorted. Recurse to resort and
- // resimplify any operands we just acquired.
- if (DeletedMul)
- return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
- }
-
- // If there are any add recurrences in the operands list, see if any other
- // added values are loop invariant. If so, we can fold them into the
- // recurrence.
- while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
- ++Idx;
-
- // Scan over all recurrences, trying to fold loop invariants into them.
- for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
- // Scan all of the other operands to this mul and add them to the vector
- // if they are loop invariant w.r.t. the recurrence.
- SmallVector<SCEVUse, 8> LIOps;
- const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
- for (unsigned i = 0, e = Ops.size(); i != e; ++i)
- if (isAvailableAtLoopEntry(Ops[i], AddRec->getLoop())) {
- LIOps.push_back(Ops[i]);
- Ops.erase(Ops.begin()+i);
- --i; --e;
- }
-
- // If we found some loop invariants, fold them into the recurrence.
- if (!LIOps.empty()) {
- // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
- SmallVector<SCEVUse, 4> NewOps;
- NewOps.reserve(AddRec->getNumOperands());
- const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
-
- // If both the mul and addrec are nuw, we can preserve nuw.
- // If both the mul and addrec are nsw, we can only preserve nsw if either
- // a) they are also nuw, or
- // b) all multiplications of addrec operands with scale are nsw.
- SCEV::NoWrapFlags Flags =
- AddRec->getNoWrapFlags(ComputeFlags({Scale, AddRec}));
-
- for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
- NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
- SCEV::FlagAnyWrap, Depth + 1));
-
- if (hasFlags(Flags, SCEV::FlagNSW) && !hasFlags(Flags, SCEV::FlagNUW)) {
- ConstantRange NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
- Instruction::Mul, getSignedRange(Scale),
- OverflowingBinaryOperator::NoSignedWrap);
- if (!NSWRegion.contains(getSignedRange(AddRec->getOperand(i))))
- Flags = clearFlags(Flags, SCEV::FlagNSW);
- }
- }
-
- const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), Flags);
-
- // If all of the other operands were loop invariant, we are done.
- if (Ops.size() == 1) return NewRec;
-
- // Otherwise, multiply the folded AddRec by the non-invariant parts.
- for (unsigned i = 0;; ++i)
- if (Ops[i] == AddRec) {
- Ops[i] = NewRec;
- break;
- }
- return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
- }
-
- // Okay, if there weren't any loop invariants to be folded, check to see
- // if there are multiple AddRec's with the same loop induction variable
- // being multiplied together. If so, we can fold them.
-
- // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
- // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
- // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
- // ]]],+,...up to x=2n}.
- // Note that the arguments to choose() are always integers with values
- // known at compile time, never SCEV objects.
- //
- // The implementation avoids pointless extra computations when the two
- // addrec's are of different length (mathematically, it's equivalent to
- // an infinite stream of zeros on the right).
- bool OpsModified = false;
- for (unsigned OtherIdx = Idx+1;
- OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
- ++OtherIdx) {
- const SCEVAddRecExpr *OtherAddRec =
- dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
- if (!OtherAddRec || OtherAddRec->getLoop() != AddRec->getLoop())
- continue;
-
- // Limit max number of arguments to avoid creation of unreasonably big
- // SCEVAddRecs with very complex operands.
- if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
- MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec}))
- continue;
-
- bool Overflow = false;
- Type *Ty = AddRec->getType();
- bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
- SmallVector<SCEVUse, 7> AddRecOps;
- for (int x = 0, xe = AddRec->getNumOperands() +
- OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
- SmallVector<SCEVUse, 7> SumOps;
- for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
- uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
- for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
- ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
- z < ze && !Overflow; ++z) {
- uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
- uint64_t Coeff;
- if (LargerThan64Bits)
- Coeff = umul_ov(Coeff1, Coeff2, Overflow);
- else
- Coeff = Coeff1*Coeff2;
- const SCEV *CoeffTerm = getConstant(Ty, Coeff);
- const SCEV *Term1 = AddRec->getOperand(y-z);
- const SCEV *Term2 = OtherAddRec->getOperand(z);
- SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
- SCEV::FlagAnyWrap, Depth + 1));
- }
- }
- if (SumOps.empty())
- SumOps.push_back(getZero(Ty));
- AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
- }
- if (!Overflow) {
- const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
- SCEV::FlagAnyWrap);
- if (Ops.size() == 2) return NewAddRec;
- Ops[Idx] = NewAddRec;
- Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
- OpsModified = true;
- AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
- if (!AddRec)
- break;
- }
- }
- if (OpsModified)
- return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
-
- // Otherwise couldn't fold anything into this recurrence. Move onto the
- // next one.
- }
-
- // Okay, it looks like we really DO need an mul expr. Check to see if we
- // already have one, otherwise create a new one.
- return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
-}
-
-/// Represents an unsigned remainder expression based on unsigned division.
-const SCEV *ScalarEvolution::getURemExpr(SCEVUse LHS, SCEVUse RHS) {
- assert(getEffectiveSCEVType(LHS->getType()) ==
- getEffectiveSCEVType(RHS->getType()) &&
- "SCEVURemExpr operand types don't match!");
-
- // Short-circuit easy cases
- if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
- // If constant is one, the result is trivial
- if (RHSC->getValue()->isOne())
- return getZero(LHS->getType()); // X urem 1 --> 0
-
- // If constant is a power of two, fold into a zext(trunc(LHS)).
- if (RHSC->getAPInt().isPowerOf2()) {
- Type *FullTy = LHS->getType();
- Type *TruncTy =
- IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
- return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
- }
- }
-
- // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
- const SCEV *UDiv = getUDivExpr(LHS, RHS);
- const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
- return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
-}
-
-/// Get a canonical unsigned division expression, or something simpler if
-/// possible.
-const SCEV *ScalarEvolution::getUDivExpr(SCEVUse LHS, SCEVUse RHS) {
- assert(!LHS->getType()->isPointerTy() &&
- "SCEVUDivExpr operand can't be pointer!");
- assert(LHS->getType() == RHS->getType() &&
- "SCEVUDivExpr operand types don't match!");
-
- FoldingSetNodeID ID;
- ID.AddInteger(scUDivExpr);
- ID.AddPointer(LHS);
- ID.AddPointer(RHS);
- void *IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
- return S;
-
- // 0 udiv Y == 0
- if (match(LHS, m_scev_Zero()))
- return LHS;
-
- if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
- if (RHSC->getValue()->isOne())
- return LHS; // X udiv 1 --> x
- // If the denominator is zero, the result of the udiv is undefined. Don't
- // try to analyze it, because the resolution chosen here may differ from
- // the resolution chosen in other parts of the compiler.
- if (!RHSC->getValue()->isZero()) {
- // Determine if the division can be folded into the operands of
- // its operands.
- // TODO: Generalize this to non-constants by using known-bits information.
- Type *Ty = LHS->getType();
- unsigned LZ = RHSC->getAPInt().countl_zero();
- unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
- // For non-power-of-two values, effectively round the value up to the
- // nearest power of two.
- if (!RHSC->getAPInt().isPowerOf2())
- ++MaxShiftAmt;
- IntegerType *ExtTy =
- IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
- if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
- if (const SCEVConstant *Step =
- dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
- // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
- const APInt &StepInt = Step->getAPInt();
- const APInt &DivInt = RHSC->getAPInt();
- if (!StepInt.urem(DivInt) &&
- getZeroExtendExpr(AR, ExtTy) ==
- getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
- getZeroExtendExpr(Step, ExtTy),
- AR->getLoop(), SCEV::FlagAnyWrap)) {
- SmallVector<SCEVUse, 4> Operands;
- for (const SCEV *Op : AR->operands())
- Operands.push_back(getUDivExpr(Op, RHS));
- return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
- }
- /// Get a canonical UDivExpr for a recurrence.
- /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
- const APInt *StartRem;
- if (!DivInt.urem(StepInt) && match(getURemExpr(AR->getStart(), Step),
- m_scev_APInt(StartRem))) {
- bool NoWrap =
- getZeroExtendExpr(AR, ExtTy) ==
- getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
- getZeroExtendExpr(Step, ExtTy), AR->getLoop(),
- SCEV::FlagAnyWrap);
-
- // With N <= C and both N, C as powers-of-2, the transformation
- // {X,+,N}/C => {(X - X%N),+,N}/C preserves division results even
- // if wrapping occurs, as the division results remain equivalent for
- // all offsets in [[(X - X%N), X).
- bool CanFoldWithWrap = StepInt.ule(DivInt) && // N <= C
- StepInt.isPowerOf2() && DivInt.isPowerOf2();
- // Only fold if the subtraction can be folded in the start
- // expression.
- const SCEV *NewStart =
- getMinusSCEV(AR->getStart(), getConstant(*StartRem));
- if (*StartRem != 0 && (NoWrap || CanFoldWithWrap) &&
- !isa<SCEVAddExpr>(NewStart)) {
- const SCEV *NewLHS =
- getAddRecExpr(NewStart, Step, AR->getLoop(),
- NoWrap ? SCEV::FlagNW : SCEV::FlagAnyWrap);
- if (LHS != NewLHS) {
- LHS = NewLHS;
-
- // Reset the ID to include the new LHS, and check if it is
- // already cached.
- ID.clear();
- ID.AddInteger(scUDivExpr);
- ID.AddPointer(LHS);
- ID.AddPointer(RHS);
- IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
- return S;
- }
- }
- }
- }
- // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
- if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
- SmallVector<SCEVUse, 4> Operands;
- for (const SCEV *Op : M->operands())
- Operands.push_back(getZeroExtendExpr(Op, ExtTy));
- if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) {
- // Find an operand that's safely divisible.
- for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
- const SCEV *Op = M->getOperand(i);
- const SCEV *Div = getUDivExpr(Op, RHSC);
- if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
- Operands = SmallVector<SCEVUse, 4>(M->operands());
- Operands[i] = Div;
- return getMulExpr(Operands);
- }
- }
-
- // Even if it's not divisible, try to remove a common factor.
- if (const auto *LHSC = dyn_cast<SCEVConstant>(M->getOperand(0))) {
- APInt Factor = APIntOps::GreatestCommonDivisor(LHSC->getAPInt(),
- RHSC->getAPInt());
- if (!Factor.isIntN(1)) {
- SmallVector<SCEVUse, 2> NewOperands;
- NewOperands.push_back(getConstant(LHSC->getAPInt().udiv(Factor)));
- append_range(NewOperands, M->operands().drop_front());
- const SCEV *NewMul = getMulExpr(NewOperands);
- return getUDivExpr(NewMul,
- getConstant(RHSC->getAPInt().udiv(Factor)));
- }
- }
- }
- }
-
- // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
- if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
- if (auto *DivisorConstant =
- dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
- bool Overflow = false;
- APInt NewRHS =
- DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
- if (Overflow) {
- return getConstant(RHSC->getType(), 0, false);
- }
- return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
- }
- }
-
- // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
- if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
- SmallVector<SCEVUse, 4> Operands;
- for (const SCEV *Op : A->operands())
- Operands.push_back(getZeroExtendExpr(Op, ExtTy));
- if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
- Operands.clear();
- for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
- const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
- if (isa<SCEVUDivExpr>(Op) ||
- getMulExpr(Op, RHS) != A->getOperand(i))
- break;
- Operands.push_back(Op);
- }
- if (Operands.size() == A->getNumOperands())
- return getAddExpr(Operands);
- }
- }
-
- // ((N - M) + (M * A)) / N --> ((N - 1) + (M * A)) / N
- // This is an idiom for rounding A up to the next multiple of N, where A
- // is aready known to be a multiple of M. In this case, instcombine can
- // see that some low bits of the added constant are unused, so can clear
- // them, but we want to canonicalise to set the low bits. This makes the
- // pattern easier to match, without needing to check for known bits in
- // A*M.
- const APInt &N = RHSC->getAPInt();
- const APInt *NMinusM, *M;
- const SCEV *A;
- if (match(LHS, m_scev_Add(m_scev_APInt(NMinusM),
- m_scev_Mul(m_scev_APInt(M), m_SCEV(A))))) {
- if (N.isPowerOf2() && M->isPowerOf2() && M->ult(N) &&
- *NMinusM == N - *M) {
- return getUDivExpr(
- getAddExpr(getConstant(N - 1), getMulExpr(getConstant(*M), A)),
- RHS);
- }
- }
-
- // Fold if both operands are constant.
- if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS))
- return getConstant(LHSC->getAPInt().udiv(RHSC->getAPInt()));
- }
- }
-
- // ((-C + (C smax %x)) /u %x) evaluates to zero, for any positive constant C.
- const APInt *NegC, *C;
- if (match(LHS,
- m_scev_Add(m_scev_APInt(NegC),
- m_scev_SMax(m_scev_APInt(C), m_scev_Specific(RHS)))) &&
- NegC->isNegative() && !NegC->isMinSignedValue() && *C == -*NegC)
- return getZero(LHS->getType());
-
- // (%a * %b)<nuw> / %b -> %a
- const auto *Mul = dyn_cast<SCEVMulExpr>(LHS);
- if (Mul && Mul->hasNoUnsignedWrap()) {
- for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
- if (Mul->getOperand(i) == RHS) {
- SmallVector<SCEVUse, 2> Operands;
- append_range(Operands, Mul->operands().take_front(i));
- append_range(Operands, Mul->operands().drop_front(i + 1));
- return getMulExpr(Operands);
- }
- }
- }
-
- // TODO: Generalize to handle any common factors.
- // udiv (mul nuw a, vscale), (mul nuw b, vscale) --> udiv a, b
- const SCEV *NewLHS, *NewRHS;
- if (match(LHS, m_scev_c_NUWMul(m_SCEV(NewLHS), m_SCEVVScale())) &&
- match(RHS, m_scev_c_NUWMul(m_SCEV(NewRHS), m_SCEVVScale())))
- return getUDivExpr(NewLHS, NewRHS);
-
- // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs
- // changes). Make sure we get a new one.
- IP = nullptr;
- if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
- SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
- LHS, RHS);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, ArrayRef<SCEVUse>({LHS, RHS}));
- return S;
-}
-
-APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
- APInt A = C1->getAPInt().abs();
- APInt B = C2->getAPInt().abs();
- uint32_t ABW = A.getBitWidth();
- uint32_t BBW = B.getBitWidth();
-
- if (ABW > BBW)
- B = B.zext(ABW);
- else if (ABW < BBW)
- A = A.zext(BBW);
-
- return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
-}
-
-/// Get a canonical unsigned division expression, or something simpler if
-/// possible. There is no representation for an exact udiv in SCEV IR, but we
-/// can attempt to optimize it prior to construction.
-const SCEV *ScalarEvolution::getUDivExactExpr(SCEVUse LHS, SCEVUse RHS) {
- // Currently there is no exact specific logic.
-
- return getUDivExpr(LHS, RHS);
-}
-
-/// Get an add recurrence expression for the specified loop. Simplify the
-/// expression as much as possible.
-const SCEV *ScalarEvolution::getAddRecExpr(SCEVUse Start, SCEVUse Step,
- const Loop *L,
- SCEV::NoWrapFlags Flags) {
- SmallVector<SCEVUse, 4> Operands;
- Operands.push_back(Start);
- if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
- if (StepChrec->getLoop() == L) {
- append_range(Operands, StepChrec->operands());
- return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
- }
-
- Operands.push_back(Step);
- return getAddRecExpr(Operands, L, Flags);
-}
-
-/// Get an add recurrence expression for the specified loop. Simplify the
-/// expression as much as possible.
-const SCEV *ScalarEvolution::getAddRecExpr(SmallVectorImpl<SCEVUse> &Operands,
- const Loop *L,
- SCEV::NoWrapFlags Flags) {
- if (Operands.size() == 1) return Operands[0];
-#ifndef NDEBUG
- Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
- for (const SCEV *Op : llvm::drop_begin(Operands)) {
- assert(getEffectiveSCEVType(Op->getType()) == ETy &&
- "SCEVAddRecExpr operand types don't match!");
- assert(!Op->getType()->isPointerTy() && "Step must be integer");
- }
- for (const SCEV *Op : Operands)
- assert(isAvailableAtLoopEntry(Op, L) &&
- "SCEVAddRecExpr operand is not available at loop entry!");
-#endif
-
- if (Operands.back()->isZero()) {
- Operands.pop_back();
- return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
- }
-
- // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
- // use that information to infer NUW and NSW flags. However, computing a
- // BE count requires calling getAddRecExpr, so we may not yet have a
- // meaningful BE count at this point (and if we don't, we'd be stuck
- // with a SCEVCouldNotCompute as the cached BE count).
-
- Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
-
- // Canonicalize nested AddRecs in by nesting them in order of loop depth.
- if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
- const Loop *NestedLoop = NestedAR->getLoop();
- if (L->contains(NestedLoop)
- ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
- : (!NestedLoop->contains(L) &&
- DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
- SmallVector<SCEVUse, 4> NestedOperands(NestedAR->operands());
- Operands[0] = NestedAR->getStart();
- // AddRecs require their operands be loop-invariant with respect to their
- // loops. Don't perform this transformation if it would break this
- // requirement.
- bool AllInvariant = all_of(
- Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
-
- if (AllInvariant) {
- // Create a recurrence for the outer loop with the same step size.
- //
- // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
- // inner recurrence has the same property.
- SCEV::NoWrapFlags OuterFlags =
- maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
-
- NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
- AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
- return isLoopInvariant(Op, NestedLoop);
- });
-
- if (AllInvariant) {
- // Ok, both add recurrences are valid after the transformation.
- //
- // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
- // the outer recurrence has the same property.
- SCEV::NoWrapFlags InnerFlags =
- maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
- return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
- }
- }
- // Reset Operands to its original state.
- Operands[0] = NestedAR;
- }
- }
-
- // Okay, it looks like we really DO need an addrec expr. Check to see if we
- // already have one, otherwise create a new one.
- return getOrCreateAddRecExpr(Operands, L, Flags);
-}
-
-const SCEV *ScalarEvolution::getGEPExpr(GEPOperator *GEP,
- ArrayRef<SCEVUse> IndexExprs) {
- const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
- // getSCEV(Base)->getType() has the same address space as Base->getType()
- // because SCEV::getType() preserves the address space.
- GEPNoWrapFlags NW = GEP->getNoWrapFlags();
- if (NW != GEPNoWrapFlags::none()) {
- // We'd like to propagate flags from the IR to the corresponding SCEV nodes,
- // but to do that, we have to ensure that said flag is valid in the entire
- // defined scope of the SCEV.
- // TODO: non-instructions have global scope. We might be able to prove
- // some global scope cases
- auto *GEPI = dyn_cast<Instruction>(GEP);
- if (!GEPI || !isSCEVExprNeverPoison(GEPI))
- NW = GEPNoWrapFlags::none();
- }
-
- return getGEPExpr(BaseExpr, IndexExprs, GEP->getSourceElementType(), NW);
-}
-
-const SCEV *ScalarEvolution::getGEPExpr(SCEVUse BaseExpr,
- ArrayRef<SCEVUse> IndexExprs,
- Type *SrcElementTy, GEPNoWrapFlags NW) {
- SCEV::NoWrapFlags OffsetWrap = SCEV::FlagAnyWrap;
- if (NW.hasNoUnsignedSignedWrap())
- OffsetWrap = setFlags(OffsetWrap, SCEV::FlagNSW);
- if (NW.hasNoUnsignedWrap())
- OffsetWrap = setFlags(OffsetWrap, SCEV::FlagNUW);
-
- Type *CurTy = BaseExpr->getType();
- Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
- bool FirstIter = true;
- SmallVector<SCEVUse, 4> Offsets;
- for (SCEVUse IndexExpr : IndexExprs) {
- // Compute the (potentially symbolic) offset in bytes for this index.
- if (StructType *STy = dyn_cast<StructType>(CurTy)) {
- // For a struct, add the member offset.
- ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
- unsigned FieldNo = Index->getZExtValue();
- const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
- Offsets.push_back(FieldOffset);
-
- // Update CurTy to the type of the field at Index.
- CurTy = STy->getTypeAtIndex(Index);
- } else {
- // Update CurTy to its element type.
- if (FirstIter) {
- assert(isa<PointerType>(CurTy) &&
- "The first index of a GEP indexes a pointer");
- CurTy = SrcElementTy;
- FirstIter = false;
- } else {
- CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0);
- }
- // For an array, add the element offset, explicitly scaled.
- const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
- // Getelementptr indices are signed.
- IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);
-
- // Multiply the index by the element size to compute the element offset.
- const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, OffsetWrap);
- Offsets.push_back(LocalOffset);
- }
- }
-
- // Handle degenerate case of GEP without offsets.
- if (Offsets.empty())
- return BaseExpr;
-
- // Add the offsets together, assuming nsw if inbounds.
- const SCEV *Offset = getAddExpr(Offsets, OffsetWrap);
- // Add the base address and the offset. We cannot use the nsw flag, as the
- // base address is unsigned. However, if we know that the offset is
- // non-negative, we can use nuw.
- bool NUW = NW.hasNoUnsignedWrap() ||
- (NW.hasNoUnsignedSignedWrap() && isKnownNonNegative(Offset));
- SCEV::NoWrapFlags BaseWrap = NUW ? SCEV::FlagNUW : SCEV::FlagAnyWrap;
- auto *GEPExpr = getAddExpr(BaseExpr, Offset, BaseWrap);
- assert(BaseExpr->getType() == GEPExpr->getType() &&
- "GEP should not change type mid-flight.");
- return GEPExpr;
-}
-
-SCEV *ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
- ArrayRef<const SCEV *> Ops) {
- FoldingSetNodeID ID;
- ID.AddInteger(SCEVType);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- void *IP = nullptr;
- return UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
-}
-
-SCEV *ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
- ArrayRef<SCEVUse> Ops) {
- FoldingSetNodeID ID;
- ID.AddInteger(SCEVType);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- void *IP = nullptr;
- return UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
-}
-
-const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) {
- SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
- return getSMaxExpr(Op, getNegativeSCEV(Op, Flags));
-}
-
-const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind,
- SmallVectorImpl<SCEVUse> &Ops) {
- assert(SCEVMinMaxExpr::isMinMaxType(Kind) && "Not a SCEVMinMaxExpr!");
- assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
- if (Ops.size() == 1) return Ops[0];
-#ifndef NDEBUG
- Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
- for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
- assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
- "Operand types don't match!");
- assert(Ops[0]->getType()->isPointerTy() ==
- Ops[i]->getType()->isPointerTy() &&
- "min/max should be consistently pointerish");
- }
-#endif
-
- bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
- bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
-
- const SCEV *Folded = constantFoldAndGroupOps(
- *this, LI, DT, Ops,
- [&](const APInt &C1, const APInt &C2) {
- switch (Kind) {
- case scSMaxExpr:
- return APIntOps::smax(C1, C2);
- case scSMinExpr:
- return APIntOps::smin(C1, C2);
- case scUMaxExpr:
- return APIntOps::umax(C1, C2);
- case scUMinExpr:
- return APIntOps::umin(C1, C2);
- default:
- llvm_unreachable("Unknown SCEV min/max opcode");
- }
- },
- [&](const APInt &C) {
- // identity
- if (IsMax)
- return IsSigned ? C.isMinSignedValue() : C.isMinValue();
- else
- return IsSigned ? C.isMaxSignedValue() : C.isMaxValue();
- },
- [&](const APInt &C) {
- // absorber
- if (IsMax)
- return IsSigned ? C.isMaxSignedValue() : C.isMaxValue();
- else
- return IsSigned ? C.isMinSignedValue() : C.isMinValue();
- });
- if (Folded)
- return Folded;
-
- // Check if we have created the same expression before.
- if (const SCEV *S = findExistingSCEVInCache(Kind, Ops)) {
- return S;
- }
-
- // Find the first operation of the same kind
- unsigned Idx = 0;
- while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
- ++Idx;
-
- // Check to see if one of the operands is of the same kind. If so, expand its
- // operands onto our operand list, and recurse to simplify.
- if (Idx < Ops.size()) {
- bool DeletedAny = false;
- while (Ops[Idx]->getSCEVType() == Kind) {
- const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
- Ops.erase(Ops.begin()+Idx);
- append_range(Ops, SMME->operands());
- DeletedAny = true;
- }
-
- if (DeletedAny)
- return getMinMaxExpr(Kind, Ops);
- }
-
- // Okay, check to see if the same value occurs in the operand list twice. If
- // so, delete one. Since we sorted the list, these values are required to
- // be adjacent.
- llvm::CmpInst::Predicate GEPred =
- IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
- llvm::CmpInst::Predicate LEPred =
- IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
- llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
- llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
- for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
- if (Ops[i] == Ops[i + 1] ||
- isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
- // X op Y op Y --> X op Y
- // X op Y --> X, if we know X, Y are ordered appropriately
- Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
- --i;
- --e;
- } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
- Ops[i + 1])) {
- // X op Y --> Y, if we know X, Y are ordered appropriately
- Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
- --i;
- --e;
- }
- }
-
- if (Ops.size() == 1) return Ops[0];
-
- assert(!Ops.empty() && "Reduced smax down to nothing!");
-
- // Okay, it looks like we really DO need an expr. Check to see if we
- // already have one, otherwise create a new one.
- FoldingSetNodeID ID;
- ID.AddInteger(Kind);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- void *IP = nullptr;
- const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
- if (ExistingSCEV)
- return ExistingSCEV;
- SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
- llvm::uninitialized_copy(Ops, O);
- SCEV *S = new (SCEVAllocator)
- SCEVMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());
-
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Ops);
- return S;
-}
-
-namespace {
-
-class SCEVSequentialMinMaxDeduplicatingVisitor final
- : public SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor,
- std::optional<const SCEV *>> {
- using RetVal = std::optional<const SCEV *>;
- using Base = SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor, RetVal>;
-
- ScalarEvolution &SE;
- const SCEVTypes RootKind; // Must be a sequential min/max expression.
- const SCEVTypes NonSequentialRootKind; // Non-sequential variant of RootKind.
- SmallPtrSet<const SCEV *, 16> SeenOps;
-
- bool canRecurseInto(SCEVTypes Kind) const {
- // We can only recurse into the SCEV expression of the same effective type
- // as the type of our root SCEV expression.
- return RootKind == Kind || NonSequentialRootKind == Kind;
- };
-
- RetVal visitAnyMinMaxExpr(const SCEV *S) {
- assert((isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) &&
- "Only for min/max expressions.");
- SCEVTypes Kind = S->getSCEVType();
-
- if (!canRecurseInto(Kind))
- return S;
-
- auto *NAry = cast<SCEVNAryExpr>(S);
- SmallVector<SCEVUse> NewOps;
- bool Changed = visit(Kind, NAry->operands(), NewOps);
-
- if (!Changed)
- return S;
- if (NewOps.empty())
- return std::nullopt;
-
- return isa<SCEVSequentialMinMaxExpr>(S)
- ? SE.getSequentialMinMaxExpr(Kind, NewOps)
- : SE.getMinMaxExpr(Kind, NewOps);
- }
-
- RetVal visit(const SCEV *S) {
- // Has the whole operand been seen already?
- if (!SeenOps.insert(S).second)
- return std::nullopt;
- return Base::visit(S);
- }
-
-public:
- SCEVSequentialMinMaxDeduplicatingVisitor(ScalarEvolution &SE,
- SCEVTypes RootKind)
- : SE(SE), RootKind(RootKind),
- NonSequentialRootKind(
- SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
- RootKind)) {}
-
- bool /*Changed*/ visit(SCEVTypes Kind, ArrayRef<SCEVUse> OrigOps,
- SmallVectorImpl<SCEVUse> &NewOps) {
- bool Changed = false;
- SmallVector<SCEVUse> Ops;
- Ops.reserve(OrigOps.size());
-
- for (const SCEV *Op : OrigOps) {
- RetVal NewOp = visit(Op);
- if (NewOp != Op)
- Changed = true;
- if (NewOp)
- Ops.emplace_back(*NewOp);
- }
-
- if (Changed)
- NewOps = std::move(Ops);
- return Changed;
- }
-
- RetVal visitConstant(const SCEVConstant *Constant) { return Constant; }
-
- RetVal visitVScale(const SCEVVScale *VScale) { return VScale; }
-
- RetVal visitPtrToAddrExpr(const SCEVPtrToAddrExpr *Expr) { return Expr; }
-
- RetVal visitTruncateExpr(const SCEVTruncateExpr *Expr) { return Expr; }
-
- RetVal visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { return Expr; }
-
- RetVal visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { return Expr; }
-
- RetVal visitAddExpr(const SCEVAddExpr *Expr) { return Expr; }
-
- RetVal visitMulExpr(const SCEVMulExpr *Expr) { return Expr; }
-
- RetVal visitUDivExpr(const SCEVUDivExpr *Expr) { return Expr; }
-
- RetVal visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
-
- RetVal visitSMaxExpr(const SCEVSMaxExpr *Expr) {
- return visitAnyMinMaxExpr(Expr);
- }
-
- RetVal visitUMaxExpr(const SCEVUMaxExpr *Expr) {
- return visitAnyMinMaxExpr(Expr);
- }
-
- RetVal visitSMinExpr(const SCEVSMinExpr *Expr) {
- return visitAnyMinMaxExpr(Expr);
- }
-
- RetVal visitUMinExpr(const SCEVUMinExpr *Expr) {
- return visitAnyMinMaxExpr(Expr);
- }
-
- RetVal visitSequentialUMinExpr(const SCEVSequentialUMinExpr *Expr) {
- return visitAnyMinMaxExpr(Expr);
- }
-
- RetVal visitUnknown(const SCEVUnknown *Expr) { return Expr; }
-
- RetVal visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { return Expr; }
-};
-
-} // namespace
-
-static bool scevUnconditionallyPropagatesPoisonFromOperands(SCEVTypes Kind) {
- switch (Kind) {
- case scConstant:
- case scVScale:
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- case scAddExpr:
- case scMulExpr:
- case scUDivExpr:
- case scAddRecExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scUnknown:
- // If any operand is poison, the whole expression is poison.
- return true;
- case scSequentialUMinExpr:
- // FIXME: if the *first* operand is poison, the whole expression is poison.
- return false; // Pessimistically, say that it does not propagate poison.
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-namespace {
-// The only way poison may be introduced in a SCEV expression is from a
-// poison SCEVUnknown (ConstantExprs are also represented as SCEVUnknown,
-// not SCEVConstant). Notably, nowrap flags in SCEV nodes can *not*
-// introduce poison -- they encode guaranteed, non-speculated knowledge.
-//
-// Additionally, all SCEV nodes propagate poison from inputs to outputs,
-// with the notable exception of umin_seq, where only poison from the first
-// operand is (unconditionally) propagated.
-struct SCEVPoisonCollector {
- bool LookThroughMaybePoisonBlocking;
- SmallPtrSet<const SCEVUnknown *, 4> MaybePoison;
- SCEVPoisonCollector(bool LookThroughMaybePoisonBlocking)
- : LookThroughMaybePoisonBlocking(LookThroughMaybePoisonBlocking) {}
-
- bool follow(const SCEV *S) {
- if (!LookThroughMaybePoisonBlocking &&
- !scevUnconditionallyPropagatesPoisonFromOperands(S->getSCEVType()))
- return false;
-
- if (auto *SU = dyn_cast<SCEVUnknown>(S)) {
- if (!isGuaranteedNotToBePoison(SU->getValue()))
- MaybePoison.insert(SU);
- }
- return true;
- }
- bool isDone() const { return false; }
-};
-} // namespace
-
-/// Return true if V is poison given that AssumedPoison is already poison.
-static bool impliesPoison(const SCEV *AssumedPoison, const SCEV *S) {
- // First collect all SCEVs that might result in AssumedPoison to be poison.
- // We need to look through potentially poison-blocking operations here,
- // because we want to find all SCEVs that *might* result in poison, not only
- // those that are *required* to.
- SCEVPoisonCollector PC1(/* LookThroughMaybePoisonBlocking */ true);
- visitAll(AssumedPoison, PC1);
-
- // AssumedPoison is never poison. As the assumption is false, the implication
- // is true. Don't bother walking the other SCEV in this case.
- if (PC1.MaybePoison.empty())
- return true;
-
- // Collect all SCEVs in S that, if poison, *will* result in S being poison
- // as well. We cannot look through potentially poison-blocking operations
- // here, as their arguments only *may* make the result poison.
- SCEVPoisonCollector PC2(/* LookThroughMaybePoisonBlocking */ false);
- visitAll(S, PC2);
-
- // Make sure that no matter which SCEV in PC1.MaybePoison is actually poison,
- // it will also make S poison by being part of PC2.MaybePoison.
- return llvm::set_is_subset(PC1.MaybePoison, PC2.MaybePoison);
-}
-
-void ScalarEvolution::getPoisonGeneratingValues(
- SmallPtrSetImpl<const Value *> &Result, const SCEV *S) {
- SCEVPoisonCollector PC(/* LookThroughMaybePoisonBlocking */ false);
- visitAll(S, PC);
- for (const SCEVUnknown *SU : PC.MaybePoison)
- Result.insert(SU->getValue());
-}
-
-bool ScalarEvolution::canReuseInstruction(
- const SCEV *S, Instruction *I,
- SmallVectorImpl<Instruction *> &DropPoisonGeneratingInsts) {
- // If the instruction cannot be poison, it's always safe to reuse.
- if (programUndefinedIfPoison(I))
- return true;
-
- // Otherwise, it is possible that I is more poisonous that S. Collect the
- // poison-contributors of S, and then check whether I has any additional
- // poison-contributors. Poison that is contributed through poison-generating
- // flags is handled by dropping those flags instead.
- SmallPtrSet<const Value *, 8> PoisonVals;
- getPoisonGeneratingValues(PoisonVals, S);
-
- SmallVector<Value *> Worklist;
- SmallPtrSet<Value *, 8> Visited;
- Worklist.push_back(I);
- while (!Worklist.empty()) {
- Value *V = Worklist.pop_back_val();
- if (!Visited.insert(V).second)
- continue;
-
- // Avoid walking large instruction graphs.
- if (Visited.size() > 16)
- return false;
-
- // Either the value can't be poison, or the S would also be poison if it
- // is.
- if (PoisonVals.contains(V) || ::isGuaranteedNotToBePoison(V))
- continue;
-
- auto *I = dyn_cast<Instruction>(V);
- if (!I)
- return false;
-
- // Disjoint or instructions are interpreted as adds by SCEV. However, we
- // can't replace an arbitrary add with disjoint or, even if we drop the
- // flag. We would need to convert the or into an add.
- if (auto *PDI = dyn_cast<PossiblyDisjointInst>(I))
- if (PDI->isDisjoint())
- return false;
-
- // FIXME: Ignore vscale, even though it technically could be poison. Do this
- // because SCEV currently assumes it can't be poison. Remove this special
- // case once we proper model when vscale can be poison.
- if (auto *II = dyn_cast<IntrinsicInst>(I);
- II && II->getIntrinsicID() == Intrinsic::vscale)
- continue;
-
- if (canCreatePoison(cast<Operator>(I), /*ConsiderFlagsAndMetadata*/ false))
- return false;
-
- // If the instruction can't create poison, we can recurse to its operands.
- if (I->hasPoisonGeneratingAnnotations())
- DropPoisonGeneratingInsts.push_back(I);
-
- llvm::append_range(Worklist, I->operands());
- }
- return true;
-}
-
-const SCEV *
-ScalarEvolution::getSequentialMinMaxExpr(SCEVTypes Kind,
- SmallVectorImpl<SCEVUse> &Ops) {
- assert(SCEVSequentialMinMaxExpr::isSequentialMinMaxType(Kind) &&
- "Not a SCEVSequentialMinMaxExpr!");
- assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
- if (Ops.size() == 1)
- return Ops[0];
-#ifndef NDEBUG
- Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
- for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
- assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
- "Operand types don't match!");
- assert(Ops[0]->getType()->isPointerTy() ==
- Ops[i]->getType()->isPointerTy() &&
- "min/max should be consistently pointerish");
- }
-#endif
-
- // Note that SCEVSequentialMinMaxExpr is *NOT* commutative,
- // so we can *NOT* do any kind of sorting of the expressions!
-
- // Check if we have created the same expression before.
- if (const SCEV *S = findExistingSCEVInCache(Kind, Ops))
- return S;
-
- // FIXME: there are *some* simplifications that we can do here.
-
- // Keep only the first instance of an operand.
- {
- SCEVSequentialMinMaxDeduplicatingVisitor Deduplicator(*this, Kind);
- bool Changed = Deduplicator.visit(Kind, Ops, Ops);
- if (Changed)
- return getSequentialMinMaxExpr(Kind, Ops);
- }
-
- // Check to see if one of the operands is of the same kind. If so, expand its
- // operands onto our operand list, and recurse to simplify.
- {
- unsigned Idx = 0;
- bool DeletedAny = false;
- while (Idx < Ops.size()) {
- if (Ops[Idx]->getSCEVType() != Kind) {
- ++Idx;
- continue;
- }
- const auto *SMME = cast<SCEVSequentialMinMaxExpr>(Ops[Idx]);
- Ops.erase(Ops.begin() + Idx);
- Ops.insert(Ops.begin() + Idx, SMME->operands().begin(),
- SMME->operands().end());
- DeletedAny = true;
- }
-
- if (DeletedAny)
- return getSequentialMinMaxExpr(Kind, Ops);
- }
-
- const SCEV *SaturationPoint;
- ICmpInst::Predicate Pred;
- switch (Kind) {
- case scSequentialUMinExpr:
- SaturationPoint = getZero(Ops[0]->getType());
- Pred = ICmpInst::ICMP_ULE;
- break;
- default:
- llvm_unreachable("Not a sequential min/max type.");
- }
-
- for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
- if (!isGuaranteedNotToCauseUB(Ops[i]))
- continue;
- // We can replace %x umin_seq %y with %x umin %y if either:
- // * %y being poison implies %x is also poison.
- // * %x cannot be the saturating value (e.g. zero for umin).
- if (::impliesPoison(Ops[i], Ops[i - 1]) ||
- isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, Ops[i - 1],
- SaturationPoint)) {
- SmallVector<SCEVUse, 2> SeqOps = {Ops[i - 1], Ops[i]};
- Ops[i - 1] = getMinMaxExpr(
- SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(Kind),
- SeqOps);
- Ops.erase(Ops.begin() + i);
- return getSequentialMinMaxExpr(Kind, Ops);
- }
- // Fold %x umin_seq %y to %x if %x ule %y.
- // TODO: We might be able to prove the predicate for a later operand.
- if (isKnownViaNonRecursiveReasoning(Pred, Ops[i - 1], Ops[i])) {
- Ops.erase(Ops.begin() + i);
- return getSequentialMinMaxExpr(Kind, Ops);
- }
- }
-
- // Okay, it looks like we really DO need an expr. Check to see if we
- // already have one, otherwise create a new one.
- FoldingSetNodeID ID;
- ID.AddInteger(Kind);
- for (const SCEV *Op : Ops)
- ID.AddPointer(Op);
- void *IP = nullptr;
- const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
- if (ExistingSCEV)
- return ExistingSCEV;
-
- SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
- llvm::uninitialized_copy(Ops, O);
- SCEV *S = new (SCEVAllocator)
- SCEVSequentialMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());
-
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- registerUser(S, Ops);
- return S;
-}
-
-const SCEV *ScalarEvolution::getSMaxExpr(SCEVUse LHS, SCEVUse RHS) {
- SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
- return getMinMaxExpr(scSMaxExpr, Ops);
-}
-
-const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<SCEVUse> &Ops) {
- return getMinMaxExpr(scSMaxExpr, Ops);
-}
-
-const SCEV *ScalarEvolution::getUMaxExpr(SCEVUse LHS, SCEVUse RHS) {
- SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
- return getMinMaxExpr(scUMaxExpr, Ops);
-}
-
-const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<SCEVUse> &Ops) {
- return getMinMaxExpr(scUMaxExpr, Ops);
-}
-
-const SCEV *ScalarEvolution::getSMinExpr(SCEVUse LHS, SCEVUse RHS) {
- SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
- return getMinMaxExpr(scSMinExpr, Ops);
-}
-
-const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<SCEVUse> &Ops) {
- return getMinMaxExpr(scSMinExpr, Ops);
-}
-
-const SCEV *ScalarEvolution::getUMinExpr(SCEVUse LHS, SCEVUse RHS,
- bool Sequential) {
- SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
- return getUMinExpr(Ops, Sequential);
-}
-
-const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<SCEVUse> &Ops,
- bool Sequential) {
- return Sequential ? getSequentialMinMaxExpr(scSequentialUMinExpr, Ops)
- : getMinMaxExpr(scUMinExpr, Ops);
-}
-
-const SCEV *
-ScalarEvolution::getSizeOfExpr(Type *IntTy, TypeSize Size) {
- const SCEV *Res = getConstant(IntTy, Size.getKnownMinValue());
- if (Size.isScalable())
- Res = getMulExpr(Res, getVScale(IntTy));
- return Res;
-}
-
-const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
- return getSizeOfExpr(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
-}
-
-const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) {
- return getSizeOfExpr(IntTy, getDataLayout().getTypeStoreSize(StoreTy));
-}
-
-const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
- StructType *STy,
- unsigned FieldNo) {
- // We can bypass creating a target-independent constant expression and then
- // folding it back into a ConstantInt. This is just a compile-time
- // optimization.
- const StructLayout *SL = getDataLayout().getStructLayout(STy);
- assert(!SL->getSizeInBits().isScalable() &&
- "Cannot get offset for structure containing scalable vector types");
- return getConstant(IntTy, SL->getElementOffset(FieldNo));
-}
-
-const SCEV *ScalarEvolution::getUnknown(Value *V) {
- // Don't attempt to do anything other than create a SCEVUnknown object
- // here. createSCEV only calls getUnknown after checking for all other
- // interesting possibilities, and any other code that calls getUnknown
- // is doing so in order to hide a value from SCEV canonicalization.
-
- FoldingSetNodeID ID;
- ID.AddInteger(scUnknown);
- ID.AddPointer(V);
- void *IP = nullptr;
- if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
- assert(cast<SCEVUnknown>(S)->getValue() == V &&
- "Stale SCEVUnknown in uniquing map!");
- return S;
- }
- SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
- FirstUnknown);
- FirstUnknown = cast<SCEVUnknown>(S);
- UniqueSCEVs.InsertNode(S, IP);
- S->computeAndSetCanonical(*this);
- return S;
-}
-
-//===----------------------------------------------------------------------===//
-// Basic SCEV Analysis and PHI Idiom Recognition Code
-//
-
-/// Test if values of the given type are analyzable within the SCEV
-/// framework. This primarily includes integer types, and it can optionally
-/// include pointer types if the ScalarEvolution class has access to
-/// target-specific information.
-bool ScalarEvolution::isSCEVable(Type *Ty) const {
- // Integers and pointers are always SCEVable.
- return Ty->isIntOrPtrTy();
-}
-
-/// Return the size in bits of the specified type, for which isSCEVable must
-/// return true.
-uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
- assert(isSCEVable(Ty) && "Type is not SCEVable!");
- if (Ty->isPointerTy())
- return getDataLayout().getIndexTypeSizeInBits(Ty);
- return getDataLayout().getTypeSizeInBits(Ty);
-}
-
-/// Return a type with the same bitwidth as the given type and which represents
-/// how SCEV will treat the given type, for which isSCEVable must return
-/// true. For pointer types, this is the pointer index sized integer type.
-Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
- assert(isSCEVable(Ty) && "Type is not SCEVable!");
-
- if (Ty->isIntegerTy())
- return Ty;
-
- // The only other support type is pointer.
- assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
- return getDataLayout().getIndexType(Ty);
-}
-
-Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
- return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
-}
-
-bool ScalarEvolution::instructionCouldExistWithOperands(const SCEV *A,
- const SCEV *B) {
- /// For a valid use point to exist, the defining scope of one operand
- /// must dominate the other.
- bool PreciseA, PreciseB;
- auto *ScopeA = getDefiningScopeBound({A}, PreciseA);
- auto *ScopeB = getDefiningScopeBound({B}, PreciseB);
- if (!PreciseA || !PreciseB)
- // Can't tell.
- return false;
- return (ScopeA == ScopeB) || DT.dominates(ScopeA, ScopeB) ||
- DT.dominates(ScopeB, ScopeA);
-}
-
-const SCEV *ScalarEvolution::getCouldNotCompute() {
- return CouldNotCompute.get();
-}
-
-bool ScalarEvolution::checkValidity(const SCEV *S) const {
- bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
- auto *SU = dyn_cast<SCEVUnknown>(S);
- return SU && SU->getValue() == nullptr;
- });
-
- return !ContainsNulls;
-}
-
-bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
- HasRecMapType::iterator I = HasRecMap.find(S);
- if (I != HasRecMap.end())
- return I->second;
-
- bool FoundAddRec =
- SCEVExprContains(S, [](const SCEV *S) { return isa<SCEVAddRecExpr>(S); });
- HasRecMap.insert({S, FoundAddRec});
- return FoundAddRec;
-}
-
-/// Return the ValueOffsetPair set for \p S. \p S can be represented
-/// by the value and offset from any ValueOffsetPair in the set.
-ArrayRef<Value *> ScalarEvolution::getSCEVValues(const SCEV *S) {
- ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
- if (SI == ExprValueMap.end())
- return {};
- return SI->second.getArrayRef();
-}
-
-/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
-/// cannot be used separately. eraseValueFromMap should be used to remove
-/// V from ValueExprMap and ExprValueMap at the same time.
-void ScalarEvolution::eraseValueFromMap(Value *V) {
- ValueExprMapType::iterator I = ValueExprMap.find_as(V);
- if (I != ValueExprMap.end()) {
- auto EVIt = ExprValueMap.find(I->second);
- bool Removed = EVIt->second.remove(V);
- (void) Removed;
- assert(Removed && "Value not in ExprValueMap?");
- ValueExprMap.erase(I);
- }
-}
-
-void ScalarEvolution::insertValueToMap(Value *V, const SCEV *S) {
- // A recursive query may have already computed the SCEV. It should be
- // equivalent, but may not necessarily be exactly the same, e.g. due to lazily
- // inferred nowrap flags.
- auto It = ValueExprMap.find_as(V);
- if (It == ValueExprMap.end()) {
- ValueExprMap.insert({SCEVCallbackVH(V, this), S});
- ExprValueMap[S].insert(V);
- }
-}
-
-/// Return an existing SCEV if it exists, otherwise analyze the expression and
-/// create a new one.
-const SCEV *ScalarEvolution::getSCEV(Value *V) {
- assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
-
- if (const SCEV *S = getExistingSCEV(V))
- return S;
- return createSCEVIter(V);
-}
-
-const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
- assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
-
- ValueExprMapType::iterator I = ValueExprMap.find_as(V);
- if (I != ValueExprMap.end()) {
- const SCEV *S = I->second;
- assert(checkValidity(S) &&
- "existing SCEV has not been properly invalidated");
- return S;
- }
- return nullptr;
-}
-
-/// Return a SCEV corresponding to -V = -1*V
-const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
- SCEV::NoWrapFlags Flags) {
- if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
- return getConstant(
- cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
-
- Type *Ty = V->getType();
- Ty = getEffectiveSCEVType(Ty);
- return getMulExpr(V, getMinusOne(Ty), Flags);
-}
-
-/// If Expr computes ~A, return A else return nullptr
-static const SCEV *MatchNotExpr(const SCEV *Expr) {
- const SCEV *MulOp;
- if (match(Expr, m_scev_Add(m_scev_AllOnes(),
- m_scev_Mul(m_scev_AllOnes(), m_SCEV(MulOp)))))
- return MulOp;
- return nullptr;
-}
-
-/// Return a SCEV corresponding to ~V = -1-V
-const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
- assert(!V->getType()->isPointerTy() && "Can't negate pointer");
-
- if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
- return getConstant(
- cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
-
- // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
- if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
- auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
- SmallVector<SCEVUse, 2> MatchedOperands;
- for (const SCEV *Operand : MME->operands()) {
- const SCEV *Matched = MatchNotExpr(Operand);
- if (!Matched)
- return (const SCEV *)nullptr;
- MatchedOperands.push_back(Matched);
- }
- return getMinMaxExpr(SCEVMinMaxExpr::negate(MME->getSCEVType()),
- MatchedOperands);
- };
- if (const SCEV *Replaced = MatchMinMaxNegation(MME))
- return Replaced;
- }
-
- Type *Ty = V->getType();
- Ty = getEffectiveSCEVType(Ty);
- return getMinusSCEV(getMinusOne(Ty), V);
-}
-
-const SCEV *ScalarEvolution::removePointerBase(const SCEV *P) {
- assert(P->getType()->isPointerTy());
-
- if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(P)) {
- // The base of an AddRec is the first operand.
- SmallVector<SCEVUse> Ops{AddRec->operands()};
- Ops[0] = removePointerBase(Ops[0]);
- // Don't try to transfer nowrap flags for now. We could in some cases
- // (for example, if pointer operand of the AddRec is a SCEVUnknown).
- return getAddRecExpr(Ops, AddRec->getLoop(), SCEV::FlagAnyWrap);
- }
- if (auto *Add = dyn_cast<SCEVAddExpr>(P)) {
- // The base of an Add is the pointer operand.
- SmallVector<SCEVUse> Ops{Add->operands()};
- SCEVUse *PtrOp = nullptr;
- for (SCEVUse &AddOp : Ops) {
- if (AddOp->getType()->isPointerTy()) {
- assert(!PtrOp && "Cannot have multiple pointer ops");
- PtrOp = &AddOp;
- }
- }
- *PtrOp = removePointerBase(*PtrOp);
- // Don't try to transfer nowrap flags for now. We could in some cases
- // (for example, if the pointer operand of the Add is a SCEVUnknown).
- return getAddExpr(Ops);
- }
- // Any other expression must be a pointer base.
- return getZero(P->getType());
-}
-
-const SCEV *ScalarEvolution::getMinusSCEV(SCEVUse LHS, SCEVUse RHS,
- SCEV::NoWrapFlags Flags,
- unsigned Depth) {
- // Fast path: X - X --> 0.
- if (LHS == RHS)
- return getZero(LHS->getType());
-
- // If we subtract two pointers with different pointer bases, bail.
- // Eventually, we're going to add an assertion to getMulExpr that we
- // can't multiply by a pointer.
- if (RHS->getType()->isPointerTy()) {
- if (!LHS->getType()->isPointerTy() ||
- getPointerBase(LHS) != getPointerBase(RHS))
- return getCouldNotCompute();
- LHS = removePointerBase(LHS);
- RHS = removePointerBase(RHS);
- }
-
- // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
- // makes it so that we cannot make much use of NUW.
- auto AddFlags = SCEV::FlagAnyWrap;
- const bool RHSIsNotMinSigned =
- !getSignedRangeMin(RHS).isMinSignedValue();
- if (hasFlags(Flags, SCEV::FlagNSW)) {
- // Let M be the minimum representable signed value. Then (-1)*RHS
- // signed-wraps if and only if RHS is M. That can happen even for
- // a NSW subtraction because e.g. (-1)*M signed-wraps even though
- // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
- // (-1)*RHS, we need to prove that RHS != M.
- //
- // If LHS is non-negative and we know that LHS - RHS does not
- // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
- // either by proving that RHS > M or that LHS >= 0.
- if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
- AddFlags = SCEV::FlagNSW;
- }
- }
-
- // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
- // RHS is NSW and LHS >= 0.
- //
- // The difficulty here is that the NSW flag may have been proven
- // relative to a loop that is to be found in a recurrence in LHS and
- // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
- // larger scope than intended.
- auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
-
- return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
-}
-
-const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
- unsigned Depth) {
- Type *SrcTy = V->getType();
- assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
- "Cannot truncate or zero extend with non-integer arguments!");
- if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
- return V; // No conversion
- if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
- return getTruncateExpr(V, Ty, Depth);
- return getZeroExtendExpr(V, Ty, Depth);
-}
-
-const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
- unsigned Depth) {
- Type *SrcTy = V->getType();
- assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
- "Cannot truncate or zero extend with non-integer arguments!");
- if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
- return V; // No conversion
- if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
- return getTruncateExpr(V, Ty, Depth);
- return getSignExtendExpr(V, Ty, Depth);
-}
-
-const SCEV *
-ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
- Type *SrcTy = V->getType();
- assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
- "Cannot noop or zero extend with non-integer arguments!");
- assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
- "getNoopOrZeroExtend cannot truncate!");
- if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
- return V; // No conversion
- return getZeroExtendExpr(V, Ty);
-}
-
-const SCEV *
-ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
- Type *SrcTy = V->getType();
- assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
- "Cannot noop or sign extend with non-integer arguments!");
- assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
- "getNoopOrSignExtend cannot truncate!");
- if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
- return V; // No conversion
- return getSignExtendExpr(V, Ty);
-}
-
-const SCEV *
-ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
- Type *SrcTy = V->getType();
- assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
- "Cannot noop or any extend with non-integer arguments!");
- assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
- "getNoopOrAnyExtend cannot truncate!");
- if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
- return V; // No conversion
- return getAnyExtendExpr(V, Ty);
-}
-
-const SCEV *
-ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
- Type *SrcTy = V->getType();
- assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
- "Cannot truncate or noop with non-integer arguments!");
- assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
- "getTruncateOrNoop cannot extend!");
- if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
- return V; // No conversion
- return getTruncateExpr(V, Ty);
-}
-
-const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
- const SCEV *RHS) {
- const SCEV *PromotedLHS = LHS;
- const SCEV *PromotedRHS = RHS;
-
- if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
- PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
- else
- PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
-
- return getUMaxExpr(PromotedLHS, PromotedRHS);
-}
-
-const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
- const SCEV *RHS,
- bool Sequential) {
- SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
- return getUMinFromMismatchedTypes(Ops, Sequential);
-}
-
-const SCEV *
-ScalarEvolution::getUMinFromMismatchedTypes(SmallVectorImpl<SCEVUse> &Ops,
- bool Sequential) {
- assert(!Ops.empty() && "At least one operand must be!");
- // Trivial case.
- if (Ops.size() == 1)
- return Ops[0];
-
- // Find the max type first.
- Type *MaxType = nullptr;
- for (SCEVUse S : Ops)
- if (MaxType)
- MaxType = getWiderType(MaxType, S->getType());
- else
- MaxType = S->getType();
- assert(MaxType && "Failed to find maximum type!");
-
- // Extend all ops to max type.
- SmallVector<SCEVUse, 2> PromotedOps;
- for (SCEVUse S : Ops)
- PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
-
- // Generate umin.
- return getUMinExpr(PromotedOps, Sequential);
-}
-
-const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
- // A pointer operand may evaluate to a nonpointer expression, such as null.
- if (!V->getType()->isPointerTy())
- return V;
-
- while (true) {
- if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
- V = AddRec->getStart();
- } else if (auto *Add = dyn_cast<SCEVAddExpr>(V)) {
- const SCEV *PtrOp = nullptr;
- for (const SCEV *AddOp : Add->operands()) {
- if (AddOp->getType()->isPointerTy()) {
- assert(!PtrOp && "Cannot have multiple pointer ops");
- PtrOp = AddOp;
- }
- }
- assert(PtrOp && "Must have pointer op");
- V = PtrOp;
- } else // Not something we can look further into.
- return V;
- }
-}
-
-/// Push users of the given Instruction onto the given Worklist.
-static void PushDefUseChildren(Instruction *I,
- SmallVectorImpl<Instruction *> &Worklist,
- SmallPtrSetImpl<Instruction *> &Visited) {
- // Push the def-use children onto the Worklist stack.
- for (User *U : I->users()) {
- auto *UserInsn = cast<Instruction>(U);
- if (Visited.insert(UserInsn).second)
- Worklist.push_back(UserInsn);
- }
-}
-
-namespace {
-
-/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
-/// expression in case its Loop is L. If it is not L then
-/// if IgnoreOtherLoops is true then use AddRec itself
-/// otherwise rewrite cannot be done.
-/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
-class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
-public:
- static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
- bool IgnoreOtherLoops = true) {
- SCEVInitRewriter Rewriter(L, SE);
- const SCEV *Result = Rewriter.visit(S);
- if (Rewriter.hasSeenLoopVariantSCEVUnknown())
- return SE.getCouldNotCompute();
- return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
- ? SE.getCouldNotCompute()
- : Result;
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- if (!SE.isLoopInvariant(Expr, L))
- SeenLoopVariantSCEVUnknown = true;
- return Expr;
- }
-
- const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
- // Only re-write AddRecExprs for this loop.
- if (Expr->getLoop() == L)
- return Expr->getStart();
- SeenOtherLoops = true;
- return Expr;
- }
-
- bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
-
- bool hasSeenOtherLoops() { return SeenOtherLoops; }
-
-private:
- explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
- : SCEVRewriteVisitor(SE), L(L) {}
-
- const Loop *L;
- bool SeenLoopVariantSCEVUnknown = false;
- bool SeenOtherLoops = false;
-};
-
-/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
-/// increment expression in case its Loop is L. If it is not L then
-/// use AddRec itself.
-/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
-class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
-public:
- static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
- SCEVPostIncRewriter Rewriter(L, SE);
- const SCEV *Result = Rewriter.visit(S);
- return Rewriter.hasSeenLoopVariantSCEVUnknown()
- ? SE.getCouldNotCompute()
- : Result;
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- if (!SE.isLoopInvariant(Expr, L))
- SeenLoopVariantSCEVUnknown = true;
- return Expr;
- }
-
- const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
- // Only re-write AddRecExprs for this loop.
- if (Expr->getLoop() == L)
- return Expr->getPostIncExpr(SE);
- SeenOtherLoops = true;
- return Expr;
- }
-
- bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
-
- bool hasSeenOtherLoops() { return SeenOtherLoops; }
-
-private:
- explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
- : SCEVRewriteVisitor(SE), L(L) {}
-
- const Loop *L;
- bool SeenLoopVariantSCEVUnknown = false;
- bool SeenOtherLoops = false;
-};
-
-/// This class evaluates the compare condition by matching it against the
-/// condition of loop latch. If there is a match we assume a true value
-/// for the condition while building SCEV nodes.
-class SCEVBackedgeConditionFolder
- : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
-public:
- static const SCEV *rewrite(const SCEV *S, const Loop *L,
- ScalarEvolution &SE) {
- bool IsPosBECond = false;
- Value *BECond = nullptr;
- if (BasicBlock *Latch = L->getLoopLatch()) {
- if (CondBrInst *BI = dyn_cast<CondBrInst>(Latch->getTerminator())) {
- assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
- "Both outgoing branches should not target same header!");
- BECond = BI->getCondition();
- IsPosBECond = BI->getSuccessor(0) == L->getHeader();
- } else {
- return S;
- }
- }
- SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
- return Rewriter.visit(S);
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- const SCEV *Result = Expr;
- bool InvariantF = SE.isLoopInvariant(Expr, L);
-
- if (!InvariantF) {
- Instruction *I = cast<Instruction>(Expr->getValue());
- switch (I->getOpcode()) {
- case Instruction::Select: {
- SelectInst *SI = cast<SelectInst>(I);
- std::optional<const SCEV *> Res =
- compareWithBackedgeCondition(SI->getCondition());
- if (Res) {
- bool IsOne = cast<SCEVConstant>(*Res)->getValue()->isOne();
- Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
- }
- break;
- }
- default: {
- std::optional<const SCEV *> Res = compareWithBackedgeCondition(I);
- if (Res)
- Result = *Res;
- break;
- }
- }
- }
- return Result;
- }
-
-private:
- explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
- bool IsPosBECond, ScalarEvolution &SE)
- : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
- IsPositiveBECond(IsPosBECond) {}
-
- std::optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
-
- const Loop *L;
- /// Loop back condition.
- Value *BackedgeCond = nullptr;
- /// Set to true if loop back is on positive branch condition.
- bool IsPositiveBECond;
-};
-
-std::optional<const SCEV *>
-SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
-
- // If value matches the backedge condition for loop latch,
- // then return a constant evolution node based on loopback
- // branch taken.
- if (BackedgeCond == IC)
- return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
- : SE.getZero(Type::getInt1Ty(SE.getContext()));
- return std::nullopt;
-}
-
-class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
-public:
- static const SCEV *rewrite(const SCEV *S, const Loop *L,
- ScalarEvolution &SE) {
- SCEVShiftRewriter Rewriter(L, SE);
- const SCEV *Result = Rewriter.visit(S);
- return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- // Only allow AddRecExprs for this loop.
- if (!SE.isLoopInvariant(Expr, L))
- Valid = false;
- return Expr;
- }
-
- const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
- if (Expr->getLoop() == L && Expr->isAffine())
- return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
- Valid = false;
- return Expr;
- }
-
- bool isValid() { return Valid; }
-
-private:
- explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
- : SCEVRewriteVisitor(SE), L(L) {}
-
- const Loop *L;
- bool Valid = true;
-};
-
-} // end anonymous namespace
-
-void ScalarEvolution::inferNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
- if (!AR->isAffine())
- return;
-
- // Force computation of ranges, which will also perform range-based flag
- // inference.
- if (!AR->hasNoSignedWrap())
- (void)getSignedRange(AR);
-
- if (!AR->hasNoUnsignedWrap())
- (void)getUnsignedRange(AR);
-
- if (!AR->hasNoSelfWrap()) {
- const SCEV *BECount = getConstantMaxBackedgeTakenCount(AR->getLoop());
- if (const SCEVConstant *BECountMax = dyn_cast<SCEVConstant>(BECount)) {
- ConstantRange StepCR = getSignedRange(AR->getStepRecurrence(*this));
- const APInt &BECountAP = BECountMax->getAPInt();
- unsigned NoOverflowBitWidth =
- BECountAP.getActiveBits() + StepCR.getMinSignedBits();
- if (NoOverflowBitWidth <= getTypeSizeInBits(AR->getType()))
- const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
- }
- }
-}
-
-SCEV::NoWrapFlags
-ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) {
- SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
-
- if (AR->hasNoSignedWrap())
- return Result;
-
- if (!AR->isAffine())
- return Result;
-
- // This function can be expensive, only try to prove NSW once per AddRec.
- if (!SignedWrapViaInductionTried.insert(AR).second)
- return Result;
-
- const SCEV *Step = AR->getStepRecurrence(*this);
- const Loop *L = AR->getLoop();
-
- // Check whether the backedge-taken count is SCEVCouldNotCompute.
- // Note that this serves two purposes: It filters out loops that are
- // simply not analyzable, and it covers the case where this code is
- // being called from within backedge-taken count analysis, such that
- // attempting to ask for the backedge-taken count would likely result
- // in infinite recursion. In the later case, the analysis code will
- // cope with a conservative value, and it will take care to purge
- // that value once it has finished.
- const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
-
- // Normally, in the cases we can prove no-overflow via a
- // backedge guarding condition, we can also compute a backedge
- // taken count for the loop. The exceptions are assumptions and
- // guards present in the loop -- SCEV is not great at exploiting
- // these to compute max backedge taken counts, but can still use
- // these to prove lack of overflow. Use this fact to avoid
- // doing extra work that may not pay off.
-
- if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
- AC.assumptions().empty())
- return Result;
-
- // If the backedge is guarded by a comparison with the pre-inc value the
- // addrec is safe. Also, if the entry is guarded by a comparison with the
- // start value and the backedge is guarded by a comparison with the post-inc
- // value, the addrec is safe.
- ICmpInst::Predicate Pred;
- const SCEV *OverflowLimit =
- getSignedOverflowLimitForStep(Step, &Pred, this);
- if (OverflowLimit &&
- (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
- isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
- Result = setFlags(Result, SCEV::FlagNSW);
- }
- return Result;
-}
-SCEV::NoWrapFlags
-ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) {
- SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
-
- if (AR->hasNoUnsignedWrap())
- return Result;
-
- if (!AR->isAffine())
- return Result;
-
- // This function can be expensive, only try to prove NUW once per AddRec.
- if (!UnsignedWrapViaInductionTried.insert(AR).second)
- return Result;
-
- const SCEV *Step = AR->getStepRecurrence(*this);
- unsigned BitWidth = getTypeSizeInBits(AR->getType());
- const Loop *L = AR->getLoop();
-
- // Check whether the backedge-taken count is SCEVCouldNotCompute.
- // Note that this serves two purposes: It filters out loops that are
- // simply not analyzable, and it covers the case where this code is
- // being called from within backedge-taken count analysis, such that
- // attempting to ask for the backedge-taken count would likely result
- // in infinite recursion. In the later case, the analysis code will
- // cope with a conservative value, and it will take care to purge
- // that value once it has finished.
- const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
-
- // Normally, in the cases we can prove no-overflow via a
- // backedge guarding condition, we can also compute a backedge
- // taken count for the loop. The exceptions are assumptions and
- // guards present in the loop -- SCEV is not great at exploiting
- // these to compute max backedge taken counts, but can still use
- // these to prove lack of overflow. Use this fact to avoid
- // doing extra work that may not pay off.
-
- if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
- AC.assumptions().empty())
- return Result;
-
- // If the backedge is guarded by a comparison with the pre-inc value the
- // addrec is safe. Also, if the entry is guarded by a comparison with the
- // start value and the backedge is guarded by a comparison with the post-inc
- // value, the addrec is safe.
- if (isKnownPositive(Step)) {
- const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
- getUnsignedRangeMax(Step));
- if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
- isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
- Result = setFlags(Result, SCEV::FlagNUW);
- }
- }
-
- return Result;
-}
-
-namespace {
-
-/// Represents an abstract binary operation. This may exist as a
-/// normal instruction or constant expression, or may have been
-/// derived from an expression tree.
-struct BinaryOp {
- unsigned Opcode;
- Value *LHS;
- Value *RHS;
- bool IsNSW = false;
- bool IsNUW = false;
-
- /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
- /// constant expression.
- Operator *Op = nullptr;
-
- explicit BinaryOp(Operator *Op)
- : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
- Op(Op) {
- if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
- IsNSW = OBO->hasNoSignedWrap();
- IsNUW = OBO->hasNoUnsignedWrap();
- }
- }
-
- explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
- bool IsNUW = false)
- : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
-};
-
-} // end anonymous namespace
-
-/// Try to map \p V into a BinaryOp, and return \c std::nullopt on failure.
-static std::optional<BinaryOp> MatchBinaryOp(Value *V, const DataLayout &DL,
- AssumptionCache &AC,
- const DominatorTree &DT,
- const Instruction *CxtI) {
- auto *Op = dyn_cast<Operator>(V);
- if (!Op)
- return std::nullopt;
-
- // Implementation detail: all the cleverness here should happen without
- // creating new SCEV expressions -- our caller knowns tricks to avoid creating
- // SCEV expressions when possible, and we should not break that.
-
- switch (Op->getOpcode()) {
- case Instruction::Add:
- case Instruction::Sub:
- case Instruction::Mul:
- case Instruction::UDiv:
- case Instruction::URem:
- case Instruction::And:
- case Instruction::AShr:
- case Instruction::Shl:
- return BinaryOp(Op);
-
- case Instruction::Or: {
- // Convert or disjoint into add nuw nsw.
- if (cast<PossiblyDisjointInst>(Op)->isDisjoint()) {
- BinaryOp BinOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1),
- /*IsNSW=*/true, /*IsNUW=*/true);
- // Keep the reference to the original instruction so that we can later
- // check whether it can produce poison value or not.
- BinOp.Op = Op;
- return BinOp;
- }
- return BinaryOp(Op);
- }
-
- case Instruction::Xor:
- if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
- // If the RHS of the xor is a signmask, then this is just an add.
- // Instcombine turns add of signmask into xor as a strength reduction step.
- if (RHSC->getValue().isSignMask())
- return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
- // Binary `xor` is a bit-wise `add`.
- if (V->getType()->isIntegerTy(1))
- return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
- return BinaryOp(Op);
-
- case Instruction::LShr:
- // Turn logical shift right of a constant into a unsigned divide.
- if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
- uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
-
- // If the shift count is not less than the bitwidth, the result of
- // the shift is undefined. Don't try to analyze it, because the
- // resolution chosen here may differ from the resolution chosen in
- // other parts of the compiler.
- if (SA->getValue().ult(BitWidth)) {
- Constant *X =
- ConstantInt::get(SA->getContext(),
- APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
- return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
- }
- }
- return BinaryOp(Op);
-
- case Instruction::ExtractValue: {
- auto *EVI = cast<ExtractValueInst>(Op);
- if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
- break;
-
- auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
- if (!WO)
- break;
-
- Instruction::BinaryOps BinOp = WO->getBinaryOp();
- bool Signed = WO->isSigned();
- // TODO: Should add nuw/nsw flags for mul as well.
- if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
- return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
-
- // Now that we know that all uses of the arithmetic-result component of
- // CI are guarded by the overflow check, we can go ahead and pretend
- // that the arithmetic is non-overflowing.
- return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
- /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
- }
-
- default:
- break;
- }
-
- // Recognise intrinsic loop.decrement.reg, and as this has exactly the same
- // semantics as a Sub, return a binary sub expression.
- if (auto *II = dyn_cast<IntrinsicInst>(V))
- if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
- return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));
-
- return std::nullopt;
-}
-
-/// Helper function to createAddRecFromPHIWithCasts. We have a phi
-/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
-/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
-/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
-/// follows one of the following patterns:
-/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
-/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
-/// If the SCEV expression of \p Op conforms with one of the expected patterns
-/// we return the type of the truncation operation, and indicate whether the
-/// truncated type should be treated as signed/unsigned by setting
-/// \p Signed to true/false, respectively.
-static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
- bool &Signed, ScalarEvolution &SE) {
- // The case where Op == SymbolicPHI (that is, with no type conversions on
- // the way) is handled by the regular add recurrence creating logic and
- // would have already been triggered in createAddRecForPHI. Reaching it here
- // means that createAddRecFromPHI had failed for this PHI before (e.g.,
- // because one of the other operands of the SCEVAddExpr updating this PHI is
- // not invariant).
- //
- // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
- // this case predicates that allow us to prove that Op == SymbolicPHI will
- // be added.
- if (Op == SymbolicPHI)
- return nullptr;
-
- unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
- unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
- if (SourceBits != NewBits)
- return nullptr;
-
- if (match(Op, m_scev_SExt(m_scev_Trunc(m_scev_Specific(SymbolicPHI))))) {
- Signed = true;
- return cast<SCEVCastExpr>(Op)->getOperand()->getType();
- }
- if (match(Op, m_scev_ZExt(m_scev_Trunc(m_scev_Specific(SymbolicPHI))))) {
- Signed = false;
- return cast<SCEVCastExpr>(Op)->getOperand()->getType();
- }
- return nullptr;
-}
-
-static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
- if (!PN->getType()->isIntegerTy())
- return nullptr;
- const Loop *L = LI.getLoopFor(PN->getParent());
- if (!L || L->getHeader() != PN->getParent())
- return nullptr;
- return L;
-}
-
-// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
-// computation that updates the phi follows the following pattern:
-// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
-// which correspond to a phi->trunc->sext/zext->add->phi update chain.
-// If so, try to see if it can be rewritten as an AddRecExpr under some
-// Predicates. If successful, return them as a pair. Also cache the results
-// of the analysis.
-//
-// Example usage scenario:
-// Say the Rewriter is called for the following SCEV:
-// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
-// where:
-// %X = phi i64 (%Start, %BEValue)
-// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
-// and call this function with %SymbolicPHI = %X.
-//
-// The analysis will find that the value coming around the backedge has
-// the following SCEV:
-// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
-// Upon concluding that this matches the desired pattern, the function
-// will return the pair {NewAddRec, SmallPredsVec} where:
-// NewAddRec = {%Start,+,%Step}
-// SmallPredsVec = {P1, P2, P3} as follows:
-// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
-// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
-// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
-// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
-// under the predicates {P1,P2,P3}.
-// This predicated rewrite will be cached in PredicatedSCEVRewrites:
-// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
-//
-// TODO's:
-//
-// 1) Extend the Induction descriptor to also support inductions that involve
-// casts: When needed (namely, when we are called in the context of the
-// vectorizer induction analysis), a Set of cast instructions will be
-// populated by this method, and provided back to isInductionPHI. This is
-// needed to allow the vectorizer to properly record them to be ignored by
-// the cost model and to avoid vectorizing them (otherwise these casts,
-// which are redundant under the runtime overflow checks, will be
-// vectorized, which can be costly).
-//
-// 2) Support additional induction/PHISCEV patterns: We also want to support
-// inductions where the sext-trunc / zext-trunc operations (partly) occur
-// after the induction update operation (the induction increment):
-//
-// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
-// which correspond to a phi->add->trunc->sext/zext->phi update chain.
-//
-// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
-// which correspond to a phi->trunc->add->sext/zext->phi update chain.
-//
-// 3) Outline common code with createAddRecFromPHI to avoid duplication.
-std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
-ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
- SmallVector<const SCEVPredicate *, 3> Predicates;
-
- // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
- // return an AddRec expression under some predicate.
-
- auto *PN = cast<PHINode>(SymbolicPHI->getValue());
- const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
- assert(L && "Expecting an integer loop header phi");
-
- // The loop may have multiple entrances or multiple exits; we can analyze
- // this phi as an addrec if it has a unique entry value and a unique
- // backedge value.
- Value *BEValueV = nullptr, *StartValueV = nullptr;
- for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
- Value *V = PN->getIncomingValue(i);
- if (L->contains(PN->getIncomingBlock(i))) {
- if (!BEValueV) {
- BEValueV = V;
- } else if (BEValueV != V) {
- BEValueV = nullptr;
- break;
- }
- } else if (!StartValueV) {
- StartValueV = V;
- } else if (StartValueV != V) {
- StartValueV = nullptr;
- break;
- }
- }
- if (!BEValueV || !StartValueV)
- return std::nullopt;
-
- const SCEV *BEValue = getSCEV(BEValueV);
-
- // If the value coming around the backedge is an add with the symbolic
- // value we just inserted, possibly with casts that we can ignore under
- // an appropriate runtime guard, then we found a simple induction variable!
- const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
- if (!Add)
- return std::nullopt;
-
- // If there is a single occurrence of the symbolic value, possibly
- // casted, replace it with a recurrence.
- unsigned FoundIndex = Add->getNumOperands();
- Type *TruncTy = nullptr;
- bool Signed;
- for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
- if ((TruncTy =
- isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
- if (FoundIndex == e) {
- FoundIndex = i;
- break;
- }
-
- if (FoundIndex == Add->getNumOperands())
- return std::nullopt;
-
- // Create an add with everything but the specified operand.
- SmallVector<SCEVUse, 8> Ops;
- for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
- if (i != FoundIndex)
- Ops.push_back(Add->getOperand(i));
- const SCEV *Accum = getAddExpr(Ops);
-
- // The runtime checks will not be valid if the step amount is
- // varying inside the loop.
- if (!isLoopInvariant(Accum, L))
- return std::nullopt;
-
- // *** Part2: Create the predicates
-
- // Analysis was successful: we have a phi-with-cast pattern for which we
- // can return an AddRec expression under the following predicates:
- //
- // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
- // fits within the truncated type (does not overflow) for i = 0 to n-1.
- // P2: An Equal predicate that guarantees that
- // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
- // P3: An Equal predicate that guarantees that
- // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
- //
- // As we next prove, the above predicates guarantee that:
- // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
- //
- //
- // More formally, we want to prove that:
- // Expr(i+1) = Start + (i+1) * Accum
- // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
- //
- // Given that:
- // 1) Expr(0) = Start
- // 2) Expr(1) = Start + Accum
- // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
- // 3) Induction hypothesis (step i):
- // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
- //
- // Proof:
- // Expr(i+1) =
- // = Start + (i+1)*Accum
- // = (Start + i*Accum) + Accum
- // = Expr(i) + Accum
- // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
- // :: from step i
- //
- // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
- //
- // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
- // + (Ext ix (Trunc iy (Accum) to ix) to iy)
- // + Accum :: from P3
- //
- // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
- // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
- //
- // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
- // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
- //
- // By induction, the same applies to all iterations 1<=i<n:
- //
-
- // Create a truncated addrec for which we will add a no overflow check (P1).
- const SCEV *StartVal = getSCEV(StartValueV);
- const SCEV *PHISCEV =
- getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
- getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
-
- // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
- // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
- // will be constant.
- //
- // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
- // add P1.
- if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
- SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
- Signed ? SCEVWrapPredicate::IncrementNSSW
- : SCEVWrapPredicate::IncrementNUSW;
- const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
- Predicates.push_back(AddRecPred);
- }
-
- // Create the Equal Predicates P2,P3:
-
- // It is possible that the predicates P2 and/or P3 are computable at
- // compile time due to StartVal and/or Accum being constants.
- // If either one is, then we can check that now and escape if either P2
- // or P3 is false.
-
- // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
- // for each of StartVal and Accum
- auto getExtendedExpr = [&](const SCEV *Expr,
- bool CreateSignExtend) -> const SCEV * {
- assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
- const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
- const SCEV *ExtendedExpr =
- CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
- : getZeroExtendExpr(TruncatedExpr, Expr->getType());
- return ExtendedExpr;
- };
-
- // Given:
- // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
- // = getExtendedExpr(Expr)
- // Determine whether the predicate P: Expr == ExtendedExpr
- // is known to be false at compile time
- auto PredIsKnownFalse = [&](const SCEV *Expr,
- const SCEV *ExtendedExpr) -> bool {
- return Expr != ExtendedExpr &&
- isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
- };
-
- const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
- if (PredIsKnownFalse(StartVal, StartExtended)) {
- LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
- return std::nullopt;
- }
-
- // The Step is always Signed (because the overflow checks are either
- // NSSW or NUSW)
- const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
- if (PredIsKnownFalse(Accum, AccumExtended)) {
- LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
- return std::nullopt;
- }
-
- auto AppendPredicate = [&](const SCEV *Expr,
- const SCEV *ExtendedExpr) -> void {
- if (Expr != ExtendedExpr &&
- !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
- const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
- LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
- Predicates.push_back(Pred);
- }
- };
-
- AppendPredicate(StartVal, StartExtended);
- AppendPredicate(Accum, AccumExtended);
-
- // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
- // which the casts had been folded away. The caller can rewrite SymbolicPHI
- // into NewAR if it will also add the runtime overflow checks specified in
- // Predicates.
- auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
-
- std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
- std::make_pair(NewAR, Predicates);
- // Remember the result of the analysis for this SCEV at this locayyytion.
- PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
- return PredRewrite;
-}
-
-std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
-ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
- auto *PN = cast<PHINode>(SymbolicPHI->getValue());
- const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
- if (!L)
- return std::nullopt;
-
- // Check to see if we already analyzed this PHI.
- auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
- if (I != PredicatedSCEVRewrites.end()) {
- std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
- I->second;
- // Analysis was done before and failed to create an AddRec:
- if (Rewrite.first == SymbolicPHI)
- return std::nullopt;
- // Analysis was done before and succeeded to create an AddRec under
- // a predicate:
- assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
- assert(!(Rewrite.second).empty() && "Expected to find Predicates");
- return Rewrite;
- }
-
- std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
- Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
-
- // Record in the cache that the analysis failed
- if (!Rewrite) {
- SmallVector<const SCEVPredicate *, 3> Predicates;
- PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
- return std::nullopt;
- }
-
- return Rewrite;
-}
-
-// FIXME: This utility is currently required because the Rewriter currently
-// does not rewrite this expression:
-// {0, +, (sext ix (trunc iy to ix) to iy)}
-// into {0, +, %step},
-// even when the following Equal predicate exists:
-// "%step == (sext ix (trunc iy to ix) to iy)".
-bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
- const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2,
- ArrayRef<const SCEVPredicate *> NoWrapPreds) const {
- if (AR1 == AR2)
- return true;
-
- SCEVUnionPredicate NoWrapUnionPred(NoWrapPreds, SE);
- SCEVUnionPredicate AllPreds = Preds->getUnionWith(&NoWrapUnionPred, SE);
- auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
- if (Expr1 != Expr2 &&
- !AllPreds.implies(SE.getEqualPredicate(Expr1, Expr2), SE) &&
- !AllPreds.implies(SE.getEqualPredicate(Expr2, Expr1), SE))
- return false;
- return true;
- };
-
- if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
- !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
- return false;
- return true;
-}
-
-/// A helper function for createAddRecFromPHI to handle simple cases.
-///
-/// This function tries to find an AddRec expression for the simplest (yet most
-/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
-/// If it fails, createAddRecFromPHI will use a more general, but slow,
-/// technique for finding the AddRec expression.
-const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
- Value *BEValueV,
- Value *StartValueV) {
- const Loop *L = LI.getLoopFor(PN->getParent());
- assert(L && L->getHeader() == PN->getParent());
- assert(BEValueV && StartValueV);
-
- auto BO = MatchBinaryOp(BEValueV, getDataLayout(), AC, DT, PN);
- if (!BO)
- return nullptr;
-
- if (BO->Opcode != Instruction::Add)
- return nullptr;
-
- const SCEV *Accum = nullptr;
- if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
- Accum = getSCEV(BO->RHS);
- else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
- Accum = getSCEV(BO->LHS);
-
- if (!Accum)
- return nullptr;
-
- SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
- if (BO->IsNUW)
- Flags = setFlags(Flags, SCEV::FlagNUW);
- if (BO->IsNSW)
- Flags = setFlags(Flags, SCEV::FlagNSW);
-
- const SCEV *StartVal = getSCEV(StartValueV);
- const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
- insertValueToMap(PN, PHISCEV);
-
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV))
- inferNoWrapViaConstantRanges(AR);
-
- // We can add Flags to the post-inc expression only if we
- // know that it is *undefined behavior* for BEValueV to
- // overflow.
- if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) {
- assert(isLoopInvariant(Accum, L) &&
- "Accum is defined outside L, but is not invariant?");
- if (isAddRecNeverPoison(BEInst, L))
- (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
- }
-
- return PHISCEV;
-}
-
-const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
- const Loop *L = LI.getLoopFor(PN->getParent());
- if (!L || L->getHeader() != PN->getParent())
- return nullptr;
-
- // The loop may have multiple entrances or multiple exits; we can analyze
- // this phi as an addrec if it has a unique entry value and a unique
- // backedge value.
- Value *BEValueV = nullptr, *StartValueV = nullptr;
- for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
- Value *V = PN->getIncomingValue(i);
- if (L->contains(PN->getIncomingBlock(i))) {
- if (!BEValueV) {
- BEValueV = V;
- } else if (BEValueV != V) {
- BEValueV = nullptr;
- break;
- }
- } else if (!StartValueV) {
- StartValueV = V;
- } else if (StartValueV != V) {
- StartValueV = nullptr;
- break;
- }
- }
- if (!BEValueV || !StartValueV)
- return nullptr;
-
- assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
- "PHI node already processed?");
-
- // First, try to find AddRec expression without creating a fictituos symbolic
- // value for PN.
- if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
- return S;
-
- // Handle PHI node value symbolically.
- const SCEV *SymbolicName = getUnknown(PN);
- insertValueToMap(PN, SymbolicName);
-
- // Using this symbolic name for the PHI, analyze the value coming around
- // the back-edge.
- const SCEV *BEValue = getSCEV(BEValueV);
-
- // NOTE: If BEValue is loop invariant, we know that the PHI node just
- // has a special value for the first iteration of the loop.
-
- // If the value coming around the backedge is an add with the symbolic
- // value we just inserted, then we found a simple induction variable!
- if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
- // If there is a single occurrence of the symbolic value, replace it
- // with a recurrence.
- unsigned FoundIndex = Add->getNumOperands();
- for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
- if (Add->getOperand(i) == SymbolicName)
- if (FoundIndex == e) {
- FoundIndex = i;
- break;
- }
-
- if (FoundIndex != Add->getNumOperands()) {
- // Create an add with everything but the specified operand.
- SmallVector<SCEVUse, 8> Ops;
- for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
- if (i != FoundIndex)
- Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
- L, *this));
- const SCEV *Accum = getAddExpr(Ops);
-
- // This is not a valid addrec if the step amount is varying each
- // loop iteration, but is not itself an addrec in this loop.
- if (isLoopInvariant(Accum, L) ||
- (isa<SCEVAddRecExpr>(Accum) &&
- cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
- SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
-
- if (auto BO = MatchBinaryOp(BEValueV, getDataLayout(), AC, DT, PN)) {
- if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
- if (BO->IsNUW)
- Flags = setFlags(Flags, SCEV::FlagNUW);
- if (BO->IsNSW)
- Flags = setFlags(Flags, SCEV::FlagNSW);
- }
- } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
- if (GEP->getOperand(0) == PN) {
- GEPNoWrapFlags NW = GEP->getNoWrapFlags();
- // If the increment has any nowrap flags, then we know the address
- // space cannot be wrapped around.
- if (NW != GEPNoWrapFlags::none())
- Flags = setFlags(Flags, SCEV::FlagNW);
- // If the GEP is nuw or nusw with non-negative offset, we know that
- // no unsigned wrap occurs. We cannot set the nsw flag as only the
- // offset is treated as signed, while the base is unsigned.
- if (NW.hasNoUnsignedWrap() ||
- (NW.hasNoUnsignedSignedWrap() && isKnownNonNegative(Accum)))
- Flags = setFlags(Flags, SCEV::FlagNUW);
- }
-
- // We cannot transfer nuw and nsw flags from subtraction
- // operations -- sub nuw X, Y is not the same as add nuw X, -Y
- // for instance.
- }
-
- const SCEV *StartVal = getSCEV(StartValueV);
- const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
-
- // Okay, for the entire analysis of this edge we assumed the PHI
- // to be symbolic. We now need to go back and purge all of the
- // entries for the scalars that use the symbolic expression.
- forgetMemoizedResults({SymbolicName});
- insertValueToMap(PN, PHISCEV);
-
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV))
- inferNoWrapViaConstantRanges(AR);
-
- // We can add Flags to the post-inc expression only if we
- // know that it is *undefined behavior* for BEValueV to
- // overflow.
- if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
- if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
- (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
-
- return PHISCEV;
- }
- }
- } else {
- // Otherwise, this could be a loop like this:
- // i = 0; for (j = 1; ..; ++j) { .... i = j; }
- // In this case, j = {1,+,1} and BEValue is j.
- // Because the other in-value of i (0) fits the evolution of BEValue
- // i really is an addrec evolution.
- //
- // We can generalize this saying that i is the shifted value of BEValue
- // by one iteration:
- // PHI(f(0), f({1,+,1})) --> f({0,+,1})
-
- // Do not allow refinement in rewriting of BEValue.
- const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
- const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
- if (Shifted != getCouldNotCompute() && Start != getCouldNotCompute() &&
- isGuaranteedNotToCauseUB(Shifted) && ::impliesPoison(Shifted, Start)) {
- const SCEV *StartVal = getSCEV(StartValueV);
- if (Start == StartVal) {
- // Okay, for the entire analysis of this edge we assumed the PHI
- // to be symbolic. We now need to go back and purge all of the
- // entries for the scalars that use the symbolic expression.
- forgetMemoizedResults({SymbolicName});
- insertValueToMap(PN, Shifted);
- return Shifted;
- }
- }
- }
-
- // Remove the temporary PHI node SCEV that has been inserted while intending
- // to create an AddRecExpr for this PHI node. We can not keep this temporary
- // as it will prevent later (possibly simpler) SCEV expressions to be added
- // to the ValueExprMap.
- eraseValueFromMap(PN);
-
- return nullptr;
-}
-
-// Try to match a control flow sequence that branches out at BI and merges back
-// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
-// match.
-static bool BrPHIToSelect(DominatorTree &DT, CondBrInst *BI, PHINode *Merge,
- Value *&C, Value *&LHS, Value *&RHS) {
- C = BI->getCondition();
-
- BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
- BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
-
- Use &LeftUse = Merge->getOperandUse(0);
- Use &RightUse = Merge->getOperandUse(1);
-
- if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
- LHS = LeftUse;
- RHS = RightUse;
- return true;
- }
-
- if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
- LHS = RightUse;
- RHS = LeftUse;
- return true;
- }
-
- return false;
-}
-
-static bool getOperandsForSelectLikePHI(DominatorTree &DT, PHINode *PN,
- Value *&Cond, Value *&LHS,
- Value *&RHS) {
- auto IsReachable =
- [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
- if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
- // Try to match
- //
- // br %cond, label %left, label %right
- // left:
- // br label %merge
- // right:
- // br label %merge
- // merge:
- // V = phi [ %x, %left ], [ %y, %right ]
- //
- // as "select %cond, %x, %y"
-
- BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
- assert(IDom && "At least the entry block should dominate PN");
-
- auto *BI = dyn_cast<CondBrInst>(IDom->getTerminator());
- return BI && BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS);
- }
- return false;
-}
-
-const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
- Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
- if (getOperandsForSelectLikePHI(DT, PN, Cond, LHS, RHS) &&
- properlyDominates(getSCEV(LHS), PN->getParent()) &&
- properlyDominates(getSCEV(RHS), PN->getParent()))
- return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
-
- return nullptr;
-}
-
-static BinaryOperator *getCommonInstForPHI(PHINode *PN) {
- BinaryOperator *CommonInst = nullptr;
- // Check if instructions are identical.
- for (Value *Incoming : PN->incoming_values()) {
- auto *IncomingInst = dyn_cast<BinaryOperator>(Incoming);
- if (!IncomingInst)
- return nullptr;
- if (CommonInst) {
- if (!CommonInst->isIdenticalToWhenDefined(IncomingInst))
- return nullptr; // Not identical, give up
- } else {
- // Remember binary operator
- CommonInst = IncomingInst;
- }
- }
- return CommonInst;
-}
-
-/// Returns SCEV for the first operand of a phi if all phi operands have
-/// identical opcodes and operands
-/// eg.
-/// a: %add = %a + %b
-/// br %c
-/// b: %add1 = %a + %b
-/// br %c
-/// c: %phi = phi [%add, a], [%add1, b]
-/// scev(%phi) => scev(%add)
-const SCEV *
-ScalarEvolution::createNodeForPHIWithIdenticalOperands(PHINode *PN) {
- BinaryOperator *CommonInst = getCommonInstForPHI(PN);
- if (!CommonInst)
- return nullptr;
-
- // Check if SCEV exprs for instructions are identical.
- const SCEV *CommonSCEV = getSCEV(CommonInst);
- bool SCEVExprsIdentical =
- all_of(drop_begin(PN->incoming_values()),
- [this, CommonSCEV](Value *V) { return CommonSCEV == getSCEV(V); });
- return SCEVExprsIdentical ? CommonSCEV : nullptr;
-}
-
-const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
- if (const SCEV *S = createAddRecFromPHI(PN))
- return S;
-
- // We do not allow simplifying phi (undef, X) to X here, to avoid reusing the
- // phi node for X.
- if (Value *V = simplifyInstruction(
- PN, {getDataLayout(), &TLI, &DT, &AC, /*CtxI=*/nullptr,
- /*UseInstrInfo=*/true, /*CanUseUndef=*/false}))
- return getSCEV(V);
-
- if (const SCEV *S = createNodeForPHIWithIdenticalOperands(PN))
- return S;
-
- if (const SCEV *S = createNodeFromSelectLikePHI(PN))
- return S;
-
- // If it's not a loop phi, we can't handle it yet.
- return getUnknown(PN);
-}
-
-bool SCEVMinMaxExprContains(const SCEV *Root, const SCEV *OperandToFind,
- SCEVTypes RootKind) {
- struct FindClosure {
- const SCEV *OperandToFind;
- const SCEVTypes RootKind; // Must be a sequential min/max expression.
- const SCEVTypes NonSequentialRootKind; // Non-seq variant of RootKind.
-
- bool Found = false;
-
- bool canRecurseInto(SCEVTypes Kind) const {
- // We can only recurse into the SCEV expression of the same effective type
- // as the type of our root SCEV expression, and into zero-extensions.
- return RootKind == Kind || NonSequentialRootKind == Kind ||
- scZeroExtend == Kind;
- };
-
- FindClosure(const SCEV *OperandToFind, SCEVTypes RootKind)
- : OperandToFind(OperandToFind), RootKind(RootKind),
- NonSequentialRootKind(
- SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
- RootKind)) {}
-
- bool follow(const SCEV *S) {
- Found = S == OperandToFind;
-
- return !isDone() && canRecurseInto(S->getSCEVType());
- }
-
- bool isDone() const { return Found; }
- };
-
- FindClosure FC(OperandToFind, RootKind);
- visitAll(Root, FC);
- return FC.Found;
-}
-
-std::optional<const SCEV *>
-ScalarEvolution::createNodeForSelectOrPHIInstWithICmpInstCond(Type *Ty,
- ICmpInst *Cond,
- Value *TrueVal,
- Value *FalseVal) {
- // Try to match some simple smax or umax patterns.
- auto *ICI = Cond;
-
- Value *LHS = ICI->getOperand(0);
- Value *RHS = ICI->getOperand(1);
-
- switch (ICI->getPredicate()) {
- case ICmpInst::ICMP_SLT:
- case ICmpInst::ICMP_SLE:
- case ICmpInst::ICMP_ULT:
- case ICmpInst::ICMP_ULE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SGT:
- case ICmpInst::ICMP_SGE:
- case ICmpInst::ICMP_UGT:
- case ICmpInst::ICMP_UGE:
- // a > b ? a+x : b+x -> max(a, b)+x
- // a > b ? b+x : a+x -> min(a, b)+x
- if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(Ty)) {
- bool Signed = ICI->isSigned();
- const SCEV *LA = getSCEV(TrueVal);
- const SCEV *RA = getSCEV(FalseVal);
- const SCEV *LS = getSCEV(LHS);
- const SCEV *RS = getSCEV(RHS);
- if (LA->getType()->isPointerTy()) {
- // FIXME: Handle cases where LS/RS are pointers not equal to LA/RA.
- // Need to make sure we can't produce weird expressions involving
- // negated pointers.
- if (LA == LS && RA == RS)
- return Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS);
- if (LA == RS && RA == LS)
- return Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS);
- }
- auto CoerceOperand = [&](const SCEV *Op) -> const SCEV * {
- if (Op->getType()->isPointerTy()) {
- Op = getPtrToAddrExpr(Op);
- if (isa<SCEVCouldNotCompute>(Op))
- return Op;
- }
- if (Signed)
- Op = getNoopOrSignExtend(Op, Ty);
- else
- Op = getNoopOrZeroExtend(Op, Ty);
- return Op;
- };
- LS = CoerceOperand(LS);
- RS = CoerceOperand(RS);
- if (isa<SCEVCouldNotCompute>(LS) || isa<SCEVCouldNotCompute>(RS))
- break;
- const SCEV *LDiff = getMinusSCEV(LA, LS);
- const SCEV *RDiff = getMinusSCEV(RA, RS);
- if (LDiff == RDiff)
- return getAddExpr(Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS),
- LDiff);
- LDiff = getMinusSCEV(LA, RS);
- RDiff = getMinusSCEV(RA, LS);
- if (LDiff == RDiff)
- return getAddExpr(Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS),
- LDiff);
- }
- break;
- case ICmpInst::ICMP_NE:
- // x != 0 ? x+y : C+y -> x == 0 ? C+y : x+y
- std::swap(TrueVal, FalseVal);
- [[fallthrough]];
- case ICmpInst::ICMP_EQ:
- // x == 0 ? C+y : x+y -> umax(x, C)+y iff C u<= 1
- if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(Ty) &&
- isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
- const SCEV *X = getNoopOrZeroExtend(getSCEV(LHS), Ty);
- const SCEV *TrueValExpr = getSCEV(TrueVal); // C+y
- const SCEV *FalseValExpr = getSCEV(FalseVal); // x+y
- const SCEV *Y = getMinusSCEV(FalseValExpr, X); // y = (x+y)-x
- const SCEV *C = getMinusSCEV(TrueValExpr, Y); // C = (C+y)-y
- if (isa<SCEVConstant>(C) && cast<SCEVConstant>(C)->getAPInt().ule(1))
- return getAddExpr(getUMaxExpr(X, C), Y);
- }
- // x == 0 ? 0 : umin (..., x, ...) -> umin_seq(x, umin (...))
- // x == 0 ? 0 : umin_seq(..., x, ...) -> umin_seq(x, umin_seq(...))
- // x == 0 ? 0 : umin (..., umin_seq(..., x, ...), ...)
- // -> umin_seq(x, umin (..., umin_seq(...), ...))
- if (isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero() &&
- isa<ConstantInt>(TrueVal) && cast<ConstantInt>(TrueVal)->isZero()) {
- const SCEV *X = getSCEV(LHS);
- while (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(X))
- X = ZExt->getOperand();
- if (getTypeSizeInBits(X->getType()) <= getTypeSizeInBits(Ty)) {
- const SCEV *FalseValExpr = getSCEV(FalseVal);
- if (SCEVMinMaxExprContains(FalseValExpr, X, scSequentialUMinExpr))
- return getUMinExpr(getNoopOrZeroExtend(X, Ty), FalseValExpr,
- /*Sequential=*/true);
- }
- }
- break;
- default:
- break;
- }
-
- return std::nullopt;
-}
-
-static std::optional<const SCEV *>
-createNodeForSelectViaUMinSeq(ScalarEvolution *SE, const SCEV *CondExpr,
- const SCEV *TrueExpr, const SCEV *FalseExpr) {
- assert(CondExpr->getType()->isIntegerTy(1) &&
- TrueExpr->getType() == FalseExpr->getType() &&
- TrueExpr->getType()->isIntegerTy(1) &&
- "Unexpected operands of a select.");
-
- // i1 cond ? i1 x : i1 C --> C + (i1 cond ? (i1 x - i1 C) : i1 0)
- // --> C + (umin_seq cond, x - C)
- //
- // i1 cond ? i1 C : i1 x --> C + (i1 cond ? i1 0 : (i1 x - i1 C))
- // --> C + (i1 ~cond ? (i1 x - i1 C) : i1 0)
- // --> C + (umin_seq ~cond, x - C)
-
- // FIXME: while we can't legally model the case where both of the hands
- // are fully variable, we only require that the *difference* is constant.
- if (!isa<SCEVConstant>(TrueExpr) && !isa<SCEVConstant>(FalseExpr))
- return std::nullopt;
-
- const SCEV *X, *C;
- if (isa<SCEVConstant>(TrueExpr)) {
- CondExpr = SE->getNotSCEV(CondExpr);
- X = FalseExpr;
- C = TrueExpr;
- } else {
- X = TrueExpr;
- C = FalseExpr;
- }
- return SE->getAddExpr(C, SE->getUMinExpr(CondExpr, SE->getMinusSCEV(X, C),
- /*Sequential=*/true));
-}
-
-static std::optional<const SCEV *>
-createNodeForSelectViaUMinSeq(ScalarEvolution *SE, Value *Cond, Value *TrueVal,
- Value *FalseVal) {
- if (!isa<ConstantInt>(TrueVal) && !isa<ConstantInt>(FalseVal))
- return std::nullopt;
-
- const auto *SECond = SE->getSCEV(Cond);
- const auto *SETrue = SE->getSCEV(TrueVal);
- const auto *SEFalse = SE->getSCEV(FalseVal);
- return createNodeForSelectViaUMinSeq(SE, SECond, SETrue, SEFalse);
-}
-
-const SCEV *ScalarEvolution::createNodeForSelectOrPHIViaUMinSeq(
- Value *V, Value *Cond, Value *TrueVal, Value *FalseVal) {
- assert(Cond->getType()->isIntegerTy(1) && "Select condition is not an i1?");
- assert(TrueVal->getType() == FalseVal->getType() &&
- V->getType() == TrueVal->getType() &&
- "Types of select hands and of the result must match.");
-
- // For now, only deal with i1-typed `select`s.
- if (!V->getType()->isIntegerTy(1))
- return getUnknown(V);
-
- if (std::optional<const SCEV *> S =
- createNodeForSelectViaUMinSeq(this, Cond, TrueVal, FalseVal))
- return *S;
-
- return getUnknown(V);
-}
-
-const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Value *V, Value *Cond,
- Value *TrueVal,
- Value *FalseVal) {
- // Handle "constant" branch or select. This can occur for instance when a
- // loop pass transforms an inner loop and moves on to process the outer loop.
- if (auto *CI = dyn_cast<ConstantInt>(Cond))
- return getSCEV(CI->isOne() ? TrueVal : FalseVal);
-
- if (auto *I = dyn_cast<Instruction>(V)) {
- if (auto *ICI = dyn_cast<ICmpInst>(Cond)) {
- if (std::optional<const SCEV *> S =
- createNodeForSelectOrPHIInstWithICmpInstCond(I->getType(), ICI,
- TrueVal, FalseVal))
- return *S;
- }
- }
-
- return createNodeForSelectOrPHIViaUMinSeq(V, Cond, TrueVal, FalseVal);
-}
-
-/// Expand GEP instructions into add and multiply operations. This allows them
-/// to be analyzed by regular SCEV code.
-const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
- assert(GEP->getSourceElementType()->isSized() &&
- "GEP source element type must be sized");
-
- SmallVector<SCEVUse, 4> IndexExprs;
- for (Value *Index : GEP->indices())
- IndexExprs.push_back(getSCEV(Index));
- return getGEPExpr(GEP, IndexExprs);
-}
-
-APInt ScalarEvolution::getConstantMultipleImpl(const SCEV *S,
- const Instruction *CtxI) {
- uint64_t BitWidth = getTypeSizeInBits(S->getType());
- auto GetShiftedByZeros = [BitWidth](uint32_t TrailingZeros) {
- return TrailingZeros >= BitWidth
- ? APInt::getZero(BitWidth)
- : APInt::getOneBitSet(BitWidth, TrailingZeros);
- };
- auto GetGCDMultiple = [this, CtxI](const SCEVNAryExpr *N) {
- // The result is GCD of all operands results.
- APInt Res = getConstantMultiple(N->getOperand(0), CtxI);
- for (unsigned I = 1, E = N->getNumOperands(); I < E && Res != 1; ++I)
- Res = APIntOps::GreatestCommonDivisor(
- Res, getConstantMultiple(N->getOperand(I), CtxI));
- return Res;
- };
-
- switch (S->getSCEVType()) {
- case scConstant:
- return cast<SCEVConstant>(S)->getAPInt();
- case scPtrToAddr:
- return getConstantMultiple(cast<SCEVCastExpr>(S)->getOperand());
- case scUDivExpr:
- case scVScale:
- return APInt(BitWidth, 1);
- case scTruncate: {
- // Only multiples that are a power of 2 will hold after truncation.
- const SCEVTruncateExpr *T = cast<SCEVTruncateExpr>(S);
- uint32_t TZ = getMinTrailingZeros(T->getOperand(), CtxI);
- return GetShiftedByZeros(TZ);
- }
- case scZeroExtend: {
- const SCEVZeroExtendExpr *Z = cast<SCEVZeroExtendExpr>(S);
- return getConstantMultiple(Z->getOperand(), CtxI).zext(BitWidth);
- }
- case scSignExtend: {
- // Only multiples that are a power of 2 will hold after sext.
- const SCEVSignExtendExpr *E = cast<SCEVSignExtendExpr>(S);
- uint32_t TZ = getMinTrailingZeros(E->getOperand(), CtxI);
- return GetShiftedByZeros(TZ);
- }
- case scMulExpr: {
- const SCEVMulExpr *M = cast<SCEVMulExpr>(S);
- if (M->hasNoUnsignedWrap()) {
- // The result is the product of all operand results.
- APInt Res = getConstantMultiple(M->getOperand(0), CtxI);
- for (const SCEV *Operand : M->operands().drop_front())
- Res = Res * getConstantMultiple(Operand, CtxI);
- return Res;
- }
-
- // If there are no wrap guarentees, find the trailing zeros, which is the
- // sum of trailing zeros for all its operands.
- uint32_t TZ = 0;
- for (const SCEV *Operand : M->operands())
- TZ += getMinTrailingZeros(Operand, CtxI);
- return GetShiftedByZeros(TZ);
- }
- case scAddExpr:
- case scAddRecExpr: {
- const SCEVNAryExpr *N = cast<SCEVNAryExpr>(S);
- if (N->hasNoUnsignedWrap())
- return GetGCDMultiple(N);
- // Find the trailing bits, which is the minimum of its operands.
- uint32_t TZ = getMinTrailingZeros(N->getOperand(0), CtxI);
- for (const SCEV *Operand : N->operands().drop_front())
- TZ = std::min(TZ, getMinTrailingZeros(Operand, CtxI));
- return GetShiftedByZeros(TZ);
- }
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr:
- return GetGCDMultiple(cast<SCEVNAryExpr>(S));
- case scUnknown: {
- // Ask ValueTracking for known bits. SCEVUnknown only become available at
- // the point their underlying IR instruction has been defined. If CtxI was
- // not provided, use:
- // * the first instruction in the entry block if it is an argument
- // * the instruction itself otherwise.
- const SCEVUnknown *U = cast<SCEVUnknown>(S);
- if (!CtxI) {
- if (isa<Argument>(U->getValue()))
- CtxI = &*F.getEntryBlock().begin();
- else if (auto *I = dyn_cast<Instruction>(U->getValue()))
- CtxI = I;
- }
- unsigned Known =
- computeKnownBits(U->getValue(),
- SimplifyQuery(getDataLayout(), &DT, &AC, CtxI)
- .allowEphemerals(true))
- .countMinTrailingZeros();
- return GetShiftedByZeros(Known);
- }
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-APInt ScalarEvolution::getConstantMultiple(const SCEV *S,
- const Instruction *CtxI) {
- // Skip looking up and updating the cache if there is a context instruction,
- // as the result will only be valid in the specified context.
- if (CtxI)
- return getConstantMultipleImpl(S, CtxI);
-
- auto I = ConstantMultipleCache.find(S);
- if (I != ConstantMultipleCache.end())
- return I->second;
-
- APInt Result = getConstantMultipleImpl(S, CtxI);
- auto InsertPair = ConstantMultipleCache.insert({S, Result});
- assert(InsertPair.second && "Should insert a new key");
- return InsertPair.first->second;
-}
-
-APInt ScalarEvolution::getNonZeroConstantMultiple(const SCEV *S) {
- APInt Multiple = getConstantMultiple(S);
- return Multiple == 0 ? APInt(Multiple.getBitWidth(), 1) : Multiple;
-}
-
-uint32_t ScalarEvolution::getMinTrailingZeros(const SCEV *S,
- const Instruction *CtxI) {
- return std::min(getConstantMultiple(S, CtxI).countTrailingZeros(),
- (unsigned)getTypeSizeInBits(S->getType()));
-}
-
-/// Helper method to assign a range to V from metadata present in the IR.
-static std::optional<ConstantRange> GetRangeFromMetadata(Value *V) {
- if (Instruction *I = dyn_cast<Instruction>(V)) {
- if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
- return getConstantRangeFromMetadata(*MD);
- if (const auto *CB = dyn_cast<CallBase>(V))
- if (std::optional<ConstantRange> Range = CB->getRange())
- return Range;
- }
- if (auto *A = dyn_cast<Argument>(V))
- if (std::optional<ConstantRange> Range = A->getRange())
- return Range;
-
- return std::nullopt;
-}
-
-void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec,
- SCEV::NoWrapFlags Flags) {
- if (AddRec->getNoWrapFlags(Flags) != Flags) {
- AddRec->setNoWrapFlags(Flags);
- UnsignedRanges.erase(AddRec);
- SignedRanges.erase(AddRec);
- ConstantMultipleCache.erase(AddRec);
- }
-}
-
-ConstantRange ScalarEvolution::
-getRangeForUnknownRecurrence(const SCEVUnknown *U) {
- const DataLayout &DL = getDataLayout();
-
- unsigned BitWidth = getTypeSizeInBits(U->getType());
- const ConstantRange FullSet(BitWidth, /*isFullSet=*/true);
-
- // Match a simple recurrence of the form: <start, ShiftOp, Step>, and then
- // use information about the trip count to improve our available range. Note
- // that the trip count independent cases are already handled by known bits.
- // WARNING: The definition of recurrence used here is subtly different than
- // the one used by AddRec (and thus most of this file). Step is allowed to
- // be arbitrarily loop varying here, where AddRec allows only loop invariant
- // and other addrecs in the same loop (for non-affine addrecs). The code
- // below intentionally handles the case where step is not loop invariant.
- auto *P = dyn_cast<PHINode>(U->getValue());
- if (!P)
- return FullSet;
-
- // Make sure that no Phi input comes from an unreachable block. Otherwise,
- // even the values that are not available in these blocks may come from them,
- // and this leads to false-positive recurrence test.
- for (auto *Pred : predecessors(P->getParent()))
- if (!DT.isReachableFromEntry(Pred))
- return FullSet;
-
- BinaryOperator *BO;
- Value *Start, *Step;
- if (!matchSimpleRecurrence(P, BO, Start, Step))
- return FullSet;
-
- // If we found a recurrence in reachable code, we must be in a loop. Note
- // that BO might be in some subloop of L, and that's completely okay.
- auto *L = LI.getLoopFor(P->getParent());
- assert(L && L->getHeader() == P->getParent());
- if (!L->contains(BO->getParent()))
- // NOTE: This bailout should be an assert instead. However, asserting
- // the condition here exposes a case where LoopFusion is querying SCEV
- // with malformed loop information during the midst of the transform.
- // There doesn't appear to be an obvious fix, so for the moment bailout
- // until the caller issue can be fixed. PR49566 tracks the bug.
- return FullSet;
-
- // TODO: Extend to other opcodes such as mul, and div
- switch (BO->getOpcode()) {
- default:
- return FullSet;
- case Instruction::AShr:
- case Instruction::LShr:
- case Instruction::Shl:
- break;
- };
-
- if (BO->getOperand(0) != P)
- // TODO: Handle the power function forms some day.
- return FullSet;
-
- unsigned TC = getSmallConstantMaxTripCount(L);
- if (!TC || TC >= BitWidth)
- return FullSet;
-
- auto KnownStart = computeKnownBits(Start, DL, &AC, nullptr, &DT);
- auto KnownStep = computeKnownBits(Step, DL, &AC, nullptr, &DT);
- assert(KnownStart.getBitWidth() == BitWidth &&
- KnownStep.getBitWidth() == BitWidth);
-
- // Compute total shift amount, being careful of overflow and bitwidths.
- auto MaxShiftAmt = KnownStep.getMaxValue();
- APInt TCAP(BitWidth, TC-1);
- bool Overflow = false;
- auto TotalShift = MaxShiftAmt.umul_ov(TCAP, Overflow);
- if (Overflow)
- return FullSet;
-
- switch (BO->getOpcode()) {
- default:
- llvm_unreachable("filtered out above");
- case Instruction::AShr: {
- // For each ashr, three cases:
- // shift = 0 => unchanged value
- // saturation => 0 or -1
- // other => a value closer to zero (of the same sign)
- // Thus, the end value is closer to zero than the start.
- auto KnownEnd = KnownBits::ashr(KnownStart,
- KnownBits::makeConstant(TotalShift));
- if (KnownStart.isNonNegative())
- // Analogous to lshr (simply not yet canonicalized)
- return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
- KnownStart.getMaxValue() + 1);
- if (KnownStart.isNegative())
- // End >=u Start && End <=s Start
- return ConstantRange::getNonEmpty(KnownStart.getMinValue(),
- KnownEnd.getMaxValue() + 1);
- break;
- }
- case Instruction::LShr: {
- // For each lshr, three cases:
- // shift = 0 => unchanged value
- // saturation => 0
- // other => a smaller positive number
- // Thus, the low end of the unsigned range is the last value produced.
- auto KnownEnd = KnownBits::lshr(KnownStart,
- KnownBits::makeConstant(TotalShift));
- return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
- KnownStart.getMaxValue() + 1);
- }
- case Instruction::Shl: {
- // Iff no bits are shifted out, value increases on every shift.
- auto KnownEnd = KnownBits::shl(KnownStart,
- KnownBits::makeConstant(TotalShift));
- if (TotalShift.ult(KnownStart.countMinLeadingZeros()))
- return ConstantRange(KnownStart.getMinValue(),
- KnownEnd.getMaxValue() + 1);
- break;
- }
- };
- return FullSet;
-}
-
-// The goal of this function is to check if recursively visiting the operands
-// of this PHI might lead to an infinite loop. If we do see such a loop,
-// there's no good way to break it, so we avoid analyzing such cases.
-//
-// getRangeRef previously used a visited set to avoid infinite loops, but this
-// caused other issues: the result was dependent on the order of getRangeRef
-// calls, and the interaction with createSCEVIter could cause a stack overflow
-// in some cases (see issue #148253).
-//
-// FIXME: The way this is implemented is overly conservative; this checks
-// for a few obviously safe patterns, but anything that doesn't lead to
-// recursion is fine.
-static bool RangeRefPHIAllowedOperands(DominatorTree &DT, PHINode *PHI) {
- Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
- if (getOperandsForSelectLikePHI(DT, PHI, Cond, LHS, RHS))
- return true;
-
- if (all_of(PHI->operands(),
- [&](Value *Operand) { return DT.dominates(Operand, PHI); }))
- return true;
-
- return false;
-}
-
-const ConstantRange &
-ScalarEvolution::getRangeRefIter(const SCEV *S,
- ScalarEvolution::RangeSignHint SignHint) {
- DenseMap<const SCEV *, ConstantRange> &Cache =
- SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
- : SignedRanges;
- SmallVector<SCEVUse> WorkList;
- SmallPtrSet<const SCEV *, 8> Seen;
-
- // Add Expr to the worklist, if Expr is either an N-ary expression or a
- // SCEVUnknown PHI node.
- auto AddToWorklist = [&WorkList, &Seen, &Cache](const SCEV *Expr) {
- if (!Seen.insert(Expr).second)
- return;
- if (Cache.contains(Expr))
- return;
- switch (Expr->getSCEVType()) {
- case scUnknown:
- if (!isa<PHINode>(cast<SCEVUnknown>(Expr)->getValue()))
- break;
- [[fallthrough]];
- case scConstant:
- case scVScale:
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- case scAddExpr:
- case scMulExpr:
- case scUDivExpr:
- case scAddRecExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr:
- WorkList.push_back(Expr);
- break;
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- };
- AddToWorklist(S);
-
- // Build worklist by queuing operands of N-ary expressions and phi nodes.
- for (unsigned I = 0; I != WorkList.size(); ++I) {
- const SCEV *P = WorkList[I];
- auto *UnknownS = dyn_cast<SCEVUnknown>(P);
- // If it is not a `SCEVUnknown`, just recurse into operands.
- if (!UnknownS) {
- for (const SCEV *Op : P->operands())
- AddToWorklist(Op);
- continue;
- }
- // `SCEVUnknown`'s require special treatment.
- if (PHINode *P = dyn_cast<PHINode>(UnknownS->getValue())) {
- if (!RangeRefPHIAllowedOperands(DT, P))
- continue;
- for (auto &Op : reverse(P->operands()))
- AddToWorklist(getSCEV(Op));
- }
- }
-
- if (!WorkList.empty()) {
- // Use getRangeRef to compute ranges for items in the worklist in reverse
- // order. This will force ranges for earlier operands to be computed before
- // their users in most cases.
- for (const SCEV *P : reverse(drop_begin(WorkList))) {
- getRangeRef(P, SignHint);
- }
- }
-
- return getRangeRef(S, SignHint, 0);
-}
-
-/// Determine the range for a particular SCEV. If SignHint is
-/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
-/// with a "cleaner" unsigned (resp. signed) representation.
-const ConstantRange &ScalarEvolution::getRangeRef(
- const SCEV *S, ScalarEvolution::RangeSignHint SignHint, unsigned Depth) {
- DenseMap<const SCEV *, ConstantRange> &Cache =
- SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
- : SignedRanges;
- ConstantRange::PreferredRangeType RangeType =
- SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? ConstantRange::Unsigned
- : ConstantRange::Signed;
-
- // See if we've computed this range already.
- auto I = Cache.find(S);
- if (I != Cache.end())
- return I->second;
-
- if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
- return setRange(C, SignHint, ConstantRange(C->getAPInt()));
-
- // Switch to iteratively computing the range for S, if it is part of a deeply
- // nested expression.
- if (Depth > RangeIterThreshold)
- return getRangeRefIter(S, SignHint);
-
- unsigned BitWidth = getTypeSizeInBits(S->getType());
- ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
- using OBO = OverflowingBinaryOperator;
-
- // If the value has known zeros, the maximum value will have those known zeros
- // as well.
- if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
- APInt Multiple = getNonZeroConstantMultiple(S);
- APInt Remainder = APInt::getMaxValue(BitWidth).urem(Multiple);
- if (!Remainder.isZero())
- ConservativeResult =
- ConstantRange(APInt::getMinValue(BitWidth),
- APInt::getMaxValue(BitWidth) - Remainder + 1);
- }
- else {
- uint32_t TZ = getMinTrailingZeros(S);
- if (TZ != 0) {
- ConservativeResult = ConstantRange(
- APInt::getSignedMinValue(BitWidth),
- APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
- }
- }
-
- switch (S->getSCEVType()) {
- case scConstant:
- llvm_unreachable("Already handled above.");
- case scVScale:
- return setRange(S, SignHint, getVScaleRange(&F, BitWidth));
- case scTruncate: {
- const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(S);
- ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint, Depth + 1);
- return setRange(
- Trunc, SignHint,
- ConservativeResult.intersectWith(X.truncate(BitWidth), RangeType));
- }
- case scZeroExtend: {
- const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(S);
- ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint, Depth + 1);
- return setRange(
- ZExt, SignHint,
- ConservativeResult.intersectWith(X.zeroExtend(BitWidth), RangeType));
- }
- case scSignExtend: {
- const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(S);
- ConstantRange X = getRangeRef(SExt->getOperand(), SignHint, Depth + 1);
- return setRange(
- SExt, SignHint,
- ConservativeResult.intersectWith(X.signExtend(BitWidth), RangeType));
- }
- case scPtrToAddr: {
- const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
- ConstantRange X = getRangeRef(Cast->getOperand(), SignHint, Depth + 1);
- return setRange(Cast, SignHint, X);
- }
- case scAddExpr: {
- const SCEVAddExpr *Add = cast<SCEVAddExpr>(S);
- // Check if this is a URem pattern: A - (A / B) * B, which is always < B.
- const SCEV *URemLHS = nullptr, *URemRHS = nullptr;
- if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED &&
- match(S, m_scev_URem(m_SCEV(URemLHS), m_SCEV(URemRHS), *this))) {
- ConstantRange LHSRange = getRangeRef(URemLHS, SignHint, Depth + 1);
- ConstantRange RHSRange = getRangeRef(URemRHS, SignHint, Depth + 1);
- ConservativeResult =
- ConservativeResult.intersectWith(LHSRange.urem(RHSRange), RangeType);
- }
- ConstantRange X = getRangeRef(Add->getOperand(0), SignHint, Depth + 1);
- unsigned WrapType = OBO::AnyWrap;
- if (Add->hasNoSignedWrap())
- WrapType |= OBO::NoSignedWrap;
- if (Add->hasNoUnsignedWrap())
- WrapType |= OBO::NoUnsignedWrap;
- for (const SCEV *Op : drop_begin(Add->operands()))
- X = X.addWithNoWrap(getRangeRef(Op, SignHint, Depth + 1), WrapType,
- RangeType);
- return setRange(Add, SignHint,
- ConservativeResult.intersectWith(X, RangeType));
- }
- case scMulExpr: {
- const SCEVMulExpr *Mul = cast<SCEVMulExpr>(S);
- ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint, Depth + 1);
- for (const SCEV *Op : drop_begin(Mul->operands()))
- X = X.multiply(getRangeRef(Op, SignHint, Depth + 1));
- return setRange(Mul, SignHint,
- ConservativeResult.intersectWith(X, RangeType));
- }
- case scUDivExpr: {
- const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
- ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint, Depth + 1);
- ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint, Depth + 1);
- return setRange(UDiv, SignHint,
- ConservativeResult.intersectWith(X.udiv(Y), RangeType));
- }
- case scAddRecExpr: {
- const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(S);
- // If there's no unsigned wrap, the value will never be less than its
- // initial value.
- if (AddRec->hasNoUnsignedWrap()) {
- APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
- if (!UnsignedMinValue.isZero())
- ConservativeResult = ConservativeResult.intersectWith(
- ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
- }
-
- // If there's no signed wrap, and all the operands except initial value have
- // the same sign or zero, the value won't ever be:
- // 1: smaller than initial value if operands are non negative,
- // 2: bigger than initial value if operands are non positive.
- // For both cases, value can not cross signed min/max boundary.
- if (AddRec->hasNoSignedWrap()) {
- bool AllNonNeg = true;
- bool AllNonPos = true;
- for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
- if (!isKnownNonNegative(AddRec->getOperand(i)))
- AllNonNeg = false;
- if (!isKnownNonPositive(AddRec->getOperand(i)))
- AllNonPos = false;
- }
- if (AllNonNeg)
- ConservativeResult = ConservativeResult.intersectWith(
- ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
- APInt::getSignedMinValue(BitWidth)),
- RangeType);
- else if (AllNonPos)
- ConservativeResult = ConservativeResult.intersectWith(
- ConstantRange::getNonEmpty(APInt::getSignedMinValue(BitWidth),
- getSignedRangeMax(AddRec->getStart()) +
- 1),
- RangeType);
- }
-
- // TODO: non-affine addrec
- if (AddRec->isAffine()) {
- const SCEV *MaxBEScev =
- getConstantMaxBackedgeTakenCount(AddRec->getLoop());
- if (!isa<SCEVCouldNotCompute>(MaxBEScev)) {
- APInt MaxBECount = cast<SCEVConstant>(MaxBEScev)->getAPInt();
-
- // Adjust MaxBECount to the same bitwidth as AddRec. We can truncate if
- // MaxBECount's active bits are all <= AddRec's bit width.
- if (MaxBECount.getBitWidth() > BitWidth &&
- MaxBECount.getActiveBits() <= BitWidth)
- MaxBECount = MaxBECount.trunc(BitWidth);
- else if (MaxBECount.getBitWidth() < BitWidth)
- MaxBECount = MaxBECount.zext(BitWidth);
-
- if (MaxBECount.getBitWidth() == BitWidth) {
- auto [RangeFromAffine, Flags] = getRangeForAffineAR(
- AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount);
- ConservativeResult =
- ConservativeResult.intersectWith(RangeFromAffine, RangeType);
- const_cast<SCEVAddRecExpr *>(AddRec)->setNoWrapFlags(Flags);
-
- auto RangeFromFactoring = getRangeViaFactoring(
- AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount);
- ConservativeResult =
- ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
- }
- }
-
- // Now try symbolic BE count and more powerful methods.
- if (UseExpensiveRangeSharpening) {
- const SCEV *SymbolicMaxBECount =
- getSymbolicMaxBackedgeTakenCount(AddRec->getLoop());
- if (!isa<SCEVCouldNotCompute>(SymbolicMaxBECount) &&
- getTypeSizeInBits(MaxBEScev->getType()) <= BitWidth &&
- AddRec->hasNoSelfWrap()) {
- auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR(
- AddRec, SymbolicMaxBECount, BitWidth, SignHint);
- ConservativeResult =
- ConservativeResult.intersectWith(RangeFromAffineNew, RangeType);
- }
- }
- }
-
- return setRange(AddRec, SignHint, std::move(ConservativeResult));
- }
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr: {
- Intrinsic::ID ID;
- switch (S->getSCEVType()) {
- case scUMaxExpr:
- ID = Intrinsic::umax;
- break;
- case scSMaxExpr:
- ID = Intrinsic::smax;
- break;
- case scUMinExpr:
- case scSequentialUMinExpr:
- ID = Intrinsic::umin;
- break;
- case scSMinExpr:
- ID = Intrinsic::smin;
- break;
- default:
- llvm_unreachable("Unknown SCEVMinMaxExpr/SCEVSequentialMinMaxExpr.");
- }
-
- const auto *NAry = cast<SCEVNAryExpr>(S);
- ConstantRange X = getRangeRef(NAry->getOperand(0), SignHint, Depth + 1);
- for (unsigned i = 1, e = NAry->getNumOperands(); i != e; ++i)
- X = X.intrinsic(
- ID, {X, getRangeRef(NAry->getOperand(i), SignHint, Depth + 1)});
- return setRange(S, SignHint,
- ConservativeResult.intersectWith(X, RangeType));
- }
- case scUnknown: {
- const SCEVUnknown *U = cast<SCEVUnknown>(S);
- Value *V = U->getValue();
-
- // Check if the IR explicitly contains !range metadata.
- std::optional<ConstantRange> MDRange = GetRangeFromMetadata(V);
- if (MDRange)
- ConservativeResult =
- ConservativeResult.intersectWith(*MDRange, RangeType);
-
- // Use facts about recurrences in the underlying IR. Note that add
- // recurrences are AddRecExprs and thus don't hit this path. This
- // primarily handles shift recurrences.
- auto CR = getRangeForUnknownRecurrence(U);
- ConservativeResult = ConservativeResult.intersectWith(CR);
-
- // See if ValueTracking can give us a useful range.
- const DataLayout &DL = getDataLayout();
- KnownBits Known = computeKnownBits(V, DL, &AC, nullptr, &DT);
- if (Known.getBitWidth() != BitWidth)
- Known = Known.zextOrTrunc(BitWidth);
-
- // ValueTracking may be able to compute a tighter result for the number of
- // sign bits than for the value of those sign bits.
- unsigned NS = ComputeNumSignBits(V, DL, &AC, nullptr, &DT);
- if (U->getType()->isPointerTy()) {
- // If the pointer size is larger than the index size type, this can cause
- // NS to be larger than BitWidth. So compensate for this.
- unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
- int ptrIdxDiff = ptrSize - BitWidth;
- if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
- NS -= ptrIdxDiff;
- }
-
- if (NS > 1) {
- // If we know any of the sign bits, we know all of the sign bits.
- if (!Known.Zero.getHiBits(NS).isZero())
- Known.Zero.setHighBits(NS);
- if (!Known.One.getHiBits(NS).isZero())
- Known.One.setHighBits(NS);
- }
-
- if (Known.getMinValue() != Known.getMaxValue() + 1)
- ConservativeResult = ConservativeResult.intersectWith(
- ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
- RangeType);
- if (NS > 1)
- ConservativeResult = ConservativeResult.intersectWith(
- ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
- APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
- RangeType);
-
- if (U->getType()->isPointerTy() && SignHint == HINT_RANGE_UNSIGNED) {
- // Strengthen the range if the underlying IR value is a
- // global/alloca/heap allocation using the size of the object.
- bool CanBeNull;
- uint64_t DerefBytes = V->getPointerDereferenceableBytes(
- DL, CanBeNull, /*CanBeFreed=*/nullptr);
- if (DerefBytes > 1 && isUIntN(BitWidth, DerefBytes)) {
- // The highest address the object can start is DerefBytes bytes before
- // the end (unsigned max value). If this value is not a multiple of the
- // alignment, the last possible start value is the next lowest multiple
- // of the alignment. Note: The computations below cannot overflow,
- // because if they would there's no possible start address for the
- // object.
- APInt MaxVal =
- APInt::getMaxValue(BitWidth) - APInt(BitWidth, DerefBytes);
- uint64_t Align = U->getValue()->getPointerAlignment(DL).value();
- uint64_t Rem = MaxVal.urem(Align);
- MaxVal -= APInt(BitWidth, Rem);
- APInt MinVal = APInt::getZero(BitWidth);
- if (llvm::isKnownNonZero(V, DL))
- MinVal = Align;
- ConservativeResult = ConservativeResult.intersectWith(
- ConstantRange::getNonEmpty(MinVal, MaxVal + 1), RangeType);
- }
- }
-
- // A range of Phi is a subset of union of all ranges of its input.
- if (PHINode *Phi = dyn_cast<PHINode>(V)) {
- // SCEVExpander sometimes creates SCEVUnknowns that are secretly
- // AddRecs; return the range for the corresponding AddRec.
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(getSCEV(V)))
- return getRangeRef(AR, SignHint, Depth + 1);
-
- // Make sure that we do not run over cycled Phis.
- if (RangeRefPHIAllowedOperands(DT, Phi)) {
- ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
-
- for (const auto &Op : Phi->operands()) {
- auto OpRange = getRangeRef(getSCEV(Op), SignHint, Depth + 1);
- RangeFromOps = RangeFromOps.unionWith(OpRange);
- // No point to continue if we already have a full set.
- if (RangeFromOps.isFullSet())
- break;
- }
- ConservativeResult =
- ConservativeResult.intersectWith(RangeFromOps, RangeType);
- }
- }
-
- // vscale can't be equal to zero
- if (const auto *II = dyn_cast<IntrinsicInst>(V))
- if (II->getIntrinsicID() == Intrinsic::vscale) {
- ConstantRange Disallowed = APInt::getZero(BitWidth);
- ConservativeResult = ConservativeResult.difference(Disallowed);
- }
-
- return setRange(U, SignHint, std::move(ConservativeResult));
- }
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
-
- return setRange(S, SignHint, std::move(ConservativeResult));
-}
-
-// Given a StartRange, Step and MaxBECount for an expression compute a range of
-// values that the expression can take. Initially, the expression has a value
-// from StartRange and then is changed by Step up to MaxBECount times. Signed
-// argument defines if we treat Step as signed or unsigned. The second return
-// value indicates that no wrapping occurred.
-static std::pair<ConstantRange, bool>
-getRangeForAffineARHelper(APInt Step, const ConstantRange &StartRange,
- const APInt &MaxBECount, bool Signed) {
- unsigned BitWidth = Step.getBitWidth();
- assert(BitWidth == StartRange.getBitWidth() &&
- BitWidth == MaxBECount.getBitWidth() && "mismatched bit widths");
- // If either Step or MaxBECount is 0, then the expression won't change, and we
- // just need to return the initial range.
- if (Step == 0 || MaxBECount == 0)
- return {StartRange, true};
-
- // If we don't know anything about the initial value (i.e. StartRange is
- // FullRange), then we don't know anything about the final range either.
- // Return FullRange.
- if (StartRange.isFullSet())
- return {ConstantRange::getFull(BitWidth), false};
-
- // If Step is signed and negative, then we use its absolute value, but we also
- // note that we're moving in the opposite direction.
- bool Descending = Signed && Step.isNegative();
-
- if (Signed)
- // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
- // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
- // This equations hold true due to the well-defined wrap-around behavior of
- // APInt.
- Step = Step.abs();
-
- // Check if Offset is more than full span of BitWidth. If it is, the
- // expression is guaranteed to overflow.
- if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
- return {ConstantRange::getFull(BitWidth), false};
-
- // Offset is by how much the expression can change. Checks above guarantee no
- // overflow here.
- APInt Offset = Step * MaxBECount;
-
- // Minimum value of the final range will match the minimal value of StartRange
- // if the expression is increasing and will be decreased by Offset otherwise.
- // Maximum value of the final range will match the maximal value of StartRange
- // if the expression is decreasing and will be increased by Offset otherwise.
- APInt StartLower = StartRange.getLower();
- APInt StartUpper = StartRange.getUpper() - 1;
- bool Overflow;
- APInt MovedBoundary;
- if (Signed) {
- // This does not use sadd_ov, as we want to check overflow for a signed
- // start with an unsigned offset.
- if (Descending) {
- MovedBoundary = StartLower - std::move(Offset);
- Overflow = MovedBoundary.sgt(StartLower) || StartRange.isSignWrappedSet();
- } else {
- MovedBoundary = StartUpper + std::move(Offset);
- Overflow = MovedBoundary.slt(StartUpper) || StartRange.isSignWrappedSet();
- }
- } else {
- MovedBoundary = StartUpper.uadd_ov(std::move(Offset), Overflow);
- Overflow |= StartRange.isWrappedSet();
- }
-
- // It's possible that the new minimum/maximum value will fall into the initial
- // range (due to wrap around). This means that the expression can take any
- // value in this bitwidth, and we have to return full range.
- if (StartRange.contains(MovedBoundary))
- return {ConstantRange::getFull(BitWidth), false};
-
- APInt NewLower =
- Descending ? std::move(MovedBoundary) : std::move(StartLower);
- APInt NewUpper =
- Descending ? std::move(StartUpper) : std::move(MovedBoundary);
- NewUpper += 1;
-
- // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
- return {ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper)),
- !Overflow};
-}
-
-std::pair<ConstantRange, SCEV::NoWrapFlags>
-ScalarEvolution::getRangeForAffineAR(const SCEV *Start, const SCEV *Step,
- const APInt &MaxBECount) {
- assert(getTypeSizeInBits(Start->getType()) ==
- getTypeSizeInBits(Step->getType()) &&
- getTypeSizeInBits(Start->getType()) == MaxBECount.getBitWidth() &&
- "mismatched bit widths");
-
- // First, consider step signed.
- ConstantRange StartSRange = getSignedRange(Start);
- ConstantRange StepSRange = getSignedRange(Step);
-
- // If Step can be both positive and negative, we need to find ranges for the
- // maximum absolute step values in both directions and union them.
- auto [SR1, NSW1] = getRangeForAffineARHelper(
- StepSRange.getSignedMin(), StartSRange, MaxBECount, /*Signed=*/true);
- auto [SR2, NSW2] = getRangeForAffineARHelper(StepSRange.getSignedMax(),
- StartSRange, MaxBECount,
- /*Signed=*/true);
- ConstantRange SR = SR1.unionWith(SR2);
-
- // Next, consider step unsigned.
- auto [UR, NUW] = getRangeForAffineARHelper(
- getUnsignedRangeMax(Step), getUnsignedRange(Start), MaxBECount,
- /*Signed=*/false);
-
- SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
- if (NUW)
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- if (NSW1 && NSW2)
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
-
- // Finally, intersect signed and unsigned ranges.
- return {SR.intersectWith(UR, ConstantRange::Smallest), Flags};
-}
-
-ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR(
- const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth,
- ScalarEvolution::RangeSignHint SignHint) {
- assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n");
- assert(AddRec->hasNoSelfWrap() &&
- "This only works for non-self-wrapping AddRecs!");
- const bool IsSigned = SignHint == HINT_RANGE_SIGNED;
- const SCEV *Step = AddRec->getStepRecurrence(*this);
- // Only deal with constant step to save compile time.
- if (!isa<SCEVConstant>(Step))
- return ConstantRange::getFull(BitWidth);
- // Let's make sure that we can prove that we do not self-wrap during
- // MaxBECount iterations. We need this because MaxBECount is a maximum
- // iteration count estimate, and we might infer nw from some exit for which we
- // do not know max exit count (or any other side reasoning).
- // TODO: Turn into assert at some point.
- if (getTypeSizeInBits(MaxBECount->getType()) >
- getTypeSizeInBits(AddRec->getType()))
- return ConstantRange::getFull(BitWidth);
- MaxBECount = getNoopOrZeroExtend(MaxBECount, AddRec->getType());
- const SCEV *RangeWidth = getMinusOne(AddRec->getType());
- const SCEV *StepAbs = getUMinExpr(Step, getNegativeSCEV(Step));
- const SCEV *MaxItersWithoutWrap = getUDivExpr(RangeWidth, StepAbs);
- if (!isKnownPredicateViaConstantRanges(ICmpInst::ICMP_ULE, MaxBECount,
- MaxItersWithoutWrap))
- return ConstantRange::getFull(BitWidth);
-
- ICmpInst::Predicate LEPred =
- IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
- ICmpInst::Predicate GEPred =
- IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
- const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
-
- // We know that there is no self-wrap. Let's take Start and End values and
- // look at all intermediate values V1, V2, ..., Vn that IndVar takes during
- // the iteration. They either lie inside the range [Min(Start, End),
- // Max(Start, End)] or outside it:
- //
- // Case 1: RangeMin ... Start V1 ... VN End ... RangeMax;
- // Case 2: RangeMin Vk ... V1 Start ... End Vn ... Vk + 1 RangeMax;
- //
- // No self wrap flag guarantees that the intermediate values cannot be BOTH
- // outside and inside the range [Min(Start, End), Max(Start, End)]. Using that
- // knowledge, let's try to prove that we are dealing with Case 1. It is so if
- // Start <= End and step is positive, or Start >= End and step is negative.
- const SCEV *Start = applyLoopGuards(AddRec->getStart(), AddRec->getLoop());
- ConstantRange StartRange = getRangeRef(Start, SignHint);
- ConstantRange EndRange = getRangeRef(End, SignHint);
- ConstantRange RangeBetween = StartRange.unionWith(EndRange);
- // If they already cover full iteration space, we will know nothing useful
- // even if we prove what we want to prove.
- if (RangeBetween.isFullSet())
- return RangeBetween;
- // Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax).
- bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet()
- : RangeBetween.isWrappedSet();
- if (IsWrappedSet)
- return ConstantRange::getFull(BitWidth);
-
- if (isKnownPositive(Step) &&
- isKnownPredicateViaConstantRanges(LEPred, Start, End))
- return RangeBetween;
- if (isKnownNegative(Step) &&
- isKnownPredicateViaConstantRanges(GEPred, Start, End))
- return RangeBetween;
- return ConstantRange::getFull(BitWidth);
-}
-
-ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
- const SCEV *Step,
- const APInt &MaxBECount) {
- // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
- // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
-
- unsigned BitWidth = MaxBECount.getBitWidth();
- assert(getTypeSizeInBits(Start->getType()) == BitWidth &&
- getTypeSizeInBits(Step->getType()) == BitWidth &&
- "mismatched bit widths");
-
- struct SelectPattern {
- Value *Condition = nullptr;
- APInt TrueValue;
- APInt FalseValue;
-
- explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
- const SCEV *S) {
- std::optional<unsigned> CastOp;
- APInt Offset(BitWidth, 0);
-
- assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
- "Should be!");
-
- // Peel off a constant offset. In the future we could consider being
- // smarter here and handle {Start+Step,+,Step} too.
- const APInt *Off;
- if (match(S, m_scev_Add(m_scev_APInt(Off), m_SCEV(S))))
- Offset = *Off;
-
- // Peel off a cast operation
- if (auto *SCast = dyn_cast<SCEVIntegralCastExpr>(S)) {
- CastOp = SCast->getSCEVType();
- S = SCast->getOperand();
- }
-
- using namespace llvm::PatternMatch;
-
- auto *SU = dyn_cast<SCEVUnknown>(S);
- const APInt *TrueVal, *FalseVal;
- if (!SU ||
- !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
- m_APInt(FalseVal)))) {
- Condition = nullptr;
- return;
- }
-
- TrueValue = *TrueVal;
- FalseValue = *FalseVal;
-
- // Re-apply the cast we peeled off earlier
- if (CastOp)
- switch (*CastOp) {
- default:
- llvm_unreachable("Unknown SCEV cast type!");
-
- case scTruncate:
- TrueValue = TrueValue.trunc(BitWidth);
- FalseValue = FalseValue.trunc(BitWidth);
- break;
- case scZeroExtend:
- TrueValue = TrueValue.zext(BitWidth);
- FalseValue = FalseValue.zext(BitWidth);
- break;
- case scSignExtend:
- TrueValue = TrueValue.sext(BitWidth);
- FalseValue = FalseValue.sext(BitWidth);
- break;
- }
-
- // Re-apply the constant offset we peeled off earlier
- TrueValue += Offset;
- FalseValue += Offset;
- }
-
- bool isRecognized() { return Condition != nullptr; }
- };
-
- SelectPattern StartPattern(*this, BitWidth, Start);
- if (!StartPattern.isRecognized())
- return ConstantRange::getFull(BitWidth);
-
- SelectPattern StepPattern(*this, BitWidth, Step);
- if (!StepPattern.isRecognized())
- return ConstantRange::getFull(BitWidth);
-
- if (StartPattern.Condition != StepPattern.Condition) {
- // We don't handle this case today; but we could, by considering four
- // possibilities below instead of two. I'm not sure if there are cases where
- // that will help over what getRange already does, though.
- return ConstantRange::getFull(BitWidth);
- }
-
- // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
- // construct arbitrary general SCEV expressions here. This function is called
- // from deep in the call stack, and calling getSCEV (on a sext instruction,
- // say) can end up caching a suboptimal value.
-
- // FIXME: without the explicit `this` receiver below, MSVC errors out with
- // C2352 and C2512 (otherwise it isn't needed).
-
- const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
- const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
- const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
- const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
-
- ConstantRange TrueRange =
- this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount).first;
- ConstantRange FalseRange =
- this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount).first;
-
- return TrueRange.unionWith(FalseRange);
-}
-
-SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
- if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
- const BinaryOperator *BinOp = cast<BinaryOperator>(V);
-
- // Return early if there are no flags to propagate to the SCEV.
- SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
- if (auto *PDI = dyn_cast<PossiblyDisjointInst>(BinOp);
- PDI && PDI->isDisjoint()) {
- Flags = ScalarEvolution::setFlags(SCEV::FlagNUW, SCEV::FlagNSW);
- } else {
- if (BinOp->hasNoUnsignedWrap())
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
- if (BinOp->hasNoSignedWrap())
- Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
- }
- if (Flags == SCEV::FlagAnyWrap)
- return SCEV::FlagAnyWrap;
-
- return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
-}
-
-const Instruction *
-ScalarEvolution::getNonTrivialDefiningScopeBound(const SCEV *S) {
- if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S))
- return &*AddRec->getLoop()->getHeader()->begin();
- if (auto *U = dyn_cast<SCEVUnknown>(S))
- if (auto *I = dyn_cast<Instruction>(U->getValue()))
- return I;
- return nullptr;
-}
-
-const Instruction *ScalarEvolution::getDefiningScopeBound(ArrayRef<SCEVUse> Ops,
- bool &Precise) {
- Precise = true;
- // Do a bounded search of the def relation of the requested SCEVs.
- SmallPtrSet<const SCEV *, 16> Visited;
- SmallVector<SCEVUse> Worklist;
- auto pushOp = [&](const SCEV *S) {
- if (!Visited.insert(S).second)
- return;
- // Threshold of 30 here is arbitrary.
- if (Visited.size() > 30) {
- Precise = false;
- return;
- }
- Worklist.push_back(S);
- };
-
- for (SCEVUse S : Ops)
- pushOp(S);
-
- const Instruction *Bound = nullptr;
- while (!Worklist.empty()) {
- SCEVUse S = Worklist.pop_back_val();
- if (auto *DefI = getNonTrivialDefiningScopeBound(S)) {
- if (!Bound || DT.dominates(Bound, DefI))
- Bound = DefI;
- } else {
- for (SCEVUse Op : S->operands())
- pushOp(Op);
- }
- }
- return Bound ? Bound : &*F.getEntryBlock().begin();
-}
-
-const Instruction *
-ScalarEvolution::getDefiningScopeBound(ArrayRef<SCEVUse> Ops) {
- bool Discard;
- return getDefiningScopeBound(Ops, Discard);
-}
-
-bool ScalarEvolution::isGuaranteedToTransferExecutionTo(const Instruction *A,
- const Instruction *B) {
- if (A->getParent() == B->getParent() &&
- isGuaranteedToTransferExecutionToSuccessor(A->getIterator(),
- B->getIterator()))
- return true;
-
- auto *BLoop = LI.getLoopFor(B->getParent());
- if (BLoop && BLoop->getHeader() == B->getParent() &&
- BLoop->getLoopPreheader() == A->getParent() &&
- isGuaranteedToTransferExecutionToSuccessor(A->getIterator(),
- A->getParent()->end()) &&
- isGuaranteedToTransferExecutionToSuccessor(B->getParent()->begin(),
- B->getIterator()))
- return true;
- return false;
-}
-
-bool ScalarEvolution::isGuaranteedNotToBePoison(const SCEV *Op) {
- SCEVPoisonCollector PC(/* LookThroughMaybePoisonBlocking */ true);
- visitAll(Op, PC);
- return PC.MaybePoison.empty();
-}
-
-bool ScalarEvolution::isGuaranteedNotToCauseUB(const SCEV *Op) {
- return !SCEVExprContains(Op, [this](const SCEV *S) {
- const SCEV *Op1;
- bool M = match(S, m_scev_UDiv(m_SCEV(), m_SCEV(Op1)));
- // The UDiv may be UB if the divisor is poison or zero. Unless the divisor
- // is a non-zero constant, we have to assume the UDiv may be UB.
- return M && (!isKnownNonZero(Op1) || !isGuaranteedNotToBePoison(Op1));
- });
-}
-
-bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
- // Only proceed if we can prove that I does not yield poison.
- if (!programUndefinedIfPoison(I))
- return false;
-
- // At this point we know that if I is executed, then it does not wrap
- // according to at least one of NSW or NUW. If I is not executed, then we do
- // not know if the calculation that I represents would wrap. Multiple
- // instructions can map to the same SCEV. If we apply NSW or NUW from I to
- // the SCEV, we must guarantee no wrapping for that SCEV also when it is
- // derived from other instructions that map to the same SCEV. We cannot make
- // that guarantee for cases where I is not executed. So we need to find a
- // upper bound on the defining scope for the SCEV, and prove that I is
- // executed every time we enter that scope. When the bounding scope is a
- // loop (the common case), this is equivalent to proving I executes on every
- // iteration of that loop.
- SmallVector<SCEVUse> SCEVOps;
- for (const Use &Op : I->operands()) {
- // I could be an extractvalue from a call to an overflow intrinsic.
- // TODO: We can do better here in some cases.
- if (isSCEVable(Op->getType()))
- SCEVOps.push_back(getSCEV(Op));
- }
- auto *DefI = getDefiningScopeBound(SCEVOps);
- return isGuaranteedToTransferExecutionTo(DefI, I);
-}
-
-bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
- // If we know that \c I can never be poison period, then that's enough.
- if (isSCEVExprNeverPoison(I))
- return true;
-
- // If the loop only has one exit, then we know that, if the loop is entered,
- // any instruction dominating that exit will be executed. If any such
- // instruction would result in UB, the addrec cannot be poison.
- //
- // This is basically the same reasoning as in isSCEVExprNeverPoison(), but
- // also handles uses outside the loop header (they just need to dominate the
- // single exit).
-
- auto *ExitingBB = L->getExitingBlock();
- if (!ExitingBB || !loopHasNoAbnormalExits(L))
- return false;
-
- SmallPtrSet<const Value *, 16> KnownPoison;
- SmallVector<const Instruction *, 8> Worklist;
-
- // We start by assuming \c I, the post-inc add recurrence, is poison. Only
- // things that are known to be poison under that assumption go on the
- // Worklist.
- KnownPoison.insert(I);
- Worklist.push_back(I);
-
- while (!Worklist.empty()) {
- const Instruction *Poison = Worklist.pop_back_val();
-
- for (const Use &U : Poison->uses()) {
- const Instruction *PoisonUser = cast<Instruction>(U.getUser());
- if (mustTriggerUB(PoisonUser, KnownPoison) &&
- DT.dominates(PoisonUser->getParent(), ExitingBB))
- return true;
-
- if (propagatesPoison(U) && L->contains(PoisonUser))
- if (KnownPoison.insert(PoisonUser).second)
- Worklist.push_back(PoisonUser);
- }
- }
-
- return false;
-}
-
-ScalarEvolution::LoopProperties
-ScalarEvolution::getLoopProperties(const Loop *L) {
- using LoopProperties = ScalarEvolution::LoopProperties;
-
- auto Itr = LoopPropertiesCache.find(L);
- if (Itr == LoopPropertiesCache.end()) {
- auto HasSideEffects = [](Instruction *I) {
- if (auto *SI = dyn_cast<StoreInst>(I))
- return !SI->isSimple();
-
- if (I->mayThrow())
- return true;
-
- // Non-volatile memset / memcpy do not count as side-effect for forward
- // progress.
- if (isa<MemIntrinsic>(I) && !I->isVolatile())
- return false;
-
- return I->mayWriteToMemory();
- };
-
- LoopProperties LP = {/* HasNoAbnormalExits */ true,
- /*HasNoSideEffects*/ true};
-
- for (auto *BB : L->getBlocks())
- for (auto &I : *BB) {
- if (!isGuaranteedToTransferExecutionToSuccessor(&I))
- LP.HasNoAbnormalExits = false;
- if (HasSideEffects(&I))
- LP.HasNoSideEffects = false;
- if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
- break; // We're already as pessimistic as we can get.
- }
-
- auto InsertPair = LoopPropertiesCache.insert({L, LP});
- assert(InsertPair.second && "We just checked!");
- Itr = InsertPair.first;
- }
-
- return Itr->second;
-}
-
-bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) {
- // A mustprogress loop without side effects must be finite.
- // TODO: The check used here is very conservative. It's only *specific*
- // side effects which are well defined in infinite loops.
- return isFinite(L) || (isMustProgress(L) && loopHasNoSideEffects(L));
-}
-
-const SCEV *ScalarEvolution::createSCEVIter(Value *V) {
- // Worklist item with a Value and a bool indicating whether all operands have
- // been visited already.
- using PointerTy = PointerIntPair<Value *, 1, bool>;
- SmallVector<PointerTy> Stack;
-
- Stack.emplace_back(V, false);
- while (!Stack.empty()) {
- auto E = Stack.back();
- Value *CurV = E.getPointer();
-
- if (getExistingSCEV(CurV)) {
- Stack.pop_back();
- continue;
- }
-
- SmallVector<Value *> Ops;
- const SCEV *CreatedSCEV = nullptr;
- // If all operands have been visited already, create the SCEV.
- if (E.getInt()) {
- CreatedSCEV = createSCEV(CurV);
- } else {
- // Otherwise get the operands we need to create SCEV's for before creating
- // the SCEV for CurV. If the SCEV for CurV can be constructed trivially,
- // just use it.
- CreatedSCEV = getOperandsToCreate(CurV, Ops);
- }
-
- if (CreatedSCEV) {
- insertValueToMap(CurV, CreatedSCEV);
- Stack.pop_back();
- } else {
- Stack.back().setInt(true);
- // Queue its operands which need to be constructed.
- for (Value *Op : Ops)
- Stack.emplace_back(Op, false);
- }
- }
-
- return getExistingSCEV(V);
-}
-
-const SCEV *
-ScalarEvolution::getOperandsToCreate(Value *V, SmallVectorImpl<Value *> &Ops) {
- if (!isSCEVable(V->getType()))
- return getUnknown(V);
-
- if (Instruction *I = dyn_cast<Instruction>(V)) {
- // Don't attempt to analyze instructions in blocks that aren't
- // reachable. Such instructions don't matter, and they aren't required
- // to obey basic rules for definitions dominating uses which this
- // analysis depends on.
- if (!DT.isReachableFromEntry(I->getParent()))
- return getUnknown(PoisonValue::get(V->getType()));
- } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
- return getConstant(CI);
- else if (isa<GlobalAlias>(V))
- return getUnknown(V);
- else if (!isa<ConstantExpr>(V))
- return getUnknown(V);
-
- Operator *U = cast<Operator>(V);
- if (auto BO =
- MatchBinaryOp(U, getDataLayout(), AC, DT, dyn_cast<Instruction>(V))) {
- bool IsConstArg = isa<ConstantInt>(BO->RHS);
- switch (BO->Opcode) {
- case Instruction::Add:
- case Instruction::Mul: {
- // For additions and multiplications, traverse add/mul chains for which we
- // can potentially create a single SCEV, to reduce the number of
- // get{Add,Mul}Expr calls.
- do {
- if (BO->Op) {
- if (BO->Op != V && getExistingSCEV(BO->Op)) {
- Ops.push_back(BO->Op);
- break;
- }
- }
- Ops.push_back(BO->RHS);
- auto NewBO = MatchBinaryOp(BO->LHS, getDataLayout(), AC, DT,
- dyn_cast<Instruction>(V));
- if (!NewBO ||
- (BO->Opcode == Instruction::Add &&
- (NewBO->Opcode != Instruction::Add &&
- NewBO->Opcode != Instruction::Sub)) ||
- (BO->Opcode == Instruction::Mul &&
- NewBO->Opcode != Instruction::Mul)) {
- Ops.push_back(BO->LHS);
- break;
- }
- // CreateSCEV calls getNoWrapFlagsFromUB, which under certain conditions
- // requires a SCEV for the LHS.
- if (BO->Op && (BO->IsNSW || BO->IsNUW)) {
- auto *I = dyn_cast<Instruction>(BO->Op);
- if (I && programUndefinedIfPoison(I)) {
- Ops.push_back(BO->LHS);
- break;
- }
- }
- BO = NewBO;
- } while (true);
- return nullptr;
- }
- case Instruction::Sub:
- case Instruction::UDiv:
- case Instruction::URem:
- break;
- case Instruction::AShr:
- case Instruction::Shl:
- case Instruction::Xor:
- if (!IsConstArg)
- return nullptr;
- break;
- case Instruction::And:
- case Instruction::Or:
- if (!IsConstArg && !BO->LHS->getType()->isIntegerTy(1))
- return nullptr;
- break;
- case Instruction::LShr:
- return getUnknown(V);
- default:
- llvm_unreachable("Unhandled binop");
- break;
- }
-
- Ops.push_back(BO->LHS);
- Ops.push_back(BO->RHS);
- return nullptr;
- }
-
- switch (U->getOpcode()) {
- case Instruction::Trunc:
- case Instruction::ZExt:
- case Instruction::SExt:
- case Instruction::PtrToAddr:
- case Instruction::PtrToInt:
- Ops.push_back(U->getOperand(0));
- return nullptr;
-
- case Instruction::BitCast:
- if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) {
- Ops.push_back(U->getOperand(0));
- return nullptr;
- }
- return getUnknown(V);
-
- case Instruction::SDiv:
- case Instruction::SRem:
- Ops.push_back(U->getOperand(0));
- Ops.push_back(U->getOperand(1));
- return nullptr;
-
- case Instruction::GetElementPtr:
- assert(cast<GEPOperator>(U)->getSourceElementType()->isSized() &&
- "GEP source element type must be sized");
- llvm::append_range(Ops, U->operands());
- return nullptr;
-
- case Instruction::IntToPtr:
- return getUnknown(V);
-
- case Instruction::PHI:
- // getNodeForPHI has four ways to turn a PHI into a SCEV; retrieve the
- // relevant nodes for each of them.
- //
- // The first is just to call simplifyInstruction, and get something back
- // that isn't a PHI.
- if (Value *V = simplifyInstruction(
- cast<PHINode>(U),
- {getDataLayout(), &TLI, &DT, &AC, /*CtxI=*/nullptr,
- /*UseInstrInfo=*/true, /*CanUseUndef=*/false})) {
- assert(V);
- Ops.push_back(V);
- return nullptr;
- }
- // The second is createNodeForPHIWithIdenticalOperands: this looks for
- // operands which all perform the same operation, but haven't been
- // CSE'ed for whatever reason.
- if (BinaryOperator *BO = getCommonInstForPHI(cast<PHINode>(U))) {
- assert(BO);
- Ops.push_back(BO);
- return nullptr;
- }
- // The third is createNodeFromSelectLikePHI; this takes a PHI which
- // is equivalent to a select, and analyzes it like a select.
- {
- Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
- if (getOperandsForSelectLikePHI(DT, cast<PHINode>(U), Cond, LHS, RHS)) {
- assert(Cond);
- assert(LHS);
- assert(RHS);
- if (auto *CondICmp = dyn_cast<ICmpInst>(Cond)) {
- Ops.push_back(CondICmp->getOperand(0));
- Ops.push_back(CondICmp->getOperand(1));
- }
- Ops.push_back(Cond);
- Ops.push_back(LHS);
- Ops.push_back(RHS);
- return nullptr;
- }
- }
- // The fourth way is createAddRecFromPHI. It's complicated to handle here,
- // so just construct it recursively.
- //
- // In addition to getNodeForPHI, also construct nodes which might be needed
- // by getRangeRef.
- if (RangeRefPHIAllowedOperands(DT, cast<PHINode>(U))) {
- for (Value *V : cast<PHINode>(U)->operands())
- Ops.push_back(V);
- return nullptr;
- }
- return nullptr;
-
- case Instruction::Select: {
- // Check if U is a select that can be simplified to a SCEVUnknown.
- auto CanSimplifyToUnknown = [this, U]() {
- if (U->getType()->isIntegerTy(1) || isa<ConstantInt>(U->getOperand(0)))
- return false;
-
- auto *ICI = dyn_cast<ICmpInst>(U->getOperand(0));
- if (!ICI)
- return false;
- Value *LHS = ICI->getOperand(0);
- Value *RHS = ICI->getOperand(1);
- if (ICI->getPredicate() == CmpInst::ICMP_EQ ||
- ICI->getPredicate() == CmpInst::ICMP_NE) {
- if (!(isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()))
- return true;
- } else if (getTypeSizeInBits(LHS->getType()) >
- getTypeSizeInBits(U->getType()))
- return true;
- return false;
- };
- if (CanSimplifyToUnknown())
- return getUnknown(U);
-
- llvm::append_range(Ops, U->operands());
- return nullptr;
- break;
- }
- case Instruction::Call:
- case Instruction::Invoke:
- if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand()) {
- Ops.push_back(RV);
- return nullptr;
- }
-
- if (auto *II = dyn_cast<IntrinsicInst>(U)) {
- switch (II->getIntrinsicID()) {
- case Intrinsic::abs:
- Ops.push_back(II->getArgOperand(0));
- return nullptr;
- case Intrinsic::umax:
- case Intrinsic::umin:
- case Intrinsic::smax:
- case Intrinsic::smin:
- case Intrinsic::usub_sat:
- case Intrinsic::uadd_sat:
- Ops.push_back(II->getArgOperand(0));
- Ops.push_back(II->getArgOperand(1));
- return nullptr;
- case Intrinsic::start_loop_iterations:
- case Intrinsic::annotation:
- case Intrinsic::ptr_annotation:
- Ops.push_back(II->getArgOperand(0));
- return nullptr;
- default:
- break;
- }
- }
- break;
- }
-
- return nullptr;
-}
-
-const SCEV *ScalarEvolution::createSCEV(Value *V) {
- if (!isSCEVable(V->getType()))
- return getUnknown(V);
-
- if (Instruction *I = dyn_cast<Instruction>(V)) {
- // Don't attempt to analyze instructions in blocks that aren't
- // reachable. Such instructions don't matter, and they aren't required
- // to obey basic rules for definitions dominating uses which this
- // analysis depends on.
- if (!DT.isReachableFromEntry(I->getParent()))
- return getUnknown(PoisonValue::get(V->getType()));
- } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
- return getConstant(CI);
- else if (isa<GlobalAlias>(V))
- return getUnknown(V);
- else if (!isa<ConstantExpr>(V))
- return getUnknown(V);
-
- const SCEV *LHS;
- const SCEV *RHS;
-
- Operator *U = cast<Operator>(V);
- if (auto BO =
- MatchBinaryOp(U, getDataLayout(), AC, DT, dyn_cast<Instruction>(V))) {
- switch (BO->Opcode) {
- case Instruction::Add: {
- // The simple thing to do would be to just call getSCEV on both operands
- // and call getAddExpr with the result. However if we're looking at a
- // bunch of things all added together, this can be quite inefficient,
- // because it leads to N-1 getAddExpr calls for N ultimate operands.
- // Instead, gather up all the operands and make a single getAddExpr call.
- // LLVM IR canonical form means we need only traverse the left operands.
- SmallVector<SCEVUse, 4> AddOps;
- do {
- if (BO->Op) {
- if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
- AddOps.push_back(OpSCEV);
- break;
- }
-
- // If a NUW or NSW flag can be applied to the SCEV for this
- // addition, then compute the SCEV for this addition by itself
- // with a separate call to getAddExpr. We need to do that
- // instead of pushing the operands of the addition onto AddOps,
- // since the flags are only known to apply to this particular
- // addition - they may not apply to other additions that can be
- // formed with operands from AddOps.
- const SCEV *RHS = getSCEV(BO->RHS);
- SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
- if (Flags != SCEV::FlagAnyWrap) {
- const SCEV *LHS = getSCEV(BO->LHS);
- if (BO->Opcode == Instruction::Sub)
- AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
- else
- AddOps.push_back(getAddExpr(LHS, RHS, Flags));
- break;
- }
- }
-
- if (BO->Opcode == Instruction::Sub)
- AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
- else
- AddOps.push_back(getSCEV(BO->RHS));
-
- auto NewBO = MatchBinaryOp(BO->LHS, getDataLayout(), AC, DT,
- dyn_cast<Instruction>(V));
- if (!NewBO || (NewBO->Opcode != Instruction::Add &&
- NewBO->Opcode != Instruction::Sub)) {
- AddOps.push_back(getSCEV(BO->LHS));
- break;
- }
- BO = NewBO;
- } while (true);
-
- return getAddExpr(AddOps);
- }
-
- case Instruction::Mul: {
- SmallVector<SCEVUse, 4> MulOps;
- do {
- if (BO->Op) {
- if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
- MulOps.push_back(OpSCEV);
- break;
- }
-
- SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
- if (Flags != SCEV::FlagAnyWrap) {
- LHS = getSCEV(BO->LHS);
- RHS = getSCEV(BO->RHS);
- MulOps.push_back(getMulExpr(LHS, RHS, Flags));
- break;
- }
- }
-
- MulOps.push_back(getSCEV(BO->RHS));
- auto NewBO = MatchBinaryOp(BO->LHS, getDataLayout(), AC, DT,
- dyn_cast<Instruction>(V));
- if (!NewBO || NewBO->Opcode != Instruction::Mul) {
- MulOps.push_back(getSCEV(BO->LHS));
- break;
- }
- BO = NewBO;
- } while (true);
-
- return getMulExpr(MulOps);
- }
- case Instruction::UDiv:
- LHS = getSCEV(BO->LHS);
- RHS = getSCEV(BO->RHS);
- return getUDivExpr(LHS, RHS);
- case Instruction::URem:
- LHS = getSCEV(BO->LHS);
- RHS = getSCEV(BO->RHS);
- return getURemExpr(LHS, RHS);
- case Instruction::Sub: {
- SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
- if (BO->Op)
- Flags = getNoWrapFlagsFromUB(BO->Op);
-
- // Try to use ptrtoaddr for subtracts with at least one ptrtoint
- // operand. While we don't model ptrtoint directly in SCEV, the
- // difference between two pointer addresses is well-defined.
- Value *PtrLHS = nullptr, *PtrRHS = nullptr;
- bool HasPtrLHS = match(BO->LHS, m_PtrToInt(m_Value(PtrLHS)));
- bool HasPtrRHS = match(BO->RHS, m_PtrToInt(m_Value(PtrRHS)));
- if (HasPtrLHS || HasPtrRHS) {
- // Convert a ptrtoint operand (OrigOp) to ptrtoaddr of its pointer
- // PtrOp. When only one side is ptrtoint (BothPtr is false), skip
- // SCEVUnknown pointers since wrapping them in ptrtoaddr adds no
- // useful structure.
- auto GetOp = [&](bool HasPtr, Value *PtrOp, Value *OrigOp,
- bool BothPtr) -> const SCEV * {
- if (!HasPtr)
- return getSCEV(OrigOp);
- const SCEV *PtrSCEV = getSCEV(PtrOp);
- if (BothPtr || !isa<SCEVUnknown>(PtrSCEV)) {
- const SCEV *Addr = getPtrToAddrExpr(PtrSCEV);
- if (!isa<SCEVCouldNotCompute>(Addr) &&
- getTypeSizeInBits(OrigOp->getType()) <=
- getTypeSizeInBits(Addr->getType()))
- return getTruncateOrNoop(Addr, OrigOp->getType());
- }
- return getSCEV(OrigOp);
- };
- const SCEV *L = GetOp(HasPtrLHS, PtrLHS, BO->LHS, HasPtrRHS);
- const SCEV *R = GetOp(HasPtrRHS, PtrRHS, BO->RHS, HasPtrLHS);
- return getMinusSCEV(L, R, Flags);
- }
-
- LHS = getSCEV(BO->LHS);
- RHS = getSCEV(BO->RHS);
- return getMinusSCEV(LHS, RHS, Flags);
- }
- case Instruction::And:
- // For an expression like x&255 that merely masks off the high bits,
- // use zext(trunc(x)) as the SCEV expression.
- if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
- if (CI->isZero())
- return getSCEV(BO->RHS);
- if (CI->isMinusOne())
- return getSCEV(BO->LHS);
- const APInt &A = CI->getValue();
-
- // Instcombine's ShrinkDemandedConstant may strip bits out of
- // constants, obscuring what would otherwise be a low-bits mask.
- // Use computeKnownBits to compute what ShrinkDemandedConstant
- // knew about to reconstruct a low-bits mask value.
- unsigned LZ = A.countl_zero();
- unsigned TZ = A.countr_zero();
- unsigned BitWidth = A.getBitWidth();
- KnownBits Known(BitWidth);
- computeKnownBits(BO->LHS, Known, getDataLayout(), &AC, nullptr, &DT);
-
- APInt EffectiveMask =
- APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
- if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
- const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
- const SCEV *LHS = getSCEV(BO->LHS);
- const SCEV *ShiftedLHS = nullptr;
- if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
- if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
- // For an expression like (x * 8) & 8, simplify the multiply.
- unsigned MulZeros = OpC->getAPInt().countr_zero();
- unsigned GCD = std::min(MulZeros, TZ);
- APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
- SmallVector<SCEVUse, 4> MulOps;
- MulOps.push_back(getConstant(OpC->getAPInt().ashr(GCD)));
- append_range(MulOps, LHSMul->operands().drop_front());
- auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
- ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
- }
- }
- if (!ShiftedLHS)
- ShiftedLHS = getUDivExpr(LHS, MulCount);
- return getMulExpr(
- getZeroExtendExpr(
- getTruncateExpr(ShiftedLHS,
- IntegerType::get(getContext(), BitWidth - LZ - TZ)),
- BO->LHS->getType()),
- MulCount);
- }
- }
- // Binary `and` is a bit-wise `umin`.
- if (BO->LHS->getType()->isIntegerTy(1)) {
- LHS = getSCEV(BO->LHS);
- RHS = getSCEV(BO->RHS);
- return getUMinExpr(LHS, RHS);
- }
- break;
-
- case Instruction::Or:
- // Binary `or` is a bit-wise `umax`.
- if (BO->LHS->getType()->isIntegerTy(1)) {
- LHS = getSCEV(BO->LHS);
- RHS = getSCEV(BO->RHS);
- return getUMaxExpr(LHS, RHS);
- }
- break;
-
- case Instruction::Xor:
- if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
- // If the RHS of xor is -1, then this is a not operation.
- if (CI->isMinusOne())
- return getNotSCEV(getSCEV(BO->LHS));
-
- // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
- // This is a variant of the check for xor with -1, and it handles
- // the case where instcombine has trimmed non-demanded bits out
- // of an xor with -1.
- if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
- if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
- if (LBO->getOpcode() == Instruction::And &&
- LCI->getValue() == CI->getValue())
- if (const SCEVZeroExtendExpr *Z =
- dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
- Type *UTy = BO->LHS->getType();
- const SCEV *Z0 = Z->getOperand();
- Type *Z0Ty = Z0->getType();
- unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
-
- // If C is a low-bits mask, the zero extend is serving to
- // mask off the high bits. Complement the operand and
- // re-apply the zext.
- if (CI->getValue().isMask(Z0TySize))
- return getZeroExtendExpr(getNotSCEV(Z0), UTy);
-
- // If C is a single bit, it may be in the sign-bit position
- // before the zero-extend. In this case, represent the xor
- // using an add, which is equivalent, and re-apply the zext.
- APInt Trunc = CI->getValue().trunc(Z0TySize);
- if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
- Trunc.isSignMask())
- return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
- UTy);
- }
- }
- break;
-
- case Instruction::Shl:
- // Turn shift left of a constant amount into a multiply.
- if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
- uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
-
- // If the shift count is not less than the bitwidth, the result of
- // the shift is undefined. Don't try to analyze it, because the
- // resolution chosen here may differ from the resolution chosen in
- // other parts of the compiler.
- if (SA->getValue().uge(BitWidth))
- break;
-
- // We can safely preserve the nuw flag in all cases. It's also safe to
- // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
- // requires special handling. It can be preserved as long as we're not
- // left shifting by bitwidth - 1.
- auto Flags = SCEV::FlagAnyWrap;
- if (BO->Op) {
- auto MulFlags = getNoWrapFlagsFromUB(BO->Op);
- if (any(MulFlags & SCEV::FlagNSW) &&
- (any(MulFlags & SCEV::FlagNUW) ||
- SA->getValue().ult(BitWidth - 1)))
- Flags = Flags | SCEV::FlagNSW;
- if (any(MulFlags & SCEV::FlagNUW))
- Flags = Flags | SCEV::FlagNUW;
- }
-
- ConstantInt *X = ConstantInt::get(
- getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
- return getMulExpr(getSCEV(BO->LHS), getConstant(X), Flags);
- }
- break;
-
- case Instruction::AShr:
- // AShr X, C, where C is a constant.
- ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
- if (!CI)
- break;
-
- Type *OuterTy = BO->LHS->getType();
- uint64_t BitWidth = getTypeSizeInBits(OuterTy);
- // If the shift count is not less than the bitwidth, the result of
- // the shift is undefined. Don't try to analyze it, because the
- // resolution chosen here may differ from the resolution chosen in
- // other parts of the compiler.
- if (CI->getValue().uge(BitWidth))
- break;
-
- if (CI->isZero())
- return getSCEV(BO->LHS); // shift by zero --> noop
-
- uint64_t AShrAmt = CI->getZExtValue();
- Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
-
- Operator *L = dyn_cast<Operator>(BO->LHS);
- const SCEV *AddTruncateExpr = nullptr;
- ConstantInt *ShlAmtCI = nullptr;
- const SCEV *AddConstant = nullptr;
-
- if (L && L->getOpcode() == Instruction::Add) {
- // X = Shl A, n
- // Y = Add X, c
- // Z = AShr Y, m
- // n, c and m are constants.
-
- Operator *LShift = dyn_cast<Operator>(L->getOperand(0));
- ConstantInt *AddOperandCI = dyn_cast<ConstantInt>(L->getOperand(1));
- if (LShift && LShift->getOpcode() == Instruction::Shl) {
- if (AddOperandCI) {
- const SCEV *ShlOp0SCEV = getSCEV(LShift->getOperand(0));
- ShlAmtCI = dyn_cast<ConstantInt>(LShift->getOperand(1));
- // since we truncate to TruncTy, the AddConstant should be of the
- // same type, so create a new Constant with type same as TruncTy.
- // Also, the Add constant should be shifted right by AShr amount.
- APInt AddOperand = AddOperandCI->getValue().ashr(AShrAmt);
- AddConstant = getConstant(AddOperand.trunc(BitWidth - AShrAmt));
- // we model the expression as sext(add(trunc(A), c << n)), since the
- // sext(trunc) part is already handled below, we create a
- // AddExpr(TruncExp) which will be used later.
- AddTruncateExpr = getTruncateExpr(ShlOp0SCEV, TruncTy);
- }
- }
- } else if (L && L->getOpcode() == Instruction::Shl) {
- // X = Shl A, n
- // Y = AShr X, m
- // Both n and m are constant.
-
- const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
- ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
- AddTruncateExpr = getTruncateExpr(ShlOp0SCEV, TruncTy);
- }
-
- if (AddTruncateExpr && ShlAmtCI) {
- // We can merge the two given cases into a single SCEV statement,
- // incase n = m, the mul expression will be 2^0, so it gets resolved to
- // a simpler case. The following code handles the two cases:
- //
- // 1) For a two-shift sext-inreg, i.e. n = m,
- // use sext(trunc(x)) as the SCEV expression.
- //
- // 2) When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
- // expression. We already checked that ShlAmt < BitWidth, so
- // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
- // ShlAmt - AShrAmt < Amt.
- const APInt &ShlAmt = ShlAmtCI->getValue();
- if (ShlAmt.ult(BitWidth) && ShlAmt.uge(AShrAmt)) {
- APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
- ShlAmtCI->getZExtValue() - AShrAmt);
- const SCEV *CompositeExpr =
- getMulExpr(AddTruncateExpr, getConstant(Mul));
- if (L->getOpcode() != Instruction::Shl)
- CompositeExpr = getAddExpr(CompositeExpr, AddConstant);
-
- return getSignExtendExpr(CompositeExpr, OuterTy);
- }
- }
- break;
- }
- }
-
- switch (U->getOpcode()) {
- case Instruction::Trunc:
- return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
-
- case Instruction::ZExt:
- return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
-
- case Instruction::SExt:
- if (auto BO = MatchBinaryOp(U->getOperand(0), getDataLayout(), AC, DT,
- dyn_cast<Instruction>(V))) {
- // The NSW flag of a subtract does not always survive the conversion to
- // A + (-1)*B. By pushing sign extension onto its operands we are much
- // more likely to preserve NSW and allow later AddRec optimisations.
- //
- // NOTE: This is effectively duplicating this logic from getSignExtend:
- // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
- // but by that point the NSW information has potentially been lost.
- if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
- Type *Ty = U->getType();
- auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
- auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
- return getMinusSCEV(V1, V2, SCEV::FlagNSW);
- }
- }
- return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
-
- case Instruction::BitCast:
- // BitCasts are no-op casts so we just eliminate the cast.
- if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
- return getSCEV(U->getOperand(0));
- break;
-
- case Instruction::PtrToAddr: {
- const SCEV *IntOp = getPtrToAddrExpr(getSCEV(U->getOperand(0)));
- if (isa<SCEVCouldNotCompute>(IntOp))
- return getUnknown(V);
- return IntOp;
- }
-
- case Instruction::PtrToInt: {
- // Keep ptrtoint as SCEVUnknown, except when the pointer operand has SCEV
- // structure (e.g. a pointer add-rec or an offset from a known base). In
- // that case model it via ptrtoaddr to preserve the integer structure
- // (induction, constant folding). A bare SCEVUnknown pointer gains no
- // structure from wrapping it in ptrtoaddr, so leave it opaque.
- const SCEV *PtrSCEV = getSCEV(U->getOperand(0));
- if (!isa<SCEVUnknown>(PtrSCEV)) {
- const SCEV *Addr = getPtrToAddrExpr(PtrSCEV);
- if (!isa<SCEVCouldNotCompute>(Addr) &&
- getTypeSizeInBits(V->getType()) <= getTypeSizeInBits(Addr->getType()))
- return getTruncateOrNoop(Addr, V->getType());
- }
- return getUnknown(V);
- }
- case Instruction::IntToPtr:
- // Just don't deal with inttoptr casts.
- return getUnknown(V);
-
- case Instruction::SDiv:
- // If both operands are non-negative, this is just an udiv.
- if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
- isKnownNonNegative(getSCEV(U->getOperand(1))))
- return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
- break;
-
- case Instruction::SRem:
- // If both operands are non-negative, this is just an urem.
- if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
- isKnownNonNegative(getSCEV(U->getOperand(1))))
- return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
- break;
-
- case Instruction::GetElementPtr:
- return createNodeForGEP(cast<GEPOperator>(U));
-
- case Instruction::PHI:
- return createNodeForPHI(cast<PHINode>(U));
-
- case Instruction::Select:
- return createNodeForSelectOrPHI(U, U->getOperand(0), U->getOperand(1),
- U->getOperand(2));
-
- case Instruction::Call:
- case Instruction::Invoke:
- if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand())
- return getSCEV(RV);
-
- if (auto *II = dyn_cast<IntrinsicInst>(U)) {
- switch (II->getIntrinsicID()) {
- case Intrinsic::abs:
- return getAbsExpr(
- getSCEV(II->getArgOperand(0)),
- /*IsNSW=*/cast<ConstantInt>(II->getArgOperand(1))->isOne());
- case Intrinsic::umax:
- LHS = getSCEV(II->getArgOperand(0));
- RHS = getSCEV(II->getArgOperand(1));
- return getUMaxExpr(LHS, RHS);
- case Intrinsic::umin:
- LHS = getSCEV(II->getArgOperand(0));
- RHS = getSCEV(II->getArgOperand(1));
- return getUMinExpr(LHS, RHS);
- case Intrinsic::smax:
- LHS = getSCEV(II->getArgOperand(0));
- RHS = getSCEV(II->getArgOperand(1));
- return getSMaxExpr(LHS, RHS);
- case Intrinsic::smin:
- LHS = getSCEV(II->getArgOperand(0));
- RHS = getSCEV(II->getArgOperand(1));
- return getSMinExpr(LHS, RHS);
- case Intrinsic::usub_sat: {
- const SCEV *X = getSCEV(II->getArgOperand(0));
- const SCEV *Y = getSCEV(II->getArgOperand(1));
- const SCEV *ClampedY = getUMinExpr(X, Y);
- return getMinusSCEV(X, ClampedY, SCEV::FlagNUW);
- }
- case Intrinsic::uadd_sat: {
- const SCEV *X = getSCEV(II->getArgOperand(0));
- const SCEV *Y = getSCEV(II->getArgOperand(1));
- const SCEV *ClampedX = getUMinExpr(X, getNotSCEV(Y));
- return getAddExpr(ClampedX, Y, SCEV::FlagNUW);
- }
- case Intrinsic::start_loop_iterations:
- case Intrinsic::annotation:
- case Intrinsic::ptr_annotation:
- // A start_loop_iterations or llvm.annotation or llvm.prt.annotation is
- // just eqivalent to the first operand for SCEV purposes.
- return getSCEV(II->getArgOperand(0));
- case Intrinsic::vscale:
- return getVScale(II->getType());
- default:
- break;
- }
- }
- break;
- }
-
- return getUnknown(V);
-}
-
-//===----------------------------------------------------------------------===//
-// Iteration Count Computation Code
-//
-
-const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount) {
- if (isa<SCEVCouldNotCompute>(ExitCount))
- return getCouldNotCompute();
-
- auto *ExitCountType = ExitCount->getType();
- assert(ExitCountType->isIntegerTy());
- auto *EvalTy = Type::getIntNTy(ExitCountType->getContext(),
- 1 + ExitCountType->getScalarSizeInBits());
- return getTripCountFromExitCount(ExitCount, EvalTy, nullptr);
-}
-
-const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount,
- Type *EvalTy,
- const Loop *L) {
- if (isa<SCEVCouldNotCompute>(ExitCount))
- return getCouldNotCompute();
-
- unsigned ExitCountSize = getTypeSizeInBits(ExitCount->getType());
- unsigned EvalSize = EvalTy->getPrimitiveSizeInBits();
-
- auto CanAddOneWithoutOverflow = [&]() {
- ConstantRange ExitCountRange =
- getRangeRef(ExitCount, RangeSignHint::HINT_RANGE_UNSIGNED);
- if (!ExitCountRange.contains(APInt::getMaxValue(ExitCountSize)))
- return true;
-
- return L && isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, ExitCount,
- getMinusOne(ExitCount->getType()));
- };
-
- // If we need to zero extend the backedge count, check if we can add one to
- // it prior to zero extending without overflow. Provided this is safe, it
- // allows better simplification of the +1.
- if (EvalSize > ExitCountSize && CanAddOneWithoutOverflow())
- return getZeroExtendExpr(
- getAddExpr(ExitCount, getOne(ExitCount->getType())), EvalTy);
-
- // Get the total trip count from the count by adding 1. This may wrap.
- return getAddExpr(getTruncateOrZeroExtend(ExitCount, EvalTy), getOne(EvalTy));
-}
-
-static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
- if (!ExitCount)
- return 0;
-
- ConstantInt *ExitConst = ExitCount->getValue();
-
- // Guard against huge trip counts.
- if (ExitConst->getValue().getActiveBits() > 32)
- return 0;
-
- // In case of integer overflow, this returns 0, which is correct.
- return ((unsigned)ExitConst->getZExtValue()) + 1;
-}
-
-unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
- auto *ExitCount = dyn_cast<SCEVConstant>(getBackedgeTakenCount(L, Exact));
- return getConstantTripCount(ExitCount);
-}
-
-unsigned
-ScalarEvolution::getSmallConstantTripCount(const Loop *L,
- const BasicBlock *ExitingBlock) {
- assert(ExitingBlock && "Must pass a non-null exiting block!");
- assert(L->isLoopExiting(ExitingBlock) &&
- "Exiting block must actually branch out of the loop!");
- const SCEVConstant *ExitCount =
- dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
- return getConstantTripCount(ExitCount);
-}
-
-unsigned ScalarEvolution::getSmallConstantMaxTripCount(
- const Loop *L, SmallVectorImpl<const SCEVPredicate *> *Predicates) {
-
- const auto *MaxExitCount =
- Predicates ? getPredicatedConstantMaxBackedgeTakenCount(L, *Predicates)
- : getConstantMaxBackedgeTakenCount(L);
- return getConstantTripCount(dyn_cast<SCEVConstant>(MaxExitCount));
-}
-
-unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
- SmallVector<BasicBlock *, 8> ExitingBlocks;
- L->getExitingBlocks(ExitingBlocks);
-
- std::optional<unsigned> Res;
- for (auto *ExitingBB : ExitingBlocks) {
- unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBB);
- if (!Res)
- Res = Multiple;
- Res = std::gcd(*Res, Multiple);
- }
- return Res.value_or(1);
-}
-
-unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
- const SCEV *ExitCount) {
- if (isa<SCEVCouldNotCompute>(ExitCount))
- return 1;
-
- // Get the trip count
- const SCEV *TCExpr = getTripCountFromExitCount(applyLoopGuards(ExitCount, L));
-
- APInt Multiple = getNonZeroConstantMultiple(TCExpr);
- // If a trip multiple is huge (>=2^32), the trip count is still divisible by
- // the greatest power of 2 divisor less than 2^32.
- return Multiple.getActiveBits() > 32
- ? 1U << std::min(31U, Multiple.countTrailingZeros())
- : (unsigned)Multiple.getZExtValue();
-}
-
-/// Returns the largest constant divisor of the trip count of this loop as a
-/// normal unsigned value, if possible. This means that the actual trip count is
-/// always a multiple of the returned value (don't forget the trip count could
-/// very well be zero as well!).
-///
-/// Returns 1 if the trip count is unknown or not guaranteed to be the
-/// multiple of a constant (which is also the case if the trip count is simply
-/// constant, use getSmallConstantTripCount for that case), Will also return 1
-/// if the trip count is very large (>= 2^32).
-///
-/// As explained in the comments for getSmallConstantTripCount, this assumes
-/// that control exits the loop via ExitingBlock.
-unsigned
-ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
- const BasicBlock *ExitingBlock) {
- assert(ExitingBlock && "Must pass a non-null exiting block!");
- assert(L->isLoopExiting(ExitingBlock) &&
- "Exiting block must actually branch out of the loop!");
- const SCEV *ExitCount = getExitCount(L, ExitingBlock);
- return getSmallConstantTripMultiple(L, ExitCount);
-}
-
-const SCEV *ScalarEvolution::getExitCount(const Loop *L,
- const BasicBlock *ExitingBlock,
- ExitCountKind Kind) {
- switch (Kind) {
- case Exact:
- return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
- case SymbolicMaximum:
- return getBackedgeTakenInfo(L).getSymbolicMax(ExitingBlock, this);
- case ConstantMaximum:
- return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this);
- };
- llvm_unreachable("Invalid ExitCountKind!");
-}
-
-const SCEV *ScalarEvolution::getPredicatedExitCount(
- const Loop *L, const BasicBlock *ExitingBlock,
- SmallVectorImpl<const SCEVPredicate *> *Predicates, ExitCountKind Kind) {
- switch (Kind) {
- case Exact:
- return getPredicatedBackedgeTakenInfo(L).getExact(ExitingBlock, this,
- Predicates);
- case SymbolicMaximum:
- return getPredicatedBackedgeTakenInfo(L).getSymbolicMax(ExitingBlock, this,
- Predicates);
- case ConstantMaximum:
- return getPredicatedBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this,
- Predicates);
- };
- llvm_unreachable("Invalid ExitCountKind!");
-}
-
-const SCEV *ScalarEvolution::getPredicatedBackedgeTakenCount(
- const Loop *L, SmallVectorImpl<const SCEVPredicate *> &Preds) {
- return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
-}
-
-const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
- ExitCountKind Kind) {
- switch (Kind) {
- case Exact:
- return getBackedgeTakenInfo(L).getExact(L, this);
- case ConstantMaximum:
- return getBackedgeTakenInfo(L).getConstantMax(this);
- case SymbolicMaximum:
- return getBackedgeTakenInfo(L).getSymbolicMax(L, this);
- };
- llvm_unreachable("Invalid ExitCountKind!");
-}
-
-const SCEV *ScalarEvolution::getPredicatedSymbolicMaxBackedgeTakenCount(
- const Loop *L, SmallVectorImpl<const SCEVPredicate *> &Preds) {
- return getPredicatedBackedgeTakenInfo(L).getSymbolicMax(L, this, &Preds);
-}
-
-const SCEV *ScalarEvolution::getPredicatedConstantMaxBackedgeTakenCount(
- const Loop *L, SmallVectorImpl<const SCEVPredicate *> &Preds) {
- return getPredicatedBackedgeTakenInfo(L).getConstantMax(this, &Preds);
-}
-
-bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
- return getBackedgeTakenInfo(L).isConstantMaxOrZero(this);
-}
-
-ScalarEvolution::BackedgeTakenInfo &
-ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
- auto &BTI = getBackedgeTakenInfo(L);
- if (BTI.hasFullInfo())
- return BTI;
-
- auto Pair = PredicatedBackedgeTakenCounts.try_emplace(L);
-
- if (!Pair.second)
- return Pair.first->second;
-
- BackedgeTakenInfo Result =
- computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
-
- return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
-}
-
-ScalarEvolution::BackedgeTakenInfo &
-ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
- // Initially insert an invalid entry for this loop. If the insertion
- // succeeds, proceed to actually compute a backedge-taken count and
- // update the value. The temporary CouldNotCompute value tells SCEV
- // code elsewhere that it shouldn't attempt to request a new
- // backedge-taken count, which could result in infinite recursion.
- std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
- BackedgeTakenCounts.try_emplace(L);
- if (!Pair.second)
- return Pair.first->second;
-
- // computeBackedgeTakenCount may allocate memory for its result. Inserting it
- // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
- // must be cleared in this scope.
- BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
-
- // Now that we know more about the trip count for this loop, forget any
- // existing SCEV values for PHI nodes in this loop since they are only
- // conservative estimates made without the benefit of trip count
- // information. This invalidation is not necessary for correctness, and is
- // only done to produce more precise results.
- if (Result.hasAnyInfo()) {
- // Invalidate any expression using an addrec in this loop.
- SmallVector<SCEVUse, 8> ToForget;
- auto LoopUsersIt = LoopUsers.find(L);
- if (LoopUsersIt != LoopUsers.end())
- append_range(ToForget, LoopUsersIt->second);
- forgetMemoizedResults(ToForget);
-
- // Invalidate constant-evolved loop header phis.
- for (PHINode &PN : L->getHeader()->phis())
- ConstantEvolutionLoopExitValue.erase(&PN);
- }
-
- // Re-lookup the insert position, since the call to
- // computeBackedgeTakenCount above could result in a
- // recusive call to getBackedgeTakenInfo (on a different
- // loop), which would invalidate the iterator computed
- // earlier.
- return BackedgeTakenCounts.find(L)->second = std::move(Result);
-}
-
-void ScalarEvolution::forgetAllLoops() {
- // This method is intended to forget all info about loops. It should
- // invalidate caches as if the following happened:
- // - The trip counts of all loops have changed arbitrarily
- // - Every llvm::Value has been updated in place to produce a different
- // result.
- BackedgeTakenCounts.clear();
- PredicatedBackedgeTakenCounts.clear();
- BECountUsers.clear();
- LoopPropertiesCache.clear();
- ConstantEvolutionLoopExitValue.clear();
- ValueExprMap.clear();
- ValuesAtScopes.clear();
- ValuesAtScopesUsers.clear();
- LoopDispositions.clear();
- BlockDispositions.clear();
- UnsignedRanges.clear();
- SignedRanges.clear();
- ExprValueMap.clear();
- HasRecMap.clear();
- ConstantMultipleCache.clear();
- PredicatedSCEVRewrites.clear();
- FoldCache.clear();
- FoldCacheUser.clear();
-}
-void ScalarEvolution::visitAndClearUsers(
- SmallVectorImpl<Instruction *> &Worklist,
- SmallPtrSetImpl<Instruction *> &Visited,
- SmallVectorImpl<SCEVUse> &ToForget) {
- while (!Worklist.empty()) {
- Instruction *I = Worklist.pop_back_val();
- if (!isSCEVable(I->getType()) && !isa<WithOverflowInst>(I))
- continue;
-
- ValueExprMapType::iterator It =
- ValueExprMap.find_as(static_cast<Value *>(I));
- if (It != ValueExprMap.end()) {
- ToForget.push_back(It->second);
- eraseValueFromMap(It->first);
- if (PHINode *PN = dyn_cast<PHINode>(I))
- ConstantEvolutionLoopExitValue.erase(PN);
- }
-
- PushDefUseChildren(I, Worklist, Visited);
- }
-}
-
-void ScalarEvolution::forgetLoop(const Loop *L) {
- SmallVector<const Loop *, 16> LoopWorklist(1, L);
- SmallVector<SCEVUse, 16> ToForget;
-
- // Iterate over all the loops and sub-loops to drop SCEV information.
- while (!LoopWorklist.empty()) {
- auto *CurrL = LoopWorklist.pop_back_val();
-
- // Drop any stored trip count value.
- forgetBackedgeTakenCounts(CurrL, /* Predicated */ false);
- forgetBackedgeTakenCounts(CurrL, /* Predicated */ true);
-
- // Drop information about predicated SCEV rewrites for this loop.
- PredicatedSCEVRewrites.remove_if(
- [&](const auto &Entry) { return Entry.first.second == CurrL; });
-
- auto LoopUsersItr = LoopUsers.find(CurrL);
- if (LoopUsersItr != LoopUsers.end())
- llvm::append_range(ToForget, LoopUsersItr->second);
-
- // Drop information about expressions based on loop-header PHIs.
- for (PHINode &PN : CurrL->getHeader()->phis()) {
- ConstantEvolutionLoopExitValue.erase(&PN);
- auto VIt = ValueExprMap.find_as(static_cast<Value *>(&PN));
- if (VIt != ValueExprMap.end())
- ToForget.push_back(VIt->second);
- }
-
- LoopPropertiesCache.erase(CurrL);
- // Forget all contained loops too, to avoid dangling entries in the
- // ValuesAtScopes map.
- LoopWorklist.append(CurrL->begin(), CurrL->end());
- }
- forgetMemoizedResults(ToForget);
-}
-
-void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
- forgetLoop(L->getOutermostLoop());
-}
-
-void ScalarEvolution::forgetValue(Value *V) {
- Instruction *I = dyn_cast<Instruction>(V);
- if (!I) return;
-
- // Drop information about expressions based on loop-header PHIs.
- SmallVector<Instruction *, 16> Worklist;
- SmallPtrSet<Instruction *, 8> Visited;
- SmallVector<SCEVUse, 8> ToForget;
- Worklist.push_back(I);
- Visited.insert(I);
- visitAndClearUsers(Worklist, Visited, ToForget);
-
- forgetMemoizedResults(ToForget);
-}
-
-void ScalarEvolution::forgetLcssaPhiWithNewPredecessor(Loop *L, PHINode *V) {
- if (!isSCEVable(V->getType()))
- return;
-
- // If SCEV looked through a trivial LCSSA phi node, we might have SCEV's
- // directly using a SCEVUnknown/SCEVAddRec defined in the loop. After an
- // extra predecessor is added, this is no longer valid. Find all Unknowns and
- // AddRecs defined in the loop and invalidate any SCEV's making use of them.
- if (const SCEV *S = getExistingSCEV(V)) {
- struct InvalidationRootCollector {
- Loop *L;
- SmallVector<SCEVUse, 8> Roots;
-
- InvalidationRootCollector(Loop *L) : L(L) {}
-
- bool follow(const SCEV *S) {
- if (auto *SU = dyn_cast<SCEVUnknown>(S)) {
- if (auto *I = dyn_cast<Instruction>(SU->getValue()))
- if (L->contains(I))
- Roots.push_back(S);
- } else if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
- if (L->contains(AddRec->getLoop()))
- Roots.push_back(S);
- }
- return true;
- }
- bool isDone() const { return false; }
- };
-
- InvalidationRootCollector C(L);
- visitAll(S, C);
- forgetMemoizedResults(C.Roots);
- }
-
- // Also perform the normal invalidation.
- forgetValue(V);
-}
-
-void ScalarEvolution::forgetLoopDispositions() { LoopDispositions.clear(); }
-
-void ScalarEvolution::forgetBlockAndLoopDispositions(Value *V) {
- // Unless a specific value is passed to invalidation, completely clear both
- // caches.
- if (!V) {
- BlockDispositions.clear();
- LoopDispositions.clear();
- return;
- }
-
- if (!isSCEVable(V->getType()))
- return;
-
- const SCEV *S = getExistingSCEV(V);
- if (!S)
- return;
-
- // Invalidate the block and loop dispositions cached for S. Dispositions of
- // S's users may change if S's disposition changes (i.e. a user may change to
- // loop-invariant, if S changes to loop invariant), so also invalidate
- // dispositions of S's users recursively.
- SmallVector<SCEVUse, 8> Worklist = {S};
- SmallPtrSet<const SCEV *, 8> Seen = {S};
- while (!Worklist.empty()) {
- const SCEV *Curr = Worklist.pop_back_val();
- bool LoopDispoRemoved = LoopDispositions.erase(Curr);
- bool BlockDispoRemoved = BlockDispositions.erase(Curr);
- if (!LoopDispoRemoved && !BlockDispoRemoved)
- continue;
- auto Users = SCEVUsers.find(Curr);
- if (Users != SCEVUsers.end())
- for (const auto *User : Users->second)
- if (Seen.insert(User).second)
- Worklist.push_back(User);
- }
-}
-
-/// Get the exact loop backedge taken count considering all loop exits. A
-/// computable result can only be returned for loops with all exiting blocks
-/// dominating the latch. howFarToZero assumes that the limit of each loop test
-/// is never skipped. This is a valid assumption as long as the loop exits via
-/// that test. For precise results, it is the caller's responsibility to specify
-/// the relevant loop exiting block using getExact(ExitingBlock, SE).
-const SCEV *ScalarEvolution::BackedgeTakenInfo::getExact(
- const Loop *L, ScalarEvolution *SE,
- SmallVectorImpl<const SCEVPredicate *> *Preds) const {
- // If any exits were not computable, the loop is not computable.
- if (!isComplete() || ExitNotTaken.empty())
- return SE->getCouldNotCompute();
-
- const BasicBlock *Latch = L->getLoopLatch();
- // All exiting blocks we have collected must dominate the only backedge.
- if (!Latch)
- return SE->getCouldNotCompute();
-
- // All exiting blocks we have gathered dominate loop's latch, so exact trip
- // count is simply a minimum out of all these calculated exit counts.
- SmallVector<SCEVUse, 2> Ops;
- for (const auto &ENT : ExitNotTaken) {
- const SCEV *BECount = ENT.ExactNotTaken;
- assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
- assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
- "We should only have known counts for exiting blocks that dominate "
- "latch!");
-
- Ops.push_back(BECount);
-
- if (Preds)
- append_range(*Preds, ENT.Predicates);
-
- assert((Preds || ENT.hasAlwaysTruePredicate()) &&
- "Predicate should be always true!");
- }
-
- // If an earlier exit exits on the first iteration (exit count zero), then
- // a later poison exit count should not propagate into the result. This are
- // exactly the semantics provided by umin_seq.
- return SE->getUMinFromMismatchedTypes(Ops, /* Sequential */ true);
-}
-
-const ScalarEvolution::ExitNotTakenInfo *
-ScalarEvolution::BackedgeTakenInfo::getExitNotTaken(
- const BasicBlock *ExitingBlock,
- SmallVectorImpl<const SCEVPredicate *> *Predicates) const {
- for (const auto &ENT : ExitNotTaken)
- if (ENT.ExitingBlock == ExitingBlock) {
- if (ENT.hasAlwaysTruePredicate())
- return &ENT;
- else if (Predicates) {
- append_range(*Predicates, ENT.Predicates);
- return &ENT;
- }
- }
-
- return nullptr;
-}
-
-/// getConstantMax - Get the constant max backedge taken count for the loop.
-const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax(
- ScalarEvolution *SE,
- SmallVectorImpl<const SCEVPredicate *> *Predicates) const {
- if (!getConstantMax())
- return SE->getCouldNotCompute();
-
- for (const auto &ENT : ExitNotTaken)
- if (!ENT.hasAlwaysTruePredicate()) {
- if (!Predicates)
- return SE->getCouldNotCompute();
- append_range(*Predicates, ENT.Predicates);
- }
-
- assert((isa<SCEVCouldNotCompute>(getConstantMax()) ||
- isa<SCEVConstant>(getConstantMax())) &&
- "No point in having a non-constant max backedge taken count!");
- return getConstantMax();
-}
-
-const SCEV *ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(
- const Loop *L, ScalarEvolution *SE,
- SmallVectorImpl<const SCEVPredicate *> *Predicates) {
- if (!SymbolicMax) {
- // Form an expression for the maximum exit count possible for this loop. We
- // merge the max and exact information to approximate a version of
- // getConstantMaxBackedgeTakenCount which isn't restricted to just
- // constants.
- SmallVector<SCEVUse, 4> ExitCounts;
-
- for (const auto &ENT : ExitNotTaken) {
- const SCEV *ExitCount = ENT.SymbolicMaxNotTaken;
- if (!isa<SCEVCouldNotCompute>(ExitCount)) {
- assert(SE->DT.dominates(ENT.ExitingBlock, L->getLoopLatch()) &&
- "We should only have known counts for exiting blocks that "
- "dominate latch!");
- ExitCounts.push_back(ExitCount);
- if (Predicates)
- append_range(*Predicates, ENT.Predicates);
-
- assert((Predicates || ENT.hasAlwaysTruePredicate()) &&
- "Predicate should be always true!");
- }
- }
- if (ExitCounts.empty())
- SymbolicMax = SE->getCouldNotCompute();
- else
- SymbolicMax =
- SE->getUMinFromMismatchedTypes(ExitCounts, /*Sequential*/ true);
- }
- return SymbolicMax;
-}
-
-bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero(
- ScalarEvolution *SE) const {
- auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
- return !ENT.hasAlwaysTruePredicate();
- };
- return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
-}
-
-ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
- : ExitLimit(E, E, E, false) {}
-
-ScalarEvolution::ExitLimit::ExitLimit(
- const SCEV *E, const SCEV *ConstantMaxNotTaken,
- const SCEV *SymbolicMaxNotTaken, bool MaxOrZero,
- ArrayRef<ArrayRef<const SCEVPredicate *>> PredLists)
- : ExactNotTaken(E), ConstantMaxNotTaken(ConstantMaxNotTaken),
- SymbolicMaxNotTaken(SymbolicMaxNotTaken), MaxOrZero(MaxOrZero) {
- // If we prove the max count is zero, so is the symbolic bound. This happens
- // in practice due to differences in a) how context sensitive we've chosen
- // to be and b) how we reason about bounds implied by UB.
- if (ConstantMaxNotTaken->isZero()) {
- this->ExactNotTaken = E = ConstantMaxNotTaken;
- this->SymbolicMaxNotTaken = SymbolicMaxNotTaken = ConstantMaxNotTaken;
- }
-
- assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
- !isa<SCEVCouldNotCompute>(ConstantMaxNotTaken)) &&
- "Exact is not allowed to be less precise than Constant Max");
- assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
- !isa<SCEVCouldNotCompute>(SymbolicMaxNotTaken)) &&
- "Exact is not allowed to be less precise than Symbolic Max");
- assert((isa<SCEVCouldNotCompute>(SymbolicMaxNotTaken) ||
- !isa<SCEVCouldNotCompute>(ConstantMaxNotTaken)) &&
- "Symbolic Max is not allowed to be less precise than Constant Max");
- assert((isa<SCEVCouldNotCompute>(ConstantMaxNotTaken) ||
- isa<SCEVConstant>(ConstantMaxNotTaken)) &&
- "No point in having a non-constant max backedge taken count!");
- SmallPtrSet<const SCEVPredicate *, 4> SeenPreds;
- for (const auto PredList : PredLists)
- for (const auto *P : PredList) {
- if (SeenPreds.contains(P))
- continue;
- assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
- SeenPreds.insert(P);
- Predicates.push_back(P);
- }
- assert((isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) &&
- "Backedge count should be int");
- assert((isa<SCEVCouldNotCompute>(ConstantMaxNotTaken) ||
- !ConstantMaxNotTaken->getType()->isPointerTy()) &&
- "Max backedge count should be int");
-}
-
-ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E,
- const SCEV *ConstantMaxNotTaken,
- const SCEV *SymbolicMaxNotTaken,
- bool MaxOrZero,
- ArrayRef<const SCEVPredicate *> PredList)
- : ExitLimit(E, ConstantMaxNotTaken, SymbolicMaxNotTaken, MaxOrZero,
- ArrayRef({PredList})) {}
-
-/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
-/// computable exit into a persistent ExitNotTakenInfo array.
-ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
- ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> ExitCounts,
- bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero)
- : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) {
- using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
-
- ExitNotTaken.reserve(ExitCounts.size());
- std::transform(ExitCounts.begin(), ExitCounts.end(),
- std::back_inserter(ExitNotTaken),
- [&](const EdgeExitInfo &EEI) {
- BasicBlock *ExitBB = EEI.first;
- const ExitLimit &EL = EEI.second;
- return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken,
- EL.ConstantMaxNotTaken, EL.SymbolicMaxNotTaken,
- EL.Predicates);
- });
- assert((isa<SCEVCouldNotCompute>(ConstantMax) ||
- isa<SCEVConstant>(ConstantMax)) &&
- "No point in having a non-constant max backedge taken count!");
-}
-
-/// Compute the number of times the backedge of the specified loop will execute.
-ScalarEvolution::BackedgeTakenInfo
-ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
- bool AllowPredicates) {
- SmallVector<BasicBlock *, 8> ExitingBlocks;
- L->getExitingBlocks(ExitingBlocks);
-
- using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
-
- SmallVector<EdgeExitInfo, 4> ExitCounts;
- bool CouldComputeBECount = true;
- BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
- const SCEV *MustExitMaxBECount = nullptr;
- const SCEV *MayExitMaxBECount = nullptr;
- bool MustExitMaxOrZero = false;
- bool IsOnlyExit = ExitingBlocks.size() == 1;
-
- // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
- // and compute maxBECount.
- // Do a union of all the predicates here.
- for (BasicBlock *ExitBB : ExitingBlocks) {
- // We canonicalize untaken exits to br (constant), ignore them so that
- // proving an exit untaken doesn't negatively impact our ability to reason
- // about the loop as whole.
- if (auto *BI = dyn_cast<CondBrInst>(ExitBB->getTerminator()))
- if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
- bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
- if (ExitIfTrue == CI->isZero())
- continue;
- }
-
- ExitLimit EL = computeExitLimit(L, ExitBB, IsOnlyExit, AllowPredicates);
-
- assert((AllowPredicates || EL.Predicates.empty()) &&
- "Predicated exit limit when predicates are not allowed!");
-
- // 1. For each exit that can be computed, add an entry to ExitCounts.
- // CouldComputeBECount is true only if all exits can be computed.
- if (EL.ExactNotTaken != getCouldNotCompute())
- ++NumExitCountsComputed;
- else
- // We couldn't compute an exact value for this exit, so
- // we won't be able to compute an exact value for the loop.
- CouldComputeBECount = false;
- // Remember exit count if either exact or symbolic is known. Because
- // Exact always implies symbolic, only check symbolic.
- if (EL.SymbolicMaxNotTaken != getCouldNotCompute())
- ExitCounts.emplace_back(ExitBB, EL);
- else {
- assert(EL.ExactNotTaken == getCouldNotCompute() &&
- "Exact is known but symbolic isn't?");
- ++NumExitCountsNotComputed;
- }
-
- // 2. Derive the loop's MaxBECount from each exit's max number of
- // non-exiting iterations. Partition the loop exits into two kinds:
- // LoopMustExits and LoopMayExits.
- //
- // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
- // is a LoopMayExit. If any computable LoopMustExit is found, then
- // MaxBECount is the minimum EL.ConstantMaxNotTaken of computable
- // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
- // EL.ConstantMaxNotTaken, where CouldNotCompute is considered greater than
- // any
- // computable EL.ConstantMaxNotTaken.
- if (EL.ConstantMaxNotTaken != getCouldNotCompute() && Latch &&
- DT.dominates(ExitBB, Latch)) {
- if (!MustExitMaxBECount) {
- MustExitMaxBECount = EL.ConstantMaxNotTaken;
- MustExitMaxOrZero = EL.MaxOrZero;
- } else {
- MustExitMaxBECount = getUMinFromMismatchedTypes(MustExitMaxBECount,
- EL.ConstantMaxNotTaken);
- }
- } else if (MayExitMaxBECount != getCouldNotCompute()) {
- if (!MayExitMaxBECount || EL.ConstantMaxNotTaken == getCouldNotCompute())
- MayExitMaxBECount = EL.ConstantMaxNotTaken;
- else {
- MayExitMaxBECount = getUMaxFromMismatchedTypes(MayExitMaxBECount,
- EL.ConstantMaxNotTaken);
- }
- }
- }
- const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
- (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
- // The loop backedge will be taken the maximum or zero times if there's
- // a single exit that must be taken the maximum or zero times.
- bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
-
- // Remember which SCEVs are used in exit limits for invalidation purposes.
- // We only care about non-constant SCEVs here, so we can ignore
- // EL.ConstantMaxNotTaken
- // and MaxBECount, which must be SCEVConstant.
- for (const auto &Pair : ExitCounts) {
- if (!isa<SCEVConstant>(Pair.second.ExactNotTaken))
- BECountUsers[Pair.second.ExactNotTaken].insert({L, AllowPredicates});
- if (!isa<SCEVConstant>(Pair.second.SymbolicMaxNotTaken))
- BECountUsers[Pair.second.SymbolicMaxNotTaken].insert(
- {L, AllowPredicates});
- }
- return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
- MaxBECount, MaxOrZero);
-}
-
-ScalarEvolution::ExitLimit
-ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
- bool IsOnlyExit, bool AllowPredicates) {
- assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
- // If our exiting block does not dominate the latch, then its connection with
- // loop's exit limit may be far from trivial.
- const BasicBlock *Latch = L->getLoopLatch();
- if (!Latch || !DT.dominates(ExitingBlock, Latch))
- return getCouldNotCompute();
-
- Instruction *Term = ExitingBlock->getTerminator();
- if (CondBrInst *BI = dyn_cast<CondBrInst>(Term)) {
- bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
- assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
- "It should have one successor in loop and one exit block!");
- // Proceed to the next level to examine the exit condition expression.
- return computeExitLimitFromCond(L, BI->getCondition(), ExitIfTrue,
- /*ControlsOnlyExit=*/IsOnlyExit,
- AllowPredicates);
- }
-
- if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
- // For switch, make sure that there is a single exit from the loop.
- BasicBlock *Exit = nullptr;
- for (auto *SBB : successors(ExitingBlock))
- if (!L->contains(SBB)) {
- if (Exit) // Multiple exit successors.
- return getCouldNotCompute();
- Exit = SBB;
- }
- assert(Exit && "Exiting block must have at least one exit");
- return computeExitLimitFromSingleExitSwitch(
- L, SI, Exit, /*ControlsOnlyExit=*/IsOnlyExit);
- }
-
- return getCouldNotCompute();
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
- const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsOnlyExit,
- bool AllowPredicates) {
- ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
- return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
- ControlsOnlyExit, AllowPredicates);
-}
-
-std::optional<ScalarEvolution::ExitLimit>
-ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
- bool ExitIfTrue, bool ControlsOnlyExit,
- bool AllowPredicates) {
- (void)this->L;
- (void)this->ExitIfTrue;
- (void)this->AllowPredicates;
-
- assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
- this->AllowPredicates == AllowPredicates &&
- "Variance in assumed invariant key components!");
- auto Itr = TripCountMap.find({ExitCond, ControlsOnlyExit});
- if (Itr == TripCountMap.end())
- return std::nullopt;
- return Itr->second;
-}
-
-void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
- bool ExitIfTrue,
- bool ControlsOnlyExit,
- bool AllowPredicates,
- const ExitLimit &EL) {
- assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
- this->AllowPredicates == AllowPredicates &&
- "Variance in assumed invariant key components!");
-
- auto InsertResult = TripCountMap.insert({{ExitCond, ControlsOnlyExit}, EL});
- assert(InsertResult.second && "Expected successful insertion!");
- (void)InsertResult;
- (void)ExitIfTrue;
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
- ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
- bool ControlsOnlyExit, bool AllowPredicates) {
-
- if (auto MaybeEL = Cache.find(L, ExitCond, ExitIfTrue, ControlsOnlyExit,
- AllowPredicates))
- return *MaybeEL;
-
- ExitLimit EL = computeExitLimitFromCondImpl(
- Cache, L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates);
- Cache.insert(L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates, EL);
- return EL;
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
- ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
- bool ControlsOnlyExit, bool AllowPredicates) {
- // Handle BinOp conditions (And, Or).
- if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp(
- Cache, L, ExitCond, ExitIfTrue, AllowPredicates))
- return *LimitFromBinOp;
-
- // With an icmp, it may be feasible to compute an exact backedge-taken count.
- // Proceed to the next level to examine the icmp.
- if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
- ExitLimit EL =
- computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsOnlyExit);
- if (EL.hasFullInfo() || !AllowPredicates)
- return EL;
-
- // Try again, but use SCEV predicates this time.
- return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue,
- ControlsOnlyExit,
- /*AllowPredicates=*/true);
- }
-
- // Check for a constant condition. These are normally stripped out by
- // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
- // preserve the CFG and is temporarily leaving constant conditions
- // in place.
- if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
- if (ExitIfTrue == !CI->getZExtValue())
- // The backedge is always taken.
- return getCouldNotCompute();
- // The backedge is never taken.
- return getZero(CI->getType());
- }
-
- // If we're exiting based on the overflow flag of an x.with.overflow intrinsic
- // with a constant step, we can form an equivalent icmp predicate and figure
- // out how many iterations will be taken before we exit.
- const WithOverflowInst *WO;
- const APInt *C;
- if (match(ExitCond, m_ExtractValue<1>(m_WithOverflowInst(WO))) &&
- match(WO->getRHS(), m_APInt(C))) {
- ConstantRange NWR =
- ConstantRange::makeExactNoWrapRegion(WO->getBinaryOp(), *C,
- WO->getNoWrapKind());
- CmpInst::Predicate Pred;
- APInt NewRHSC, Offset;
- NWR.getEquivalentICmp(Pred, NewRHSC, Offset);
- if (!ExitIfTrue)
- Pred = ICmpInst::getInversePredicate(Pred);
- auto *LHS = getSCEV(WO->getLHS());
- if (Offset != 0)
- LHS = getAddExpr(LHS, getConstant(Offset));
- auto EL = computeExitLimitFromICmp(L, Pred, LHS, getConstant(NewRHSC),
- ControlsOnlyExit, AllowPredicates);
- if (EL.hasAnyInfo())
- return EL;
- }
-
- // If it's not an integer or pointer comparison then compute it the hard way.
- return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
-}
-
-std::optional<ScalarEvolution::ExitLimit>
-ScalarEvolution::computeExitLimitFromCondFromBinOp(ExitLimitCacheTy &Cache,
- const Loop *L,
- Value *ExitCond,
- bool ExitIfTrue,
- bool AllowPredicates) {
- // Check if the controlling expression for this loop is an And or Or.
- Value *Op0, *Op1;
- bool IsAnd;
- if (match(ExitCond, m_LogicalAnd(m_Value(Op0), m_Value(Op1))))
- IsAnd = true;
- else if (match(ExitCond, m_LogicalOr(m_Value(Op0), m_Value(Op1))))
- IsAnd = false;
- else
- return std::nullopt;
-
- // A sub-condition of a non-trivial binop never solely controls the exit,
- // whether we exit always depends on both conditions.
- ExitLimit EL0 = computeExitLimitFromCondCached(
- Cache, L, Op0, ExitIfTrue, /*ControlsOnlyExit=*/false, AllowPredicates);
- ExitLimit EL1 = computeExitLimitFromCondCached(
- Cache, L, Op1, ExitIfTrue, /*ControlsOnlyExit=*/false, AllowPredicates);
-
- // EitherMayExit is true in these two cases:
- // br (and Op0 Op1), loop, exit
- // br (or Op0 Op1), exit, loop
- bool EitherMayExit = IsAnd ^ ExitIfTrue;
-
- const SCEV *BECount = getCouldNotCompute();
- const SCEV *ConstantMaxBECount = getCouldNotCompute();
- const SCEV *SymbolicMaxBECount = getCouldNotCompute();
- if (EitherMayExit) {
- bool UseSequentialUMin = !isa<BinaryOperator>(ExitCond);
- // Both conditions must be same for the loop to continue executing.
- // Choose the less conservative count.
- if (EL0.ExactNotTaken != getCouldNotCompute() &&
- EL1.ExactNotTaken != getCouldNotCompute()) {
- BECount = getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken,
- UseSequentialUMin);
- }
- if (EL0.ConstantMaxNotTaken == getCouldNotCompute())
- ConstantMaxBECount = EL1.ConstantMaxNotTaken;
- else if (EL1.ConstantMaxNotTaken == getCouldNotCompute())
- ConstantMaxBECount = EL0.ConstantMaxNotTaken;
- else
- ConstantMaxBECount = getUMinFromMismatchedTypes(EL0.ConstantMaxNotTaken,
- EL1.ConstantMaxNotTaken);
- if (EL0.SymbolicMaxNotTaken == getCouldNotCompute())
- SymbolicMaxBECount = EL1.SymbolicMaxNotTaken;
- else if (EL1.SymbolicMaxNotTaken == getCouldNotCompute())
- SymbolicMaxBECount = EL0.SymbolicMaxNotTaken;
- else
- SymbolicMaxBECount = getUMinFromMismatchedTypes(
- EL0.SymbolicMaxNotTaken, EL1.SymbolicMaxNotTaken, UseSequentialUMin);
- } else {
- // Both conditions must be same at the same time for the loop to exit.
- // For now, be conservative.
- if (EL0.ExactNotTaken == EL1.ExactNotTaken)
- BECount = EL0.ExactNotTaken;
- }
-
- // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
- // to be more aggressive when computing BECount than when computing
- // ConstantMaxBECount. In these cases it is possible for EL0.ExactNotTaken
- // and
- // EL1.ExactNotTaken to match, but for EL0.ConstantMaxNotTaken and
- // EL1.ConstantMaxNotTaken to not.
- if (isa<SCEVCouldNotCompute>(ConstantMaxBECount) &&
- !isa<SCEVCouldNotCompute>(BECount))
- ConstantMaxBECount = getConstant(getUnsignedRangeMax(BECount));
- if (isa<SCEVCouldNotCompute>(SymbolicMaxBECount))
- SymbolicMaxBECount =
- isa<SCEVCouldNotCompute>(BECount) ? ConstantMaxBECount : BECount;
- return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, false,
- {ArrayRef(EL0.Predicates), ArrayRef(EL1.Predicates)});
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(
- const Loop *L, ICmpInst *ExitCond, bool ExitIfTrue, bool ControlsOnlyExit,
- bool AllowPredicates) {
- // If the condition was exit on true, convert the condition to exit on false
- CmpPredicate Pred;
- if (!ExitIfTrue)
- Pred = ExitCond->getCmpPredicate();
- else
- Pred = ExitCond->getInverseCmpPredicate();
- const ICmpInst::Predicate OriginalPred = Pred;
-
- const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
- const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
-
- ExitLimit EL = computeExitLimitFromICmp(L, Pred, LHS, RHS, ControlsOnlyExit,
- AllowPredicates);
- if (EL.hasAnyInfo())
- return EL;
-
- auto *ExhaustiveCount =
- computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
-
- if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
- return ExhaustiveCount;
-
- return computeShiftCompareExitLimit(ExitCond->getOperand(0),
- ExitCond->getOperand(1), L, OriginalPred);
-}
-ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(
- const Loop *L, CmpPredicate Pred, SCEVUse LHS, SCEVUse RHS,
- bool ControlsOnlyExit, bool AllowPredicates) {
-
- // Try to evaluate any dependencies out of the loop.
- LHS = getSCEVAtScope(LHS, L);
- RHS = getSCEVAtScope(RHS, L);
-
- // At this point, we would like to compute how many iterations of the
- // loop the predicate will return true for these inputs.
- if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
- // If there is a loop-invariant, force it into the RHS.
- std::swap(LHS, RHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- }
-
- bool ControllingFiniteLoop = ControlsOnlyExit && loopHasNoAbnormalExits(L) &&
- loopIsFiniteByAssumption(L);
- // Simplify the operands before analyzing them.
- (void)SimplifyICmpOperands(Pred, LHS, RHS, /*Depth=*/0);
-
- // If we have a comparison of a chrec against a constant, try to use value
- // ranges to answer this query.
- if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
- if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
- if (AddRec->getLoop() == L) {
- // Form the constant range.
- ConstantRange CompRange =
- ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
-
- const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
- if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
- }
-
- // If this loop must exit based on this condition (or execute undefined
- // behaviour), see if we can improve wrap flags. This is essentially
- // a must execute style proof.
- if (ControllingFiniteLoop && isLoopInvariant(RHS, L)) {
- // If we can prove the test sequence produced must repeat the same values
- // on self-wrap of the IV, then we can infer that IV doesn't self wrap
- // because if it did, we'd have an infinite (undefined) loop.
- // TODO: We can peel off any functions which are invertible *in L*. Loop
- // invariant terms are effectively constants for our purposes here.
- SCEVUse InnerLHS = LHS;
- if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS))
- InnerLHS = ZExt->getOperand();
- if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(InnerLHS);
- AR && !AR->hasNoSelfWrap() && AR->getLoop() == L && AR->isAffine() &&
- isKnownToBeAPowerOfTwo(AR->getStepRecurrence(*this), /*OrZero=*/true,
- /*OrNegative=*/true)) {
- auto Flags = AR->getNoWrapFlags();
- Flags = setFlags(Flags, SCEV::FlagNW);
- SmallVector<SCEVUse> Operands{AR->operands()};
- Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
- }
-
- // For a slt/ult condition with a positive step, can we prove nsw/nuw?
- // From no-self-wrap, this follows trivially from the fact that every
- // (un)signed-wrapped, but not self-wrapped value must be LT than the
- // last value before (un)signed wrap. Since we know that last value
- // didn't exit, nor will any smaller one.
- if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_ULT) {
- auto WrapType = Pred == ICmpInst::ICMP_SLT ? SCEV::FlagNSW : SCEV::FlagNUW;
- if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS);
- AR && AR->getLoop() == L && AR->isAffine() &&
- !AR->getNoWrapFlags(WrapType) && AR->hasNoSelfWrap() &&
- isKnownPositive(AR->getStepRecurrence(*this))) {
- auto Flags = AR->getNoWrapFlags();
- Flags = setFlags(Flags, WrapType);
- SmallVector<SCEVUse> Operands{AR->operands()};
- Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
- }
- }
- }
-
- switch (Pred) {
- case ICmpInst::ICMP_NE: { // while (X != Y)
- // Convert to: while (X-Y != 0)
- if (LHS->getType()->isPointerTy()) {
- LHS = getPtrToAddrExpr(LHS);
- if (isa<SCEVCouldNotCompute>(LHS))
- return LHS;
- }
- if (RHS->getType()->isPointerTy()) {
- RHS = getPtrToAddrExpr(RHS);
- if (isa<SCEVCouldNotCompute>(RHS))
- return RHS;
- }
- ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsOnlyExit,
- AllowPredicates);
- if (EL.hasAnyInfo())
- return EL;
- break;
- }
- case ICmpInst::ICMP_EQ: { // while (X == Y)
- // Convert to: while (X-Y == 0)
- if (LHS->getType()->isPointerTy()) {
- LHS = getPtrToAddrExpr(LHS);
- if (isa<SCEVCouldNotCompute>(LHS))
- return LHS;
- }
- if (RHS->getType()->isPointerTy()) {
- RHS = getPtrToAddrExpr(RHS);
- if (isa<SCEVCouldNotCompute>(RHS))
- return RHS;
- }
- ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
- if (EL.hasAnyInfo()) return EL;
- break;
- }
- case ICmpInst::ICMP_SLE:
- case ICmpInst::ICMP_ULE:
- // Since the loop is finite, an invariant RHS cannot include the boundary
- // value, otherwise it would loop forever.
- if (!EnableFiniteLoopControl || !ControllingFiniteLoop ||
- !isLoopInvariant(RHS, L)) {
- // Otherwise, perform the addition in a wider type, to avoid overflow.
- // If the LHS is an addrec with the appropriate nowrap flag, the
- // extension will be sunk into it and the exit count can be analyzed.
- auto *OldType = dyn_cast<IntegerType>(LHS->getType());
- if (!OldType)
- break;
- // Prefer doubling the bitwidth over adding a single bit to make it more
- // likely that we use a legal type.
- auto *NewType =
- Type::getIntNTy(OldType->getContext(), OldType->getBitWidth() * 2);
- if (ICmpInst::isSigned(Pred)) {
- LHS = getSignExtendExpr(LHS, NewType);
- RHS = getSignExtendExpr(RHS, NewType);
- } else {
- LHS = getZeroExtendExpr(LHS, NewType);
- RHS = getZeroExtendExpr(RHS, NewType);
- }
- }
- RHS = getAddExpr(getOne(RHS->getType()), RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SLT:
- case ICmpInst::ICMP_ULT: { // while (X < Y)
- bool IsSigned = ICmpInst::isSigned(Pred);
- ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsOnlyExit,
- AllowPredicates);
- if (EL.hasAnyInfo())
- return EL;
- break;
- }
- case ICmpInst::ICMP_SGE:
- case ICmpInst::ICMP_UGE:
- // Since the loop is finite, an invariant RHS cannot include the boundary
- // value, otherwise it would loop forever.
- if (!EnableFiniteLoopControl || !ControllingFiniteLoop ||
- !isLoopInvariant(RHS, L))
- break;
- RHS = getAddExpr(getMinusOne(RHS->getType()), RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SGT:
- case ICmpInst::ICMP_UGT: { // while (X > Y)
- bool IsSigned = ICmpInst::isSigned(Pred);
- ExitLimit EL = howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsOnlyExit,
- AllowPredicates);
- if (EL.hasAnyInfo())
- return EL;
- break;
- }
- default:
- break;
- }
-
- return getCouldNotCompute();
-}
-
-ScalarEvolution::ExitLimit
-ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
- SwitchInst *Switch,
- BasicBlock *ExitingBlock,
- bool ControlsOnlyExit) {
- assert(!L->contains(ExitingBlock) && "Not an exiting block!");
-
- // Give up if the exit is the default dest of a switch.
- if (Switch->getDefaultDest() == ExitingBlock)
- return getCouldNotCompute();
-
- assert(L->contains(Switch->getDefaultDest()) &&
- "Default case must not exit the loop!");
- const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
- const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
-
- // while (X != Y) --> while (X-Y != 0)
- ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsOnlyExit);
- if (EL.hasAnyInfo())
- return EL;
-
- return getCouldNotCompute();
-}
-
-static ConstantInt *
-EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
- ScalarEvolution &SE) {
- const SCEV *InVal = SE.getConstant(C);
- const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
- assert(isa<SCEVConstant>(Val) &&
- "Evaluation of SCEV at constant didn't fold correctly?");
- return cast<SCEVConstant>(Val)->getValue();
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
- Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
- ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
- if (!RHS)
- return getCouldNotCompute();
-
- const BasicBlock *Latch = L->getLoopLatch();
- if (!Latch)
- return getCouldNotCompute();
-
- const BasicBlock *Predecessor = L->getLoopPredecessor();
- if (!Predecessor)
- return getCouldNotCompute();
-
- // Return true if V is of the form "LHS `shift_op` <positive constant>".
- // Return LHS in OutLHS, shift_op in OutOpCode, and the shift amount in
- // OutShiftAmt.
- auto MatchPositiveShift = [](Value *V, Value *&OutLHS,
- Instruction::BinaryOps &OutOpCode,
- unsigned &OutShiftAmt) {
- using namespace PatternMatch;
-
- ConstantInt *ShiftAmt;
- if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
- OutOpCode = Instruction::LShr;
- else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
- OutOpCode = Instruction::AShr;
- else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
- OutOpCode = Instruction::Shl;
- else
- return false;
-
- uint64_t Amt = ShiftAmt->getValue().getLimitedValue();
- if (Amt == 0 || Amt >= OutLHS->getType()->getScalarSizeInBits())
- return false;
- OutShiftAmt = Amt;
- return true;
- };
-
- // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
- //
- // loop:
- // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
- // %iv.shifted = lshr i32 %iv, <positive constant>
- //
- // Return true on a successful match. Return the corresponding PHI node (%iv
- // above) in PNOut, the opcode of the shift operation in OpCodeOut, and the
- // shift amount in ShiftAmtOut.
- auto MatchShiftRecurrence = [&](Value *V, PHINode *&PNOut,
- Instruction::BinaryOps &OpCodeOut,
- unsigned &ShiftAmtOut) {
- std::optional<Instruction::BinaryOps> PostShiftOpCode;
-
- {
- Instruction::BinaryOps OpC;
- Value *V;
- unsigned Amt;
-
- // If we encounter a shift instruction, "peel off" the shift operation,
- // and remember that we did so. Later when we inspect %iv's backedge
- // value, we will make sure that the backedge value uses the same
- // operation.
- //
- // Note: the peeled shift operation does not have to be the same
- // instruction as the one feeding into the PHI's backedge value. We only
- // really care about it being the same *kind* of shift instruction --
- // that's all that is required for our later inferences to hold.
- if (MatchPositiveShift(LHS, V, OpC, Amt)) {
- PostShiftOpCode = OpC;
- LHS = V;
- }
- }
-
- PNOut = dyn_cast<PHINode>(LHS);
- if (!PNOut || PNOut->getParent() != L->getHeader())
- return false;
-
- Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
- Value *OpLHS;
-
- return
- // The backedge value for the PHI node must be a shift by a positive
- // amount
- MatchPositiveShift(BEValue, OpLHS, OpCodeOut, ShiftAmtOut) &&
-
- // of the PHI node itself
- OpLHS == PNOut &&
-
- // and the kind of shift should be match the kind of shift we peeled
- // off, if any.
- (!PostShiftOpCode || *PostShiftOpCode == OpCodeOut);
- };
-
- PHINode *PN;
- Instruction::BinaryOps OpCode;
- unsigned ShiftAmt;
- if (!MatchShiftRecurrence(LHS, PN, OpCode, ShiftAmt))
- return getCouldNotCompute();
-
- const DataLayout &DL = getDataLayout();
-
- // The key rationale for this optimization is that for some kinds of shift
- // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
- // within a finite number of iterations. If the condition guarding the
- // backedge (in the sense that the backedge is taken if the condition is true)
- // is false for the value the shift recurrence stabilizes to, then we know
- // that the backedge is taken only a finite number of times.
-
- ConstantInt *StableValue = nullptr;
- switch (OpCode) {
- default:
- llvm_unreachable("Impossible case!");
-
- case Instruction::AShr: {
- // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
- // bitwidth(K) iterations.
- Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
- KnownBits Known = computeKnownBits(FirstValue, DL, &AC,
- Predecessor->getTerminator(), &DT);
- auto *Ty = cast<IntegerType>(RHS->getType());
- if (Known.isNonNegative())
- StableValue = ConstantInt::get(Ty, 0);
- else if (Known.isNegative())
- StableValue = ConstantInt::get(Ty, -1, true);
- else
- return getCouldNotCompute();
-
- break;
- }
- case Instruction::LShr:
- case Instruction::Shl:
- // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
- // stabilize to 0 in at most bitwidth(K) iterations.
- StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
- break;
- }
-
- auto *Result =
- ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
- assert(Result->getType()->isIntegerTy(1) &&
- "Otherwise cannot be an operand to a branch instruction");
-
- if (Result->isNullValue()) {
- unsigned BitWidth = getTypeSizeInBits(RHS->getType());
- unsigned MaxBTC = BitWidth;
-
- // For right-shift recurrences (lshr/ashr with non-negative start), we can
- // compute a tighter max backedge-taken count from the range of the start
- // value. After k shifts of ShiftAmt, value = start >> (k * ShiftAmt).
- // The value reaches 0 (the stable value) when k * ShiftAmt >=
- // activeBits(start), so max BTC = ceil(activeBits(maxStart) / ShiftAmt).
- if (OpCode == Instruction::LShr || OpCode == Instruction::AShr) {
- Value *StartValue = PN->getIncomingValueForBlock(Predecessor);
- const SCEV *StartSCEV = getSCEV(StartValue);
- APInt MaxStart = getUnsignedRangeMax(StartSCEV);
- if (MaxStart.isStrictlyPositive()) {
- unsigned ActiveBits = MaxStart.getActiveBits();
- unsigned RangeBTC = divideCeil(ActiveBits, ShiftAmt);
- MaxBTC = std::min(MaxBTC, RangeBTC);
- }
- }
-
- const SCEV *UpperBound =
- getConstant(getEffectiveSCEVType(RHS->getType()), MaxBTC);
- return ExitLimit(getCouldNotCompute(), UpperBound, UpperBound, false);
- }
-
- return getCouldNotCompute();
-}
-
-/// Return true if we can constant fold an instruction of the specified type,
-/// assuming that all operands were constants.
-static bool CanConstantFold(const Instruction *I) {
- if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
- isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
- isa<LoadInst>(I) || isa<ExtractValueInst>(I))
- return true;
-
- if (const CallInst *CI = dyn_cast<CallInst>(I))
- if (const Function *F = CI->getCalledFunction())
- return canConstantFoldCallTo(CI, F);
- return false;
-}
-
-/// Determine whether this instruction can constant evolve within this loop
-/// assuming its operands can all constant evolve.
-static bool canConstantEvolve(Instruction *I, const Loop *L) {
- // An instruction outside of the loop can't be derived from a loop PHI.
- if (!L->contains(I)) return false;
-
- if (isa<PHINode>(I)) {
- // We don't currently keep track of the control flow needed to evaluate
- // PHIs, so we cannot handle PHIs inside of loops.
- return L->getHeader() == I->getParent();
- }
-
- // If we won't be able to constant fold this expression even if the operands
- // are constants, bail early.
- return CanConstantFold(I);
-}
-
-/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
-/// recursing through each instruction operand until reaching a loop header phi.
-static PHINode *
-getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
- DenseMap<Instruction *, PHINode *> &PHIMap,
- unsigned Depth) {
- if (Depth > MaxConstantEvolvingDepth)
- return nullptr;
-
- // Otherwise, we can evaluate this instruction if all of its operands are
- // constant or derived from a PHI node themselves.
- PHINode *PHI = nullptr;
- for (Value *Op : UseInst->operands()) {
- if (isa<Constant>(Op)) continue;
-
- Instruction *OpInst = dyn_cast<Instruction>(Op);
- if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
-
- PHINode *P = dyn_cast<PHINode>(OpInst);
- if (!P)
- // If this operand is already visited, reuse the prior result.
- // We may have P != PHI if this is the deepest point at which the
- // inconsistent paths meet.
- P = PHIMap.lookup(OpInst);
- if (!P) {
- // Recurse and memoize the results, whether a phi is found or not.
- // This recursive call invalidates pointers into PHIMap.
- P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
- PHIMap[OpInst] = P;
- }
- if (!P)
- return nullptr; // Not evolving from PHI
- if (PHI && PHI != P)
- return nullptr; // Evolving from multiple different PHIs.
- PHI = P;
- }
- // This is a expression evolving from a constant PHI!
- return PHI;
-}
-
-/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
-/// in the loop that V is derived from. We allow arbitrary operations along the
-/// way, but the operands of an operation must either be constants or a value
-/// derived from a constant PHI. If this expression does not fit with these
-/// constraints, return null.
-static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
- Instruction *I = dyn_cast<Instruction>(V);
- if (!I || !canConstantEvolve(I, L)) return nullptr;
-
- if (PHINode *PN = dyn_cast<PHINode>(I))
- return PN;
-
- // Record non-constant instructions contained by the loop.
- DenseMap<Instruction *, PHINode *> PHIMap;
- return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
-}
-
-/// EvaluateExpression - Given an expression that passes the
-/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
-/// in the loop has the value PHIVal. If we can't fold this expression for some
-/// reason, return null.
-static Constant *EvaluateExpression(Value *V, const Loop *L,
- DenseMap<Instruction *, Constant *> &Vals,
- const DataLayout &DL,
- const TargetLibraryInfo *TLI) {
- // Convenient constant check, but redundant for recursive calls.
- if (Constant *C = dyn_cast<Constant>(V)) return C;
- Instruction *I = dyn_cast<Instruction>(V);
- if (!I) return nullptr;
-
- if (Constant *C = Vals.lookup(I)) return C;
-
- // An instruction inside the loop depends on a value outside the loop that we
- // weren't given a mapping for, or a value such as a call inside the loop.
- if (!canConstantEvolve(I, L)) return nullptr;
-
- // An unmapped PHI can be due to a branch or another loop inside this loop,
- // or due to this not being the initial iteration through a loop where we
- // couldn't compute the evolution of this particular PHI last time.
- if (isa<PHINode>(I)) return nullptr;
-
- std::vector<Constant*> Operands(I->getNumOperands());
-
- for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
- Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
- if (!Operand) {
- Operands[i] = dyn_cast<Constant>(I->getOperand(i));
- if (!Operands[i]) return nullptr;
- continue;
- }
- Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
- Vals[Operand] = C;
- if (!C) return nullptr;
- Operands[i] = C;
- }
-
- return ConstantFoldInstOperands(I, Operands, DL, TLI,
- /*AllowNonDeterministic=*/false);
-}
-
-
-// If every incoming value to PN except the one for BB is a specific Constant,
-// return that, else return nullptr.
-static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
- Constant *IncomingVal = nullptr;
-
- for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
- if (PN->getIncomingBlock(i) == BB)
- continue;
-
- auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
- if (!CurrentVal)
- return nullptr;
-
- if (IncomingVal != CurrentVal) {
- if (IncomingVal)
- return nullptr;
- IncomingVal = CurrentVal;
- }
- }
-
- return IncomingVal;
-}
-
-/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
-/// in the header of its containing loop, we know the loop executes a
-/// constant number of times, and the PHI node is just a recurrence
-/// involving constants, fold it.
-Constant *
-ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
- const APInt &BEs,
- const Loop *L) {
- auto [I, Inserted] = ConstantEvolutionLoopExitValue.try_emplace(PN);
- if (!Inserted)
- return I->second;
-
- if (BEs.ugt(MaxBruteForceIterations))
- return nullptr; // Not going to evaluate it.
-
- Constant *&RetVal = I->second;
-
- DenseMap<Instruction *, Constant *> CurrentIterVals;
- BasicBlock *Header = L->getHeader();
- assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
-
- BasicBlock *Latch = L->getLoopLatch();
- if (!Latch)
- return nullptr;
-
- for (PHINode &PHI : Header->phis()) {
- if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
- CurrentIterVals[&PHI] = StartCST;
- }
- if (!CurrentIterVals.count(PN))
- return RetVal = nullptr;
-
- Value *BEValue = PN->getIncomingValueForBlock(Latch);
-
- // Execute the loop symbolically to determine the exit value.
- assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
- "BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
-
- unsigned NumIterations = BEs.getZExtValue(); // must be in range
- unsigned IterationNum = 0;
- const DataLayout &DL = getDataLayout();
- for (; ; ++IterationNum) {
- if (IterationNum == NumIterations)
- return RetVal = CurrentIterVals[PN]; // Got exit value!
-
- // Compute the value of the PHIs for the next iteration.
- // EvaluateExpression adds non-phi values to the CurrentIterVals map.
- DenseMap<Instruction *, Constant *> NextIterVals;
- Constant *NextPHI =
- EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
- if (!NextPHI)
- return nullptr; // Couldn't evaluate!
- NextIterVals[PN] = NextPHI;
-
- bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
-
- // Also evaluate the other PHI nodes. However, we don't get to stop if we
- // cease to be able to evaluate one of them or if they stop evolving,
- // because that doesn't necessarily prevent us from computing PN.
- SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
- for (const auto &I : CurrentIterVals) {
- PHINode *PHI = dyn_cast<PHINode>(I.first);
- if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
- PHIsToCompute.emplace_back(PHI, I.second);
- }
- // We use two distinct loops because EvaluateExpression may invalidate any
- // iterators into CurrentIterVals.
- for (const auto &I : PHIsToCompute) {
- PHINode *PHI = I.first;
- Constant *&NextPHI = NextIterVals[PHI];
- if (!NextPHI) { // Not already computed.
- Value *BEValue = PHI->getIncomingValueForBlock(Latch);
- NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
- }
- if (NextPHI != I.second)
- StoppedEvolving = false;
- }
-
- // If all entries in CurrentIterVals == NextIterVals then we can stop
- // iterating, the loop can't continue to change.
- if (StoppedEvolving)
- return RetVal = CurrentIterVals[PN];
-
- CurrentIterVals.swap(NextIterVals);
- }
-}
-
-const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
- Value *Cond,
- bool ExitWhen) {
- PHINode *PN = getConstantEvolvingPHI(Cond, L);
- if (!PN) return getCouldNotCompute();
-
- // If the loop is canonicalized, the PHI will have exactly two entries.
- // That's the only form we support here.
- if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
-
- DenseMap<Instruction *, Constant *> CurrentIterVals;
- BasicBlock *Header = L->getHeader();
- assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
-
- BasicBlock *Latch = L->getLoopLatch();
- assert(Latch && "Should follow from NumIncomingValues == 2!");
-
- for (PHINode &PHI : Header->phis()) {
- if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
- CurrentIterVals[&PHI] = StartCST;
- }
- if (!CurrentIterVals.count(PN))
- return getCouldNotCompute();
-
- // Okay, we find a PHI node that defines the trip count of this loop. Execute
- // the loop symbolically to determine when the condition gets a value of
- // "ExitWhen".
- unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
- const DataLayout &DL = getDataLayout();
- for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
- auto *CondVal = dyn_cast_or_null<ConstantInt>(
- EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
-
- // Couldn't symbolically evaluate.
- if (!CondVal) return getCouldNotCompute();
-
- if (CondVal->getValue() == uint64_t(ExitWhen)) {
- ++NumBruteForceTripCountsComputed;
- return getConstant(Type::getInt32Ty(getContext()), IterationNum);
- }
-
- // Update all the PHI nodes for the next iteration.
- DenseMap<Instruction *, Constant *> NextIterVals;
-
- // Create a list of which PHIs we need to compute. We want to do this before
- // calling EvaluateExpression on them because that may invalidate iterators
- // into CurrentIterVals.
- SmallVector<PHINode *, 8> PHIsToCompute;
- for (const auto &I : CurrentIterVals) {
- PHINode *PHI = dyn_cast<PHINode>(I.first);
- if (!PHI || PHI->getParent() != Header) continue;
- PHIsToCompute.push_back(PHI);
- }
- for (PHINode *PHI : PHIsToCompute) {
- Constant *&NextPHI = NextIterVals[PHI];
- if (NextPHI) continue; // Already computed!
-
- Value *BEValue = PHI->getIncomingValueForBlock(Latch);
- NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
- }
- CurrentIterVals.swap(NextIterVals);
- }
-
- // Too many iterations were needed to evaluate.
- return getCouldNotCompute();
-}
-
-const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
- SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
- ValuesAtScopes[V];
- // Check to see if we've folded this expression at this loop before.
- for (auto &LS : Values)
- if (LS.first == L)
- return LS.second ? LS.second : V;
-
- Values.emplace_back(L, nullptr);
-
- // Otherwise compute it.
- const SCEV *C = computeSCEVAtScope(V, L);
- for (auto &LS : reverse(ValuesAtScopes[V]))
- if (LS.first == L) {
- LS.second = C;
- if (!isa<SCEVConstant>(C))
- ValuesAtScopesUsers[C].push_back({L, V});
- break;
- }
- return C;
-}
-
-/// This builds up a Constant using the ConstantExpr interface. That way, we
-/// will return Constants for objects which aren't represented by a
-/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
-/// Returns NULL if the SCEV isn't representable as a Constant.
-static Constant *BuildConstantFromSCEV(const SCEV *V) {
- switch (V->getSCEVType()) {
- case scCouldNotCompute:
- case scAddRecExpr:
- case scVScale:
- return nullptr;
- case scConstant:
- return cast<SCEVConstant>(V)->getValue();
- case scUnknown:
- return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
- case scPtrToAddr: {
- const SCEVPtrToAddrExpr *P2I = cast<SCEVPtrToAddrExpr>(V);
- if (Constant *CastOp = BuildConstantFromSCEV(P2I->getOperand()))
- return ConstantExpr::getPtrToAddr(CastOp, P2I->getType());
-
- return nullptr;
- }
- case scTruncate: {
- const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
- if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
- return ConstantExpr::getTrunc(CastOp, ST->getType());
- return nullptr;
- }
- case scAddExpr: {
- const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
- Constant *C = nullptr;
- for (const SCEV *Op : SA->operands()) {
- Constant *OpC = BuildConstantFromSCEV(Op);
- if (!OpC)
- return nullptr;
- if (!C) {
- C = OpC;
- continue;
- }
- assert(!C->getType()->isPointerTy() &&
- "Can only have one pointer, and it must be last");
- if (OpC->getType()->isPointerTy()) {
- // The offsets have been converted to bytes. We can add bytes using
- // an i8 GEP.
- C = ConstantExpr::getPtrAdd(OpC, C);
- } else {
- C = ConstantExpr::getAdd(C, OpC);
- }
- }
- return C;
- }
- case scMulExpr:
- case scSignExtend:
- case scZeroExtend:
- case scUDivExpr:
- case scSMaxExpr:
- case scUMaxExpr:
- case scSMinExpr:
- case scUMinExpr:
- case scSequentialUMinExpr:
- return nullptr;
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-const SCEV *ScalarEvolution::getWithOperands(const SCEV *S,
- SmallVectorImpl<SCEVUse> &NewOps) {
- switch (S->getSCEVType()) {
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- return getCastExpr(S->getSCEVType(), NewOps[0], S->getType());
- case scAddRecExpr: {
- auto *AddRec = cast<SCEVAddRecExpr>(S);
- return getAddRecExpr(NewOps, AddRec->getLoop(), AddRec->getNoWrapFlags());
- }
- case scAddExpr:
- return getAddExpr(NewOps, cast<SCEVAddExpr>(S)->getNoWrapFlags());
- case scMulExpr:
- return getMulExpr(NewOps, cast<SCEVMulExpr>(S)->getNoWrapFlags());
- case scUDivExpr:
- return getUDivExpr(NewOps[0], NewOps[1]);
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- return getMinMaxExpr(S->getSCEVType(), NewOps);
- case scSequentialUMinExpr:
- return getSequentialMinMaxExpr(S->getSCEVType(), NewOps);
- case scConstant:
- case scVScale:
- case scUnknown:
- return S;
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
- switch (V->getSCEVType()) {
- case scConstant:
- case scVScale:
- return V;
- case scAddRecExpr: {
- // If this is a loop recurrence for a loop that does not contain L, then we
- // are dealing with the final value computed by the loop.
- const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(V);
- // First, attempt to evaluate each operand.
- // Avoid performing the look-up in the common case where the specified
- // expression has no loop-variant portions.
- for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
- const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
- if (OpAtScope == AddRec->getOperand(i))
- continue;
-
- // Okay, at least one of these operands is loop variant but might be
- // foldable. Build a new instance of the folded commutative expression.
- SmallVector<SCEVUse, 8> NewOps;
- NewOps.reserve(AddRec->getNumOperands());
- append_range(NewOps, AddRec->operands().take_front(i));
- NewOps.push_back(OpAtScope);
- for (++i; i != e; ++i)
- NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
-
- const SCEV *FoldedRec = getAddRecExpr(
- NewOps, AddRec->getLoop(), AddRec->getNoWrapFlags(SCEV::FlagNW));
- AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
- // The addrec may be folded to a nonrecurrence, for example, if the
- // induction variable is multiplied by zero after constant folding. Go
- // ahead and return the folded value.
- if (!AddRec)
- return FoldedRec;
- break;
- }
-
- // If the scope is outside the addrec's loop, evaluate it by using the
- // loop exit value of the addrec.
- if (!AddRec->getLoop()->contains(L)) {
- // To evaluate this recurrence, we need to know how many times the AddRec
- // loop iterates. Compute this now.
- const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
- if (BackedgeTakenCount == getCouldNotCompute())
- return AddRec;
-
- // Then, evaluate the AddRec.
- return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
- }
-
- return AddRec;
- }
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- case scAddExpr:
- case scMulExpr:
- case scUDivExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr: {
- ArrayRef<SCEVUse> Ops = V->operands();
- // Avoid performing the look-up in the common case where the specified
- // expression has no loop-variant portions.
- for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
- const SCEV *OpAtScope = getSCEVAtScope(Ops[i].getPointer(), L);
- if (OpAtScope != Ops[i].getPointer()) {
- // Okay, at least one of these operands is loop variant but might be
- // foldable. Build a new instance of the folded commutative expression.
- SmallVector<SCEVUse, 8> NewOps;
- NewOps.reserve(Ops.size());
- append_range(NewOps, Ops.take_front(i));
- NewOps.push_back(OpAtScope);
-
- for (++i; i != e; ++i) {
- OpAtScope = getSCEVAtScope(Ops[i].getPointer(), L);
- NewOps.push_back(OpAtScope);
- }
-
- return getWithOperands(V, NewOps);
- }
- }
- // If we got here, all operands are loop invariant.
- return V;
- }
- case scUnknown: {
- // If this instruction is evolved from a constant-evolving PHI, compute the
- // exit value from the loop without using SCEVs.
- const SCEVUnknown *SU = cast<SCEVUnknown>(V);
- Instruction *I = dyn_cast<Instruction>(SU->getValue());
- if (!I)
- return V; // This is some other type of SCEVUnknown, just return it.
-
- if (PHINode *PN = dyn_cast<PHINode>(I)) {
- const Loop *CurrLoop = this->LI[I->getParent()];
- // Looking for loop exit value.
- if (CurrLoop && CurrLoop->getParentLoop() == L &&
- PN->getParent() == CurrLoop->getHeader()) {
- // Okay, there is no closed form solution for the PHI node. Check
- // to see if the loop that contains it has a known backedge-taken
- // count. If so, we may be able to force computation of the exit
- // value.
- const SCEV *BackedgeTakenCount = getBackedgeTakenCount(CurrLoop);
- // This trivial case can show up in some degenerate cases where
- // the incoming IR has not yet been fully simplified.
- if (BackedgeTakenCount->isZero()) {
- Value *InitValue = nullptr;
- bool MultipleInitValues = false;
- for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
- if (!CurrLoop->contains(PN->getIncomingBlock(i))) {
- if (!InitValue)
- InitValue = PN->getIncomingValue(i);
- else if (InitValue != PN->getIncomingValue(i)) {
- MultipleInitValues = true;
- break;
- }
- }
- }
- if (!MultipleInitValues && InitValue)
- return getSCEV(InitValue);
- }
- // Do we have a loop invariant value flowing around the backedge
- // for a loop which must execute the backedge?
- if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
- isKnownNonZero(BackedgeTakenCount) &&
- PN->getNumIncomingValues() == 2) {
-
- unsigned InLoopPred =
- CurrLoop->contains(PN->getIncomingBlock(0)) ? 0 : 1;
- Value *BackedgeVal = PN->getIncomingValue(InLoopPred);
- if (CurrLoop->isLoopInvariant(BackedgeVal))
- return getSCEV(BackedgeVal);
- }
- if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
- // Okay, we know how many times the containing loop executes. If
- // this is a constant evolving PHI node, get the final value at
- // the specified iteration number.
- Constant *RV =
- getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), CurrLoop);
- if (RV)
- return getSCEV(RV);
- }
- }
- }
-
- // Okay, this is an expression that we cannot symbolically evaluate
- // into a SCEV. Check to see if it's possible to symbolically evaluate
- // the arguments into constants, and if so, try to constant propagate the
- // result. This is particularly useful for computing loop exit values.
- if (!CanConstantFold(I))
- return V; // This is some other type of SCEVUnknown, just return it.
-
- SmallVector<Constant *, 4> Operands;
- Operands.reserve(I->getNumOperands());
- bool MadeImprovement = false;
- for (Value *Op : I->operands()) {
- if (Constant *C = dyn_cast<Constant>(Op)) {
- Operands.push_back(C);
- continue;
- }
-
- // If any of the operands is non-constant and if they are
- // non-integer and non-pointer, don't even try to analyze them
- // with scev techniques.
- if (!isSCEVable(Op->getType()))
- return V;
-
- const SCEV *OrigV = getSCEV(Op);
- const SCEV *OpV = getSCEVAtScope(OrigV, L);
- MadeImprovement |= OrigV != OpV;
-
- Constant *C = BuildConstantFromSCEV(OpV);
- if (!C)
- return V;
- assert(C->getType() == Op->getType() && "Type mismatch");
- Operands.push_back(C);
- }
-
- // Check to see if getSCEVAtScope actually made an improvement.
- if (!MadeImprovement)
- return V; // This is some other type of SCEVUnknown, just return it.
-
- Constant *C = nullptr;
- const DataLayout &DL = getDataLayout();
- C = ConstantFoldInstOperands(I, Operands, DL, &TLI,
- /*AllowNonDeterministic=*/false);
- if (!C)
- return V;
- return getSCEV(C);
- }
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV type!");
-}
-
-const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
- return getSCEVAtScope(getSCEV(V), L);
-}
-
-const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
- if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
- return stripInjectiveFunctions(ZExt->getOperand());
- if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
- return stripInjectiveFunctions(SExt->getOperand());
- return S;
-}
-
-/// Finds the minimum unsigned root of the following equation:
-///
-/// A * X = B (mod N)
-///
-/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
-/// A and B isn't important.
-///
-/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
-static const SCEV *
-SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
- SmallVectorImpl<const SCEVPredicate *> *Predicates,
- ScalarEvolution &SE, const Loop *L) {
- uint32_t BW = A.getBitWidth();
- assert(BW == SE.getTypeSizeInBits(B->getType()));
- assert(A != 0 && "A must be non-zero.");
-
- // 1. D = gcd(A, N)
- //
- // The gcd of A and N may have only one prime factor: 2. The number of
- // trailing zeros in A is its multiplicity
- uint32_t Mult2 = A.countr_zero();
- // D = 2^Mult2
-
- // 2. Check if B is divisible by D.
- //
- // B is divisible by D if and only if the multiplicity of prime factor 2 for B
- // is not less than multiplicity of this prime factor for D.
- unsigned MinTZ = SE.getMinTrailingZeros(B);
- // Try again with the terminator of the loop predecessor for context-specific
- // result, if MinTZ s too small.
- if (MinTZ < Mult2 && L->getLoopPredecessor())
- MinTZ = SE.getMinTrailingZeros(B, L->getLoopPredecessor()->getTerminator());
- if (MinTZ < Mult2) {
- // Check if we can prove there's no remainder using URem.
- const SCEV *URem =
- SE.getURemExpr(B, SE.getConstant(APInt::getOneBitSet(BW, Mult2)));
- const SCEV *Zero = SE.getZero(B->getType());
- if (!SE.isKnownPredicate(CmpInst::ICMP_EQ, URem, Zero)) {
- // Try to add a predicate ensuring B is a multiple of 1 << Mult2.
- if (!Predicates)
- return SE.getCouldNotCompute();
-
- // Avoid adding a predicate that is known to be false.
- if (SE.isKnownPredicate(CmpInst::ICMP_NE, URem, Zero))
- return SE.getCouldNotCompute();
- Predicates->push_back(SE.getEqualPredicate(URem, Zero));
- }
- }
-
- // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
- // modulo (N / D).
- //
- // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
- // (N / D) in general. The inverse itself always fits into BW bits, though,
- // so we immediately truncate it.
- APInt AD = A.lshr(Mult2).trunc(BW - Mult2); // AD = A / D
- APInt I = AD.multiplicativeInverse().zext(BW);
-
- // 4. Compute the minimum unsigned root of the equation:
- // I * (B / D) mod (N / D)
- // To simplify the computation, we factor out the divide by D:
- // (I * B mod N) / D
- const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
- return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
-}
-
-/// For a given quadratic addrec, generate coefficients of the corresponding
-/// quadratic equation, multiplied by a common value to ensure that they are
-/// integers.
-/// The returned value is a tuple { A, B, C, M, BitWidth }, where
-/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
-/// were multiplied by, and BitWidth is the bit width of the original addrec
-/// coefficients.
-/// This function returns std::nullopt if the addrec coefficients are not
-/// compile- time constants.
-static std::optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
-GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
- assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
- const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
- const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
- const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
- LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
- << *AddRec << '\n');
-
- // We currently can only solve this if the coefficients are constants.
- if (!LC || !MC || !NC) {
- LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
- return std::nullopt;
- }
-
- APInt L = LC->getAPInt();
- APInt M = MC->getAPInt();
- APInt N = NC->getAPInt();
- assert(!N.isZero() && "This is not a quadratic addrec");
-
- unsigned BitWidth = LC->getAPInt().getBitWidth();
- unsigned NewWidth = BitWidth + 1;
- LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
- << BitWidth << '\n');
- // The sign-extension (as opposed to a zero-extension) here matches the
- // extension used in SolveQuadraticEquationWrap (with the same motivation).
- N = N.sext(NewWidth);
- M = M.sext(NewWidth);
- L = L.sext(NewWidth);
-
- // The increments are M, M+N, M+2N, ..., so the accumulated values are
- // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
- // L+M, L+2M+N, L+3M+3N, ...
- // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
- //
- // The equation Acc = 0 is then
- // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
- // In a quadratic form it becomes:
- // N n^2 + (2M-N) n + 2L = 0.
-
- APInt A = N;
- APInt B = 2 * M - A;
- APInt C = 2 * L;
- APInt T = APInt(NewWidth, 2);
- LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
- << "x + " << C << ", coeff bw: " << NewWidth
- << ", multiplied by " << T << '\n');
- return std::make_tuple(A, B, C, T, BitWidth);
-}
-
-/// Helper function to compare optional APInts:
-/// (a) if X and Y both exist, return min(X, Y),
-/// (b) if neither X nor Y exist, return std::nullopt,
-/// (c) if exactly one of X and Y exists, return that value.
-static std::optional<APInt> MinOptional(std::optional<APInt> X,
- std::optional<APInt> Y) {
- if (X && Y) {
- unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
- APInt XW = X->sext(W);
- APInt YW = Y->sext(W);
- return XW.slt(YW) ? *X : *Y;
- }
- if (!X && !Y)
- return std::nullopt;
- return X ? *X : *Y;
-}
-
-/// Helper function to truncate an optional APInt to a given BitWidth.
-/// When solving addrec-related equations, it is preferable to return a value
-/// that has the same bit width as the original addrec's coefficients. If the
-/// solution fits in the original bit width, truncate it (except for i1).
-/// Returning a value of a different bit width may inhibit some optimizations.
-///
-/// In general, a solution to a quadratic equation generated from an addrec
-/// may require BW+1 bits, where BW is the bit width of the addrec's
-/// coefficients. The reason is that the coefficients of the quadratic
-/// equation are BW+1 bits wide (to avoid truncation when converting from
-/// the addrec to the equation).
-static std::optional<APInt> TruncIfPossible(std::optional<APInt> X,
- unsigned BitWidth) {
- if (!X)
- return std::nullopt;
- unsigned W = X->getBitWidth();
- if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
- return X->trunc(BitWidth);
- return X;
-}
-
-/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
-/// iterations. The values L, M, N are assumed to be signed, and they
-/// should all have the same bit widths.
-/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
-/// where BW is the bit width of the addrec's coefficients.
-/// If the calculated value is a BW-bit integer (for BW > 1), it will be
-/// returned as such, otherwise the bit width of the returned value may
-/// be greater than BW.
-///
-/// This function returns std::nullopt if
-/// (a) the addrec coefficients are not constant, or
-/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
-/// like x^2 = 5, no integer solutions exist, in other cases an integer
-/// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
-static std::optional<APInt>
-SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
- APInt A, B, C, M;
- unsigned BitWidth;
- auto T = GetQuadraticEquation(AddRec);
- if (!T)
- return std::nullopt;
-
- std::tie(A, B, C, M, BitWidth) = *T;
- LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
- std::optional<APInt> X =
- APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth + 1);
- if (!X)
- return std::nullopt;
-
- ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
- ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
- if (!V->isZero())
- return std::nullopt;
-
- return TruncIfPossible(X, BitWidth);
-}
-
-/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
-/// iterations. The values M, N are assumed to be signed, and they
-/// should all have the same bit widths.
-/// Find the least n such that c(n) does not belong to the given range,
-/// while c(n-1) does.
-///
-/// This function returns std::nullopt if
-/// (a) the addrec coefficients are not constant, or
-/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
-/// bounds of the range.
-static std::optional<APInt>
-SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
- const ConstantRange &Range, ScalarEvolution &SE) {
- assert(AddRec->getOperand(0)->isZero() &&
- "Starting value of addrec should be 0");
- LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
- << Range << ", addrec " << *AddRec << '\n');
- // This case is handled in getNumIterationsInRange. Here we can assume that
- // we start in the range.
- assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
- "Addrec's initial value should be in range");
-
- APInt A, B, C, M;
- unsigned BitWidth;
- auto T = GetQuadraticEquation(AddRec);
- if (!T)
- return std::nullopt;
-
- // Be careful about the return value: there can be two reasons for not
- // returning an actual number. First, if no solutions to the equations
- // were found, and second, if the solutions don't leave the given range.
- // The first case means that the actual solution is "unknown", the second
- // means that it's known, but not valid. If the solution is unknown, we
- // cannot make any conclusions.
- // Return a pair: the optional solution and a flag indicating if the
- // solution was found.
- auto SolveForBoundary =
- [&](APInt Bound) -> std::pair<std::optional<APInt>, bool> {
- // Solve for signed overflow and unsigned overflow, pick the lower
- // solution.
- LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
- << Bound << " (before multiplying by " << M << ")\n");
- Bound *= M; // The quadratic equation multiplier.
-
- std::optional<APInt> SO;
- if (BitWidth > 1) {
- LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
- "signed overflow\n");
- SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
- }
- LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
- "unsigned overflow\n");
- std::optional<APInt> UO =
- APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth + 1);
-
- auto LeavesRange = [&] (const APInt &X) {
- ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
- ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
- if (Range.contains(V0->getValue()))
- return false;
- // X should be at least 1, so X-1 is non-negative.
- ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
- ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
- if (Range.contains(V1->getValue()))
- return true;
- return false;
- };
-
- // If SolveQuadraticEquationWrap returns std::nullopt, it means that there
- // can be a solution, but the function failed to find it. We cannot treat it
- // as "no solution".
- if (!SO || !UO)
- return {std::nullopt, false};
-
- // Check the smaller value first to see if it leaves the range.
- // At this point, both SO and UO must have values.
- std::optional<APInt> Min = MinOptional(SO, UO);
- if (LeavesRange(*Min))
- return { Min, true };
- std::optional<APInt> Max = Min == SO ? UO : SO;
- if (LeavesRange(*Max))
- return { Max, true };
-
- // Solutions were found, but were eliminated, hence the "true".
- return {std::nullopt, true};
- };
-
- std::tie(A, B, C, M, BitWidth) = *T;
- // Lower bound is inclusive, subtract 1 to represent the exiting value.
- APInt Lower = Range.getLower().sext(A.getBitWidth()) - 1;
- APInt Upper = Range.getUpper().sext(A.getBitWidth());
- auto SL = SolveForBoundary(Lower);
- auto SU = SolveForBoundary(Upper);
- // If any of the solutions was unknown, no meaninigful conclusions can
- // be made.
- if (!SL.second || !SU.second)
- return std::nullopt;
-
- // Claim: The correct solution is not some value between Min and Max.
- //
- // Justification: Assuming that Min and Max are different values, one of
- // them is when the first signed overflow happens, the other is when the
- // first unsigned overflow happens. Crossing the range boundary is only
- // possible via an overflow (treating 0 as a special case of it, modeling
- // an overflow as crossing k*2^W for some k).
- //
- // The interesting case here is when Min was eliminated as an invalid
- // solution, but Max was not. The argument is that if there was another
- // overflow between Min and Max, it would also have been eliminated if
- // it was considered.
- //
- // For a given boundary, it is possible to have two overflows of the same
- // type (signed/unsigned) without having the other type in between: this
- // can happen when the vertex of the parabola is between the iterations
- // corresponding to the overflows. This is only possible when the two
- // overflows cross k*2^W for the same k. In such case, if the second one
- // left the range (and was the first one to do so), the first overflow
- // would have to enter the range, which would mean that either we had left
- // the range before or that we started outside of it. Both of these cases
- // are contradictions.
- //
- // Claim: In the case where SolveForBoundary returns std::nullopt, the correct
- // solution is not some value between the Max for this boundary and the
- // Min of the other boundary.
- //
- // Justification: Assume that we had such Max_A and Min_B corresponding
- // to range boundaries A and B and such that Max_A < Min_B. If there was
- // a solution between Max_A and Min_B, it would have to be caused by an
- // overflow corresponding to either A or B. It cannot correspond to B,
- // since Min_B is the first occurrence of such an overflow. If it
- // corresponded to A, it would have to be either a signed or an unsigned
- // overflow that is larger than both eliminated overflows for A. But
- // between the eliminated overflows and this overflow, the values would
- // cover the entire value space, thus crossing the other boundary, which
- // is a contradiction.
-
- return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::howFarToZero(const SCEV *V,
- const Loop *L,
- bool ControlsOnlyExit,
- bool AllowPredicates) {
-
- // This is only used for loops with a "x != y" exit test. The exit condition
- // is now expressed as a single expression, V = x-y. So the exit test is
- // effectively V != 0. We know and take advantage of the fact that this
- // expression only being used in a comparison by zero context.
-
- SmallVector<const SCEVPredicate *> Predicates;
- // If the value is a constant
- if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
- // If the value is already zero, the branch will execute zero times.
- if (C->getValue()->isZero()) return C;
- return getCouldNotCompute(); // Otherwise it will loop infinitely.
- }
-
- const SCEVAddRecExpr *AddRec =
- dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
-
- if (!AddRec && AllowPredicates)
- // Try to make this an AddRec using runtime tests, in the first X
- // iterations of this loop, where X is the SCEV expression found by the
- // algorithm below.
- AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
-
- if (!AddRec || AddRec->getLoop() != L)
- return getCouldNotCompute();
-
- // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
- // the quadratic equation to solve it.
- if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
- // We can only use this value if the chrec ends up with an exact zero
- // value at this index. When solving for "X*X != 5", for example, we
- // should not accept a root of 2.
- if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
- const auto *R = cast<SCEVConstant>(getConstant(*S));
- return ExitLimit(R, R, R, false, Predicates);
- }
- return getCouldNotCompute();
- }
-
- // Otherwise we can only handle this if it is affine.
- if (!AddRec->isAffine())
- return getCouldNotCompute();
-
- // If this is an affine expression, the execution count of this branch is
- // the minimum unsigned root of the following equation:
- //
- // Start + Step*N = 0 (mod 2^BW)
- //
- // equivalent to:
- //
- // Step*N = -Start (mod 2^BW)
- //
- // where BW is the common bit width of Start and Step.
-
- // Get the initial value for the loop.
- const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
- const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
-
- if (!isLoopInvariant(Step, L))
- return getCouldNotCompute();
-
- LoopGuards Guards = LoopGuards::collect(L, *this);
- // Specialize step for this loop so we get context sensitive facts below.
- const SCEV *StepWLG = applyLoopGuards(Step, Guards);
-
- // For positive steps (counting up until unsigned overflow):
- // N = -Start/Step (as unsigned)
- // For negative steps (counting down to zero):
- // N = Start/-Step
- // First compute the unsigned distance from zero in the direction of Step.
- bool CountDown = isKnownNegative(StepWLG);
- if (!CountDown && !isKnownNonNegative(StepWLG))
- return getCouldNotCompute();
-
- const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
- // Handle unitary steps, which cannot wraparound.
- // 1*N = -Start; -1*N = Start (mod 2^BW), so:
- // N = Distance (as unsigned)
-
- if (match(Step, m_CombineOr(m_scev_One(), m_scev_AllOnes()))) {
- APInt MaxBECount = getUnsignedRangeMax(applyLoopGuards(Distance, Guards));
- MaxBECount = APIntOps::umin(MaxBECount, getUnsignedRangeMax(Distance));
-
- // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
- // we end up with a loop whose backedge-taken count is n - 1. Detect this
- // case, and see if we can improve the bound.
- //
- // Explicitly handling this here is necessary because getUnsignedRange
- // isn't context-sensitive; it doesn't know that we only care about the
- // range inside the loop.
- const SCEV *Zero = getZero(Distance->getType());
- const SCEV *One = getOne(Distance->getType());
- const SCEV *DistancePlusOne = getAddExpr(Distance, One);
- if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
- // If Distance + 1 doesn't overflow, we can compute the maximum distance
- // as "unsigned_max(Distance + 1) - 1".
- ConstantRange CR = getUnsignedRange(DistancePlusOne);
- MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
- }
- return ExitLimit(Distance, getConstant(MaxBECount), Distance, false,
- Predicates);
- }
-
- // If the condition controls loop exit (the loop exits only if the expression
- // is true) and the addition is no-wrap we can use unsigned divide to
- // compute the backedge count. In this case, the step may not divide the
- // distance, but we don't care because if the condition is "missed" the loop
- // will have undefined behavior due to wrapping.
- if (ControlsOnlyExit && AddRec->hasNoSelfWrap() &&
- loopHasNoAbnormalExits(AddRec->getLoop())) {
-
- // If the stride is zero and the start is non-zero, the loop must be
- // infinite. In C++, most loops are finite by assumption, in which case the
- // step being zero implies UB must execute if the loop is entered.
- if (!(loopIsFiniteByAssumption(L) && isKnownNonZero(Start)) &&
- !isKnownNonZero(StepWLG))
- return getCouldNotCompute();
-
- const SCEV *Exact =
- getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
- const SCEV *ConstantMax = getCouldNotCompute();
- if (Exact != getCouldNotCompute()) {
- APInt MaxInt = getUnsignedRangeMax(applyLoopGuards(Exact, Guards));
- ConstantMax =
- getConstant(APIntOps::umin(MaxInt, getUnsignedRangeMax(Exact)));
- }
- const SCEV *SymbolicMax =
- isa<SCEVCouldNotCompute>(Exact) ? ConstantMax : Exact;
- return ExitLimit(Exact, ConstantMax, SymbolicMax, false, Predicates);
- }
-
- // Solve the general equation.
- const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
- if (!StepC || StepC->getValue()->isZero())
- return getCouldNotCompute();
- const SCEV *E = SolveLinEquationWithOverflow(
- StepC->getAPInt(), getNegativeSCEV(Start),
- AllowPredicates ? &Predicates : nullptr, *this, L);
-
- const SCEV *M = E;
- if (E != getCouldNotCompute()) {
- APInt MaxWithGuards = getUnsignedRangeMax(applyLoopGuards(E, Guards));
- M = getConstant(APIntOps::umin(MaxWithGuards, getUnsignedRangeMax(E)));
- }
- auto *S = isa<SCEVCouldNotCompute>(E) ? M : E;
- return ExitLimit(E, M, S, false, Predicates);
-}
-
-ScalarEvolution::ExitLimit
-ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
- // Loops that look like: while (X == 0) are very strange indeed. We don't
- // handle them yet except for the trivial case. This could be expanded in the
- // future as needed.
-
- // If the value is a constant, check to see if it is known to be non-zero
- // already. If so, the backedge will execute zero times.
- if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
- if (!C->getValue()->isZero())
- return getZero(C->getType());
- return getCouldNotCompute(); // Otherwise it will loop infinitely.
- }
-
- // We could implement others, but I really doubt anyone writes loops like
- // this, and if they did, they would already be constant folded.
- return getCouldNotCompute();
-}
-
-std::pair<const BasicBlock *, const BasicBlock *>
-ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB)
- const {
- // If the block has a unique predecessor, then there is no path from the
- // predecessor to the block that does not go through the direct edge
- // from the predecessor to the block.
- if (const BasicBlock *Pred = BB->getSinglePredecessor())
- return {Pred, BB};
-
- // A loop's header is defined to be a block that dominates the loop.
- // If the header has a unique predecessor outside the loop, it must be
- // a block that has exactly one successor that can reach the loop.
- if (const Loop *L = LI.getLoopFor(BB))
- return {L->getLoopPredecessor(), L->getHeader()};
-
- return {nullptr, BB};
-}
-
-/// SCEV structural equivalence is usually sufficient for testing whether two
-/// expressions are equal, however for the purposes of looking for a condition
-/// guarding a loop, it can be useful to be a little more general, since a
-/// front-end may have replicated the controlling expression.
-static bool HasSameValue(const SCEV *A, const SCEV *B) {
- // Quick check to see if they are the same SCEV.
- if (A == B) return true;
-
- auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
- // Not all instructions that are "identical" compute the same value. For
- // instance, two distinct alloca instructions allocating the same type are
- // identical and do not read memory; but compute distinct values.
- return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
- };
-
- // Otherwise, if they're both SCEVUnknown, it's possible that they hold
- // two different instructions with the same value. Check for this case.
- if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
- if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
- if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
- if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
- if (ComputesEqualValues(AI, BI))
- return true;
-
- // Otherwise assume they may have a different value.
- return false;
-}
-
-static bool MatchBinarySub(const SCEV *S, SCEVUse &LHS, SCEVUse &RHS) {
- const SCEV *Op0, *Op1;
- if (!match(S, m_scev_Add(m_SCEV(Op0), m_SCEV(Op1))))
- return false;
- if (match(Op0, m_scev_Mul(m_scev_AllOnes(), m_SCEV(RHS)))) {
- LHS = Op1;
- return true;
- }
- if (match(Op1, m_scev_Mul(m_scev_AllOnes(), m_SCEV(RHS)))) {
- LHS = Op0;
- return true;
- }
- return false;
-}
-
-bool ScalarEvolution::SimplifyICmpOperands(CmpPredicate &Pred, SCEVUse &LHS,
- SCEVUse &RHS, unsigned Depth) {
- bool Changed = false;
- // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
- // '0 != 0'.
- auto TrivialCase = [&](bool TriviallyTrue) {
- LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
- Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
- return true;
- };
- // If we hit the max recursion limit bail out.
- if (Depth >= 3)
- return false;
-
- const SCEV *NewLHS, *NewRHS;
- if (match(LHS, m_scev_c_Mul(m_SCEV(NewLHS), m_SCEVVScale())) &&
- match(RHS, m_scev_c_Mul(m_SCEV(NewRHS), m_SCEVVScale()))) {
- const SCEVMulExpr *LMul = cast<SCEVMulExpr>(LHS);
- const SCEVMulExpr *RMul = cast<SCEVMulExpr>(RHS);
-
- // (X * vscale) pred (Y * vscale) ==> X pred Y
- // when both multiples are NSW.
- // (X * vscale) uicmp/eq/ne (Y * vscale) ==> X uicmp/eq/ne Y
- // when both multiples are NUW.
- if ((LMul->hasNoSignedWrap() && RMul->hasNoSignedWrap()) ||
- (LMul->hasNoUnsignedWrap() && RMul->hasNoUnsignedWrap() &&
- !ICmpInst::isSigned(Pred))) {
- LHS = NewLHS;
- RHS = NewRHS;
- Changed = true;
- }
- }
-
- // Canonicalize a constant to the right side.
- if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
- // Check for both operands constant.
- if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
- if (!ICmpInst::compare(LHSC->getAPInt(), RHSC->getAPInt(), Pred))
- return TrivialCase(false);
- return TrivialCase(true);
- }
- // Otherwise swap the operands to put the constant on the right.
- std::swap(LHS, RHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- Changed = true;
- }
-
- // (K + A) pred (K + B) --> A pred B
- // For equality, no flags are needed.
- // For signed, both adds must be NSW. For unsigned, both must be NUW.
- {
- const SCEVConstant *C = nullptr;
- if (match(LHS, m_scev_Add(m_SCEVConstant(C), m_SCEV(NewLHS))) &&
- match(RHS, m_scev_Add(m_scev_Specific(C), m_SCEV(NewRHS)))) {
- const auto *LAdd = cast<SCEVAddExpr>(LHS);
- const auto *RAdd = cast<SCEVAddExpr>(RHS);
- if (ICmpInst::isEquality(Pred) ||
- (ICmpInst::isSigned(Pred) && LAdd->hasNoSignedWrap() &&
- RAdd->hasNoSignedWrap()) ||
- (ICmpInst::isUnsigned(Pred) && LAdd->hasNoUnsignedWrap() &&
- RAdd->hasNoUnsignedWrap())) {
- LHS = NewLHS;
- RHS = NewRHS;
- Changed = true;
- }
- }
- }
-
- // (C * A) pred (C * B) --> A pred B
- // For equality predicates, both muls must be NUW or both must be NSW
- // (either suffices to make multiplication by C injective; C == 0 is
- // impossible because SCEV folds 0 * X to 0).
- // For signed ordering, C must be positive and both muls must be NSW.
- // For unsigned ordering, both muls must be NUW.
- {
- const SCEVConstant *C = nullptr;
- if (match(LHS, m_scev_Mul(m_SCEVConstant(C), m_SCEV(NewLHS))) &&
- match(RHS, m_scev_Mul(m_scev_Specific(C), m_SCEV(NewRHS)))) {
- const auto *LMul = cast<SCEVMulExpr>(LHS);
- const auto *RMul = cast<SCEVMulExpr>(RHS);
- bool BothNUW = LMul->hasNoUnsignedWrap() && RMul->hasNoUnsignedWrap();
- bool BothNSW = LMul->hasNoSignedWrap() && RMul->hasNoSignedWrap();
- if ((ICmpInst::isEquality(Pred) && (BothNUW || BothNSW)) ||
- (ICmpInst::isSigned(Pred) && BothNSW &&
- C->getAPInt().isStrictlyPositive()) ||
- (ICmpInst::isUnsigned(Pred) && BothNUW)) {
- LHS = NewLHS;
- RHS = NewRHS;
- Changed = true;
- }
- }
- }
-
- // If we're comparing an addrec with a value which is loop-invariant in the
- // addrec's loop, put the addrec on the left. Also make a dominance check,
- // as both operands could be addrecs loop-invariant in each other's loop.
- if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
- const Loop *L = AR->getLoop();
- if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
- std::swap(LHS, RHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- Changed = true;
- }
- }
-
- // If there's a constant operand, canonicalize comparisons with boundary
- // cases, and canonicalize *-or-equal comparisons to regular comparisons.
- if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
- const APInt &RA = RC->getAPInt();
-
- bool SimplifiedByConstantRange = false;
-
- if (!ICmpInst::isEquality(Pred)) {
- ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
- if (ExactCR.isFullSet())
- return TrivialCase(true);
- if (ExactCR.isEmptySet())
- return TrivialCase(false);
-
- APInt NewRHS;
- CmpInst::Predicate NewPred;
- if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
- ICmpInst::isEquality(NewPred)) {
- // We were able to convert an inequality to an equality.
- Pred = NewPred;
- RHS = getConstant(NewRHS);
- Changed = SimplifiedByConstantRange = true;
- }
- }
-
- if (!SimplifiedByConstantRange) {
- switch (Pred) {
- default:
- break;
- case ICmpInst::ICMP_EQ:
- case ICmpInst::ICMP_NE:
- // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
- if (RA.isZero() && MatchBinarySub(LHS, LHS, RHS))
- Changed = true;
- break;
-
- // The "Should have been caught earlier!" messages refer to the fact
- // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
- // should have fired on the corresponding cases, and canonicalized the
- // check to trivial case.
-
- case ICmpInst::ICMP_UGE:
- assert(!RA.isMinValue() && "Should have been caught earlier!");
- Pred = ICmpInst::ICMP_UGT;
- RHS = getConstant(RA - 1);
- Changed = true;
- break;
- case ICmpInst::ICMP_ULE:
- assert(!RA.isMaxValue() && "Should have been caught earlier!");
- Pred = ICmpInst::ICMP_ULT;
- RHS = getConstant(RA + 1);
- Changed = true;
- break;
- case ICmpInst::ICMP_SGE:
- assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
- Pred = ICmpInst::ICMP_SGT;
- RHS = getConstant(RA - 1);
- Changed = true;
- break;
- case ICmpInst::ICMP_SLE:
- assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
- Pred = ICmpInst::ICMP_SLT;
- RHS = getConstant(RA + 1);
- Changed = true;
- break;
- }
- }
- }
-
- // Check for obvious equality.
- if (HasSameValue(LHS, RHS)) {
- if (ICmpInst::isTrueWhenEqual(Pred))
- return TrivialCase(true);
- if (ICmpInst::isFalseWhenEqual(Pred))
- return TrivialCase(false);
- }
-
- // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
- // adding or subtracting 1 from one of the operands.
- switch (Pred) {
- case ICmpInst::ICMP_SLE:
- if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
- RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
- SCEV::FlagNSW);
- Pred = ICmpInst::ICMP_SLT;
- Changed = true;
- } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
- LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
- SCEV::FlagNSW);
- Pred = ICmpInst::ICMP_SLT;
- Changed = true;
- }
- break;
- case ICmpInst::ICMP_SGE:
- if (!getSignedRangeMin(RHS).isMinSignedValue()) {
- RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
- SCEV::FlagNSW);
- Pred = ICmpInst::ICMP_SGT;
- Changed = true;
- } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
- LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
- SCEV::FlagNSW);
- Pred = ICmpInst::ICMP_SGT;
- Changed = true;
- }
- break;
- case ICmpInst::ICMP_ULE:
- if (!getUnsignedRangeMax(RHS).isMaxValue()) {
- RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
- SCEV::FlagNUW);
- Pred = ICmpInst::ICMP_ULT;
- Changed = true;
- } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
- LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
- Pred = ICmpInst::ICMP_ULT;
- Changed = true;
- }
- break;
- case ICmpInst::ICMP_UGE:
- // If RHS is an op we can fold the -1, try that first.
- // Otherwise prefer LHS to preserve the nuw flag.
- if ((isa<SCEVConstant>(RHS) ||
- (isa<SCEVAddExpr, SCEVAddRecExpr>(RHS) &&
- isa<SCEVConstant>(cast<SCEVNAryExpr>(RHS)->getOperand(0)))) &&
- !getUnsignedRangeMin(RHS).isMinValue()) {
- RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
- Pred = ICmpInst::ICMP_UGT;
- Changed = true;
- } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
- LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
- SCEV::FlagNUW);
- Pred = ICmpInst::ICMP_UGT;
- Changed = true;
- } else if (!getUnsignedRangeMin(RHS).isMinValue()) {
- RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
- Pred = ICmpInst::ICMP_UGT;
- Changed = true;
- }
- break;
- default:
- break;
- }
-
- // TODO: More simplifications are possible here.
-
- // Recursively simplify until we either hit a recursion limit or nothing
- // changes.
- if (Changed)
- (void)SimplifyICmpOperands(Pred, LHS, RHS, Depth + 1);
-
- return Changed;
-}
-
-bool ScalarEvolution::isKnownNegative(const SCEV *S) {
- return getSignedRangeMax(S).isNegative();
-}
-
-bool ScalarEvolution::isKnownPositive(const SCEV *S) {
- return getSignedRangeMin(S).isStrictlyPositive();
-}
-
-bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
- return !getSignedRangeMin(S).isNegative();
-}
-
-bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
- return !getSignedRangeMax(S).isStrictlyPositive();
-}
-
-bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
- // Query push down for cases where the unsigned range is
- // less than sufficient.
- if (const auto *SExt = dyn_cast<SCEVSignExtendExpr>(S))
- return isKnownNonZero(SExt->getOperand(0));
- return getUnsignedRangeMin(S) != 0;
-}
-
-bool ScalarEvolution::isKnownToBeAPowerOfTwo(const SCEV *S, bool OrZero,
- bool OrNegative) {
- auto NonRecursive = [OrNegative](const SCEV *S) {
- if (auto *C = dyn_cast<SCEVConstant>(S))
- return C->getAPInt().isPowerOf2() ||
- (OrNegative && C->getAPInt().isNegatedPowerOf2());
-
- // vscale is a power-of-two.
- return isa<SCEVVScale>(S);
- };
-
- if (NonRecursive(S))
- return true;
-
- auto *Mul = dyn_cast<SCEVMulExpr>(S);
- if (!Mul)
- return false;
- return all_of(Mul->operands(), NonRecursive) && (OrZero || isKnownNonZero(S));
-}
-
-bool ScalarEvolution::isKnownMultipleOf(
- const SCEV *S, uint64_t M,
- SmallVectorImpl<const SCEVPredicate *> &Assumptions) {
- if (M == 0)
- return false;
- if (M == 1)
- return true;
-
- // Recursively check AddRec operands. An AddRecExpr S is a multiple of M if S
- // starts with a multiple of M and at every iteration step S only adds
- // multiples of M.
- if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S))
- return isKnownMultipleOf(AddRec->getStart(), M, Assumptions) &&
- isKnownMultipleOf(AddRec->getStepRecurrence(*this), M, Assumptions);
-
- // For a constant, check that "S % M == 0".
- if (auto *Cst = dyn_cast<SCEVConstant>(S)) {
- APInt C = Cst->getAPInt();
- return C.urem(M) == 0;
- }
-
- // TODO: Also check other SCEV expressions, i.e., SCEVAddRecExpr, etc.
-
- // Basic tests have failed.
- // Check "S % M == 0" at compile time and record runtime Assumptions.
- auto *STy = dyn_cast<IntegerType>(S->getType());
- const SCEV *SmodM =
- getURemExpr(S, getConstant(ConstantInt::get(STy, M, false)));
- const SCEV *Zero = getZero(STy);
-
- // Check whether "S % M == 0" is known at compile time.
- if (isKnownPredicate(ICmpInst::ICMP_EQ, SmodM, Zero))
- return true;
-
- // Check whether "S % M != 0" is known at compile time.
- if (isKnownPredicate(ICmpInst::ICMP_NE, SmodM, Zero))
- return false;
-
- const SCEVPredicate *P = getComparePredicate(ICmpInst::ICMP_EQ, SmodM, Zero);
-
- // Detect redundant predicates.
- for (auto *A : Assumptions)
- if (A->implies(P, *this))
- return true;
-
- // Only record non-redundant predicates.
- Assumptions.push_back(P);
- return true;
-}
-
-bool ScalarEvolution::haveSameSign(const SCEV *S1, const SCEV *S2) {
- return ((isKnownNonNegative(S1) && isKnownNonNegative(S2)) ||
- (isKnownNegative(S1) && isKnownNegative(S2)));
-}
-
-std::pair<const SCEV *, const SCEV *>
-ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
- // Compute SCEV on entry of loop L.
- const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
- if (Start == getCouldNotCompute())
- return { Start, Start };
- // Compute post increment SCEV for loop L.
- const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
- assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
- return { Start, PostInc };
-}
-
-bool ScalarEvolution::isKnownViaInduction(CmpPredicate Pred, SCEVUse LHS,
- SCEVUse RHS) {
- // First collect all loops.
- SmallPtrSet<const Loop *, 8> LoopsUsed;
- getUsedLoops(LHS, LoopsUsed);
- getUsedLoops(RHS, LoopsUsed);
-
- if (LoopsUsed.empty())
- return false;
-
- // Domination relationship must be a linear order on collected loops.
-#ifndef NDEBUG
- for (const auto *L1 : LoopsUsed)
- for (const auto *L2 : LoopsUsed)
- assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
- DT.dominates(L2->getHeader(), L1->getHeader())) &&
- "Domination relationship is not a linear order");
-#endif
-
- const Loop *MDL =
- *llvm::max_element(LoopsUsed, [&](const Loop *L1, const Loop *L2) {
- return DT.properlyDominates(L1->getHeader(), L2->getHeader());
- });
-
- // Get init and post increment value for LHS.
- auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
- // if LHS contains unknown non-invariant SCEV then bail out.
- if (SplitLHS.first == getCouldNotCompute())
- return false;
- assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
- // Get init and post increment value for RHS.
- auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
- // if RHS contains unknown non-invariant SCEV then bail out.
- if (SplitRHS.first == getCouldNotCompute())
- return false;
- assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
- // It is possible that init SCEV contains an invariant load but it does
- // not dominate MDL and is not available at MDL loop entry, so we should
- // check it here.
- if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
- !isAvailableAtLoopEntry(SplitRHS.first, MDL))
- return false;
-
- // It seems backedge guard check is faster than entry one so in some cases
- // it can speed up whole estimation by short circuit
- return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
- SplitRHS.second) &&
- isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first);
-}
-
-bool ScalarEvolution::isKnownPredicate(CmpPredicate Pred, SCEVUse LHS,
- SCEVUse RHS) {
- // Canonicalize the inputs first.
- (void)SimplifyICmpOperands(Pred, LHS, RHS);
-
- if (isKnownViaInduction(Pred, LHS, RHS))
- return true;
-
- if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
- return true;
-
- // Otherwise see what can be done with some simple reasoning.
- return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
-}
-
-std::optional<bool> ScalarEvolution::evaluatePredicate(CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS) {
- if (isKnownPredicate(Pred, LHS, RHS))
- return true;
- if (isKnownPredicate(ICmpInst::getInverseCmpPredicate(Pred), LHS, RHS))
- return false;
- return std::nullopt;
-}
-
-bool ScalarEvolution::isKnownPredicateAt(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS,
- const Instruction *CtxI) {
- // TODO: Analyze guards and assumes from Context's block.
- return isKnownPredicate(Pred, LHS, RHS) ||
- isBasicBlockEntryGuardedByCond(CtxI->getParent(), Pred, LHS, RHS);
-}
-
-std::optional<bool>
-ScalarEvolution::evaluatePredicateAt(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS, const Instruction *CtxI) {
- std::optional<bool> KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS);
- if (KnownWithoutContext)
- return KnownWithoutContext;
-
- if (isBasicBlockEntryGuardedByCond(CtxI->getParent(), Pred, LHS, RHS))
- return true;
- if (isBasicBlockEntryGuardedByCond(
- CtxI->getParent(), ICmpInst::getInverseCmpPredicate(Pred), LHS, RHS))
- return false;
- return std::nullopt;
-}
-
-bool ScalarEvolution::isKnownOnEveryIteration(CmpPredicate Pred,
- const SCEVAddRecExpr *LHS,
- const SCEV *RHS) {
- const Loop *L = LHS->getLoop();
- return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
- isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
-}
-
-std::optional<ScalarEvolution::MonotonicPredicateType>
-ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS,
- ICmpInst::Predicate Pred) {
- auto Result = getMonotonicPredicateTypeImpl(LHS, Pred);
-
-#ifndef NDEBUG
- // Verify an invariant: inverting the predicate should turn a monotonically
- // increasing change to a monotonically decreasing one, and vice versa.
- if (Result) {
- auto ResultSwapped =
- getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred));
-
- assert(*ResultSwapped != *Result &&
- "monotonicity should flip as we flip the predicate");
- }
-#endif
-
- return Result;
-}
-
-std::optional<ScalarEvolution::MonotonicPredicateType>
-ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS,
- ICmpInst::Predicate Pred) {
- // A zero step value for LHS means the induction variable is essentially a
- // loop invariant value. We don't really depend on the predicate actually
- // flipping from false to true (for increasing predicates, and the other way
- // around for decreasing predicates), all we care about is that *if* the
- // predicate changes then it only changes from false to true.
- //
- // A zero step value in itself is not very useful, but there may be places
- // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
- // as general as possible.
-
- // Only handle LE/LT/GE/GT predicates.
- if (!ICmpInst::isRelational(Pred))
- return std::nullopt;
-
- bool IsGreater = ICmpInst::isGE(Pred) || ICmpInst::isGT(Pred);
- assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) &&
- "Should be greater or less!");
-
- // Check that AR does not wrap.
- if (ICmpInst::isUnsigned(Pred)) {
- if (!LHS->hasNoUnsignedWrap())
- return std::nullopt;
- return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
- }
- assert(ICmpInst::isSigned(Pred) &&
- "Relational predicate is either signed or unsigned!");
- if (!LHS->hasNoSignedWrap())
- return std::nullopt;
-
- const SCEV *Step = LHS->getStepRecurrence(*this);
-
- if (isKnownNonNegative(Step))
- return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
-
- if (isKnownNonPositive(Step))
- return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
-
- return std::nullopt;
-}
-
-std::optional<ScalarEvolution::LoopInvariantPredicate>
-ScalarEvolution::getLoopInvariantPredicate(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS, const Loop *L,
- const Instruction *CtxI) {
- // If there is a loop-invariant, force it into the RHS, otherwise bail out.
- if (!isLoopInvariant(RHS, L)) {
- if (!isLoopInvariant(LHS, L))
- return std::nullopt;
-
- std::swap(LHS, RHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- }
-
- const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
- if (!ArLHS || ArLHS->getLoop() != L)
- return std::nullopt;
-
- auto MonotonicType = getMonotonicPredicateType(ArLHS, Pred);
- if (!MonotonicType)
- return std::nullopt;
- // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
- // true as the loop iterates, and the backedge is control dependent on
- // "ArLHS `Pred` RHS" == true then we can reason as follows:
- //
- // * if the predicate was false in the first iteration then the predicate
- // is never evaluated again, since the loop exits without taking the
- // backedge.
- // * if the predicate was true in the first iteration then it will
- // continue to be true for all future iterations since it is
- // monotonically increasing.
- //
- // For both the above possibilities, we can replace the loop varying
- // predicate with its value on the first iteration of the loop (which is
- // loop invariant).
- //
- // A similar reasoning applies for a monotonically decreasing predicate, by
- // replacing true with false and false with true in the above two bullets.
- bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing;
- auto P = Increasing ? Pred : ICmpInst::getInverseCmpPredicate(Pred);
-
- if (isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
- return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(),
- RHS);
-
- if (!CtxI)
- return std::nullopt;
- // Try to prove via context.
- // TODO: Support other cases.
- switch (Pred) {
- default:
- break;
- case ICmpInst::ICMP_ULE:
- case ICmpInst::ICMP_ULT: {
- assert(ArLHS->hasNoUnsignedWrap() && "Is a requirement of monotonicity!");
- // Given preconditions
- // (1) ArLHS does not cross the border of positive and negative parts of
- // range because of:
- // - Positive step; (TODO: lift this limitation)
- // - nuw - does not cross zero boundary;
- // - nsw - does not cross SINT_MAX boundary;
- // (2) ArLHS <s RHS
- // (3) RHS >=s 0
- // we can replace the loop variant ArLHS <u RHS condition with loop
- // invariant Start(ArLHS) <u RHS.
- //
- // Because of (1) there are two options:
- // - ArLHS is always negative. It means that ArLHS <u RHS is always false;
- // - ArLHS is always non-negative. Because of (3) RHS is also non-negative.
- // It means that ArLHS <s RHS <=> ArLHS <u RHS.
- // Because of (2) ArLHS <u RHS is trivially true.
- // All together it means that ArLHS <u RHS <=> Start(ArLHS) >=s 0.
- // We can strengthen this to Start(ArLHS) <u RHS.
- auto SignFlippedPred = ICmpInst::getFlippedSignednessPredicate(Pred);
- if (ArLHS->hasNoSignedWrap() && ArLHS->isAffine() &&
- isKnownPositive(ArLHS->getStepRecurrence(*this)) &&
- isKnownNonNegative(RHS) &&
- isKnownPredicateAt(SignFlippedPred, ArLHS, RHS, CtxI))
- return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(),
- RHS);
- }
- }
-
- return std::nullopt;
-}
-
-std::optional<ScalarEvolution::LoopInvariantPredicate>
-ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations(
- CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
- const Instruction *CtxI, const SCEV *MaxIter) {
- if (auto LIP = getLoopInvariantExitCondDuringFirstIterationsImpl(
- Pred, LHS, RHS, L, CtxI, MaxIter))
- return LIP;
- if (auto *UMin = dyn_cast<SCEVUMinExpr>(MaxIter))
- // Number of iterations expressed as UMIN isn't always great for expressing
- // the value on the last iteration. If the straightforward approach didn't
- // work, try the following trick: if the a predicate is invariant for X, it
- // is also invariant for umin(X, ...). So try to find something that works
- // among subexpressions of MaxIter expressed as umin.
- for (SCEVUse Op : UMin->operands())
- if (auto LIP = getLoopInvariantExitCondDuringFirstIterationsImpl(
- Pred, LHS, RHS, L, CtxI, Op))
- return LIP;
- return std::nullopt;
-}
-
-std::optional<ScalarEvolution::LoopInvariantPredicate>
-ScalarEvolution::getLoopInvariantExitCondDuringFirstIterationsImpl(
- CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
- const Instruction *CtxI, const SCEV *MaxIter) {
- // Try to prove the following set of facts:
- // - The predicate is monotonic in the iteration space.
- // - If the check does not fail on the 1st iteration:
- // - No overflow will happen during first MaxIter iterations;
- // - It will not fail on the MaxIter'th iteration.
- // If the check does fail on the 1st iteration, we leave the loop and no
- // other checks matter.
-
- // If there is a loop-invariant, force it into the RHS, otherwise bail out.
- if (!isLoopInvariant(RHS, L)) {
- if (!isLoopInvariant(LHS, L))
- return std::nullopt;
-
- std::swap(LHS, RHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- }
-
- auto *AR = dyn_cast<SCEVAddRecExpr>(LHS);
- if (!AR || AR->getLoop() != L)
- return std::nullopt;
-
- // Even if both are valid, we need to consistently chose the unsigned or the
- // signed predicate below, not mixtures of both. For now, prefer the unsigned
- // predicate.
- Pred = Pred.dropSameSign();
-
- // The predicate must be relational (i.e. <, <=, >=, >).
- if (!ICmpInst::isRelational(Pred))
- return std::nullopt;
-
- // TODO: Support steps other than +/- 1.
- const SCEV *Step = AR->getStepRecurrence(*this);
- auto *One = getOne(Step->getType());
- auto *MinusOne = getNegativeSCEV(One);
- if (Step != One && Step != MinusOne)
- return std::nullopt;
-
- // Type mismatch here means that MaxIter is potentially larger than max
- // unsigned value in start type, which mean we cannot prove no wrap for the
- // indvar.
- if (AR->getType() != MaxIter->getType())
- return std::nullopt;
-
- // Value of IV on suggested last iteration.
- const SCEV *Last = AR->evaluateAtIteration(MaxIter, *this);
- // Does it still meet the requirement?
- if (!isLoopBackedgeGuardedByCond(L, Pred, Last, RHS))
- return std::nullopt;
- // Because step is +/- 1 and MaxIter has same type as Start (i.e. it does
- // not exceed max unsigned value of this type), this effectively proves
- // that there is no wrap during the iteration. To prove that there is no
- // signed/unsigned wrap, we need to check that
- // Start <= Last for step = 1 or Start >= Last for step = -1.
- ICmpInst::Predicate NoOverflowPred =
- CmpInst::isSigned(Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
- if (Step == MinusOne)
- NoOverflowPred = ICmpInst::getSwappedPredicate(NoOverflowPred);
- const SCEV *Start = AR->getStart();
- if (!isKnownPredicateAt(NoOverflowPred, Start, Last, CtxI))
- return std::nullopt;
-
- // Everything is fine.
- return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS);
-}
-
-bool ScalarEvolution::isKnownPredicateViaConstantRanges(CmpPredicate Pred,
- SCEVUse LHS,
- SCEVUse RHS) {
- if (HasSameValue(LHS, RHS))
- return ICmpInst::isTrueWhenEqual(Pred);
-
- auto CheckRange = [&](bool IsSigned) {
- auto RangeLHS = IsSigned ? getSignedRange(LHS) : getUnsignedRange(LHS);
- auto RangeRHS = IsSigned ? getSignedRange(RHS) : getUnsignedRange(RHS);
- return RangeLHS.icmp(Pred, RangeRHS);
- };
-
- // The check at the top of the function catches the case where the values are
- // known to be equal.
- if (Pred == CmpInst::ICMP_EQ)
- return false;
-
- if (Pred == CmpInst::ICMP_NE) {
- if (CheckRange(true) || CheckRange(false))
- return true;
- auto *Diff = getMinusSCEV(LHS, RHS);
- return !isa<SCEVCouldNotCompute>(Diff) && isKnownNonZero(Diff);
- }
-
- return CheckRange(CmpInst::isSigned(Pred));
-}
-
-bool ScalarEvolution::isKnownPredicateViaNoOverflow(CmpPredicate Pred,
- SCEVUse LHS, SCEVUse RHS) {
- // Match X to (A + C1)<ExpectedFlags> and Y to (A + C2)<ExpectedFlags>, where
- // C1 and C2 are constant integers. If either X or Y are not add expressions,
- // consider them as X + 0 and Y + 0 respectively. C1 and C2 are returned via
- // OutC1 and OutC2.
- auto MatchBinaryAddToConst = [this](SCEVUse X, SCEVUse Y, APInt &OutC1,
- APInt &OutC2,
- SCEV::NoWrapFlags ExpectedFlags) {
- SCEVUse XNonConstOp, XConstOp;
- SCEVUse YNonConstOp, YConstOp;
- SCEV::NoWrapFlags XFlagsPresent;
- SCEV::NoWrapFlags YFlagsPresent;
-
- if (!splitBinaryAdd(X, XConstOp, XNonConstOp, XFlagsPresent)) {
- XConstOp = getZero(X->getType());
- XNonConstOp = X;
- XFlagsPresent = ExpectedFlags;
- }
- if (!isa<SCEVConstant>(XConstOp))
- return false;
-
- if (!splitBinaryAdd(Y, YConstOp, YNonConstOp, YFlagsPresent)) {
- YConstOp = getZero(Y->getType());
- YNonConstOp = Y;
- YFlagsPresent = ExpectedFlags;
- }
-
- if (YNonConstOp != XNonConstOp)
- return false;
-
- if (!isa<SCEVConstant>(YConstOp))
- return false;
-
- // When matching ADDs with NUW flags (and unsigned predicates), only the
- // second ADD (with the larger constant) requires NUW.
- if ((YFlagsPresent & ExpectedFlags) != ExpectedFlags)
- return false;
- if (ExpectedFlags != SCEV::FlagNUW &&
- (XFlagsPresent & ExpectedFlags) != ExpectedFlags) {
- return false;
- }
-
- OutC1 = cast<SCEVConstant>(XConstOp)->getAPInt();
- OutC2 = cast<SCEVConstant>(YConstOp)->getAPInt();
-
- return true;
- };
-
- APInt C1;
- APInt C2;
-
- switch (Pred) {
- default:
- break;
-
- case ICmpInst::ICMP_SGE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SLE:
- // (X + C1)<nsw> s<= (X + C2)<nsw> if C1 s<= C2.
- if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.sle(C2))
- return true;
-
- break;
-
- case ICmpInst::ICMP_SGT:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SLT:
- // (X + C1)<nsw> s< (X + C2)<nsw> if C1 s< C2.
- if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.slt(C2))
- return true;
-
- break;
-
- case ICmpInst::ICMP_UGE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_ULE:
- // (X + C1) u<= (X + C2)<nuw> for C1 u<= C2.
- if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNUW) && C1.ule(C2))
- return true;
-
- break;
-
- case ICmpInst::ICMP_UGT:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_ULT:
- // (X + C1) u< (X + C2)<nuw> if C1 u< C2.
- if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNUW) && C1.ult(C2))
- return true;
- break;
- }
-
- return false;
-}
-
-bool ScalarEvolution::isKnownPredicateViaSplitting(CmpPredicate Pred,
- SCEVUse LHS, SCEVUse RHS) {
- if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
- return false;
-
- // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
- // the stack can result in exponential time complexity.
- SaveAndRestore Restore(ProvingSplitPredicate, true);
-
- // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
- //
- // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
- // isKnownPredicate. isKnownPredicate is more powerful, but also more
- // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
- // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
- // use isKnownPredicate later if needed.
- return isKnownNonNegative(RHS) &&
- isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
- isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
-}
-
-bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB, CmpPredicate Pred,
- const SCEV *LHS, const SCEV *RHS) {
- // No need to even try if we know the module has no guards.
- if (!HasGuards)
- return false;
-
- return any_of(*BB, [&](const Instruction &I) {
- using namespace llvm::PatternMatch;
-
- Value *Condition;
- return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
- m_Value(Condition))) &&
- isImpliedCond(Pred, LHS, RHS, Condition, false);
- });
-}
-
-/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
-/// protected by a conditional between LHS and RHS. This is used to
-/// to eliminate casts.
-bool ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
- CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS) {
- // Interpret a null as meaning no loop, where there is obviously no guard
- // (interprocedural conditions notwithstanding). Do not bother about
- // unreachable loops.
- if (!L || !DT.isReachableFromEntry(L->getHeader()))
- return true;
-
- if (VerifyIR)
- assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
- "This cannot be done on broken IR!");
-
-
- if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
- return true;
-
- BasicBlock *Latch = L->getLoopLatch();
- if (!Latch)
- return false;
-
- CondBrInst *LoopContinuePredicate =
- dyn_cast<CondBrInst>(Latch->getTerminator());
- if (LoopContinuePredicate &&
- isImpliedCond(Pred, LHS, RHS, LoopContinuePredicate->getCondition(),
- LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
- return true;
-
- // We don't want more than one activation of the following loops on the stack
- // -- that can lead to O(n!) time complexity.
- if (WalkingBEDominatingConds)
- return false;
-
- SaveAndRestore ClearOnExit(WalkingBEDominatingConds, true);
-
- // See if we can exploit a trip count to prove the predicate.
- const auto &BETakenInfo = getBackedgeTakenInfo(L);
- const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
- if (LatchBECount != getCouldNotCompute()) {
- // We know that Latch branches back to the loop header exactly
- // LatchBECount times. This means the backdege condition at Latch is
- // equivalent to "{0,+,1} u< LatchBECount".
- Type *Ty = LatchBECount->getType();
- auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
- const SCEV *LoopCounter =
- getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
- if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
- LatchBECount))
- return true;
- }
-
- // Check conditions due to any @llvm.assume intrinsics.
- for (auto &AssumeVH : AC.assumptions()) {
- if (!AssumeVH)
- continue;
- auto *CI = cast<CallInst>(AssumeVH);
- if (!DT.dominates(CI, Latch->getTerminator()))
- continue;
-
- if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
- return true;
- }
-
- if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
- return true;
-
- for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
- DTN != HeaderDTN; DTN = DTN->getIDom()) {
- assert(DTN && "should reach the loop header before reaching the root!");
-
- BasicBlock *BB = DTN->getBlock();
- if (isImpliedViaGuard(BB, Pred, LHS, RHS))
- return true;
-
- BasicBlock *PBB = BB->getSinglePredecessor();
- if (!PBB)
- continue;
-
- CondBrInst *ContBr = dyn_cast<CondBrInst>(PBB->getTerminator());
- if (!ContBr || ContBr->getSuccessor(0) == ContBr->getSuccessor(1))
- continue;
-
- // If we have an edge `E` within the loop body that dominates the only
- // latch, the condition guarding `E` also guards the backedge. This
- // reasoning works only for loops with a single latch.
- // We're constructively (and conservatively) enumerating edges within the
- // loop body that dominate the latch. The dominator tree better agree
- // with us on this:
- assert(DT.dominates(BasicBlockEdge(PBB, BB), Latch) && "should be!");
- if (isImpliedCond(Pred, LHS, RHS, ContBr->getCondition(),
- BB != ContBr->getSuccessor(0)))
- return true;
- }
-
- return false;
-}
-
-bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB,
- CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS) {
- // Do not bother proving facts for unreachable code.
- if (!DT.isReachableFromEntry(BB))
- return true;
- if (VerifyIR)
- assert(!verifyFunction(*BB->getParent(), &dbgs()) &&
- "This cannot be done on broken IR!");
-
- // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
- // the facts (a >= b && a != b) separately. A typical situation is when the
- // non-strict comparison is known from ranges and non-equality is known from
- // dominating predicates. If we are proving strict comparison, we always try
- // to prove non-equality and non-strict comparison separately.
- CmpPredicate NonStrictPredicate = ICmpInst::getNonStrictCmpPredicate(Pred);
- const bool ProvingStrictComparison =
- Pred != NonStrictPredicate.dropSameSign();
- bool ProvedNonStrictComparison = false;
- bool ProvedNonEquality = false;
-
- auto SplitAndProve = [&](std::function<bool(CmpPredicate)> Fn) -> bool {
- if (!ProvedNonStrictComparison)
- ProvedNonStrictComparison = Fn(NonStrictPredicate);
- if (!ProvedNonEquality)
- ProvedNonEquality = Fn(ICmpInst::ICMP_NE);
- if (ProvedNonStrictComparison && ProvedNonEquality)
- return true;
- return false;
- };
-
- if (ProvingStrictComparison) {
- auto ProofFn = [&](CmpPredicate P) {
- return isKnownViaNonRecursiveReasoning(P, LHS, RHS);
- };
- if (SplitAndProve(ProofFn))
- return true;
- }
-
- // Try to prove (Pred, LHS, RHS) using isImpliedCond.
- auto ProveViaCond = [&](const Value *Condition, bool Inverse) {
- const Instruction *CtxI = &BB->front();
- if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse, CtxI))
- return true;
- if (ProvingStrictComparison) {
- auto ProofFn = [&](CmpPredicate P) {
- return isImpliedCond(P, LHS, RHS, Condition, Inverse, CtxI);
- };
- if (SplitAndProve(ProofFn))
- return true;
- }
- return false;
- };
-
- // Starting at the block's predecessor, climb up the predecessor chain, as long
- // as there are predecessors that can be found that have unique successors
- // leading to the original block.
- const Loop *ContainingLoop = LI.getLoopFor(BB);
- const BasicBlock *PredBB;
- if (ContainingLoop && ContainingLoop->getHeader() == BB)
- PredBB = ContainingLoop->getLoopPredecessor();
- else
- PredBB = BB->getSinglePredecessor();
- for (std::pair<const BasicBlock *, const BasicBlock *> Pair(PredBB, BB);
- Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
- const CondBrInst *BlockEntryPredicate =
- dyn_cast<CondBrInst>(Pair.first->getTerminator());
- if (!BlockEntryPredicate)
- continue;
-
- if (ProveViaCond(BlockEntryPredicate->getCondition(),
- BlockEntryPredicate->getSuccessor(0) != Pair.second))
- return true;
- }
-
- // Check conditions due to any @llvm.assume intrinsics.
- for (auto &AssumeVH : AC.assumptions()) {
- if (!AssumeVH)
- continue;
- auto *CI = cast<CallInst>(AssumeVH);
- if (!DT.dominates(CI, BB))
- continue;
-
- if (ProveViaCond(CI->getArgOperand(0), false))
- return true;
- }
-
- // Check conditions due to any @llvm.experimental.guard intrinsics.
- auto *GuardDecl = Intrinsic::getDeclarationIfExists(
- F.getParent(), Intrinsic::experimental_guard);
- if (GuardDecl)
- for (const auto *GU : GuardDecl->users())
- if (const auto *Guard = dyn_cast<IntrinsicInst>(GU))
- if (Guard->getFunction() == BB->getParent() && DT.dominates(Guard, BB))
- if (ProveViaCond(Guard->getArgOperand(0), false))
- return true;
- return false;
-}
-
-bool ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS) {
- // Interpret a null as meaning no loop, where there is obviously no guard
- // (interprocedural conditions notwithstanding).
- if (!L)
- return false;
-
- // Both LHS and RHS must be available at loop entry.
- assert(isAvailableAtLoopEntry(LHS, L) &&
- "LHS is not available at Loop Entry");
- assert(isAvailableAtLoopEntry(RHS, L) &&
- "RHS is not available at Loop Entry");
-
- if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
- return true;
-
- return isBasicBlockEntryGuardedByCond(L->getHeader(), Pred, LHS, RHS);
-}
-
-bool ScalarEvolution::isImpliedCond(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS,
- const Value *FoundCondValue, bool Inverse,
- const Instruction *CtxI) {
- // False conditions implies anything. Do not bother analyzing it further.
- if (FoundCondValue ==
- ConstantInt::getBool(FoundCondValue->getContext(), Inverse))
- return true;
-
- if (!PendingLoopPredicates.insert(FoundCondValue).second)
- return false;
-
- llvm::scope_exit ClearOnExit(
- [&]() { PendingLoopPredicates.erase(FoundCondValue); });
-
- // Recursively handle And and Or conditions.
- const Value *Op0, *Op1;
- if (match(FoundCondValue, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) {
- if (!Inverse)
- return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, CtxI) ||
- isImpliedCond(Pred, LHS, RHS, Op1, Inverse, CtxI);
- } else if (match(FoundCondValue, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) {
- if (Inverse)
- return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, CtxI) ||
- isImpliedCond(Pred, LHS, RHS, Op1, Inverse, CtxI);
- }
-
- const ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
- if (!ICI) return false;
-
- // Now that we found a conditional branch that dominates the loop or controls
- // the loop latch. Check to see if it is the comparison we are looking for.
- CmpPredicate FoundPred;
- if (Inverse)
- FoundPred = ICI->getInverseCmpPredicate();
- else
- FoundPred = ICI->getCmpPredicate();
-
- const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
- const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
-
- return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, CtxI);
-}
-
-bool ScalarEvolution::isImpliedCond(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS, CmpPredicate FoundPred,
- const SCEV *FoundLHS, const SCEV *FoundRHS,
- const Instruction *CtxI) {
- // Balance the types.
- if (getTypeSizeInBits(LHS->getType()) <
- getTypeSizeInBits(FoundLHS->getType())) {
- // For unsigned and equality predicates, try to prove that both found
- // operands fit into narrow unsigned range. If so, try to prove facts in
- // narrow types.
- if (!CmpInst::isSigned(FoundPred) && !FoundLHS->getType()->isPointerTy() &&
- !FoundRHS->getType()->isPointerTy()) {
- auto *NarrowType = LHS->getType();
- auto *WideType = FoundLHS->getType();
- auto BitWidth = getTypeSizeInBits(NarrowType);
- const SCEV *MaxValue = getZeroExtendExpr(
- getConstant(APInt::getMaxValue(BitWidth)), WideType);
- if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, FoundLHS,
- MaxValue) &&
- isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, FoundRHS,
- MaxValue)) {
- const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType);
- const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType);
- // We cannot preserve samesign after truncation.
- if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred.dropSameSign(),
- TruncFoundLHS, TruncFoundRHS, CtxI))
- return true;
- }
- }
-
- if (LHS->getType()->isPointerTy() || RHS->getType()->isPointerTy())
- return false;
- if (CmpInst::isSigned(Pred)) {
- LHS = getSignExtendExpr(LHS, FoundLHS->getType());
- RHS = getSignExtendExpr(RHS, FoundLHS->getType());
- } else {
- LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
- RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
- }
- } else if (getTypeSizeInBits(LHS->getType()) >
- getTypeSizeInBits(FoundLHS->getType())) {
- if (FoundLHS->getType()->isPointerTy() || FoundRHS->getType()->isPointerTy())
- return false;
- if (CmpInst::isSigned(FoundPred)) {
- FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
- FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
- } else {
- FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
- FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
- }
- }
- return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS,
- FoundRHS, CtxI);
-}
-
-bool ScalarEvolution::isImpliedCondBalancedTypes(
- CmpPredicate Pred, SCEVUse LHS, SCEVUse RHS, CmpPredicate FoundPred,
- SCEVUse FoundLHS, SCEVUse FoundRHS, const Instruction *CtxI) {
- assert(getTypeSizeInBits(LHS->getType()) ==
- getTypeSizeInBits(FoundLHS->getType()) &&
- "Types should be balanced!");
- // Canonicalize the query to match the way instcombine will have
- // canonicalized the comparison.
- if (SimplifyICmpOperands(Pred, LHS, RHS))
- if (LHS == RHS)
- return CmpInst::isTrueWhenEqual(Pred);
- if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
- if (FoundLHS == FoundRHS)
- return CmpInst::isFalseWhenEqual(FoundPred);
-
- // Check to see if we can make the LHS or RHS match.
- if (LHS == FoundRHS || RHS == FoundLHS) {
- if (isa<SCEVConstant>(RHS)) {
- std::swap(FoundLHS, FoundRHS);
- FoundPred = ICmpInst::getSwappedCmpPredicate(FoundPred);
- } else {
- std::swap(LHS, RHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- }
- }
-
- // Check whether the found predicate is the same as the desired predicate.
- if (auto P = CmpPredicate::getMatching(FoundPred, Pred))
- return isImpliedCondOperands(*P, LHS, RHS, FoundLHS, FoundRHS, CtxI);
-
- // Check whether swapping the found predicate makes it the same as the
- // desired predicate.
- if (auto P = CmpPredicate::getMatching(
- ICmpInst::getSwappedCmpPredicate(FoundPred), Pred)) {
- // We can write the implication
- // 0. LHS Pred RHS <- FoundLHS SwapPred FoundRHS
- // using one of the following ways:
- // 1. LHS Pred RHS <- FoundRHS Pred FoundLHS
- // 2. RHS SwapPred LHS <- FoundLHS SwapPred FoundRHS
- // 3. LHS Pred RHS <- ~FoundLHS Pred ~FoundRHS
- // 4. ~LHS SwapPred ~RHS <- FoundLHS SwapPred FoundRHS
- // Forms 1. and 2. require swapping the operands of one condition. Don't
- // do this if it would break canonical constant/addrec ordering.
- if (!isa<SCEVConstant>(RHS) && !isa<SCEVAddRecExpr>(LHS))
- return isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(*P), RHS,
- LHS, FoundLHS, FoundRHS, CtxI);
- if (!isa<SCEVConstant>(FoundRHS) && !isa<SCEVAddRecExpr>(FoundLHS))
- return isImpliedCondOperands(*P, LHS, RHS, FoundRHS, FoundLHS, CtxI);
-
- // There's no clear preference between forms 3. and 4., try both. Avoid
- // forming getNotSCEV of pointer values as the resulting subtract is
- // not legal.
- if (!LHS->getType()->isPointerTy() && !RHS->getType()->isPointerTy() &&
- isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(*P),
- getNotSCEV(LHS), getNotSCEV(RHS), FoundLHS,
- FoundRHS, CtxI))
- return true;
-
- if (!FoundLHS->getType()->isPointerTy() &&
- !FoundRHS->getType()->isPointerTy() &&
- isImpliedCondOperands(*P, LHS, RHS, getNotSCEV(FoundLHS),
- getNotSCEV(FoundRHS), CtxI))
- return true;
-
- return false;
- }
-
- auto IsSignFlippedPredicate = [](CmpInst::Predicate P1,
- CmpInst::Predicate P2) {
- assert(P1 != P2 && "Handled earlier!");
- return CmpInst::isRelational(P2) &&
- P1 == ICmpInst::getFlippedSignednessPredicate(P2);
- };
- if (IsSignFlippedPredicate(Pred, FoundPred)) {
- // Unsigned comparison is the same as signed comparison when both the
- // operands are non-negative or negative.
- if (haveSameSign(FoundLHS, FoundRHS))
- return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI);
- // Create local copies that we can freely swap and canonicalize our
- // conditions to "le/lt".
- CmpPredicate CanonicalPred = Pred, CanonicalFoundPred = FoundPred;
- const SCEV *CanonicalLHS = LHS, *CanonicalRHS = RHS,
- *CanonicalFoundLHS = FoundLHS, *CanonicalFoundRHS = FoundRHS;
- if (ICmpInst::isGT(CanonicalPred) || ICmpInst::isGE(CanonicalPred)) {
- CanonicalPred = ICmpInst::getSwappedCmpPredicate(CanonicalPred);
- CanonicalFoundPred = ICmpInst::getSwappedCmpPredicate(CanonicalFoundPred);
- std::swap(CanonicalLHS, CanonicalRHS);
- std::swap(CanonicalFoundLHS, CanonicalFoundRHS);
- }
- assert((ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) &&
- "Must be!");
- assert((ICmpInst::isLT(CanonicalFoundPred) ||
- ICmpInst::isLE(CanonicalFoundPred)) &&
- "Must be!");
- if (ICmpInst::isSigned(CanonicalPred) && isKnownNonNegative(CanonicalRHS))
- // Use implication:
- // x <u y && y >=s 0 --> x <s y.
- // If we can prove the left part, the right part is also proven.
- return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
- CanonicalRHS, CanonicalFoundLHS,
- CanonicalFoundRHS);
- if (ICmpInst::isUnsigned(CanonicalPred) && isKnownNegative(CanonicalRHS))
- // Use implication:
- // x <s y && y <s 0 --> x <u y.
- // If we can prove the left part, the right part is also proven.
- return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
- CanonicalRHS, CanonicalFoundLHS,
- CanonicalFoundRHS);
- }
-
- // Check if we can make progress by sharpening ranges.
- if (FoundPred == ICmpInst::ICMP_NE &&
- (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
-
- const SCEVConstant *C = nullptr;
- const SCEV *V = nullptr;
-
- if (isa<SCEVConstant>(FoundLHS)) {
- C = cast<SCEVConstant>(FoundLHS);
- V = FoundRHS;
- } else {
- C = cast<SCEVConstant>(FoundRHS);
- V = FoundLHS;
- }
-
- // The guarding predicate tells us that C != V. If the known range
- // of V is [C, t), we can sharpen the range to [C + 1, t). The
- // range we consider has to correspond to same signedness as the
- // predicate we're interested in folding.
-
- APInt Min = ICmpInst::isSigned(Pred) ?
- getSignedRangeMin(V) : getUnsignedRangeMin(V);
-
- if (Min == C->getAPInt()) {
- // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
- // This is true even if (Min + 1) wraps around -- in case of
- // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
-
- APInt SharperMin = Min + 1;
-
- switch (Pred) {
- case ICmpInst::ICMP_SGE:
- case ICmpInst::ICMP_UGE:
- // We know V `Pred` SharperMin. If this implies LHS `Pred`
- // RHS, we're done.
- if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(SharperMin),
- CtxI))
- return true;
- [[fallthrough]];
-
- case ICmpInst::ICMP_SGT:
- case ICmpInst::ICMP_UGT:
- // We know from the range information that (V `Pred` Min ||
- // V == Min). We know from the guarding condition that !(V
- // == Min). This gives us
- //
- // V `Pred` Min || V == Min && !(V == Min)
- // => V `Pred` Min
- //
- // If V `Pred` Min implies LHS `Pred` RHS, we're done.
-
- if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min), CtxI))
- return true;
- break;
-
- // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively.
- case ICmpInst::ICMP_SLE:
- case ICmpInst::ICMP_ULE:
- if (isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(Pred), RHS,
- LHS, V, getConstant(SharperMin), CtxI))
- return true;
- [[fallthrough]];
-
- case ICmpInst::ICMP_SLT:
- case ICmpInst::ICMP_ULT:
- if (isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(Pred), RHS,
- LHS, V, getConstant(Min), CtxI))
- return true;
- break;
-
- default:
- // No change
- break;
- }
- }
- }
-
- // Check whether the actual condition is beyond sufficient.
- if (FoundPred == ICmpInst::ICMP_EQ)
- if (ICmpInst::isTrueWhenEqual(Pred))
- if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI))
- return true;
- if (Pred == ICmpInst::ICMP_NE)
- if (!ICmpInst::isTrueWhenEqual(FoundPred))
- if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS, CtxI))
- return true;
-
- if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS))
- return true;
-
- // Otherwise assume the worst.
- return false;
-}
-
-bool ScalarEvolution::splitBinaryAdd(SCEVUse Expr, SCEVUse &L, SCEVUse &R,
- SCEV::NoWrapFlags &Flags) {
- if (!match(Expr, m_scev_Add(m_SCEV(L), m_SCEV(R))))
- return false;
-
- Flags = cast<SCEVAddExpr>(Expr)->getNoWrapFlags();
- return true;
-}
-
-std::optional<APInt>
-ScalarEvolution::computeConstantDifference(const SCEV *More, const SCEV *Less) {
- // We avoid subtracting expressions here because this function is usually
- // fairly deep in the call stack (i.e. is called many times).
-
- unsigned BW = getTypeSizeInBits(More->getType());
- APInt Diff(BW, 0);
- APInt DiffMul(BW, 1);
- // Try various simplifications to reduce the difference to a constant. Limit
- // the number of allowed simplifications to keep compile-time low.
- for (unsigned I = 0; I < 8; ++I) {
- if (More == Less)
- return Diff;
-
- // Reduce addrecs with identical steps to their start value.
- if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
- const auto *LAR = cast<SCEVAddRecExpr>(Less);
- const auto *MAR = cast<SCEVAddRecExpr>(More);
-
- if (LAR->getLoop() != MAR->getLoop())
- return std::nullopt;
-
- // We look at affine expressions only; not for correctness but to keep
- // getStepRecurrence cheap.
- if (!LAR->isAffine() || !MAR->isAffine())
- return std::nullopt;
-
- if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
- return std::nullopt;
-
- Less = LAR->getStart();
- More = MAR->getStart();
- continue;
- }
-
- // Try to match a common constant multiply.
- auto MatchConstMul =
- [](const SCEV *S) -> std::optional<std::pair<const SCEV *, APInt>> {
- const APInt *C;
- const SCEV *Op;
- if (match(S, m_scev_Mul(m_scev_APInt(C), m_SCEV(Op))))
- return {{Op, *C}};
- return std::nullopt;
- };
- if (auto MatchedMore = MatchConstMul(More)) {
- if (auto MatchedLess = MatchConstMul(Less)) {
- if (MatchedMore->second == MatchedLess->second) {
- More = MatchedMore->first;
- Less = MatchedLess->first;
- DiffMul *= MatchedMore->second;
- continue;
- }
- }
- }
-
- // Try to cancel out common factors in two add expressions.
- SmallDenseMap<const SCEV *, int, 8> Multiplicity;
- auto Add = [&](const SCEV *S, int Mul) {
- if (auto *C = dyn_cast<SCEVConstant>(S)) {
- if (Mul == 1) {
- Diff += C->getAPInt() * DiffMul;
- } else {
- assert(Mul == -1);
- Diff -= C->getAPInt() * DiffMul;
- }
- } else
- Multiplicity[S] += Mul;
- };
- auto Decompose = [&](const SCEV *S, int Mul) {
- if (isa<SCEVAddExpr>(S)) {
- for (const SCEV *Op : S->operands())
- Add(Op, Mul);
- } else
- Add(S, Mul);
- };
- Decompose(More, 1);
- Decompose(Less, -1);
-
- // Check whether all the non-constants cancel out, or reduce to new
- // More/Less values.
- const SCEV *NewMore = nullptr, *NewLess = nullptr;
- for (const auto &[S, Mul] : Multiplicity) {
- if (Mul == 0)
- continue;
- if (Mul == 1) {
- if (NewMore)
- return std::nullopt;
- NewMore = S;
- } else if (Mul == -1) {
- if (NewLess)
- return std::nullopt;
- NewLess = S;
- } else
- return std::nullopt;
- }
-
- // Values stayed the same, no point in trying further.
- if (NewMore == More || NewLess == Less)
- return std::nullopt;
-
- More = NewMore;
- Less = NewLess;
-
- // Reduced to constant.
- if (!More && !Less)
- return Diff;
-
- // Left with variable on only one side, bail out.
- if (!More || !Less)
- return std::nullopt;
- }
-
- // Did not reduce to constant.
- return std::nullopt;
-}
-
-bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart(
- CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS,
- const SCEV *FoundRHS, const Instruction *CtxI) {
- // Try to recognize the following pattern:
- //
- // FoundRHS = ...
- // ...
- // loop:
- // FoundLHS = {Start,+,W}
- // context_bb: // Basic block from the same loop
- // known(Pred, FoundLHS, FoundRHS)
- //
- // If some predicate is known in the context of a loop, it is also known on
- // each iteration of this loop, including the first iteration. Therefore, in
- // this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to
- // prove the original pred using this fact.
- if (!CtxI)
- return false;
- const BasicBlock *ContextBB = CtxI->getParent();
- // Make sure AR varies in the context block.
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundLHS)) {
- const Loop *L = AR->getLoop();
- const auto *Latch = L->getLoopLatch();
- // Make sure that context belongs to the loop and executes on 1st iteration
- // (if it ever executes at all).
- if (!L->contains(ContextBB) || !Latch || !DT.dominates(ContextBB, Latch))
- return false;
- if (!isAvailableAtLoopEntry(FoundRHS, AR->getLoop()))
- return false;
- return isImpliedCondOperands(Pred, LHS, RHS, AR->getStart(), FoundRHS);
- }
-
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundRHS)) {
- const Loop *L = AR->getLoop();
- const auto *Latch = L->getLoopLatch();
- // Make sure that context belongs to the loop and executes on 1st iteration
- // (if it ever executes at all).
- if (!L->contains(ContextBB) || !Latch || !DT.dominates(ContextBB, Latch))
- return false;
- if (!isAvailableAtLoopEntry(FoundLHS, AR->getLoop()))
- return false;
- return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, AR->getStart());
- }
-
- return false;
-}
-
-bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS,
- const SCEV *FoundLHS,
- const SCEV *FoundRHS) {
- if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
- return false;
-
- const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
- if (!AddRecLHS)
- return false;
-
- const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
- if (!AddRecFoundLHS)
- return false;
-
- // We'd like to let SCEV reason about control dependencies, so we constrain
- // both the inequalities to be about add recurrences on the same loop. This
- // way we can use isLoopEntryGuardedByCond later.
-
- const Loop *L = AddRecFoundLHS->getLoop();
- if (L != AddRecLHS->getLoop())
- return false;
-
- // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
- //
- // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
- // ... (2)
- //
- // Informal proof for (2), assuming (1) [*]:
- //
- // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
- //
- // Then
- //
- // FoundLHS s< FoundRHS s< INT_MIN - C
- // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
- // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
- // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
- // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
- // <=> FoundLHS + C s< FoundRHS + C
- //
- // [*]: (1) can be proved by ruling out overflow.
- //
- // [**]: This can be proved by analyzing all the four possibilities:
- // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
- // (A s>= 0, B s>= 0).
- //
- // Note:
- // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
- // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
- // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
- // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
- // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
- // C)".
-
- std::optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
- if (!LDiff)
- return false;
- std::optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
- if (!RDiff || *LDiff != *RDiff)
- return false;
-
- if (LDiff->isMinValue())
- return true;
-
- APInt FoundRHSLimit;
-
- if (Pred == CmpInst::ICMP_ULT) {
- FoundRHSLimit = -(*RDiff);
- } else {
- assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
- FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
- }
-
- // Try to prove (1) or (2), as needed.
- return isAvailableAtLoopEntry(FoundRHS, L) &&
- isLoopEntryGuardedByCond(L, Pred, FoundRHS,
- getConstant(FoundRHSLimit));
-}
-
-bool ScalarEvolution::isImpliedViaMerge(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS, const SCEV *FoundLHS,
- const SCEV *FoundRHS, unsigned Depth) {
- const PHINode *LPhi = nullptr, *RPhi = nullptr;
-
- llvm::scope_exit ClearOnExit([&]() {
- if (LPhi) {
- bool Erased = PendingMerges.erase(LPhi);
- assert(Erased && "Failed to erase LPhi!");
- (void)Erased;
- }
- if (RPhi) {
- bool Erased = PendingMerges.erase(RPhi);
- assert(Erased && "Failed to erase RPhi!");
- (void)Erased;
- }
- });
-
- // Find respective Phis and check that they are not being pending.
- if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
- if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
- if (!PendingMerges.insert(Phi).second)
- return false;
- LPhi = Phi;
- }
- if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
- if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
- // If we detect a loop of Phi nodes being processed by this method, for
- // example:
- //
- // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
- // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
- //
- // we don't want to deal with a case that complex, so return conservative
- // answer false.
- if (!PendingMerges.insert(Phi).second)
- return false;
- RPhi = Phi;
- }
-
- // If none of LHS, RHS is a Phi, nothing to do here.
- if (!LPhi && !RPhi)
- return false;
-
- // If there is a SCEVUnknown Phi we are interested in, make it left.
- if (!LPhi) {
- std::swap(LHS, RHS);
- std::swap(FoundLHS, FoundRHS);
- std::swap(LPhi, RPhi);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- }
-
- assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
- const BasicBlock *LBB = LPhi->getParent();
- const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
-
- auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
- return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
- isImpliedCondOperandsViaRanges(Pred, S1, S2, Pred, FoundLHS, FoundRHS) ||
- isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
- };
-
- if (RPhi && RPhi->getParent() == LBB) {
- // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
- // If we compare two Phis from the same block, and for each entry block
- // the predicate is true for incoming values from this block, then the
- // predicate is also true for the Phis.
- for (const BasicBlock *IncBB : predecessors(LBB)) {
- const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
- const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
- if (!ProvedEasily(L, R))
- return false;
- }
- } else if (RAR && RAR->getLoop()->getHeader() == LBB) {
- // Case two: RHS is also a Phi from the same basic block, and it is an
- // AddRec. It means that there is a loop which has both AddRec and Unknown
- // PHIs, for it we can compare incoming values of AddRec from above the loop
- // and latch with their respective incoming values of LPhi.
- // TODO: Generalize to handle loops with many inputs in a header.
- if (LPhi->getNumIncomingValues() != 2) return false;
-
- auto *RLoop = RAR->getLoop();
- auto *Predecessor = RLoop->getLoopPredecessor();
- assert(Predecessor && "Loop with AddRec with no predecessor?");
- const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
- if (!ProvedEasily(L1, RAR->getStart()))
- return false;
- auto *Latch = RLoop->getLoopLatch();
- assert(Latch && "Loop with AddRec with no latch?");
- const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
- if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
- return false;
- } else {
- // In all other cases go over inputs of LHS and compare each of them to RHS,
- // the predicate is true for (LHS, RHS) if it is true for all such pairs.
- // At this point RHS is either a non-Phi, or it is a Phi from some block
- // different from LBB.
- for (const BasicBlock *IncBB : predecessors(LBB)) {
- // Check that RHS is available in this block.
- if (!dominates(RHS, IncBB))
- return false;
- const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
- // Make sure L does not refer to a value from a potentially previous
- // iteration of a loop.
- if (!properlyDominates(L, LBB))
- return false;
- // Addrecs are considered to properly dominate their loop, so are missed
- // by the previous check. Discard any values that have computable
- // evolution in this loop.
- if (auto *Loop = LI.getLoopFor(LBB))
- if (hasComputableLoopEvolution(L, Loop))
- return false;
- if (!ProvedEasily(L, RHS))
- return false;
- }
- }
- return true;
-}
-
-bool ScalarEvolution::isImpliedCondOperandsViaShift(CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS,
- const SCEV *FoundLHS,
- const SCEV *FoundRHS) {
- // We want to imply LHS < RHS from LHS < (RHS >> shiftvalue). First, make
- // sure that we are dealing with same LHS.
- if (RHS == FoundRHS) {
- std::swap(LHS, RHS);
- std::swap(FoundLHS, FoundRHS);
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- }
- if (LHS != FoundLHS)
- return false;
-
- auto *SUFoundRHS = dyn_cast<SCEVUnknown>(FoundRHS);
- if (!SUFoundRHS)
- return false;
-
- Value *Shiftee, *ShiftValue;
-
- using namespace PatternMatch;
- if (match(SUFoundRHS->getValue(),
- m_LShr(m_Value(Shiftee), m_Value(ShiftValue)))) {
- auto *ShifteeS = getSCEV(Shiftee);
- // Prove one of the following:
- // LHS <u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <u RHS
- // LHS <=u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <=u RHS
- // LHS <s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
- // ---> LHS <s RHS
- // LHS <=s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
- // ---> LHS <=s RHS
- if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_ULE)
- return isKnownPredicate(ICmpInst::ICMP_ULE, ShifteeS, RHS);
- if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE)
- if (isKnownNonNegative(ShifteeS))
- return isKnownPredicate(ICmpInst::ICMP_SLE, ShifteeS, RHS);
- }
-
- return false;
-}
-
-bool ScalarEvolution::isImpliedCondOperandsViaMatchingDiff(
- CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS,
- const SCEV *FoundRHS) {
- // Only valid for equality predicates: (A == B) implies (C == D) when
- // the SCEV difference A - B equals C - D (they check the same
- // underlying relationship at every iteration).
- if (!ICmpInst::isEquality(Pred))
- return false;
-
- // Restrict to cases involving loop recurrences - that's where this
- // pattern arises (correlated IV comparisons). This avoids calling
- // getMinusSCEV on arbitrary non-loop expressions.
- if ((!isa<SCEVAddRecExpr>(LHS) && !isa<SCEVAddRecExpr>(RHS)) ||
- (!isa<SCEVAddRecExpr>(FoundLHS) && !isa<SCEVAddRecExpr>(FoundRHS)))
- return false;
-
- // AddRecs from different loops can never produce matching differences.
- const SCEVAddRecExpr *QueryAddRec = dyn_cast<SCEVAddRecExpr>(LHS);
- if (!QueryAddRec)
- QueryAddRec = cast<SCEVAddRecExpr>(RHS);
- const SCEVAddRecExpr *FoundAddRec = dyn_cast<SCEVAddRecExpr>(FoundLHS);
- if (!FoundAddRec)
- FoundAddRec = cast<SCEVAddRecExpr>(FoundRHS);
- if (QueryAddRec->getLoop() != FoundAddRec->getLoop())
- return false;
-
- // If the strides differ, the differences can never match.
- if (QueryAddRec->getStepRecurrence(*this) !=
- FoundAddRec->getStepRecurrence(*this))
- return false;
-
- // Compute differences. For pointer-typed operands sharing the same base,
- // getMinusSCEV strips the common base and returns an integer SCEV.
- // For example, {base,+,8} - (base+8*n) = {-8n,+,8}
- const SCEV *FoundDiff = getMinusSCEV(FoundLHS, FoundRHS);
- if (isa<SCEVCouldNotCompute>(FoundDiff))
- return false;
-
- const SCEV *Diff = getMinusSCEV(LHS, RHS);
- if (isa<SCEVCouldNotCompute>(Diff))
- return false;
-
- return Diff == FoundDiff;
-}
-
-bool ScalarEvolution::isImpliedCondOperands(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS,
- const SCEV *FoundLHS,
- const SCEV *FoundRHS,
- const Instruction *CtxI) {
- return isImpliedCondOperandsViaRanges(Pred, LHS, RHS, Pred, FoundLHS,
- FoundRHS) ||
- isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS,
- FoundRHS) ||
- isImpliedCondOperandsViaShift(Pred, LHS, RHS, FoundLHS, FoundRHS) ||
- isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS,
- CtxI) ||
- isImpliedCondOperandsViaMatchingDiff(Pred, LHS, RHS, FoundLHS,
- FoundRHS) ||
- isImpliedCondOperandsHelper(Pred, LHS, RHS, FoundLHS, FoundRHS);
-}
-
-/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
-template <typename MinMaxExprType>
-static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
- const SCEV *Candidate) {
- const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
- if (!MinMaxExpr)
- return false;
-
- return is_contained(MinMaxExpr->operands(), Candidate);
-}
-
-static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
- CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS) {
- // If both sides are affine addrecs for the same loop, with equal
- // steps, and we know the recurrences don't wrap, then we only
- // need to check the predicate on the starting values.
-
- if (!ICmpInst::isRelational(Pred))
- return false;
-
- const SCEV *LStart, *RStart, *Step;
- const Loop *L;
- if (!match(LHS,
- m_scev_AffineAddRec(m_SCEV(LStart), m_SCEV(Step), m_Loop(L))) ||
- !match(RHS, m_scev_AffineAddRec(m_SCEV(RStart), m_scev_Specific(Step),
- m_SpecificLoop(L))))
- return false;
- const SCEVAddRecExpr *LAR = cast<SCEVAddRecExpr>(LHS);
- const SCEVAddRecExpr *RAR = cast<SCEVAddRecExpr>(RHS);
- SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
- SCEV::FlagNSW : SCEV::FlagNUW;
- if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
- return false;
-
- return SE.isKnownPredicate(Pred, LStart, RStart);
-}
-
-/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
-/// expression?
-static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE, CmpPredicate Pred,
- const SCEV *LHS, const SCEV *RHS) {
- switch (Pred) {
- default:
- return false;
-
- case ICmpInst::ICMP_SGE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SLE:
- return
- // min(A, ...) <= A
- IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
- // A <= max(A, ...)
- IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
-
- case ICmpInst::ICMP_UGE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_ULE:
- return
- // min(A, ...) <= A
- // FIXME: what about umin_seq?
- IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
- // A <= max(A, ...)
- IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
-
- case ICmpInst::ICMP_UGT:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_ULT:
- // umin(Ops) u<= each Op, so proving Op u< RHS for any Op proves
- // umin(Ops) u< RHS.
- //
- // Use computeConstantDifference instead of the more powerful
- // isKnownPredicate to keep this check cheap: isKnownPredicateViaMinOrMax
- // is called from isKnownViaNonRecursiveReasoning, so recursing into
- // the full predicate prover would be expensive.
- if (const auto *Min = dyn_cast<SCEVUMinExpr>(LHS)) {
- for (SCEVUse Op : Min->operands()) {
- std::optional<APInt> Diff = SE.computeConstantDifference(RHS, Op);
- // When Op and RHS share a common base differing by a
- // constant offset D (RHS - Op = D), Op u< RHS holds iff D != 0 and
- // RHS >= D (unsigned), i.e. the subtraction doesn't underflow.
- if (Diff && !Diff->isZero() && SE.getUnsignedRangeMin(RHS).uge(*Diff))
- return true;
- }
- }
- return false;
- }
-
- llvm_unreachable("covered switch fell through?!");
-}
-
-bool ScalarEvolution::isImpliedViaOperations(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS,
- const SCEV *FoundLHS,
- const SCEV *FoundRHS,
- unsigned Depth) {
- assert(getTypeSizeInBits(LHS->getType()) ==
- getTypeSizeInBits(RHS->getType()) &&
- "LHS and RHS have different sizes?");
- assert(getTypeSizeInBits(FoundLHS->getType()) ==
- getTypeSizeInBits(FoundRHS->getType()) &&
- "FoundLHS and FoundRHS have different sizes?");
- // We want to avoid hurting the compile time with analysis of too big trees.
- if (Depth > MaxSCEVOperationsImplicationDepth)
- return false;
-
- // We only want to work with GT comparison so far.
- if (ICmpInst::isLT(Pred)) {
- Pred = ICmpInst::getSwappedCmpPredicate(Pred);
- std::swap(LHS, RHS);
- std::swap(FoundLHS, FoundRHS);
- }
-
- CmpInst::Predicate P = Pred.getPreferredSignedPredicate();
-
- // For unsigned, try to reduce it to corresponding signed comparison.
- if (P == ICmpInst::ICMP_UGT)
- // We can replace unsigned predicate with its signed counterpart if all
- // involved values are non-negative.
- // TODO: We could have better support for unsigned.
- if (isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) {
- // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing
- // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us
- // use this fact to prove that LHS and RHS are non-negative.
- const SCEV *MinusOne = getMinusOne(LHS->getType());
- if (isImpliedCondOperands(ICmpInst::ICMP_SGT, LHS, MinusOne, FoundLHS,
- FoundRHS) &&
- isImpliedCondOperands(ICmpInst::ICMP_SGT, RHS, MinusOne, FoundLHS,
- FoundRHS))
- P = ICmpInst::ICMP_SGT;
- }
-
- if (P != ICmpInst::ICMP_SGT)
- return false;
-
- auto GetOpFromSExt = [&](const SCEV *S) -> const SCEV * {
- if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
- return Ext->getOperand();
- // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
- // the constant in some cases.
- return S;
- };
-
- // Acquire values from extensions.
- auto *OrigLHS = LHS;
- auto *OrigFoundLHS = FoundLHS;
- LHS = GetOpFromSExt(LHS);
- FoundLHS = GetOpFromSExt(FoundLHS);
-
- // Is the SGT predicate can be proved trivially or using the found context.
- auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
- return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
- isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
- FoundRHS, Depth + 1);
- };
-
- if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
- // We want to avoid creation of any new non-constant SCEV. Since we are
- // going to compare the operands to RHS, we should be certain that we don't
- // need any size extensions for this. So let's decline all cases when the
- // sizes of types of LHS and RHS do not match.
- // TODO: Maybe try to get RHS from sext to catch more cases?
- if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
- return false;
-
- // Should not overflow.
- if (!LHSAddExpr->hasNoSignedWrap())
- return false;
-
- SCEVUse LL = LHSAddExpr->getOperand(0);
- SCEVUse LR = LHSAddExpr->getOperand(1);
- auto *MinusOne = getMinusOne(RHS->getType());
-
- // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
- auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
- return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
- };
- // Try to prove the following rule:
- // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
- // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
- if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
- return true;
- } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
- Value *LL, *LR;
- // FIXME: Once we have SDiv implemented, we can get rid of this matching.
-
- using namespace llvm::PatternMatch;
-
- if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
- // Rules for division.
- // We are going to perform some comparisons with Denominator and its
- // derivative expressions. In general case, creating a SCEV for it may
- // lead to a complex analysis of the entire graph, and in particular it
- // can request trip count recalculation for the same loop. This would
- // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
- // this, we only want to create SCEVs that are constants in this section.
- // So we bail if Denominator is not a constant.
- if (!isa<ConstantInt>(LR))
- return false;
-
- auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
-
- // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
- // then a SCEV for the numerator already exists and matches with FoundLHS.
- auto *Numerator = getExistingSCEV(LL);
- if (!Numerator || Numerator->getType() != FoundLHS->getType())
- return false;
-
- // Make sure that the numerator matches with FoundLHS and the denominator
- // is positive.
- if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
- return false;
-
- auto *DTy = Denominator->getType();
- auto *FRHSTy = FoundRHS->getType();
- if (DTy->isPointerTy() != FRHSTy->isPointerTy())
- // One of types is a pointer and another one is not. We cannot extend
- // them properly to a wider type, so let us just reject this case.
- // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
- // to avoid this check.
- return false;
-
- // Given that:
- // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
- auto *WTy = getWiderType(DTy, FRHSTy);
- auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
- auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
-
- // Try to prove the following rule:
- // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
- // For example, given that FoundLHS > 2. It means that FoundLHS is at
- // least 3. If we divide it by Denominator < 4, we will have at least 1.
- auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
- if (isKnownNonPositive(RHS) &&
- IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
- return true;
-
- // Try to prove the following rule:
- // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
- // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
- // If we divide it by Denominator > 2, then:
- // 1. If FoundLHS is negative, then the result is 0.
- // 2. If FoundLHS is non-negative, then the result is non-negative.
- // Anyways, the result is non-negative.
- auto *MinusOne = getMinusOne(WTy);
- auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
- if (isKnownNegative(RHS) &&
- IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
- return true;
- }
- }
-
- // If our expression contained SCEVUnknown Phis, and we split it down and now
- // need to prove something for them, try to prove the predicate for every
- // possible incoming values of those Phis.
- if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
- return true;
-
- return false;
-}
-
-static bool isKnownPredicateExtendIdiom(CmpPredicate Pred, const SCEV *LHS,
- const SCEV *RHS) {
- // zext x u<= sext x, sext x s<= zext x
- const SCEV *Op;
- switch (Pred) {
- case ICmpInst::ICMP_SGE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_SLE: {
- // If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
- return match(LHS, m_scev_SExt(m_SCEV(Op))) &&
- match(RHS, m_scev_ZExt(m_scev_Specific(Op)));
- }
- case ICmpInst::ICMP_UGE:
- std::swap(LHS, RHS);
- [[fallthrough]];
- case ICmpInst::ICMP_ULE: {
- // If operand >=u 0 then ZExt == SExt. If operand <u 0 then ZExt <u SExt.
- return match(LHS, m_scev_ZExt(m_SCEV(Op))) &&
- match(RHS, m_scev_SExt(m_scev_Specific(Op)));
- }
- default:
- return false;
- };
- llvm_unreachable("unhandled case");
-}
-
-bool ScalarEvolution::isKnownViaNonRecursiveReasoning(CmpPredicate Pred,
- SCEVUse LHS,
- SCEVUse RHS) {
- return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
- isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
- IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
- IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
- isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
-}
-
-bool ScalarEvolution::isImpliedCondOperandsHelper(CmpPredicate Pred,
- const SCEV *LHS,
- const SCEV *RHS,
- const SCEV *FoundLHS,
- const SCEV *FoundRHS) {
- switch (Pred) {
- default:
- llvm_unreachable("Unexpected CmpPredicate value!");
- case ICmpInst::ICMP_EQ:
- case ICmpInst::ICMP_NE:
- if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
- return true;
- break;
- case ICmpInst::ICMP_SLT:
- case ICmpInst::ICMP_SLE:
- if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
- isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
- return true;
- break;
- case ICmpInst::ICMP_SGT:
- case ICmpInst::ICMP_SGE:
- if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
- isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
- return true;
- break;
- case ICmpInst::ICMP_ULT:
- case ICmpInst::ICMP_ULE:
- if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
- isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
- return true;
- break;
- case ICmpInst::ICMP_UGT:
- case ICmpInst::ICMP_UGE:
- if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
- isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
- return true;
- break;
- }
-
- // Maybe it can be proved via operations?
- if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
- return true;
-
- return false;
-}
-
-bool ScalarEvolution::isImpliedCondOperandsViaRanges(
- CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, CmpPredicate FoundPred,
- const SCEV *FoundLHS, const SCEV *FoundRHS) {
- if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
- // The restriction on `FoundRHS` be lifted easily -- it exists only to
- // reduce the compile time impact of this optimization.
- return false;
-
- std::optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
- if (!Addend)
- return false;
-
- const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
-
- // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
- // antecedent "`FoundLHS` `FoundPred` `FoundRHS`".
- ConstantRange FoundLHSRange =
- ConstantRange::makeExactICmpRegion(FoundPred, ConstFoundRHS);
-
- // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
- ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
-
- // We can also compute the range of values for `LHS` that satisfy the
- // consequent, "`LHS` `Pred` `RHS`":
- const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
- // The antecedent implies the consequent if every value of `LHS` that
- // satisfies the antecedent also satisfies the consequent.
- return LHSRange.icmp(Pred, ConstRHS);
-}
-
-bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
- bool IsSigned) {
- assert(isKnownPositive(Stride) && "Positive stride expected!");
-
- unsigned BitWidth = getTypeSizeInBits(RHS->getType());
- const SCEV *One = getOne(Stride->getType());
-
- if (IsSigned) {
- APInt MaxRHS = getSignedRangeMax(RHS);
- APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
- APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
-
- // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
- return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
- }
-
- APInt MaxRHS = getUnsignedRangeMax(RHS);
- APInt MaxValue = APInt::getMaxValue(BitWidth);
- APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
-
- // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
- return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
-}
-
-bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
- bool IsSigned) {
-
- unsigned BitWidth = getTypeSizeInBits(RHS->getType());
- const SCEV *One = getOne(Stride->getType());
-
- if (IsSigned) {
- APInt MinRHS = getSignedRangeMin(RHS);
- APInt MinValue = APInt::getSignedMinValue(BitWidth);
- APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
-
- // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
- return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
- }
-
- APInt MinRHS = getUnsignedRangeMin(RHS);
- APInt MinValue = APInt::getMinValue(BitWidth);
- APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
-
- // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
- return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
-}
-
-const SCEV *ScalarEvolution::getUDivCeilSCEV(const SCEV *N, const SCEV *D) {
- // umin(N, 1) + floor((N - umin(N, 1)) / D)
- // This is equivalent to "1 + floor((N - 1) / D)" for N != 0. The umin
- // expression fixes the case of N=0.
- const SCEV *MinNOne = getUMinExpr(N, getOne(N->getType()));
- const SCEV *NMinusOne = getMinusSCEV(N, MinNOne);
- return getAddExpr(MinNOne, getUDivExpr(NMinusOne, D));
-}
-
-const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
- const SCEV *Stride,
- const SCEV *End,
- unsigned BitWidth,
- bool IsSigned) {
- // The logic in this function assumes we can represent a positive stride.
- // If we can't, the backedge-taken count must be zero.
- if (IsSigned && BitWidth == 1)
- return getZero(Stride->getType());
-
- // This code below only been closely audited for negative strides in the
- // unsigned comparison case, it may be correct for signed comparison, but
- // that needs to be established.
- if (IsSigned && isKnownNegative(Stride))
- return getCouldNotCompute();
-
- // Calculate the maximum backedge count based on the range of values
- // permitted by Start, End, and Stride.
- APInt MinStart =
- IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
-
- APInt MinStride =
- IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
-
- // We assume either the stride is positive, or the backedge-taken count
- // is zero. So force StrideForMaxBECount to be at least one.
- APInt One(BitWidth, 1);
- APInt StrideForMaxBECount = IsSigned ? APIntOps::smax(One, MinStride)
- : APIntOps::umax(One, MinStride);
-
- APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
- : APInt::getMaxValue(BitWidth);
- APInt Limit = MaxValue - (StrideForMaxBECount - 1);
-
- // Although End can be a MAX expression we estimate MaxEnd considering only
- // the case End = RHS of the loop termination condition. This is safe because
- // in the other case (End - Start) is zero, leading to a zero maximum backedge
- // taken count.
- APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
- : APIntOps::umin(getUnsignedRangeMax(End), Limit);
-
- // MaxBECount = ceil((max(MaxEnd, MinStart) - MinStart) / Stride)
- MaxEnd = IsSigned ? APIntOps::smax(MaxEnd, MinStart)
- : APIntOps::umax(MaxEnd, MinStart);
-
- return getUDivCeilSCEV(getConstant(MaxEnd - MinStart) /* Delta */,
- getConstant(StrideForMaxBECount) /* Step */);
-}
-
-ScalarEvolution::ExitLimit
-ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
- const Loop *L, bool IsSigned,
- bool ControlsOnlyExit, bool AllowPredicates) {
- SmallVector<const SCEVPredicate *> Predicates;
-
- const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
- bool PredicatedIV = false;
- if (!IV) {
- if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS)) {
- const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(ZExt->getOperand());
- if (AR && AR->getLoop() == L && AR->isAffine()) {
- auto canProveNUW = [&]() {
- // We can use the comparison to infer no-wrap flags only if it fully
- // controls the loop exit.
- if (!ControlsOnlyExit)
- return false;
-
- if (!isLoopInvariant(RHS, L))
- return false;
-
- if (!isKnownNonZero(AR->getStepRecurrence(*this)))
- // We need the sequence defined by AR to strictly increase in the
- // unsigned integer domain for the logic below to hold.
- return false;
-
- const unsigned InnerBitWidth = getTypeSizeInBits(AR->getType());
- const unsigned OuterBitWidth = getTypeSizeInBits(RHS->getType());
- // If RHS <=u Limit, then there must exist a value V in the sequence
- // defined by AR (e.g. {Start,+,Step}) such that V >u RHS, and
- // V <=u UINT_MAX. Thus, we must exit the loop before unsigned
- // overflow occurs. This limit also implies that a signed comparison
- // (in the wide bitwidth) is equivalent to an unsigned comparison as
- // the high bits on both sides must be zero.
- APInt StrideMax = getUnsignedRangeMax(AR->getStepRecurrence(*this));
- APInt Limit = APInt::getMaxValue(InnerBitWidth) - (StrideMax - 1);
- Limit = Limit.zext(OuterBitWidth);
- return getUnsignedRangeMax(applyLoopGuards(RHS, L)).ule(Limit);
- };
- auto Flags = AR->getNoWrapFlags();
- if (!hasFlags(Flags, SCEV::FlagNUW) && canProveNUW())
- Flags = setFlags(Flags, SCEV::FlagNUW);
-
- setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
- if (AR->hasNoUnsignedWrap()) {
- // Emulate what getZeroExtendExpr would have done during construction
- // if we'd been able to infer the fact just above at that time.
- const SCEV *Step = AR->getStepRecurrence(*this);
- Type *Ty = ZExt->getType();
- auto *S = getAddRecExpr(
- getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 0),
- getZeroExtendExpr(Step, Ty, 0), L, AR->getNoWrapFlags());
- IV = dyn_cast<SCEVAddRecExpr>(S);
- }
- }
- }
- }
-
-
- if (!IV && AllowPredicates) {
- // Try to make this an AddRec using runtime tests, in the first X
- // iterations of this loop, where X is the SCEV expression found by the
- // algorithm below.
- IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
- PredicatedIV = true;
- }
-
- // Avoid weird loops
- if (!IV || IV->getLoop() != L || !IV->isAffine())
- return getCouldNotCompute();
-
- // A precondition of this method is that the condition being analyzed
- // reaches an exiting branch which dominates the latch. Given that, we can
- // assume that an increment which violates the nowrap specification and
- // produces poison must cause undefined behavior when the resulting poison
- // value is branched upon and thus we can conclude that the backedge is
- // taken no more often than would be required to produce that poison value.
- // Note that a well defined loop can exit on the iteration which violates
- // the nowrap specification if there is another exit (either explicit or
- // implicit/exceptional) which causes the loop to execute before the
- // exiting instruction we're analyzing would trigger UB.
- auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
- bool NoWrap = ControlsOnlyExit && any(IV->getNoWrapFlags(WrapType));
- ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT;
-
- const SCEV *Stride = IV->getStepRecurrence(*this);
-
- bool PositiveStride = isKnownPositive(Stride);
-
- // Avoid negative or zero stride values.
- if (!PositiveStride) {
- // We can compute the correct backedge taken count for loops with unknown
- // strides if we can prove that the loop is not an infinite loop with side
- // effects. Here's the loop structure we are trying to handle -
- //
- // i = start
- // do {
- // A[i] = i;
- // i += s;
- // } while (i < end);
- //
- // The backedge taken count for such loops is evaluated as -
- // (max(end, start + stride) - start - 1) /u stride
- //
- // The additional preconditions that we need to check to prove correctness
- // of the above formula is as follows -
- //
- // a) IV is either nuw or nsw depending upon signedness (indicated by the
- // NoWrap flag).
- // b) the loop is guaranteed to be finite (e.g. is mustprogress and has
- // no side effects within the loop)
- // c) loop has a single static exit (with no abnormal exits)
- //
- // Precondition a) implies that if the stride is negative, this is a single
- // trip loop. The backedge taken count formula reduces to zero in this case.
- //
- // Precondition b) and c) combine to imply that if rhs is invariant in L,
- // then a zero stride means the backedge can't be taken without executing
- // undefined behavior.
- //
- // The positive stride case is the same as isKnownPositive(Stride) returning
- // true (original behavior of the function).
- //
- if (PredicatedIV || !NoWrap || !loopIsFiniteByAssumption(L) ||
- !loopHasNoAbnormalExits(L))
- return getCouldNotCompute();
-
- if (!isKnownNonZero(Stride)) {
- // If we have a step of zero, and RHS isn't invariant in L, we don't know
- // if it might eventually be greater than start and if so, on which
- // iteration. We can't even produce a useful upper bound.
- if (!isLoopInvariant(RHS, L))
- return getCouldNotCompute();
-
- // We allow a potentially zero stride, but we need to divide by stride
- // below. Since the loop can't be infinite and this check must control
- // the sole exit, we can infer the exit must be taken on the first
- // iteration (e.g. backedge count = 0) if the stride is zero. Given that,
- // we know the numerator in the divides below must be zero, so we can
- // pick an arbitrary non-zero value for the denominator (e.g. stride)
- // and produce the right result.
- // FIXME: Handle the case where Stride is poison?
- auto wouldZeroStrideBeUB = [&]() {
- // Proof by contradiction. Suppose the stride were zero. If we can
- // prove that the backedge *is* taken on the first iteration, then since
- // we know this condition controls the sole exit, we must have an
- // infinite loop. We can't have a (well defined) infinite loop per
- // check just above.
- // Note: The (Start - Stride) term is used to get the start' term from
- // (start' + stride,+,stride). Remember that we only care about the
- // result of this expression when stride == 0 at runtime.
- auto *StartIfZero = getMinusSCEV(IV->getStart(), Stride);
- return isLoopEntryGuardedByCond(L, Cond, StartIfZero, RHS);
- };
- if (!wouldZeroStrideBeUB()) {
- Stride = getUMaxExpr(Stride, getOne(Stride->getType()));
- }
- }
- }else if (!NoWrap) {
- // Avoid proven overflow cases: this will ensure that the backedge taken
- // count will not generate any unsigned overflow.
- if (canIVOverflowOnLT(RHS, Stride, IsSigned)) {
- if (!AllowPredicates)
- return getCouldNotCompute();
-
- unsigned BitWidth = getTypeSizeInBits(RHS->getType());
- const SCEV *One = getOne(Stride->getType());
- const SCEV *StrideMinusOne = getMinusSCEV(Stride, One);
-
- APInt MaxStrideMinusOne = IsSigned ? getSignedRangeMax(StrideMinusOne)
- : getUnsignedRangeMax(StrideMinusOne);
- APInt Limit = (IsSigned ? APInt::getSignedMaxValue(BitWidth)
- : APInt::getMaxValue(BitWidth)) -
- MaxStrideMinusOne;
-
- Predicates.push_back(getComparePredicate(
- IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE, RHS,
- getConstant(Limit)));
- }
- }
-
- // On all paths just preceeding, we established the following invariant:
- // IV can be assumed not to overflow up to and including the exiting
- // iteration. We proved this in one of two ways:
- // 1) We can show overflow doesn't occur before the exiting iteration
- // 1a) canIVOverflowOnLT, and b) step of one
- // 2) We can show that if overflow occurs, the loop must execute UB
- // before any possible exit.
- // Note that we have not yet proved RHS invariant (in general).
-
- const SCEV *Start = IV->getStart();
-
- // Preserve pointer-typed Start/RHS to pass to isLoopEntryGuardedByCond.
- // If we convert to integers, isLoopEntryGuardedByCond will miss some cases.
- // Use integer-typed versions for actual computation; we can't subtract
- // pointers in general.
- const SCEV *OrigStart = Start;
- const SCEV *OrigRHS = RHS;
- if (Start->getType()->isPointerTy()) {
- Start = getPtrToAddrExpr(Start);
- if (isa<SCEVCouldNotCompute>(Start))
- return Start;
- }
- if (RHS->getType()->isPointerTy()) {
- RHS = getPtrToAddrExpr(RHS);
- if (isa<SCEVCouldNotCompute>(RHS))
- return RHS;
- }
-
- const SCEV *End = nullptr, *BECount = nullptr,
- *BECountIfBackedgeTaken = nullptr;
- if (!isLoopInvariant(RHS, L)) {
- const auto *RHSAddRec = dyn_cast<SCEVAddRecExpr>(RHS);
- if (PositiveStride && RHSAddRec != nullptr && RHSAddRec->getLoop() == L &&
- any(RHSAddRec->getNoWrapFlags())) {
- // The structure of loop we are trying to calculate backedge count of:
- //
- // left = left_start
- // right = right_start
- //
- // while(left < right){
- // ... do something here ...
- // left += s1; // stride of left is s1 (s1 > 0)
- // right += s2; // stride of right is s2 (s2 < 0)
- // }
- //
-
- const SCEV *RHSStart = RHSAddRec->getStart();
- const SCEV *RHSStride = RHSAddRec->getStepRecurrence(*this);
-
- // If Stride - RHSStride is positive and does not overflow, we can write
- // backedge count as ->
- // ceil((End - Start) /u (Stride - RHSStride))
- // Where, End = max(RHSStart, Start)
-
- // Check if RHSStride < 0 and Stride - RHSStride will not overflow.
- if (isKnownNegative(RHSStride) &&
- willNotOverflow(Instruction::Sub, /*Signed=*/true, Stride,
- RHSStride)) {
-
- const SCEV *Denominator = getMinusSCEV(Stride, RHSStride);
- if (isKnownPositive(Denominator)) {
- End = IsSigned ? getSMaxExpr(RHSStart, Start)
- : getUMaxExpr(RHSStart, Start);
-
- // We can do this because End >= Start, as End = max(RHSStart, Start)
- const SCEV *Delta = getMinusSCEV(End, Start);
-
- BECount = getUDivCeilSCEV(Delta, Denominator);
- BECountIfBackedgeTaken =
- getUDivCeilSCEV(getMinusSCEV(RHSStart, Start), Denominator);
- }
- }
- }
- if (BECount == nullptr) {
- // If we cannot calculate ExactBECount, we can calculate the MaxBECount,
- // given the start, stride and max value for the end bound of the
- // loop (RHS), and the fact that IV does not overflow (which is
- // checked above).
- const SCEV *MaxBECount = computeMaxBECountForLT(
- Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
- return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
- MaxBECount, false /*MaxOrZero*/, Predicates);
- }
- } else {
- // We use the expression (max(End,Start)-Start)/Stride to describe the
- // backedge count, as if the backedge is taken at least once
- // max(End,Start) is End and so the result is as above, and if not
- // max(End,Start) is Start so we get a backedge count of zero.
- auto *OrigStartMinusStride = getMinusSCEV(OrigStart, Stride);
- assert(isAvailableAtLoopEntry(OrigStartMinusStride, L) && "Must be!");
- assert(isAvailableAtLoopEntry(OrigStart, L) && "Must be!");
- assert(isAvailableAtLoopEntry(OrigRHS, L) && "Must be!");
- // Can we prove (max(RHS,Start) > Start - Stride?
- if (isLoopEntryGuardedByCond(L, Cond, OrigStartMinusStride, OrigStart) &&
- isLoopEntryGuardedByCond(L, Cond, OrigStartMinusStride, OrigRHS)) {
- // In this case, we can use a refined formula for computing backedge
- // taken count. The general formula remains:
- // "End-Start /uceiling Stride" where "End = max(RHS,Start)"
- // We want to use the alternate formula:
- // "((End - 1) - (Start - Stride)) /u Stride"
- // Let's do a quick case analysis to show these are equivalent under
- // our precondition that max(RHS,Start) > Start - Stride.
- // * For RHS <= Start, the backedge-taken count must be zero.
- // "((End - 1) - (Start - Stride)) /u Stride" reduces to
- // "((Start - 1) - (Start - Stride)) /u Stride" which simplies to
- // "Stride - 1 /u Stride" which is indeed zero for all non-zero values
- // of Stride. For 0 stride, we've use umin(1,Stride) above,
- // reducing this to the stride of 1 case.
- // * For RHS >= Start, the backedge count must be "RHS-Start /uceil
- // Stride".
- // "((End - 1) - (Start - Stride)) /u Stride" reduces to
- // "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to
- // "((RHS - (Start - Stride) - 1) /u Stride".
- // Our preconditions trivially imply no overflow in that form.
- const SCEV *MinusOne = getMinusOne(Stride->getType());
- const SCEV *Numerator =
- getMinusSCEV(getAddExpr(RHS, MinusOne), getMinusSCEV(Start, Stride));
- BECount = getUDivExpr(Numerator, Stride);
- }
-
- if (!BECount) {
- auto canProveRHSGreaterThanEqualStart = [&]() {
- auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
- const SCEV *GuardedRHS = applyLoopGuards(OrigRHS, L);
- const SCEV *GuardedStart = applyLoopGuards(OrigStart, L);
-
- if (isLoopEntryGuardedByCond(L, CondGE, OrigRHS, OrigStart) ||
- isKnownPredicate(CondGE, GuardedRHS, GuardedStart))
- return true;
-
- // (RHS > Start - 1) implies RHS >= Start.
- // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if
- // "Start - 1" doesn't overflow.
- // * For signed comparison, if Start - 1 does overflow, it's equal
- // to INT_MAX, and "RHS >s INT_MAX" is trivially false.
- // * For unsigned comparison, if Start - 1 does overflow, it's equal
- // to UINT_MAX, and "RHS >u UINT_MAX" is trivially false.
- //
- // FIXME: Should isLoopEntryGuardedByCond do this for us?
- auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
- auto *StartMinusOne =
- getAddExpr(OrigStart, getMinusOne(OrigStart->getType()));
- return isLoopEntryGuardedByCond(L, CondGT, OrigRHS, StartMinusOne);
- };
-
- // If we know that RHS >= Start in the context of loop, then we know
- // that max(RHS, Start) = RHS at this point.
- if (canProveRHSGreaterThanEqualStart()) {
- End = RHS;
- } else {
- // If RHS < Start, the backedge will be taken zero times. So in
- // general, we can write the backedge-taken count as:
- //
- // RHS >= Start ? ceil(RHS - Start) / Stride : 0
- //
- // We convert it to the following to make it more convenient for SCEV:
- //
- // ceil(max(RHS, Start) - Start) / Stride
- End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
-
- // See what would happen if we assume the backedge is taken. This is
- // used to compute MaxBECount.
- BECountIfBackedgeTaken =
- getUDivCeilSCEV(getMinusSCEV(RHS, Start), Stride);
- }
-
- // At this point, we know:
- //
- // 1. If IsSigned, Start <=s End; otherwise, Start <=u End
- // 2. The index variable doesn't overflow.
- //
- // Therefore, we know N exists such that
- // (Start + Stride * N) >= End, and computing "(Start + Stride * N)"
- // doesn't overflow.
- //
- // Using this information, try to prove whether the addition in
- // "(Start - End) + (Stride - 1)" has unsigned overflow.
- const SCEV *One = getOne(Stride->getType());
- bool MayAddOverflow = [&] {
- if (isKnownToBeAPowerOfTwo(Stride)) {
- // Suppose Stride is a power of two, and Start/End are unsigned
- // integers. Let UMAX be the largest representable unsigned
- // integer.
- //
- // By the preconditions of this function, we know
- // "(Start + Stride * N) >= End", and this doesn't overflow.
- // As a formula:
- //
- // End <= (Start + Stride * N) <= UMAX
- //
- // Subtracting Start from all the terms:
- //
- // End - Start <= Stride * N <= UMAX - Start
- //
- // Since Start is unsigned, UMAX - Start <= UMAX. Therefore:
- //
- // End - Start <= Stride * N <= UMAX
- //
- // Stride * N is a multiple of Stride. Therefore,
- //
- // End - Start <= Stride * N <= UMAX - (UMAX mod Stride)
- //
- // Since Stride is a power of two, UMAX + 1 is divisible by
- // Stride. Therefore, UMAX mod Stride == Stride - 1. So we can
- // write:
- //
- // End - Start <= Stride * N <= UMAX - Stride - 1
- //
- // Dropping the middle term:
- //
- // End - Start <= UMAX - Stride - 1
- //
- // Adding Stride - 1 to both sides:
- //
- // (End - Start) + (Stride - 1) <= UMAX
- //
- // In other words, the addition doesn't have unsigned overflow.
- //
- // A similar proof works if we treat Start/End as signed values.
- // Just rewrite steps before "End - Start <= Stride * N <= UMAX"
- // to use signed max instead of unsigned max. Note that we're
- // trying to prove a lack of unsigned overflow in either case.
- return false;
- }
- if (Start == Stride || Start == getMinusSCEV(Stride, One)) {
- // If Start is equal to Stride, (End - Start) + (Stride - 1) == End
- // - 1. If !IsSigned, 0 <u Stride == Start <=u End; so 0 <u End - 1
- // <u End. If IsSigned, 0 <s Stride == Start <=s End; so 0 <s End -
- // 1 <s End.
- //
- // If Start is equal to Stride - 1, (End - Start) + Stride - 1 ==
- // End.
- return false;
- }
- return true;
- }();
-
- const SCEV *Delta = getMinusSCEV(End, Start);
- if (!MayAddOverflow) {
- // floor((D + (S - 1)) / S)
- // We prefer this formulation if it's legal because it's fewer
- // operations.
- BECount =
- getUDivExpr(getAddExpr(Delta, getMinusSCEV(Stride, One)), Stride);
- } else {
- BECount = getUDivCeilSCEV(Delta, Stride);
- }
- }
- }
-
- const SCEV *ConstantMaxBECount;
- bool MaxOrZero = false;
- if (isa<SCEVConstant>(BECount)) {
- ConstantMaxBECount = BECount;
- } else if (BECountIfBackedgeTaken &&
- isa<SCEVConstant>(BECountIfBackedgeTaken)) {
- // If we know exactly how many times the backedge will be taken if it's
- // taken at least once, then the backedge count will either be that or
- // zero.
- ConstantMaxBECount = BECountIfBackedgeTaken;
- MaxOrZero = true;
- } else {
- ConstantMaxBECount = computeMaxBECountForLT(
- Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
- }
-
- if (isa<SCEVCouldNotCompute>(ConstantMaxBECount) &&
- !isa<SCEVCouldNotCompute>(BECount))
- ConstantMaxBECount = getConstant(getUnsignedRangeMax(BECount));
-
- const SCEV *SymbolicMaxBECount =
- isa<SCEVCouldNotCompute>(BECount) ? ConstantMaxBECount : BECount;
- return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, MaxOrZero,
- Predicates);
-}
-
-ScalarEvolution::ExitLimit ScalarEvolution::howManyGreaterThans(
- const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned,
- bool ControlsOnlyExit, bool AllowPredicates) {
- SmallVector<const SCEVPredicate *> Predicates;
- // We handle only IV > Invariant
- if (!isLoopInvariant(RHS, L))
- return getCouldNotCompute();
-
- const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
- if (!IV && AllowPredicates)
- // Try to make this an AddRec using runtime tests, in the first X
- // iterations of this loop, where X is the SCEV expression found by the
- // algorithm below.
- IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
-
- // Avoid weird loops
- if (!IV || IV->getLoop() != L || !IV->isAffine())
- return getCouldNotCompute();
-
- auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
- bool NoWrap = ControlsOnlyExit && any(IV->getNoWrapFlags(WrapType));
- ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
-
- const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
-
- // Avoid negative or zero stride values
- if (!isKnownPositive(Stride))
- return getCouldNotCompute();
-
- // Avoid proven overflow cases: this will ensure that the backedge taken count
- // will not generate any unsigned overflow. Relaxed no-overflow conditions
- // exploit NoWrapFlags, allowing to optimize in presence of undefined
- // behaviors like the case of C language.
- if (!Stride->isOne() && !NoWrap)
- if (canIVOverflowOnGT(RHS, Stride, IsSigned))
- return getCouldNotCompute();
-
- const SCEV *Start = IV->getStart();
- const SCEV *End = RHS;
- if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
- // If we know that Start >= RHS in the context of loop, then we know that
- // min(RHS, Start) = RHS at this point.
- if (isLoopEntryGuardedByCond(
- L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS))
- End = RHS;
- else
- End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
- }
-
- if (Start->getType()->isPointerTy()) {
- Start = getPtrToAddrExpr(Start);
- if (isa<SCEVCouldNotCompute>(Start))
- return Start;
- }
- if (End->getType()->isPointerTy()) {
- End = getPtrToAddrExpr(End);
- if (isa<SCEVCouldNotCompute>(End))
- return End;
- }
-
- // Compute ((Start - End) + (Stride - 1)) / Stride.
- // FIXME: This can overflow. Holding off on fixing this for now;
- // howManyGreaterThans will hopefully be gone soon.
- const SCEV *One = getOne(Stride->getType());
- const SCEV *BECount = getUDivExpr(
- getAddExpr(getMinusSCEV(Start, End), getMinusSCEV(Stride, One)), Stride);
-
- APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
- : getUnsignedRangeMax(Start);
-
- APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
- : getUnsignedRangeMin(Stride);
-
- unsigned BitWidth = getTypeSizeInBits(LHS->getType());
- APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
- : APInt::getMinValue(BitWidth) + (MinStride - 1);
-
- // Although End can be a MIN expression we estimate MinEnd considering only
- // the case End = RHS. This is safe because in the other case (Start - End)
- // is zero, leading to a zero maximum backedge taken count.
- APInt MinEnd =
- IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
- : APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
-
- const SCEV *ConstantMaxBECount =
- isa<SCEVConstant>(BECount)
- ? BECount
- : getUDivCeilSCEV(getConstant(MaxStart - MinEnd),
- getConstant(MinStride));
-
- if (isa<SCEVCouldNotCompute>(ConstantMaxBECount))
- ConstantMaxBECount = BECount;
- const SCEV *SymbolicMaxBECount =
- isa<SCEVCouldNotCompute>(BECount) ? ConstantMaxBECount : BECount;
-
- return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, false,
- Predicates);
-}
-
-const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
- ScalarEvolution &SE) const {
- if (Range.isFullSet()) // Infinite loop.
- return SE.getCouldNotCompute();
-
- // If the start is a non-zero constant, shift the range to simplify things.
- if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
- if (!SC->getValue()->isZero()) {
- SmallVector<SCEVUse, 4> Operands(operands());
- Operands[0] = SE.getZero(SC->getType());
- const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
- getNoWrapFlags(FlagNW));
- if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
- return ShiftedAddRec->getNumIterationsInRange(
- Range.subtract(SC->getAPInt()), SE);
- // This is strange and shouldn't happen.
- return SE.getCouldNotCompute();
- }
-
- // The only time we can solve this is when we have all constant indices.
- // Otherwise, we cannot determine the overflow conditions.
- if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
- return SE.getCouldNotCompute();
-
- // Okay at this point we know that all elements of the chrec are constants and
- // that the start element is zero.
-
- // First check to see if the range contains zero. If not, the first
- // iteration exits.
- unsigned BitWidth = SE.getTypeSizeInBits(getType());
- if (!Range.contains(APInt(BitWidth, 0)))
- return SE.getZero(getType());
-
- if (isAffine()) {
- // If this is an affine expression then we have this situation:
- // Solve {0,+,A} in Range === Ax in Range
-
- // We know that zero is in the range. If A is positive then we know that
- // the upper value of the range must be the first possible exit value.
- // If A is negative then the lower of the range is the last possible loop
- // value. Also note that we already checked for a full range.
- APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
- APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
-
- // The exit value should be (End+A)/A.
- APInt ExitVal = (End + A).udiv(A);
- ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
-
- // Evaluate at the exit value. If we really did fall out of the valid
- // range, then we computed our trip count, otherwise wrap around or other
- // things must have happened.
- ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
- if (Range.contains(Val->getValue()))
- return SE.getCouldNotCompute(); // Something strange happened
-
- // Ensure that the previous value is in the range.
- assert(Range.contains(
- EvaluateConstantChrecAtConstant(this,
- ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
- "Linear scev computation is off in a bad way!");
- return SE.getConstant(ExitValue);
- }
-
- if (isQuadratic()) {
- if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
- return SE.getConstant(*S);
- }
-
- return SE.getCouldNotCompute();
-}
-
-const SCEVAddRecExpr *
-SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
- assert(getNumOperands() > 1 && "AddRec with zero step?");
- // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
- // but in this case we cannot guarantee that the value returned will be an
- // AddRec because SCEV does not have a fixed point where it stops
- // simplification: it is legal to return ({rec1} + {rec2}). For example, it
- // may happen if we reach arithmetic depth limit while simplifying. So we
- // construct the returned value explicitly.
- SmallVector<SCEVUse, 3> Ops;
- // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
- // (this + Step) is {A+B,+,B+C,+...,+,N}.
- for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
- Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
- // We know that the last operand is not a constant zero (otherwise it would
- // have been popped out earlier). This guarantees us that if the result has
- // the same last operand, then it will also not be popped out, meaning that
- // the returned value will be an AddRec.
- const SCEV *Last = getOperand(getNumOperands() - 1);
- assert(!Last->isZero() && "Recurrency with zero step?");
- Ops.push_back(Last);
- return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
- SCEV::FlagAnyWrap));
-}
-
-// Return true when S contains at least an undef value.
-bool ScalarEvolution::containsUndefs(const SCEV *S) const {
- return SCEVExprContains(
- S, [](const SCEV *S) { return match(S, m_scev_UndefOrPoison()); });
-}
-
-// Return true when S contains a value that is a nullptr.
-bool ScalarEvolution::containsErasedValue(const SCEV *S) const {
- return SCEVExprContains(S, [](const SCEV *S) {
- if (const auto *SU = dyn_cast<SCEVUnknown>(S))
- return SU->getValue() == nullptr;
- return false;
- });
-}
-
-/// Return the size of an element read or written by Inst.
-const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
- Type *Ty;
- Type *PtrTy;
- if (StoreInst *Store = dyn_cast<StoreInst>(Inst)) {
- Ty = Store->getValueOperand()->getType();
- PtrTy = Store->getPointerOperandType();
- } else if (LoadInst *Load = dyn_cast<LoadInst>(Inst)) {
- Ty = Load->getType();
- PtrTy = Load->getPointerOperandType();
- } else {
- return nullptr;
- }
-
- Type *ETy = getEffectiveSCEVType(PtrTy);
- return getSizeOfExpr(ETy, Ty);
-}
-
-//===----------------------------------------------------------------------===//
-// SCEVCallbackVH Class Implementation
-//===----------------------------------------------------------------------===//
-
-void ScalarEvolution::SCEVCallbackVH::deleted() {
- assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
- if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
- SE->ConstantEvolutionLoopExitValue.erase(PN);
- SE->eraseValueFromMap(getValPtr());
- // this now dangles!
-}
-
-void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
- assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
-
- // Forget all the expressions associated with users of the old value,
- // so that future queries will recompute the expressions using the new
- // value.
- SE->forgetValue(getValPtr());
- // this now dangles!
-}
-
-ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
- : CallbackVH(V), SE(se) {}
-
-//===----------------------------------------------------------------------===//
-// ScalarEvolution Class Implementation
-//===----------------------------------------------------------------------===//
-
-ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
- AssumptionCache &AC, DominatorTree &DT,
- LoopInfo &LI)
- : F(F), DL(F.getDataLayout()), TLI(TLI), AC(AC), DT(DT), LI(LI),
- CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
- LoopDispositions(64), BlockDispositions(64) {
- // To use guards for proving predicates, we need to scan every instruction in
- // relevant basic blocks, and not just terminators. Doing this is a waste of
- // time if the IR does not actually contain any calls to
- // @llvm.experimental.guard, so do a quick check and remember this beforehand.
- //
- // This pessimizes the case where a pass that preserves ScalarEvolution wants
- // to _add_ guards to the module when there weren't any before, and wants
- // ScalarEvolution to optimize based on those guards. For now we prefer to be
- // efficient in lieu of being smart in that rather obscure case.
-
- auto *GuardDecl = Intrinsic::getDeclarationIfExists(
- F.getParent(), Intrinsic::experimental_guard);
- HasGuards = GuardDecl && !GuardDecl->use_empty();
-}
-
-ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
- : F(Arg.F), DL(Arg.DL), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC),
- DT(Arg.DT), LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
- ValueExprMap(std::move(Arg.ValueExprMap)),
- PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
- PendingMerges(std::move(Arg.PendingMerges)),
- ConstantMultipleCache(std::move(Arg.ConstantMultipleCache)),
- BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
- PredicatedBackedgeTakenCounts(
- std::move(Arg.PredicatedBackedgeTakenCounts)),
- BECountUsers(std::move(Arg.BECountUsers)),
- ConstantEvolutionLoopExitValue(
- std::move(Arg.ConstantEvolutionLoopExitValue)),
- ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
- ValuesAtScopesUsers(std::move(Arg.ValuesAtScopesUsers)),
- LoopDispositions(std::move(Arg.LoopDispositions)),
- LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
- BlockDispositions(std::move(Arg.BlockDispositions)),
- SCEVUsers(std::move(Arg.SCEVUsers)),
- UnsignedRanges(std::move(Arg.UnsignedRanges)),
- SignedRanges(std::move(Arg.SignedRanges)),
- UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
- UniquePreds(std::move(Arg.UniquePreds)),
- SCEVAllocator(std::move(Arg.SCEVAllocator)),
- ConstantSCEVs(std::move(Arg.ConstantSCEVs)),
- LoopUsers(std::move(Arg.LoopUsers)),
- PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
- FirstUnknown(Arg.FirstUnknown) {
- Arg.FirstUnknown = nullptr;
-}
-
-ScalarEvolution::~ScalarEvolution() {
- // Iterate through all the SCEVUnknown instances and call their
- // destructors, so that they release their references to their values.
- for (SCEVUnknown *U = FirstUnknown; U;) {
- SCEVUnknown *Tmp = U;
- U = U->Next;
- Tmp->~SCEVUnknown();
- }
- FirstUnknown = nullptr;
-
- ExprValueMap.clear();
- ValueExprMap.clear();
- HasRecMap.clear();
- BackedgeTakenCounts.clear();
- PredicatedBackedgeTakenCounts.clear();
-
- assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
- assert(PendingMerges.empty() && "isImpliedViaMerge garbage");
- assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
- assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
-}
-
-bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
- return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
-}
-
-/// When printing a top-level SCEV for trip counts, it's helpful to include
-/// a type for constants which are otherwise hard to disambiguate.
-static void PrintSCEVWithTypeHint(raw_ostream &OS, const SCEV* S) {
- if (isa<SCEVConstant>(S))
- OS << *S->getType() << " ";
- OS << *S;
-}
-
-static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
- const Loop *L) {
- // Print all inner loops first
- for (Loop *I : *L)
- PrintLoopInfo(OS, SE, I);
-
- OS << "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
-
- SmallVector<BasicBlock *, 8> ExitingBlocks;
- L->getExitingBlocks(ExitingBlocks);
- if (ExitingBlocks.size() != 1)
- OS << "<multiple exits> ";
-
- auto *BTC = SE->getBackedgeTakenCount(L);
- if (!isa<SCEVCouldNotCompute>(BTC)) {
- OS << "backedge-taken count is ";
- PrintSCEVWithTypeHint(OS, BTC);
- } else
- OS << "Unpredictable backedge-taken count.";
- OS << "\n";
-
- if (ExitingBlocks.size() > 1)
- for (BasicBlock *ExitingBlock : ExitingBlocks) {
- OS << " exit count for " << ExitingBlock->getName() << ": ";
- const SCEV *EC = SE->getExitCount(L, ExitingBlock);
- PrintSCEVWithTypeHint(OS, EC);
- if (isa<SCEVCouldNotCompute>(EC)) {
- // Retry with predicates.
- SmallVector<const SCEVPredicate *> Predicates;
- EC = SE->getPredicatedExitCount(L, ExitingBlock, &Predicates);
- if (!isa<SCEVCouldNotCompute>(EC)) {
- OS << "\n predicated exit count for " << ExitingBlock->getName()
- << ": ";
- PrintSCEVWithTypeHint(OS, EC);
- OS << "\n Predicates:\n";
- for (const auto *P : Predicates)
- P->print(OS, 4);
- }
- }
- OS << "\n";
- }
-
- OS << "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
-
- auto *ConstantBTC = SE->getConstantMaxBackedgeTakenCount(L);
- if (!isa<SCEVCouldNotCompute>(ConstantBTC)) {
- OS << "constant max backedge-taken count is ";
- PrintSCEVWithTypeHint(OS, ConstantBTC);
- if (SE->isBackedgeTakenCountMaxOrZero(L))
- OS << ", actual taken count either this or zero.";
- } else {
- OS << "Unpredictable constant max backedge-taken count. ";
- }
-
- OS << "\n"
- "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
-
- auto *SymbolicBTC = SE->getSymbolicMaxBackedgeTakenCount(L);
- if (!isa<SCEVCouldNotCompute>(SymbolicBTC)) {
- OS << "symbolic max backedge-taken count is ";
- PrintSCEVWithTypeHint(OS, SymbolicBTC);
- if (SE->isBackedgeTakenCountMaxOrZero(L))
- OS << ", actual taken count either this or zero.";
- } else {
- OS << "Unpredictable symbolic max backedge-taken count. ";
- }
- OS << "\n";
-
- if (ExitingBlocks.size() > 1)
- for (BasicBlock *ExitingBlock : ExitingBlocks) {
- OS << " symbolic max exit count for " << ExitingBlock->getName() << ": ";
- auto *ExitBTC = SE->getExitCount(L, ExitingBlock,
- ScalarEvolution::SymbolicMaximum);
- PrintSCEVWithTypeHint(OS, ExitBTC);
- if (isa<SCEVCouldNotCompute>(ExitBTC)) {
- // Retry with predicates.
- SmallVector<const SCEVPredicate *> Predicates;
- ExitBTC = SE->getPredicatedExitCount(L, ExitingBlock, &Predicates,
- ScalarEvolution::SymbolicMaximum);
- if (!isa<SCEVCouldNotCompute>(ExitBTC)) {
- OS << "\n predicated symbolic max exit count for "
- << ExitingBlock->getName() << ": ";
- PrintSCEVWithTypeHint(OS, ExitBTC);
- OS << "\n Predicates:\n";
- for (const auto *P : Predicates)
- P->print(OS, 4);
- }
- }
- OS << "\n";
- }
-
- SmallVector<const SCEVPredicate *, 4> Preds;
- auto *PBT = SE->getPredicatedBackedgeTakenCount(L, Preds);
- if (PBT != BTC) {
- OS << "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
- if (!isa<SCEVCouldNotCompute>(PBT)) {
- OS << "Predicated backedge-taken count is ";
- PrintSCEVWithTypeHint(OS, PBT);
- } else
- OS << "Unpredictable predicated backedge-taken count.";
- OS << "\n";
- OS << " Predicates:\n";
- for (const auto *P : Preds)
- P->print(OS, 4);
- }
- Preds.clear();
-
- auto *PredConstantMax =
- SE->getPredicatedConstantMaxBackedgeTakenCount(L, Preds);
- if (PredConstantMax != ConstantBTC) {
- OS << "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
- if (!isa<SCEVCouldNotCompute>(PredConstantMax)) {
- OS << "Predicated constant max backedge-taken count is ";
- PrintSCEVWithTypeHint(OS, PredConstantMax);
- } else
- OS << "Unpredictable predicated constant max backedge-taken count.";
- OS << "\n";
- OS << " Predicates:\n";
- for (const auto *P : Preds)
- P->print(OS, 4);
- }
- Preds.clear();
-
- auto *PredSymbolicMax =
- SE->getPredicatedSymbolicMaxBackedgeTakenCount(L, Preds);
- if (SymbolicBTC != PredSymbolicMax) {
- OS << "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
- if (!isa<SCEVCouldNotCompute>(PredSymbolicMax)) {
- OS << "Predicated symbolic max backedge-taken count is ";
- PrintSCEVWithTypeHint(OS, PredSymbolicMax);
- } else
- OS << "Unpredictable predicated symbolic max backedge-taken count.";
- OS << "\n";
- OS << " Predicates:\n";
- for (const auto *P : Preds)
- P->print(OS, 4);
- }
-
- if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
- OS << "Loop ";
- L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": ";
- OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
- }
-}
-
-namespace llvm {
-// Note: these overloaded operators need to be in the llvm namespace for them
-// to be resolved correctly. If we put them outside the llvm namespace, the
-//
-// OS << ": " << SE.getLoopDisposition(SV, InnerL);
-//
-// code below "breaks" and start printing raw enum values as opposed to the
-// string values.
-static raw_ostream &operator<<(raw_ostream &OS,
- ScalarEvolution::LoopDisposition LD) {
- switch (LD) {
- case ScalarEvolution::LoopVariant:
- OS << "Variant";
- break;
- case ScalarEvolution::LoopInvariant:
- OS << "Invariant";
- break;
- case ScalarEvolution::LoopUniform:
- OS << "Uniform";
- break;
- case ScalarEvolution::LoopComputable:
- OS << "Computable";
- break;
- }
- return OS;
-}
-
-static raw_ostream &operator<<(raw_ostream &OS,
- llvm::ScalarEvolution::BlockDisposition BD) {
- switch (BD) {
- case ScalarEvolution::DoesNotDominateBlock:
- OS << "DoesNotDominate";
- break;
- case ScalarEvolution::DominatesBlock:
- OS << "Dominates";
- break;
- case ScalarEvolution::ProperlyDominatesBlock:
- OS << "ProperlyDominates";
- break;
- }
- return OS;
-}
-} // namespace llvm
-
-void ScalarEvolution::print(raw_ostream &OS) const {
- // ScalarEvolution's implementation of the print method is to print
- // out SCEV values of all instructions that are interesting. Doing
- // this potentially causes it to create new SCEV objects though,
- // which technically conflicts with the const qualifier. This isn't
- // observable from outside the class though, so casting away the
- // const isn't dangerous.
- ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
-
- if (ClassifyExpressions) {
- OS << "Classifying expressions for: ";
- F.printAsOperand(OS, /*PrintType=*/false);
- OS << "\n";
- for (Instruction &I : instructions(F))
- if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
- OS << I << '\n';
- OS << " --> ";
- const SCEV *SV = SE.getSCEV(&I);
- SV->print(OS);
- if (!isa<SCEVCouldNotCompute>(SV)) {
- OS << " U: ";
- SE.getUnsignedRange(SV).print(OS);
- OS << " S: ";
- SE.getSignedRange(SV).print(OS);
- }
-
- const Loop *L = LI.getLoopFor(I.getParent());
-
- const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
- if (AtUse != SV) {
- OS << " --> ";
- AtUse->print(OS);
- if (!isa<SCEVCouldNotCompute>(AtUse)) {
- OS << " U: ";
- SE.getUnsignedRange(AtUse).print(OS);
- OS << " S: ";
- SE.getSignedRange(AtUse).print(OS);
- }
- }
-
- if (L) {
- OS << "\t\t" "Exits: ";
- const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
- if (!SE.isLoopInvariant(ExitValue, L)) {
- OS << "<<Unknown>>";
- } else {
- OS << *ExitValue;
- }
-
- ListSeparator LS(", ", "\t\tLoopDispositions: { ");
- for (const auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
- OS << LS;
- Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": " << SE.getLoopDisposition(SV, Iter);
- }
-
- for (const auto *InnerL : depth_first(L)) {
- if (InnerL == L)
- continue;
- OS << LS;
- InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
- OS << ": " << SE.getLoopDisposition(SV, InnerL);
- }
-
- OS << " }";
- }
-
- OS << "\n";
- }
- }
-
- OS << "Determining loop execution counts for: ";
- F.printAsOperand(OS, /*PrintType=*/false);
- OS << "\n";
- for (Loop *I : LI)
- PrintLoopInfo(OS, &SE, I);
-}
-
-ScalarEvolution::LoopDisposition
-ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
- auto &Values = LoopDispositions[S];
- for (auto &V : Values) {
- if (V.getPointer() == L)
- return V.getInt();
- }
- Values.emplace_back(L, LoopVariant);
- LoopDisposition D = computeLoopDisposition(S, L);
- auto &Values2 = LoopDispositions[S];
- for (auto &V : llvm::reverse(Values2)) {
- if (V.getPointer() == L) {
- V.setInt(D);
- break;
- }
- }
- return D;
-}
-
-ScalarEvolution::LoopDisposition
-ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
- switch (S->getSCEVType()) {
- case scConstant:
- case scVScale:
- return LoopInvariant;
- case scAddRecExpr: {
- const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
-
- // If L is the addrec's loop, it's computable.
- if (AR->getLoop() == L)
- return LoopComputable;
-
- // Add recurrences are never invariant in the function-body (null loop).
- if (!L)
- return LoopVariant;
-
- // Everything that is not defined at loop entry is variant.
- if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader())) {
- if (L->contains(AR->getLoop()) &&
- llvm::all_of(AR->operands(),
- [&](const SCEV *Op) { return isLoopUniform(Op, L); }))
- return LoopUniform;
-
- return LoopVariant;
- }
- assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
- " dominate the contained loop's header?");
-
- // This recurrence is invariant w.r.t. L if AR's loop contains L.
- if (AR->getLoop()->contains(L))
- return LoopInvariant;
-
- // This recurrence is variant w.r.t. L if any of its operands
- // are variant.
- for (SCEVUse Op : AR->operands())
- if (!isLoopInvariant(Op, L))
- return LoopVariant;
-
- // Otherwise it's loop-invariant.
- return LoopInvariant;
- }
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- case scAddExpr:
- case scMulExpr:
- case scUDivExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr: {
- bool HasVarying = false;
- bool HasUniform = false;
- for (SCEVUse Op : S->operands()) {
- LoopDisposition D = getLoopDisposition(Op, L);
- if (D == LoopVariant)
- return LoopVariant;
- if (D == LoopComputable)
- HasVarying = true;
- if (D == LoopUniform)
- HasUniform = true;
- }
- return HasVarying ? (HasUniform ? LoopVariant : LoopComputable)
- : (HasUniform ? LoopUniform : LoopInvariant);
- }
- case scUnknown:
- // All non-instruction values are loop invariant. All instructions are loop
- // invariant if they are not contained in the specified loop.
- // Instructions are never considered invariant in the function body
- // (null loop) because they are defined within the "loop".
- if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
- return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
- return LoopInvariant;
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-bool ScalarEvolution::isLoopUniform(const SCEV *S, const Loop *L) {
- LoopDisposition D = getLoopDisposition(S, L);
- return D == LoopUniform || D == LoopInvariant;
-}
-
-bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
- return getLoopDisposition(S, L) == LoopInvariant;
-}
-
-bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
- return getLoopDisposition(S, L) == LoopComputable;
-}
-
-ScalarEvolution::BlockDisposition
-ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
- auto &Values = BlockDispositions[S];
- for (auto &V : Values) {
- if (V.getPointer() == BB)
- return V.getInt();
- }
- Values.emplace_back(BB, DoesNotDominateBlock);
- BlockDisposition D = computeBlockDisposition(S, BB);
- auto &Values2 = BlockDispositions[S];
- for (auto &V : llvm::reverse(Values2)) {
- if (V.getPointer() == BB) {
- V.setInt(D);
- break;
- }
- }
- return D;
-}
-
-ScalarEvolution::BlockDisposition
-ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
- switch (S->getSCEVType()) {
- case scConstant:
- case scVScale:
- return ProperlyDominatesBlock;
- case scAddRecExpr: {
- // This uses a "dominates" query instead of "properly dominates" query
- // to test for proper dominance too, because the instruction which
- // produces the addrec's value is a PHI, and a PHI effectively properly
- // dominates its entire containing block.
- const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
- if (!DT.dominates(AR->getLoop()->getHeader(), BB))
- return DoesNotDominateBlock;
-
- // Fall through into SCEVNAryExpr handling.
- [[fallthrough]];
- }
- case scTruncate:
- case scZeroExtend:
- case scSignExtend:
- case scPtrToAddr:
- case scAddExpr:
- case scMulExpr:
- case scUDivExpr:
- case scUMaxExpr:
- case scSMaxExpr:
- case scUMinExpr:
- case scSMinExpr:
- case scSequentialUMinExpr: {
- bool Proper = true;
- for (const SCEV *NAryOp : S->operands()) {
- BlockDisposition D = getBlockDisposition(NAryOp, BB);
- if (D == DoesNotDominateBlock)
- return DoesNotDominateBlock;
- if (D == DominatesBlock)
- Proper = false;
- }
- return Proper ? ProperlyDominatesBlock : DominatesBlock;
- }
- case scUnknown:
- if (Instruction *I =
- dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
- if (I->getParent() == BB)
- return DominatesBlock;
- if (DT.properlyDominates(I->getParent(), BB))
- return ProperlyDominatesBlock;
- return DoesNotDominateBlock;
- }
- return ProperlyDominatesBlock;
- case scCouldNotCompute:
- llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
- }
- llvm_unreachable("Unknown SCEV kind!");
-}
-
-bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
- return getBlockDisposition(S, BB) >= DominatesBlock;
-}
-
-bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
- return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
-}
-
-bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
- return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
-}
-
-void ScalarEvolution::forgetBackedgeTakenCounts(const Loop *L,
- bool Predicated) {
- auto &BECounts =
- Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
- auto It = BECounts.find(L);
- if (It != BECounts.end()) {
- for (const ExitNotTakenInfo &ENT : It->second.ExitNotTaken) {
- for (const SCEV *S : {ENT.ExactNotTaken, ENT.SymbolicMaxNotTaken}) {
- if (!isa<SCEVConstant>(S)) {
- auto UserIt = BECountUsers.find(S);
- assert(UserIt != BECountUsers.end());
- UserIt->second.erase({L, Predicated});
- }
- }
- }
- BECounts.erase(It);
- }
-}
-
-void ScalarEvolution::forgetMemoizedResults(ArrayRef<SCEVUse> SCEVs) {
- SmallPtrSet<const SCEV *, 8> ToForget(llvm::from_range, SCEVs);
- SmallVector<SCEVUse, 8> Worklist(ToForget.begin(), ToForget.end());
-
- while (!Worklist.empty()) {
- const SCEV *Curr = Worklist.pop_back_val();
- auto Users = SCEVUsers.find(Curr);
- if (Users != SCEVUsers.end())
- for (const auto *User : Users->second)
- if (ToForget.insert(User).second)
- Worklist.push_back(User);
- }
-
- for (const auto *S : ToForget)
- forgetMemoizedResultsImpl(S);
-
- PredicatedSCEVRewrites.remove_if(
- [&](const auto &Entry) { return ToForget.count(Entry.first.first); });
-}
-
-void ScalarEvolution::forgetMemoizedResultsImpl(const SCEV *S) {
- LoopDispositions.erase(S);
- BlockDispositions.erase(S);
- UnsignedRanges.erase(S);
- SignedRanges.erase(S);
- HasRecMap.erase(S);
- ConstantMultipleCache.erase(S);
-
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(S)) {
- UnsignedWrapViaInductionTried.erase(AR);
- SignedWrapViaInductionTried.erase(AR);
- }
-
- auto ExprIt = ExprValueMap.find(S);
- if (ExprIt != ExprValueMap.end()) {
- for (Value *V : ExprIt->second) {
- auto ValueIt = ValueExprMap.find_as(V);
- if (ValueIt != ValueExprMap.end())
- ValueExprMap.erase(ValueIt);
- }
- ExprValueMap.erase(ExprIt);
- }
-
- auto ScopeIt = ValuesAtScopes.find(S);
- if (ScopeIt != ValuesAtScopes.end()) {
- for (const auto &Pair : ScopeIt->second)
- if (!isa_and_nonnull<SCEVConstant>(Pair.second))
- llvm::erase(ValuesAtScopesUsers[Pair.second],
- std::make_pair(Pair.first, S));
- ValuesAtScopes.erase(ScopeIt);
- }
-
- auto ScopeUserIt = ValuesAtScopesUsers.find(S);
- if (ScopeUserIt != ValuesAtScopesUsers.end()) {
- for (const auto &Pair : ScopeUserIt->second)
- llvm::erase(ValuesAtScopes[Pair.second], std::make_pair(Pair.first, S));
- ValuesAtScopesUsers.erase(ScopeUserIt);
- }
-
- auto BEUsersIt = BECountUsers.find(S);
- if (BEUsersIt != BECountUsers.end()) {
- // Work on a copy, as forgetBackedgeTakenCounts() will modify the original.
- auto Copy = BEUsersIt->second;
- for (const auto &Pair : Copy)
- forgetBackedgeTakenCounts(Pair.getPointer(), Pair.getInt());
- BECountUsers.erase(BEUsersIt);
- }
-
- auto FoldUser = FoldCacheUser.find(S);
- if (FoldUser != FoldCacheUser.end())
- for (auto &KV : FoldUser->second)
- FoldCache.erase(KV);
- FoldCacheUser.erase(S);
-}
-
-void
-ScalarEvolution::getUsedLoops(const SCEV *S,
- SmallPtrSetImpl<const Loop *> &LoopsUsed) {
- struct FindUsedLoops {
- FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
- : LoopsUsed(LoopsUsed) {}
- SmallPtrSetImpl<const Loop *> &LoopsUsed;
- bool follow(const SCEV *S) {
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
- LoopsUsed.insert(AR->getLoop());
- return true;
- }
-
- bool isDone() const { return false; }
- };
-
- FindUsedLoops F(LoopsUsed);
- SCEVTraversal<FindUsedLoops>(F).visitAll(S);
-}
-
-void ScalarEvolution::getReachableBlocks(
- SmallPtrSetImpl<BasicBlock *> &Reachable, Function &F) {
- SmallVector<BasicBlock *> Worklist;
- Worklist.push_back(&F.getEntryBlock());
- while (!Worklist.empty()) {
- BasicBlock *BB = Worklist.pop_back_val();
- if (!Reachable.insert(BB).second)
- continue;
-
- Value *Cond;
- BasicBlock *TrueBB, *FalseBB;
- if (match(BB->getTerminator(), m_Br(m_Value(Cond), m_BasicBlock(TrueBB),
- m_BasicBlock(FalseBB)))) {
- if (auto *C = dyn_cast<ConstantInt>(Cond)) {
- Worklist.push_back(C->isOne() ? TrueBB : FalseBB);
- continue;
- }
-
- if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) {
- const SCEV *L = getSCEV(Cmp->getOperand(0));
- const SCEV *R = getSCEV(Cmp->getOperand(1));
- if (isKnownPredicateViaConstantRanges(Cmp->getCmpPredicate(), L, R)) {
- Worklist.push_back(TrueBB);
- continue;
- }
- if (isKnownPredicateViaConstantRanges(Cmp->getInverseCmpPredicate(), L,
- R)) {
- Worklist.push_back(FalseBB);
- continue;
- }
- }
- }
-
- append_range(Worklist, successors(BB));
- }
-}
-
-void ScalarEvolution::verify() const {
- ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
- ScalarEvolution SE2(F, TLI, AC, DT, LI);
-
- SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
-
- // Map's SCEV expressions from one ScalarEvolution "universe" to another.
- struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
- SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
-
- const SCEV *visitConstant(const SCEVConstant *Constant) {
- return SE.getConstant(Constant->getAPInt());
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- return SE.getUnknown(Expr->getValue());
- }
-
- const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
- return SE.getCouldNotCompute();
- }
- };
-
- SCEVMapper SCM(SE2);
- SmallPtrSet<BasicBlock *, 16> ReachableBlocks;
- SE2.getReachableBlocks(ReachableBlocks, F);
-
- auto GetDelta = [&](const SCEV *Old, const SCEV *New) -> const SCEV * {
- if (containsUndefs(Old) || containsUndefs(New)) {
- // SCEV treats "undef" as an unknown but consistent value (i.e. it does
- // not propagate undef aggressively). This means we can (and do) fail
- // verification in cases where a transform makes a value go from "undef"
- // to "undef+1" (say). The transform is fine, since in both cases the
- // result is "undef", but SCEV thinks the value increased by 1.
- return nullptr;
- }
-
- // Unless VerifySCEVStrict is set, we only compare constant deltas.
- const SCEV *Delta = SE2.getMinusSCEV(Old, New);
- if (!VerifySCEVStrict && !isa<SCEVConstant>(Delta))
- return nullptr;
-
- return Delta;
- };
-
- while (!LoopStack.empty()) {
- auto *L = LoopStack.pop_back_val();
- llvm::append_range(LoopStack, *L);
-
- // Only verify BECounts in reachable loops. For an unreachable loop,
- // any BECount is legal.
- if (!ReachableBlocks.contains(L->getHeader()))
- continue;
-
- // Only verify cached BECounts. Computing new BECounts may change the
- // results of subsequent SCEV uses.
- auto It = BackedgeTakenCounts.find(L);
- if (It == BackedgeTakenCounts.end())
- continue;
-
- auto *CurBECount =
- SCM.visit(It->second.getExact(L, const_cast<ScalarEvolution *>(this)));
- auto *NewBECount = SE2.getBackedgeTakenCount(L);
-
- if (CurBECount == SE2.getCouldNotCompute() ||
- NewBECount == SE2.getCouldNotCompute()) {
- // NB! This situation is legal, but is very suspicious -- whatever pass
- // change the loop to make a trip count go from could not compute to
- // computable or vice-versa *should have* invalidated SCEV. However, we
- // choose not to assert here (for now) since we don't want false
- // positives.
- continue;
- }
-
- if (SE.getTypeSizeInBits(CurBECount->getType()) >
- SE.getTypeSizeInBits(NewBECount->getType()))
- NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
- else if (SE.getTypeSizeInBits(CurBECount->getType()) <
- SE.getTypeSizeInBits(NewBECount->getType()))
- CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
-
- const SCEV *Delta = GetDelta(CurBECount, NewBECount);
- if (Delta && !Delta->isZero()) {
- dbgs() << "Trip Count for " << *L << " Changed!\n";
- dbgs() << "Old: " << *CurBECount << "\n";
- dbgs() << "New: " << *NewBECount << "\n";
- dbgs() << "Delta: " << *Delta << "\n";
- std::abort();
- }
- }
-
- // Collect all valid loops currently in LoopInfo.
- SmallPtrSet<Loop *, 32> ValidLoops;
- SmallVector<Loop *, 32> Worklist(LI.begin(), LI.end());
- while (!Worklist.empty()) {
- Loop *L = Worklist.pop_back_val();
- if (ValidLoops.insert(L).second)
- Worklist.append(L->begin(), L->end());
- }
- for (const auto &KV : ValueExprMap) {
-#ifndef NDEBUG
- // Check for SCEV expressions referencing invalid/deleted loops.
- if (auto *AR = dyn_cast<SCEVAddRecExpr>(KV.second)) {
- assert(ValidLoops.contains(AR->getLoop()) &&
- "AddRec references invalid loop");
- }
-#endif
-
- // Check that the value is also part of the reverse map.
- auto It = ExprValueMap.find(KV.second);
- if (It == ExprValueMap.end() || !It->second.contains(KV.first)) {
- dbgs() << "Value " << *KV.first
- << " is in ValueExprMap but not in ExprValueMap\n";
- std::abort();
- }
-
- if (auto *I = dyn_cast<Instruction>(&*KV.first)) {
- if (!ReachableBlocks.contains(I->getParent()))
- continue;
- const SCEV *OldSCEV = SCM.visit(KV.second);
- const SCEV *NewSCEV = SE2.getSCEV(I);
- const SCEV *Delta = GetDelta(OldSCEV, NewSCEV);
- if (Delta && !Delta->isZero()) {
- dbgs() << "SCEV for value " << *I << " changed!\n"
- << "Old: " << *OldSCEV << "\n"
- << "New: " << *NewSCEV << "\n"
- << "Delta: " << *Delta << "\n";
- std::abort();
- }
- }
- }
-
- for (const auto &KV : ExprValueMap) {
- for (Value *V : KV.second) {
- const SCEV *S = ValueExprMap.lookup(V);
- if (!S) {
- dbgs() << "Value " << *V
- << " is in ExprValueMap but not in ValueExprMap\n";
- std::abort();
- }
- if (S != KV.first) {
- dbgs() << "Value " << *V << " mapped to " << *S << " rather than "
- << *KV.first << "\n";
- std::abort();
- }
- }
- }
-
- // Verify integrity of SCEV users.
- for (const auto &S : UniqueSCEVs) {
- for (SCEVUse Op : S.operands()) {
- // We do not store dependencies of constants.
- if (isa<SCEVConstant>(Op))
- continue;
- auto It = SCEVUsers.find(Op);
- if (It != SCEVUsers.end() && It->second.count(&S))
- continue;
- dbgs() << "Use of operand " << *Op << " by user " << S
- << " is not being tracked!\n";
- std::abort();
- }
- }
-
- // Verify integrity of ValuesAtScopes users.
- for (const auto &ValueAndVec : ValuesAtScopes) {
- const SCEV *Value = ValueAndVec.first;
- for (const auto &LoopAndValueAtScope : ValueAndVec.second) {
- const Loop *L = LoopAndValueAtScope.first;
- const SCEV *ValueAtScope = LoopAndValueAtScope.second;
- if (!isa<SCEVConstant>(ValueAtScope)) {
- auto It = ValuesAtScopesUsers.find(ValueAtScope);
- if (It != ValuesAtScopesUsers.end() &&
- is_contained(It->second, std::make_pair(L, Value)))
- continue;
- dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
- << *ValueAtScope << " missing in ValuesAtScopesUsers\n";
- std::abort();
- }
- }
- }
-
- for (const auto &ValueAtScopeAndVec : ValuesAtScopesUsers) {
- const SCEV *ValueAtScope = ValueAtScopeAndVec.first;
- for (const auto &LoopAndValue : ValueAtScopeAndVec.second) {
- const Loop *L = LoopAndValue.first;
- const SCEV *Value = LoopAndValue.second;
- assert(!isa<SCEVConstant>(Value));
- auto It = ValuesAtScopes.find(Value);
- if (It != ValuesAtScopes.end() &&
- is_contained(It->second, std::make_pair(L, ValueAtScope)))
- continue;
- dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
- << *ValueAtScope << " missing in ValuesAtScopes\n";
- std::abort();
- }
- }
-
- // Verify integrity of BECountUsers.
- auto VerifyBECountUsers = [&](bool Predicated) {
- auto &BECounts =
- Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
- for (const auto &LoopAndBEInfo : BECounts) {
- for (const ExitNotTakenInfo &ENT : LoopAndBEInfo.second.ExitNotTaken) {
- for (const SCEV *S : {ENT.ExactNotTaken, ENT.SymbolicMaxNotTaken}) {
- if (!isa<SCEVConstant>(S)) {
- auto UserIt = BECountUsers.find(S);
- if (UserIt != BECountUsers.end() &&
- UserIt->second.contains({ LoopAndBEInfo.first, Predicated }))
- continue;
- dbgs() << "Value " << *S << " for loop " << *LoopAndBEInfo.first
- << " missing from BECountUsers\n";
- std::abort();
- }
- }
- }
- }
- };
- VerifyBECountUsers(/* Predicated */ false);
- VerifyBECountUsers(/* Predicated */ true);
-
- // Verify intergity of loop disposition cache.
- for (auto &[S, Values] : LoopDispositions) {
- for (auto [Loop, CachedDisposition] : Values) {
- const auto RecomputedDisposition = SE2.getLoopDisposition(S, Loop);
- if (CachedDisposition != RecomputedDisposition) {
- dbgs() << "Cached disposition of " << *S << " for loop " << *Loop
- << " is incorrect: cached " << CachedDisposition << ", actual "
- << RecomputedDisposition << "\n";
- std::abort();
- }
- }
- }
-
- // Verify integrity of the block disposition cache.
- for (auto &[S, Values] : BlockDispositions) {
- for (auto [BB, CachedDisposition] : Values) {
- const auto RecomputedDisposition = SE2.getBlockDisposition(S, BB);
- if (CachedDisposition != RecomputedDisposition) {
- dbgs() << "Cached disposition of " << *S << " for block %"
- << BB->getName() << " is incorrect: cached " << CachedDisposition
- << ", actual " << RecomputedDisposition << "\n";
- std::abort();
- }
- }
- }
-
- // Verify FoldCache/FoldCacheUser caches.
- for (auto [FoldID, Expr] : FoldCache) {
- auto I = FoldCacheUser.find(Expr);
- if (I == FoldCacheUser.end()) {
- dbgs() << "Missing entry in FoldCacheUser for cached expression " << *Expr
- << "!\n";
- std::abort();
- }
- if (!is_contained(I->second, FoldID)) {
- dbgs() << "Missing FoldID in cached users of " << *Expr << "!\n";
- std::abort();
- }
- }
- for (auto [Expr, IDs] : FoldCacheUser) {
- for (auto &FoldID : IDs) {
- const SCEV *S = FoldCache.lookup(FoldID);
- if (!S) {
- dbgs() << "Missing entry in FoldCache for expression " << *Expr
- << "!\n";
- std::abort();
- }
- if (S != Expr) {
- dbgs() << "Entry in FoldCache doesn't match FoldCacheUser: " << *S
- << " != " << *Expr << "!\n";
- std::abort();
- }
- }
- }
-
- // Verify that ConstantMultipleCache computations are correct. We check that
- // cached multiples and recomputed multiples are multiples of each other to
- // verify correctness. It is possible that a recomputed multiple is different
- // from the cached multiple due to strengthened no wrap flags or changes in
- // KnownBits computations.
- for (auto [S, Multiple] : ConstantMultipleCache) {
- APInt RecomputedMultiple = SE2.getConstantMultiple(S);
- if ((Multiple != 0 && RecomputedMultiple != 0 &&
- Multiple.urem(RecomputedMultiple) != 0 &&
- RecomputedMultiple.urem(Multiple) != 0)) {
- dbgs() << "Incorrect cached computation in ConstantMultipleCache for "
- << *S << " : Computed " << RecomputedMultiple
- << " but cache contains " << Multiple << "!\n";
- std::abort();
- }
- }
-}
-
-bool ScalarEvolution::invalidate(
- Function &F, const PreservedAnalyses &PA,
- FunctionAnalysisManager::Invalidator &Inv) {
- // Invalidate the ScalarEvolution object whenever it isn't preserved or one
- // of its dependencies is invalidated.
- auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
- return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
- Inv.invalidate<AssumptionAnalysis>(F, PA) ||
- Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
- Inv.invalidate<LoopAnalysis>(F, PA);
-}
-
-AnalysisKey ScalarEvolutionAnalysis::Key;
-
-ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
- FunctionAnalysisManager &AM) {
- auto &TLI = AM.getResult<TargetLibraryAnalysis>(F);
- auto &AC = AM.getResult<AssumptionAnalysis>(F);
- auto &DT = AM.getResult<DominatorTreeAnalysis>(F);
- auto &LI = AM.getResult<LoopAnalysis>(F);
- return ScalarEvolution(F, TLI, AC, DT, LI);
-}
-
-PreservedAnalyses
-ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
- AM.getResult<ScalarEvolutionAnalysis>(F).verify();
- return PreservedAnalyses::all();
-}
-
-PreservedAnalyses
-ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
- // For compatibility with opt's -analyze feature under legacy pass manager
- // which was not ported to NPM. This keeps tests using
- // update_analyze_test_checks.py working.
- OS << "Printing analysis 'Scalar Evolution Analysis' for function '"
- << F.getName() << "':\n";
- AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
- return PreservedAnalyses::all();
-}
-
-INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
- "Scalar Evolution Analysis", false, true)
-INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
-INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
-INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
-INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
-INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
- "Scalar Evolution Analysis", false, true)
-
-char ScalarEvolutionWrapperPass::ID = 0;
-
-ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {}
-
-bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
- SE.reset(new ScalarEvolution(
- F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
- getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
- getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
- getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
- return false;
-}
-
-void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
-
-void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
- SE->print(OS);
-}
-
-void ScalarEvolutionWrapperPass::verifyAnalysis() const {
- if (!VerifySCEV)
- return;
-
- SE->verify();
-}
-
-void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
- AU.setPreservesAll();
- AU.addRequiredTransitive<AssumptionCacheTracker>();
- AU.addRequiredTransitive<LoopInfoWrapperPass>();
- AU.addRequiredTransitive<DominatorTreeWrapperPass>();
- AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
-}
-
-const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
- const SCEV *RHS) {
- return getComparePredicate(ICmpInst::ICMP_EQ, LHS, RHS);
-}
-
-const SCEVPredicate *
-ScalarEvolution::getComparePredicate(const ICmpInst::Predicate Pred,
- const SCEV *LHS, const SCEV *RHS) {
- FoldingSetNodeID ID;
- assert(LHS->getType() == RHS->getType() &&
- "Type mismatch between LHS and RHS");
- // Unique this node based on the arguments
- ID.AddInteger(SCEVPredicate::P_Compare);
- ID.AddInteger(Pred);
- ID.AddPointer(LHS);
- ID.AddPointer(RHS);
- void *IP = nullptr;
- if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
- return S;
- SCEVComparePredicate *Eq = new (SCEVAllocator)
- SCEVComparePredicate(ID.Intern(SCEVAllocator), Pred, LHS, RHS);
- UniquePreds.InsertNode(Eq, IP);
- return Eq;
-}
-
-const SCEVPredicate *ScalarEvolution::getWrapPredicate(
- const SCEVAddRecExpr *AR,
- SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
- FoldingSetNodeID ID;
- // Unique this node based on the arguments
- ID.AddInteger(SCEVPredicate::P_Wrap);
- ID.AddPointer(AR);
- ID.AddInteger(AddedFlags);
- void *IP = nullptr;
- if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
- return S;
- auto *OF = new (SCEVAllocator)
- SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
- UniquePreds.InsertNode(OF, IP);
- return OF;
-}
-
-namespace {
-
-class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
-public:
-
- /// Rewrites \p S in the context of a loop L and the SCEV predication
- /// infrastructure.
- ///
- /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
- /// equivalences present in \p Pred.
- ///
- /// If \p NewPreds is non-null, rewrite is free to add further predicates to
- /// \p NewPreds such that the result will be an AddRecExpr.
- static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
- SmallVectorImpl<const SCEVPredicate *> *NewPreds,
- const SCEVPredicate *Pred) {
- SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
- return Rewriter.visit(S);
- }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- if (Pred) {
- if (auto *U = dyn_cast<SCEVUnionPredicate>(Pred)) {
- for (const auto *Pred : U->getPredicates())
- if (const auto *IPred = dyn_cast<SCEVComparePredicate>(Pred))
- if (IPred->getLHS() == Expr &&
- IPred->getPredicate() == ICmpInst::ICMP_EQ)
- return IPred->getRHS();
- } else if (const auto *IPred = dyn_cast<SCEVComparePredicate>(Pred)) {
- if (IPred->getLHS() == Expr &&
- IPred->getPredicate() == ICmpInst::ICMP_EQ)
- return IPred->getRHS();
- }
- }
- return convertToAddRecWithPreds(Expr);
- }
-
- const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
- const SCEV *Operand = visit(Expr->getOperand());
- const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
- if (AR && AR->getLoop() == L && AR->isAffine()) {
- // This couldn't be folded because the operand didn't have the nuw
- // flag. Add the nusw flag as an assumption that we could make.
- const SCEV *Step = AR->getStepRecurrence(SE);
- Type *Ty = Expr->getType();
- if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
- return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
- SE.getSignExtendExpr(Step, Ty), L,
- AR->getNoWrapFlags());
- }
- return SE.getZeroExtendExpr(Operand, Expr->getType());
- }
-
- const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
- const SCEV *Operand = visit(Expr->getOperand());
- const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
- if (AR && AR->getLoop() == L && AR->isAffine()) {
- // This couldn't be folded because the operand didn't have the nsw
- // flag. Add the nssw flag as an assumption that we could make.
- const SCEV *Step = AR->getStepRecurrence(SE);
- Type *Ty = Expr->getType();
- if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
- return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
- SE.getSignExtendExpr(Step, Ty), L,
- AR->getNoWrapFlags());
- }
- return SE.getSignExtendExpr(Operand, Expr->getType());
- }
-
-private:
- explicit SCEVPredicateRewriter(
- const Loop *L, ScalarEvolution &SE,
- SmallVectorImpl<const SCEVPredicate *> *NewPreds,
- const SCEVPredicate *Pred)
- : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
-
- bool addOverflowAssumption(const SCEVPredicate *P) {
- if (!NewPreds) {
- // Check if we've already made this assumption.
- return Pred && Pred->implies(P, SE);
- }
- NewPreds->push_back(P);
- return true;
- }
-
- bool addOverflowAssumption(const SCEVAddRecExpr *AR,
- SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
- auto *A = SE.getWrapPredicate(AR, AddedFlags);
- return addOverflowAssumption(A);
- }
-
- // If \p Expr represents a PHINode, we try to see if it can be represented
- // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
- // to add this predicate as a runtime overflow check, we return the AddRec.
- // If \p Expr does not meet these conditions (is not a PHI node, or we
- // couldn't create an AddRec for it, or couldn't add the predicate), we just
- // return \p Expr.
- const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
- if (!isa<PHINode>(Expr->getValue()))
- return Expr;
- std::optional<
- std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
- PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
- if (!PredicatedRewrite)
- return Expr;
- for (const auto *P : PredicatedRewrite->second){
- // Wrap predicates from outer loops are not supported.
- if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
- if (L != WP->getExpr()->getLoop())
- return Expr;
- }
- if (!addOverflowAssumption(P))
- return Expr;
- }
- return PredicatedRewrite->first;
- }
-
- SmallVectorImpl<const SCEVPredicate *> *NewPreds;
- const SCEVPredicate *Pred;
- const Loop *L;
-};
-
-} // end anonymous namespace
-
-const SCEV *
-ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
- const SCEVPredicate &Preds) {
- return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
-}
-
-const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
- const SCEV *S, const Loop *L,
- SmallVectorImpl<const SCEVPredicate *> &Preds) {
- SmallVector<const SCEVPredicate *> TransformPreds;
- S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
- auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
-
- if (!AddRec)
- return nullptr;
-
- // Check if any of the transformed predicates is known to be false. In that
- // case, it doesn't make sense to convert to a predicated AddRec, as the
- // versioned loop will never execute.
- for (const SCEVPredicate *Pred : TransformPreds) {
- auto *WrapPred = dyn_cast<SCEVWrapPredicate>(Pred);
- if (!WrapPred || WrapPred->getFlags() != SCEVWrapPredicate::IncrementNSSW)
- continue;
-
- const SCEVAddRecExpr *AddRecToCheck = WrapPred->getExpr();
- const SCEV *ExitCount = getBackedgeTakenCount(AddRecToCheck->getLoop());
- if (isa<SCEVCouldNotCompute>(ExitCount))
- continue;
-
- const SCEV *Step = AddRecToCheck->getStepRecurrence(*this);
- if (!Step->isOne())
- continue;
-
- ExitCount = getTruncateOrSignExtend(ExitCount, Step->getType());
- const SCEV *Add = getAddExpr(AddRecToCheck->getStart(), ExitCount);
- if (isKnownPredicate(CmpInst::ICMP_SLT, Add, AddRecToCheck->getStart()))
- return nullptr;
- }
-
- // Since the transformation was successful, we can now transfer the SCEV
- // predicates.
- Preds.append(TransformPreds.begin(), TransformPreds.end());
-
- return AddRec;
-}
-
-/// SCEV predicates
-SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
- SCEVPredicateKind Kind)
- : FastID(ID), Kind(Kind) {}
-
-SCEVComparePredicate::SCEVComparePredicate(const FoldingSetNodeIDRef ID,
- const ICmpInst::Predicate Pred,
- const SCEV *LHS, const SCEV *RHS)
- : SCEVPredicate(ID, P_Compare), Pred(Pred), LHS(LHS), RHS(RHS) {
- assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
- assert(LHS != RHS && "LHS and RHS are the same SCEV");
-}
-
-bool SCEVComparePredicate::implies(const SCEVPredicate *N,
- ScalarEvolution &SE) const {
- const auto *Op = dyn_cast<SCEVComparePredicate>(N);
-
- if (!Op)
- return false;
-
- if (Pred != ICmpInst::ICMP_EQ)
- return false;
-
- return Op->LHS == LHS && Op->RHS == RHS;
-}
-
-bool SCEVComparePredicate::isAlwaysTrue() const { return false; }
-
-void SCEVComparePredicate::print(raw_ostream &OS, unsigned Depth) const {
- if (Pred == ICmpInst::ICMP_EQ)
- OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
- else
- OS.indent(Depth) << "Compare predicate: " << *LHS << " " << Pred << ") "
- << *RHS << "\n";
-
-}
-
-SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
- const SCEVAddRecExpr *AR,
- IncrementWrapFlags Flags)
- : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
-
-const SCEVAddRecExpr *SCEVWrapPredicate::getExpr() const { return AR; }
-
-bool SCEVWrapPredicate::implies(const SCEVPredicate *N,
- ScalarEvolution &SE) const {
- const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
- if (!Op || setFlags(Flags, Op->Flags) != Flags)
- return false;
-
- if (Op->AR == AR)
- return true;
-
- if (Flags != SCEVWrapPredicate::IncrementNSSW &&
- Flags != SCEVWrapPredicate::IncrementNUSW)
- return false;
-
- const SCEV *Start = AR->getStart();
- const SCEV *OpStart = Op->AR->getStart();
- if (Start->getType()->isPointerTy() != OpStart->getType()->isPointerTy())
- return false;
-
- // Reject pointers to different address spaces.
- if (Start->getType()->isPointerTy() && Start->getType() != OpStart->getType())
- return false;
-
- // NUSW/NSSW on a wider-type AddRec does not imply the same on a
- // narrower-type AddRec.
- if (SE.getTypeSizeInBits(AR->getType()) >
- SE.getTypeSizeInBits(Op->AR->getType()))
- return false;
-
- const SCEV *Step = AR->getStepRecurrence(SE);
- const SCEV *OpStep = Op->AR->getStepRecurrence(SE);
- if (!SE.isKnownPositive(Step) || !SE.isKnownPositive(OpStep))
- return false;
-
- // If both steps are positive, this implies N, if N's start and step are
- // ULE/SLE (for NSUW/NSSW) than this'.
- Type *WiderTy = SE.getWiderType(Step->getType(), OpStep->getType());
- Step = SE.getNoopOrZeroExtend(Step, WiderTy);
- OpStep = SE.getNoopOrZeroExtend(OpStep, WiderTy);
-
- bool IsNUW = Flags == SCEVWrapPredicate::IncrementNUSW;
- OpStart = IsNUW ? SE.getNoopOrZeroExtend(OpStart, WiderTy)
- : SE.getNoopOrSignExtend(OpStart, WiderTy);
- Start = IsNUW ? SE.getNoopOrZeroExtend(Start, WiderTy)
- : SE.getNoopOrSignExtend(Start, WiderTy);
- CmpInst::Predicate Pred = IsNUW ? CmpInst::ICMP_ULE : CmpInst::ICMP_SLE;
- return SE.isKnownPredicate(Pred, OpStep, Step) &&
- SE.isKnownPredicate(Pred, OpStart, Start);
-}
-
-bool SCEVWrapPredicate::isAlwaysTrue() const {
- SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
- IncrementWrapFlags IFlags = Flags;
-
- if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
- IFlags = clearFlags(IFlags, IncrementNSSW);
-
- return IFlags == IncrementAnyWrap;
-}
-
-void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
- OS.indent(Depth) << *getExpr() << " Added Flags: ";
- if (SCEVWrapPredicate::IncrementNUSW & getFlags())
- OS << "<nusw>";
- if (SCEVWrapPredicate::IncrementNSSW & getFlags())
- OS << "<nssw>";
- OS << "\n";
-}
-
-SCEVWrapPredicate::IncrementWrapFlags
-SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
- ScalarEvolution &SE) {
- IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
- SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
-
- // We can safely transfer the NSW flag as NSSW.
- if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
- ImpliedFlags = IncrementNSSW;
-
- if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
- // If the increment is positive, the SCEV NUW flag will also imply the
- // WrapPredicate NUSW flag.
- if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
- if (Step->getValue()->getValue().isNonNegative())
- ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
- }
-
- return ImpliedFlags;
-}
-
-/// Union predicates don't get cached so create a dummy set ID for it.
-SCEVUnionPredicate::SCEVUnionPredicate(ArrayRef<const SCEVPredicate *> Preds,
- ScalarEvolution &SE)
- : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {
- for (const auto *P : Preds)
- add(P, SE);
-}
-
-bool SCEVUnionPredicate::isAlwaysTrue() const {
- return all_of(Preds,
- [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
-}
-
-bool SCEVUnionPredicate::implies(const SCEVPredicate *N,
- ScalarEvolution &SE) const {
- if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
- return all_of(Set->Preds, [this, &SE](const SCEVPredicate *I) {
- return this->implies(I, SE);
- });
-
- if (any_of(Preds,
- [N, &SE](const SCEVPredicate *I) { return I->implies(N, SE); }))
- return true;
-
- // A wrap predicate may be implied by a wrap predicate in Preds after applying
- // equal predicates.
- const auto *NWrap = dyn_cast<SCEVWrapPredicate>(N);
- if (!NWrap)
- return false;
- const Loop *L = NWrap->getExpr()->getLoop();
- return any_of(Preds, [&](const SCEVPredicate *I) {
- const auto *IWrap = dyn_cast<SCEVWrapPredicate>(I);
- if (!IWrap)
- return false;
- const auto *RewrittenAR = dyn_cast<SCEVAddRecExpr>(
- SE.rewriteUsingPredicate(IWrap->getExpr(), L, *this));
- return RewrittenAR &&
- SE.getWrapPredicate(RewrittenAR, IWrap->getFlags())->implies(N, SE);
- });
-}
-
-void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
- for (const auto *Pred : Preds)
- Pred->print(OS, Depth);
-}
-
-void SCEVUnionPredicate::add(const SCEVPredicate *N, ScalarEvolution &SE) {
- if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
- for (const auto *Pred : Set->Preds)
- add(Pred, SE);
- return;
- }
-
- // Implication checks are quadratic in the number of predicates. Stop doing
- // them if there are many predicates, as they should be too expensive to use
- // anyway at that point.
- bool CheckImplies = Preds.size() < 16;
-
- // Only add predicate if it is not already implied by this union predicate.
- if (CheckImplies && implies(N, SE))
- return;
-
- // Build a new vector containing the current predicates, except the ones that
- // are implied by the new predicate N.
- SmallVector<const SCEVPredicate *> PrunedPreds;
- for (auto *P : Preds) {
- if (CheckImplies && N->implies(P, SE))
- continue;
- PrunedPreds.push_back(P);
- }
- Preds = std::move(PrunedPreds);
- Preds.push_back(N);
-}
-
-PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
- Loop &L)
- : SE(SE), L(L) {
- SmallVector<const SCEVPredicate*, 4> Empty;
- Preds = std::make_unique<SCEVUnionPredicate>(Empty, SE);
-}
-
-void ScalarEvolution::registerUser(const SCEV *User,
- ArrayRef<const SCEV *> Ops) {
- for (const auto *Op : Ops)
- // We do not expect that forgetting cached data for SCEVConstants will ever
- // open any prospects for sharpening or introduce any correctness issues,
- // so we don't bother storing their dependencies.
- if (!isa<SCEVConstant>(Op))
- SCEVUsers[Op].insert(User);
-}
-
-void ScalarEvolution::registerUser(const SCEV *User, ArrayRef<SCEVUse> Ops) {
- for (const SCEV *Op : Ops)
- // We do not expect that forgetting cached data for SCEVConstants will ever
- // open any prospects for sharpening or introduce any correctness issues,
- // so we don't bother storing their dependencies.
- if (!isa<SCEVConstant>(Op))
- SCEVUsers[Op].insert(User);
-}
-
-const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
- const SCEV *Expr = SE.getSCEV(V);
- return getPredicatedSCEV(Expr);
-}
-
-const SCEV *PredicatedScalarEvolution::getPredicatedSCEV(const SCEV *Expr) {
- RewriteEntry &Entry = RewriteMap[Expr];
-
- // If we already have an entry and the version matches, return it.
- if (Entry.second && Generation == Entry.first)
- return Entry.second;
-
- // We found an entry but it's stale. Rewrite the stale entry
- // according to the current predicate.
- if (Entry.second)
- Expr = Entry.second;
-
- const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, *Preds);
- Entry = {Generation, NewSCEV};
-
- return NewSCEV;
-}
-
-const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
- if (!BackedgeCount) {
- SmallVector<const SCEVPredicate *, 4> Preds;
- BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, Preds);
- for (const auto *P : Preds)
- addPredicate(*P);
- }
- return BackedgeCount;
-}
-
-const SCEV *PredicatedScalarEvolution::getSymbolicMaxBackedgeTakenCount() {
- if (!SymbolicMaxBackedgeCount) {
- SmallVector<const SCEVPredicate *, 4> Preds;
- SymbolicMaxBackedgeCount =
- SE.getPredicatedSymbolicMaxBackedgeTakenCount(&L, Preds);
- for (const auto *P : Preds)
- addPredicate(*P);
- }
- return SymbolicMaxBackedgeCount;
-}
-
-unsigned PredicatedScalarEvolution::getSmallConstantMaxTripCount() {
- if (!SmallConstantMaxTripCount) {
- SmallVector<const SCEVPredicate *, 4> Preds;
- SmallConstantMaxTripCount = SE.getSmallConstantMaxTripCount(&L, &Preds);
- for (const auto *P : Preds)
- addPredicate(*P);
- }
- return *SmallConstantMaxTripCount;
-}
-
-void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
- if (Preds->implies(&Pred, SE))
- return;
-
- SmallVector<const SCEVPredicate *, 4> NewPreds(Preds->getPredicates());
- NewPreds.push_back(&Pred);
- Preds = std::make_unique<SCEVUnionPredicate>(NewPreds, SE);
- updateGeneration();
-}
-
-void PredicatedScalarEvolution::addPredicates(
- ArrayRef<const SCEVPredicate *> Preds) {
- for (const SCEVPredicate *P : Preds)
- addPredicate(*P);
-}
-
-const SCEVPredicate &PredicatedScalarEvolution::getPredicate() const {
- return *Preds;
-}
-
-void PredicatedScalarEvolution::updateGeneration() {
- // If the generation number wrapped recompute everything.
- if (++Generation == 0) {
- for (auto &II : RewriteMap) {
- const SCEV *Rewritten = II.second.second;
- II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, *Preds)};
- }
- }
-}
-
-bool PredicatedScalarEvolution::hasNoOverflow(
- Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
- const auto *AR = dyn_cast<SCEVAddRecExpr>(getSCEV(V));
- if (!AR)
- return false;
-
- Flags = SCEVWrapPredicate::clearFlags(
- Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
-
- return Flags == SCEVWrapPredicate::IncrementAnyWrap;
-}
-
-const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(
- Value *V, SmallVectorImpl<const SCEVPredicate *> *ExtraPreds) {
- const SCEV *Expr = this->getSCEV(V);
- SmallVector<const SCEVPredicate *, 4> NewPreds;
- auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
-
- if (!New)
- return nullptr;
-
- if (ExtraPreds) {
- ExtraPreds->append(NewPreds);
- return New;
- }
-
- addPredicates(NewPreds);
-
- RewriteMap[SE.getSCEV(V)] = {Generation, New};
- return New;
-}
-
-PredicatedScalarEvolution::PredicatedScalarEvolution(
- const PredicatedScalarEvolution &Init)
- : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L),
- Preds(std::make_unique<SCEVUnionPredicate>(Init.Preds->getPredicates(),
- SE)),
- Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {}
-
-void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
- // For each block.
- for (auto *BB : L.getBlocks())
- for (auto &I : *BB) {
- if (!SE.isSCEVable(I.getType()))
- continue;
-
- auto *Expr = SE.getSCEV(&I);
- auto II = RewriteMap.find(Expr);
-
- if (II == RewriteMap.end())
- continue;
-
- // Don't print things that are not interesting.
- if (II->second.second == Expr)
- continue;
-
- OS.indent(Depth) << "[PSE]" << I << ":\n";
- OS.indent(Depth + 2) << *Expr << "\n";
- OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
- }
-}
-
-ScalarEvolution::LoopGuards
-ScalarEvolution::LoopGuards::collect(const Loop *L, ScalarEvolution &SE) {
- BasicBlock *Header = L->getHeader();
- BasicBlock *Pred = L->getLoopPredecessor();
- LoopGuards Guards(SE);
- if (!Pred)
- return Guards;
- SmallPtrSet<const BasicBlock *, 8> VisitedBlocks;
- collectFromBlock(SE, Guards, Header, Pred, VisitedBlocks);
- return Guards;
-}
-
-void ScalarEvolution::LoopGuards::collectFromPHI(
- ScalarEvolution &SE, ScalarEvolution::LoopGuards &Guards,
- const PHINode &Phi, SmallPtrSetImpl<const BasicBlock *> &VisitedBlocks,
- SmallDenseMap<const BasicBlock *, LoopGuards> &IncomingGuards,
- unsigned Depth) {
- if (!SE.isSCEVable(Phi.getType()))
- return;
-
- using MinMaxPattern = std::pair<const SCEVConstant *, SCEVTypes>;
- auto GetMinMaxConst = [&](unsigned IncomingIdx) -> MinMaxPattern {
- const BasicBlock *InBlock = Phi.getIncomingBlock(IncomingIdx);
- if (!VisitedBlocks.insert(InBlock).second)
- return {nullptr, scCouldNotCompute};
-
- // Avoid analyzing unreachable blocks so that we don't get trapped
- // traversing cycles with ill-formed dominance or infinite cycles
- if (!SE.DT.isReachableFromEntry(InBlock))
- return {nullptr, scCouldNotCompute};
-
- auto [G, Inserted] = IncomingGuards.try_emplace(InBlock, LoopGuards(SE));
- if (Inserted)
- collectFromBlock(SE, G->second, Phi.getParent(), InBlock, VisitedBlocks,
- Depth + 1);
- auto &RewriteMap = G->second.RewriteMap;
- if (RewriteMap.empty())
- return {nullptr, scCouldNotCompute};
- auto S = RewriteMap.find(SE.getSCEV(Phi.getIncomingValue(IncomingIdx)));
- if (S == RewriteMap.end())
- return {nullptr, scCouldNotCompute};
- auto *SM = dyn_cast_if_present<SCEVMinMaxExpr>(S->second);
- if (!SM)
- return {nullptr, scCouldNotCompute};
- if (const SCEVConstant *C0 = dyn_cast<SCEVConstant>(SM->getOperand(0)))
- return {C0, SM->getSCEVType()};
- return {nullptr, scCouldNotCompute};
- };
- auto MergeMinMaxConst = [](MinMaxPattern P1,
- MinMaxPattern P2) -> MinMaxPattern {
- auto [C1, T1] = P1;
- auto [C2, T2] = P2;
- if (!C1 || !C2 || T1 != T2)
- return {nullptr, scCouldNotCompute};
- switch (T1) {
- case scUMaxExpr:
- return {C1->getAPInt().ult(C2->getAPInt()) ? C1 : C2, T1};
- case scSMaxExpr:
- return {C1->getAPInt().slt(C2->getAPInt()) ? C1 : C2, T1};
- case scUMinExpr:
- return {C1->getAPInt().ugt(C2->getAPInt()) ? C1 : C2, T1};
- case scSMinExpr:
- return {C1->getAPInt().sgt(C2->getAPInt()) ? C1 : C2, T1};
- default:
- llvm_unreachable("Trying to merge non-MinMaxExpr SCEVs.");
- }
- };
- auto P = GetMinMaxConst(0);
- for (unsigned int In = 1; In < Phi.getNumIncomingValues(); In++) {
- if (!P.first)
- break;
- P = MergeMinMaxConst(P, GetMinMaxConst(In));
- }
- if (P.first) {
- const SCEV *LHS = SE.getSCEV(const_cast<PHINode *>(&Phi));
- SmallVector<SCEVUse, 2> Ops({P.first, LHS});
- const SCEV *RHS = SE.getMinMaxExpr(P.second, Ops);
- Guards.RewriteMap.insert({LHS, RHS});
- }
-}
-
-// Return a new SCEV that modifies \p Expr to the closest number divides by
-// \p Divisor and less or equal than Expr. For now, only handle constant
-// Expr.
-static const SCEV *getPreviousSCEVDivisibleByDivisor(const SCEV *Expr,
- const APInt &DivisorVal,
- ScalarEvolution &SE) {
- const APInt *ExprVal;
- if (!match(Expr, m_scev_APInt(ExprVal)) || ExprVal->isNegative() ||
- DivisorVal.isNonPositive())
- return Expr;
- APInt Rem = ExprVal->urem(DivisorVal);
- // return the SCEV: Expr - Expr % Divisor
- return SE.getConstant(*ExprVal - Rem);
-}
-
-// Return a new SCEV that modifies \p Expr to the closest number divides by
-// \p Divisor and greater or equal than Expr. For now, only handle constant
-// Expr.
-static const SCEV *getNextSCEVDivisibleByDivisor(const SCEV *Expr,
- const APInt &DivisorVal,
- ScalarEvolution &SE) {
- const APInt *ExprVal;
- if (!match(Expr, m_scev_APInt(ExprVal)) || ExprVal->isNegative() ||
- DivisorVal.isNonPositive())
- return Expr;
- APInt Rem = ExprVal->urem(DivisorVal);
- if (Rem.isZero())
- return Expr;
- // return the SCEV: Expr + Divisor - Expr % Divisor
- return SE.getConstant(*ExprVal + DivisorVal - Rem);
-}
-
-static bool collectDivisibilityInformation(
- ICmpInst::Predicate Predicate, const SCEV *LHS, const SCEV *RHS,
- DenseMap<const SCEV *, const SCEV *> &DivInfo,
- DenseMap<const SCEV *, APInt> &Multiples, ScalarEvolution &SE) {
- // If we have LHS == 0, check if LHS is computing a property of some unknown
- // SCEV %v which we can rewrite %v to express explicitly.
- if (Predicate != CmpInst::ICMP_EQ || !match(RHS, m_scev_Zero()))
- return false;
- // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to
- // explicitly express that.
- const SCEVUnknown *URemLHS = nullptr;
- const SCEV *URemRHS = nullptr;
- if (!match(LHS, m_scev_URem(m_SCEVUnknown(URemLHS), m_SCEV(URemRHS), SE)))
- return false;
-
- const SCEV *Multiple =
- SE.getMulExpr(SE.getUDivExpr(URemLHS, URemRHS), URemRHS);
- DivInfo[URemLHS] = Multiple;
- if (auto *C = dyn_cast<SCEVConstant>(URemRHS))
- Multiples[URemLHS] = C->getAPInt();
- return true;
-}
-
-// Check if the condition is a divisibility guard (A % B == 0).
-static bool isDivisibilityGuard(const SCEV *LHS, const SCEV *RHS,
- ScalarEvolution &SE) {
- const SCEV *X, *Y;
- return match(LHS, m_scev_URem(m_SCEV(X), m_SCEV(Y), SE)) && RHS->isZero();
-}
-
-// Apply divisibility by \p Divisor on MinMaxExpr with constant values,
-// recursively. This is done by aligning up/down the constant value to the
-// Divisor.
-static const SCEV *applyDivisibilityOnMinMaxExpr(const SCEV *MinMaxExpr,
- APInt Divisor,
- ScalarEvolution &SE) {
- // Return true if \p Expr is a MinMax SCEV expression with a non-negative
- // constant operand. If so, return in \p SCTy the SCEV type and in \p RHS
- // the non-constant operand and in \p LHS the constant operand.
- auto IsMinMaxSCEVWithNonNegativeConstant =
- [&](const SCEV *Expr, SCEVTypes &SCTy, const SCEV *&LHS,
- const SCEV *&RHS) {
- if (auto *MinMax = dyn_cast<SCEVMinMaxExpr>(Expr)) {
- if (MinMax->getNumOperands() != 2)
- return false;
- if (auto *C = dyn_cast<SCEVConstant>(MinMax->getOperand(0))) {
- if (C->getAPInt().isNegative())
- return false;
- SCTy = MinMax->getSCEVType();
- LHS = MinMax->getOperand(0);
- RHS = MinMax->getOperand(1);
- return true;
- }
- }
- return false;
- };
-
- const SCEV *MinMaxLHS = nullptr, *MinMaxRHS = nullptr;
- SCEVTypes SCTy;
- if (!IsMinMaxSCEVWithNonNegativeConstant(MinMaxExpr, SCTy, MinMaxLHS,
- MinMaxRHS))
- return MinMaxExpr;
- auto IsMin = isa<SCEVSMinExpr>(MinMaxExpr) || isa<SCEVUMinExpr>(MinMaxExpr);
- assert(SE.isKnownNonNegative(MinMaxLHS) && "Expected non-negative operand!");
- auto *DivisibleExpr =
- IsMin ? getPreviousSCEVDivisibleByDivisor(MinMaxLHS, Divisor, SE)
- : getNextSCEVDivisibleByDivisor(MinMaxLHS, Divisor, SE);
- SmallVector<SCEVUse> Ops = {
- applyDivisibilityOnMinMaxExpr(MinMaxRHS, Divisor, SE), DivisibleExpr};
- return SE.getMinMaxExpr(SCTy, Ops);
-}
-
-void ScalarEvolution::LoopGuards::collectFromBlock(
- ScalarEvolution &SE, ScalarEvolution::LoopGuards &Guards,
- const BasicBlock *Block, const BasicBlock *Pred,
- SmallPtrSetImpl<const BasicBlock *> &VisitedBlocks, unsigned Depth) {
-
- assert(SE.DT.isReachableFromEntry(Block) && SE.DT.isReachableFromEntry(Pred));
-
- SmallVector<SCEVUse> ExprsToRewrite;
- auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS,
- const SCEV *RHS,
- DenseMap<const SCEV *, const SCEV *> &RewriteMap,
- const LoopGuards &DivGuards) {
- // WARNING: It is generally unsound to apply any wrap flags to the proposed
- // replacement SCEV which isn't directly implied by the structure of that
- // SCEV. In particular, using contextual facts to imply flags is *NOT*
- // legal. See the scoping rules for flags in the header to understand why.
-
- // Puts rewrite rule \p From -> \p To into the rewrite map. Also if \p From
- // and \p FromRewritten are the same (i.e. there has been no rewrite
- // registered for \p From), then puts this value in the list of rewritten
- // expressions.
- auto AddRewrite = [&](const SCEV *From, const SCEV *FromRewritten,
- const SCEV *To) {
- if (From == FromRewritten)
- ExprsToRewrite.push_back(From);
- RewriteMap[From] = To;
- };
-
- // Checks whether \p S has already been rewritten. In that case returns the
- // existing rewrite because we want to chain further rewrites onto the
- // already rewritten value. Otherwise returns \p S.
- auto GetMaybeRewritten = [&](const SCEV *S) {
- return RewriteMap.lookup_or(S, S);
- };
-
- // Check for a condition of the form (-C1 + X < C2). InstCombine will
- // create this form when combining two checks of the form (X u< C2 + C1) and
- // (X >=u C1).
- auto MatchRangeCheckIdiom = [&](ICmpInst::Predicate Pred,
- const SCEV *MatchLHS,
- const SCEV *MatchRHS) {
- const SCEVConstant *C1;
- const SCEVUnknown *LHSUnknown;
- auto *C2 = dyn_cast<SCEVConstant>(MatchRHS);
- if (!match(MatchLHS,
- m_scev_Add(m_SCEVConstant(C1), m_SCEVUnknown(LHSUnknown))) ||
- !C2)
- return false;
-
- auto ExactRegion =
- ConstantRange::makeExactICmpRegion(Pred, C2->getAPInt())
- .sub(C1->getAPInt());
-
- // Tighten the raw range with what we already know about LHSUnknown
- // from prior guards recorded in RewriteMap, or from SCEV's own range
- // analysis.
- const SCEV *RewrittenLHS = GetMaybeRewritten(LHSUnknown);
- ExactRegion = ExactRegion.intersectWith(SE.getUnsignedRange(RewrittenLHS),
- ConstantRange::Unsigned);
-
- // Bail if the guard is inconsistent with prior facts, or if the range
- // is still not a monotonic non-wrapping interval after tightening.
- if (ExactRegion.isEmptySet() || ExactRegion.isWrappedSet() ||
- ExactRegion.isFullSet())
- return false;
-
- const SCEV *RegionMin = SE.getConstant(ExactRegion.getUnsignedMin());
- const SCEV *RegionMax = SE.getConstant(ExactRegion.getUnsignedMax());
- const SCEV *ClampedLHS =
- SE.getUMaxExpr(RegionMin, SE.getUMinExpr(RewrittenLHS, RegionMax));
- AddRewrite(LHSUnknown, RewrittenLHS, ClampedLHS);
- return true;
- };
- if (MatchRangeCheckIdiom(Predicate, LHS, RHS))
- return;
-
- // Do not apply information for constants or if RHS contains an AddRec.
- if (isa<SCEVConstant>(LHS) || SE.containsAddRecurrence(RHS))
- return;
-
- // If RHS is SCEVUnknown, make sure the information is applied to it.
- if (!isa<SCEVUnknown>(LHS) && isa<SCEVUnknown>(RHS)) {
- std::swap(LHS, RHS);
- Predicate = CmpInst::getSwappedPredicate(Predicate);
- }
-
- const SCEV *RewrittenLHS = GetMaybeRewritten(LHS);
- // Apply divisibility information when computing the constant multiple.
- const APInt &DividesBy =
- SE.getConstantMultiple(DivGuards.rewrite(RewrittenLHS));
-
- // Collect rewrites for LHS and its transitive operands based on the
- // condition.
- // For min/max expressions, also apply the guard to its operands:
- // 'min(a, b) >= c' -> '(a >= c) and (b >= c)',
- // 'min(a, b) > c' -> '(a > c) and (b > c)',
- // 'max(a, b) <= c' -> '(a <= c) and (b <= c)',
- // 'max(a, b) < c' -> '(a < c) and (b < c)'.
-
- // We cannot express strict predicates in SCEV, so instead we replace them
- // with non-strict ones against plus or minus one of RHS depending on the
- // predicate.
- const SCEV *One = SE.getOne(RHS->getType());
- switch (Predicate) {
- case CmpInst::ICMP_ULT:
- if (RHS->getType()->isPointerTy())
- return;
- RHS = SE.getUMaxExpr(RHS, One);
- [[fallthrough]];
- case CmpInst::ICMP_SLT: {
- RHS = SE.getMinusSCEV(RHS, One);
- RHS = getPreviousSCEVDivisibleByDivisor(RHS, DividesBy, SE);
- break;
- }
- case CmpInst::ICMP_UGT:
- case CmpInst::ICMP_SGT:
- RHS = SE.getAddExpr(RHS, One);
- RHS = getNextSCEVDivisibleByDivisor(RHS, DividesBy, SE);
- break;
- case CmpInst::ICMP_ULE:
- case CmpInst::ICMP_SLE:
- RHS = getPreviousSCEVDivisibleByDivisor(RHS, DividesBy, SE);
- break;
- case CmpInst::ICMP_UGE:
- case CmpInst::ICMP_SGE:
- RHS = getNextSCEVDivisibleByDivisor(RHS, DividesBy, SE);
- break;
- default:
- break;
- }
-
- SmallVector<SCEVUse, 16> Worklist(1, LHS);
- SmallPtrSet<const SCEV *, 16> Visited;
-
- auto EnqueueOperands = [&Worklist](const SCEVNAryExpr *S) {
- append_range(Worklist, S->operands());
- };
-
- while (!Worklist.empty()) {
- const SCEV *From = Worklist.pop_back_val();
- if (isa<SCEVConstant>(From))
- continue;
- if (!Visited.insert(From).second)
- continue;
- const SCEV *FromRewritten = GetMaybeRewritten(From);
- const SCEV *To = nullptr;
-
- switch (Predicate) {
- case CmpInst::ICMP_ULT:
- case CmpInst::ICMP_ULE:
- To = SE.getUMinExpr(FromRewritten, RHS);
- if (auto *UMax = dyn_cast<SCEVUMaxExpr>(FromRewritten))
- EnqueueOperands(UMax);
- break;
- case CmpInst::ICMP_SLT:
- case CmpInst::ICMP_SLE:
- To = SE.getSMinExpr(FromRewritten, RHS);
- if (auto *SMax = dyn_cast<SCEVSMaxExpr>(FromRewritten))
- EnqueueOperands(SMax);
- break;
- case CmpInst::ICMP_UGT:
- case CmpInst::ICMP_UGE:
- To = SE.getUMaxExpr(FromRewritten, RHS);
- if (auto *UMin = dyn_cast<SCEVUMinExpr>(FromRewritten))
- EnqueueOperands(UMin);
- break;
- case CmpInst::ICMP_SGT:
- case CmpInst::ICMP_SGE:
- To = SE.getSMaxExpr(FromRewritten, RHS);
- if (auto *SMin = dyn_cast<SCEVSMinExpr>(FromRewritten))
- EnqueueOperands(SMin);
- break;
- case CmpInst::ICMP_EQ:
- if (isa<SCEVConstant>(RHS))
- To = RHS;
- break;
- case CmpInst::ICMP_NE:
- if (match(RHS, m_scev_Zero())) {
- const SCEV *OneAlignedUp =
- getNextSCEVDivisibleByDivisor(One, DividesBy, SE);
- To = SE.getUMaxExpr(FromRewritten, OneAlignedUp);
- } else {
- // LHS != RHS can be rewritten as (LHS - RHS) = UMax(1, LHS - RHS),
- // but creating the subtraction eagerly is expensive. Track the
- // inequalities in a separate map, and materialize the rewrite lazily
- // when encountering a suitable subtraction while re-writing.
- if (LHS->getType()->isPointerTy()) {
- LHS = SE.getPtrToAddrExpr(LHS);
- RHS = SE.getPtrToAddrExpr(RHS);
- if (isa<SCEVCouldNotCompute>(LHS) || isa<SCEVCouldNotCompute>(RHS))
- break;
- }
- const SCEVConstant *C;
- const SCEV *A, *B;
- if (match(RHS, m_scev_Add(m_SCEVConstant(C), m_SCEV(A))) &&
- match(LHS, m_scev_Add(m_scev_Specific(C), m_SCEV(B)))) {
- RHS = A;
- LHS = B;
- }
- if (LHS > RHS)
- std::swap(LHS, RHS);
- Guards.NotEqual.insert({LHS, RHS});
- continue;
- }
- break;
- default:
- break;
- }
-
- if (To)
- AddRewrite(From, FromRewritten, To);
- }
- };
-
- SmallVector<PointerIntPair<Value *, 1, bool>> Terms;
- // First, collect information from assumptions dominating the loop.
- for (auto &AssumeVH : SE.AC.assumptions()) {
- if (!AssumeVH)
- continue;
- auto *AssumeI = cast<CallInst>(AssumeVH);
- if (!SE.DT.dominates(AssumeI, Block))
- continue;
- Terms.emplace_back(AssumeI->getOperand(0), true);
- }
-
- // Second, collect information from llvm.experimental.guards dominating the loop.
- auto *GuardDecl = Intrinsic::getDeclarationIfExists(
- SE.F.getParent(), Intrinsic::experimental_guard);
- if (GuardDecl)
- for (const auto *GU : GuardDecl->users())
- if (const auto *Guard = dyn_cast<IntrinsicInst>(GU))
- if (Guard->getFunction() == Block->getParent() &&
- SE.DT.dominates(Guard, Block))
- Terms.emplace_back(Guard->getArgOperand(0), true);
-
- // Third, collect conditions from dominating branches. Starting at the loop
- // predecessor, climb up the predecessor chain, as long as there are
- // predecessors that can be found that have unique successors leading to the
- // original header.
- // TODO: share this logic with isLoopEntryGuardedByCond.
- unsigned NumCollectedConditions = 0;
- VisitedBlocks.insert(Block);
- std::pair<const BasicBlock *, const BasicBlock *> Pair(Pred, Block);
- for (; Pair.first;
- Pair = SE.getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
- VisitedBlocks.insert(Pair.second);
- const CondBrInst *LoopEntryPredicate =
- dyn_cast<CondBrInst>(Pair.first->getTerminator());
- if (!LoopEntryPredicate)
- continue;
-
- Terms.emplace_back(LoopEntryPredicate->getCondition(),
- LoopEntryPredicate->getSuccessor(0) == Pair.second);
- NumCollectedConditions++;
-
- // If we are recursively collecting guards stop after 2
- // conditions to limit compile-time impact for now.
- if (Depth > 0 && NumCollectedConditions == 2)
- break;
- }
- // Finally, if we stopped climbing the predecessor chain because
- // there wasn't a unique one to continue, try to collect conditions
- // for PHINodes by recursively following all of their incoming
- // blocks and try to merge the found conditions to build a new one
- // for the Phi.
- if (Pair.second->hasNPredecessorsOrMore(2) &&
- Depth < MaxLoopGuardCollectionDepth) {
- SmallDenseMap<const BasicBlock *, LoopGuards> IncomingGuards;
- for (auto &Phi : Pair.second->phis())
- collectFromPHI(SE, Guards, Phi, VisitedBlocks, IncomingGuards, Depth);
- }
-
- // Now apply the information from the collected conditions to
- // Guards.RewriteMap. Conditions are processed in reverse order, so the
- // earliest conditions is processed first, except guards with divisibility
- // information, which are moved to the back. This ensures the SCEVs with the
- // shortest dependency chains are constructed first.
- SmallVector<std::tuple<CmpInst::Predicate, const SCEV *, const SCEV *>>
- GuardsToProcess;
- for (auto [Term, EnterIfTrue] : reverse(Terms)) {
- SmallVector<Value *, 8> Worklist;
- SmallPtrSet<Value *, 8> Visited;
- Worklist.push_back(Term);
- while (!Worklist.empty()) {
- Value *Cond = Worklist.pop_back_val();
- if (!Visited.insert(Cond).second)
- continue;
-
- if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) {
- auto Predicate =
- EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate();
- const auto *LHS = SE.getSCEV(Cmp->getOperand(0));
- const auto *RHS = SE.getSCEV(Cmp->getOperand(1));
- // If LHS is a constant, apply information to the other expression.
- // TODO: If LHS is not a constant, check if using CompareSCEVComplexity
- // can improve results.
- if (isa<SCEVConstant>(LHS)) {
- std::swap(LHS, RHS);
- Predicate = CmpInst::getSwappedPredicate(Predicate);
- }
- GuardsToProcess.emplace_back(Predicate, LHS, RHS);
- continue;
- }
-
- Value *L, *R;
- if (EnterIfTrue ? match(Cond, m_LogicalAnd(m_Value(L), m_Value(R)))
- : match(Cond, m_LogicalOr(m_Value(L), m_Value(R)))) {
- Worklist.push_back(L);
- Worklist.push_back(R);
- }
- }
- }
-
- // Process divisibility guards in reverse order to populate DivGuards early.
- DenseMap<const SCEV *, APInt> Multiples;
- LoopGuards DivGuards(SE);
- for (const auto &[Predicate, LHS, RHS] : GuardsToProcess) {
- if (!isDivisibilityGuard(LHS, RHS, SE))
- continue;
- collectDivisibilityInformation(Predicate, LHS, RHS, DivGuards.RewriteMap,
- Multiples, SE);
- }
-
- for (const auto &[Predicate, LHS, RHS] : GuardsToProcess)
- CollectCondition(Predicate, LHS, RHS, Guards.RewriteMap, DivGuards);
-
- // Apply divisibility information last. This ensures it is applied to the
- // outermost expression after other rewrites for the given value.
- for (const auto &[K, Divisor] : Multiples) {
- const SCEV *DivisorSCEV = SE.getConstant(Divisor);
- Guards.RewriteMap[K] =
- SE.getMulExpr(SE.getUDivExpr(applyDivisibilityOnMinMaxExpr(
- Guards.rewrite(K), Divisor, SE),
- DivisorSCEV),
- DivisorSCEV);
- ExprsToRewrite.push_back(K);
- }
-
- // Let the rewriter preserve NUW/NSW flags if the unsigned/signed ranges of
- // the replacement expressions are contained in the ranges of the replaced
- // expressions.
- Guards.PreserveNUW = true;
- Guards.PreserveNSW = true;
- for (const SCEV *Expr : ExprsToRewrite) {
- const SCEV *RewriteTo = Guards.RewriteMap[Expr];
- Guards.PreserveNUW &=
- SE.getUnsignedRange(Expr).contains(SE.getUnsignedRange(RewriteTo));
- Guards.PreserveNSW &=
- SE.getSignedRange(Expr).contains(SE.getSignedRange(RewriteTo));
- }
-
- // Now that all rewrite information is collect, rewrite the collected
- // expressions with the information in the map. This applies information to
- // sub-expressions.
- if (ExprsToRewrite.size() > 1) {
- for (const SCEV *Expr : ExprsToRewrite) {
- const SCEV *RewriteTo = Guards.RewriteMap[Expr];
- Guards.RewriteMap.erase(Expr);
- Guards.RewriteMap.insert({Expr, Guards.rewrite(RewriteTo)});
- }
- }
-}
-
-const SCEV *ScalarEvolution::LoopGuards::rewrite(const SCEV *Expr) const {
- /// A rewriter to replace SCEV expressions in Map with the corresponding entry
- /// in the map. It skips AddRecExpr because we cannot guarantee that the
- /// replacement is loop invariant in the loop of the AddRec.
- class SCEVLoopGuardRewriter
- : public SCEVRewriteVisitor<SCEVLoopGuardRewriter> {
- const DenseMap<const SCEV *, const SCEV *> ⤅
- const SmallDenseSet<std::pair<const SCEV *, const SCEV *>> ≠
-
- SCEV::NoWrapFlags FlagMask = SCEV::FlagAnyWrap;
-
- public:
- SCEVLoopGuardRewriter(ScalarEvolution &SE,
- const ScalarEvolution::LoopGuards &Guards)
- : SCEVRewriteVisitor(SE), Map(Guards.RewriteMap),
- NotEqual(Guards.NotEqual) {
- if (Guards.PreserveNUW)
- FlagMask = ScalarEvolution::setFlags(FlagMask, SCEV::FlagNUW);
- if (Guards.PreserveNSW)
- FlagMask = ScalarEvolution::setFlags(FlagMask, SCEV::FlagNSW);
- }
-
- const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
-
- const SCEV *visitUnknown(const SCEVUnknown *Expr) {
- return Map.lookup_or(Expr, Expr);
- }
-
- const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
- if (const SCEV *S = Map.lookup(Expr))
- return S;
-
- // If we didn't find the extact ZExt expr in the map, check if there's
- // an entry for a smaller ZExt we can use instead.
- Type *Ty = Expr->getType();
- const SCEV *Op = Expr->getOperand(0);
- unsigned Bitwidth = Ty->getScalarSizeInBits() / 2;
- while (Bitwidth % 8 == 0 && Bitwidth >= 8 &&
- Bitwidth > Op->getType()->getScalarSizeInBits()) {
- Type *NarrowTy = IntegerType::get(SE.getContext(), Bitwidth);
- auto *NarrowExt = SE.getZeroExtendExpr(Op, NarrowTy);
- if (const SCEV *S = Map.lookup(NarrowExt))
- return SE.getZeroExtendExpr(S, Ty);
- Bitwidth = Bitwidth / 2;
- }
-
- return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitZeroExtendExpr(
- Expr);
- }
-
- const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
- if (const SCEV *S = Map.lookup(Expr))
- return S;
- return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitSignExtendExpr(
- Expr);
- }
-
- const SCEV *visitUMinExpr(const SCEVUMinExpr *Expr) {
- if (const SCEV *S = Map.lookup(Expr))
- return S;
- return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitUMinExpr(Expr);
- }
-
- const SCEV *visitSMinExpr(const SCEVSMinExpr *Expr) {
- if (const SCEV *S = Map.lookup(Expr))
- return S;
- return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitSMinExpr(Expr);
- }
-
- const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
- if (const SCEV *S = Map.lookup(Expr))
- return S;
-
- // Helper to check if S is a subtraction (A - B) where A != B, and if so,
- // return UMax(S, 1).
- auto RewriteSubtraction = [&](const SCEV *S) -> const SCEV * {
- SCEVUse LHS, RHS;
- if (MatchBinarySub(S, LHS, RHS)) {
- if (LHS > RHS)
- std::swap(LHS, RHS);
- if (NotEqual.contains({LHS, RHS})) {
- const SCEV *OneAlignedUp = getNextSCEVDivisibleByDivisor(
- SE.getOne(S->getType()), SE.getConstantMultiple(S), SE);
- return SE.getUMaxExpr(OneAlignedUp, S);
- }
- }
- return nullptr;
- };
-
- // Check if Expr itself is a subtraction pattern with guard info.
- if (const SCEV *Rewritten = RewriteSubtraction(Expr))
- return Rewritten;
-
- // Trip count expressions sometimes consist of adding 3 operands, i.e.
- // (Const + A + B). There may be guard info for A + B, and if so, apply
- // it.
- // TODO: Could more generally apply guards to Add sub-expressions.
- if (isa<SCEVConstant>(Expr->getOperand(0))) {
- if (Expr->getNumOperands() == 3) {
- const SCEV *Add =
- SE.getAddExpr(Expr->getOperand(1), Expr->getOperand(2));
- if (const SCEV *Rewritten = RewriteSubtraction(Add))
- return SE.getAddExpr(
- Expr->getOperand(0), Rewritten,
- ScalarEvolution::maskFlags(Expr->getNoWrapFlags(), FlagMask));
- if (const SCEV *S = Map.lookup(Add))
- return SE.getAddExpr(Expr->getOperand(0), S);
- }
-
- // For expressions of the form (Const + A), check if we have guard info
- // for (Const + 1 + A), and rewrite to ((Const + 1 + A) - 1). This makes
- // sure we don't lose information when rewriting expressions based on
- // back-edge taken counts in some cases.
- if (Expr->getNumOperands() == 2) {
- const SCEV *S = nullptr;
- // Handle (-1 + 1 + A) without constructing SCEVs.
- if (match(Expr->getOperand(0), m_scev_AllOnes())) {
- S = Map.lookup(Expr->getOperand(1));
- } else {
- const SCEV *NewC =
- SE.getAddExpr(Expr->getOperand(0), SE.getOne(Expr->getType()));
- S = Map.lookup(SE.getAddExpr(NewC, Expr->getOperand(1)));
- }
- if (S)
- return SE.getAddExpr(S, SE.getMinusOne(Expr->getType()));
- }
- }
- SmallVector<SCEVUse, 2> Operands;
- bool Changed = false;
- for (SCEVUse Op : Expr->operands()) {
- Operands.push_back(
- SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visit(Op));
- Changed |= Op != Operands.back();
- }
- // We are only replacing operands with equivalent values, so transfer the
- // flags from the original expression.
- return !Changed ? Expr
- : SE.getAddExpr(Operands,
- ScalarEvolution::maskFlags(
- Expr->getNoWrapFlags(), FlagMask));
- }
-
- const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
- SmallVector<SCEVUse, 2> Operands;
- bool Changed = false;
- for (SCEVUse Op : Expr->operands()) {
- Operands.push_back(
- SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visit(Op));
- Changed |= Op != Operands.back();
- }
- // We are only replacing operands with equivalent values, so transfer the
- // flags from the original expression.
- return !Changed ? Expr
- : SE.getMulExpr(Operands,
- ScalarEvolution::maskFlags(
- Expr->getNoWrapFlags(), FlagMask));
- }
- };
-
- if (RewriteMap.empty() && NotEqual.empty())
- return Expr;
-
- SCEVLoopGuardRewriter Rewriter(SE, *this);
- return Rewriter.visit(Expr);
-}
-
-const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) {
- return applyLoopGuards(Expr, LoopGuards::collect(L, *this));
-}
-
-const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr,
- const LoopGuards &Guards) {
- return Guards.rewrite(Expr);
-}
+//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// This file contains the implementation of the scalar evolution analysis
+// engine, which is used primarily to analyze expressions involving induction
+// variables in loops.
+//
+// There are several aspects to this library. First is the representation of
+// scalar expressions, which are represented as subclasses of the SCEV class.
+// These classes are used to represent certain types of subexpressions that we
+// can handle. We only create one SCEV of a particular shape, so
+// pointer-comparisons for equality are legal.
+//
+// One important aspect of the SCEV objects is that they are never cyclic, even
+// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
+// the PHI node is one of the idioms that we can represent (e.g., a polynomial
+// recurrence) then we represent it directly as a recurrence node, otherwise we
+// represent it as a SCEVUnknown node.
+//
+// In addition to being able to represent expressions of various types, we also
+// have folders that are used to build the *canonical* representation for a
+// particular expression. These folders are capable of using a variety of
+// rewrite rules to simplify the expressions.
+//
+// Once the folders are defined, we can implement the more interesting
+// higher-level code, such as the code that recognizes PHI nodes of various
+// types, computes the execution count of a loop, etc.
+//
+// TODO: We should use these routines and value representations to implement
+// dependence analysis!
+//
+//===----------------------------------------------------------------------===//
+//
+// There are several good references for the techniques used in this analysis.
+//
+// Chains of recurrences -- a method to expedite the evaluation
+// of closed-form functions
+// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
+//
+// On computational properties of chains of recurrences
+// Eugene V. Zima
+//
+// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
+// Robert A. van Engelen
+//
+// Efficient Symbolic Analysis for Optimizing Compilers
+// Robert A. van Engelen
+//
+// Using the chains of recurrences algebra for data dependence testing and
+// induction variable substitution
+// MS Thesis, Johnie Birch
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/ScalarEvolution.h"
+#include "llvm/ADT/APInt.h"
+#include "llvm/ADT/ArrayRef.h"
+#include "llvm/ADT/DenseMap.h"
+#include "llvm/ADT/DepthFirstIterator.h"
+#include "llvm/ADT/FoldingSet.h"
+#include "llvm/ADT/STLExtras.h"
+#include "llvm/ADT/ScopeExit.h"
+#include "llvm/ADT/Sequence.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/ADT/Statistic.h"
+#include "llvm/ADT/StringExtras.h"
+#include "llvm/ADT/StringRef.h"
+#include "llvm/Analysis/AssumptionCache.h"
+#include "llvm/Analysis/ConstantFolding.h"
+#include "llvm/Analysis/InstructionSimplify.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Analysis/MemoryBuiltins.h"
+#include "llvm/Analysis/ScalarEvolutionExpressions.h"
+#include "llvm/Analysis/ScalarEvolutionPatternMatch.h"
+#include "llvm/Analysis/TargetLibraryInfo.h"
+#include "llvm/Analysis/ValueTracking.h"
+#include "llvm/Config/llvm-config.h"
+#include "llvm/IR/Argument.h"
+#include "llvm/IR/BasicBlock.h"
+#include "llvm/IR/CFG.h"
+#include "llvm/IR/Constant.h"
+#include "llvm/IR/ConstantRange.h"
+#include "llvm/IR/Constants.h"
+#include "llvm/IR/DataLayout.h"
+#include "llvm/IR/DerivedTypes.h"
+#include "llvm/IR/Dominators.h"
+#include "llvm/IR/Function.h"
+#include "llvm/IR/GlobalAlias.h"
+#include "llvm/IR/GlobalValue.h"
+#include "llvm/IR/InstIterator.h"
+#include "llvm/IR/InstrTypes.h"
+#include "llvm/IR/Instruction.h"
+#include "llvm/IR/Instructions.h"
+#include "llvm/IR/IntrinsicInst.h"
+#include "llvm/IR/Intrinsics.h"
+#include "llvm/IR/LLVMContext.h"
+#include "llvm/IR/Operator.h"
+#include "llvm/IR/PatternMatch.h"
+#include "llvm/IR/Type.h"
+#include "llvm/IR/Use.h"
+#include "llvm/IR/User.h"
+#include "llvm/IR/Value.h"
+#include "llvm/IR/Verifier.h"
+#include "llvm/InitializePasses.h"
+#include "llvm/Pass.h"
+#include "llvm/Support/Casting.h"
+#include "llvm/Support/CommandLine.h"
+#include "llvm/Support/Compiler.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/ErrorHandling.h"
+#include "llvm/Support/InterleavedRange.h"
+#include "llvm/Support/KnownBits.h"
+#include "llvm/Support/SaveAndRestore.h"
+#include "llvm/Support/raw_ostream.h"
+#include <algorithm>
+#include <cassert>
+#include <climits>
+#include <cstdint>
+#include <cstdlib>
+#include <map>
+#include <memory>
+#include <numeric>
+#include <optional>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+using namespace llvm;
+using namespace PatternMatch;
+using namespace SCEVPatternMatch;
+
+#define DEBUG_TYPE "scalar-evolution"
+
+STATISTIC(NumExitCountsComputed,
+ "Number of loop exits with predictable exit counts");
+STATISTIC(NumExitCountsNotComputed,
+ "Number of loop exits without predictable exit counts");
+STATISTIC(NumBruteForceTripCountsComputed,
+ "Number of loops with trip counts computed by force");
+
+#ifdef EXPENSIVE_CHECKS
+bool llvm::VerifySCEV = true;
+#else
+bool llvm::VerifySCEV = false;
+#endif
+
+static cl::opt<unsigned>
+ MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
+ cl::desc("Maximum number of iterations SCEV will "
+ "symbolically execute a constant "
+ "derived loop"),
+ cl::init(100));
+
+static cl::opt<bool, true> VerifySCEVOpt(
+ "verify-scev", cl::Hidden, cl::location(VerifySCEV),
+ cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
+static cl::opt<bool> VerifySCEVStrict(
+ "verify-scev-strict", cl::Hidden,
+ cl::desc("Enable stricter verification with -verify-scev is passed"));
+
+static cl::opt<bool> VerifyIR(
+ "scev-verify-ir", cl::Hidden,
+ cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
+ cl::init(false));
+
+static cl::opt<unsigned> MulOpsInlineThreshold(
+ "scev-mulops-inline-threshold", cl::Hidden,
+ cl::desc("Threshold for inlining multiplication operands into a SCEV"),
+ cl::init(32));
+
+static cl::opt<unsigned> AddOpsInlineThreshold(
+ "scev-addops-inline-threshold", cl::Hidden,
+ cl::desc("Threshold for inlining addition operands into a SCEV"),
+ cl::init(500));
+
+static cl::opt<unsigned> MaxSCEVCompareDepth(
+ "scalar-evolution-max-scev-compare-depth", cl::Hidden,
+ cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
+ cl::init(32));
+
+static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
+ "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
+ cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
+ cl::init(2));
+
+static cl::opt<unsigned> MaxValueCompareDepth(
+ "scalar-evolution-max-value-compare-depth", cl::Hidden,
+ cl::desc("Maximum depth of recursive value complexity comparisons"),
+ cl::init(2));
+
+static cl::opt<unsigned>
+ MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
+ cl::desc("Maximum depth of recursive arithmetics"),
+ cl::init(32));
+
+static cl::opt<unsigned> MaxConstantEvolvingDepth(
+ "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
+ cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
+
+static cl::opt<unsigned>
+ MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
+ cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
+ cl::init(8));
+
+static cl::opt<unsigned>
+ MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
+ cl::desc("Max coefficients in AddRec during evolving"),
+ cl::init(8));
+
+static cl::opt<unsigned>
+ HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
+ cl::desc("Size of the expression which is considered huge"),
+ cl::init(4096));
+
+static cl::opt<unsigned> RangeIterThreshold(
+ "scev-range-iter-threshold", cl::Hidden,
+ cl::desc("Threshold for switching to iteratively computing SCEV ranges"),
+ cl::init(32));
+
+static cl::opt<unsigned> MaxLoopGuardCollectionDepth(
+ "scalar-evolution-max-loop-guard-collection-depth", cl::Hidden,
+ cl::desc("Maximum depth for recursive loop guard collection"), cl::init(1));
+
+static cl::opt<bool>
+ClassifyExpressions("scalar-evolution-classify-expressions",
+ cl::Hidden, cl::init(true),
+ cl::desc("When printing analysis, include information on every instruction"));
+
+static cl::opt<bool> UseExpensiveRangeSharpening(
+ "scalar-evolution-use-expensive-range-sharpening", cl::Hidden,
+ cl::init(false),
+ cl::desc("Use more powerful methods of sharpening expression ranges. May "
+ "be costly in terms of compile time"));
+
+static cl::opt<unsigned> MaxPhiSCCAnalysisSize(
+ "scalar-evolution-max-scc-analysis-depth", cl::Hidden,
+ cl::desc("Maximum amount of nodes to process while searching SCEVUnknown "
+ "Phi strongly connected components"),
+ cl::init(8));
+
+static cl::opt<bool>
+ EnableFiniteLoopControl("scalar-evolution-finite-loop", cl::Hidden,
+ cl::desc("Handle <= and >= in finite loops"),
+ cl::init(true));
+
+static cl::opt<bool> UseContextForNoWrapFlagInference(
+ "scalar-evolution-use-context-for-no-wrap-flag-strenghening", cl::Hidden,
+ cl::desc("Infer nuw/nsw flags using context where suitable"),
+ cl::init(true));
+
+//===----------------------------------------------------------------------===//
+// SCEV class definitions
+//===----------------------------------------------------------------------===//
+
+void SCEV::computeAndSetCanonical(ScalarEvolution &SE) {
+ // Leaf nodes are always their own canonical.
+ switch (getSCEVType()) {
+ case scConstant:
+ case scVScale:
+ case scUnknown:
+ CanonicalSCEV = this;
+ return;
+ default:
+ break;
+ }
+
+ // For all other expressions, check whether any immediate operand has a
+ // different canonical. Since operands are always created before their parent,
+ // their canonical pointers are already set — no recursion needed.
+ bool Changed = false;
+ SmallVector<SCEVUse, 4> CanonOps;
+ for (SCEVUse Op : operands()) {
+ CanonOps.push_back(Op->getCanonical());
+ Changed |= CanonOps.back() != Op.getPointer();
+ }
+
+ if (!Changed) {
+ CanonicalSCEV = this;
+ return;
+ }
+
+ auto *NAry = dyn_cast<SCEVNAryExpr>(this);
+ SCEV::NoWrapFlags Flags = NAry ? NAry->getNoWrapFlags() : SCEV::FlagAnyWrap;
+ switch (getSCEVType()) {
+ case scPtrToAddr:
+ CanonicalSCEV = SE.getPtrToAddrExpr(CanonOps[0]);
+ return;
+ case scTruncate:
+ CanonicalSCEV = SE.getTruncateExpr(CanonOps[0], getType());
+ return;
+ case scZeroExtend:
+ CanonicalSCEV = SE.getZeroExtendExpr(CanonOps[0], getType());
+ return;
+ case scSignExtend:
+ CanonicalSCEV = SE.getSignExtendExpr(CanonOps[0], getType());
+ return;
+ case scUDivExpr:
+ CanonicalSCEV = SE.getUDivExpr(CanonOps[0], CanonOps[1]);
+ return;
+ case scAddExpr:
+ CanonicalSCEV = SE.getAddExpr(CanonOps, Flags);
+ return;
+ case scMulExpr:
+ CanonicalSCEV = SE.getMulExpr(CanonOps, Flags);
+ return;
+ case scAddRecExpr:
+ CanonicalSCEV = SE.getAddRecExpr(
+ CanonOps, cast<SCEVAddRecExpr>(this)->getLoop(), Flags);
+ return;
+ case scSMaxExpr:
+ CanonicalSCEV = SE.getSMaxExpr(CanonOps);
+ return;
+ case scUMaxExpr:
+ CanonicalSCEV = SE.getUMaxExpr(CanonOps);
+ return;
+ case scSMinExpr:
+ CanonicalSCEV = SE.getSMinExpr(CanonOps);
+ return;
+ case scUMinExpr:
+ CanonicalSCEV = SE.getUMinExpr(CanonOps);
+ return;
+ case scSequentialUMinExpr:
+ CanonicalSCEV = SE.getUMinExpr(CanonOps, /*Sequential=*/true);
+ return;
+ default:
+ llvm_unreachable("Unknown SCEV type");
+ }
+}
+
+//===----------------------------------------------------------------------===//
+// Implementation of the SCEV class.
+//
+
+#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
+LLVM_DUMP_METHOD void SCEV::dump() const {
+ print(dbgs());
+ dbgs() << '\n';
+}
+#endif
+
+void SCEV::print(raw_ostream &OS) const {
+ switch (getSCEVType()) {
+ case scConstant:
+ cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
+ return;
+ case scVScale:
+ OS << "vscale";
+ return;
+ case scPtrToAddr: {
+ const SCEVCastExpr *PtrCast = cast<SCEVCastExpr>(this);
+ const SCEV *Op = PtrCast->getOperand();
+ OS << "(ptrtoaddr " << *Op->getType() << " " << *Op << " to "
+ << *PtrCast->getType() << ")";
+ return;
+ }
+ case scTruncate: {
+ const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
+ const SCEV *Op = Trunc->getOperand();
+ OS << "(trunc " << *Op->getType() << " " << *Op << " to "
+ << *Trunc->getType() << ")";
+ return;
+ }
+ case scZeroExtend: {
+ const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
+ const SCEV *Op = ZExt->getOperand();
+ OS << "(zext " << *Op->getType() << " " << *Op << " to "
+ << *ZExt->getType() << ")";
+ return;
+ }
+ case scSignExtend: {
+ const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
+ const SCEV *Op = SExt->getOperand();
+ OS << "(sext " << *Op->getType() << " " << *Op << " to "
+ << *SExt->getType() << ")";
+ return;
+ }
+ case scAddRecExpr: {
+ const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
+ OS << "{" << *AR->getOperand(0);
+ for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
+ OS << ",+," << *AR->getOperand(i);
+ OS << "}<";
+ if (AR->hasNoUnsignedWrap())
+ OS << "nuw><";
+ if (AR->hasNoSignedWrap())
+ OS << "nsw><";
+ if (AR->hasNoSelfWrap() && !AR->hasNoUnsignedWrap() &&
+ !AR->hasNoSignedWrap())
+ OS << "nw><";
+ AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ">";
+ return;
+ }
+ case scAddExpr:
+ case scMulExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr: {
+ const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
+ const char *OpStr = nullptr;
+ switch (NAry->getSCEVType()) {
+ case scAddExpr: OpStr = " + "; break;
+ case scMulExpr: OpStr = " * "; break;
+ case scUMaxExpr: OpStr = " umax "; break;
+ case scSMaxExpr: OpStr = " smax "; break;
+ case scUMinExpr:
+ OpStr = " umin ";
+ break;
+ case scSMinExpr:
+ OpStr = " smin ";
+ break;
+ case scSequentialUMinExpr:
+ OpStr = " umin_seq ";
+ break;
+ default:
+ llvm_unreachable("There are no other nary expression types.");
+ }
+ OS << "("
+ << llvm::interleaved(llvm::make_pointee_range(NAry->operands()), OpStr)
+ << ")";
+ switch (NAry->getSCEVType()) {
+ case scAddExpr:
+ case scMulExpr:
+ if (NAry->hasNoUnsignedWrap())
+ OS << "<nuw>";
+ if (NAry->hasNoSignedWrap())
+ OS << "<nsw>";
+ break;
+ default:
+ // Nothing to print for other nary expressions.
+ break;
+ }
+ return;
+ }
+ case scUDivExpr: {
+ const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
+ OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
+ return;
+ }
+ case scUnknown:
+ cast<SCEVUnknown>(this)->getValue()->printAsOperand(OS, false);
+ return;
+ case scCouldNotCompute:
+ OS << "***COULDNOTCOMPUTE***";
+ return;
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+ArrayRef<SCEVUse> SCEV::operands() const {
+ switch (getSCEVType()) {
+ case scConstant:
+ case scVScale:
+ case scUnknown:
+ return {};
+ case scPtrToAddr:
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ return cast<SCEVCastExpr>(this)->operands();
+ case scAddRecExpr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr:
+ return cast<SCEVNAryExpr>(this)->operands();
+ case scUDivExpr:
+ return cast<SCEVUDivExpr>(this)->operands();
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+bool SCEV::isZero() const { return match(this, m_scev_Zero()); }
+
+bool SCEV::isOne() const { return match(this, m_scev_One()); }
+
+bool SCEV::isAllOnesValue() const { return match(this, m_scev_AllOnes()); }
+
+bool SCEV::isNonConstantNegative() const {
+ const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
+ if (!Mul) return false;
+
+ // If there is a constant factor, it will be first.
+ const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
+ if (!SC) return false;
+
+ // Return true if the value is negative, this matches things like (-42 * V).
+ return SC->getAPInt().isNegative();
+}
+
+SCEVCouldNotCompute::SCEVCouldNotCompute()
+ : SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0, nullptr) {}
+
+bool SCEVCouldNotCompute::classof(const SCEV *S) {
+ return S->getSCEVType() == scCouldNotCompute;
+}
+
+const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
+ auto &Entry = ConstantSCEVs[V];
+ if (Entry)
+ return Entry;
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scConstant);
+ ID.AddPointer(V);
+ void *IP = nullptr;
+ if (SCEVConstant *S =
+ static_cast<SCEVConstant *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)))
+ return Entry = S;
+ SCEVConstant *S =
+ new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ return Entry = S;
+}
+
+const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
+ return getConstant(ConstantInt::get(getContext(), Val));
+}
+
+const SCEV *
+ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
+ IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
+ // TODO: Avoid implicit trunc?
+ // See https://github.com/llvm/llvm-project/issues/112510.
+ return getConstant(
+ ConstantInt::get(ITy, V, isSigned, /*ImplicitTrunc=*/true));
+}
+
+const SCEV *ScalarEvolution::getVScale(Type *Ty) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(scVScale);
+ ID.AddPointer(Ty);
+ void *IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
+ return S;
+ SCEV *S = new (SCEVAllocator) SCEVVScale(ID.Intern(SCEVAllocator), Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getElementCount(Type *Ty, ElementCount EC,
+ SCEV::NoWrapFlags Flags) {
+ const SCEV *Res = getConstant(Ty, EC.getKnownMinValue());
+ if (EC.isScalable())
+ Res = getMulExpr(Res, getVScale(Ty), Flags);
+ return Res;
+}
+
+SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
+ SCEVUse op, Type *ty)
+ : SCEV(ID, SCEVTy, computeExpressionSize(op), ty), Op(op) {}
+
+SCEVPtrToAddrExpr::SCEVPtrToAddrExpr(const FoldingSetNodeIDRef ID,
+ const SCEV *Op, Type *ITy)
+ : SCEVCastExpr(ID, scPtrToAddr, Op, ITy) {
+ assert(getOperand()->getType()->isPointerTy() && getType()->isIntegerTy() &&
+ "Must be a non-bit-width-changing pointer-to-integer cast!");
+}
+
+SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID,
+ SCEVTypes SCEVTy, SCEVUse op,
+ Type *ty)
+ : SCEVCastExpr(ID, SCEVTy, op, ty) {}
+
+SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, SCEVUse op,
+ Type *ty)
+ : SCEVIntegralCastExpr(ID, scTruncate, op, ty) {
+ assert(getOperand()->getType()->isIntOrPtrTy() && getType()->isIntOrPtrTy() &&
+ "Cannot truncate non-integer value!");
+}
+
+SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, SCEVUse op,
+ Type *ty)
+ : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) {
+ assert(getOperand()->getType()->isIntOrPtrTy() && getType()->isIntOrPtrTy() &&
+ "Cannot zero extend non-integer value!");
+}
+
+SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, SCEVUse op,
+ Type *ty)
+ : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) {
+ assert(getOperand()->getType()->isIntOrPtrTy() && getType()->isIntOrPtrTy() &&
+ "Cannot sign extend non-integer value!");
+}
+
+void SCEVUnknown::deleted() {
+ // Clear this SCEVUnknown from various maps.
+ SE->forgetMemoizedResults({this});
+
+ // Remove this SCEVUnknown from the uniquing map.
+ SE->UniqueSCEVs.RemoveNode(this);
+
+ // Release the value.
+ setValPtr(nullptr);
+}
+
+void SCEVUnknown::allUsesReplacedWith(Value *New) {
+ // Clear this SCEVUnknown from various maps.
+ SE->forgetMemoizedResults({this});
+
+ // Remove this SCEVUnknown from the uniquing map.
+ SE->UniqueSCEVs.RemoveNode(this);
+
+ // Replace the value pointer in case someone is still using this SCEVUnknown.
+ setValPtr(New);
+}
+
+//===----------------------------------------------------------------------===//
+// SCEV Utilities
+//===----------------------------------------------------------------------===//
+
+/// Compare the two values \p LV and \p RV in terms of their "complexity" where
+/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
+/// operands in SCEV expressions.
+static int CompareValueComplexity(const LoopInfo *const LI, Value *LV,
+ Value *RV, unsigned Depth) {
+ if (Depth > MaxValueCompareDepth)
+ return 0;
+
+ // Order pointer values after integer values. This helps SCEVExpander form
+ // GEPs.
+ bool LIsPointer = LV->getType()->isPointerTy(),
+ RIsPointer = RV->getType()->isPointerTy();
+ if (LIsPointer != RIsPointer)
+ return (int)LIsPointer - (int)RIsPointer;
+
+ // Compare getValueID values.
+ unsigned LID = LV->getValueID(), RID = RV->getValueID();
+ if (LID != RID)
+ return (int)LID - (int)RID;
+
+ // Sort arguments by their position.
+ if (const auto *LA = dyn_cast<Argument>(LV)) {
+ const auto *RA = cast<Argument>(RV);
+ unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
+ return (int)LArgNo - (int)RArgNo;
+ }
+
+ if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
+ const auto *RGV = cast<GlobalValue>(RV);
+
+ if (auto L = LGV->getLinkage() - RGV->getLinkage())
+ return L;
+
+ const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
+ auto LT = GV->getLinkage();
+ return !(GlobalValue::isPrivateLinkage(LT) ||
+ GlobalValue::isInternalLinkage(LT));
+ };
+
+ // Use the names to distinguish the two values, but only if the
+ // names are semantically important.
+ if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
+ return LGV->getName().compare(RGV->getName());
+ }
+
+ // For instructions, compare their loop depth, and their operand count. This
+ // is pretty loose.
+ if (const auto *LInst = dyn_cast<Instruction>(LV)) {
+ const auto *RInst = cast<Instruction>(RV);
+
+ // Compare loop depths.
+ const BasicBlock *LParent = LInst->getParent(),
+ *RParent = RInst->getParent();
+ if (LParent != RParent) {
+ unsigned LDepth = LI->getLoopDepth(LParent),
+ RDepth = LI->getLoopDepth(RParent);
+ if (LDepth != RDepth)
+ return (int)LDepth - (int)RDepth;
+ }
+
+ // Compare the number of operands.
+ unsigned LNumOps = LInst->getNumOperands(),
+ RNumOps = RInst->getNumOperands();
+ if (LNumOps != RNumOps)
+ return (int)LNumOps - (int)RNumOps;
+
+ for (unsigned Idx : seq(LNumOps)) {
+ int Result = CompareValueComplexity(LI, LInst->getOperand(Idx),
+ RInst->getOperand(Idx), Depth + 1);
+ if (Result != 0)
+ return Result;
+ }
+ }
+
+ return 0;
+}
+
+// Return negative, zero, or positive, if LHS is less than, equal to, or greater
+// than RHS, respectively. A three-way result allows recursive comparisons to be
+// more efficient.
+// If the max analysis depth was reached, return std::nullopt, assuming we do
+// not know if they are equivalent for sure.
+static std::optional<int>
+CompareSCEVComplexity(const LoopInfo *const LI, const SCEV *LHS,
+ const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) {
+ // Fast-path: SCEVs are uniqued so we can do a quick equality check.
+ if (LHS == RHS)
+ return 0;
+
+ // Primarily, sort the SCEVs by their getSCEVType().
+ SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
+ if (LType != RType)
+ return (int)LType - (int)RType;
+
+ if (Depth > MaxSCEVCompareDepth)
+ return std::nullopt;
+
+ // Aside from the getSCEVType() ordering, the particular ordering
+ // isn't very important except that it's beneficial to be consistent,
+ // so that (a + b) and (b + a) don't end up as different expressions.
+ switch (LType) {
+ case scUnknown: {
+ const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
+ const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
+
+ int X =
+ CompareValueComplexity(LI, LU->getValue(), RU->getValue(), Depth + 1);
+ return X;
+ }
+
+ case scConstant: {
+ const SCEVConstant *LC = cast<SCEVConstant>(LHS);
+ const SCEVConstant *RC = cast<SCEVConstant>(RHS);
+
+ // Compare constant values.
+ const APInt &LA = LC->getAPInt();
+ const APInt &RA = RC->getAPInt();
+ unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
+ if (LBitWidth != RBitWidth)
+ return (int)LBitWidth - (int)RBitWidth;
+ return LA.ult(RA) ? -1 : 1;
+ }
+
+ case scVScale: {
+ const auto *LTy = cast<IntegerType>(cast<SCEVVScale>(LHS)->getType());
+ const auto *RTy = cast<IntegerType>(cast<SCEVVScale>(RHS)->getType());
+ return LTy->getBitWidth() - RTy->getBitWidth();
+ }
+
+ case scAddRecExpr: {
+ const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
+ const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
+
+ // There is always a dominance between two recs that are used by one SCEV,
+ // so we can safely sort recs by loop header dominance. We require such
+ // order in getAddExpr.
+ const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
+ if (LLoop != RLoop) {
+ const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
+ assert(LHead != RHead && "Two loops share the same header?");
+ if (DT.dominates(LHead, RHead))
+ return 1;
+ assert(DT.dominates(RHead, LHead) &&
+ "No dominance between recurrences used by one SCEV?");
+ return -1;
+ }
+
+ [[fallthrough]];
+ }
+
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUDivExpr:
+ case scSMaxExpr:
+ case scUMaxExpr:
+ case scSMinExpr:
+ case scUMinExpr:
+ case scSequentialUMinExpr: {
+ ArrayRef<SCEVUse> LOps = LHS->operands();
+ ArrayRef<SCEVUse> ROps = RHS->operands();
+
+ // Lexicographically compare n-ary-like expressions.
+ unsigned LNumOps = LOps.size(), RNumOps = ROps.size();
+ if (LNumOps != RNumOps)
+ return (int)LNumOps - (int)RNumOps;
+
+ for (unsigned i = 0; i != LNumOps; ++i) {
+ auto X = CompareSCEVComplexity(LI, LOps[i].getPointer(),
+ ROps[i].getPointer(), DT, Depth + 1);
+ if (X != 0)
+ return X;
+ }
+ return 0;
+ }
+
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+/// Given a list of SCEV objects, order them by their complexity, and group
+/// objects of the same complexity together by value. When this routine is
+/// finished, we know that any duplicates in the vector are consecutive and that
+/// complexity is monotonically increasing.
+///
+/// Note that we go take special precautions to ensure that we get deterministic
+/// results from this routine. In other words, we don't want the results of
+/// this to depend on where the addresses of various SCEV objects happened to
+/// land in memory.
+static void GroupByComplexity(SmallVectorImpl<SCEVUse> &Ops, LoopInfo *LI,
+ DominatorTree &DT) {
+ if (Ops.size() < 2) return; // Noop
+
+ // Whether LHS has provably less complexity than RHS.
+ auto IsLessComplex = [&](SCEVUse LHS, SCEVUse RHS) {
+ auto Complexity = CompareSCEVComplexity(LI, LHS, RHS, DT);
+ return Complexity && *Complexity < 0;
+ };
+ if (Ops.size() == 2) {
+ // This is the common case, which also happens to be trivially simple.
+ // Special case it.
+ SCEVUse &LHS = Ops[0], &RHS = Ops[1];
+ if (IsLessComplex(RHS, LHS))
+ std::swap(LHS, RHS);
+ return;
+ }
+
+ // Do the rough sort by complexity.
+ llvm::stable_sort(
+ Ops, [&](SCEVUse LHS, SCEVUse RHS) { return IsLessComplex(LHS, RHS); });
+
+ // Now that we are sorted by complexity, group elements of the same
+ // complexity. Note that this is, at worst, N^2, but the vector is likely to
+ // be extremely short in practice. Note that we take this approach because we
+ // do not want to depend on the addresses of the objects we are grouping.
+ for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
+ const SCEV *S = Ops[i];
+ unsigned Complexity = S->getSCEVType();
+
+ // If there are any objects of the same complexity and same value as this
+ // one, group them.
+ for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
+ if (Ops[j] == S) { // Found a duplicate.
+ // Move it to immediately after i'th element.
+ std::swap(Ops[i+1], Ops[j]);
+ ++i; // no need to rescan it.
+ if (i == e-2) return; // Done!
+ }
+ }
+ }
+}
+
+/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
+/// least HugeExprThreshold nodes).
+static bool hasHugeExpression(ArrayRef<SCEVUse> Ops) {
+ return any_of(Ops, [](const SCEV *S) {
+ return S->getExpressionSize() >= HugeExprThreshold;
+ });
+}
+
+/// Performs a number of common optimizations on the passed \p Ops. If the
+/// whole expression reduces down to a single operand, it will be returned.
+///
+/// The following optimizations are performed:
+/// * Fold constants using the \p Fold function.
+/// * Remove identity constants satisfying \p IsIdentity.
+/// * If a constant satisfies \p IsAbsorber, return it.
+/// * Sort operands by complexity.
+template <typename FoldT, typename IsIdentityT, typename IsAbsorberT>
+static const SCEV *
+constantFoldAndGroupOps(ScalarEvolution &SE, LoopInfo &LI, DominatorTree &DT,
+ SmallVectorImpl<SCEVUse> &Ops, FoldT Fold,
+ IsIdentityT IsIdentity, IsAbsorberT IsAbsorber) {
+ const SCEVConstant *Folded = nullptr;
+ for (unsigned Idx = 0; Idx < Ops.size();) {
+ const SCEV *Op = Ops[Idx];
+ if (const auto *C = dyn_cast<SCEVConstant>(Op)) {
+ if (!Folded)
+ Folded = C;
+ else
+ Folded = cast<SCEVConstant>(
+ SE.getConstant(Fold(Folded->getAPInt(), C->getAPInt())));
+ Ops.erase(Ops.begin() + Idx);
+ continue;
+ }
+ ++Idx;
+ }
+
+ if (Ops.empty()) {
+ assert(Folded && "Must have folded value");
+ return Folded;
+ }
+
+ if (Folded && IsAbsorber(Folded->getAPInt()))
+ return Folded;
+
+ GroupByComplexity(Ops, &LI, DT);
+ if (Folded && !IsIdentity(Folded->getAPInt()))
+ Ops.insert(Ops.begin(), Folded);
+
+ return Ops.size() == 1 ? Ops[0] : nullptr;
+}
+
+//===----------------------------------------------------------------------===//
+// Simple SCEV method implementations
+//===----------------------------------------------------------------------===//
+
+/// Compute BC(It, K). The result has width W. Assume, K > 0.
+static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
+ ScalarEvolution &SE,
+ Type *ResultTy) {
+ // Handle the simplest case efficiently.
+ if (K == 1)
+ return SE.getTruncateOrZeroExtend(It, ResultTy);
+
+ // We are using the following formula for BC(It, K):
+ //
+ // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
+ //
+ // Suppose, W is the bitwidth of the return value. We must be prepared for
+ // overflow. Hence, we must assure that the result of our computation is
+ // equal to the accurate one modulo 2^W. Unfortunately, division isn't
+ // safe in modular arithmetic.
+ //
+ // However, this code doesn't use exactly that formula; the formula it uses
+ // is something like the following, where T is the number of factors of 2 in
+ // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
+ // exponentiation:
+ //
+ // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
+ //
+ // This formula is trivially equivalent to the previous formula. However,
+ // this formula can be implemented much more efficiently. The trick is that
+ // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
+ // arithmetic. To do exact division in modular arithmetic, all we have
+ // to do is multiply by the inverse. Therefore, this step can be done at
+ // width W.
+ //
+ // The next issue is how to safely do the division by 2^T. The way this
+ // is done is by doing the multiplication step at a width of at least W + T
+ // bits. This way, the bottom W+T bits of the product are accurate. Then,
+ // when we perform the division by 2^T (which is equivalent to a right shift
+ // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
+ // truncated out after the division by 2^T.
+ //
+ // In comparison to just directly using the first formula, this technique
+ // is much more efficient; using the first formula requires W * K bits,
+ // but this formula less than W + K bits. Also, the first formula requires
+ // a division step, whereas this formula only requires multiplies and shifts.
+ //
+ // It doesn't matter whether the subtraction step is done in the calculation
+ // width or the input iteration count's width; if the subtraction overflows,
+ // the result must be zero anyway. We prefer here to do it in the width of
+ // the induction variable because it helps a lot for certain cases; CodeGen
+ // isn't smart enough to ignore the overflow, which leads to much less
+ // efficient code if the width of the subtraction is wider than the native
+ // register width.
+ //
+ // (It's possible to not widen at all by pulling out factors of 2 before
+ // the multiplication; for example, K=2 can be calculated as
+ // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
+ // extra arithmetic, so it's not an obvious win, and it gets
+ // much more complicated for K > 3.)
+
+ // Protection from insane SCEVs; this bound is conservative,
+ // but it probably doesn't matter.
+ if (K > 1000)
+ return SE.getCouldNotCompute();
+
+ unsigned W = SE.getTypeSizeInBits(ResultTy);
+
+ // Calculate K! / 2^T and T; we divide out the factors of two before
+ // multiplying for calculating K! / 2^T to avoid overflow.
+ // Other overflow doesn't matter because we only care about the bottom
+ // W bits of the result.
+ APInt OddFactorial(W, 1);
+ unsigned T = 1;
+ for (unsigned i = 3; i <= K; ++i) {
+ unsigned TwoFactors = countr_zero(i);
+ T += TwoFactors;
+ OddFactorial *= (i >> TwoFactors);
+ }
+
+ // We need at least W + T bits for the multiplication step
+ unsigned CalculationBits = W + T;
+
+ // Calculate 2^T, at width T+W.
+ APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
+
+ // Calculate the multiplicative inverse of K! / 2^T;
+ // this multiplication factor will perform the exact division by
+ // K! / 2^T.
+ APInt MultiplyFactor = OddFactorial.multiplicativeInverse();
+
+ // Calculate the product, at width T+W
+ IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
+ CalculationBits);
+ const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
+ for (unsigned i = 1; i != K; ++i) {
+ const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
+ Dividend = SE.getMulExpr(Dividend,
+ SE.getTruncateOrZeroExtend(S, CalculationTy));
+ }
+
+ // Divide by 2^T
+ const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
+
+ // Truncate the result, and divide by K! / 2^T.
+
+ return SE.getMulExpr(SE.getConstant(MultiplyFactor),
+ SE.getTruncateOrZeroExtend(DivResult, ResultTy));
+}
+
+/// Return the value of this chain of recurrences at the specified iteration
+/// number. We can evaluate this recurrence by multiplying each element in the
+/// chain by the binomial coefficient corresponding to it. In other words, we
+/// can evaluate {A,+,B,+,C,+,D} as:
+///
+/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
+///
+/// where BC(It, k) stands for binomial coefficient.
+const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
+ ScalarEvolution &SE) const {
+ return evaluateAtIteration(operands(), It, SE);
+}
+
+const SCEV *SCEVAddRecExpr::evaluateAtIteration(ArrayRef<SCEVUse> Operands,
+ const SCEV *It,
+ ScalarEvolution &SE) {
+ assert(Operands.size() > 0);
+ const SCEV *Result = Operands[0].getPointer();
+ for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
+ // The computation is correct in the face of overflow provided that the
+ // multiplication is performed _after_ the evaluation of the binomial
+ // coefficient.
+ const SCEV *Coeff = BinomialCoefficient(It, i, SE, Result->getType());
+ if (isa<SCEVCouldNotCompute>(Coeff))
+ return Coeff;
+
+ Result =
+ SE.getAddExpr(Result, SE.getMulExpr(Operands[i].getPointer(), Coeff));
+ }
+ return Result;
+}
+
+//===----------------------------------------------------------------------===//
+// SCEV Expression folder implementations
+//===----------------------------------------------------------------------===//
+
+/// The SCEVCastSinkingRewriter takes a scalar evolution expression,
+/// which computes a pointer-typed value, and rewrites the whole expression
+/// tree so that *all* the computations are done on integers, and the only
+/// pointer-typed operands in the expression are SCEVUnknown.
+/// The CreatePtrCast callback is invoked to create the actual conversion
+/// (ptrtoint or ptrtoaddr) at the SCEVUnknown leaves.
+class SCEVCastSinkingRewriter
+ : public SCEVRewriteVisitor<SCEVCastSinkingRewriter> {
+ using Base = SCEVRewriteVisitor<SCEVCastSinkingRewriter>;
+ using ConversionFn = function_ref<const SCEV *(const SCEVUnknown *)>;
+ Type *TargetTy;
+ ConversionFn CreatePtrCast;
+
+public:
+ SCEVCastSinkingRewriter(ScalarEvolution &SE, Type *TargetTy,
+ ConversionFn CreatePtrCast)
+ : Base(SE), TargetTy(TargetTy), CreatePtrCast(std::move(CreatePtrCast)) {}
+
+ static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
+ Type *TargetTy, ConversionFn CreatePtrCast) {
+ SCEVCastSinkingRewriter Rewriter(SE, TargetTy, std::move(CreatePtrCast));
+ return Rewriter.visit(Scev);
+ }
+
+ const SCEV *visit(const SCEV *S) {
+ Type *STy = S->getType();
+ // If the expression is not pointer-typed, just keep it as-is.
+ if (!STy->isPointerTy())
+ return S;
+ // Else, recursively sink the cast down into it.
+ return Base::visit(S);
+ }
+
+ const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
+ // Preserve wrap flags on rewritten SCEVAddExpr, which the default
+ // implementation drops.
+ SmallVector<SCEVUse, 2> Operands;
+ bool Changed = false;
+ for (SCEVUse Op : Expr->operands()) {
+ Operands.push_back(visit(Op.getPointer()));
+ Changed |= Op.getPointer() != Operands.back();
+ }
+ return !Changed ? Expr : SE.getAddExpr(Operands, Expr->getNoWrapFlags());
+ }
+
+ const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
+ SmallVector<SCEVUse, 2> Operands;
+ bool Changed = false;
+ for (SCEVUse Op : Expr->operands()) {
+ Operands.push_back(visit(Op.getPointer()));
+ Changed |= Op.getPointer() != Operands.back();
+ }
+ return !Changed ? Expr : SE.getMulExpr(Operands, Expr->getNoWrapFlags());
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ assert(Expr->getType()->isPointerTy() &&
+ "Should only reach pointer-typed SCEVUnknown's.");
+ // Perform some basic constant folding. If the operand of the cast is a
+ // null pointer, don't create a cast SCEV expression (that will be left
+ // as-is), but produce a zero constant.
+ if (isa<ConstantPointerNull>(Expr->getValue()))
+ return SE.getZero(TargetTy);
+ return CreatePtrCast(Expr);
+ }
+};
+
+const SCEV *ScalarEvolution::getPtrToAddrExpr(const SCEV *Op) {
+ assert(Op->getType()->isPointerTy() && "Op must be a pointer");
+
+ // Treat pointers with unstable representation conservatively, since the
+ // address bits may change.
+ if (DL.hasUnstableRepresentation(Op->getType()))
+ return getCouldNotCompute();
+
+ Type *Ty = DL.getAddressType(Op->getType());
+
+ // Use the rewriter to sink the cast down to SCEVUnknown leaves.
+ // The rewriter handles null pointer constant folding.
+ const SCEV *IntOp = SCEVCastSinkingRewriter::rewrite(
+ Op, *this, Ty, [this, Ty](const SCEVUnknown *U) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(scPtrToAddr);
+ ID.AddPointer(U);
+ ID.AddPointer(Ty);
+ void *IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
+ return S;
+ SCEV *S = new (SCEVAllocator)
+ SCEVPtrToAddrExpr(ID.Intern(SCEVAllocator), U, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, U);
+ return static_cast<const SCEV *>(S);
+ });
+ assert(IntOp->getType()->isIntegerTy() &&
+ "We must have succeeded in sinking the cast, "
+ "and ending up with an integer-typed expression!");
+ return IntOp;
+}
+
+const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
+ unsigned Depth) {
+ assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
+ "This is not a truncating conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ assert(!Op->getType()->isPointerTy() && "Can't truncate pointer!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scTruncate);
+ ID.AddPointer(Op);
+ ID.AddPointer(Ty);
+ void *IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+
+ // Fold if the operand is constant.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return getConstant(
+ cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
+
+ // trunc(trunc(x)) --> trunc(x)
+ if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
+ return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
+
+ // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
+ if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
+ return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
+
+ // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
+ if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
+ return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
+
+ if (Depth > MaxCastDepth) {
+ SCEV *S =
+ new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Op);
+ return S;
+ }
+
+ // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
+ // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
+ // if after transforming we have at most one truncate, not counting truncates
+ // that replace other casts.
+ if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
+ auto *CommOp = cast<SCEVCommutativeExpr>(Op);
+ SmallVector<SCEVUse, 4> Operands;
+ unsigned numTruncs = 0;
+ for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
+ ++i) {
+ const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
+ if (!isa<SCEVIntegralCastExpr>(CommOp->getOperand(i)) &&
+ isa<SCEVTruncateExpr>(S))
+ numTruncs++;
+ Operands.push_back(S);
+ }
+ if (numTruncs < 2) {
+ if (isa<SCEVAddExpr>(Op))
+ return getAddExpr(Operands);
+ if (isa<SCEVMulExpr>(Op))
+ return getMulExpr(Operands);
+ llvm_unreachable("Unexpected SCEV type for Op.");
+ }
+ // Although we checked in the beginning that ID is not in the cache, it is
+ // possible that during recursion and different modification ID was inserted
+ // into the cache. So if we find it, just return it.
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
+ return S;
+ }
+
+ // If the input value is a chrec scev, truncate the chrec's operands.
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
+ SmallVector<SCEVUse, 4> Operands;
+ for (const SCEV *Op : AddRec->operands())
+ Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
+ return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
+ }
+
+ // Return zero if truncating to known zeros.
+ uint32_t MinTrailingZeros = getMinTrailingZeros(Op);
+ if (MinTrailingZeros >= getTypeSizeInBits(Ty))
+ return getZero(Ty);
+
+ // The cast wasn't folded; create an explicit cast node. We can reuse
+ // the existing insert position since if we get here, we won't have
+ // made any changes which would invalidate it.
+ SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
+ Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Op);
+ return S;
+}
+
+// Get the limit of a recurrence such that incrementing by Step cannot cause
+// signed overflow as long as the value of the recurrence within the
+// loop does not exceed this limit before incrementing.
+static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
+ ICmpInst::Predicate *Pred,
+ ScalarEvolution *SE) {
+ unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
+ if (SE->isKnownPositive(Step)) {
+ *Pred = ICmpInst::ICMP_SLT;
+ return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
+ SE->getSignedRangeMax(Step));
+ }
+ if (SE->isKnownNegative(Step)) {
+ *Pred = ICmpInst::ICMP_SGT;
+ return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
+ SE->getSignedRangeMin(Step));
+ }
+ return nullptr;
+}
+
+// Get the limit of a recurrence such that incrementing by Step cannot cause
+// unsigned overflow as long as the value of the recurrence within the loop does
+// not exceed this limit before incrementing.
+static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
+ ICmpInst::Predicate *Pred,
+ ScalarEvolution *SE) {
+ unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
+ *Pred = ICmpInst::ICMP_ULT;
+
+ return SE->getConstant(APInt::getMinValue(BitWidth) -
+ SE->getUnsignedRangeMax(Step));
+}
+
+namespace {
+
+struct ExtendOpTraitsBase {
+ typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
+ unsigned);
+};
+
+// Used to make code generic over signed and unsigned overflow.
+template <typename ExtendOp> struct ExtendOpTraits {
+ // Members present:
+ //
+ // static const SCEV::NoWrapFlags WrapType;
+ //
+ // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
+ //
+ // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
+ // ICmpInst::Predicate *Pred,
+ // ScalarEvolution *SE);
+};
+
+template <>
+struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
+ static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
+
+ static const GetExtendExprTy GetExtendExpr;
+
+ static const SCEV *getOverflowLimitForStep(const SCEV *Step,
+ ICmpInst::Predicate *Pred,
+ ScalarEvolution *SE) {
+ return getSignedOverflowLimitForStep(Step, Pred, SE);
+ }
+};
+
+const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
+ SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
+
+template <>
+struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
+ static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
+
+ static const GetExtendExprTy GetExtendExpr;
+
+ static const SCEV *getOverflowLimitForStep(const SCEV *Step,
+ ICmpInst::Predicate *Pred,
+ ScalarEvolution *SE) {
+ return getUnsignedOverflowLimitForStep(Step, Pred, SE);
+ }
+};
+
+const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
+ SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
+
+} // end anonymous namespace
+
+// The recurrence AR has been shown to have no signed/unsigned wrap or something
+// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
+// easily prove NSW/NUW for its preincrement or postincrement sibling. This
+// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
+// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
+// expression "Step + sext/zext(PreIncAR)" is congruent with
+// "sext/zext(PostIncAR)"
+template <typename ExtendOpTy>
+static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
+ ScalarEvolution *SE, unsigned Depth) {
+ auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
+ auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
+
+ const Loop *L = AR->getLoop();
+ const SCEV *Start = AR->getStart();
+ const SCEV *Step = AR->getStepRecurrence(*SE);
+
+ // Check for a simple looking step prior to loop entry.
+ const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
+ if (!SA)
+ return nullptr;
+
+ // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
+ // subtraction is expensive. For this purpose, perform a quick and dirty
+ // difference, by checking for Step in the operand list. Note, that
+ // SA might have repeated ops, like %a + %a + ..., so only remove one.
+ SmallVector<SCEVUse, 4> DiffOps(SA->operands());
+ for (auto It = DiffOps.begin(); It != DiffOps.end(); ++It)
+ if (*It == Step) {
+ DiffOps.erase(It);
+ break;
+ }
+
+ if (DiffOps.size() == SA->getNumOperands())
+ return nullptr;
+
+ // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
+ // `Step`:
+
+ // 1. NSW/NUW flags on the step increment.
+ auto PreStartFlags =
+ ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
+ const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
+ const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
+ SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
+
+ // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
+ // "S+X does not sign/unsign-overflow".
+ //
+
+ const SCEV *BECount = SE->getBackedgeTakenCount(L);
+ if (PreAR && any(PreAR->getNoWrapFlags(WrapType)) &&
+ !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
+ return PreStart;
+
+ // 2. Direct overflow check on the step operation's expression.
+ unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
+ Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
+ const SCEV *OperandExtendedStart =
+ SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
+ (SE->*GetExtendExpr)(Step, WideTy, Depth));
+ if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
+ if (PreAR && any(AR->getNoWrapFlags(WrapType))) {
+ // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
+ // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
+ // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
+ SE->setNoWrapFlags(const_cast<SCEVAddRecExpr *>(PreAR), WrapType);
+ }
+ return PreStart;
+ }
+
+ // 3. Loop precondition.
+ ICmpInst::Predicate Pred;
+ const SCEV *OverflowLimit =
+ ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
+
+ if (OverflowLimit &&
+ SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
+ return PreStart;
+
+ return nullptr;
+}
+
+// Get the normalized zero or sign extended expression for this AddRec's Start.
+template <typename ExtendOpTy>
+static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
+ ScalarEvolution *SE,
+ unsigned Depth) {
+ auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
+
+ const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
+ if (!PreStart)
+ return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
+
+ return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
+ Depth),
+ (SE->*GetExtendExpr)(PreStart, Ty, Depth));
+}
+
+// Try to prove away overflow by looking at "nearby" add recurrences. A
+// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
+// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
+//
+// Formally:
+//
+// {S,+,X} == {S-T,+,X} + T
+// => Ext({S,+,X}) == Ext({S-T,+,X} + T)
+//
+// If ({S-T,+,X} + T) does not overflow ... (1)
+//
+// RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
+//
+// If {S-T,+,X} does not overflow ... (2)
+//
+// RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
+// == {Ext(S-T)+Ext(T),+,Ext(X)}
+//
+// If (S-T)+T does not overflow ... (3)
+//
+// RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
+// == {Ext(S),+,Ext(X)} == LHS
+//
+// Thus, if (1), (2) and (3) are true for some T, then
+// Ext({S,+,X}) == {Ext(S),+,Ext(X)}
+//
+// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
+// does not overflow" restricted to the 0th iteration. Therefore we only need
+// to check for (1) and (2).
+//
+// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
+// is `Delta` (defined below).
+template <typename ExtendOpTy>
+bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
+ const SCEV *Step,
+ const Loop *L) {
+ auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
+
+ // We restrict `Start` to a constant to prevent SCEV from spending too much
+ // time here. It is correct (but more expensive) to continue with a
+ // non-constant `Start` and do a general SCEV subtraction to compute
+ // `PreStart` below.
+ const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
+ if (!StartC)
+ return false;
+
+ APInt StartAI = StartC->getAPInt();
+
+ for (unsigned Delta : {-2, -1, 1, 2}) {
+ const SCEV *PreStart = getConstant(StartAI - Delta);
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scAddRecExpr);
+ ID.AddPointer(PreStart);
+ ID.AddPointer(Step);
+ ID.AddPointer(L);
+ void *IP = nullptr;
+ const auto *PreAR =
+ static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+
+ // Give up if we don't already have the add recurrence we need because
+ // actually constructing an add recurrence is relatively expensive.
+ if (PreAR && any(PreAR->getNoWrapFlags(WrapType))) { // proves (2)
+ const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
+ ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
+ const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
+ DeltaS, &Pred, this);
+ if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
+ return true;
+ }
+ }
+
+ return false;
+}
+
+// Finds an integer D for an expression (C + x + y + ...) such that the top
+// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
+// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
+// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
+// the (C + x + y + ...) expression is \p WholeAddExpr.
+static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
+ const SCEVConstant *ConstantTerm,
+ const SCEVAddExpr *WholeAddExpr) {
+ const APInt &C = ConstantTerm->getAPInt();
+ const unsigned BitWidth = C.getBitWidth();
+ // Find number of trailing zeros of (x + y + ...) w/o the C first:
+ uint32_t TZ = BitWidth;
+ for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
+ TZ = std::min(TZ, SE.getMinTrailingZeros(WholeAddExpr->getOperand(I)));
+ if (TZ) {
+ // Set D to be as many least significant bits of C as possible while still
+ // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
+ return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
+ }
+ return APInt(BitWidth, 0);
+}
+
+// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
+// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
+// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
+// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
+static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
+ const APInt &ConstantStart,
+ const SCEV *Step) {
+ const unsigned BitWidth = ConstantStart.getBitWidth();
+ const uint32_t TZ = SE.getMinTrailingZeros(Step);
+ if (TZ)
+ return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
+ : ConstantStart;
+ return APInt(BitWidth, 0);
+}
+
+static void insertFoldCacheEntry(
+ const ScalarEvolution::FoldID &ID, const SCEV *S,
+ DenseMap<ScalarEvolution::FoldID, const SCEV *> &FoldCache,
+ DenseMap<const SCEV *, SmallVector<ScalarEvolution::FoldID, 2>>
+ &FoldCacheUser) {
+ auto I = FoldCache.insert({ID, S});
+ if (!I.second) {
+ // Remove FoldCacheUser entry for ID when replacing an existing FoldCache
+ // entry.
+ auto &UserIDs = FoldCacheUser[I.first->second];
+ assert(count(UserIDs, ID) == 1 && "unexpected duplicates in UserIDs");
+ for (unsigned I = 0; I != UserIDs.size(); ++I)
+ if (UserIDs[I] == ID) {
+ std::swap(UserIDs[I], UserIDs.back());
+ break;
+ }
+ UserIDs.pop_back();
+ I.first->second = S;
+ }
+ FoldCacheUser[S].push_back(ID);
+}
+
+const SCEV *
+ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ FoldID ID(scZeroExtend, Op, Ty);
+ if (const SCEV *S = FoldCache.lookup(ID))
+ return S;
+
+ const SCEV *S = getZeroExtendExprImpl(Op, Ty, Depth);
+ if (!isa<SCEVZeroExtendExpr>(S))
+ insertFoldCacheEntry(ID, S, FoldCache, FoldCacheUser);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getZeroExtendExprImpl(const SCEV *Op, Type *Ty,
+ unsigned Depth) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!");
+ assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
+
+ // Fold if the operand is constant.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return getConstant(SC->getAPInt().zext(getTypeSizeInBits(Ty)));
+
+ // zext(zext(x)) --> zext(x)
+ if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
+ return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
+
+ // If the operand is an affine AddRec with the no-unsigned-wrap flag, the
+ // zero-extension distributes over the recurrence.
+ const SCEV *Start, *Step;
+ const Loop *L;
+ if (Depth <= MaxCastDepth &&
+ match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
+ const auto *AR = cast<SCEVAddRecExpr>(Op);
+ if (AR->hasNoUnsignedWrap()) {
+ Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getZeroExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ }
+
+ // Before doing any expensive analysis, check to see if we've already
+ // computed a SCEV for this Op and Ty.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scZeroExtend);
+ ID.AddPointer(Op);
+ ID.AddPointer(Ty);
+ void *IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ if (Depth > MaxCastDepth) {
+ SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
+ Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Op);
+ return S;
+ }
+
+ // zext(trunc(x)) --> zext(x) or x or trunc(x)
+ if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
+ // It's possible the bits taken off by the truncate were all zero bits. If
+ // so, we should be able to simplify this further.
+ const SCEV *X = ST->getOperand();
+ ConstantRange CR = getUnsignedRange(X);
+ unsigned TruncBits = getTypeSizeInBits(ST->getType());
+ unsigned NewBits = getTypeSizeInBits(Ty);
+ if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
+ CR.zextOrTrunc(NewBits)))
+ return getTruncateOrZeroExtend(X, Ty, Depth);
+ }
+
+ // If the input value is a chrec scev, and we can prove that the value
+ // did not overflow the old, smaller, value, we can zero extend all of the
+ // operands (often constants). This allows analysis of something like
+ // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
+ if (match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
+ const auto *AR = cast<SCEVAddRecExpr>(Op);
+ unsigned BitWidth = getTypeSizeInBits(AR->getType());
+
+ // The no-unsigned-wrap case is handled before the uniquing lookup above.
+
+ // Check whether the backedge-taken count is SCEVCouldNotCompute.
+ // Note that this serves two purposes: It filters out loops that are
+ // simply not analyzable, and it covers the case where this code is
+ // being called from within backedge-taken count analysis, such that
+ // attempting to ask for the backedge-taken count would likely result
+ // in infinite recursion. In the later case, the analysis code will
+ // cope with a conservative value, and it will take care to purge
+ // that value once it has finished.
+ const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
+ // Manually compute the final value for AR, checking for overflow.
+
+ // Check whether the backedge-taken count can be losslessly casted to
+ // the addrec's type. The count is always unsigned.
+ const SCEV *CastedMaxBECount =
+ getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
+ const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
+ CastedMaxBECount, MaxBECount->getType(), Depth);
+ if (MaxBECount == RecastedMaxBECount) {
+ Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
+ // Check whether Start+Step*MaxBECount has no unsigned overflow.
+ const SCEV *ZMul =
+ getMulExpr(CastedMaxBECount, Step, SCEV::FlagAnyWrap, Depth + 1);
+ const SCEV *ZAdd = getZeroExtendExpr(
+ getAddExpr(Start, ZMul, SCEV::FlagAnyWrap, Depth + 1), WideTy,
+ Depth + 1);
+ const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
+ const SCEV *WideMaxBECount =
+ getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
+ const SCEV *OperandExtendedAdd =
+ getAddExpr(WideStart,
+ getMulExpr(WideMaxBECount,
+ getZeroExtendExpr(Step, WideTy, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1);
+ if (ZAdd == OperandExtendedAdd) {
+ // Cache knowledge of AR NUW, which is propagated to this AddRec.
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
+ // Return the expression with the addrec on the outside.
+ Start =
+ getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getZeroExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ // Similar to above, only this time treat the step value as signed.
+ // This covers loops that count down.
+ OperandExtendedAdd =
+ getAddExpr(WideStart,
+ getMulExpr(WideMaxBECount,
+ getSignExtendExpr(Step, WideTy, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1);
+ if (ZAdd == OperandExtendedAdd) {
+ // Cache knowledge of AR NW, which is propagated to this AddRec.
+ // Negative step causes unsigned wrap, but it still can't self-wrap.
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
+ // Return the expression with the addrec on the outside.
+ Start =
+ getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getSignExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ }
+ }
+
+ // Normally, in the cases we can prove no-overflow via a
+ // backedge guarding condition, we can also compute a backedge
+ // taken count for the loop. The exceptions are assumptions and
+ // guards present in the loop -- SCEV is not great at exploiting
+ // these to compute max backedge taken counts, but can still use
+ // these to prove lack of overflow. Use this fact to avoid
+ // doing extra work that may not pay off.
+ if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
+ !AC.assumptions().empty()) {
+
+ auto NewFlags = proveNoUnsignedWrapViaInduction(AR);
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
+ if (AR->hasNoUnsignedWrap()) {
+ // Same as nuw case above - duplicated here to avoid a compile time
+ // issue. It's not clear that the order of checks does matter, but
+ // it's one of two issue possible causes for a change which was
+ // reverted. Be conservative for the moment.
+ Start =
+ getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getZeroExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+
+ // For a negative step, we can extend the operands iff doing so only
+ // traverses values in the range zext([0,UINT_MAX]).
+ if (isKnownNegative(Step)) {
+ const SCEV *N =
+ getConstant(APInt::getMaxValue(BitWidth) - getSignedRangeMin(Step));
+ if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
+ isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
+ // Cache knowledge of AR NW, which is propagated to this
+ // AddRec. Negative step causes unsigned wrap, but it
+ // still can't self-wrap.
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
+ // Return the expression with the addrec on the outside.
+ Start =
+ getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getSignExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ }
+ }
+
+ // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
+ // if D + (C - D + Step * n) could be proven to not unsigned wrap
+ // where D maximizes the number of trailing zeros of (C - D + Step * n)
+ if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
+ const APInt &C = SC->getAPInt();
+ const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
+ if (D != 0) {
+ const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
+ const SCEV *SResidual =
+ getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
+ const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
+ return getAddExpr(SZExtD, SZExtR, SCEV::FlagNSW | SCEV::FlagNUW,
+ Depth + 1);
+ }
+ }
+
+ if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
+ Start = getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getZeroExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ }
+
+ // zext(A % B) --> zext(A) % zext(B)
+ {
+ const SCEV *LHS;
+ const SCEV *RHS;
+ if (match(Op, m_scev_URem(m_SCEV(LHS), m_SCEV(RHS), *this)))
+ return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
+ getZeroExtendExpr(RHS, Ty, Depth + 1));
+ }
+
+ // zext(A / B) --> zext(A) / zext(B).
+ if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
+ return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
+ getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
+
+ if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
+ // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
+ if (SA->hasNoUnsignedWrap()) {
+ // If the addition does not unsign overflow then we can, by definition,
+ // commute the zero extension with the addition operation.
+ SmallVector<SCEVUse, 4> Ops;
+ for (SCEVUse Op : SA->operands())
+ Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
+ return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
+ }
+
+ const APInt *C, *C2;
+ // zext (C + A)<nsw> -> (sext(C) + sext(A))<nsw> if zext (C + A)<nsw> >=s 0.
+ // Currently the non-negative check is done manually, as isKnownNonNegative
+ // is too expensive.
+ if (SA->hasNoSignedWrap() &&
+ match(SA, m_scev_Add(m_scev_APInt(C),
+ m_scev_SMax(m_scev_APInt(C2), m_SCEV()))) &&
+ C->isNegative() && !C->isMinSignedValue() && C2->sge(C->abs())) {
+ assert(isKnownNonNegative(SA) && "incorrectly determined non-negative");
+ return getAddExpr(getSignExtendExpr(SA->getOperand(0), Ty, Depth + 1),
+ getSignExtendExpr(SA->getOperand(1), Ty, Depth + 1),
+ SCEV::FlagNSW, Depth + 1);
+ }
+
+ // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
+ // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
+ // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
+ //
+ // Often address arithmetics contain expressions like
+ // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
+ // This transformation is useful while proving that such expressions are
+ // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
+ if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
+ const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
+ if (D != 0) {
+ const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
+ const SCEV *SResidual =
+ getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
+ const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
+ return getAddExpr(SZExtD, SZExtR, (SCEV::FlagNSW | SCEV::FlagNUW),
+ Depth + 1);
+ }
+ }
+ }
+
+ if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
+ // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
+ if (SM->hasNoUnsignedWrap()) {
+ // If the multiply does not unsign overflow then we can, by definition,
+ // commute the zero extension with the multiply operation.
+ SmallVector<SCEVUse, 4> Ops;
+ for (SCEVUse Op : SM->operands())
+ Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
+ return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
+ }
+
+ // zext(2^K * (trunc X to iN)) to iM ->
+ // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
+ //
+ // Proof:
+ //
+ // zext(2^K * (trunc X to iN)) to iM
+ // = zext((trunc X to iN) << K) to iM
+ // = zext((trunc X to i{N-K}) << K)<nuw> to iM
+ // (because shl removes the top K bits)
+ // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
+ // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
+ //
+ const APInt *C;
+ const SCEV *TruncRHS;
+ if (match(SM,
+ m_scev_Mul(m_scev_APInt(C), m_scev_Trunc(m_SCEV(TruncRHS)))) &&
+ C->isPowerOf2()) {
+ int NewTruncBits =
+ getTypeSizeInBits(SM->getOperand(1)->getType()) - C->logBase2();
+ Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
+ return getMulExpr(
+ getZeroExtendExpr(SM->getOperand(0), Ty),
+ getZeroExtendExpr(getTruncateExpr(TruncRHS, NewTruncTy), Ty),
+ SCEV::FlagNUW, Depth + 1);
+ }
+ }
+
+ // zext(umin(x, y)) -> umin(zext(x), zext(y))
+ // zext(umax(x, y)) -> umax(zext(x), zext(y))
+ if (isa<SCEVUMinExpr>(Op) || isa<SCEVUMaxExpr>(Op)) {
+ auto *MinMax = cast<SCEVMinMaxExpr>(Op);
+ SmallVector<SCEVUse, 4> Operands;
+ for (SCEVUse Operand : MinMax->operands())
+ Operands.push_back(getZeroExtendExpr(Operand, Ty));
+ if (isa<SCEVUMinExpr>(MinMax))
+ return getUMinExpr(Operands);
+ return getUMaxExpr(Operands);
+ }
+
+ // zext(umin_seq(x, y)) -> umin_seq(zext(x), zext(y))
+ if (auto *MinMax = dyn_cast<SCEVSequentialMinMaxExpr>(Op)) {
+ assert(isa<SCEVSequentialUMinExpr>(MinMax) && "Not supported!");
+ SmallVector<SCEVUse, 4> Operands;
+ for (SCEVUse Operand : MinMax->operands())
+ Operands.push_back(getZeroExtendExpr(Operand, Ty));
+ return getUMinExpr(Operands, /*Sequential*/ true);
+ }
+
+ // The cast wasn't folded; create an explicit cast node.
+ // Recompute the insert position, as it may have been invalidated.
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
+ Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Op);
+ return S;
+}
+
+const SCEV *
+ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ FoldID ID(scSignExtend, Op, Ty);
+ if (const SCEV *S = FoldCache.lookup(ID))
+ return S;
+
+ const SCEV *S = getSignExtendExprImpl(Op, Ty, Depth);
+ if (!isa<SCEVSignExtendExpr>(S))
+ insertFoldCacheEntry(ID, S, FoldCache, FoldCacheUser);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getSignExtendExprImpl(const SCEV *Op, Type *Ty,
+ unsigned Depth) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!");
+ assert(!Op->getType()->isPointerTy() && "Can't extend pointer!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ // Fold if the operand is constant.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return getConstant(SC->getAPInt().sext(getTypeSizeInBits(Ty)));
+
+ // sext(sext(x)) --> sext(x)
+ if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
+ return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
+
+ // sext(zext(x)) --> zext(x)
+ if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
+ return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
+
+ // If the operand is an affine AddRec with the no-signed-wrap flag, the
+ // sign-extension distributes over the recurrence.
+ const SCEV *Start, *Step;
+ const Loop *L;
+ if (Depth <= MaxCastDepth &&
+ match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
+ const auto *AR = cast<SCEVAddRecExpr>(Op);
+ if (AR->hasNoSignedWrap()) {
+ Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getSignExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, SCEV::FlagNSW);
+ }
+ }
+
+ // Before doing any expensive analysis, check to see if we've already
+ // computed a SCEV for this Op and Ty.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scSignExtend);
+ ID.AddPointer(Op);
+ ID.AddPointer(Ty);
+ void *IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ // Limit recursion depth.
+ if (Depth > MaxCastDepth) {
+ SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
+ Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Op);
+ return S;
+ }
+
+ // sext(trunc(x)) --> sext(x) or x or trunc(x)
+ if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
+ // It's possible the bits taken off by the truncate were all sign bits. If
+ // so, we should be able to simplify this further.
+ const SCEV *X = ST->getOperand();
+ ConstantRange CR = getSignedRange(X);
+ unsigned TruncBits = getTypeSizeInBits(ST->getType());
+ unsigned NewBits = getTypeSizeInBits(Ty);
+ if (CR.truncate(TruncBits).signExtend(NewBits).contains(
+ CR.sextOrTrunc(NewBits)))
+ return getTruncateOrSignExtend(X, Ty, Depth);
+ }
+
+ if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
+ // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
+ if (SA->hasNoSignedWrap()) {
+ // If the addition does not sign overflow then we can, by definition,
+ // commute the sign extension with the addition operation.
+ SmallVector<SCEVUse, 4> Ops;
+ for (SCEVUse Op : SA->operands())
+ Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
+ return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
+ }
+
+ // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
+ // if D + (C - D + x + y + ...) could be proven to not signed wrap
+ // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
+ //
+ // For instance, this will bring two seemingly different expressions:
+ // 1 + sext(5 + 20 * %x + 24 * %y) and
+ // sext(6 + 20 * %x + 24 * %y)
+ // to the same form:
+ // 2 + sext(4 + 20 * %x + 24 * %y)
+ if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
+ const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
+ if (D != 0) {
+ const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
+ const SCEV *SResidual =
+ getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
+ const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
+ return getAddExpr(SSExtD, SSExtR, (SCEV::FlagNSW | SCEV::FlagNUW),
+ Depth + 1);
+ }
+ }
+ }
+ // If the input value is a chrec scev, and we can prove that the value
+ // did not overflow the old, smaller, value, we can sign extend all of the
+ // operands (often constants). This allows analysis of something like
+ // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
+ if (match(Op, m_scev_AffineAddRec(m_SCEV(Start), m_SCEV(Step), m_Loop(L)))) {
+ const auto *AR = cast<SCEVAddRecExpr>(Op);
+ unsigned BitWidth = getTypeSizeInBits(AR->getType());
+
+ // The no-signed-wrap case is handled before the uniquing lookup above.
+
+ // Check whether the backedge-taken count is SCEVCouldNotCompute.
+ // Note that this serves two purposes: It filters out loops that are
+ // simply not analyzable, and it covers the case where this code is
+ // being called from within backedge-taken count analysis, such that
+ // attempting to ask for the backedge-taken count would likely result
+ // in infinite recursion. In the later case, the analysis code will
+ // cope with a conservative value, and it will take care to purge
+ // that value once it has finished.
+ const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
+ // Manually compute the final value for AR, checking for
+ // overflow.
+
+ // Check whether the backedge-taken count can be losslessly casted to
+ // the addrec's type. The count is always unsigned.
+ const SCEV *CastedMaxBECount =
+ getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
+ const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
+ CastedMaxBECount, MaxBECount->getType(), Depth);
+ if (MaxBECount == RecastedMaxBECount) {
+ Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
+ // Check whether Start+Step*MaxBECount has no signed overflow.
+ const SCEV *SMul =
+ getMulExpr(CastedMaxBECount, Step, SCEV::FlagAnyWrap, Depth + 1);
+ const SCEV *SAdd = getSignExtendExpr(
+ getAddExpr(Start, SMul, SCEV::FlagAnyWrap, Depth + 1), WideTy,
+ Depth + 1);
+ const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
+ const SCEV *WideMaxBECount =
+ getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
+ const SCEV *OperandExtendedAdd =
+ getAddExpr(WideStart,
+ getMulExpr(WideMaxBECount,
+ getSignExtendExpr(Step, WideTy, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1);
+ if (SAdd == OperandExtendedAdd) {
+ // Cache knowledge of AR NSW, which is propagated to this AddRec.
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
+ // Return the expression with the addrec on the outside.
+ Start =
+ getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getSignExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ // Similar to above, only this time treat the step value as unsigned.
+ // This covers loops that count up with an unsigned step.
+ OperandExtendedAdd =
+ getAddExpr(WideStart,
+ getMulExpr(WideMaxBECount,
+ getZeroExtendExpr(Step, WideTy, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1);
+ if (SAdd == OperandExtendedAdd) {
+ // If AR wraps around then
+ //
+ // abs(Step) * MaxBECount > unsigned-max(AR->getType())
+ // => SAdd != OperandExtendedAdd
+ //
+ // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
+ // (SAdd == OperandExtendedAdd => AR is NW)
+
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
+
+ // Return the expression with the addrec on the outside.
+ Start =
+ getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getZeroExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ }
+ }
+
+ auto NewFlags = proveNoSignedWrapViaInduction(AR);
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
+ if (AR->hasNoSignedWrap()) {
+ // Same as nsw case above - duplicated here to avoid a compile time
+ // issue. It's not clear that the order of checks does matter, but
+ // it's one of two issue possible causes for a change which was
+ // reverted. Be conservative for the moment.
+ Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getSignExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+
+ // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
+ // if D + (C - D + Step * n) could be proven to not signed wrap
+ // where D maximizes the number of trailing zeros of (C - D + Step * n)
+ if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
+ const APInt &C = SC->getAPInt();
+ const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
+ if (D != 0) {
+ const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
+ const SCEV *SResidual =
+ getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
+ const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
+ return getAddExpr(SSExtD, SSExtR, (SCEV::FlagNSW | SCEV::FlagNUW),
+ Depth + 1);
+ }
+ }
+
+ if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
+ Start = getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1);
+ Step = getSignExtendExpr(Step, Ty, Depth + 1);
+ return getAddRecExpr(Start, Step, L, AR->getNoWrapFlags());
+ }
+ }
+
+ // If the input value is provably positive and we could not simplify
+ // away the sext build a zext instead.
+ if (isKnownNonNegative(Op))
+ return getZeroExtendExpr(Op, Ty, Depth + 1);
+
+ // sext(smin(x, y)) -> smin(sext(x), sext(y))
+ // sext(smax(x, y)) -> smax(sext(x), sext(y))
+ if (isa<SCEVSMinExpr>(Op) || isa<SCEVSMaxExpr>(Op)) {
+ auto *MinMax = cast<SCEVMinMaxExpr>(Op);
+ SmallVector<SCEVUse, 4> Operands;
+ for (SCEVUse Operand : MinMax->operands())
+ Operands.push_back(getSignExtendExpr(Operand, Ty));
+ if (isa<SCEVSMinExpr>(MinMax))
+ return getSMinExpr(Operands);
+ return getSMaxExpr(Operands);
+ }
+
+ // The cast wasn't folded; create an explicit cast node.
+ // Recompute the insert position, as it may have been invalidated.
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
+ Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Op);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getCastExpr(SCEVTypes Kind, const SCEV *Op,
+ Type *Ty) {
+ switch (Kind) {
+ case scTruncate:
+ return getTruncateExpr(Op, Ty);
+ case scZeroExtend:
+ return getZeroExtendExpr(Op, Ty);
+ case scSignExtend:
+ return getSignExtendExpr(Op, Ty);
+ case scPtrToAddr: {
+ const SCEV *Expr = getPtrToAddrExpr(Op);
+ assert(Expr->getType() == Ty && "requested type must match");
+ return Expr;
+ }
+ default:
+ llvm_unreachable("Not a SCEV cast expression!");
+ }
+}
+
+/// getAnyExtendExpr - Return a SCEV for the given operand extended with
+/// unspecified bits out to the given type.
+const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
+ Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ // Sign-extend negative constants.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ if (SC->getAPInt().isNegative())
+ return getSignExtendExpr(Op, Ty);
+
+ // Peel off a truncate cast.
+ if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
+ const SCEV *NewOp = T->getOperand();
+ if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
+ return getAnyExtendExpr(NewOp, Ty);
+ return getTruncateOrNoop(NewOp, Ty);
+ }
+
+ // Next try a zext cast. If the cast is folded, use it.
+ const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
+ if (!isa<SCEVZeroExtendExpr>(ZExt))
+ return ZExt;
+
+ // Next try a sext cast. If the cast is folded, use it.
+ const SCEV *SExt = getSignExtendExpr(Op, Ty);
+ if (!isa<SCEVSignExtendExpr>(SExt))
+ return SExt;
+
+ // Force the cast to be folded into the operands of an addrec.
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
+ SmallVector<SCEVUse, 4> Ops;
+ for (const SCEV *Op : AR->operands())
+ Ops.push_back(getAnyExtendExpr(Op, Ty));
+ return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
+ }
+
+ // If the expression is obviously signed, use the sext cast value.
+ if (isa<SCEVSMaxExpr>(Op))
+ return SExt;
+
+ // Absent any other information, use the zext cast value.
+ return ZExt;
+}
+
+/// Process the given Ops list, which is a list of operands to be added under
+/// the given scale, update the given map. This is a helper function for
+/// getAddRecExpr. As an example of what it does, given a sequence of operands
+/// that would form an add expression like this:
+///
+/// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
+///
+/// where A and B are constants, update the map with these values:
+///
+/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
+///
+/// and add 13 + A*B*29 to AccumulatedConstant.
+/// This will allow getAddRecExpr to produce this:
+///
+/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
+///
+/// This form often exposes folding opportunities that are hidden in
+/// the original operand list.
+///
+/// Return true iff it appears that any interesting folding opportunities
+/// may be exposed. This helps getAddRecExpr short-circuit extra work in
+/// the common case where no interesting opportunities are present, and
+/// is also used as a check to avoid infinite recursion.
+static bool CollectAddOperandsWithScales(SmallDenseMap<SCEVUse, APInt, 16> &M,
+ SmallVectorImpl<SCEVUse> &NewOps,
+ APInt &AccumulatedConstant,
+ ArrayRef<SCEVUse> Ops,
+ const APInt &Scale,
+ ScalarEvolution &SE) {
+ bool Interesting = false;
+
+ // Iterate over the add operands. They are sorted, with constants first.
+ unsigned i = 0;
+ while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
+ ++i;
+ // Pull a buried constant out to the outside.
+ if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
+ Interesting = true;
+ AccumulatedConstant += Scale * C->getAPInt();
+ }
+
+ // Next comes everything else. We're especially interested in multiplies
+ // here, but they're in the middle, so just visit the rest with one loop.
+ for (; i != Ops.size(); ++i) {
+ const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
+ if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
+ APInt NewScale =
+ Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
+ if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
+ // A multiplication of a constant with another add; recurse.
+ const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
+ Interesting |= CollectAddOperandsWithScales(
+ M, NewOps, AccumulatedConstant, Add->operands(), NewScale, SE);
+ } else {
+ // A multiplication of a constant with some other value. Update
+ // the map.
+ SmallVector<SCEVUse, 4> MulOps(drop_begin(Mul->operands()));
+ const SCEV *Key = SE.getMulExpr(MulOps);
+ auto Pair = M.insert({Key, NewScale});
+ if (Pair.second) {
+ NewOps.push_back(Pair.first->first);
+ } else {
+ Pair.first->second += NewScale;
+ // The map already had an entry for this value, which may indicate
+ // a folding opportunity.
+ Interesting = true;
+ }
+ }
+ } else {
+ // An ordinary operand. Update the map.
+ auto Pair = M.insert({Ops[i], Scale});
+ if (Pair.second) {
+ NewOps.push_back(Pair.first->first);
+ } else {
+ Pair.first->second += Scale;
+ // The map already had an entry for this value, which may indicate
+ // a folding opportunity.
+ Interesting = true;
+ }
+ }
+ }
+
+ return Interesting;
+}
+
+bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed,
+ const SCEV *LHS, const SCEV *RHS,
+ const Instruction *CtxI) {
+ const SCEV *(ScalarEvolution::*Operation)(SCEVUse, SCEVUse, SCEV::NoWrapFlags,
+ unsigned);
+ switch (BinOp) {
+ default:
+ llvm_unreachable("Unsupported binary op");
+ case Instruction::Add:
+ Operation = &ScalarEvolution::getAddExpr;
+ break;
+ case Instruction::Sub:
+ Operation = &ScalarEvolution::getMinusSCEV;
+ break;
+ case Instruction::Mul:
+ Operation = &ScalarEvolution::getMulExpr;
+ break;
+ }
+
+ const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) =
+ Signed ? &ScalarEvolution::getSignExtendExpr
+ : &ScalarEvolution::getZeroExtendExpr;
+
+ // Check ext(LHS op RHS) == ext(LHS) op ext(RHS)
+ auto *NarrowTy = cast<IntegerType>(LHS->getType());
+ auto *WideTy =
+ IntegerType::get(NarrowTy->getContext(), NarrowTy->getBitWidth() * 2);
+
+ const SCEV *A = (this->*Extension)(
+ (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0);
+ const SCEV *LHSB = (this->*Extension)(LHS, WideTy, 0);
+ const SCEV *RHSB = (this->*Extension)(RHS, WideTy, 0);
+ const SCEV *B = (this->*Operation)(LHSB, RHSB, SCEV::FlagAnyWrap, 0);
+ if (A == B)
+ return true;
+ // Can we use context to prove the fact we need?
+ if (!CtxI)
+ return false;
+ // TODO: Support mul.
+ if (BinOp == Instruction::Mul)
+ return false;
+ auto *RHSC = dyn_cast<SCEVConstant>(RHS);
+ // TODO: Lift this limitation.
+ if (!RHSC)
+ return false;
+ APInt C = RHSC->getAPInt();
+ unsigned NumBits = C.getBitWidth();
+ bool IsSub = (BinOp == Instruction::Sub);
+ bool IsNegativeConst = (Signed && C.isNegative());
+ // Compute the direction and magnitude by which we need to check overflow.
+ bool OverflowDown = IsSub ^ IsNegativeConst;
+ APInt Magnitude = C;
+ if (IsNegativeConst) {
+ if (C == APInt::getSignedMinValue(NumBits))
+ // TODO: SINT_MIN on inversion gives the same negative value, we don't
+ // want to deal with that.
+ return false;
+ Magnitude = -C;
+ }
+
+ ICmpInst::Predicate Pred = Signed ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
+ if (OverflowDown) {
+ // To avoid overflow down, we need to make sure that MIN + Magnitude <= LHS.
+ APInt Min = Signed ? APInt::getSignedMinValue(NumBits)
+ : APInt::getMinValue(NumBits);
+ APInt Limit = Min + Magnitude;
+ return isKnownPredicateAt(Pred, getConstant(Limit), LHS, CtxI);
+ } else {
+ // To avoid overflow up, we need to make sure that LHS <= MAX - Magnitude.
+ APInt Max = Signed ? APInt::getSignedMaxValue(NumBits)
+ : APInt::getMaxValue(NumBits);
+ APInt Limit = Max - Magnitude;
+ return isKnownPredicateAt(Pred, LHS, getConstant(Limit), CtxI);
+ }
+}
+
+std::optional<SCEV::NoWrapFlags>
+ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp(
+ const OverflowingBinaryOperator *OBO) {
+ // It cannot be done any better.
+ if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap())
+ return std::nullopt;
+
+ SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap;
+
+ if (OBO->hasNoUnsignedWrap())
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ if (OBO->hasNoSignedWrap())
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
+
+ bool Deduced = false;
+
+ Instruction::BinaryOps Opcode = (Instruction::BinaryOps)OBO->getOpcode();
+ const SCEV *LHS = getSCEV(OBO->getOperand(0));
+ const SCEV *RHS = getSCEV(OBO->getOperand(1));
+
+ bool CanUseNSW = true;
+ const APInt *ShiftAmt;
+ // Treat `shl %a, C` as `mul %a, 1 << C`.
+ if (match(OBO, m_Shl(m_Value(), m_APInt(ShiftAmt)))) {
+ unsigned BitWidth = ShiftAmt->getBitWidth();
+ if (ShiftAmt->uge(BitWidth))
+ return std::nullopt;
+ // NSW only transfers if the shift amount is < BitWidth - 1, as INT_MIN * -1
+ // overflows.
+ CanUseNSW = ShiftAmt->ult(BitWidth - 1);
+ Opcode = Instruction::Mul;
+ RHS = getConstant(APInt::getOneBitSet(BitWidth, ShiftAmt->getZExtValue()));
+ } else if (Opcode != Instruction::Add && Opcode != Instruction::Sub &&
+ Opcode != Instruction::Mul) {
+ return std::nullopt;
+ }
+
+ const Instruction *CtxI =
+ UseContextForNoWrapFlagInference ? dyn_cast<Instruction>(OBO) : nullptr;
+ if (!OBO->hasNoUnsignedWrap() &&
+ willNotOverflow(Opcode, /* Signed */ false, LHS, RHS, CtxI)) {
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ Deduced = true;
+ }
+
+ if (CanUseNSW && !OBO->hasNoSignedWrap() &&
+ willNotOverflow(Opcode, /* Signed */ true, LHS, RHS, CtxI)) {
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
+ Deduced = true;
+ }
+
+ if (Deduced)
+ return Flags;
+ return std::nullopt;
+}
+
+// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
+// `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
+// can't-overflow flags for the operation if possible.
+static SCEV::NoWrapFlags StrengthenNoWrapFlags(ScalarEvolution *SE,
+ SCEVTypes Type,
+ ArrayRef<SCEVUse> Ops,
+ SCEV::NoWrapFlags Flags) {
+ using namespace std::placeholders;
+
+ using OBO = OverflowingBinaryOperator;
+
+ bool CanAnalyze =
+ Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
+ (void)CanAnalyze;
+ assert(CanAnalyze && "don't call from other places!");
+
+ SCEV::NoWrapFlags SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
+ SCEV::NoWrapFlags SignOrUnsignWrap =
+ ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
+
+ // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
+ auto IsKnownNonNegative = [&](SCEVUse U) {
+ return SE->isKnownNonNegative(U);
+ };
+
+ if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
+ Flags = ScalarEvolution::setFlags(Flags, SignOrUnsignMask);
+
+ SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
+
+ if (SignOrUnsignWrap != SignOrUnsignMask &&
+ (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
+ isa<SCEVConstant>(Ops[0])) {
+
+ auto Opcode = [&] {
+ switch (Type) {
+ case scAddExpr:
+ return Instruction::Add;
+ case scMulExpr:
+ return Instruction::Mul;
+ default:
+ llvm_unreachable("Unexpected SCEV op.");
+ }
+ }();
+
+ const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
+
+ // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
+ if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
+ auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
+ Opcode, C, OBO::NoSignedWrap);
+ if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
+ }
+
+ // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
+ if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
+ auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
+ Opcode, C, OBO::NoUnsignedWrap);
+ if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ }
+ }
+
+ // <0,+,nonnegative><nw> is also nuw
+ // TODO: Add corresponding nsw case
+ if (Type == scAddRecExpr && ScalarEvolution::hasFlags(Flags, SCEV::FlagNW) &&
+ !ScalarEvolution::hasFlags(Flags, SCEV::FlagNUW) && Ops.size() == 2 &&
+ Ops[0]->isZero() && IsKnownNonNegative(Ops[1]))
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+
+ // both (udiv X, Y) * Y and Y * (udiv X, Y) are always NUW
+ if (Type == scMulExpr && !ScalarEvolution::hasFlags(Flags, SCEV::FlagNUW) &&
+ Ops.size() == 2) {
+ if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Ops[0]))
+ if (UDiv->getOperand(1) == Ops[1])
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Ops[1]))
+ if (UDiv->getOperand(1) == Ops[0])
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ }
+
+ return Flags;
+}
+
+bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
+ return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
+}
+
+/// Get a canonical add expression, or something simpler if possible.
+const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<SCEVUse> &Ops,
+ SCEV::NoWrapFlags OrigFlags,
+ unsigned Depth) {
+ assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
+ "only nuw or nsw allowed");
+ assert(!Ops.empty() && "Cannot get empty add!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i)
+ assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
+ "SCEVAddExpr operand types don't match!");
+ unsigned NumPtrs = count_if(
+ Ops, [](const SCEV *Op) { return Op->getType()->isPointerTy(); });
+ assert(NumPtrs <= 1 && "add has at most one pointer operand");
+#endif
+
+ const SCEV *Folded = constantFoldAndGroupOps(
+ *this, LI, DT, Ops,
+ [](const APInt &C1, const APInt &C2) { return C1 + C2; },
+ [](const APInt &C) { return C.isZero(); }, // identity
+ [](const APInt &C) { return false; }); // absorber
+ if (Folded)
+ return Folded;
+
+ unsigned Idx = isa<SCEVConstant>(Ops[0]) ? 1 : 0;
+
+ // Delay expensive flag strengthening until necessary.
+ auto ComputeFlags = [this, OrigFlags](ArrayRef<SCEVUse> Ops) {
+ return StrengthenNoWrapFlags(this, scAddExpr, Ops, OrigFlags);
+ };
+
+ // Limit recursion calls depth.
+ if (Depth > MaxArithDepth || hasHugeExpression(Ops))
+ return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
+
+ if (SCEV *S = findExistingSCEVInCache(scAddExpr, Ops)) {
+ // Don't strengthen flags if we have no new information.
+ SCEVAddExpr *Add = static_cast<SCEVAddExpr *>(S);
+ if (Add->getNoWrapFlags(OrigFlags) != OrigFlags)
+ Add->setNoWrapFlags(ComputeFlags(Ops));
+ return S;
+ }
+
+ // Okay, check to see if the same value occurs in the operand list more than
+ // once. If so, merge them together into an multiply expression. Since we
+ // sorted the list, these values are required to be adjacent.
+ Type *Ty = Ops[0]->getType();
+ bool FoundMatch = false;
+ for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
+ if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
+ // Scan ahead to count how many equal operands there are.
+ unsigned Count = 2;
+ while (i+Count != e && Ops[i+Count] == Ops[i])
+ ++Count;
+ // Merge the values into a multiply.
+ SCEVUse Scale = getConstant(Ty, Count);
+ const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
+ if (Ops.size() == Count)
+ return Mul;
+ Ops[i] = Mul;
+ Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
+ --i; e -= Count - 1;
+ FoundMatch = true;
+ }
+ if (FoundMatch)
+ return getAddExpr(Ops, OrigFlags, Depth + 1);
+
+ // Check for truncates. If all the operands are truncated from the same
+ // type, see if factoring out the truncate would permit the result to be
+ // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
+ // if the contents of the resulting outer trunc fold to something simple.
+ auto FindTruncSrcType = [&]() -> Type * {
+ // We're ultimately looking to fold an addrec of truncs and muls of only
+ // constants and truncs, so if we find any other types of SCEV
+ // as operands of the addrec then we bail and return nullptr here.
+ // Otherwise, we return the type of the operand of a trunc that we find.
+ if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
+ return T->getOperand()->getType();
+ if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
+ SCEVUse LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
+ if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
+ return T->getOperand()->getType();
+ }
+ return nullptr;
+ };
+ if (auto *SrcType = FindTruncSrcType()) {
+ SmallVector<SCEVUse, 8> LargeOps;
+ bool Ok = true;
+ // Check all the operands to see if they can be represented in the
+ // source type of the truncate.
+ for (const SCEV *Op : Ops) {
+ if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
+ if (T->getOperand()->getType() != SrcType) {
+ Ok = false;
+ break;
+ }
+ LargeOps.push_back(T->getOperand());
+ } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Op)) {
+ LargeOps.push_back(getAnyExtendExpr(C, SrcType));
+ } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Op)) {
+ SmallVector<SCEVUse, 8> LargeMulOps;
+ for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
+ if (const SCEVTruncateExpr *T =
+ dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
+ if (T->getOperand()->getType() != SrcType) {
+ Ok = false;
+ break;
+ }
+ LargeMulOps.push_back(T->getOperand());
+ } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
+ LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
+ } else {
+ Ok = false;
+ break;
+ }
+ }
+ if (Ok)
+ LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
+ } else {
+ Ok = false;
+ break;
+ }
+ }
+ if (Ok) {
+ // Evaluate the expression in the larger type.
+ const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
+ // If it folds to something simple, use it. Otherwise, don't.
+ if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
+ return getTruncateExpr(Fold, Ty);
+ }
+ }
+
+ if (Ops.size() == 2) {
+ // Check if we have an expression of the form ((X + C1) - C2), where C1 and
+ // C2 can be folded in a way that allows retaining wrapping flags of (X +
+ // C1).
+ const SCEV *A = Ops[0];
+ const SCEV *B = Ops[1];
+ auto *AddExpr = dyn_cast<SCEVAddExpr>(B);
+ auto *C = dyn_cast<SCEVConstant>(A);
+ if (AddExpr && C && isa<SCEVConstant>(AddExpr->getOperand(0))) {
+ auto C1 = cast<SCEVConstant>(AddExpr->getOperand(0))->getAPInt();
+ auto C2 = C->getAPInt();
+ SCEV::NoWrapFlags PreservedFlags = SCEV::FlagAnyWrap;
+
+ APInt ConstAdd = C1 + C2;
+ auto AddFlags = AddExpr->getNoWrapFlags();
+ // Adding a smaller constant is NUW if the original AddExpr was NUW.
+ if (ScalarEvolution::hasFlags(AddFlags, SCEV::FlagNUW) &&
+ ConstAdd.ule(C1)) {
+ PreservedFlags =
+ ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNUW);
+ }
+
+ // Adding a constant with the same sign and small magnitude is NSW, if the
+ // original AddExpr was NSW.
+ if (ScalarEvolution::hasFlags(AddFlags, SCEV::FlagNSW) &&
+ C1.isSignBitSet() == ConstAdd.isSignBitSet() &&
+ ConstAdd.abs().ule(C1.abs())) {
+ PreservedFlags =
+ ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNSW);
+ }
+
+ if (PreservedFlags != SCEV::FlagAnyWrap) {
+ SmallVector<SCEVUse, 4> NewOps(AddExpr->operands());
+ NewOps[0] = getConstant(ConstAdd);
+ return getAddExpr(NewOps, PreservedFlags);
+ }
+ }
+
+ // Try to push the constant operand into a ZExt: A + zext (-A + B) -> zext
+ // (B), if trunc (A) + -A + B does not unsigned-wrap.
+ const SCEVAddExpr *InnerAdd;
+ if (match(B, m_scev_ZExt(m_scev_Add(InnerAdd)))) {
+ const SCEV *NarrowA = getTruncateExpr(A, InnerAdd->getType());
+ if (NarrowA == getNegativeSCEV(InnerAdd->getOperand(0)) &&
+ getZeroExtendExpr(NarrowA, B->getType()) == A &&
+ hasFlags(StrengthenNoWrapFlags(this, scAddExpr, {NarrowA, InnerAdd},
+ SCEV::FlagAnyWrap),
+ SCEV::FlagNUW)) {
+ return getZeroExtendExpr(getAddExpr(NarrowA, InnerAdd), B->getType());
+ }
+ }
+ }
+
+ // Canonicalize (-1 * urem X, Y) + X --> (Y * X/Y)
+ const SCEV *Y;
+ if (Ops.size() == 2 &&
+ match(Ops[0],
+ m_scev_Mul(m_scev_AllOnes(),
+ m_scev_URem(m_scev_Specific(Ops[1]), m_SCEV(Y), *this))))
+ return getMulExpr(Y, getUDivExpr(Ops[1], Y));
+
+ // Skip past any other cast SCEVs.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
+ ++Idx;
+
+ // If there are add operands they would be next.
+ if (Idx < Ops.size()) {
+ bool DeletedAdd = false;
+ // If the original flags and all inlined SCEVAddExprs are NUW, use the
+ // common NUW flag for expression after inlining. Other flags cannot be
+ // preserved, because they may depend on the original order of operations.
+ SCEV::NoWrapFlags CommonFlags = maskFlags(OrigFlags, SCEV::FlagNUW);
+ while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
+ if (Ops.size() > AddOpsInlineThreshold ||
+ Add->getNumOperands() > AddOpsInlineThreshold)
+ break;
+ // If we have an add, expand the add operands onto the end of the operands
+ // list.
+ Ops.erase(Ops.begin()+Idx);
+ append_range(Ops, Add->operands());
+ DeletedAdd = true;
+ CommonFlags = maskFlags(CommonFlags, Add->getNoWrapFlags());
+ }
+
+ // If we deleted at least one add, we added operands to the end of the list,
+ // and they are not necessarily sorted. Recurse to resort and resimplify
+ // any operands we just acquired.
+ if (DeletedAdd)
+ return getAddExpr(Ops, CommonFlags, Depth + 1);
+ }
+
+ // Skip over the add expression until we get to a multiply.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
+ ++Idx;
+
+ // Check to see if there are any folding opportunities present with
+ // operands multiplied by constant values.
+ if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
+ uint64_t BitWidth = getTypeSizeInBits(Ty);
+ SmallDenseMap<SCEVUse, APInt, 16> M;
+ SmallVector<SCEVUse, 8> NewOps;
+ APInt AccumulatedConstant(BitWidth, 0);
+ if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
+ Ops, APInt(BitWidth, 1), *this)) {
+ struct APIntCompare {
+ bool operator()(const APInt &LHS, const APInt &RHS) const {
+ return LHS.ult(RHS);
+ }
+ };
+
+ // Some interesting folding opportunity is present, so its worthwhile to
+ // re-generate the operands list. Group the operands by constant scale,
+ // to avoid multiplying by the same constant scale multiple times.
+ std::map<APInt, SmallVector<SCEVUse, 4>, APIntCompare> MulOpLists;
+ for (const SCEV *NewOp : NewOps)
+ MulOpLists[M.find(NewOp)->second].push_back(NewOp);
+ // Re-generate the operands list.
+ Ops.clear();
+ if (AccumulatedConstant != 0)
+ Ops.push_back(getConstant(AccumulatedConstant));
+ for (auto &MulOp : MulOpLists) {
+ if (MulOp.first == 1) {
+ Ops.push_back(getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1));
+ } else if (MulOp.first != 0) {
+ Ops.push_back(getMulExpr(
+ getConstant(MulOp.first),
+ getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
+ SCEV::FlagAnyWrap, Depth + 1));
+ }
+ }
+ if (Ops.empty())
+ return getZero(Ty);
+ if (Ops.size() == 1)
+ return Ops[0];
+ return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+ }
+ }
+
+ // Given a SCEVMulExpr and an operand index, return the product of all
+ // operands except the one at OpIdx.
+ auto StripFactor = [&](const SCEVMulExpr *M, unsigned OpIdx) -> SCEVUse {
+ if (M->getNumOperands() == 2)
+ return M->getOperand(OpIdx == 0);
+ SmallVector<SCEVUse, 4> Remaining(M->operands().take_front(OpIdx));
+ append_range(Remaining, M->operands().drop_front(OpIdx + 1));
+ return getMulExpr(Remaining, SCEV::FlagAnyWrap, Depth + 1);
+ };
+
+ // If we are adding something to a multiply expression, make sure the
+ // something is not already an operand of the multiply. If so, merge it into
+ // the multiply.
+ for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
+ const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
+ for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
+ // Scan all terms to find every occurrence of common factor MulOpSCEV
+ // and fold them in one shot:
+ // A1*X + A2*X + ... + An*X --> X * (A1 + A2 + ... + An)
+ const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
+ if (isa<SCEVConstant>(MulOpSCEV))
+ continue;
+
+ // Cofactors: 1 for bare addends matching MulOpSCEV, or the
+ // remaining product for multiply terms containing MulOpSCEV.
+ SmallVector<SCEVUse, 4> Cofactors;
+ SmallVector<unsigned, 4> DeadIndices;
+ for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) {
+ if (MulOpSCEV == Ops[AddOp]) {
+ // W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
+ Cofactors.push_back(getOne(Ty));
+ DeadIndices.push_back(AddOp);
+ continue;
+ }
+
+ if (AddOp <= Idx || !isa<SCEVMulExpr>(Ops[AddOp]))
+ continue;
+
+ const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[AddOp]);
+ for (unsigned OMulOp = 0, OE = OtherMul->getNumOperands(); OMulOp != OE;
+ ++OMulOp) {
+ if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
+ // (A*B*C) + (A*D*E) --> A * (B*C + D*E)
+ Cofactors.push_back(StripFactor(OtherMul, OMulOp));
+ DeadIndices.push_back(AddOp);
+ break;
+ }
+ }
+ }
+
+ // Fold all collected cofactors with the anchor multiply's cofactor:
+ // MulOpSCEV * (Cofactor_1 + ... + Cofactor_n + AnchorCofactor)
+ if (!Cofactors.empty()) {
+ Cofactors.push_back(StripFactor(Mul, MulOp));
+
+ SCEVUse InnerSum = getAddExpr(Cofactors, SCEV::FlagAnyWrap, Depth + 1);
+ SCEVUse OuterMul =
+ getMulExpr(MulOpSCEV, InnerSum, SCEV::FlagAnyWrap, Depth + 1);
+
+ // DeadIndices does not include Idx (the anchor), hence +1.
+ if (Ops.size() == DeadIndices.size() + 1)
+ return OuterMul;
+
+ // Erase Ops[Idx] first, then erase DeadIndices in reverse order.
+ // The -1 adjustment accounts for the shift from removing Idx;
+ // reverse order means each erasure only shifts later positions,
+ // which have already been processed.
+ Ops.erase(Ops.begin() + Idx);
+ for (unsigned Dead : reverse(DeadIndices))
+ Ops.erase(Ops.begin() + (Dead > Idx ? Dead - 1 : Dead));
+
+ Ops.push_back(OuterMul);
+ return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+ }
+ }
+ }
+
+ // If there are any add recurrences in the operands list, see if any other
+ // added values are loop invariant. If so, we can fold them into the
+ // recurrence.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
+ ++Idx;
+
+ // Scan over all recurrences, trying to fold loop invariants into them.
+ for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
+ // Scan all of the other operands to this add and add them to the vector if
+ // they are loop invariant w.r.t. the recurrence.
+ SmallVector<SCEVUse, 8> LIOps;
+ const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
+ const Loop *AddRecLoop = AddRec->getLoop();
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
+ LIOps.push_back(Ops[i]);
+ Ops.erase(Ops.begin()+i);
+ --i; --e;
+ }
+
+ // If we found some loop invariants, fold them into the recurrence.
+ if (!LIOps.empty()) {
+ // Compute nowrap flags for the addition of the loop-invariant ops and
+ // the addrec. Temporarily push it as an operand for that purpose. These
+ // flags are valid in the scope of the addrec only.
+ LIOps.push_back(AddRec);
+ SCEV::NoWrapFlags Flags = ComputeFlags(LIOps);
+ LIOps.pop_back();
+
+ // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
+ LIOps.push_back(AddRec->getStart());
+
+ SmallVector<SCEVUse, 4> AddRecOps(AddRec->operands());
+
+ // It is not in general safe to propagate flags valid on an add within
+ // the addrec scope to one outside it. We must prove that the inner
+ // scope is guaranteed to execute if the outer one does to be able to
+ // safely propagate. We know the program is undefined if poison is
+ // produced on the inner scoped addrec. We also know that *for this use*
+ // the outer scoped add can't overflow (because of the flags we just
+ // computed for the inner scoped add) without the program being undefined.
+ // Proving that entry to the outer scope neccesitates entry to the inner
+ // scope, thus proves the program undefined if the flags would be violated
+ // in the outer scope.
+ SCEV::NoWrapFlags AddFlags = Flags;
+ if (AddFlags != SCEV::FlagAnyWrap) {
+ auto *DefI = getDefiningScopeBound(LIOps);
+ auto *ReachI = &*AddRecLoop->getHeader()->begin();
+ if (!isGuaranteedToTransferExecutionTo(DefI, ReachI))
+ AddFlags = SCEV::FlagAnyWrap;
+ }
+ AddRecOps[0] = getAddExpr(LIOps, AddFlags, Depth + 1);
+
+ // Build the new addrec. Propagate the NUW and NSW flags if both the
+ // outer add and the inner addrec are guaranteed to have no overflow.
+ // Always propagate NW.
+ Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
+ const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
+
+ // If all of the other operands were loop invariant, we are done.
+ if (Ops.size() == 1) return NewRec;
+
+ // Otherwise, add the folded AddRec by the non-invariant parts.
+ for (unsigned i = 0;; ++i)
+ if (Ops[i] == AddRec) {
+ Ops[i] = NewRec;
+ break;
+ }
+ return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+ }
+
+ // Okay, if there weren't any loop invariants to be folded, check to see if
+ // there are multiple AddRec's with the same loop induction variable being
+ // added together. If so, we can fold them.
+ for (unsigned OtherIdx = Idx+1;
+ OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
+ ++OtherIdx) {
+ // We expect the AddRecExpr's to be sorted in reverse dominance order,
+ // so that the 1st found AddRecExpr is dominated by all others.
+ assert(DT.dominates(
+ cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
+ AddRec->getLoop()->getHeader()) &&
+ "AddRecExprs are not sorted in reverse dominance order?");
+ if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
+ // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
+ SmallVector<SCEVUse, 4> AddRecOps(AddRec->operands());
+ for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
+ ++OtherIdx) {
+ const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
+ if (OtherAddRec->getLoop() == AddRecLoop) {
+ for (unsigned i = 0, e = OtherAddRec->getNumOperands();
+ i != e; ++i) {
+ if (i >= AddRecOps.size()) {
+ append_range(AddRecOps, OtherAddRec->operands().drop_front(i));
+ break;
+ }
+ AddRecOps[i] =
+ getAddExpr(AddRecOps[i], OtherAddRec->getOperand(i),
+ SCEV::FlagAnyWrap, Depth + 1);
+ }
+ Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
+ }
+ }
+ // Step size has changed, so we cannot guarantee no self-wraparound.
+ Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
+ return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+ }
+ }
+
+ // Otherwise couldn't fold anything into this recurrence. Move onto the
+ // next one.
+ }
+
+ // Okay, it looks like we really DO need an add expr. Check to see if we
+ // already have one, otherwise create a new one.
+ return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
+}
+
+const SCEV *ScalarEvolution::getOrCreateAddExpr(ArrayRef<SCEVUse> Ops,
+ SCEV::NoWrapFlags Flags) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(scAddExpr);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ void *IP = nullptr;
+ SCEVAddExpr *S =
+ static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+ if (!S) {
+ SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
+ llvm::uninitialized_copy(Ops, O);
+ S = new (SCEVAllocator)
+ SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Ops);
+ }
+ S->setNoWrapFlags(Flags);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<SCEVUse> Ops,
+ const Loop *L,
+ SCEV::NoWrapFlags Flags) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(scAddRecExpr);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ ID.AddPointer(L);
+ void *IP = nullptr;
+ SCEVAddRecExpr *S =
+ static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+ if (!S) {
+ SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
+ llvm::uninitialized_copy(Ops, O);
+ S = new (SCEVAllocator)
+ SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ LoopUsers[L].push_back(S);
+ registerUser(S, Ops);
+ }
+ setNoWrapFlags(S, Flags);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getOrCreateMulExpr(ArrayRef<SCEVUse> Ops,
+ SCEV::NoWrapFlags Flags) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(scMulExpr);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ void *IP = nullptr;
+ SCEVMulExpr *S =
+ static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+ if (!S) {
+ SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
+ llvm::uninitialized_copy(Ops, O);
+ S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
+ O, Ops.size());
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Ops);
+ }
+ S->setNoWrapFlags(Flags);
+ return S;
+}
+
+static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
+ uint64_t k = i*j;
+ if (j > 1 && k / j != i) Overflow = true;
+ return k;
+}
+
+/// Compute the result of "n choose k", the binomial coefficient. If an
+/// intermediate computation overflows, Overflow will be set and the return will
+/// be garbage. Overflow is not cleared on absence of overflow.
+static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
+ // We use the multiplicative formula:
+ // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
+ // At each iteration, we take the n-th term of the numeral and divide by the
+ // (k-n)th term of the denominator. This division will always produce an
+ // integral result, and helps reduce the chance of overflow in the
+ // intermediate computations. However, we can still overflow even when the
+ // final result would fit.
+
+ if (n == 0 || n == k) return 1;
+ if (k > n) return 0;
+
+ if (k > n/2)
+ k = n-k;
+
+ uint64_t r = 1;
+ for (uint64_t i = 1; i <= k; ++i) {
+ r = umul_ov(r, n-(i-1), Overflow);
+ r /= i;
+ }
+ return r;
+}
+
+/// Determine if any of the operands in this SCEV are a constant or if
+/// any of the add or multiply expressions in this SCEV contain a constant.
+static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
+ struct FindConstantInAddMulChain {
+ bool FoundConstant = false;
+
+ bool follow(const SCEV *S) {
+ FoundConstant |= isa<SCEVConstant>(S);
+ return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
+ }
+
+ bool isDone() const {
+ return FoundConstant;
+ }
+ };
+
+ FindConstantInAddMulChain F;
+ SCEVTraversal<FindConstantInAddMulChain> ST(F);
+ ST.visitAll(StartExpr);
+ return F.FoundConstant;
+}
+
+/// Get a canonical multiply expression, or something simpler if possible.
+const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<SCEVUse> &Ops,
+ SCEV::NoWrapFlags OrigFlags,
+ unsigned Depth) {
+ assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) &&
+ "only nuw or nsw allowed");
+ assert(!Ops.empty() && "Cannot get empty mul!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ Type *ETy = Ops[0]->getType();
+ assert(!ETy->isPointerTy());
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i)
+ assert(Ops[i]->getType() == ETy &&
+ "SCEVMulExpr operand types don't match!");
+#endif
+
+ const SCEV *Folded = constantFoldAndGroupOps(
+ *this, LI, DT, Ops,
+ [](const APInt &C1, const APInt &C2) { return C1 * C2; },
+ [](const APInt &C) { return C.isOne(); }, // identity
+ [](const APInt &C) { return C.isZero(); }); // absorber
+ if (Folded)
+ return Folded;
+
+ // Delay expensive flag strengthening until necessary.
+ auto ComputeFlags = [this, OrigFlags](const ArrayRef<SCEVUse> Ops) {
+ return StrengthenNoWrapFlags(this, scMulExpr, Ops, OrigFlags);
+ };
+
+ // Limit recursion calls depth.
+ if (Depth > MaxArithDepth || hasHugeExpression(Ops))
+ return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
+
+ if (SCEV *S = findExistingSCEVInCache(scMulExpr, Ops)) {
+ // Don't strengthen flags if we have no new information.
+ SCEVMulExpr *Mul = static_cast<SCEVMulExpr *>(S);
+ if (Mul->getNoWrapFlags(OrigFlags) != OrigFlags)
+ Mul->setNoWrapFlags(ComputeFlags(Ops));
+ return S;
+ }
+
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ if (Ops.size() == 2) {
+ // C1*(C2+V) -> C1*C2 + C1*V
+ // If any of Add's ops are Adds or Muls with a constant, apply this
+ // transformation as well.
+ //
+ // TODO: There are some cases where this transformation is not
+ // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
+ // this transformation should be narrowed down.
+ const SCEV *Op0, *Op1;
+ if (match(Ops[1], m_scev_Add(m_SCEV(Op0), m_SCEV(Op1))) &&
+ containsConstantInAddMulChain(Ops[1])) {
+ const SCEV *LHS = getMulExpr(LHSC, Op0, SCEV::FlagAnyWrap, Depth + 1);
+ const SCEV *RHS = getMulExpr(LHSC, Op1, SCEV::FlagAnyWrap, Depth + 1);
+ return getAddExpr(LHS, RHS, SCEV::FlagAnyWrap, Depth + 1);
+ }
+
+ if (Ops[0]->isAllOnesValue()) {
+ // If we have a mul by -1 of an add, try distributing the -1 among the
+ // add operands.
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
+ SmallVector<SCEVUse, 4> NewOps;
+ bool AnyFolded = false;
+ for (const SCEV *AddOp : Add->operands()) {
+ const SCEV *Mul = getMulExpr(Ops[0], SCEVUse(AddOp),
+ SCEV::FlagAnyWrap, Depth + 1);
+ if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
+ NewOps.push_back(Mul);
+ }
+ if (AnyFolded)
+ return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
+ } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
+ // Negation preserves a recurrence's no self-wrap property.
+ SmallVector<SCEVUse, 4> Operands;
+ for (const SCEV *AddRecOp : AddRec->operands())
+ Operands.push_back(getMulExpr(Ops[0], SCEVUse(AddRecOp),
+ SCEV::FlagAnyWrap, Depth + 1));
+ // Let M be the minimum representable signed value. AddRec with nsw
+ // multiplied by -1 can have signed overflow if and only if it takes a
+ // value of M: M * (-1) would stay M and (M + 1) * (-1) would be the
+ // maximum signed value. In all other cases signed overflow is
+ // impossible.
+ auto FlagsMask = SCEV::FlagNW;
+ if (AddRec->hasNoSignedWrap()) {
+ auto MinInt =
+ APInt::getSignedMinValue(getTypeSizeInBits(AddRec->getType()));
+ if (getSignedRangeMin(AddRec) != MinInt)
+ FlagsMask = setFlags(FlagsMask, SCEV::FlagNSW);
+ }
+ return getAddRecExpr(Operands, AddRec->getLoop(),
+ AddRec->getNoWrapFlags(FlagsMask));
+ }
+ }
+
+ // Try to push the constant operand into a ZExt: C * zext (A + B) ->
+ // zext (C*A + C*B) if trunc (C) * (A + B) does not unsigned-wrap.
+ const SCEVAddExpr *InnerAdd;
+ if (match(Ops[1], m_scev_ZExt(m_scev_Add(InnerAdd)))) {
+ const SCEV *NarrowC = getTruncateExpr(LHSC, InnerAdd->getType());
+ if (isa<SCEVConstant>(InnerAdd->getOperand(0)) &&
+ getZeroExtendExpr(NarrowC, Ops[1]->getType()) == LHSC &&
+ hasFlags(StrengthenNoWrapFlags(this, scMulExpr, {NarrowC, InnerAdd},
+ SCEV::FlagAnyWrap),
+ SCEV::FlagNUW)) {
+ auto *Res = getMulExpr(NarrowC, InnerAdd, SCEV::FlagNUW, Depth + 1);
+ return getZeroExtendExpr(Res, Ops[1]->getType(), Depth + 1);
+ };
+ }
+
+ // Try to fold (C1 * D /u C2) -> C1/C2 * D, if C1 and C2 are powers-of-2,
+ // D is a multiple of C2, and C1 is a multiple of C2. If C2 is a multiple
+ // of C1, fold to (D /u (C2 /u C1)).
+ const SCEV *D;
+ APInt C1V = LHSC->getAPInt();
+ // (C1 * D /u C2) == -1 * -C1 * D /u C2 when C1 != INT_MIN. Don't treat -1
+ // as -1 * 1, as it won't enable additional folds.
+ if (C1V.isNegative() && !C1V.isMinSignedValue() && !C1V.isAllOnes())
+ C1V = C1V.abs();
+ const SCEVConstant *C2;
+ if (C1V.isPowerOf2() &&
+ match(Ops[1], m_scev_UDiv(m_SCEV(D), m_SCEVConstant(C2))) &&
+ C2->getAPInt().isPowerOf2() &&
+ C1V.logBase2() <= getMinTrailingZeros(D)) {
+ const SCEV *NewMul = nullptr;
+ if (C1V.uge(C2->getAPInt())) {
+ NewMul = getMulExpr(getUDivExpr(getConstant(C1V), C2), D);
+ } else if (C2->getAPInt().logBase2() <= getMinTrailingZeros(D)) {
+ assert(C1V.ugt(1) && "C1 <= 1 should have been folded earlier");
+ NewMul = getUDivExpr(D, getUDivExpr(C2, getConstant(C1V)));
+ }
+ if (NewMul)
+ return C1V == LHSC->getAPInt() ? NewMul : getNegativeSCEV(NewMul);
+ }
+ }
+ }
+
+ // Skip over the add expression until we get to a multiply.
+ unsigned Idx = 0;
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
+ ++Idx;
+
+ // If there are mul operands inline them all into this expression.
+ if (Idx < Ops.size()) {
+ bool DeletedMul = false;
+ while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
+ if (Ops.size() > MulOpsInlineThreshold)
+ break;
+ // If we have an mul, expand the mul operands onto the end of the
+ // operands list.
+ Ops.erase(Ops.begin()+Idx);
+ append_range(Ops, Mul->operands());
+ DeletedMul = true;
+ }
+
+ // If we deleted at least one mul, we added operands to the end of the
+ // list, and they are not necessarily sorted. Recurse to resort and
+ // resimplify any operands we just acquired.
+ if (DeletedMul)
+ return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+ }
+
+ // If there are any add recurrences in the operands list, see if any other
+ // added values are loop invariant. If so, we can fold them into the
+ // recurrence.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
+ ++Idx;
+
+ // Scan over all recurrences, trying to fold loop invariants into them.
+ for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
+ // Scan all of the other operands to this mul and add them to the vector
+ // if they are loop invariant w.r.t. the recurrence.
+ SmallVector<SCEVUse, 8> LIOps;
+ const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ if (isAvailableAtLoopEntry(Ops[i], AddRec->getLoop())) {
+ LIOps.push_back(Ops[i]);
+ Ops.erase(Ops.begin()+i);
+ --i; --e;
+ }
+
+ // If we found some loop invariants, fold them into the recurrence.
+ if (!LIOps.empty()) {
+ // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
+ SmallVector<SCEVUse, 4> NewOps;
+ NewOps.reserve(AddRec->getNumOperands());
+ const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
+
+ // If both the mul and addrec are nuw, we can preserve nuw.
+ // If both the mul and addrec are nsw, we can only preserve nsw if either
+ // a) they are also nuw, or
+ // b) all multiplications of addrec operands with scale are nsw.
+ SCEV::NoWrapFlags Flags =
+ AddRec->getNoWrapFlags(ComputeFlags({Scale, AddRec}));
+
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
+ NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
+ SCEV::FlagAnyWrap, Depth + 1));
+
+ if (hasFlags(Flags, SCEV::FlagNSW) && !hasFlags(Flags, SCEV::FlagNUW)) {
+ ConstantRange NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
+ Instruction::Mul, getSignedRange(Scale),
+ OverflowingBinaryOperator::NoSignedWrap);
+ if (!NSWRegion.contains(getSignedRange(AddRec->getOperand(i))))
+ Flags = clearFlags(Flags, SCEV::FlagNSW);
+ }
+ }
+
+ const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), Flags);
+
+ // If all of the other operands were loop invariant, we are done.
+ if (Ops.size() == 1) return NewRec;
+
+ // Otherwise, multiply the folded AddRec by the non-invariant parts.
+ for (unsigned i = 0;; ++i)
+ if (Ops[i] == AddRec) {
+ Ops[i] = NewRec;
+ break;
+ }
+ return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+ }
+
+ // Okay, if there weren't any loop invariants to be folded, check to see
+ // if there are multiple AddRec's with the same loop induction variable
+ // being multiplied together. If so, we can fold them.
+
+ // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
+ // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
+ // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
+ // ]]],+,...up to x=2n}.
+ // Note that the arguments to choose() are always integers with values
+ // known at compile time, never SCEV objects.
+ //
+ // The implementation avoids pointless extra computations when the two
+ // addrec's are of different length (mathematically, it's equivalent to
+ // an infinite stream of zeros on the right).
+ bool OpsModified = false;
+ for (unsigned OtherIdx = Idx+1;
+ OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
+ ++OtherIdx) {
+ const SCEVAddRecExpr *OtherAddRec =
+ dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
+ if (!OtherAddRec || OtherAddRec->getLoop() != AddRec->getLoop())
+ continue;
+
+ // Limit max number of arguments to avoid creation of unreasonably big
+ // SCEVAddRecs with very complex operands.
+ if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
+ MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec}))
+ continue;
+
+ bool Overflow = false;
+ Type *Ty = AddRec->getType();
+ bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
+ SmallVector<SCEVUse, 7> AddRecOps;
+ for (int x = 0, xe = AddRec->getNumOperands() +
+ OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
+ SmallVector<SCEVUse, 7> SumOps;
+ for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
+ uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
+ for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
+ ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
+ z < ze && !Overflow; ++z) {
+ uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
+ uint64_t Coeff;
+ if (LargerThan64Bits)
+ Coeff = umul_ov(Coeff1, Coeff2, Overflow);
+ else
+ Coeff = Coeff1*Coeff2;
+ const SCEV *CoeffTerm = getConstant(Ty, Coeff);
+ const SCEV *Term1 = AddRec->getOperand(y-z);
+ const SCEV *Term2 = OtherAddRec->getOperand(z);
+ SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
+ SCEV::FlagAnyWrap, Depth + 1));
+ }
+ }
+ if (SumOps.empty())
+ SumOps.push_back(getZero(Ty));
+ AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
+ }
+ if (!Overflow) {
+ const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
+ SCEV::FlagAnyWrap);
+ if (Ops.size() == 2) return NewAddRec;
+ Ops[Idx] = NewAddRec;
+ Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
+ OpsModified = true;
+ AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
+ if (!AddRec)
+ break;
+ }
+ }
+ if (OpsModified)
+ return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
+
+ // Otherwise couldn't fold anything into this recurrence. Move onto the
+ // next one.
+ }
+
+ // Okay, it looks like we really DO need an mul expr. Check to see if we
+ // already have one, otherwise create a new one.
+ return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
+}
+
+/// Represents an unsigned remainder expression based on unsigned division.
+const SCEV *ScalarEvolution::getURemExpr(SCEVUse LHS, SCEVUse RHS) {
+ assert(getEffectiveSCEVType(LHS->getType()) ==
+ getEffectiveSCEVType(RHS->getType()) &&
+ "SCEVURemExpr operand types don't match!");
+
+ // Short-circuit easy cases
+ if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
+ // If constant is one, the result is trivial
+ if (RHSC->getValue()->isOne())
+ return getZero(LHS->getType()); // X urem 1 --> 0
+
+ // If constant is a power of two, fold into a zext(trunc(LHS)).
+ if (RHSC->getAPInt().isPowerOf2()) {
+ Type *FullTy = LHS->getType();
+ Type *TruncTy =
+ IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
+ return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
+ }
+ }
+
+ // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
+ const SCEV *UDiv = getUDivExpr(LHS, RHS);
+ const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
+ return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
+}
+
+/// Get a canonical unsigned division expression, or something simpler if
+/// possible.
+const SCEV *ScalarEvolution::getUDivExpr(SCEVUse LHS, SCEVUse RHS) {
+ assert(!LHS->getType()->isPointerTy() &&
+ "SCEVUDivExpr operand can't be pointer!");
+ assert(LHS->getType() == RHS->getType() &&
+ "SCEVUDivExpr operand types don't match!");
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scUDivExpr);
+ ID.AddPointer(LHS);
+ ID.AddPointer(RHS);
+ void *IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
+ return S;
+
+ // 0 udiv Y == 0
+ if (match(LHS, m_scev_Zero()))
+ return LHS;
+
+ if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
+ if (RHSC->getValue()->isOne())
+ return LHS; // X udiv 1 --> x
+ // If the denominator is zero, the result of the udiv is undefined. Don't
+ // try to analyze it, because the resolution chosen here may differ from
+ // the resolution chosen in other parts of the compiler.
+ if (!RHSC->getValue()->isZero()) {
+ // Determine if the division can be folded into the operands of
+ // its operands.
+ // TODO: Generalize this to non-constants by using known-bits information.
+ Type *Ty = LHS->getType();
+ unsigned LZ = RHSC->getAPInt().countl_zero();
+ unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
+ // For non-power-of-two values, effectively round the value up to the
+ // nearest power of two.
+ if (!RHSC->getAPInt().isPowerOf2())
+ ++MaxShiftAmt;
+ IntegerType *ExtTy =
+ IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
+ if (const SCEVConstant *Step =
+ dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
+ // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
+ const APInt &StepInt = Step->getAPInt();
+ const APInt &DivInt = RHSC->getAPInt();
+ if (!StepInt.urem(DivInt) &&
+ getZeroExtendExpr(AR, ExtTy) ==
+ getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
+ getZeroExtendExpr(Step, ExtTy),
+ AR->getLoop(), SCEV::FlagAnyWrap)) {
+ SmallVector<SCEVUse, 4> Operands;
+ for (const SCEV *Op : AR->operands())
+ Operands.push_back(getUDivExpr(Op, RHS));
+ return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
+ }
+ /// Get a canonical UDivExpr for a recurrence.
+ /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
+ const APInt *StartRem;
+ if (!DivInt.urem(StepInt) && match(getURemExpr(AR->getStart(), Step),
+ m_scev_APInt(StartRem))) {
+ bool NoWrap =
+ getZeroExtendExpr(AR, ExtTy) ==
+ getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
+ getZeroExtendExpr(Step, ExtTy), AR->getLoop(),
+ SCEV::FlagAnyWrap);
+
+ // With N <= C and both N, C as powers-of-2, the transformation
+ // {X,+,N}/C => {(X - X%N),+,N}/C preserves division results even
+ // if wrapping occurs, as the division results remain equivalent for
+ // all offsets in [[(X - X%N), X).
+ bool CanFoldWithWrap = StepInt.ule(DivInt) && // N <= C
+ StepInt.isPowerOf2() && DivInt.isPowerOf2();
+ // Only fold if the subtraction can be folded in the start
+ // expression.
+ const SCEV *NewStart =
+ getMinusSCEV(AR->getStart(), getConstant(*StartRem));
+ if (*StartRem != 0 && (NoWrap || CanFoldWithWrap) &&
+ !isa<SCEVAddExpr>(NewStart)) {
+ const SCEV *NewLHS =
+ getAddRecExpr(NewStart, Step, AR->getLoop(),
+ NoWrap ? SCEV::FlagNW : SCEV::FlagAnyWrap);
+ if (LHS != NewLHS) {
+ LHS = NewLHS;
+
+ // Reset the ID to include the new LHS, and check if it is
+ // already cached.
+ ID.clear();
+ ID.AddInteger(scUDivExpr);
+ ID.AddPointer(LHS);
+ ID.AddPointer(RHS);
+ IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
+ return S;
+ }
+ }
+ }
+ }
+ // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
+ if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
+ SmallVector<SCEVUse, 4> Operands;
+ for (const SCEV *Op : M->operands())
+ Operands.push_back(getZeroExtendExpr(Op, ExtTy));
+ if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) {
+ // Find an operand that's safely divisible.
+ for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
+ const SCEV *Op = M->getOperand(i);
+ const SCEV *Div = getUDivExpr(Op, RHSC);
+ if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
+ Operands = SmallVector<SCEVUse, 4>(M->operands());
+ Operands[i] = Div;
+ return getMulExpr(Operands);
+ }
+ }
+
+ // Even if it's not divisible, try to remove a common factor.
+ if (const auto *LHSC = dyn_cast<SCEVConstant>(M->getOperand(0))) {
+ APInt Factor = APIntOps::GreatestCommonDivisor(LHSC->getAPInt(),
+ RHSC->getAPInt());
+ if (!Factor.isIntN(1)) {
+ SmallVector<SCEVUse, 2> NewOperands;
+ NewOperands.push_back(getConstant(LHSC->getAPInt().udiv(Factor)));
+ append_range(NewOperands, M->operands().drop_front());
+ const SCEV *NewMul = getMulExpr(NewOperands);
+ return getUDivExpr(NewMul,
+ getConstant(RHSC->getAPInt().udiv(Factor)));
+ }
+ }
+ }
+ }
+
+ // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
+ if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
+ if (auto *DivisorConstant =
+ dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
+ bool Overflow = false;
+ APInt NewRHS =
+ DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
+ if (Overflow) {
+ return getConstant(RHSC->getType(), 0, false);
+ }
+ return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
+ }
+ }
+
+ // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
+ if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
+ SmallVector<SCEVUse, 4> Operands;
+ for (const SCEV *Op : A->operands())
+ Operands.push_back(getZeroExtendExpr(Op, ExtTy));
+ if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
+ Operands.clear();
+ for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
+ const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
+ if (isa<SCEVUDivExpr>(Op) ||
+ getMulExpr(Op, RHS) != A->getOperand(i))
+ break;
+ Operands.push_back(Op);
+ }
+ if (Operands.size() == A->getNumOperands())
+ return getAddExpr(Operands);
+ }
+ }
+
+ // ((N - M) + (M * A)) / N --> ((N - 1) + (M * A)) / N
+ // This is an idiom for rounding A up to the next multiple of N, where A
+ // is aready known to be a multiple of M. In this case, instcombine can
+ // see that some low bits of the added constant are unused, so can clear
+ // them, but we want to canonicalise to set the low bits. This makes the
+ // pattern easier to match, without needing to check for known bits in
+ // A*M.
+ const APInt &N = RHSC->getAPInt();
+ const APInt *NMinusM, *M;
+ const SCEV *A;
+ if (match(LHS, m_scev_Add(m_scev_APInt(NMinusM),
+ m_scev_Mul(m_scev_APInt(M), m_SCEV(A))))) {
+ if (N.isPowerOf2() && M->isPowerOf2() && M->ult(N) &&
+ *NMinusM == N - *M) {
+ return getUDivExpr(
+ getAddExpr(getConstant(N - 1), getMulExpr(getConstant(*M), A)),
+ RHS);
+ }
+ }
+
+ // Fold if both operands are constant.
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS))
+ return getConstant(LHSC->getAPInt().udiv(RHSC->getAPInt()));
+ }
+ }
+
+ // ((-C + (C smax %x)) /u %x) evaluates to zero, for any positive constant C.
+ const APInt *NegC, *C;
+ if (match(LHS,
+ m_scev_Add(m_scev_APInt(NegC),
+ m_scev_SMax(m_scev_APInt(C), m_scev_Specific(RHS)))) &&
+ NegC->isNegative() && !NegC->isMinSignedValue() && *C == -*NegC)
+ return getZero(LHS->getType());
+
+ // (%a * %b)<nuw> / %b -> %a
+ const auto *Mul = dyn_cast<SCEVMulExpr>(LHS);
+ if (Mul && Mul->hasNoUnsignedWrap()) {
+ for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
+ if (Mul->getOperand(i) == RHS) {
+ SmallVector<SCEVUse, 2> Operands;
+ append_range(Operands, Mul->operands().take_front(i));
+ append_range(Operands, Mul->operands().drop_front(i + 1));
+ return getMulExpr(Operands);
+ }
+ }
+ }
+
+ // TODO: Generalize to handle any common factors.
+ // udiv (mul nuw a, vscale), (mul nuw b, vscale) --> udiv a, b
+ const SCEV *NewLHS, *NewRHS;
+ if (match(LHS, m_scev_c_NUWMul(m_SCEV(NewLHS), m_SCEVVScale())) &&
+ match(RHS, m_scev_c_NUWMul(m_SCEV(NewRHS), m_SCEVVScale())))
+ return getUDivExpr(NewLHS, NewRHS);
+
+ // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs
+ // changes). Make sure we get a new one.
+ IP = nullptr;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
+ LHS, RHS);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, ArrayRef<SCEVUse>({LHS, RHS}));
+ return S;
+}
+
+APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
+ APInt A = C1->getAPInt().abs();
+ APInt B = C2->getAPInt().abs();
+ uint32_t ABW = A.getBitWidth();
+ uint32_t BBW = B.getBitWidth();
+
+ if (ABW > BBW)
+ B = B.zext(ABW);
+ else if (ABW < BBW)
+ A = A.zext(BBW);
+
+ return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
+}
+
+/// Get a canonical unsigned division expression, or something simpler if
+/// possible. There is no representation for an exact udiv in SCEV IR, but we
+/// can attempt to optimize it prior to construction.
+const SCEV *ScalarEvolution::getUDivExactExpr(SCEVUse LHS, SCEVUse RHS) {
+ // Currently there is no exact specific logic.
+
+ return getUDivExpr(LHS, RHS);
+}
+
+/// Get an add recurrence expression for the specified loop. Simplify the
+/// expression as much as possible.
+const SCEV *ScalarEvolution::getAddRecExpr(SCEVUse Start, SCEVUse Step,
+ const Loop *L,
+ SCEV::NoWrapFlags Flags) {
+ SmallVector<SCEVUse, 4> Operands;
+ Operands.push_back(Start);
+ if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
+ if (StepChrec->getLoop() == L) {
+ append_range(Operands, StepChrec->operands());
+ return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
+ }
+
+ Operands.push_back(Step);
+ return getAddRecExpr(Operands, L, Flags);
+}
+
+/// Get an add recurrence expression for the specified loop. Simplify the
+/// expression as much as possible.
+const SCEV *ScalarEvolution::getAddRecExpr(SmallVectorImpl<SCEVUse> &Operands,
+ const Loop *L,
+ SCEV::NoWrapFlags Flags) {
+ if (Operands.size() == 1) return Operands[0];
+#ifndef NDEBUG
+ Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
+ for (const SCEV *Op : llvm::drop_begin(Operands)) {
+ assert(getEffectiveSCEVType(Op->getType()) == ETy &&
+ "SCEVAddRecExpr operand types don't match!");
+ assert(!Op->getType()->isPointerTy() && "Step must be integer");
+ }
+ for (const SCEV *Op : Operands)
+ assert(isAvailableAtLoopEntry(Op, L) &&
+ "SCEVAddRecExpr operand is not available at loop entry!");
+#endif
+
+ if (Operands.back()->isZero()) {
+ Operands.pop_back();
+ return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
+ }
+
+ // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
+ // use that information to infer NUW and NSW flags. However, computing a
+ // BE count requires calling getAddRecExpr, so we may not yet have a
+ // meaningful BE count at this point (and if we don't, we'd be stuck
+ // with a SCEVCouldNotCompute as the cached BE count).
+
+ Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
+
+ // Canonicalize nested AddRecs in by nesting them in order of loop depth.
+ if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
+ const Loop *NestedLoop = NestedAR->getLoop();
+ if (L->contains(NestedLoop)
+ ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
+ : (!NestedLoop->contains(L) &&
+ DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
+ SmallVector<SCEVUse, 4> NestedOperands(NestedAR->operands());
+ Operands[0] = NestedAR->getStart();
+ // AddRecs require their operands be loop-invariant with respect to their
+ // loops. Don't perform this transformation if it would break this
+ // requirement.
+ bool AllInvariant = all_of(
+ Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
+
+ if (AllInvariant) {
+ // Create a recurrence for the outer loop with the same step size.
+ //
+ // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
+ // inner recurrence has the same property.
+ SCEV::NoWrapFlags OuterFlags =
+ maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
+
+ NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
+ AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
+ return isLoopInvariant(Op, NestedLoop);
+ });
+
+ if (AllInvariant) {
+ // Ok, both add recurrences are valid after the transformation.
+ //
+ // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
+ // the outer recurrence has the same property.
+ SCEV::NoWrapFlags InnerFlags =
+ maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
+ return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
+ }
+ }
+ // Reset Operands to its original state.
+ Operands[0] = NestedAR;
+ }
+ }
+
+ // Okay, it looks like we really DO need an addrec expr. Check to see if we
+ // already have one, otherwise create a new one.
+ return getOrCreateAddRecExpr(Operands, L, Flags);
+}
+
+const SCEV *ScalarEvolution::getGEPExpr(GEPOperator *GEP,
+ ArrayRef<SCEVUse> IndexExprs) {
+ const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
+ // getSCEV(Base)->getType() has the same address space as Base->getType()
+ // because SCEV::getType() preserves the address space.
+ GEPNoWrapFlags NW = GEP->getNoWrapFlags();
+ if (NW != GEPNoWrapFlags::none()) {
+ // We'd like to propagate flags from the IR to the corresponding SCEV nodes,
+ // but to do that, we have to ensure that said flag is valid in the entire
+ // defined scope of the SCEV.
+ // TODO: non-instructions have global scope. We might be able to prove
+ // some global scope cases
+ auto *GEPI = dyn_cast<Instruction>(GEP);
+ if (!GEPI || !isSCEVExprNeverPoison(GEPI))
+ NW = GEPNoWrapFlags::none();
+ }
+
+ return getGEPExpr(BaseExpr, IndexExprs, GEP->getSourceElementType(), NW);
+}
+
+const SCEV *ScalarEvolution::getGEPExpr(SCEVUse BaseExpr,
+ ArrayRef<SCEVUse> IndexExprs,
+ Type *SrcElementTy, GEPNoWrapFlags NW) {
+ SCEV::NoWrapFlags OffsetWrap = SCEV::FlagAnyWrap;
+ if (NW.hasNoUnsignedSignedWrap())
+ OffsetWrap = setFlags(OffsetWrap, SCEV::FlagNSW);
+ if (NW.hasNoUnsignedWrap())
+ OffsetWrap = setFlags(OffsetWrap, SCEV::FlagNUW);
+
+ Type *CurTy = BaseExpr->getType();
+ Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
+ bool FirstIter = true;
+ SmallVector<SCEVUse, 4> Offsets;
+ for (SCEVUse IndexExpr : IndexExprs) {
+ // Compute the (potentially symbolic) offset in bytes for this index.
+ if (StructType *STy = dyn_cast<StructType>(CurTy)) {
+ // For a struct, add the member offset.
+ ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
+ unsigned FieldNo = Index->getZExtValue();
+ const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
+ Offsets.push_back(FieldOffset);
+
+ // Update CurTy to the type of the field at Index.
+ CurTy = STy->getTypeAtIndex(Index);
+ } else {
+ // Update CurTy to its element type.
+ if (FirstIter) {
+ assert(isa<PointerType>(CurTy) &&
+ "The first index of a GEP indexes a pointer");
+ CurTy = SrcElementTy;
+ FirstIter = false;
+ } else {
+ CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0);
+ }
+ // For an array, add the element offset, explicitly scaled.
+ const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
+ // Getelementptr indices are signed.
+ IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);
+
+ // Multiply the index by the element size to compute the element offset.
+ const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, OffsetWrap);
+ Offsets.push_back(LocalOffset);
+ }
+ }
+
+ // Handle degenerate case of GEP without offsets.
+ if (Offsets.empty())
+ return BaseExpr;
+
+ // Add the offsets together, assuming nsw if inbounds.
+ const SCEV *Offset = getAddExpr(Offsets, OffsetWrap);
+ // Add the base address and the offset. We cannot use the nsw flag, as the
+ // base address is unsigned. However, if we know that the offset is
+ // non-negative, we can use nuw.
+ bool NUW = NW.hasNoUnsignedWrap() ||
+ (NW.hasNoUnsignedSignedWrap() && isKnownNonNegative(Offset));
+ SCEV::NoWrapFlags BaseWrap = NUW ? SCEV::FlagNUW : SCEV::FlagAnyWrap;
+ auto *GEPExpr = getAddExpr(BaseExpr, Offset, BaseWrap);
+ assert(BaseExpr->getType() == GEPExpr->getType() &&
+ "GEP should not change type mid-flight.");
+ return GEPExpr;
+}
+
+SCEV *ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
+ ArrayRef<const SCEV *> Ops) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(SCEVType);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ void *IP = nullptr;
+ return UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
+}
+
+SCEV *ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
+ ArrayRef<SCEVUse> Ops) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(SCEVType);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ void *IP = nullptr;
+ return UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
+}
+
+const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) {
+ SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
+ return getSMaxExpr(Op, getNegativeSCEV(Op, Flags));
+}
+
+const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind,
+ SmallVectorImpl<SCEVUse> &Ops) {
+ assert(SCEVMinMaxExpr::isMinMaxType(Kind) && "Not a SCEVMinMaxExpr!");
+ assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
+ assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
+ "Operand types don't match!");
+ assert(Ops[0]->getType()->isPointerTy() ==
+ Ops[i]->getType()->isPointerTy() &&
+ "min/max should be consistently pointerish");
+ }
+#endif
+
+ bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
+ bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
+
+ const SCEV *Folded = constantFoldAndGroupOps(
+ *this, LI, DT, Ops,
+ [&](const APInt &C1, const APInt &C2) {
+ switch (Kind) {
+ case scSMaxExpr:
+ return APIntOps::smax(C1, C2);
+ case scSMinExpr:
+ return APIntOps::smin(C1, C2);
+ case scUMaxExpr:
+ return APIntOps::umax(C1, C2);
+ case scUMinExpr:
+ return APIntOps::umin(C1, C2);
+ default:
+ llvm_unreachable("Unknown SCEV min/max opcode");
+ }
+ },
+ [&](const APInt &C) {
+ // identity
+ if (IsMax)
+ return IsSigned ? C.isMinSignedValue() : C.isMinValue();
+ else
+ return IsSigned ? C.isMaxSignedValue() : C.isMaxValue();
+ },
+ [&](const APInt &C) {
+ // absorber
+ if (IsMax)
+ return IsSigned ? C.isMaxSignedValue() : C.isMaxValue();
+ else
+ return IsSigned ? C.isMinSignedValue() : C.isMinValue();
+ });
+ if (Folded)
+ return Folded;
+
+ // Check if we have created the same expression before.
+ if (const SCEV *S = findExistingSCEVInCache(Kind, Ops)) {
+ return S;
+ }
+
+ // Find the first operation of the same kind
+ unsigned Idx = 0;
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
+ ++Idx;
+
+ // Check to see if one of the operands is of the same kind. If so, expand its
+ // operands onto our operand list, and recurse to simplify.
+ if (Idx < Ops.size()) {
+ bool DeletedAny = false;
+ while (Ops[Idx]->getSCEVType() == Kind) {
+ const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
+ Ops.erase(Ops.begin()+Idx);
+ append_range(Ops, SMME->operands());
+ DeletedAny = true;
+ }
+
+ if (DeletedAny)
+ return getMinMaxExpr(Kind, Ops);
+ }
+
+ // Okay, check to see if the same value occurs in the operand list twice. If
+ // so, delete one. Since we sorted the list, these values are required to
+ // be adjacent.
+ llvm::CmpInst::Predicate GEPred =
+ IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
+ llvm::CmpInst::Predicate LEPred =
+ IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
+ llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
+ llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
+ for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
+ if (Ops[i] == Ops[i + 1] ||
+ isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
+ // X op Y op Y --> X op Y
+ // X op Y --> X, if we know X, Y are ordered appropriately
+ Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
+ --i;
+ --e;
+ } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
+ Ops[i + 1])) {
+ // X op Y --> Y, if we know X, Y are ordered appropriately
+ Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
+ --i;
+ --e;
+ }
+ }
+
+ if (Ops.size() == 1) return Ops[0];
+
+ assert(!Ops.empty() && "Reduced smax down to nothing!");
+
+ // Okay, it looks like we really DO need an expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(Kind);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ void *IP = nullptr;
+ const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
+ if (ExistingSCEV)
+ return ExistingSCEV;
+ SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
+ llvm::uninitialized_copy(Ops, O);
+ SCEV *S = new (SCEVAllocator)
+ SCEVMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());
+
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Ops);
+ return S;
+}
+
+namespace {
+
+class SCEVSequentialMinMaxDeduplicatingVisitor final
+ : public SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor,
+ std::optional<const SCEV *>> {
+ using RetVal = std::optional<const SCEV *>;
+ using Base = SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor, RetVal>;
+
+ ScalarEvolution &SE;
+ const SCEVTypes RootKind; // Must be a sequential min/max expression.
+ const SCEVTypes NonSequentialRootKind; // Non-sequential variant of RootKind.
+ SmallPtrSet<const SCEV *, 16> SeenOps;
+
+ bool canRecurseInto(SCEVTypes Kind) const {
+ // We can only recurse into the SCEV expression of the same effective type
+ // as the type of our root SCEV expression.
+ return RootKind == Kind || NonSequentialRootKind == Kind;
+ };
+
+ RetVal visitAnyMinMaxExpr(const SCEV *S) {
+ assert((isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) &&
+ "Only for min/max expressions.");
+ SCEVTypes Kind = S->getSCEVType();
+
+ if (!canRecurseInto(Kind))
+ return S;
+
+ auto *NAry = cast<SCEVNAryExpr>(S);
+ SmallVector<SCEVUse> NewOps;
+ bool Changed = visit(Kind, NAry->operands(), NewOps);
+
+ if (!Changed)
+ return S;
+ if (NewOps.empty())
+ return std::nullopt;
+
+ return isa<SCEVSequentialMinMaxExpr>(S)
+ ? SE.getSequentialMinMaxExpr(Kind, NewOps)
+ : SE.getMinMaxExpr(Kind, NewOps);
+ }
+
+ RetVal visit(const SCEV *S) {
+ // Has the whole operand been seen already?
+ if (!SeenOps.insert(S).second)
+ return std::nullopt;
+ return Base::visit(S);
+ }
+
+public:
+ SCEVSequentialMinMaxDeduplicatingVisitor(ScalarEvolution &SE,
+ SCEVTypes RootKind)
+ : SE(SE), RootKind(RootKind),
+ NonSequentialRootKind(
+ SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
+ RootKind)) {}
+
+ bool /*Changed*/ visit(SCEVTypes Kind, ArrayRef<SCEVUse> OrigOps,
+ SmallVectorImpl<SCEVUse> &NewOps) {
+ bool Changed = false;
+ SmallVector<SCEVUse> Ops;
+ Ops.reserve(OrigOps.size());
+
+ for (const SCEV *Op : OrigOps) {
+ RetVal NewOp = visit(Op);
+ if (NewOp != Op)
+ Changed = true;
+ if (NewOp)
+ Ops.emplace_back(*NewOp);
+ }
+
+ if (Changed)
+ NewOps = std::move(Ops);
+ return Changed;
+ }
+
+ RetVal visitConstant(const SCEVConstant *Constant) { return Constant; }
+
+ RetVal visitVScale(const SCEVVScale *VScale) { return VScale; }
+
+ RetVal visitPtrToAddrExpr(const SCEVPtrToAddrExpr *Expr) { return Expr; }
+
+ RetVal visitTruncateExpr(const SCEVTruncateExpr *Expr) { return Expr; }
+
+ RetVal visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { return Expr; }
+
+ RetVal visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { return Expr; }
+
+ RetVal visitAddExpr(const SCEVAddExpr *Expr) { return Expr; }
+
+ RetVal visitMulExpr(const SCEVMulExpr *Expr) { return Expr; }
+
+ RetVal visitUDivExpr(const SCEVUDivExpr *Expr) { return Expr; }
+
+ RetVal visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
+
+ RetVal visitSMaxExpr(const SCEVSMaxExpr *Expr) {
+ return visitAnyMinMaxExpr(Expr);
+ }
+
+ RetVal visitUMaxExpr(const SCEVUMaxExpr *Expr) {
+ return visitAnyMinMaxExpr(Expr);
+ }
+
+ RetVal visitSMinExpr(const SCEVSMinExpr *Expr) {
+ return visitAnyMinMaxExpr(Expr);
+ }
+
+ RetVal visitUMinExpr(const SCEVUMinExpr *Expr) {
+ return visitAnyMinMaxExpr(Expr);
+ }
+
+ RetVal visitSequentialUMinExpr(const SCEVSequentialUMinExpr *Expr) {
+ return visitAnyMinMaxExpr(Expr);
+ }
+
+ RetVal visitUnknown(const SCEVUnknown *Expr) { return Expr; }
+
+ RetVal visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { return Expr; }
+};
+
+} // namespace
+
+static bool scevUnconditionallyPropagatesPoisonFromOperands(SCEVTypes Kind) {
+ switch (Kind) {
+ case scConstant:
+ case scVScale:
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUDivExpr:
+ case scAddRecExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scUnknown:
+ // If any operand is poison, the whole expression is poison.
+ return true;
+ case scSequentialUMinExpr:
+ // FIXME: if the *first* operand is poison, the whole expression is poison.
+ return false; // Pessimistically, say that it does not propagate poison.
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+namespace {
+// The only way poison may be introduced in a SCEV expression is from a
+// poison SCEVUnknown (ConstantExprs are also represented as SCEVUnknown,
+// not SCEVConstant). Notably, nowrap flags in SCEV nodes can *not*
+// introduce poison -- they encode guaranteed, non-speculated knowledge.
+//
+// Additionally, all SCEV nodes propagate poison from inputs to outputs,
+// with the notable exception of umin_seq, where only poison from the first
+// operand is (unconditionally) propagated.
+struct SCEVPoisonCollector {
+ bool LookThroughMaybePoisonBlocking;
+ SmallPtrSet<const SCEVUnknown *, 4> MaybePoison;
+ SCEVPoisonCollector(bool LookThroughMaybePoisonBlocking)
+ : LookThroughMaybePoisonBlocking(LookThroughMaybePoisonBlocking) {}
+
+ bool follow(const SCEV *S) {
+ if (!LookThroughMaybePoisonBlocking &&
+ !scevUnconditionallyPropagatesPoisonFromOperands(S->getSCEVType()))
+ return false;
+
+ if (auto *SU = dyn_cast<SCEVUnknown>(S)) {
+ if (!isGuaranteedNotToBePoison(SU->getValue()))
+ MaybePoison.insert(SU);
+ }
+ return true;
+ }
+ bool isDone() const { return false; }
+};
+} // namespace
+
+/// Return true if V is poison given that AssumedPoison is already poison.
+static bool impliesPoison(const SCEV *AssumedPoison, const SCEV *S) {
+ // First collect all SCEVs that might result in AssumedPoison to be poison.
+ // We need to look through potentially poison-blocking operations here,
+ // because we want to find all SCEVs that *might* result in poison, not only
+ // those that are *required* to.
+ SCEVPoisonCollector PC1(/* LookThroughMaybePoisonBlocking */ true);
+ visitAll(AssumedPoison, PC1);
+
+ // AssumedPoison is never poison. As the assumption is false, the implication
+ // is true. Don't bother walking the other SCEV in this case.
+ if (PC1.MaybePoison.empty())
+ return true;
+
+ // Collect all SCEVs in S that, if poison, *will* result in S being poison
+ // as well. We cannot look through potentially poison-blocking operations
+ // here, as their arguments only *may* make the result poison.
+ SCEVPoisonCollector PC2(/* LookThroughMaybePoisonBlocking */ false);
+ visitAll(S, PC2);
+
+ // Make sure that no matter which SCEV in PC1.MaybePoison is actually poison,
+ // it will also make S poison by being part of PC2.MaybePoison.
+ return llvm::set_is_subset(PC1.MaybePoison, PC2.MaybePoison);
+}
+
+void ScalarEvolution::getPoisonGeneratingValues(
+ SmallPtrSetImpl<const Value *> &Result, const SCEV *S) {
+ SCEVPoisonCollector PC(/* LookThroughMaybePoisonBlocking */ false);
+ visitAll(S, PC);
+ for (const SCEVUnknown *SU : PC.MaybePoison)
+ Result.insert(SU->getValue());
+}
+
+bool ScalarEvolution::canReuseInstruction(
+ const SCEV *S, Instruction *I,
+ SmallVectorImpl<Instruction *> &DropPoisonGeneratingInsts) {
+ // If the instruction cannot be poison, it's always safe to reuse.
+ if (programUndefinedIfPoison(I))
+ return true;
+
+ // Otherwise, it is possible that I is more poisonous that S. Collect the
+ // poison-contributors of S, and then check whether I has any additional
+ // poison-contributors. Poison that is contributed through poison-generating
+ // flags is handled by dropping those flags instead.
+ SmallPtrSet<const Value *, 8> PoisonVals;
+ getPoisonGeneratingValues(PoisonVals, S);
+
+ SmallVector<Value *> Worklist;
+ SmallPtrSet<Value *, 8> Visited;
+ Worklist.push_back(I);
+ while (!Worklist.empty()) {
+ Value *V = Worklist.pop_back_val();
+ if (!Visited.insert(V).second)
+ continue;
+
+ // Avoid walking large instruction graphs.
+ if (Visited.size() > 16)
+ return false;
+
+ // Either the value can't be poison, or the S would also be poison if it
+ // is.
+ if (PoisonVals.contains(V) || ::isGuaranteedNotToBePoison(V))
+ continue;
+
+ auto *I = dyn_cast<Instruction>(V);
+ if (!I)
+ return false;
+
+ // Disjoint or instructions are interpreted as adds by SCEV. However, we
+ // can't replace an arbitrary add with disjoint or, even if we drop the
+ // flag. We would need to convert the or into an add.
+ if (auto *PDI = dyn_cast<PossiblyDisjointInst>(I))
+ if (PDI->isDisjoint())
+ return false;
+
+ // FIXME: Ignore vscale, even though it technically could be poison. Do this
+ // because SCEV currently assumes it can't be poison. Remove this special
+ // case once we proper model when vscale can be poison.
+ if (auto *II = dyn_cast<IntrinsicInst>(I);
+ II && II->getIntrinsicID() == Intrinsic::vscale)
+ continue;
+
+ if (canCreatePoison(cast<Operator>(I), /*ConsiderFlagsAndMetadata*/ false))
+ return false;
+
+ // If the instruction can't create poison, we can recurse to its operands.
+ if (I->hasPoisonGeneratingAnnotations())
+ DropPoisonGeneratingInsts.push_back(I);
+
+ llvm::append_range(Worklist, I->operands());
+ }
+ return true;
+}
+
+const SCEV *
+ScalarEvolution::getSequentialMinMaxExpr(SCEVTypes Kind,
+ SmallVectorImpl<SCEVUse> &Ops) {
+ assert(SCEVSequentialMinMaxExpr::isSequentialMinMaxType(Kind) &&
+ "Not a SCEVSequentialMinMaxExpr!");
+ assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
+ if (Ops.size() == 1)
+ return Ops[0];
+#ifndef NDEBUG
+ Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
+ assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
+ "Operand types don't match!");
+ assert(Ops[0]->getType()->isPointerTy() ==
+ Ops[i]->getType()->isPointerTy() &&
+ "min/max should be consistently pointerish");
+ }
+#endif
+
+ // Note that SCEVSequentialMinMaxExpr is *NOT* commutative,
+ // so we can *NOT* do any kind of sorting of the expressions!
+
+ // Check if we have created the same expression before.
+ if (const SCEV *S = findExistingSCEVInCache(Kind, Ops))
+ return S;
+
+ // FIXME: there are *some* simplifications that we can do here.
+
+ // Keep only the first instance of an operand.
+ {
+ SCEVSequentialMinMaxDeduplicatingVisitor Deduplicator(*this, Kind);
+ bool Changed = Deduplicator.visit(Kind, Ops, Ops);
+ if (Changed)
+ return getSequentialMinMaxExpr(Kind, Ops);
+ }
+
+ // Check to see if one of the operands is of the same kind. If so, expand its
+ // operands onto our operand list, and recurse to simplify.
+ {
+ unsigned Idx = 0;
+ bool DeletedAny = false;
+ while (Idx < Ops.size()) {
+ if (Ops[Idx]->getSCEVType() != Kind) {
+ ++Idx;
+ continue;
+ }
+ const auto *SMME = cast<SCEVSequentialMinMaxExpr>(Ops[Idx]);
+ Ops.erase(Ops.begin() + Idx);
+ Ops.insert(Ops.begin() + Idx, SMME->operands().begin(),
+ SMME->operands().end());
+ DeletedAny = true;
+ }
+
+ if (DeletedAny)
+ return getSequentialMinMaxExpr(Kind, Ops);
+ }
+
+ const SCEV *SaturationPoint;
+ ICmpInst::Predicate Pred;
+ switch (Kind) {
+ case scSequentialUMinExpr:
+ SaturationPoint = getZero(Ops[0]->getType());
+ Pred = ICmpInst::ICMP_ULE;
+ break;
+ default:
+ llvm_unreachable("Not a sequential min/max type.");
+ }
+
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
+ if (!isGuaranteedNotToCauseUB(Ops[i]))
+ continue;
+ // We can replace %x umin_seq %y with %x umin %y if either:
+ // * %y being poison implies %x is also poison.
+ // * %x cannot be the saturating value (e.g. zero for umin).
+ if (::impliesPoison(Ops[i], Ops[i - 1]) ||
+ isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, Ops[i - 1],
+ SaturationPoint)) {
+ SmallVector<SCEVUse, 2> SeqOps = {Ops[i - 1], Ops[i]};
+ Ops[i - 1] = getMinMaxExpr(
+ SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(Kind),
+ SeqOps);
+ Ops.erase(Ops.begin() + i);
+ return getSequentialMinMaxExpr(Kind, Ops);
+ }
+ // Fold %x umin_seq %y to %x if %x ule %y.
+ // TODO: We might be able to prove the predicate for a later operand.
+ if (isKnownViaNonRecursiveReasoning(Pred, Ops[i - 1], Ops[i])) {
+ Ops.erase(Ops.begin() + i);
+ return getSequentialMinMaxExpr(Kind, Ops);
+ }
+ }
+
+ // Okay, it looks like we really DO need an expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(Kind);
+ for (const SCEV *Op : Ops)
+ ID.AddPointer(Op);
+ void *IP = nullptr;
+ const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
+ if (ExistingSCEV)
+ return ExistingSCEV;
+
+ SCEVUse *O = SCEVAllocator.Allocate<SCEVUse>(Ops.size());
+ llvm::uninitialized_copy(Ops, O);
+ SCEV *S = new (SCEVAllocator)
+ SCEVSequentialMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());
+
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ registerUser(S, Ops);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getSMaxExpr(SCEVUse LHS, SCEVUse RHS) {
+ SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
+ return getMinMaxExpr(scSMaxExpr, Ops);
+}
+
+const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<SCEVUse> &Ops) {
+ return getMinMaxExpr(scSMaxExpr, Ops);
+}
+
+const SCEV *ScalarEvolution::getUMaxExpr(SCEVUse LHS, SCEVUse RHS) {
+ SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
+ return getMinMaxExpr(scUMaxExpr, Ops);
+}
+
+const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<SCEVUse> &Ops) {
+ return getMinMaxExpr(scUMaxExpr, Ops);
+}
+
+const SCEV *ScalarEvolution::getSMinExpr(SCEVUse LHS, SCEVUse RHS) {
+ SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
+ return getMinMaxExpr(scSMinExpr, Ops);
+}
+
+const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<SCEVUse> &Ops) {
+ return getMinMaxExpr(scSMinExpr, Ops);
+}
+
+const SCEV *ScalarEvolution::getUMinExpr(SCEVUse LHS, SCEVUse RHS,
+ bool Sequential) {
+ SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
+ return getUMinExpr(Ops, Sequential);
+}
+
+const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<SCEVUse> &Ops,
+ bool Sequential) {
+ return Sequential ? getSequentialMinMaxExpr(scSequentialUMinExpr, Ops)
+ : getMinMaxExpr(scUMinExpr, Ops);
+}
+
+const SCEV *
+ScalarEvolution::getSizeOfExpr(Type *IntTy, TypeSize Size) {
+ const SCEV *Res = getConstant(IntTy, Size.getKnownMinValue());
+ if (Size.isScalable())
+ Res = getMulExpr(Res, getVScale(IntTy));
+ return Res;
+}
+
+const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
+ return getSizeOfExpr(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
+}
+
+const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) {
+ return getSizeOfExpr(IntTy, getDataLayout().getTypeStoreSize(StoreTy));
+}
+
+const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
+ StructType *STy,
+ unsigned FieldNo) {
+ // We can bypass creating a target-independent constant expression and then
+ // folding it back into a ConstantInt. This is just a compile-time
+ // optimization.
+ const StructLayout *SL = getDataLayout().getStructLayout(STy);
+ assert(!SL->getSizeInBits().isScalable() &&
+ "Cannot get offset for structure containing scalable vector types");
+ return getConstant(IntTy, SL->getElementOffset(FieldNo));
+}
+
+const SCEV *ScalarEvolution::getUnknown(Value *V) {
+ // Don't attempt to do anything other than create a SCEVUnknown object
+ // here. createSCEV only calls getUnknown after checking for all other
+ // interesting possibilities, and any other code that calls getUnknown
+ // is doing so in order to hide a value from SCEV canonicalization.
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scUnknown);
+ ID.AddPointer(V);
+ void *IP = nullptr;
+ if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
+ assert(cast<SCEVUnknown>(S)->getValue() == V &&
+ "Stale SCEVUnknown in uniquing map!");
+ return S;
+ }
+ SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
+ FirstUnknown);
+ FirstUnknown = cast<SCEVUnknown>(S);
+ UniqueSCEVs.InsertNode(S, IP);
+ S->computeAndSetCanonical(*this);
+ return S;
+}
+
+//===----------------------------------------------------------------------===//
+// Basic SCEV Analysis and PHI Idiom Recognition Code
+//
+
+/// Test if values of the given type are analyzable within the SCEV
+/// framework. This primarily includes integer types, and it can optionally
+/// include pointer types if the ScalarEvolution class has access to
+/// target-specific information.
+bool ScalarEvolution::isSCEVable(Type *Ty) const {
+ // Integers and pointers are always SCEVable.
+ return Ty->isIntOrPtrTy();
+}
+
+/// Return the size in bits of the specified type, for which isSCEVable must
+/// return true.
+uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
+ assert(isSCEVable(Ty) && "Type is not SCEVable!");
+ if (Ty->isPointerTy())
+ return getDataLayout().getIndexTypeSizeInBits(Ty);
+ return getDataLayout().getTypeSizeInBits(Ty);
+}
+
+/// Return a type with the same bitwidth as the given type and which represents
+/// how SCEV will treat the given type, for which isSCEVable must return
+/// true. For pointer types, this is the pointer index sized integer type.
+Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
+ assert(isSCEVable(Ty) && "Type is not SCEVable!");
+
+ if (Ty->isIntegerTy())
+ return Ty;
+
+ // The only other support type is pointer.
+ assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
+ return getDataLayout().getIndexType(Ty);
+}
+
+Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
+ return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
+}
+
+bool ScalarEvolution::instructionCouldExistWithOperands(const SCEV *A,
+ const SCEV *B) {
+ /// For a valid use point to exist, the defining scope of one operand
+ /// must dominate the other.
+ bool PreciseA, PreciseB;
+ auto *ScopeA = getDefiningScopeBound({A}, PreciseA);
+ auto *ScopeB = getDefiningScopeBound({B}, PreciseB);
+ if (!PreciseA || !PreciseB)
+ // Can't tell.
+ return false;
+ return (ScopeA == ScopeB) || DT.dominates(ScopeA, ScopeB) ||
+ DT.dominates(ScopeB, ScopeA);
+}
+
+const SCEV *ScalarEvolution::getCouldNotCompute() {
+ return CouldNotCompute.get();
+}
+
+bool ScalarEvolution::checkValidity(const SCEV *S) const {
+ bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
+ auto *SU = dyn_cast<SCEVUnknown>(S);
+ return SU && SU->getValue() == nullptr;
+ });
+
+ return !ContainsNulls;
+}
+
+bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
+ HasRecMapType::iterator I = HasRecMap.find(S);
+ if (I != HasRecMap.end())
+ return I->second;
+
+ bool FoundAddRec =
+ SCEVExprContains(S, [](const SCEV *S) { return isa<SCEVAddRecExpr>(S); });
+ HasRecMap.insert({S, FoundAddRec});
+ return FoundAddRec;
+}
+
+/// Return the ValueOffsetPair set for \p S. \p S can be represented
+/// by the value and offset from any ValueOffsetPair in the set.
+ArrayRef<Value *> ScalarEvolution::getSCEVValues(const SCEV *S) {
+ ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
+ if (SI == ExprValueMap.end())
+ return {};
+ return SI->second.getArrayRef();
+}
+
+/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
+/// cannot be used separately. eraseValueFromMap should be used to remove
+/// V from ValueExprMap and ExprValueMap at the same time.
+void ScalarEvolution::eraseValueFromMap(Value *V) {
+ ValueExprMapType::iterator I = ValueExprMap.find_as(V);
+ if (I != ValueExprMap.end()) {
+ auto EVIt = ExprValueMap.find(I->second);
+ bool Removed = EVIt->second.remove(V);
+ (void) Removed;
+ assert(Removed && "Value not in ExprValueMap?");
+ ValueExprMap.erase(I);
+ }
+}
+
+void ScalarEvolution::insertValueToMap(Value *V, const SCEV *S) {
+ // A recursive query may have already computed the SCEV. It should be
+ // equivalent, but may not necessarily be exactly the same, e.g. due to lazily
+ // inferred nowrap flags.
+ auto It = ValueExprMap.find_as(V);
+ if (It == ValueExprMap.end()) {
+ ValueExprMap.insert({SCEVCallbackVH(V, this), S});
+ ExprValueMap[S].insert(V);
+ }
+}
+
+/// Return an existing SCEV if it exists, otherwise analyze the expression and
+/// create a new one.
+const SCEV *ScalarEvolution::getSCEV(Value *V) {
+ assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
+
+ if (const SCEV *S = getExistingSCEV(V))
+ return S;
+ return createSCEVIter(V);
+}
+
+const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
+ assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
+
+ ValueExprMapType::iterator I = ValueExprMap.find_as(V);
+ if (I != ValueExprMap.end()) {
+ const SCEV *S = I->second;
+ assert(checkValidity(S) &&
+ "existing SCEV has not been properly invalidated");
+ return S;
+ }
+ return nullptr;
+}
+
+/// Return a SCEV corresponding to -V = -1*V
+const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
+ SCEV::NoWrapFlags Flags) {
+ if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getConstant(
+ cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
+
+ Type *Ty = V->getType();
+ Ty = getEffectiveSCEVType(Ty);
+ return getMulExpr(V, getMinusOne(Ty), Flags);
+}
+
+/// If Expr computes ~A, return A else return nullptr
+static const SCEV *MatchNotExpr(const SCEV *Expr) {
+ const SCEV *MulOp;
+ if (match(Expr, m_scev_Add(m_scev_AllOnes(),
+ m_scev_Mul(m_scev_AllOnes(), m_SCEV(MulOp)))))
+ return MulOp;
+ return nullptr;
+}
+
+/// Return a SCEV corresponding to ~V = -1-V
+const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
+ assert(!V->getType()->isPointerTy() && "Can't negate pointer");
+
+ if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getConstant(
+ cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
+
+ // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
+ if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
+ auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
+ SmallVector<SCEVUse, 2> MatchedOperands;
+ for (const SCEV *Operand : MME->operands()) {
+ const SCEV *Matched = MatchNotExpr(Operand);
+ if (!Matched)
+ return (const SCEV *)nullptr;
+ MatchedOperands.push_back(Matched);
+ }
+ return getMinMaxExpr(SCEVMinMaxExpr::negate(MME->getSCEVType()),
+ MatchedOperands);
+ };
+ if (const SCEV *Replaced = MatchMinMaxNegation(MME))
+ return Replaced;
+ }
+
+ Type *Ty = V->getType();
+ Ty = getEffectiveSCEVType(Ty);
+ return getMinusSCEV(getMinusOne(Ty), V);
+}
+
+const SCEV *ScalarEvolution::removePointerBase(const SCEV *P) {
+ assert(P->getType()->isPointerTy());
+
+ if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(P)) {
+ // The base of an AddRec is the first operand.
+ SmallVector<SCEVUse> Ops{AddRec->operands()};
+ Ops[0] = removePointerBase(Ops[0]);
+ // Don't try to transfer nowrap flags for now. We could in some cases
+ // (for example, if pointer operand of the AddRec is a SCEVUnknown).
+ return getAddRecExpr(Ops, AddRec->getLoop(), SCEV::FlagAnyWrap);
+ }
+ if (auto *Add = dyn_cast<SCEVAddExpr>(P)) {
+ // The base of an Add is the pointer operand.
+ SmallVector<SCEVUse> Ops{Add->operands()};
+ SCEVUse *PtrOp = nullptr;
+ for (SCEVUse &AddOp : Ops) {
+ if (AddOp->getType()->isPointerTy()) {
+ assert(!PtrOp && "Cannot have multiple pointer ops");
+ PtrOp = &AddOp;
+ }
+ }
+ *PtrOp = removePointerBase(*PtrOp);
+ // Don't try to transfer nowrap flags for now. We could in some cases
+ // (for example, if the pointer operand of the Add is a SCEVUnknown).
+ return getAddExpr(Ops);
+ }
+ // Any other expression must be a pointer base.
+ return getZero(P->getType());
+}
+
+const SCEV *ScalarEvolution::getMinusSCEV(SCEVUse LHS, SCEVUse RHS,
+ SCEV::NoWrapFlags Flags,
+ unsigned Depth) {
+ // Fast path: X - X --> 0.
+ if (LHS == RHS)
+ return getZero(LHS->getType());
+
+ // If we subtract two pointers with different pointer bases, bail.
+ // Eventually, we're going to add an assertion to getMulExpr that we
+ // can't multiply by a pointer.
+ if (RHS->getType()->isPointerTy()) {
+ if (!LHS->getType()->isPointerTy() ||
+ getPointerBase(LHS) != getPointerBase(RHS))
+ return getCouldNotCompute();
+ LHS = removePointerBase(LHS);
+ RHS = removePointerBase(RHS);
+ }
+
+ // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
+ // makes it so that we cannot make much use of NUW.
+ auto AddFlags = SCEV::FlagAnyWrap;
+ const bool RHSIsNotMinSigned =
+ !getSignedRangeMin(RHS).isMinSignedValue();
+ if (hasFlags(Flags, SCEV::FlagNSW)) {
+ // Let M be the minimum representable signed value. Then (-1)*RHS
+ // signed-wraps if and only if RHS is M. That can happen even for
+ // a NSW subtraction because e.g. (-1)*M signed-wraps even though
+ // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
+ // (-1)*RHS, we need to prove that RHS != M.
+ //
+ // If LHS is non-negative and we know that LHS - RHS does not
+ // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
+ // either by proving that RHS > M or that LHS >= 0.
+ if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
+ AddFlags = SCEV::FlagNSW;
+ }
+ }
+
+ // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
+ // RHS is NSW and LHS >= 0.
+ //
+ // The difficulty here is that the NSW flag may have been proven
+ // relative to a loop that is to be found in a recurrence in LHS and
+ // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
+ // larger scope than intended.
+ auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
+
+ return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
+}
+
+const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
+ unsigned Depth) {
+ Type *SrcTy = V->getType();
+ assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
+ "Cannot truncate or zero extend with non-integer arguments!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
+ return getTruncateExpr(V, Ty, Depth);
+ return getZeroExtendExpr(V, Ty, Depth);
+}
+
+const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
+ unsigned Depth) {
+ Type *SrcTy = V->getType();
+ assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
+ "Cannot truncate or zero extend with non-integer arguments!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
+ return getTruncateExpr(V, Ty, Depth);
+ return getSignExtendExpr(V, Ty, Depth);
+}
+
+const SCEV *
+ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
+ Type *SrcTy = V->getType();
+ assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
+ "Cannot noop or zero extend with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
+ "getNoopOrZeroExtend cannot truncate!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getZeroExtendExpr(V, Ty);
+}
+
+const SCEV *
+ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
+ Type *SrcTy = V->getType();
+ assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
+ "Cannot noop or sign extend with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
+ "getNoopOrSignExtend cannot truncate!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getSignExtendExpr(V, Ty);
+}
+
+const SCEV *
+ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
+ Type *SrcTy = V->getType();
+ assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
+ "Cannot noop or any extend with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
+ "getNoopOrAnyExtend cannot truncate!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getAnyExtendExpr(V, Ty);
+}
+
+const SCEV *
+ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
+ Type *SrcTy = V->getType();
+ assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
+ "Cannot truncate or noop with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
+ "getTruncateOrNoop cannot extend!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getTruncateExpr(V, Ty);
+}
+
+const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
+ const SCEV *RHS) {
+ const SCEV *PromotedLHS = LHS;
+ const SCEV *PromotedRHS = RHS;
+
+ if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
+ PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
+ else
+ PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
+
+ return getUMaxExpr(PromotedLHS, PromotedRHS);
+}
+
+const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
+ const SCEV *RHS,
+ bool Sequential) {
+ SmallVector<SCEVUse, 2> Ops = {LHS, RHS};
+ return getUMinFromMismatchedTypes(Ops, Sequential);
+}
+
+const SCEV *
+ScalarEvolution::getUMinFromMismatchedTypes(SmallVectorImpl<SCEVUse> &Ops,
+ bool Sequential) {
+ assert(!Ops.empty() && "At least one operand must be!");
+ // Trivial case.
+ if (Ops.size() == 1)
+ return Ops[0];
+
+ // Find the max type first.
+ Type *MaxType = nullptr;
+ for (SCEVUse S : Ops)
+ if (MaxType)
+ MaxType = getWiderType(MaxType, S->getType());
+ else
+ MaxType = S->getType();
+ assert(MaxType && "Failed to find maximum type!");
+
+ // Extend all ops to max type.
+ SmallVector<SCEVUse, 2> PromotedOps;
+ for (SCEVUse S : Ops)
+ PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
+
+ // Generate umin.
+ return getUMinExpr(PromotedOps, Sequential);
+}
+
+const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
+ // A pointer operand may evaluate to a nonpointer expression, such as null.
+ if (!V->getType()->isPointerTy())
+ return V;
+
+ while (true) {
+ if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
+ V = AddRec->getStart();
+ } else if (auto *Add = dyn_cast<SCEVAddExpr>(V)) {
+ const SCEV *PtrOp = nullptr;
+ for (const SCEV *AddOp : Add->operands()) {
+ if (AddOp->getType()->isPointerTy()) {
+ assert(!PtrOp && "Cannot have multiple pointer ops");
+ PtrOp = AddOp;
+ }
+ }
+ assert(PtrOp && "Must have pointer op");
+ V = PtrOp;
+ } else // Not something we can look further into.
+ return V;
+ }
+}
+
+/// Push users of the given Instruction onto the given Worklist.
+static void PushDefUseChildren(Instruction *I,
+ SmallVectorImpl<Instruction *> &Worklist,
+ SmallPtrSetImpl<Instruction *> &Visited) {
+ // Push the def-use children onto the Worklist stack.
+ for (User *U : I->users()) {
+ auto *UserInsn = cast<Instruction>(U);
+ if (Visited.insert(UserInsn).second)
+ Worklist.push_back(UserInsn);
+ }
+}
+
+namespace {
+
+/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
+/// expression in case its Loop is L. If it is not L then
+/// if IgnoreOtherLoops is true then use AddRec itself
+/// otherwise rewrite cannot be done.
+/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
+class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
+public:
+ static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
+ bool IgnoreOtherLoops = true) {
+ SCEVInitRewriter Rewriter(L, SE);
+ const SCEV *Result = Rewriter.visit(S);
+ if (Rewriter.hasSeenLoopVariantSCEVUnknown())
+ return SE.getCouldNotCompute();
+ return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
+ ? SE.getCouldNotCompute()
+ : Result;
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ if (!SE.isLoopInvariant(Expr, L))
+ SeenLoopVariantSCEVUnknown = true;
+ return Expr;
+ }
+
+ const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
+ // Only re-write AddRecExprs for this loop.
+ if (Expr->getLoop() == L)
+ return Expr->getStart();
+ SeenOtherLoops = true;
+ return Expr;
+ }
+
+ bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
+
+ bool hasSeenOtherLoops() { return SeenOtherLoops; }
+
+private:
+ explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
+ : SCEVRewriteVisitor(SE), L(L) {}
+
+ const Loop *L;
+ bool SeenLoopVariantSCEVUnknown = false;
+ bool SeenOtherLoops = false;
+};
+
+/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
+/// increment expression in case its Loop is L. If it is not L then
+/// use AddRec itself.
+/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
+class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
+public:
+ static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
+ SCEVPostIncRewriter Rewriter(L, SE);
+ const SCEV *Result = Rewriter.visit(S);
+ return Rewriter.hasSeenLoopVariantSCEVUnknown()
+ ? SE.getCouldNotCompute()
+ : Result;
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ if (!SE.isLoopInvariant(Expr, L))
+ SeenLoopVariantSCEVUnknown = true;
+ return Expr;
+ }
+
+ const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
+ // Only re-write AddRecExprs for this loop.
+ if (Expr->getLoop() == L)
+ return Expr->getPostIncExpr(SE);
+ SeenOtherLoops = true;
+ return Expr;
+ }
+
+ bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
+
+ bool hasSeenOtherLoops() { return SeenOtherLoops; }
+
+private:
+ explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
+ : SCEVRewriteVisitor(SE), L(L) {}
+
+ const Loop *L;
+ bool SeenLoopVariantSCEVUnknown = false;
+ bool SeenOtherLoops = false;
+};
+
+/// This class evaluates the compare condition by matching it against the
+/// condition of loop latch. If there is a match we assume a true value
+/// for the condition while building SCEV nodes.
+class SCEVBackedgeConditionFolder
+ : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
+public:
+ static const SCEV *rewrite(const SCEV *S, const Loop *L,
+ ScalarEvolution &SE) {
+ bool IsPosBECond = false;
+ Value *BECond = nullptr;
+ if (BasicBlock *Latch = L->getLoopLatch()) {
+ if (CondBrInst *BI = dyn_cast<CondBrInst>(Latch->getTerminator())) {
+ assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
+ "Both outgoing branches should not target same header!");
+ BECond = BI->getCondition();
+ IsPosBECond = BI->getSuccessor(0) == L->getHeader();
+ } else {
+ return S;
+ }
+ }
+ SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
+ return Rewriter.visit(S);
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ const SCEV *Result = Expr;
+ bool InvariantF = SE.isLoopInvariant(Expr, L);
+
+ if (!InvariantF) {
+ Instruction *I = cast<Instruction>(Expr->getValue());
+ switch (I->getOpcode()) {
+ case Instruction::Select: {
+ SelectInst *SI = cast<SelectInst>(I);
+ std::optional<const SCEV *> Res =
+ compareWithBackedgeCondition(SI->getCondition());
+ if (Res) {
+ bool IsOne = cast<SCEVConstant>(*Res)->getValue()->isOne();
+ Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
+ }
+ break;
+ }
+ default: {
+ std::optional<const SCEV *> Res = compareWithBackedgeCondition(I);
+ if (Res)
+ Result = *Res;
+ break;
+ }
+ }
+ }
+ return Result;
+ }
+
+private:
+ explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
+ bool IsPosBECond, ScalarEvolution &SE)
+ : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
+ IsPositiveBECond(IsPosBECond) {}
+
+ std::optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
+
+ const Loop *L;
+ /// Loop back condition.
+ Value *BackedgeCond = nullptr;
+ /// Set to true if loop back is on positive branch condition.
+ bool IsPositiveBECond;
+};
+
+std::optional<const SCEV *>
+SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
+
+ // If value matches the backedge condition for loop latch,
+ // then return a constant evolution node based on loopback
+ // branch taken.
+ if (BackedgeCond == IC)
+ return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
+ : SE.getZero(Type::getInt1Ty(SE.getContext()));
+ return std::nullopt;
+}
+
+class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
+public:
+ static const SCEV *rewrite(const SCEV *S, const Loop *L,
+ ScalarEvolution &SE) {
+ SCEVShiftRewriter Rewriter(L, SE);
+ const SCEV *Result = Rewriter.visit(S);
+ return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ // Only allow AddRecExprs for this loop.
+ if (!SE.isLoopInvariant(Expr, L))
+ Valid = false;
+ return Expr;
+ }
+
+ const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
+ if (Expr->getLoop() == L && Expr->isAffine())
+ return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
+ Valid = false;
+ return Expr;
+ }
+
+ bool isValid() { return Valid; }
+
+private:
+ explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
+ : SCEVRewriteVisitor(SE), L(L) {}
+
+ const Loop *L;
+ bool Valid = true;
+};
+
+} // end anonymous namespace
+
+void ScalarEvolution::inferNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
+ if (!AR->isAffine())
+ return;
+
+ // Force computation of ranges, which will also perform range-based flag
+ // inference.
+ if (!AR->hasNoSignedWrap())
+ (void)getSignedRange(AR);
+
+ if (!AR->hasNoUnsignedWrap())
+ (void)getUnsignedRange(AR);
+
+ if (!AR->hasNoSelfWrap()) {
+ const SCEV *BECount = getConstantMaxBackedgeTakenCount(AR->getLoop());
+ if (const SCEVConstant *BECountMax = dyn_cast<SCEVConstant>(BECount)) {
+ ConstantRange StepCR = getSignedRange(AR->getStepRecurrence(*this));
+ const APInt &BECountAP = BECountMax->getAPInt();
+ unsigned NoOverflowBitWidth =
+ BECountAP.getActiveBits() + StepCR.getMinSignedBits();
+ if (NoOverflowBitWidth <= getTypeSizeInBits(AR->getType()))
+ const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
+ }
+ }
+}
+
+SCEV::NoWrapFlags
+ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) {
+ SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
+
+ if (AR->hasNoSignedWrap())
+ return Result;
+
+ if (!AR->isAffine())
+ return Result;
+
+ // This function can be expensive, only try to prove NSW once per AddRec.
+ if (!SignedWrapViaInductionTried.insert(AR).second)
+ return Result;
+
+ const SCEV *Step = AR->getStepRecurrence(*this);
+ const Loop *L = AR->getLoop();
+
+ // Check whether the backedge-taken count is SCEVCouldNotCompute.
+ // Note that this serves two purposes: It filters out loops that are
+ // simply not analyzable, and it covers the case where this code is
+ // being called from within backedge-taken count analysis, such that
+ // attempting to ask for the backedge-taken count would likely result
+ // in infinite recursion. In the later case, the analysis code will
+ // cope with a conservative value, and it will take care to purge
+ // that value once it has finished.
+ const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
+
+ // Normally, in the cases we can prove no-overflow via a
+ // backedge guarding condition, we can also compute a backedge
+ // taken count for the loop. The exceptions are assumptions and
+ // guards present in the loop -- SCEV is not great at exploiting
+ // these to compute max backedge taken counts, but can still use
+ // these to prove lack of overflow. Use this fact to avoid
+ // doing extra work that may not pay off.
+
+ if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
+ AC.assumptions().empty())
+ return Result;
+
+ // If the backedge is guarded by a comparison with the pre-inc value the
+ // addrec is safe. Also, if the entry is guarded by a comparison with the
+ // start value and the backedge is guarded by a comparison with the post-inc
+ // value, the addrec is safe.
+ ICmpInst::Predicate Pred;
+ const SCEV *OverflowLimit =
+ getSignedOverflowLimitForStep(Step, &Pred, this);
+ if (OverflowLimit &&
+ (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
+ isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
+ Result = setFlags(Result, SCEV::FlagNSW);
+ }
+ return Result;
+}
+SCEV::NoWrapFlags
+ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) {
+ SCEV::NoWrapFlags Result = AR->getNoWrapFlags();
+
+ if (AR->hasNoUnsignedWrap())
+ return Result;
+
+ if (!AR->isAffine())
+ return Result;
+
+ // This function can be expensive, only try to prove NUW once per AddRec.
+ if (!UnsignedWrapViaInductionTried.insert(AR).second)
+ return Result;
+
+ const SCEV *Step = AR->getStepRecurrence(*this);
+ unsigned BitWidth = getTypeSizeInBits(AR->getType());
+ const Loop *L = AR->getLoop();
+
+ // Check whether the backedge-taken count is SCEVCouldNotCompute.
+ // Note that this serves two purposes: It filters out loops that are
+ // simply not analyzable, and it covers the case where this code is
+ // being called from within backedge-taken count analysis, such that
+ // attempting to ask for the backedge-taken count would likely result
+ // in infinite recursion. In the later case, the analysis code will
+ // cope with a conservative value, and it will take care to purge
+ // that value once it has finished.
+ const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
+
+ // Normally, in the cases we can prove no-overflow via a
+ // backedge guarding condition, we can also compute a backedge
+ // taken count for the loop. The exceptions are assumptions and
+ // guards present in the loop -- SCEV is not great at exploiting
+ // these to compute max backedge taken counts, but can still use
+ // these to prove lack of overflow. Use this fact to avoid
+ // doing extra work that may not pay off.
+
+ if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
+ AC.assumptions().empty())
+ return Result;
+
+ // If the backedge is guarded by a comparison with the pre-inc value the
+ // addrec is safe. Also, if the entry is guarded by a comparison with the
+ // start value and the backedge is guarded by a comparison with the post-inc
+ // value, the addrec is safe.
+ if (isKnownPositive(Step)) {
+ const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
+ getUnsignedRangeMax(Step));
+ if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
+ isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
+ Result = setFlags(Result, SCEV::FlagNUW);
+ }
+ }
+
+ return Result;
+}
+
+namespace {
+
+/// Represents an abstract binary operation. This may exist as a
+/// normal instruction or constant expression, or may have been
+/// derived from an expression tree.
+struct BinaryOp {
+ unsigned Opcode;
+ Value *LHS;
+ Value *RHS;
+ bool IsNSW = false;
+ bool IsNUW = false;
+
+ /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
+ /// constant expression.
+ Operator *Op = nullptr;
+
+ explicit BinaryOp(Operator *Op)
+ : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
+ Op(Op) {
+ if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
+ IsNSW = OBO->hasNoSignedWrap();
+ IsNUW = OBO->hasNoUnsignedWrap();
+ }
+ }
+
+ explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
+ bool IsNUW = false)
+ : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
+};
+
+} // end anonymous namespace
+
+/// Try to map \p V into a BinaryOp, and return \c std::nullopt on failure.
+static std::optional<BinaryOp> MatchBinaryOp(Value *V, const DataLayout &DL,
+ AssumptionCache &AC,
+ const DominatorTree &DT,
+ const Instruction *CxtI) {
+ auto *Op = dyn_cast<Operator>(V);
+ if (!Op)
+ return std::nullopt;
+
+ // Implementation detail: all the cleverness here should happen without
+ // creating new SCEV expressions -- our caller knowns tricks to avoid creating
+ // SCEV expressions when possible, and we should not break that.
+
+ switch (Op->getOpcode()) {
+ case Instruction::Add:
+ case Instruction::Sub:
+ case Instruction::Mul:
+ case Instruction::UDiv:
+ case Instruction::URem:
+ case Instruction::And:
+ case Instruction::AShr:
+ case Instruction::Shl:
+ return BinaryOp(Op);
+
+ case Instruction::Or: {
+ // Convert or disjoint into add nuw nsw.
+ if (cast<PossiblyDisjointInst>(Op)->isDisjoint()) {
+ BinaryOp BinOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1),
+ /*IsNSW=*/true, /*IsNUW=*/true);
+ // Keep the reference to the original instruction so that we can later
+ // check whether it can produce poison value or not.
+ BinOp.Op = Op;
+ return BinOp;
+ }
+ return BinaryOp(Op);
+ }
+
+ case Instruction::Xor:
+ if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
+ // If the RHS of the xor is a signmask, then this is just an add.
+ // Instcombine turns add of signmask into xor as a strength reduction step.
+ if (RHSC->getValue().isSignMask())
+ return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
+ // Binary `xor` is a bit-wise `add`.
+ if (V->getType()->isIntegerTy(1))
+ return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
+ return BinaryOp(Op);
+
+ case Instruction::LShr:
+ // Turn logical shift right of a constant into a unsigned divide.
+ if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
+ uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
+
+ // If the shift count is not less than the bitwidth, the result of
+ // the shift is undefined. Don't try to analyze it, because the
+ // resolution chosen here may differ from the resolution chosen in
+ // other parts of the compiler.
+ if (SA->getValue().ult(BitWidth)) {
+ Constant *X =
+ ConstantInt::get(SA->getContext(),
+ APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
+ return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
+ }
+ }
+ return BinaryOp(Op);
+
+ case Instruction::ExtractValue: {
+ auto *EVI = cast<ExtractValueInst>(Op);
+ if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
+ break;
+
+ auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
+ if (!WO)
+ break;
+
+ Instruction::BinaryOps BinOp = WO->getBinaryOp();
+ bool Signed = WO->isSigned();
+ // TODO: Should add nuw/nsw flags for mul as well.
+ if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
+ return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
+
+ // Now that we know that all uses of the arithmetic-result component of
+ // CI are guarded by the overflow check, we can go ahead and pretend
+ // that the arithmetic is non-overflowing.
+ return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
+ /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
+ }
+
+ default:
+ break;
+ }
+
+ // Recognise intrinsic loop.decrement.reg, and as this has exactly the same
+ // semantics as a Sub, return a binary sub expression.
+ if (auto *II = dyn_cast<IntrinsicInst>(V))
+ if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
+ return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));
+
+ return std::nullopt;
+}
+
+/// Helper function to createAddRecFromPHIWithCasts. We have a phi
+/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
+/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
+/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
+/// follows one of the following patterns:
+/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
+/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
+/// If the SCEV expression of \p Op conforms with one of the expected patterns
+/// we return the type of the truncation operation, and indicate whether the
+/// truncated type should be treated as signed/unsigned by setting
+/// \p Signed to true/false, respectively.
+static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
+ bool &Signed, ScalarEvolution &SE) {
+ // The case where Op == SymbolicPHI (that is, with no type conversions on
+ // the way) is handled by the regular add recurrence creating logic and
+ // would have already been triggered in createAddRecForPHI. Reaching it here
+ // means that createAddRecFromPHI had failed for this PHI before (e.g.,
+ // because one of the other operands of the SCEVAddExpr updating this PHI is
+ // not invariant).
+ //
+ // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
+ // this case predicates that allow us to prove that Op == SymbolicPHI will
+ // be added.
+ if (Op == SymbolicPHI)
+ return nullptr;
+
+ unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
+ unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
+ if (SourceBits != NewBits)
+ return nullptr;
+
+ if (match(Op, m_scev_SExt(m_scev_Trunc(m_scev_Specific(SymbolicPHI))))) {
+ Signed = true;
+ return cast<SCEVCastExpr>(Op)->getOperand()->getType();
+ }
+ if (match(Op, m_scev_ZExt(m_scev_Trunc(m_scev_Specific(SymbolicPHI))))) {
+ Signed = false;
+ return cast<SCEVCastExpr>(Op)->getOperand()->getType();
+ }
+ return nullptr;
+}
+
+static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
+ if (!PN->getType()->isIntegerTy())
+ return nullptr;
+ const Loop *L = LI.getLoopFor(PN->getParent());
+ if (!L || L->getHeader() != PN->getParent())
+ return nullptr;
+ return L;
+}
+
+// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
+// computation that updates the phi follows the following pattern:
+// (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
+// which correspond to a phi->trunc->sext/zext->add->phi update chain.
+// If so, try to see if it can be rewritten as an AddRecExpr under some
+// Predicates. If successful, return them as a pair. Also cache the results
+// of the analysis.
+//
+// Example usage scenario:
+// Say the Rewriter is called for the following SCEV:
+// 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
+// where:
+// %X = phi i64 (%Start, %BEValue)
+// It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
+// and call this function with %SymbolicPHI = %X.
+//
+// The analysis will find that the value coming around the backedge has
+// the following SCEV:
+// BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
+// Upon concluding that this matches the desired pattern, the function
+// will return the pair {NewAddRec, SmallPredsVec} where:
+// NewAddRec = {%Start,+,%Step}
+// SmallPredsVec = {P1, P2, P3} as follows:
+// P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
+// P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
+// P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
+// The returned pair means that SymbolicPHI can be rewritten into NewAddRec
+// under the predicates {P1,P2,P3}.
+// This predicated rewrite will be cached in PredicatedSCEVRewrites:
+// PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
+//
+// TODO's:
+//
+// 1) Extend the Induction descriptor to also support inductions that involve
+// casts: When needed (namely, when we are called in the context of the
+// vectorizer induction analysis), a Set of cast instructions will be
+// populated by this method, and provided back to isInductionPHI. This is
+// needed to allow the vectorizer to properly record them to be ignored by
+// the cost model and to avoid vectorizing them (otherwise these casts,
+// which are redundant under the runtime overflow checks, will be
+// vectorized, which can be costly).
+//
+// 2) Support additional induction/PHISCEV patterns: We also want to support
+// inductions where the sext-trunc / zext-trunc operations (partly) occur
+// after the induction update operation (the induction increment):
+//
+// (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
+// which correspond to a phi->add->trunc->sext/zext->phi update chain.
+//
+// (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
+// which correspond to a phi->trunc->add->sext/zext->phi update chain.
+//
+// 3) Outline common code with createAddRecFromPHI to avoid duplication.
+std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
+ SmallVector<const SCEVPredicate *, 3> Predicates;
+
+ // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
+ // return an AddRec expression under some predicate.
+
+ auto *PN = cast<PHINode>(SymbolicPHI->getValue());
+ const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
+ assert(L && "Expecting an integer loop header phi");
+
+ // The loop may have multiple entrances or multiple exits; we can analyze
+ // this phi as an addrec if it has a unique entry value and a unique
+ // backedge value.
+ Value *BEValueV = nullptr, *StartValueV = nullptr;
+ for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
+ Value *V = PN->getIncomingValue(i);
+ if (L->contains(PN->getIncomingBlock(i))) {
+ if (!BEValueV) {
+ BEValueV = V;
+ } else if (BEValueV != V) {
+ BEValueV = nullptr;
+ break;
+ }
+ } else if (!StartValueV) {
+ StartValueV = V;
+ } else if (StartValueV != V) {
+ StartValueV = nullptr;
+ break;
+ }
+ }
+ if (!BEValueV || !StartValueV)
+ return std::nullopt;
+
+ const SCEV *BEValue = getSCEV(BEValueV);
+
+ // If the value coming around the backedge is an add with the symbolic
+ // value we just inserted, possibly with casts that we can ignore under
+ // an appropriate runtime guard, then we found a simple induction variable!
+ const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
+ if (!Add)
+ return std::nullopt;
+
+ // If there is a single occurrence of the symbolic value, possibly
+ // casted, replace it with a recurrence.
+ unsigned FoundIndex = Add->getNumOperands();
+ Type *TruncTy = nullptr;
+ bool Signed;
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if ((TruncTy =
+ isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
+ if (FoundIndex == e) {
+ FoundIndex = i;
+ break;
+ }
+
+ if (FoundIndex == Add->getNumOperands())
+ return std::nullopt;
+
+ // Create an add with everything but the specified operand.
+ SmallVector<SCEVUse, 8> Ops;
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if (i != FoundIndex)
+ Ops.push_back(Add->getOperand(i));
+ const SCEV *Accum = getAddExpr(Ops);
+
+ // The runtime checks will not be valid if the step amount is
+ // varying inside the loop.
+ if (!isLoopInvariant(Accum, L))
+ return std::nullopt;
+
+ // *** Part2: Create the predicates
+
+ // Analysis was successful: we have a phi-with-cast pattern for which we
+ // can return an AddRec expression under the following predicates:
+ //
+ // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
+ // fits within the truncated type (does not overflow) for i = 0 to n-1.
+ // P2: An Equal predicate that guarantees that
+ // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
+ // P3: An Equal predicate that guarantees that
+ // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
+ //
+ // As we next prove, the above predicates guarantee that:
+ // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
+ //
+ //
+ // More formally, we want to prove that:
+ // Expr(i+1) = Start + (i+1) * Accum
+ // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
+ //
+ // Given that:
+ // 1) Expr(0) = Start
+ // 2) Expr(1) = Start + Accum
+ // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
+ // 3) Induction hypothesis (step i):
+ // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
+ //
+ // Proof:
+ // Expr(i+1) =
+ // = Start + (i+1)*Accum
+ // = (Start + i*Accum) + Accum
+ // = Expr(i) + Accum
+ // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
+ // :: from step i
+ //
+ // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
+ //
+ // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
+ // + (Ext ix (Trunc iy (Accum) to ix) to iy)
+ // + Accum :: from P3
+ //
+ // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
+ // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
+ //
+ // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
+ // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
+ //
+ // By induction, the same applies to all iterations 1<=i<n:
+ //
+
+ // Create a truncated addrec for which we will add a no overflow check (P1).
+ const SCEV *StartVal = getSCEV(StartValueV);
+ const SCEV *PHISCEV =
+ getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
+ getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
+
+ // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
+ // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
+ // will be constant.
+ //
+ // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
+ // add P1.
+ if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
+ SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
+ Signed ? SCEVWrapPredicate::IncrementNSSW
+ : SCEVWrapPredicate::IncrementNUSW;
+ const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
+ Predicates.push_back(AddRecPred);
+ }
+
+ // Create the Equal Predicates P2,P3:
+
+ // It is possible that the predicates P2 and/or P3 are computable at
+ // compile time due to StartVal and/or Accum being constants.
+ // If either one is, then we can check that now and escape if either P2
+ // or P3 is false.
+
+ // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
+ // for each of StartVal and Accum
+ auto getExtendedExpr = [&](const SCEV *Expr,
+ bool CreateSignExtend) -> const SCEV * {
+ assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
+ const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
+ const SCEV *ExtendedExpr =
+ CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
+ : getZeroExtendExpr(TruncatedExpr, Expr->getType());
+ return ExtendedExpr;
+ };
+
+ // Given:
+ // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
+ // = getExtendedExpr(Expr)
+ // Determine whether the predicate P: Expr == ExtendedExpr
+ // is known to be false at compile time
+ auto PredIsKnownFalse = [&](const SCEV *Expr,
+ const SCEV *ExtendedExpr) -> bool {
+ return Expr != ExtendedExpr &&
+ isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
+ };
+
+ const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
+ if (PredIsKnownFalse(StartVal, StartExtended)) {
+ LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
+ return std::nullopt;
+ }
+
+ // The Step is always Signed (because the overflow checks are either
+ // NSSW or NUSW)
+ const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
+ if (PredIsKnownFalse(Accum, AccumExtended)) {
+ LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
+ return std::nullopt;
+ }
+
+ auto AppendPredicate = [&](const SCEV *Expr,
+ const SCEV *ExtendedExpr) -> void {
+ if (Expr != ExtendedExpr &&
+ !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
+ const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
+ LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
+ Predicates.push_back(Pred);
+ }
+ };
+
+ AppendPredicate(StartVal, StartExtended);
+ AppendPredicate(Accum, AccumExtended);
+
+ // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
+ // which the casts had been folded away. The caller can rewrite SymbolicPHI
+ // into NewAR if it will also add the runtime overflow checks specified in
+ // Predicates.
+ auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
+
+ std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
+ std::make_pair(NewAR, Predicates);
+ // Remember the result of the analysis for this SCEV at this locayyytion.
+ PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
+ return PredRewrite;
+}
+
+std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
+ auto *PN = cast<PHINode>(SymbolicPHI->getValue());
+ const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
+ if (!L)
+ return std::nullopt;
+
+ // Check to see if we already analyzed this PHI.
+ auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
+ if (I != PredicatedSCEVRewrites.end()) {
+ std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
+ I->second;
+ // Analysis was done before and failed to create an AddRec:
+ if (Rewrite.first == SymbolicPHI)
+ return std::nullopt;
+ // Analysis was done before and succeeded to create an AddRec under
+ // a predicate:
+ assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
+ assert(!(Rewrite.second).empty() && "Expected to find Predicates");
+ return Rewrite;
+ }
+
+ std::optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
+
+ // Record in the cache that the analysis failed
+ if (!Rewrite) {
+ SmallVector<const SCEVPredicate *, 3> Predicates;
+ PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
+ return std::nullopt;
+ }
+
+ return Rewrite;
+}
+
+// FIXME: This utility is currently required because the Rewriter currently
+// does not rewrite this expression:
+// {0, +, (sext ix (trunc iy to ix) to iy)}
+// into {0, +, %step},
+// even when the following Equal predicate exists:
+// "%step == (sext ix (trunc iy to ix) to iy)".
+bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
+ const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2,
+ ArrayRef<const SCEVPredicate *> NoWrapPreds) const {
+ if (AR1 == AR2)
+ return true;
+
+ SCEVUnionPredicate NoWrapUnionPred(NoWrapPreds, SE);
+ SCEVUnionPredicate AllPreds = Preds->getUnionWith(&NoWrapUnionPred, SE);
+ auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
+ if (Expr1 != Expr2 &&
+ !AllPreds.implies(SE.getEqualPredicate(Expr1, Expr2), SE) &&
+ !AllPreds.implies(SE.getEqualPredicate(Expr2, Expr1), SE))
+ return false;
+ return true;
+ };
+
+ if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
+ !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
+ return false;
+ return true;
+}
+
+/// A helper function for createAddRecFromPHI to handle simple cases.
+///
+/// This function tries to find an AddRec expression for the simplest (yet most
+/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
+/// If it fails, createAddRecFromPHI will use a more general, but slow,
+/// technique for finding the AddRec expression.
+const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
+ Value *BEValueV,
+ Value *StartValueV) {
+ const Loop *L = LI.getLoopFor(PN->getParent());
+ assert(L && L->getHeader() == PN->getParent());
+ assert(BEValueV && StartValueV);
+
+ auto BO = MatchBinaryOp(BEValueV, getDataLayout(), AC, DT, PN);
+ if (!BO)
+ return nullptr;
+
+ if (BO->Opcode != Instruction::Add)
+ return nullptr;
+
+ const SCEV *Accum = nullptr;
+ if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
+ Accum = getSCEV(BO->RHS);
+ else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
+ Accum = getSCEV(BO->LHS);
+
+ if (!Accum)
+ return nullptr;
+
+ SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
+ if (BO->IsNUW)
+ Flags = setFlags(Flags, SCEV::FlagNUW);
+ if (BO->IsNSW)
+ Flags = setFlags(Flags, SCEV::FlagNSW);
+
+ const SCEV *StartVal = getSCEV(StartValueV);
+ const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
+ insertValueToMap(PN, PHISCEV);
+
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV))
+ inferNoWrapViaConstantRanges(AR);
+
+ // We can add Flags to the post-inc expression only if we
+ // know that it is *undefined behavior* for BEValueV to
+ // overflow.
+ if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) {
+ assert(isLoopInvariant(Accum, L) &&
+ "Accum is defined outside L, but is not invariant?");
+ if (isAddRecNeverPoison(BEInst, L))
+ (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
+ }
+
+ return PHISCEV;
+}
+
+const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
+ const Loop *L = LI.getLoopFor(PN->getParent());
+ if (!L || L->getHeader() != PN->getParent())
+ return nullptr;
+
+ // The loop may have multiple entrances or multiple exits; we can analyze
+ // this phi as an addrec if it has a unique entry value and a unique
+ // backedge value.
+ Value *BEValueV = nullptr, *StartValueV = nullptr;
+ for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
+ Value *V = PN->getIncomingValue(i);
+ if (L->contains(PN->getIncomingBlock(i))) {
+ if (!BEValueV) {
+ BEValueV = V;
+ } else if (BEValueV != V) {
+ BEValueV = nullptr;
+ break;
+ }
+ } else if (!StartValueV) {
+ StartValueV = V;
+ } else if (StartValueV != V) {
+ StartValueV = nullptr;
+ break;
+ }
+ }
+ if (!BEValueV || !StartValueV)
+ return nullptr;
+
+ assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
+ "PHI node already processed?");
+
+ // First, try to find AddRec expression without creating a fictituos symbolic
+ // value for PN.
+ if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
+ return S;
+
+ // Handle PHI node value symbolically.
+ const SCEV *SymbolicName = getUnknown(PN);
+ insertValueToMap(PN, SymbolicName);
+
+ // Using this symbolic name for the PHI, analyze the value coming around
+ // the back-edge.
+ const SCEV *BEValue = getSCEV(BEValueV);
+
+ // NOTE: If BEValue is loop invariant, we know that the PHI node just
+ // has a special value for the first iteration of the loop.
+
+ // If the value coming around the backedge is an add with the symbolic
+ // value we just inserted, then we found a simple induction variable!
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
+ // If there is a single occurrence of the symbolic value, replace it
+ // with a recurrence.
+ unsigned FoundIndex = Add->getNumOperands();
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if (Add->getOperand(i) == SymbolicName)
+ if (FoundIndex == e) {
+ FoundIndex = i;
+ break;
+ }
+
+ if (FoundIndex != Add->getNumOperands()) {
+ // Create an add with everything but the specified operand.
+ SmallVector<SCEVUse, 8> Ops;
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if (i != FoundIndex)
+ Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
+ L, *this));
+ const SCEV *Accum = getAddExpr(Ops);
+
+ // This is not a valid addrec if the step amount is varying each
+ // loop iteration, but is not itself an addrec in this loop.
+ if (isLoopInvariant(Accum, L) ||
+ (isa<SCEVAddRecExpr>(Accum) &&
+ cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
+ SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
+
+ if (auto BO = MatchBinaryOp(BEValueV, getDataLayout(), AC, DT, PN)) {
+ if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
+ if (BO->IsNUW)
+ Flags = setFlags(Flags, SCEV::FlagNUW);
+ if (BO->IsNSW)
+ Flags = setFlags(Flags, SCEV::FlagNSW);
+ }
+ } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
+ if (GEP->getOperand(0) == PN) {
+ GEPNoWrapFlags NW = GEP->getNoWrapFlags();
+ // If the increment has any nowrap flags, then we know the address
+ // space cannot be wrapped around.
+ if (NW != GEPNoWrapFlags::none())
+ Flags = setFlags(Flags, SCEV::FlagNW);
+ // If the GEP is nuw or nusw with non-negative offset, we know that
+ // no unsigned wrap occurs. We cannot set the nsw flag as only the
+ // offset is treated as signed, while the base is unsigned.
+ if (NW.hasNoUnsignedWrap() ||
+ (NW.hasNoUnsignedSignedWrap() && isKnownNonNegative(Accum)))
+ Flags = setFlags(Flags, SCEV::FlagNUW);
+ }
+
+ // We cannot transfer nuw and nsw flags from subtraction
+ // operations -- sub nuw X, Y is not the same as add nuw X, -Y
+ // for instance.
+ }
+
+ const SCEV *StartVal = getSCEV(StartValueV);
+ const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
+
+ // Okay, for the entire analysis of this edge we assumed the PHI
+ // to be symbolic. We now need to go back and purge all of the
+ // entries for the scalars that use the symbolic expression.
+ forgetMemoizedResults({SymbolicName});
+ insertValueToMap(PN, PHISCEV);
+
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV))
+ inferNoWrapViaConstantRanges(AR);
+
+ // We can add Flags to the post-inc expression only if we
+ // know that it is *undefined behavior* for BEValueV to
+ // overflow.
+ if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
+ if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
+ (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
+
+ return PHISCEV;
+ }
+ }
+ } else {
+ // Otherwise, this could be a loop like this:
+ // i = 0; for (j = 1; ..; ++j) { .... i = j; }
+ // In this case, j = {1,+,1} and BEValue is j.
+ // Because the other in-value of i (0) fits the evolution of BEValue
+ // i really is an addrec evolution.
+ //
+ // We can generalize this saying that i is the shifted value of BEValue
+ // by one iteration:
+ // PHI(f(0), f({1,+,1})) --> f({0,+,1})
+
+ // Do not allow refinement in rewriting of BEValue.
+ const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
+ const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
+ if (Shifted != getCouldNotCompute() && Start != getCouldNotCompute() &&
+ isGuaranteedNotToCauseUB(Shifted) && ::impliesPoison(Shifted, Start)) {
+ const SCEV *StartVal = getSCEV(StartValueV);
+ if (Start == StartVal) {
+ // Okay, for the entire analysis of this edge we assumed the PHI
+ // to be symbolic. We now need to go back and purge all of the
+ // entries for the scalars that use the symbolic expression.
+ forgetMemoizedResults({SymbolicName});
+ insertValueToMap(PN, Shifted);
+ return Shifted;
+ }
+ }
+ }
+
+ // Remove the temporary PHI node SCEV that has been inserted while intending
+ // to create an AddRecExpr for this PHI node. We can not keep this temporary
+ // as it will prevent later (possibly simpler) SCEV expressions to be added
+ // to the ValueExprMap.
+ eraseValueFromMap(PN);
+
+ return nullptr;
+}
+
+// Try to match a control flow sequence that branches out at BI and merges back
+// at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
+// match.
+static bool BrPHIToSelect(DominatorTree &DT, CondBrInst *BI, PHINode *Merge,
+ Value *&C, Value *&LHS, Value *&RHS) {
+ C = BI->getCondition();
+
+ BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
+ BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
+
+ Use &LeftUse = Merge->getOperandUse(0);
+ Use &RightUse = Merge->getOperandUse(1);
+
+ if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
+ LHS = LeftUse;
+ RHS = RightUse;
+ return true;
+ }
+
+ if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
+ LHS = RightUse;
+ RHS = LeftUse;
+ return true;
+ }
+
+ return false;
+}
+
+static bool getOperandsForSelectLikePHI(DominatorTree &DT, PHINode *PN,
+ Value *&Cond, Value *&LHS,
+ Value *&RHS) {
+ auto IsReachable =
+ [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
+ if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
+ // Try to match
+ //
+ // br %cond, label %left, label %right
+ // left:
+ // br label %merge
+ // right:
+ // br label %merge
+ // merge:
+ // V = phi [ %x, %left ], [ %y, %right ]
+ //
+ // as "select %cond, %x, %y"
+
+ BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
+ assert(IDom && "At least the entry block should dominate PN");
+
+ auto *BI = dyn_cast<CondBrInst>(IDom->getTerminator());
+ return BI && BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS);
+ }
+ return false;
+}
+
+const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
+ Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
+ if (getOperandsForSelectLikePHI(DT, PN, Cond, LHS, RHS) &&
+ properlyDominates(getSCEV(LHS), PN->getParent()) &&
+ properlyDominates(getSCEV(RHS), PN->getParent()))
+ return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
+
+ return nullptr;
+}
+
+static BinaryOperator *getCommonInstForPHI(PHINode *PN) {
+ BinaryOperator *CommonInst = nullptr;
+ // Check if instructions are identical.
+ for (Value *Incoming : PN->incoming_values()) {
+ auto *IncomingInst = dyn_cast<BinaryOperator>(Incoming);
+ if (!IncomingInst)
+ return nullptr;
+ if (CommonInst) {
+ if (!CommonInst->isIdenticalToWhenDefined(IncomingInst))
+ return nullptr; // Not identical, give up
+ } else {
+ // Remember binary operator
+ CommonInst = IncomingInst;
+ }
+ }
+ return CommonInst;
+}
+
+/// Returns SCEV for the first operand of a phi if all phi operands have
+/// identical opcodes and operands
+/// eg.
+/// a: %add = %a + %b
+/// br %c
+/// b: %add1 = %a + %b
+/// br %c
+/// c: %phi = phi [%add, a], [%add1, b]
+/// scev(%phi) => scev(%add)
+const SCEV *
+ScalarEvolution::createNodeForPHIWithIdenticalOperands(PHINode *PN) {
+ BinaryOperator *CommonInst = getCommonInstForPHI(PN);
+ if (!CommonInst)
+ return nullptr;
+
+ // Check if SCEV exprs for instructions are identical.
+ const SCEV *CommonSCEV = getSCEV(CommonInst);
+ bool SCEVExprsIdentical =
+ all_of(drop_begin(PN->incoming_values()),
+ [this, CommonSCEV](Value *V) { return CommonSCEV == getSCEV(V); });
+ return SCEVExprsIdentical ? CommonSCEV : nullptr;
+}
+
+const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
+ if (const SCEV *S = createAddRecFromPHI(PN))
+ return S;
+
+ // We do not allow simplifying phi (undef, X) to X here, to avoid reusing the
+ // phi node for X.
+ if (Value *V = simplifyInstruction(
+ PN, {getDataLayout(), &TLI, &DT, &AC, /*CtxI=*/nullptr,
+ /*UseInstrInfo=*/true, /*CanUseUndef=*/false}))
+ return getSCEV(V);
+
+ if (const SCEV *S = createNodeForPHIWithIdenticalOperands(PN))
+ return S;
+
+ if (const SCEV *S = createNodeFromSelectLikePHI(PN))
+ return S;
+
+ // If it's not a loop phi, we can't handle it yet.
+ return getUnknown(PN);
+}
+
+bool SCEVMinMaxExprContains(const SCEV *Root, const SCEV *OperandToFind,
+ SCEVTypes RootKind) {
+ struct FindClosure {
+ const SCEV *OperandToFind;
+ const SCEVTypes RootKind; // Must be a sequential min/max expression.
+ const SCEVTypes NonSequentialRootKind; // Non-seq variant of RootKind.
+
+ bool Found = false;
+
+ bool canRecurseInto(SCEVTypes Kind) const {
+ // We can only recurse into the SCEV expression of the same effective type
+ // as the type of our root SCEV expression, and into zero-extensions.
+ return RootKind == Kind || NonSequentialRootKind == Kind ||
+ scZeroExtend == Kind;
+ };
+
+ FindClosure(const SCEV *OperandToFind, SCEVTypes RootKind)
+ : OperandToFind(OperandToFind), RootKind(RootKind),
+ NonSequentialRootKind(
+ SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
+ RootKind)) {}
+
+ bool follow(const SCEV *S) {
+ Found = S == OperandToFind;
+
+ return !isDone() && canRecurseInto(S->getSCEVType());
+ }
+
+ bool isDone() const { return Found; }
+ };
+
+ FindClosure FC(OperandToFind, RootKind);
+ visitAll(Root, FC);
+ return FC.Found;
+}
+
+std::optional<const SCEV *>
+ScalarEvolution::createNodeForSelectOrPHIInstWithICmpInstCond(Type *Ty,
+ ICmpInst *Cond,
+ Value *TrueVal,
+ Value *FalseVal) {
+ // Try to match some simple smax or umax patterns.
+ auto *ICI = Cond;
+
+ Value *LHS = ICI->getOperand(0);
+ Value *RHS = ICI->getOperand(1);
+
+ switch (ICI->getPredicate()) {
+ case ICmpInst::ICMP_SLT:
+ case ICmpInst::ICMP_SLE:
+ case ICmpInst::ICMP_ULT:
+ case ICmpInst::ICMP_ULE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SGT:
+ case ICmpInst::ICMP_SGE:
+ case ICmpInst::ICMP_UGT:
+ case ICmpInst::ICMP_UGE:
+ // a > b ? a+x : b+x -> max(a, b)+x
+ // a > b ? b+x : a+x -> min(a, b)+x
+ if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(Ty)) {
+ bool Signed = ICI->isSigned();
+ const SCEV *LA = getSCEV(TrueVal);
+ const SCEV *RA = getSCEV(FalseVal);
+ const SCEV *LS = getSCEV(LHS);
+ const SCEV *RS = getSCEV(RHS);
+ if (LA->getType()->isPointerTy()) {
+ // FIXME: Handle cases where LS/RS are pointers not equal to LA/RA.
+ // Need to make sure we can't produce weird expressions involving
+ // negated pointers.
+ if (LA == LS && RA == RS)
+ return Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS);
+ if (LA == RS && RA == LS)
+ return Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS);
+ }
+ auto CoerceOperand = [&](const SCEV *Op) -> const SCEV * {
+ if (Op->getType()->isPointerTy()) {
+ Op = getPtrToAddrExpr(Op);
+ if (isa<SCEVCouldNotCompute>(Op))
+ return Op;
+ }
+ if (Signed)
+ Op = getNoopOrSignExtend(Op, Ty);
+ else
+ Op = getNoopOrZeroExtend(Op, Ty);
+ return Op;
+ };
+ LS = CoerceOperand(LS);
+ RS = CoerceOperand(RS);
+ if (isa<SCEVCouldNotCompute>(LS) || isa<SCEVCouldNotCompute>(RS))
+ break;
+ const SCEV *LDiff = getMinusSCEV(LA, LS);
+ const SCEV *RDiff = getMinusSCEV(RA, RS);
+ if (LDiff == RDiff)
+ return getAddExpr(Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS),
+ LDiff);
+ LDiff = getMinusSCEV(LA, RS);
+ RDiff = getMinusSCEV(RA, LS);
+ if (LDiff == RDiff)
+ return getAddExpr(Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS),
+ LDiff);
+ }
+ break;
+ case ICmpInst::ICMP_NE:
+ // x != 0 ? x+y : C+y -> x == 0 ? C+y : x+y
+ std::swap(TrueVal, FalseVal);
+ [[fallthrough]];
+ case ICmpInst::ICMP_EQ:
+ // x == 0 ? C+y : x+y -> umax(x, C)+y iff C u<= 1
+ if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(Ty) &&
+ isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
+ const SCEV *X = getNoopOrZeroExtend(getSCEV(LHS), Ty);
+ const SCEV *TrueValExpr = getSCEV(TrueVal); // C+y
+ const SCEV *FalseValExpr = getSCEV(FalseVal); // x+y
+ const SCEV *Y = getMinusSCEV(FalseValExpr, X); // y = (x+y)-x
+ const SCEV *C = getMinusSCEV(TrueValExpr, Y); // C = (C+y)-y
+ if (isa<SCEVConstant>(C) && cast<SCEVConstant>(C)->getAPInt().ule(1))
+ return getAddExpr(getUMaxExpr(X, C), Y);
+ }
+ // x == 0 ? 0 : umin (..., x, ...) -> umin_seq(x, umin (...))
+ // x == 0 ? 0 : umin_seq(..., x, ...) -> umin_seq(x, umin_seq(...))
+ // x == 0 ? 0 : umin (..., umin_seq(..., x, ...), ...)
+ // -> umin_seq(x, umin (..., umin_seq(...), ...))
+ if (isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero() &&
+ isa<ConstantInt>(TrueVal) && cast<ConstantInt>(TrueVal)->isZero()) {
+ const SCEV *X = getSCEV(LHS);
+ while (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(X))
+ X = ZExt->getOperand();
+ if (getTypeSizeInBits(X->getType()) <= getTypeSizeInBits(Ty)) {
+ const SCEV *FalseValExpr = getSCEV(FalseVal);
+ if (SCEVMinMaxExprContains(FalseValExpr, X, scSequentialUMinExpr))
+ return getUMinExpr(getNoopOrZeroExtend(X, Ty), FalseValExpr,
+ /*Sequential=*/true);
+ }
+ }
+ break;
+ default:
+ break;
+ }
+
+ return std::nullopt;
+}
+
+static std::optional<const SCEV *>
+createNodeForSelectViaUMinSeq(ScalarEvolution *SE, const SCEV *CondExpr,
+ const SCEV *TrueExpr, const SCEV *FalseExpr) {
+ assert(CondExpr->getType()->isIntegerTy(1) &&
+ TrueExpr->getType() == FalseExpr->getType() &&
+ TrueExpr->getType()->isIntegerTy(1) &&
+ "Unexpected operands of a select.");
+
+ // i1 cond ? i1 x : i1 C --> C + (i1 cond ? (i1 x - i1 C) : i1 0)
+ // --> C + (umin_seq cond, x - C)
+ //
+ // i1 cond ? i1 C : i1 x --> C + (i1 cond ? i1 0 : (i1 x - i1 C))
+ // --> C + (i1 ~cond ? (i1 x - i1 C) : i1 0)
+ // --> C + (umin_seq ~cond, x - C)
+
+ // FIXME: while we can't legally model the case where both of the hands
+ // are fully variable, we only require that the *difference* is constant.
+ if (!isa<SCEVConstant>(TrueExpr) && !isa<SCEVConstant>(FalseExpr))
+ return std::nullopt;
+
+ const SCEV *X, *C;
+ if (isa<SCEVConstant>(TrueExpr)) {
+ CondExpr = SE->getNotSCEV(CondExpr);
+ X = FalseExpr;
+ C = TrueExpr;
+ } else {
+ X = TrueExpr;
+ C = FalseExpr;
+ }
+ return SE->getAddExpr(C, SE->getUMinExpr(CondExpr, SE->getMinusSCEV(X, C),
+ /*Sequential=*/true));
+}
+
+static std::optional<const SCEV *>
+createNodeForSelectViaUMinSeq(ScalarEvolution *SE, Value *Cond, Value *TrueVal,
+ Value *FalseVal) {
+ if (!isa<ConstantInt>(TrueVal) && !isa<ConstantInt>(FalseVal))
+ return std::nullopt;
+
+ const auto *SECond = SE->getSCEV(Cond);
+ const auto *SETrue = SE->getSCEV(TrueVal);
+ const auto *SEFalse = SE->getSCEV(FalseVal);
+ return createNodeForSelectViaUMinSeq(SE, SECond, SETrue, SEFalse);
+}
+
+const SCEV *ScalarEvolution::createNodeForSelectOrPHIViaUMinSeq(
+ Value *V, Value *Cond, Value *TrueVal, Value *FalseVal) {
+ assert(Cond->getType()->isIntegerTy(1) && "Select condition is not an i1?");
+ assert(TrueVal->getType() == FalseVal->getType() &&
+ V->getType() == TrueVal->getType() &&
+ "Types of select hands and of the result must match.");
+
+ // For now, only deal with i1-typed `select`s.
+ if (!V->getType()->isIntegerTy(1))
+ return getUnknown(V);
+
+ if (std::optional<const SCEV *> S =
+ createNodeForSelectViaUMinSeq(this, Cond, TrueVal, FalseVal))
+ return *S;
+
+ return getUnknown(V);
+}
+
+const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Value *V, Value *Cond,
+ Value *TrueVal,
+ Value *FalseVal) {
+ // Handle "constant" branch or select. This can occur for instance when a
+ // loop pass transforms an inner loop and moves on to process the outer loop.
+ if (auto *CI = dyn_cast<ConstantInt>(Cond))
+ return getSCEV(CI->isOne() ? TrueVal : FalseVal);
+
+ if (auto *I = dyn_cast<Instruction>(V)) {
+ if (auto *ICI = dyn_cast<ICmpInst>(Cond)) {
+ if (std::optional<const SCEV *> S =
+ createNodeForSelectOrPHIInstWithICmpInstCond(I->getType(), ICI,
+ TrueVal, FalseVal))
+ return *S;
+ }
+ }
+
+ return createNodeForSelectOrPHIViaUMinSeq(V, Cond, TrueVal, FalseVal);
+}
+
+/// Expand GEP instructions into add and multiply operations. This allows them
+/// to be analyzed by regular SCEV code.
+const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
+ assert(GEP->getSourceElementType()->isSized() &&
+ "GEP source element type must be sized");
+
+ SmallVector<SCEVUse, 4> IndexExprs;
+ for (Value *Index : GEP->indices())
+ IndexExprs.push_back(getSCEV(Index));
+ return getGEPExpr(GEP, IndexExprs);
+}
+
+APInt ScalarEvolution::getConstantMultipleImpl(const SCEV *S,
+ const Instruction *CtxI) {
+ uint64_t BitWidth = getTypeSizeInBits(S->getType());
+ auto GetShiftedByZeros = [BitWidth](uint32_t TrailingZeros) {
+ return TrailingZeros >= BitWidth
+ ? APInt::getZero(BitWidth)
+ : APInt::getOneBitSet(BitWidth, TrailingZeros);
+ };
+ auto GetGCDMultiple = [this, CtxI](const SCEVNAryExpr *N) {
+ // The result is GCD of all operands results.
+ APInt Res = getConstantMultiple(N->getOperand(0), CtxI);
+ for (unsigned I = 1, E = N->getNumOperands(); I < E && Res != 1; ++I)
+ Res = APIntOps::GreatestCommonDivisor(
+ Res, getConstantMultiple(N->getOperand(I), CtxI));
+ return Res;
+ };
+
+ switch (S->getSCEVType()) {
+ case scConstant:
+ return cast<SCEVConstant>(S)->getAPInt();
+ case scPtrToAddr:
+ return getConstantMultiple(cast<SCEVCastExpr>(S)->getOperand());
+ case scUDivExpr:
+ case scVScale:
+ return APInt(BitWidth, 1);
+ case scTruncate: {
+ // Only multiples that are a power of 2 will hold after truncation.
+ const SCEVTruncateExpr *T = cast<SCEVTruncateExpr>(S);
+ uint32_t TZ = getMinTrailingZeros(T->getOperand(), CtxI);
+ return GetShiftedByZeros(TZ);
+ }
+ case scZeroExtend: {
+ const SCEVZeroExtendExpr *Z = cast<SCEVZeroExtendExpr>(S);
+ return getConstantMultiple(Z->getOperand(), CtxI).zext(BitWidth);
+ }
+ case scSignExtend: {
+ // Only multiples that are a power of 2 will hold after sext.
+ const SCEVSignExtendExpr *E = cast<SCEVSignExtendExpr>(S);
+ uint32_t TZ = getMinTrailingZeros(E->getOperand(), CtxI);
+ return GetShiftedByZeros(TZ);
+ }
+ case scMulExpr: {
+ const SCEVMulExpr *M = cast<SCEVMulExpr>(S);
+ if (M->hasNoUnsignedWrap()) {
+ // The result is the product of all operand results.
+ APInt Res = getConstantMultiple(M->getOperand(0), CtxI);
+ for (const SCEV *Operand : M->operands().drop_front())
+ Res = Res * getConstantMultiple(Operand, CtxI);
+ return Res;
+ }
+
+ // If there are no wrap guarentees, find the trailing zeros, which is the
+ // sum of trailing zeros for all its operands.
+ uint32_t TZ = 0;
+ for (const SCEV *Operand : M->operands())
+ TZ += getMinTrailingZeros(Operand, CtxI);
+ return GetShiftedByZeros(TZ);
+ }
+ case scAddExpr:
+ case scAddRecExpr: {
+ const SCEVNAryExpr *N = cast<SCEVNAryExpr>(S);
+ if (N->hasNoUnsignedWrap())
+ return GetGCDMultiple(N);
+ // Find the trailing bits, which is the minimum of its operands.
+ uint32_t TZ = getMinTrailingZeros(N->getOperand(0), CtxI);
+ for (const SCEV *Operand : N->operands().drop_front())
+ TZ = std::min(TZ, getMinTrailingZeros(Operand, CtxI));
+ return GetShiftedByZeros(TZ);
+ }
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr:
+ return GetGCDMultiple(cast<SCEVNAryExpr>(S));
+ case scUnknown: {
+ // Ask ValueTracking for known bits. SCEVUnknown only become available at
+ // the point their underlying IR instruction has been defined. If CtxI was
+ // not provided, use:
+ // * the first instruction in the entry block if it is an argument
+ // * the instruction itself otherwise.
+ const SCEVUnknown *U = cast<SCEVUnknown>(S);
+ if (!CtxI) {
+ if (isa<Argument>(U->getValue()))
+ CtxI = &*F.getEntryBlock().begin();
+ else if (auto *I = dyn_cast<Instruction>(U->getValue()))
+ CtxI = I;
+ }
+ unsigned Known =
+ computeKnownBits(U->getValue(),
+ SimplifyQuery(getDataLayout(), &DT, &AC, CtxI)
+ .allowEphemerals(true))
+ .countMinTrailingZeros();
+ return GetShiftedByZeros(Known);
+ }
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+APInt ScalarEvolution::getConstantMultiple(const SCEV *S,
+ const Instruction *CtxI) {
+ // Skip looking up and updating the cache if there is a context instruction,
+ // as the result will only be valid in the specified context.
+ if (CtxI)
+ return getConstantMultipleImpl(S, CtxI);
+
+ auto I = ConstantMultipleCache.find(S);
+ if (I != ConstantMultipleCache.end())
+ return I->second;
+
+ APInt Result = getConstantMultipleImpl(S, CtxI);
+ auto InsertPair = ConstantMultipleCache.insert({S, Result});
+ assert(InsertPair.second && "Should insert a new key");
+ return InsertPair.first->second;
+}
+
+APInt ScalarEvolution::getNonZeroConstantMultiple(const SCEV *S) {
+ APInt Multiple = getConstantMultiple(S);
+ return Multiple == 0 ? APInt(Multiple.getBitWidth(), 1) : Multiple;
+}
+
+uint32_t ScalarEvolution::getMinTrailingZeros(const SCEV *S,
+ const Instruction *CtxI) {
+ return std::min(getConstantMultiple(S, CtxI).countTrailingZeros(),
+ (unsigned)getTypeSizeInBits(S->getType()));
+}
+
+/// Helper method to assign a range to V from metadata present in the IR.
+static std::optional<ConstantRange> GetRangeFromMetadata(Value *V) {
+ if (Instruction *I = dyn_cast<Instruction>(V)) {
+ if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
+ return getConstantRangeFromMetadata(*MD);
+ if (const auto *CB = dyn_cast<CallBase>(V))
+ if (std::optional<ConstantRange> Range = CB->getRange())
+ return Range;
+ }
+ if (auto *A = dyn_cast<Argument>(V))
+ if (std::optional<ConstantRange> Range = A->getRange())
+ return Range;
+
+ return std::nullopt;
+}
+
+void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec,
+ SCEV::NoWrapFlags Flags) {
+ if (AddRec->getNoWrapFlags(Flags) != Flags) {
+ AddRec->setNoWrapFlags(Flags);
+ UnsignedRanges.erase(AddRec);
+ SignedRanges.erase(AddRec);
+ ConstantMultipleCache.erase(AddRec);
+ }
+}
+
+ConstantRange ScalarEvolution::
+getRangeForUnknownRecurrence(const SCEVUnknown *U) {
+ const DataLayout &DL = getDataLayout();
+
+ unsigned BitWidth = getTypeSizeInBits(U->getType());
+ const ConstantRange FullSet(BitWidth, /*isFullSet=*/true);
+
+ // Match a simple recurrence of the form: <start, ShiftOp, Step>, and then
+ // use information about the trip count to improve our available range. Note
+ // that the trip count independent cases are already handled by known bits.
+ // WARNING: The definition of recurrence used here is subtly different than
+ // the one used by AddRec (and thus most of this file). Step is allowed to
+ // be arbitrarily loop varying here, where AddRec allows only loop invariant
+ // and other addrecs in the same loop (for non-affine addrecs). The code
+ // below intentionally handles the case where step is not loop invariant.
+ auto *P = dyn_cast<PHINode>(U->getValue());
+ if (!P)
+ return FullSet;
+
+ // Make sure that no Phi input comes from an unreachable block. Otherwise,
+ // even the values that are not available in these blocks may come from them,
+ // and this leads to false-positive recurrence test.
+ for (auto *Pred : predecessors(P->getParent()))
+ if (!DT.isReachableFromEntry(Pred))
+ return FullSet;
+
+ BinaryOperator *BO;
+ Value *Start, *Step;
+ if (!matchSimpleRecurrence(P, BO, Start, Step))
+ return FullSet;
+
+ // If we found a recurrence in reachable code, we must be in a loop. Note
+ // that BO might be in some subloop of L, and that's completely okay.
+ auto *L = LI.getLoopFor(P->getParent());
+ assert(L && L->getHeader() == P->getParent());
+ if (!L->contains(BO->getParent()))
+ // NOTE: This bailout should be an assert instead. However, asserting
+ // the condition here exposes a case where LoopFusion is querying SCEV
+ // with malformed loop information during the midst of the transform.
+ // There doesn't appear to be an obvious fix, so for the moment bailout
+ // until the caller issue can be fixed. PR49566 tracks the bug.
+ return FullSet;
+
+ // TODO: Extend to other opcodes such as mul, and div
+ switch (BO->getOpcode()) {
+ default:
+ return FullSet;
+ case Instruction::AShr:
+ case Instruction::LShr:
+ case Instruction::Shl:
+ break;
+ };
+
+ if (BO->getOperand(0) != P)
+ // TODO: Handle the power function forms some day.
+ return FullSet;
+
+ unsigned TC = getSmallConstantMaxTripCount(L);
+ if (!TC || TC >= BitWidth)
+ return FullSet;
+
+ auto KnownStart = computeKnownBits(Start, DL, &AC, nullptr, &DT);
+ auto KnownStep = computeKnownBits(Step, DL, &AC, nullptr, &DT);
+ assert(KnownStart.getBitWidth() == BitWidth &&
+ KnownStep.getBitWidth() == BitWidth);
+
+ // Compute total shift amount, being careful of overflow and bitwidths.
+ auto MaxShiftAmt = KnownStep.getMaxValue();
+ APInt TCAP(BitWidth, TC-1);
+ bool Overflow = false;
+ auto TotalShift = MaxShiftAmt.umul_ov(TCAP, Overflow);
+ if (Overflow)
+ return FullSet;
+
+ switch (BO->getOpcode()) {
+ default:
+ llvm_unreachable("filtered out above");
+ case Instruction::AShr: {
+ // For each ashr, three cases:
+ // shift = 0 => unchanged value
+ // saturation => 0 or -1
+ // other => a value closer to zero (of the same sign)
+ // Thus, the end value is closer to zero than the start.
+ auto KnownEnd = KnownBits::ashr(KnownStart,
+ KnownBits::makeConstant(TotalShift));
+ if (KnownStart.isNonNegative())
+ // Analogous to lshr (simply not yet canonicalized)
+ return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
+ KnownStart.getMaxValue() + 1);
+ if (KnownStart.isNegative())
+ // End >=u Start && End <=s Start
+ return ConstantRange::getNonEmpty(KnownStart.getMinValue(),
+ KnownEnd.getMaxValue() + 1);
+ break;
+ }
+ case Instruction::LShr: {
+ // For each lshr, three cases:
+ // shift = 0 => unchanged value
+ // saturation => 0
+ // other => a smaller positive number
+ // Thus, the low end of the unsigned range is the last value produced.
+ auto KnownEnd = KnownBits::lshr(KnownStart,
+ KnownBits::makeConstant(TotalShift));
+ return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
+ KnownStart.getMaxValue() + 1);
+ }
+ case Instruction::Shl: {
+ // Iff no bits are shifted out, value increases on every shift.
+ auto KnownEnd = KnownBits::shl(KnownStart,
+ KnownBits::makeConstant(TotalShift));
+ if (TotalShift.ult(KnownStart.countMinLeadingZeros()))
+ return ConstantRange(KnownStart.getMinValue(),
+ KnownEnd.getMaxValue() + 1);
+ break;
+ }
+ };
+ return FullSet;
+}
+
+// The goal of this function is to check if recursively visiting the operands
+// of this PHI might lead to an infinite loop. If we do see such a loop,
+// there's no good way to break it, so we avoid analyzing such cases.
+//
+// getRangeRef previously used a visited set to avoid infinite loops, but this
+// caused other issues: the result was dependent on the order of getRangeRef
+// calls, and the interaction with createSCEVIter could cause a stack overflow
+// in some cases (see issue #148253).
+//
+// FIXME: The way this is implemented is overly conservative; this checks
+// for a few obviously safe patterns, but anything that doesn't lead to
+// recursion is fine.
+static bool RangeRefPHIAllowedOperands(DominatorTree &DT, PHINode *PHI) {
+ Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
+ if (getOperandsForSelectLikePHI(DT, PHI, Cond, LHS, RHS))
+ return true;
+
+ if (all_of(PHI->operands(),
+ [&](Value *Operand) { return DT.dominates(Operand, PHI); }))
+ return true;
+
+ return false;
+}
+
+const ConstantRange &
+ScalarEvolution::getRangeRefIter(const SCEV *S,
+ ScalarEvolution::RangeSignHint SignHint) {
+ DenseMap<const SCEV *, ConstantRange> &Cache =
+ SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
+ : SignedRanges;
+ SmallVector<SCEVUse> WorkList;
+ SmallPtrSet<const SCEV *, 8> Seen;
+
+ // Add Expr to the worklist, if Expr is either an N-ary expression or a
+ // SCEVUnknown PHI node.
+ auto AddToWorklist = [&WorkList, &Seen, &Cache](const SCEV *Expr) {
+ if (!Seen.insert(Expr).second)
+ return;
+ if (Cache.contains(Expr))
+ return;
+ switch (Expr->getSCEVType()) {
+ case scUnknown:
+ if (!isa<PHINode>(cast<SCEVUnknown>(Expr)->getValue()))
+ break;
+ [[fallthrough]];
+ case scConstant:
+ case scVScale:
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUDivExpr:
+ case scAddRecExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr:
+ WorkList.push_back(Expr);
+ break;
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ };
+ AddToWorklist(S);
+
+ // Build worklist by queuing operands of N-ary expressions and phi nodes.
+ for (unsigned I = 0; I != WorkList.size(); ++I) {
+ const SCEV *P = WorkList[I];
+ auto *UnknownS = dyn_cast<SCEVUnknown>(P);
+ // If it is not a `SCEVUnknown`, just recurse into operands.
+ if (!UnknownS) {
+ for (const SCEV *Op : P->operands())
+ AddToWorklist(Op);
+ continue;
+ }
+ // `SCEVUnknown`'s require special treatment.
+ if (PHINode *P = dyn_cast<PHINode>(UnknownS->getValue())) {
+ if (!RangeRefPHIAllowedOperands(DT, P))
+ continue;
+ for (auto &Op : reverse(P->operands()))
+ AddToWorklist(getSCEV(Op));
+ }
+ }
+
+ if (!WorkList.empty()) {
+ // Use getRangeRef to compute ranges for items in the worklist in reverse
+ // order. This will force ranges for earlier operands to be computed before
+ // their users in most cases.
+ for (const SCEV *P : reverse(drop_begin(WorkList))) {
+ getRangeRef(P, SignHint);
+ }
+ }
+
+ return getRangeRef(S, SignHint, 0);
+}
+
+/// Determine the range for a particular SCEV. If SignHint is
+/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
+/// with a "cleaner" unsigned (resp. signed) representation.
+const ConstantRange &ScalarEvolution::getRangeRef(
+ const SCEV *S, ScalarEvolution::RangeSignHint SignHint, unsigned Depth) {
+ DenseMap<const SCEV *, ConstantRange> &Cache =
+ SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
+ : SignedRanges;
+ ConstantRange::PreferredRangeType RangeType =
+ SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? ConstantRange::Unsigned
+ : ConstantRange::Signed;
+
+ // See if we've computed this range already.
+ auto I = Cache.find(S);
+ if (I != Cache.end())
+ return I->second;
+
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
+ return setRange(C, SignHint, ConstantRange(C->getAPInt()));
+
+ // Switch to iteratively computing the range for S, if it is part of a deeply
+ // nested expression.
+ if (Depth > RangeIterThreshold)
+ return getRangeRefIter(S, SignHint);
+
+ unsigned BitWidth = getTypeSizeInBits(S->getType());
+ ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
+ using OBO = OverflowingBinaryOperator;
+
+ // If the value has known zeros, the maximum value will have those known zeros
+ // as well.
+ if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
+ APInt Multiple = getNonZeroConstantMultiple(S);
+ APInt Remainder = APInt::getMaxValue(BitWidth).urem(Multiple);
+ if (!Remainder.isZero())
+ ConservativeResult =
+ ConstantRange(APInt::getMinValue(BitWidth),
+ APInt::getMaxValue(BitWidth) - Remainder + 1);
+ }
+ else {
+ uint32_t TZ = getMinTrailingZeros(S);
+ if (TZ != 0) {
+ ConservativeResult = ConstantRange(
+ APInt::getSignedMinValue(BitWidth),
+ APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
+ }
+ }
+
+ switch (S->getSCEVType()) {
+ case scConstant:
+ llvm_unreachable("Already handled above.");
+ case scVScale:
+ return setRange(S, SignHint, getVScaleRange(&F, BitWidth));
+ case scTruncate: {
+ const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(S);
+ ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint, Depth + 1);
+ return setRange(
+ Trunc, SignHint,
+ ConservativeResult.intersectWith(X.truncate(BitWidth), RangeType));
+ }
+ case scZeroExtend: {
+ const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(S);
+ ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint, Depth + 1);
+ return setRange(
+ ZExt, SignHint,
+ ConservativeResult.intersectWith(X.zeroExtend(BitWidth), RangeType));
+ }
+ case scSignExtend: {
+ const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(S);
+ ConstantRange X = getRangeRef(SExt->getOperand(), SignHint, Depth + 1);
+ return setRange(
+ SExt, SignHint,
+ ConservativeResult.intersectWith(X.signExtend(BitWidth), RangeType));
+ }
+ case scPtrToAddr: {
+ const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
+ ConstantRange X = getRangeRef(Cast->getOperand(), SignHint, Depth + 1);
+ return setRange(Cast, SignHint, X);
+ }
+ case scAddExpr: {
+ const SCEVAddExpr *Add = cast<SCEVAddExpr>(S);
+ // Check if this is a URem pattern: A - (A / B) * B, which is always < B.
+ const SCEV *URemLHS = nullptr, *URemRHS = nullptr;
+ if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED &&
+ match(S, m_scev_URem(m_SCEV(URemLHS), m_SCEV(URemRHS), *this))) {
+ ConstantRange LHSRange = getRangeRef(URemLHS, SignHint, Depth + 1);
+ ConstantRange RHSRange = getRangeRef(URemRHS, SignHint, Depth + 1);
+ ConservativeResult =
+ ConservativeResult.intersectWith(LHSRange.urem(RHSRange), RangeType);
+ }
+ ConstantRange X = getRangeRef(Add->getOperand(0), SignHint, Depth + 1);
+ unsigned WrapType = OBO::AnyWrap;
+ if (Add->hasNoSignedWrap())
+ WrapType |= OBO::NoSignedWrap;
+ if (Add->hasNoUnsignedWrap())
+ WrapType |= OBO::NoUnsignedWrap;
+ for (const SCEV *Op : drop_begin(Add->operands()))
+ X = X.addWithNoWrap(getRangeRef(Op, SignHint, Depth + 1), WrapType,
+ RangeType);
+ return setRange(Add, SignHint,
+ ConservativeResult.intersectWith(X, RangeType));
+ }
+ case scMulExpr: {
+ const SCEVMulExpr *Mul = cast<SCEVMulExpr>(S);
+ ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint, Depth + 1);
+ for (const SCEV *Op : drop_begin(Mul->operands()))
+ X = X.multiply(getRangeRef(Op, SignHint, Depth + 1));
+ return setRange(Mul, SignHint,
+ ConservativeResult.intersectWith(X, RangeType));
+ }
+ case scUDivExpr: {
+ const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
+ ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint, Depth + 1);
+ ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint, Depth + 1);
+ return setRange(UDiv, SignHint,
+ ConservativeResult.intersectWith(X.udiv(Y), RangeType));
+ }
+ case scAddRecExpr: {
+ const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(S);
+ // If there's no unsigned wrap, the value will never be less than its
+ // initial value.
+ if (AddRec->hasNoUnsignedWrap()) {
+ APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
+ if (!UnsignedMinValue.isZero())
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
+ }
+
+ // If there's no signed wrap, and all the operands except initial value have
+ // the same sign or zero, the value won't ever be:
+ // 1: smaller than initial value if operands are non negative,
+ // 2: bigger than initial value if operands are non positive.
+ // For both cases, value can not cross signed min/max boundary.
+ if (AddRec->hasNoSignedWrap()) {
+ bool AllNonNeg = true;
+ bool AllNonPos = true;
+ for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
+ if (!isKnownNonNegative(AddRec->getOperand(i)))
+ AllNonNeg = false;
+ if (!isKnownNonPositive(AddRec->getOperand(i)))
+ AllNonPos = false;
+ }
+ if (AllNonNeg)
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
+ APInt::getSignedMinValue(BitWidth)),
+ RangeType);
+ else if (AllNonPos)
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange::getNonEmpty(APInt::getSignedMinValue(BitWidth),
+ getSignedRangeMax(AddRec->getStart()) +
+ 1),
+ RangeType);
+ }
+
+ // TODO: non-affine addrec
+ if (AddRec->isAffine()) {
+ const SCEV *MaxBEScev =
+ getConstantMaxBackedgeTakenCount(AddRec->getLoop());
+ if (!isa<SCEVCouldNotCompute>(MaxBEScev)) {
+ APInt MaxBECount = cast<SCEVConstant>(MaxBEScev)->getAPInt();
+
+ // Adjust MaxBECount to the same bitwidth as AddRec. We can truncate if
+ // MaxBECount's active bits are all <= AddRec's bit width.
+ if (MaxBECount.getBitWidth() > BitWidth &&
+ MaxBECount.getActiveBits() <= BitWidth)
+ MaxBECount = MaxBECount.trunc(BitWidth);
+ else if (MaxBECount.getBitWidth() < BitWidth)
+ MaxBECount = MaxBECount.zext(BitWidth);
+
+ if (MaxBECount.getBitWidth() == BitWidth) {
+ auto [RangeFromAffine, Flags] = getRangeForAffineAR(
+ AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount);
+ ConservativeResult =
+ ConservativeResult.intersectWith(RangeFromAffine, RangeType);
+ const_cast<SCEVAddRecExpr *>(AddRec)->setNoWrapFlags(Flags);
+
+ auto RangeFromFactoring = getRangeViaFactoring(
+ AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount);
+ ConservativeResult =
+ ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
+ }
+ }
+
+ // Now try symbolic BE count and more powerful methods.
+ if (UseExpensiveRangeSharpening) {
+ const SCEV *SymbolicMaxBECount =
+ getSymbolicMaxBackedgeTakenCount(AddRec->getLoop());
+ if (!isa<SCEVCouldNotCompute>(SymbolicMaxBECount) &&
+ getTypeSizeInBits(MaxBEScev->getType()) <= BitWidth &&
+ AddRec->hasNoSelfWrap()) {
+ auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR(
+ AddRec, SymbolicMaxBECount, BitWidth, SignHint);
+ ConservativeResult =
+ ConservativeResult.intersectWith(RangeFromAffineNew, RangeType);
+ }
+ }
+ }
+
+ return setRange(AddRec, SignHint, std::move(ConservativeResult));
+ }
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr: {
+ Intrinsic::ID ID;
+ switch (S->getSCEVType()) {
+ case scUMaxExpr:
+ ID = Intrinsic::umax;
+ break;
+ case scSMaxExpr:
+ ID = Intrinsic::smax;
+ break;
+ case scUMinExpr:
+ case scSequentialUMinExpr:
+ ID = Intrinsic::umin;
+ break;
+ case scSMinExpr:
+ ID = Intrinsic::smin;
+ break;
+ default:
+ llvm_unreachable("Unknown SCEVMinMaxExpr/SCEVSequentialMinMaxExpr.");
+ }
+
+ const auto *NAry = cast<SCEVNAryExpr>(S);
+ ConstantRange X = getRangeRef(NAry->getOperand(0), SignHint, Depth + 1);
+ for (unsigned i = 1, e = NAry->getNumOperands(); i != e; ++i)
+ X = X.intrinsic(
+ ID, {X, getRangeRef(NAry->getOperand(i), SignHint, Depth + 1)});
+ return setRange(S, SignHint,
+ ConservativeResult.intersectWith(X, RangeType));
+ }
+ case scUnknown: {
+ const SCEVUnknown *U = cast<SCEVUnknown>(S);
+ Value *V = U->getValue();
+
+ // Check if the IR explicitly contains !range metadata.
+ std::optional<ConstantRange> MDRange = GetRangeFromMetadata(V);
+ if (MDRange)
+ ConservativeResult =
+ ConservativeResult.intersectWith(*MDRange, RangeType);
+
+ // Use facts about recurrences in the underlying IR. Note that add
+ // recurrences are AddRecExprs and thus don't hit this path. This
+ // primarily handles shift recurrences.
+ auto CR = getRangeForUnknownRecurrence(U);
+ ConservativeResult = ConservativeResult.intersectWith(CR);
+
+ // See if ValueTracking can give us a useful range.
+ const DataLayout &DL = getDataLayout();
+ KnownBits Known = computeKnownBits(V, DL, &AC, nullptr, &DT);
+ if (Known.getBitWidth() != BitWidth)
+ Known = Known.zextOrTrunc(BitWidth);
+
+ // ValueTracking may be able to compute a tighter result for the number of
+ // sign bits than for the value of those sign bits.
+ unsigned NS = ComputeNumSignBits(V, DL, &AC, nullptr, &DT);
+ if (U->getType()->isPointerTy()) {
+ // If the pointer size is larger than the index size type, this can cause
+ // NS to be larger than BitWidth. So compensate for this.
+ unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
+ int ptrIdxDiff = ptrSize - BitWidth;
+ if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
+ NS -= ptrIdxDiff;
+ }
+
+ if (NS > 1) {
+ // If we know any of the sign bits, we know all of the sign bits.
+ if (!Known.Zero.getHiBits(NS).isZero())
+ Known.Zero.setHighBits(NS);
+ if (!Known.One.getHiBits(NS).isZero())
+ Known.One.setHighBits(NS);
+ }
+
+ if (Known.getMinValue() != Known.getMaxValue() + 1)
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
+ RangeType);
+ if (NS > 1)
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
+ APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
+ RangeType);
+
+ if (U->getType()->isPointerTy() && SignHint == HINT_RANGE_UNSIGNED) {
+ // Strengthen the range if the underlying IR value is a
+ // global/alloca/heap allocation using the size of the object.
+ bool CanBeNull;
+ uint64_t DerefBytes = V->getPointerDereferenceableBytes(
+ DL, CanBeNull, /*CanBeFreed=*/nullptr);
+ if (DerefBytes > 1 && isUIntN(BitWidth, DerefBytes)) {
+ // The highest address the object can start is DerefBytes bytes before
+ // the end (unsigned max value). If this value is not a multiple of the
+ // alignment, the last possible start value is the next lowest multiple
+ // of the alignment. Note: The computations below cannot overflow,
+ // because if they would there's no possible start address for the
+ // object.
+ APInt MaxVal =
+ APInt::getMaxValue(BitWidth) - APInt(BitWidth, DerefBytes);
+ uint64_t Align = U->getValue()->getPointerAlignment(DL).value();
+ uint64_t Rem = MaxVal.urem(Align);
+ MaxVal -= APInt(BitWidth, Rem);
+ APInt MinVal = APInt::getZero(BitWidth);
+ if (llvm::isKnownNonZero(V, DL))
+ MinVal = Align;
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange::getNonEmpty(MinVal, MaxVal + 1), RangeType);
+ }
+ }
+
+ // A range of Phi is a subset of union of all ranges of its input.
+ if (PHINode *Phi = dyn_cast<PHINode>(V)) {
+ // SCEVExpander sometimes creates SCEVUnknowns that are secretly
+ // AddRecs; return the range for the corresponding AddRec.
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(getSCEV(V)))
+ return getRangeRef(AR, SignHint, Depth + 1);
+
+ // Make sure that we do not run over cycled Phis.
+ if (RangeRefPHIAllowedOperands(DT, Phi)) {
+ ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
+
+ for (const auto &Op : Phi->operands()) {
+ auto OpRange = getRangeRef(getSCEV(Op), SignHint, Depth + 1);
+ RangeFromOps = RangeFromOps.unionWith(OpRange);
+ // No point to continue if we already have a full set.
+ if (RangeFromOps.isFullSet())
+ break;
+ }
+ ConservativeResult =
+ ConservativeResult.intersectWith(RangeFromOps, RangeType);
+ }
+ }
+
+ // vscale can't be equal to zero
+ if (const auto *II = dyn_cast<IntrinsicInst>(V))
+ if (II->getIntrinsicID() == Intrinsic::vscale) {
+ ConstantRange Disallowed = APInt::getZero(BitWidth);
+ ConservativeResult = ConservativeResult.difference(Disallowed);
+ }
+
+ return setRange(U, SignHint, std::move(ConservativeResult));
+ }
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+
+ return setRange(S, SignHint, std::move(ConservativeResult));
+}
+
+// Given a StartRange, Step and MaxBECount for an expression compute a range of
+// values that the expression can take. Initially, the expression has a value
+// from StartRange and then is changed by Step up to MaxBECount times. Signed
+// argument defines if we treat Step as signed or unsigned. The second return
+// value indicates that no wrapping occurred.
+static std::pair<ConstantRange, bool>
+getRangeForAffineARHelper(APInt Step, const ConstantRange &StartRange,
+ const APInt &MaxBECount, bool Signed) {
+ unsigned BitWidth = Step.getBitWidth();
+ assert(BitWidth == StartRange.getBitWidth() &&
+ BitWidth == MaxBECount.getBitWidth() && "mismatched bit widths");
+ // If either Step or MaxBECount is 0, then the expression won't change, and we
+ // just need to return the initial range.
+ if (Step == 0 || MaxBECount == 0)
+ return {StartRange, true};
+
+ // If we don't know anything about the initial value (i.e. StartRange is
+ // FullRange), then we don't know anything about the final range either.
+ // Return FullRange.
+ if (StartRange.isFullSet())
+ return {ConstantRange::getFull(BitWidth), false};
+
+ // If Step is signed and negative, then we use its absolute value, but we also
+ // note that we're moving in the opposite direction.
+ bool Descending = Signed && Step.isNegative();
+
+ if (Signed)
+ // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
+ // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
+ // This equations hold true due to the well-defined wrap-around behavior of
+ // APInt.
+ Step = Step.abs();
+
+ // Check if Offset is more than full span of BitWidth. If it is, the
+ // expression is guaranteed to overflow.
+ if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
+ return {ConstantRange::getFull(BitWidth), false};
+
+ // Offset is by how much the expression can change. Checks above guarantee no
+ // overflow here.
+ APInt Offset = Step * MaxBECount;
+
+ // Minimum value of the final range will match the minimal value of StartRange
+ // if the expression is increasing and will be decreased by Offset otherwise.
+ // Maximum value of the final range will match the maximal value of StartRange
+ // if the expression is decreasing and will be increased by Offset otherwise.
+ APInt StartLower = StartRange.getLower();
+ APInt StartUpper = StartRange.getUpper() - 1;
+ bool Overflow;
+ APInt MovedBoundary;
+ if (Signed) {
+ // This does not use sadd_ov, as we want to check overflow for a signed
+ // start with an unsigned offset.
+ if (Descending) {
+ MovedBoundary = StartLower - std::move(Offset);
+ Overflow = MovedBoundary.sgt(StartLower) || StartRange.isSignWrappedSet();
+ } else {
+ MovedBoundary = StartUpper + std::move(Offset);
+ Overflow = MovedBoundary.slt(StartUpper) || StartRange.isSignWrappedSet();
+ }
+ } else {
+ MovedBoundary = StartUpper.uadd_ov(std::move(Offset), Overflow);
+ Overflow |= StartRange.isWrappedSet();
+ }
+
+ // It's possible that the new minimum/maximum value will fall into the initial
+ // range (due to wrap around). This means that the expression can take any
+ // value in this bitwidth, and we have to return full range.
+ if (StartRange.contains(MovedBoundary))
+ return {ConstantRange::getFull(BitWidth), false};
+
+ APInt NewLower =
+ Descending ? std::move(MovedBoundary) : std::move(StartLower);
+ APInt NewUpper =
+ Descending ? std::move(StartUpper) : std::move(MovedBoundary);
+ NewUpper += 1;
+
+ // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
+ return {ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper)),
+ !Overflow};
+}
+
+std::pair<ConstantRange, SCEV::NoWrapFlags>
+ScalarEvolution::getRangeForAffineAR(const SCEV *Start, const SCEV *Step,
+ const APInt &MaxBECount) {
+ assert(getTypeSizeInBits(Start->getType()) ==
+ getTypeSizeInBits(Step->getType()) &&
+ getTypeSizeInBits(Start->getType()) == MaxBECount.getBitWidth() &&
+ "mismatched bit widths");
+
+ // First, consider step signed.
+ ConstantRange StartSRange = getSignedRange(Start);
+ ConstantRange StepSRange = getSignedRange(Step);
+
+ // If Step can be both positive and negative, we need to find ranges for the
+ // maximum absolute step values in both directions and union them.
+ auto [SR1, NSW1] = getRangeForAffineARHelper(
+ StepSRange.getSignedMin(), StartSRange, MaxBECount, /*Signed=*/true);
+ auto [SR2, NSW2] = getRangeForAffineARHelper(StepSRange.getSignedMax(),
+ StartSRange, MaxBECount,
+ /*Signed=*/true);
+ ConstantRange SR = SR1.unionWith(SR2);
+
+ // Next, consider step unsigned.
+ auto [UR, NUW] = getRangeForAffineARHelper(
+ getUnsignedRangeMax(Step), getUnsignedRange(Start), MaxBECount,
+ /*Signed=*/false);
+
+ SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
+ if (NUW)
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ if (NSW1 && NSW2)
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
+
+ // Finally, intersect signed and unsigned ranges.
+ return {SR.intersectWith(UR, ConstantRange::Smallest), Flags};
+}
+
+ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR(
+ const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth,
+ ScalarEvolution::RangeSignHint SignHint) {
+ assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n");
+ assert(AddRec->hasNoSelfWrap() &&
+ "This only works for non-self-wrapping AddRecs!");
+ const bool IsSigned = SignHint == HINT_RANGE_SIGNED;
+ const SCEV *Step = AddRec->getStepRecurrence(*this);
+ // Only deal with constant step to save compile time.
+ if (!isa<SCEVConstant>(Step))
+ return ConstantRange::getFull(BitWidth);
+ // Let's make sure that we can prove that we do not self-wrap during
+ // MaxBECount iterations. We need this because MaxBECount is a maximum
+ // iteration count estimate, and we might infer nw from some exit for which we
+ // do not know max exit count (or any other side reasoning).
+ // TODO: Turn into assert at some point.
+ if (getTypeSizeInBits(MaxBECount->getType()) >
+ getTypeSizeInBits(AddRec->getType()))
+ return ConstantRange::getFull(BitWidth);
+ MaxBECount = getNoopOrZeroExtend(MaxBECount, AddRec->getType());
+ const SCEV *RangeWidth = getMinusOne(AddRec->getType());
+ const SCEV *StepAbs = getUMinExpr(Step, getNegativeSCEV(Step));
+ const SCEV *MaxItersWithoutWrap = getUDivExpr(RangeWidth, StepAbs);
+ if (!isKnownPredicateViaConstantRanges(ICmpInst::ICMP_ULE, MaxBECount,
+ MaxItersWithoutWrap))
+ return ConstantRange::getFull(BitWidth);
+
+ ICmpInst::Predicate LEPred =
+ IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
+ ICmpInst::Predicate GEPred =
+ IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
+ const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
+
+ // We know that there is no self-wrap. Let's take Start and End values and
+ // look at all intermediate values V1, V2, ..., Vn that IndVar takes during
+ // the iteration. They either lie inside the range [Min(Start, End),
+ // Max(Start, End)] or outside it:
+ //
+ // Case 1: RangeMin ... Start V1 ... VN End ... RangeMax;
+ // Case 2: RangeMin Vk ... V1 Start ... End Vn ... Vk + 1 RangeMax;
+ //
+ // No self wrap flag guarantees that the intermediate values cannot be BOTH
+ // outside and inside the range [Min(Start, End), Max(Start, End)]. Using that
+ // knowledge, let's try to prove that we are dealing with Case 1. It is so if
+ // Start <= End and step is positive, or Start >= End and step is negative.
+ const SCEV *Start = applyLoopGuards(AddRec->getStart(), AddRec->getLoop());
+ ConstantRange StartRange = getRangeRef(Start, SignHint);
+ ConstantRange EndRange = getRangeRef(End, SignHint);
+ ConstantRange RangeBetween = StartRange.unionWith(EndRange);
+ // If they already cover full iteration space, we will know nothing useful
+ // even if we prove what we want to prove.
+ if (RangeBetween.isFullSet())
+ return RangeBetween;
+ // Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax).
+ bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet()
+ : RangeBetween.isWrappedSet();
+ if (IsWrappedSet)
+ return ConstantRange::getFull(BitWidth);
+
+ if (isKnownPositive(Step) &&
+ isKnownPredicateViaConstantRanges(LEPred, Start, End))
+ return RangeBetween;
+ if (isKnownNegative(Step) &&
+ isKnownPredicateViaConstantRanges(GEPred, Start, End))
+ return RangeBetween;
+ return ConstantRange::getFull(BitWidth);
+}
+
+ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
+ const SCEV *Step,
+ const APInt &MaxBECount) {
+ // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
+ // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
+
+ unsigned BitWidth = MaxBECount.getBitWidth();
+ assert(getTypeSizeInBits(Start->getType()) == BitWidth &&
+ getTypeSizeInBits(Step->getType()) == BitWidth &&
+ "mismatched bit widths");
+
+ struct SelectPattern {
+ Value *Condition = nullptr;
+ APInt TrueValue;
+ APInt FalseValue;
+
+ explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
+ const SCEV *S) {
+ std::optional<unsigned> CastOp;
+ APInt Offset(BitWidth, 0);
+
+ assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
+ "Should be!");
+
+ // Peel off a constant offset. In the future we could consider being
+ // smarter here and handle {Start+Step,+,Step} too.
+ const APInt *Off;
+ if (match(S, m_scev_Add(m_scev_APInt(Off), m_SCEV(S))))
+ Offset = *Off;
+
+ // Peel off a cast operation
+ if (auto *SCast = dyn_cast<SCEVIntegralCastExpr>(S)) {
+ CastOp = SCast->getSCEVType();
+ S = SCast->getOperand();
+ }
+
+ using namespace llvm::PatternMatch;
+
+ auto *SU = dyn_cast<SCEVUnknown>(S);
+ const APInt *TrueVal, *FalseVal;
+ if (!SU ||
+ !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
+ m_APInt(FalseVal)))) {
+ Condition = nullptr;
+ return;
+ }
+
+ TrueValue = *TrueVal;
+ FalseValue = *FalseVal;
+
+ // Re-apply the cast we peeled off earlier
+ if (CastOp)
+ switch (*CastOp) {
+ default:
+ llvm_unreachable("Unknown SCEV cast type!");
+
+ case scTruncate:
+ TrueValue = TrueValue.trunc(BitWidth);
+ FalseValue = FalseValue.trunc(BitWidth);
+ break;
+ case scZeroExtend:
+ TrueValue = TrueValue.zext(BitWidth);
+ FalseValue = FalseValue.zext(BitWidth);
+ break;
+ case scSignExtend:
+ TrueValue = TrueValue.sext(BitWidth);
+ FalseValue = FalseValue.sext(BitWidth);
+ break;
+ }
+
+ // Re-apply the constant offset we peeled off earlier
+ TrueValue += Offset;
+ FalseValue += Offset;
+ }
+
+ bool isRecognized() { return Condition != nullptr; }
+ };
+
+ SelectPattern StartPattern(*this, BitWidth, Start);
+ if (!StartPattern.isRecognized())
+ return ConstantRange::getFull(BitWidth);
+
+ SelectPattern StepPattern(*this, BitWidth, Step);
+ if (!StepPattern.isRecognized())
+ return ConstantRange::getFull(BitWidth);
+
+ if (StartPattern.Condition != StepPattern.Condition) {
+ // We don't handle this case today; but we could, by considering four
+ // possibilities below instead of two. I'm not sure if there are cases where
+ // that will help over what getRange already does, though.
+ return ConstantRange::getFull(BitWidth);
+ }
+
+ // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
+ // construct arbitrary general SCEV expressions here. This function is called
+ // from deep in the call stack, and calling getSCEV (on a sext instruction,
+ // say) can end up caching a suboptimal value.
+
+ // FIXME: without the explicit `this` receiver below, MSVC errors out with
+ // C2352 and C2512 (otherwise it isn't needed).
+
+ const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
+ const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
+ const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
+ const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
+
+ ConstantRange TrueRange =
+ this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount).first;
+ ConstantRange FalseRange =
+ this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount).first;
+
+ return TrueRange.unionWith(FalseRange);
+}
+
+SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
+ if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
+ const BinaryOperator *BinOp = cast<BinaryOperator>(V);
+
+ // Return early if there are no flags to propagate to the SCEV.
+ SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
+ if (auto *PDI = dyn_cast<PossiblyDisjointInst>(BinOp);
+ PDI && PDI->isDisjoint()) {
+ Flags = ScalarEvolution::setFlags(SCEV::FlagNUW, SCEV::FlagNSW);
+ } else {
+ if (BinOp->hasNoUnsignedWrap())
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
+ if (BinOp->hasNoSignedWrap())
+ Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
+ }
+ if (Flags == SCEV::FlagAnyWrap)
+ return SCEV::FlagAnyWrap;
+
+ return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
+}
+
+const Instruction *
+ScalarEvolution::getNonTrivialDefiningScopeBound(const SCEV *S) {
+ if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S))
+ return &*AddRec->getLoop()->getHeader()->begin();
+ if (auto *U = dyn_cast<SCEVUnknown>(S))
+ if (auto *I = dyn_cast<Instruction>(U->getValue()))
+ return I;
+ return nullptr;
+}
+
+const Instruction *ScalarEvolution::getDefiningScopeBound(ArrayRef<SCEVUse> Ops,
+ bool &Precise) {
+ Precise = true;
+ // Do a bounded search of the def relation of the requested SCEVs.
+ SmallPtrSet<const SCEV *, 16> Visited;
+ SmallVector<SCEVUse> Worklist;
+ auto pushOp = [&](const SCEV *S) {
+ if (!Visited.insert(S).second)
+ return;
+ // Threshold of 30 here is arbitrary.
+ if (Visited.size() > 30) {
+ Precise = false;
+ return;
+ }
+ Worklist.push_back(S);
+ };
+
+ for (SCEVUse S : Ops)
+ pushOp(S);
+
+ const Instruction *Bound = nullptr;
+ while (!Worklist.empty()) {
+ SCEVUse S = Worklist.pop_back_val();
+ if (auto *DefI = getNonTrivialDefiningScopeBound(S)) {
+ if (!Bound || DT.dominates(Bound, DefI))
+ Bound = DefI;
+ } else {
+ for (SCEVUse Op : S->operands())
+ pushOp(Op);
+ }
+ }
+ return Bound ? Bound : &*F.getEntryBlock().begin();
+}
+
+const Instruction *
+ScalarEvolution::getDefiningScopeBound(ArrayRef<SCEVUse> Ops) {
+ bool Discard;
+ return getDefiningScopeBound(Ops, Discard);
+}
+
+bool ScalarEvolution::isGuaranteedToTransferExecutionTo(const Instruction *A,
+ const Instruction *B) {
+ if (A->getParent() == B->getParent() &&
+ isGuaranteedToTransferExecutionToSuccessor(A->getIterator(),
+ B->getIterator()))
+ return true;
+
+ auto *BLoop = LI.getLoopFor(B->getParent());
+ if (BLoop && BLoop->getHeader() == B->getParent() &&
+ BLoop->getLoopPreheader() == A->getParent() &&
+ isGuaranteedToTransferExecutionToSuccessor(A->getIterator(),
+ A->getParent()->end()) &&
+ isGuaranteedToTransferExecutionToSuccessor(B->getParent()->begin(),
+ B->getIterator()))
+ return true;
+ return false;
+}
+
+bool ScalarEvolution::isGuaranteedNotToBePoison(const SCEV *Op) {
+ SCEVPoisonCollector PC(/* LookThroughMaybePoisonBlocking */ true);
+ visitAll(Op, PC);
+ return PC.MaybePoison.empty();
+}
+
+bool ScalarEvolution::isGuaranteedNotToCauseUB(const SCEV *Op) {
+ return !SCEVExprContains(Op, [this](const SCEV *S) {
+ const SCEV *Op1;
+ bool M = match(S, m_scev_UDiv(m_SCEV(), m_SCEV(Op1)));
+ // The UDiv may be UB if the divisor is poison or zero. Unless the divisor
+ // is a non-zero constant, we have to assume the UDiv may be UB.
+ return M && (!isKnownNonZero(Op1) || !isGuaranteedNotToBePoison(Op1));
+ });
+}
+
+bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
+ // Only proceed if we can prove that I does not yield poison.
+ if (!programUndefinedIfPoison(I))
+ return false;
+
+ // At this point we know that if I is executed, then it does not wrap
+ // according to at least one of NSW or NUW. If I is not executed, then we do
+ // not know if the calculation that I represents would wrap. Multiple
+ // instructions can map to the same SCEV. If we apply NSW or NUW from I to
+ // the SCEV, we must guarantee no wrapping for that SCEV also when it is
+ // derived from other instructions that map to the same SCEV. We cannot make
+ // that guarantee for cases where I is not executed. So we need to find a
+ // upper bound on the defining scope for the SCEV, and prove that I is
+ // executed every time we enter that scope. When the bounding scope is a
+ // loop (the common case), this is equivalent to proving I executes on every
+ // iteration of that loop.
+ SmallVector<SCEVUse> SCEVOps;
+ for (const Use &Op : I->operands()) {
+ // I could be an extractvalue from a call to an overflow intrinsic.
+ // TODO: We can do better here in some cases.
+ if (isSCEVable(Op->getType()))
+ SCEVOps.push_back(getSCEV(Op));
+ }
+ auto *DefI = getDefiningScopeBound(SCEVOps);
+ return isGuaranteedToTransferExecutionTo(DefI, I);
+}
+
+bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
+ // If we know that \c I can never be poison period, then that's enough.
+ if (isSCEVExprNeverPoison(I))
+ return true;
+
+ // If the loop only has one exit, then we know that, if the loop is entered,
+ // any instruction dominating that exit will be executed. If any such
+ // instruction would result in UB, the addrec cannot be poison.
+ //
+ // This is basically the same reasoning as in isSCEVExprNeverPoison(), but
+ // also handles uses outside the loop header (they just need to dominate the
+ // single exit).
+
+ auto *ExitingBB = L->getExitingBlock();
+ if (!ExitingBB || !loopHasNoAbnormalExits(L))
+ return false;
+
+ SmallPtrSet<const Value *, 16> KnownPoison;
+ SmallVector<const Instruction *, 8> Worklist;
+
+ // We start by assuming \c I, the post-inc add recurrence, is poison. Only
+ // things that are known to be poison under that assumption go on the
+ // Worklist.
+ KnownPoison.insert(I);
+ Worklist.push_back(I);
+
+ while (!Worklist.empty()) {
+ const Instruction *Poison = Worklist.pop_back_val();
+
+ for (const Use &U : Poison->uses()) {
+ const Instruction *PoisonUser = cast<Instruction>(U.getUser());
+ if (mustTriggerUB(PoisonUser, KnownPoison) &&
+ DT.dominates(PoisonUser->getParent(), ExitingBB))
+ return true;
+
+ if (propagatesPoison(U) && L->contains(PoisonUser))
+ if (KnownPoison.insert(PoisonUser).second)
+ Worklist.push_back(PoisonUser);
+ }
+ }
+
+ return false;
+}
+
+ScalarEvolution::LoopProperties
+ScalarEvolution::getLoopProperties(const Loop *L) {
+ using LoopProperties = ScalarEvolution::LoopProperties;
+
+ auto Itr = LoopPropertiesCache.find(L);
+ if (Itr == LoopPropertiesCache.end()) {
+ auto HasSideEffects = [](Instruction *I) {
+ if (auto *SI = dyn_cast<StoreInst>(I))
+ return !SI->isSimple();
+
+ if (I->mayThrow())
+ return true;
+
+ // Non-volatile memset / memcpy do not count as side-effect for forward
+ // progress.
+ if (isa<MemIntrinsic>(I) && !I->isVolatile())
+ return false;
+
+ return I->mayWriteToMemory();
+ };
+
+ LoopProperties LP = {/* HasNoAbnormalExits */ true,
+ /*HasNoSideEffects*/ true};
+
+ for (auto *BB : L->getBlocks())
+ for (auto &I : *BB) {
+ if (!isGuaranteedToTransferExecutionToSuccessor(&I))
+ LP.HasNoAbnormalExits = false;
+ if (HasSideEffects(&I))
+ LP.HasNoSideEffects = false;
+ if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
+ break; // We're already as pessimistic as we can get.
+ }
+
+ auto InsertPair = LoopPropertiesCache.insert({L, LP});
+ assert(InsertPair.second && "We just checked!");
+ Itr = InsertPair.first;
+ }
+
+ return Itr->second;
+}
+
+bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) {
+ // A mustprogress loop without side effects must be finite.
+ // TODO: The check used here is very conservative. It's only *specific*
+ // side effects which are well defined in infinite loops.
+ return isFinite(L) || (isMustProgress(L) && loopHasNoSideEffects(L));
+}
+
+const SCEV *ScalarEvolution::createSCEVIter(Value *V) {
+ // Worklist item with a Value and a bool indicating whether all operands have
+ // been visited already.
+ using PointerTy = PointerIntPair<Value *, 1, bool>;
+ SmallVector<PointerTy> Stack;
+
+ Stack.emplace_back(V, false);
+ while (!Stack.empty()) {
+ auto E = Stack.back();
+ Value *CurV = E.getPointer();
+
+ if (getExistingSCEV(CurV)) {
+ Stack.pop_back();
+ continue;
+ }
+
+ SmallVector<Value *> Ops;
+ const SCEV *CreatedSCEV = nullptr;
+ // If all operands have been visited already, create the SCEV.
+ if (E.getInt()) {
+ CreatedSCEV = createSCEV(CurV);
+ } else {
+ // Otherwise get the operands we need to create SCEV's for before creating
+ // the SCEV for CurV. If the SCEV for CurV can be constructed trivially,
+ // just use it.
+ CreatedSCEV = getOperandsToCreate(CurV, Ops);
+ }
+
+ if (CreatedSCEV) {
+ insertValueToMap(CurV, CreatedSCEV);
+ Stack.pop_back();
+ } else {
+ Stack.back().setInt(true);
+ // Queue its operands which need to be constructed.
+ for (Value *Op : Ops)
+ Stack.emplace_back(Op, false);
+ }
+ }
+
+ return getExistingSCEV(V);
+}
+
+const SCEV *
+ScalarEvolution::getOperandsToCreate(Value *V, SmallVectorImpl<Value *> &Ops) {
+ if (!isSCEVable(V->getType()))
+ return getUnknown(V);
+
+ if (Instruction *I = dyn_cast<Instruction>(V)) {
+ // Don't attempt to analyze instructions in blocks that aren't
+ // reachable. Such instructions don't matter, and they aren't required
+ // to obey basic rules for definitions dominating uses which this
+ // analysis depends on.
+ if (!DT.isReachableFromEntry(I->getParent()))
+ return getUnknown(PoisonValue::get(V->getType()));
+ } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
+ return getConstant(CI);
+ else if (isa<GlobalAlias>(V))
+ return getUnknown(V);
+ else if (!isa<ConstantExpr>(V))
+ return getUnknown(V);
+
+ Operator *U = cast<Operator>(V);
+ if (auto BO =
+ MatchBinaryOp(U, getDataLayout(), AC, DT, dyn_cast<Instruction>(V))) {
+ bool IsConstArg = isa<ConstantInt>(BO->RHS);
+ switch (BO->Opcode) {
+ case Instruction::Add:
+ case Instruction::Mul: {
+ // For additions and multiplications, traverse add/mul chains for which we
+ // can potentially create a single SCEV, to reduce the number of
+ // get{Add,Mul}Expr calls.
+ do {
+ if (BO->Op) {
+ if (BO->Op != V && getExistingSCEV(BO->Op)) {
+ Ops.push_back(BO->Op);
+ break;
+ }
+ }
+ Ops.push_back(BO->RHS);
+ auto NewBO = MatchBinaryOp(BO->LHS, getDataLayout(), AC, DT,
+ dyn_cast<Instruction>(V));
+ if (!NewBO ||
+ (BO->Opcode == Instruction::Add &&
+ (NewBO->Opcode != Instruction::Add &&
+ NewBO->Opcode != Instruction::Sub)) ||
+ (BO->Opcode == Instruction::Mul &&
+ NewBO->Opcode != Instruction::Mul)) {
+ Ops.push_back(BO->LHS);
+ break;
+ }
+ // CreateSCEV calls getNoWrapFlagsFromUB, which under certain conditions
+ // requires a SCEV for the LHS.
+ if (BO->Op && (BO->IsNSW || BO->IsNUW)) {
+ auto *I = dyn_cast<Instruction>(BO->Op);
+ if (I && programUndefinedIfPoison(I)) {
+ Ops.push_back(BO->LHS);
+ break;
+ }
+ }
+ BO = NewBO;
+ } while (true);
+ return nullptr;
+ }
+ case Instruction::Sub:
+ case Instruction::UDiv:
+ case Instruction::URem:
+ break;
+ case Instruction::AShr:
+ case Instruction::Shl:
+ case Instruction::Xor:
+ if (!IsConstArg)
+ return nullptr;
+ break;
+ case Instruction::And:
+ case Instruction::Or:
+ if (!IsConstArg && !BO->LHS->getType()->isIntegerTy(1))
+ return nullptr;
+ break;
+ case Instruction::LShr:
+ return getUnknown(V);
+ default:
+ llvm_unreachable("Unhandled binop");
+ break;
+ }
+
+ Ops.push_back(BO->LHS);
+ Ops.push_back(BO->RHS);
+ return nullptr;
+ }
+
+ switch (U->getOpcode()) {
+ case Instruction::Trunc:
+ case Instruction::ZExt:
+ case Instruction::SExt:
+ case Instruction::PtrToAddr:
+ case Instruction::PtrToInt:
+ Ops.push_back(U->getOperand(0));
+ return nullptr;
+
+ case Instruction::BitCast:
+ if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) {
+ Ops.push_back(U->getOperand(0));
+ return nullptr;
+ }
+ return getUnknown(V);
+
+ case Instruction::SDiv:
+ case Instruction::SRem:
+ Ops.push_back(U->getOperand(0));
+ Ops.push_back(U->getOperand(1));
+ return nullptr;
+
+ case Instruction::GetElementPtr:
+ assert(cast<GEPOperator>(U)->getSourceElementType()->isSized() &&
+ "GEP source element type must be sized");
+ llvm::append_range(Ops, U->operands());
+ return nullptr;
+
+ case Instruction::IntToPtr:
+ return getUnknown(V);
+
+ case Instruction::PHI:
+ // getNodeForPHI has four ways to turn a PHI into a SCEV; retrieve the
+ // relevant nodes for each of them.
+ //
+ // The first is just to call simplifyInstruction, and get something back
+ // that isn't a PHI.
+ if (Value *V = simplifyInstruction(
+ cast<PHINode>(U),
+ {getDataLayout(), &TLI, &DT, &AC, /*CtxI=*/nullptr,
+ /*UseInstrInfo=*/true, /*CanUseUndef=*/false})) {
+ assert(V);
+ Ops.push_back(V);
+ return nullptr;
+ }
+ // The second is createNodeForPHIWithIdenticalOperands: this looks for
+ // operands which all perform the same operation, but haven't been
+ // CSE'ed for whatever reason.
+ if (BinaryOperator *BO = getCommonInstForPHI(cast<PHINode>(U))) {
+ assert(BO);
+ Ops.push_back(BO);
+ return nullptr;
+ }
+ // The third is createNodeFromSelectLikePHI; this takes a PHI which
+ // is equivalent to a select, and analyzes it like a select.
+ {
+ Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
+ if (getOperandsForSelectLikePHI(DT, cast<PHINode>(U), Cond, LHS, RHS)) {
+ assert(Cond);
+ assert(LHS);
+ assert(RHS);
+ if (auto *CondICmp = dyn_cast<ICmpInst>(Cond)) {
+ Ops.push_back(CondICmp->getOperand(0));
+ Ops.push_back(CondICmp->getOperand(1));
+ }
+ Ops.push_back(Cond);
+ Ops.push_back(LHS);
+ Ops.push_back(RHS);
+ return nullptr;
+ }
+ }
+ // The fourth way is createAddRecFromPHI. It's complicated to handle here,
+ // so just construct it recursively.
+ //
+ // In addition to getNodeForPHI, also construct nodes which might be needed
+ // by getRangeRef.
+ if (RangeRefPHIAllowedOperands(DT, cast<PHINode>(U))) {
+ for (Value *V : cast<PHINode>(U)->operands())
+ Ops.push_back(V);
+ return nullptr;
+ }
+ return nullptr;
+
+ case Instruction::Select: {
+ // Check if U is a select that can be simplified to a SCEVUnknown.
+ auto CanSimplifyToUnknown = [this, U]() {
+ if (U->getType()->isIntegerTy(1) || isa<ConstantInt>(U->getOperand(0)))
+ return false;
+
+ auto *ICI = dyn_cast<ICmpInst>(U->getOperand(0));
+ if (!ICI)
+ return false;
+ Value *LHS = ICI->getOperand(0);
+ Value *RHS = ICI->getOperand(1);
+ if (ICI->getPredicate() == CmpInst::ICMP_EQ ||
+ ICI->getPredicate() == CmpInst::ICMP_NE) {
+ if (!(isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()))
+ return true;
+ } else if (getTypeSizeInBits(LHS->getType()) >
+ getTypeSizeInBits(U->getType()))
+ return true;
+ return false;
+ };
+ if (CanSimplifyToUnknown())
+ return getUnknown(U);
+
+ llvm::append_range(Ops, U->operands());
+ return nullptr;
+ break;
+ }
+ case Instruction::Call:
+ case Instruction::Invoke:
+ if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand()) {
+ Ops.push_back(RV);
+ return nullptr;
+ }
+
+ if (auto *II = dyn_cast<IntrinsicInst>(U)) {
+ switch (II->getIntrinsicID()) {
+ case Intrinsic::abs:
+ Ops.push_back(II->getArgOperand(0));
+ return nullptr;
+ case Intrinsic::umax:
+ case Intrinsic::umin:
+ case Intrinsic::smax:
+ case Intrinsic::smin:
+ case Intrinsic::usub_sat:
+ case Intrinsic::uadd_sat:
+ Ops.push_back(II->getArgOperand(0));
+ Ops.push_back(II->getArgOperand(1));
+ return nullptr;
+ case Intrinsic::start_loop_iterations:
+ case Intrinsic::annotation:
+ case Intrinsic::ptr_annotation:
+ Ops.push_back(II->getArgOperand(0));
+ return nullptr;
+ default:
+ break;
+ }
+ }
+ break;
+ }
+
+ return nullptr;
+}
+
+const SCEV *ScalarEvolution::createSCEV(Value *V) {
+ if (!isSCEVable(V->getType()))
+ return getUnknown(V);
+
+ if (Instruction *I = dyn_cast<Instruction>(V)) {
+ // Don't attempt to analyze instructions in blocks that aren't
+ // reachable. Such instructions don't matter, and they aren't required
+ // to obey basic rules for definitions dominating uses which this
+ // analysis depends on.
+ if (!DT.isReachableFromEntry(I->getParent()))
+ return getUnknown(PoisonValue::get(V->getType()));
+ } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
+ return getConstant(CI);
+ else if (isa<GlobalAlias>(V))
+ return getUnknown(V);
+ else if (!isa<ConstantExpr>(V))
+ return getUnknown(V);
+
+ const SCEV *LHS;
+ const SCEV *RHS;
+
+ Operator *U = cast<Operator>(V);
+ if (auto BO =
+ MatchBinaryOp(U, getDataLayout(), AC, DT, dyn_cast<Instruction>(V))) {
+ switch (BO->Opcode) {
+ case Instruction::Add: {
+ // The simple thing to do would be to just call getSCEV on both operands
+ // and call getAddExpr with the result. However if we're looking at a
+ // bunch of things all added together, this can be quite inefficient,
+ // because it leads to N-1 getAddExpr calls for N ultimate operands.
+ // Instead, gather up all the operands and make a single getAddExpr call.
+ // LLVM IR canonical form means we need only traverse the left operands.
+ SmallVector<SCEVUse, 4> AddOps;
+ do {
+ if (BO->Op) {
+ if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
+ AddOps.push_back(OpSCEV);
+ break;
+ }
+
+ // If a NUW or NSW flag can be applied to the SCEV for this
+ // addition, then compute the SCEV for this addition by itself
+ // with a separate call to getAddExpr. We need to do that
+ // instead of pushing the operands of the addition onto AddOps,
+ // since the flags are only known to apply to this particular
+ // addition - they may not apply to other additions that can be
+ // formed with operands from AddOps.
+ const SCEV *RHS = getSCEV(BO->RHS);
+ SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
+ if (Flags != SCEV::FlagAnyWrap) {
+ const SCEV *LHS = getSCEV(BO->LHS);
+ if (BO->Opcode == Instruction::Sub)
+ AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
+ else
+ AddOps.push_back(getAddExpr(LHS, RHS, Flags));
+ break;
+ }
+ }
+
+ if (BO->Opcode == Instruction::Sub)
+ AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
+ else
+ AddOps.push_back(getSCEV(BO->RHS));
+
+ auto NewBO = MatchBinaryOp(BO->LHS, getDataLayout(), AC, DT,
+ dyn_cast<Instruction>(V));
+ if (!NewBO || (NewBO->Opcode != Instruction::Add &&
+ NewBO->Opcode != Instruction::Sub)) {
+ AddOps.push_back(getSCEV(BO->LHS));
+ break;
+ }
+ BO = NewBO;
+ } while (true);
+
+ return getAddExpr(AddOps);
+ }
+
+ case Instruction::Mul: {
+ SmallVector<SCEVUse, 4> MulOps;
+ do {
+ if (BO->Op) {
+ if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
+ MulOps.push_back(OpSCEV);
+ break;
+ }
+
+ SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
+ if (Flags != SCEV::FlagAnyWrap) {
+ LHS = getSCEV(BO->LHS);
+ RHS = getSCEV(BO->RHS);
+ MulOps.push_back(getMulExpr(LHS, RHS, Flags));
+ break;
+ }
+ }
+
+ MulOps.push_back(getSCEV(BO->RHS));
+ auto NewBO = MatchBinaryOp(BO->LHS, getDataLayout(), AC, DT,
+ dyn_cast<Instruction>(V));
+ if (!NewBO || NewBO->Opcode != Instruction::Mul) {
+ MulOps.push_back(getSCEV(BO->LHS));
+ break;
+ }
+ BO = NewBO;
+ } while (true);
+
+ return getMulExpr(MulOps);
+ }
+ case Instruction::UDiv:
+ LHS = getSCEV(BO->LHS);
+ RHS = getSCEV(BO->RHS);
+ return getUDivExpr(LHS, RHS);
+ case Instruction::URem:
+ LHS = getSCEV(BO->LHS);
+ RHS = getSCEV(BO->RHS);
+ return getURemExpr(LHS, RHS);
+ case Instruction::Sub: {
+ SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
+ if (BO->Op)
+ Flags = getNoWrapFlagsFromUB(BO->Op);
+
+ // Try to use ptrtoaddr for subtracts with at least one ptrtoint
+ // operand. While we don't model ptrtoint directly in SCEV, the
+ // difference between two pointer addresses is well-defined.
+ Value *PtrLHS = nullptr, *PtrRHS = nullptr;
+ bool HasPtrLHS = match(BO->LHS, m_PtrToInt(m_Value(PtrLHS)));
+ bool HasPtrRHS = match(BO->RHS, m_PtrToInt(m_Value(PtrRHS)));
+ if (HasPtrLHS || HasPtrRHS) {
+ // Convert a ptrtoint operand (OrigOp) to ptrtoaddr of its pointer
+ // PtrOp. When only one side is ptrtoint (BothPtr is false), skip
+ // SCEVUnknown pointers since wrapping them in ptrtoaddr adds no
+ // useful structure.
+ auto GetOp = [&](bool HasPtr, Value *PtrOp, Value *OrigOp,
+ bool BothPtr) -> const SCEV * {
+ if (!HasPtr)
+ return getSCEV(OrigOp);
+ const SCEV *PtrSCEV = getSCEV(PtrOp);
+ if (BothPtr || !isa<SCEVUnknown>(PtrSCEV)) {
+ const SCEV *Addr = getPtrToAddrExpr(PtrSCEV);
+ if (!isa<SCEVCouldNotCompute>(Addr) &&
+ getTypeSizeInBits(OrigOp->getType()) <=
+ getTypeSizeInBits(Addr->getType()))
+ return getTruncateOrNoop(Addr, OrigOp->getType());
+ }
+ return getSCEV(OrigOp);
+ };
+ const SCEV *L = GetOp(HasPtrLHS, PtrLHS, BO->LHS, HasPtrRHS);
+ const SCEV *R = GetOp(HasPtrRHS, PtrRHS, BO->RHS, HasPtrLHS);
+ return getMinusSCEV(L, R, Flags);
+ }
+
+ LHS = getSCEV(BO->LHS);
+ RHS = getSCEV(BO->RHS);
+ return getMinusSCEV(LHS, RHS, Flags);
+ }
+ case Instruction::And:
+ // For an expression like x&255 that merely masks off the high bits,
+ // use zext(trunc(x)) as the SCEV expression.
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
+ if (CI->isZero())
+ return getSCEV(BO->RHS);
+ if (CI->isMinusOne())
+ return getSCEV(BO->LHS);
+ const APInt &A = CI->getValue();
+
+ // Instcombine's ShrinkDemandedConstant may strip bits out of
+ // constants, obscuring what would otherwise be a low-bits mask.
+ // Use computeKnownBits to compute what ShrinkDemandedConstant
+ // knew about to reconstruct a low-bits mask value.
+ unsigned LZ = A.countl_zero();
+ unsigned TZ = A.countr_zero();
+ unsigned BitWidth = A.getBitWidth();
+ KnownBits Known(BitWidth);
+ computeKnownBits(BO->LHS, Known, getDataLayout(), &AC, nullptr, &DT);
+
+ APInt EffectiveMask =
+ APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
+ if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
+ const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
+ const SCEV *LHS = getSCEV(BO->LHS);
+ const SCEV *ShiftedLHS = nullptr;
+ if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
+ if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
+ // For an expression like (x * 8) & 8, simplify the multiply.
+ unsigned MulZeros = OpC->getAPInt().countr_zero();
+ unsigned GCD = std::min(MulZeros, TZ);
+ APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
+ SmallVector<SCEVUse, 4> MulOps;
+ MulOps.push_back(getConstant(OpC->getAPInt().ashr(GCD)));
+ append_range(MulOps, LHSMul->operands().drop_front());
+ auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
+ ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
+ }
+ }
+ if (!ShiftedLHS)
+ ShiftedLHS = getUDivExpr(LHS, MulCount);
+ return getMulExpr(
+ getZeroExtendExpr(
+ getTruncateExpr(ShiftedLHS,
+ IntegerType::get(getContext(), BitWidth - LZ - TZ)),
+ BO->LHS->getType()),
+ MulCount);
+ }
+ }
+ // Binary `and` is a bit-wise `umin`.
+ if (BO->LHS->getType()->isIntegerTy(1)) {
+ LHS = getSCEV(BO->LHS);
+ RHS = getSCEV(BO->RHS);
+ return getUMinExpr(LHS, RHS);
+ }
+ break;
+
+ case Instruction::Or:
+ // Binary `or` is a bit-wise `umax`.
+ if (BO->LHS->getType()->isIntegerTy(1)) {
+ LHS = getSCEV(BO->LHS);
+ RHS = getSCEV(BO->RHS);
+ return getUMaxExpr(LHS, RHS);
+ }
+ break;
+
+ case Instruction::Xor:
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
+ // If the RHS of xor is -1, then this is a not operation.
+ if (CI->isMinusOne())
+ return getNotSCEV(getSCEV(BO->LHS));
+
+ // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
+ // This is a variant of the check for xor with -1, and it handles
+ // the case where instcombine has trimmed non-demanded bits out
+ // of an xor with -1.
+ if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
+ if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
+ if (LBO->getOpcode() == Instruction::And &&
+ LCI->getValue() == CI->getValue())
+ if (const SCEVZeroExtendExpr *Z =
+ dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
+ Type *UTy = BO->LHS->getType();
+ const SCEV *Z0 = Z->getOperand();
+ Type *Z0Ty = Z0->getType();
+ unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
+
+ // If C is a low-bits mask, the zero extend is serving to
+ // mask off the high bits. Complement the operand and
+ // re-apply the zext.
+ if (CI->getValue().isMask(Z0TySize))
+ return getZeroExtendExpr(getNotSCEV(Z0), UTy);
+
+ // If C is a single bit, it may be in the sign-bit position
+ // before the zero-extend. In this case, represent the xor
+ // using an add, which is equivalent, and re-apply the zext.
+ APInt Trunc = CI->getValue().trunc(Z0TySize);
+ if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
+ Trunc.isSignMask())
+ return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
+ UTy);
+ }
+ }
+ break;
+
+ case Instruction::Shl:
+ // Turn shift left of a constant amount into a multiply.
+ if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
+ uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
+
+ // If the shift count is not less than the bitwidth, the result of
+ // the shift is undefined. Don't try to analyze it, because the
+ // resolution chosen here may differ from the resolution chosen in
+ // other parts of the compiler.
+ if (SA->getValue().uge(BitWidth))
+ break;
+
+ // We can safely preserve the nuw flag in all cases. It's also safe to
+ // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
+ // requires special handling. It can be preserved as long as we're not
+ // left shifting by bitwidth - 1.
+ auto Flags = SCEV::FlagAnyWrap;
+ if (BO->Op) {
+ auto MulFlags = getNoWrapFlagsFromUB(BO->Op);
+ if (any(MulFlags & SCEV::FlagNSW) &&
+ (any(MulFlags & SCEV::FlagNUW) ||
+ SA->getValue().ult(BitWidth - 1)))
+ Flags = Flags | SCEV::FlagNSW;
+ if (any(MulFlags & SCEV::FlagNUW))
+ Flags = Flags | SCEV::FlagNUW;
+ }
+
+ ConstantInt *X = ConstantInt::get(
+ getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
+ return getMulExpr(getSCEV(BO->LHS), getConstant(X), Flags);
+ }
+ break;
+
+ case Instruction::AShr:
+ // AShr X, C, where C is a constant.
+ ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
+ if (!CI)
+ break;
+
+ Type *OuterTy = BO->LHS->getType();
+ uint64_t BitWidth = getTypeSizeInBits(OuterTy);
+ // If the shift count is not less than the bitwidth, the result of
+ // the shift is undefined. Don't try to analyze it, because the
+ // resolution chosen here may differ from the resolution chosen in
+ // other parts of the compiler.
+ if (CI->getValue().uge(BitWidth))
+ break;
+
+ if (CI->isZero())
+ return getSCEV(BO->LHS); // shift by zero --> noop
+
+ uint64_t AShrAmt = CI->getZExtValue();
+ Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
+
+ Operator *L = dyn_cast<Operator>(BO->LHS);
+ const SCEV *AddTruncateExpr = nullptr;
+ ConstantInt *ShlAmtCI = nullptr;
+ const SCEV *AddConstant = nullptr;
+
+ if (L && L->getOpcode() == Instruction::Add) {
+ // X = Shl A, n
+ // Y = Add X, c
+ // Z = AShr Y, m
+ // n, c and m are constants.
+
+ Operator *LShift = dyn_cast<Operator>(L->getOperand(0));
+ ConstantInt *AddOperandCI = dyn_cast<ConstantInt>(L->getOperand(1));
+ if (LShift && LShift->getOpcode() == Instruction::Shl) {
+ if (AddOperandCI) {
+ const SCEV *ShlOp0SCEV = getSCEV(LShift->getOperand(0));
+ ShlAmtCI = dyn_cast<ConstantInt>(LShift->getOperand(1));
+ // since we truncate to TruncTy, the AddConstant should be of the
+ // same type, so create a new Constant with type same as TruncTy.
+ // Also, the Add constant should be shifted right by AShr amount.
+ APInt AddOperand = AddOperandCI->getValue().ashr(AShrAmt);
+ AddConstant = getConstant(AddOperand.trunc(BitWidth - AShrAmt));
+ // we model the expression as sext(add(trunc(A), c << n)), since the
+ // sext(trunc) part is already handled below, we create a
+ // AddExpr(TruncExp) which will be used later.
+ AddTruncateExpr = getTruncateExpr(ShlOp0SCEV, TruncTy);
+ }
+ }
+ } else if (L && L->getOpcode() == Instruction::Shl) {
+ // X = Shl A, n
+ // Y = AShr X, m
+ // Both n and m are constant.
+
+ const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
+ ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
+ AddTruncateExpr = getTruncateExpr(ShlOp0SCEV, TruncTy);
+ }
+
+ if (AddTruncateExpr && ShlAmtCI) {
+ // We can merge the two given cases into a single SCEV statement,
+ // incase n = m, the mul expression will be 2^0, so it gets resolved to
+ // a simpler case. The following code handles the two cases:
+ //
+ // 1) For a two-shift sext-inreg, i.e. n = m,
+ // use sext(trunc(x)) as the SCEV expression.
+ //
+ // 2) When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
+ // expression. We already checked that ShlAmt < BitWidth, so
+ // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
+ // ShlAmt - AShrAmt < Amt.
+ const APInt &ShlAmt = ShlAmtCI->getValue();
+ if (ShlAmt.ult(BitWidth) && ShlAmt.uge(AShrAmt)) {
+ APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
+ ShlAmtCI->getZExtValue() - AShrAmt);
+ const SCEV *CompositeExpr =
+ getMulExpr(AddTruncateExpr, getConstant(Mul));
+ if (L->getOpcode() != Instruction::Shl)
+ CompositeExpr = getAddExpr(CompositeExpr, AddConstant);
+
+ return getSignExtendExpr(CompositeExpr, OuterTy);
+ }
+ }
+ break;
+ }
+ }
+
+ switch (U->getOpcode()) {
+ case Instruction::Trunc:
+ return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
+
+ case Instruction::ZExt:
+ return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
+
+ case Instruction::SExt:
+ if (auto BO = MatchBinaryOp(U->getOperand(0), getDataLayout(), AC, DT,
+ dyn_cast<Instruction>(V))) {
+ // The NSW flag of a subtract does not always survive the conversion to
+ // A + (-1)*B. By pushing sign extension onto its operands we are much
+ // more likely to preserve NSW and allow later AddRec optimisations.
+ //
+ // NOTE: This is effectively duplicating this logic from getSignExtend:
+ // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
+ // but by that point the NSW information has potentially been lost.
+ if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
+ Type *Ty = U->getType();
+ auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
+ auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
+ return getMinusSCEV(V1, V2, SCEV::FlagNSW);
+ }
+ }
+ return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
+
+ case Instruction::BitCast:
+ // BitCasts are no-op casts so we just eliminate the cast.
+ if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
+ return getSCEV(U->getOperand(0));
+ break;
+
+ case Instruction::PtrToAddr: {
+ const SCEV *IntOp = getPtrToAddrExpr(getSCEV(U->getOperand(0)));
+ if (isa<SCEVCouldNotCompute>(IntOp))
+ return getUnknown(V);
+ return IntOp;
+ }
+
+ case Instruction::PtrToInt: {
+ // Keep ptrtoint as SCEVUnknown, except when the pointer operand has SCEV
+ // structure (e.g. a pointer add-rec or an offset from a known base). In
+ // that case model it via ptrtoaddr to preserve the integer structure
+ // (induction, constant folding). A bare SCEVUnknown pointer gains no
+ // structure from wrapping it in ptrtoaddr, so leave it opaque.
+ const SCEV *PtrSCEV = getSCEV(U->getOperand(0));
+ if (!isa<SCEVUnknown>(PtrSCEV)) {
+ const SCEV *Addr = getPtrToAddrExpr(PtrSCEV);
+ if (!isa<SCEVCouldNotCompute>(Addr) &&
+ getTypeSizeInBits(V->getType()) <= getTypeSizeInBits(Addr->getType()))
+ return getTruncateOrNoop(Addr, V->getType());
+ }
+ return getUnknown(V);
+ }
+ case Instruction::IntToPtr:
+ // Just don't deal with inttoptr casts.
+ return getUnknown(V);
+
+ case Instruction::SDiv:
+ // If both operands are non-negative, this is just an udiv.
+ if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
+ isKnownNonNegative(getSCEV(U->getOperand(1))))
+ return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
+ break;
+
+ case Instruction::SRem:
+ // If both operands are non-negative, this is just an urem.
+ if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
+ isKnownNonNegative(getSCEV(U->getOperand(1))))
+ return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
+ break;
+
+ case Instruction::GetElementPtr:
+ return createNodeForGEP(cast<GEPOperator>(U));
+
+ case Instruction::PHI:
+ return createNodeForPHI(cast<PHINode>(U));
+
+ case Instruction::Select:
+ return createNodeForSelectOrPHI(U, U->getOperand(0), U->getOperand(1),
+ U->getOperand(2));
+
+ case Instruction::Call:
+ case Instruction::Invoke:
+ if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand())
+ return getSCEV(RV);
+
+ if (auto *II = dyn_cast<IntrinsicInst>(U)) {
+ switch (II->getIntrinsicID()) {
+ case Intrinsic::abs:
+ return getAbsExpr(
+ getSCEV(II->getArgOperand(0)),
+ /*IsNSW=*/cast<ConstantInt>(II->getArgOperand(1))->isOne());
+ case Intrinsic::umax:
+ LHS = getSCEV(II->getArgOperand(0));
+ RHS = getSCEV(II->getArgOperand(1));
+ return getUMaxExpr(LHS, RHS);
+ case Intrinsic::umin:
+ LHS = getSCEV(II->getArgOperand(0));
+ RHS = getSCEV(II->getArgOperand(1));
+ return getUMinExpr(LHS, RHS);
+ case Intrinsic::smax:
+ LHS = getSCEV(II->getArgOperand(0));
+ RHS = getSCEV(II->getArgOperand(1));
+ return getSMaxExpr(LHS, RHS);
+ case Intrinsic::smin:
+ LHS = getSCEV(II->getArgOperand(0));
+ RHS = getSCEV(II->getArgOperand(1));
+ return getSMinExpr(LHS, RHS);
+ case Intrinsic::usub_sat: {
+ const SCEV *X = getSCEV(II->getArgOperand(0));
+ const SCEV *Y = getSCEV(II->getArgOperand(1));
+ const SCEV *ClampedY = getUMinExpr(X, Y);
+ return getMinusSCEV(X, ClampedY, SCEV::FlagNUW);
+ }
+ case Intrinsic::uadd_sat: {
+ const SCEV *X = getSCEV(II->getArgOperand(0));
+ const SCEV *Y = getSCEV(II->getArgOperand(1));
+ const SCEV *ClampedX = getUMinExpr(X, getNotSCEV(Y));
+ return getAddExpr(ClampedX, Y, SCEV::FlagNUW);
+ }
+ case Intrinsic::start_loop_iterations:
+ case Intrinsic::annotation:
+ case Intrinsic::ptr_annotation:
+ // A start_loop_iterations or llvm.annotation or llvm.prt.annotation is
+ // just eqivalent to the first operand for SCEV purposes.
+ return getSCEV(II->getArgOperand(0));
+ case Intrinsic::vscale:
+ return getVScale(II->getType());
+ default:
+ break;
+ }
+ }
+ break;
+ }
+
+ return getUnknown(V);
+}
+
+//===----------------------------------------------------------------------===//
+// Iteration Count Computation Code
+//
+
+const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount) {
+ if (isa<SCEVCouldNotCompute>(ExitCount))
+ return getCouldNotCompute();
+
+ auto *ExitCountType = ExitCount->getType();
+ assert(ExitCountType->isIntegerTy());
+ auto *EvalTy = Type::getIntNTy(ExitCountType->getContext(),
+ 1 + ExitCountType->getScalarSizeInBits());
+ return getTripCountFromExitCount(ExitCount, EvalTy, nullptr);
+}
+
+const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount,
+ Type *EvalTy,
+ const Loop *L) {
+ if (isa<SCEVCouldNotCompute>(ExitCount))
+ return getCouldNotCompute();
+
+ unsigned ExitCountSize = getTypeSizeInBits(ExitCount->getType());
+ unsigned EvalSize = EvalTy->getPrimitiveSizeInBits();
+
+ auto CanAddOneWithoutOverflow = [&]() {
+ ConstantRange ExitCountRange =
+ getRangeRef(ExitCount, RangeSignHint::HINT_RANGE_UNSIGNED);
+ if (!ExitCountRange.contains(APInt::getMaxValue(ExitCountSize)))
+ return true;
+
+ return L && isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, ExitCount,
+ getMinusOne(ExitCount->getType()));
+ };
+
+ // If we need to zero extend the backedge count, check if we can add one to
+ // it prior to zero extending without overflow. Provided this is safe, it
+ // allows better simplification of the +1.
+ if (EvalSize > ExitCountSize && CanAddOneWithoutOverflow())
+ return getZeroExtendExpr(
+ getAddExpr(ExitCount, getOne(ExitCount->getType())), EvalTy);
+
+ // Get the total trip count from the count by adding 1. This may wrap.
+ return getAddExpr(getTruncateOrZeroExtend(ExitCount, EvalTy), getOne(EvalTy));
+}
+
+static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
+ if (!ExitCount)
+ return 0;
+
+ ConstantInt *ExitConst = ExitCount->getValue();
+
+ // Guard against huge trip counts.
+ if (ExitConst->getValue().getActiveBits() > 32)
+ return 0;
+
+ // In case of integer overflow, this returns 0, which is correct.
+ return ((unsigned)ExitConst->getZExtValue()) + 1;
+}
+
+unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
+ auto *ExitCount = dyn_cast<SCEVConstant>(getBackedgeTakenCount(L, Exact));
+ return getConstantTripCount(ExitCount);
+}
+
+unsigned
+ScalarEvolution::getSmallConstantTripCount(const Loop *L,
+ const BasicBlock *ExitingBlock) {
+ assert(ExitingBlock && "Must pass a non-null exiting block!");
+ assert(L->isLoopExiting(ExitingBlock) &&
+ "Exiting block must actually branch out of the loop!");
+ const SCEVConstant *ExitCount =
+ dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
+ return getConstantTripCount(ExitCount);
+}
+
+unsigned ScalarEvolution::getSmallConstantMaxTripCount(
+ const Loop *L, SmallVectorImpl<const SCEVPredicate *> *Predicates) {
+
+ const auto *MaxExitCount =
+ Predicates ? getPredicatedConstantMaxBackedgeTakenCount(L, *Predicates)
+ : getConstantMaxBackedgeTakenCount(L);
+ return getConstantTripCount(dyn_cast<SCEVConstant>(MaxExitCount));
+}
+
+unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
+ SmallVector<BasicBlock *, 8> ExitingBlocks;
+ L->getExitingBlocks(ExitingBlocks);
+
+ std::optional<unsigned> Res;
+ for (auto *ExitingBB : ExitingBlocks) {
+ unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBB);
+ if (!Res)
+ Res = Multiple;
+ Res = std::gcd(*Res, Multiple);
+ }
+ return Res.value_or(1);
+}
+
+unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
+ const SCEV *ExitCount) {
+ if (isa<SCEVCouldNotCompute>(ExitCount))
+ return 1;
+
+ // Get the trip count
+ const SCEV *TCExpr = getTripCountFromExitCount(applyLoopGuards(ExitCount, L));
+
+ APInt Multiple = getNonZeroConstantMultiple(TCExpr);
+ // If a trip multiple is huge (>=2^32), the trip count is still divisible by
+ // the greatest power of 2 divisor less than 2^32.
+ return Multiple.getActiveBits() > 32
+ ? 1U << std::min(31U, Multiple.countTrailingZeros())
+ : (unsigned)Multiple.getZExtValue();
+}
+
+/// Returns the largest constant divisor of the trip count of this loop as a
+/// normal unsigned value, if possible. This means that the actual trip count is
+/// always a multiple of the returned value (don't forget the trip count could
+/// very well be zero as well!).
+///
+/// Returns 1 if the trip count is unknown or not guaranteed to be the
+/// multiple of a constant (which is also the case if the trip count is simply
+/// constant, use getSmallConstantTripCount for that case), Will also return 1
+/// if the trip count is very large (>= 2^32).
+///
+/// As explained in the comments for getSmallConstantTripCount, this assumes
+/// that control exits the loop via ExitingBlock.
+unsigned
+ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
+ const BasicBlock *ExitingBlock) {
+ assert(ExitingBlock && "Must pass a non-null exiting block!");
+ assert(L->isLoopExiting(ExitingBlock) &&
+ "Exiting block must actually branch out of the loop!");
+ const SCEV *ExitCount = getExitCount(L, ExitingBlock);
+ return getSmallConstantTripMultiple(L, ExitCount);
+}
+
+const SCEV *ScalarEvolution::getExitCount(const Loop *L,
+ const BasicBlock *ExitingBlock,
+ ExitCountKind Kind) {
+ switch (Kind) {
+ case Exact:
+ return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
+ case SymbolicMaximum:
+ return getBackedgeTakenInfo(L).getSymbolicMax(ExitingBlock, this);
+ case ConstantMaximum:
+ return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this);
+ };
+ llvm_unreachable("Invalid ExitCountKind!");
+}
+
+const SCEV *ScalarEvolution::getPredicatedExitCount(
+ const Loop *L, const BasicBlock *ExitingBlock,
+ SmallVectorImpl<const SCEVPredicate *> *Predicates, ExitCountKind Kind) {
+ switch (Kind) {
+ case Exact:
+ return getPredicatedBackedgeTakenInfo(L).getExact(ExitingBlock, this,
+ Predicates);
+ case SymbolicMaximum:
+ return getPredicatedBackedgeTakenInfo(L).getSymbolicMax(ExitingBlock, this,
+ Predicates);
+ case ConstantMaximum:
+ return getPredicatedBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this,
+ Predicates);
+ };
+ llvm_unreachable("Invalid ExitCountKind!");
+}
+
+const SCEV *ScalarEvolution::getPredicatedBackedgeTakenCount(
+ const Loop *L, SmallVectorImpl<const SCEVPredicate *> &Preds) {
+ return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
+}
+
+const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
+ ExitCountKind Kind) {
+ switch (Kind) {
+ case Exact:
+ return getBackedgeTakenInfo(L).getExact(L, this);
+ case ConstantMaximum:
+ return getBackedgeTakenInfo(L).getConstantMax(this);
+ case SymbolicMaximum:
+ return getBackedgeTakenInfo(L).getSymbolicMax(L, this);
+ };
+ llvm_unreachable("Invalid ExitCountKind!");
+}
+
+const SCEV *ScalarEvolution::getPredicatedSymbolicMaxBackedgeTakenCount(
+ const Loop *L, SmallVectorImpl<const SCEVPredicate *> &Preds) {
+ return getPredicatedBackedgeTakenInfo(L).getSymbolicMax(L, this, &Preds);
+}
+
+const SCEV *ScalarEvolution::getPredicatedConstantMaxBackedgeTakenCount(
+ const Loop *L, SmallVectorImpl<const SCEVPredicate *> &Preds) {
+ return getPredicatedBackedgeTakenInfo(L).getConstantMax(this, &Preds);
+}
+
+bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
+ return getBackedgeTakenInfo(L).isConstantMaxOrZero(this);
+}
+
+ScalarEvolution::BackedgeTakenInfo &
+ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
+ auto &BTI = getBackedgeTakenInfo(L);
+ if (BTI.hasFullInfo())
+ return BTI;
+
+ auto Pair = PredicatedBackedgeTakenCounts.try_emplace(L);
+
+ if (!Pair.second)
+ return Pair.first->second;
+
+ BackedgeTakenInfo Result =
+ computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
+
+ return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
+}
+
+ScalarEvolution::BackedgeTakenInfo &
+ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
+ // Initially insert an invalid entry for this loop. If the insertion
+ // succeeds, proceed to actually compute a backedge-taken count and
+ // update the value. The temporary CouldNotCompute value tells SCEV
+ // code elsewhere that it shouldn't attempt to request a new
+ // backedge-taken count, which could result in infinite recursion.
+ std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
+ BackedgeTakenCounts.try_emplace(L);
+ if (!Pair.second)
+ return Pair.first->second;
+
+ // computeBackedgeTakenCount may allocate memory for its result. Inserting it
+ // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
+ // must be cleared in this scope.
+ BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
+
+ // Now that we know more about the trip count for this loop, forget any
+ // existing SCEV values for PHI nodes in this loop since they are only
+ // conservative estimates made without the benefit of trip count
+ // information. This invalidation is not necessary for correctness, and is
+ // only done to produce more precise results.
+ if (Result.hasAnyInfo()) {
+ // Invalidate any expression using an addrec in this loop.
+ SmallVector<SCEVUse, 8> ToForget;
+ auto LoopUsersIt = LoopUsers.find(L);
+ if (LoopUsersIt != LoopUsers.end())
+ append_range(ToForget, LoopUsersIt->second);
+ forgetMemoizedResults(ToForget);
+
+ // Invalidate constant-evolved loop header phis.
+ for (PHINode &PN : L->getHeader()->phis())
+ ConstantEvolutionLoopExitValue.erase(&PN);
+ }
+
+ // Re-lookup the insert position, since the call to
+ // computeBackedgeTakenCount above could result in a
+ // recusive call to getBackedgeTakenInfo (on a different
+ // loop), which would invalidate the iterator computed
+ // earlier.
+ return BackedgeTakenCounts.find(L)->second = std::move(Result);
+}
+
+void ScalarEvolution::forgetAllLoops() {
+ // This method is intended to forget all info about loops. It should
+ // invalidate caches as if the following happened:
+ // - The trip counts of all loops have changed arbitrarily
+ // - Every llvm::Value has been updated in place to produce a different
+ // result.
+ BackedgeTakenCounts.clear();
+ PredicatedBackedgeTakenCounts.clear();
+ BECountUsers.clear();
+ LoopPropertiesCache.clear();
+ ConstantEvolutionLoopExitValue.clear();
+ ValueExprMap.clear();
+ ValuesAtScopes.clear();
+ ValuesAtScopesUsers.clear();
+ LoopDispositions.clear();
+ BlockDispositions.clear();
+ UnsignedRanges.clear();
+ SignedRanges.clear();
+ ExprValueMap.clear();
+ HasRecMap.clear();
+ ConstantMultipleCache.clear();
+ PredicatedSCEVRewrites.clear();
+ FoldCache.clear();
+ FoldCacheUser.clear();
+}
+void ScalarEvolution::visitAndClearUsers(
+ SmallVectorImpl<Instruction *> &Worklist,
+ SmallPtrSetImpl<Instruction *> &Visited,
+ SmallVectorImpl<SCEVUse> &ToForget) {
+ while (!Worklist.empty()) {
+ Instruction *I = Worklist.pop_back_val();
+ if (!isSCEVable(I->getType()) && !isa<WithOverflowInst>(I))
+ continue;
+
+ ValueExprMapType::iterator It =
+ ValueExprMap.find_as(static_cast<Value *>(I));
+ if (It != ValueExprMap.end()) {
+ ToForget.push_back(It->second);
+ eraseValueFromMap(It->first);
+ if (PHINode *PN = dyn_cast<PHINode>(I))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ }
+
+ PushDefUseChildren(I, Worklist, Visited);
+ }
+}
+
+void ScalarEvolution::forgetLoop(const Loop *L) {
+ SmallVector<const Loop *, 16> LoopWorklist(1, L);
+ SmallVector<SCEVUse, 16> ToForget;
+
+ // Iterate over all the loops and sub-loops to drop SCEV information.
+ while (!LoopWorklist.empty()) {
+ auto *CurrL = LoopWorklist.pop_back_val();
+
+ // Drop any stored trip count value.
+ forgetBackedgeTakenCounts(CurrL, /* Predicated */ false);
+ forgetBackedgeTakenCounts(CurrL, /* Predicated */ true);
+
+ // Drop information about predicated SCEV rewrites for this loop.
+ PredicatedSCEVRewrites.remove_if(
+ [&](const auto &Entry) { return Entry.first.second == CurrL; });
+
+ auto LoopUsersItr = LoopUsers.find(CurrL);
+ if (LoopUsersItr != LoopUsers.end())
+ llvm::append_range(ToForget, LoopUsersItr->second);
+
+ // Drop information about expressions based on loop-header PHIs.
+ for (PHINode &PN : CurrL->getHeader()->phis()) {
+ ConstantEvolutionLoopExitValue.erase(&PN);
+ auto VIt = ValueExprMap.find_as(static_cast<Value *>(&PN));
+ if (VIt != ValueExprMap.end())
+ ToForget.push_back(VIt->second);
+ }
+
+ LoopPropertiesCache.erase(CurrL);
+ // Forget all contained loops too, to avoid dangling entries in the
+ // ValuesAtScopes map.
+ LoopWorklist.append(CurrL->begin(), CurrL->end());
+ }
+ forgetMemoizedResults(ToForget);
+}
+
+void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
+ forgetLoop(L->getOutermostLoop());
+}
+
+void ScalarEvolution::forgetValue(Value *V) {
+ Instruction *I = dyn_cast<Instruction>(V);
+ if (!I) return;
+
+ // Drop information about expressions based on loop-header PHIs.
+ SmallVector<Instruction *, 16> Worklist;
+ SmallPtrSet<Instruction *, 8> Visited;
+ SmallVector<SCEVUse, 8> ToForget;
+ Worklist.push_back(I);
+ Visited.insert(I);
+ visitAndClearUsers(Worklist, Visited, ToForget);
+
+ forgetMemoizedResults(ToForget);
+}
+
+void ScalarEvolution::forgetLcssaPhiWithNewPredecessor(Loop *L, PHINode *V) {
+ if (!isSCEVable(V->getType()))
+ return;
+
+ // If SCEV looked through a trivial LCSSA phi node, we might have SCEV's
+ // directly using a SCEVUnknown/SCEVAddRec defined in the loop. After an
+ // extra predecessor is added, this is no longer valid. Find all Unknowns and
+ // AddRecs defined in the loop and invalidate any SCEV's making use of them.
+ if (const SCEV *S = getExistingSCEV(V)) {
+ struct InvalidationRootCollector {
+ Loop *L;
+ SmallVector<SCEVUse, 8> Roots;
+
+ InvalidationRootCollector(Loop *L) : L(L) {}
+
+ bool follow(const SCEV *S) {
+ if (auto *SU = dyn_cast<SCEVUnknown>(S)) {
+ if (auto *I = dyn_cast<Instruction>(SU->getValue()))
+ if (L->contains(I))
+ Roots.push_back(S);
+ } else if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
+ if (L->contains(AddRec->getLoop()))
+ Roots.push_back(S);
+ }
+ return true;
+ }
+ bool isDone() const { return false; }
+ };
+
+ InvalidationRootCollector C(L);
+ visitAll(S, C);
+ forgetMemoizedResults(C.Roots);
+ }
+
+ // Also perform the normal invalidation.
+ forgetValue(V);
+}
+
+void ScalarEvolution::forgetLoopDispositions() { LoopDispositions.clear(); }
+
+void ScalarEvolution::forgetBlockAndLoopDispositions(Value *V) {
+ // Unless a specific value is passed to invalidation, completely clear both
+ // caches.
+ if (!V) {
+ BlockDispositions.clear();
+ LoopDispositions.clear();
+ return;
+ }
+
+ if (!isSCEVable(V->getType()))
+ return;
+
+ const SCEV *S = getExistingSCEV(V);
+ if (!S)
+ return;
+
+ // Invalidate the block and loop dispositions cached for S. Dispositions of
+ // S's users may change if S's disposition changes (i.e. a user may change to
+ // loop-invariant, if S changes to loop invariant), so also invalidate
+ // dispositions of S's users recursively.
+ SmallVector<SCEVUse, 8> Worklist = {S};
+ SmallPtrSet<const SCEV *, 8> Seen = {S};
+ while (!Worklist.empty()) {
+ const SCEV *Curr = Worklist.pop_back_val();
+ bool LoopDispoRemoved = LoopDispositions.erase(Curr);
+ bool BlockDispoRemoved = BlockDispositions.erase(Curr);
+ if (!LoopDispoRemoved && !BlockDispoRemoved)
+ continue;
+ auto Users = SCEVUsers.find(Curr);
+ if (Users != SCEVUsers.end())
+ for (const auto *User : Users->second)
+ if (Seen.insert(User).second)
+ Worklist.push_back(User);
+ }
+}
+
+/// Get the exact loop backedge taken count considering all loop exits. A
+/// computable result can only be returned for loops with all exiting blocks
+/// dominating the latch. howFarToZero assumes that the limit of each loop test
+/// is never skipped. This is a valid assumption as long as the loop exits via
+/// that test. For precise results, it is the caller's responsibility to specify
+/// the relevant loop exiting block using getExact(ExitingBlock, SE).
+const SCEV *ScalarEvolution::BackedgeTakenInfo::getExact(
+ const Loop *L, ScalarEvolution *SE,
+ SmallVectorImpl<const SCEVPredicate *> *Preds) const {
+ // If any exits were not computable, the loop is not computable.
+ if (!isComplete() || ExitNotTaken.empty())
+ return SE->getCouldNotCompute();
+
+ const BasicBlock *Latch = L->getLoopLatch();
+ // All exiting blocks we have collected must dominate the only backedge.
+ if (!Latch)
+ return SE->getCouldNotCompute();
+
+ // All exiting blocks we have gathered dominate loop's latch, so exact trip
+ // count is simply a minimum out of all these calculated exit counts.
+ SmallVector<SCEVUse, 2> Ops;
+ for (const auto &ENT : ExitNotTaken) {
+ const SCEV *BECount = ENT.ExactNotTaken;
+ assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
+ assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
+ "We should only have known counts for exiting blocks that dominate "
+ "latch!");
+
+ Ops.push_back(BECount);
+
+ if (Preds)
+ append_range(*Preds, ENT.Predicates);
+
+ assert((Preds || ENT.hasAlwaysTruePredicate()) &&
+ "Predicate should be always true!");
+ }
+
+ // If an earlier exit exits on the first iteration (exit count zero), then
+ // a later poison exit count should not propagate into the result. This are
+ // exactly the semantics provided by umin_seq.
+ return SE->getUMinFromMismatchedTypes(Ops, /* Sequential */ true);
+}
+
+const ScalarEvolution::ExitNotTakenInfo *
+ScalarEvolution::BackedgeTakenInfo::getExitNotTaken(
+ const BasicBlock *ExitingBlock,
+ SmallVectorImpl<const SCEVPredicate *> *Predicates) const {
+ for (const auto &ENT : ExitNotTaken)
+ if (ENT.ExitingBlock == ExitingBlock) {
+ if (ENT.hasAlwaysTruePredicate())
+ return &ENT;
+ else if (Predicates) {
+ append_range(*Predicates, ENT.Predicates);
+ return &ENT;
+ }
+ }
+
+ return nullptr;
+}
+
+/// getConstantMax - Get the constant max backedge taken count for the loop.
+const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax(
+ ScalarEvolution *SE,
+ SmallVectorImpl<const SCEVPredicate *> *Predicates) const {
+ if (!getConstantMax())
+ return SE->getCouldNotCompute();
+
+ for (const auto &ENT : ExitNotTaken)
+ if (!ENT.hasAlwaysTruePredicate()) {
+ if (!Predicates)
+ return SE->getCouldNotCompute();
+ append_range(*Predicates, ENT.Predicates);
+ }
+
+ assert((isa<SCEVCouldNotCompute>(getConstantMax()) ||
+ isa<SCEVConstant>(getConstantMax())) &&
+ "No point in having a non-constant max backedge taken count!");
+ return getConstantMax();
+}
+
+const SCEV *ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(
+ const Loop *L, ScalarEvolution *SE,
+ SmallVectorImpl<const SCEVPredicate *> *Predicates) {
+ if (!SymbolicMax) {
+ // Form an expression for the maximum exit count possible for this loop. We
+ // merge the max and exact information to approximate a version of
+ // getConstantMaxBackedgeTakenCount which isn't restricted to just
+ // constants.
+ SmallVector<SCEVUse, 4> ExitCounts;
+
+ for (const auto &ENT : ExitNotTaken) {
+ const SCEV *ExitCount = ENT.SymbolicMaxNotTaken;
+ if (!isa<SCEVCouldNotCompute>(ExitCount)) {
+ assert(SE->DT.dominates(ENT.ExitingBlock, L->getLoopLatch()) &&
+ "We should only have known counts for exiting blocks that "
+ "dominate latch!");
+ ExitCounts.push_back(ExitCount);
+ if (Predicates)
+ append_range(*Predicates, ENT.Predicates);
+
+ assert((Predicates || ENT.hasAlwaysTruePredicate()) &&
+ "Predicate should be always true!");
+ }
+ }
+ if (ExitCounts.empty())
+ SymbolicMax = SE->getCouldNotCompute();
+ else
+ SymbolicMax =
+ SE->getUMinFromMismatchedTypes(ExitCounts, /*Sequential*/ true);
+ }
+ return SymbolicMax;
+}
+
+bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero(
+ ScalarEvolution *SE) const {
+ auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
+ return !ENT.hasAlwaysTruePredicate();
+ };
+ return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
+}
+
+ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
+ : ExitLimit(E, E, E, false) {}
+
+ScalarEvolution::ExitLimit::ExitLimit(
+ const SCEV *E, const SCEV *ConstantMaxNotTaken,
+ const SCEV *SymbolicMaxNotTaken, bool MaxOrZero,
+ ArrayRef<ArrayRef<const SCEVPredicate *>> PredLists)
+ : ExactNotTaken(E), ConstantMaxNotTaken(ConstantMaxNotTaken),
+ SymbolicMaxNotTaken(SymbolicMaxNotTaken), MaxOrZero(MaxOrZero) {
+ // If we prove the max count is zero, so is the symbolic bound. This happens
+ // in practice due to differences in a) how context sensitive we've chosen
+ // to be and b) how we reason about bounds implied by UB.
+ if (ConstantMaxNotTaken->isZero()) {
+ this->ExactNotTaken = E = ConstantMaxNotTaken;
+ this->SymbolicMaxNotTaken = SymbolicMaxNotTaken = ConstantMaxNotTaken;
+ }
+
+ assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
+ !isa<SCEVCouldNotCompute>(ConstantMaxNotTaken)) &&
+ "Exact is not allowed to be less precise than Constant Max");
+ assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
+ !isa<SCEVCouldNotCompute>(SymbolicMaxNotTaken)) &&
+ "Exact is not allowed to be less precise than Symbolic Max");
+ assert((isa<SCEVCouldNotCompute>(SymbolicMaxNotTaken) ||
+ !isa<SCEVCouldNotCompute>(ConstantMaxNotTaken)) &&
+ "Symbolic Max is not allowed to be less precise than Constant Max");
+ assert((isa<SCEVCouldNotCompute>(ConstantMaxNotTaken) ||
+ isa<SCEVConstant>(ConstantMaxNotTaken)) &&
+ "No point in having a non-constant max backedge taken count!");
+ SmallPtrSet<const SCEVPredicate *, 4> SeenPreds;
+ for (const auto PredList : PredLists)
+ for (const auto *P : PredList) {
+ if (SeenPreds.contains(P))
+ continue;
+ assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
+ SeenPreds.insert(P);
+ Predicates.push_back(P);
+ }
+ assert((isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) &&
+ "Backedge count should be int");
+ assert((isa<SCEVCouldNotCompute>(ConstantMaxNotTaken) ||
+ !ConstantMaxNotTaken->getType()->isPointerTy()) &&
+ "Max backedge count should be int");
+}
+
+ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E,
+ const SCEV *ConstantMaxNotTaken,
+ const SCEV *SymbolicMaxNotTaken,
+ bool MaxOrZero,
+ ArrayRef<const SCEVPredicate *> PredList)
+ : ExitLimit(E, ConstantMaxNotTaken, SymbolicMaxNotTaken, MaxOrZero,
+ ArrayRef({PredList})) {}
+
+/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
+/// computable exit into a persistent ExitNotTakenInfo array.
+ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
+ ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> ExitCounts,
+ bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero)
+ : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) {
+ using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
+
+ ExitNotTaken.reserve(ExitCounts.size());
+ std::transform(ExitCounts.begin(), ExitCounts.end(),
+ std::back_inserter(ExitNotTaken),
+ [&](const EdgeExitInfo &EEI) {
+ BasicBlock *ExitBB = EEI.first;
+ const ExitLimit &EL = EEI.second;
+ return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken,
+ EL.ConstantMaxNotTaken, EL.SymbolicMaxNotTaken,
+ EL.Predicates);
+ });
+ assert((isa<SCEVCouldNotCompute>(ConstantMax) ||
+ isa<SCEVConstant>(ConstantMax)) &&
+ "No point in having a non-constant max backedge taken count!");
+}
+
+/// Compute the number of times the backedge of the specified loop will execute.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
+ bool AllowPredicates) {
+ SmallVector<BasicBlock *, 8> ExitingBlocks;
+ L->getExitingBlocks(ExitingBlocks);
+
+ using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
+
+ SmallVector<EdgeExitInfo, 4> ExitCounts;
+ bool CouldComputeBECount = true;
+ BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
+ const SCEV *MustExitMaxBECount = nullptr;
+ const SCEV *MayExitMaxBECount = nullptr;
+ bool MustExitMaxOrZero = false;
+ bool IsOnlyExit = ExitingBlocks.size() == 1;
+
+ // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
+ // and compute maxBECount.
+ // Do a union of all the predicates here.
+ for (BasicBlock *ExitBB : ExitingBlocks) {
+ // We canonicalize untaken exits to br (constant), ignore them so that
+ // proving an exit untaken doesn't negatively impact our ability to reason
+ // about the loop as whole.
+ if (auto *BI = dyn_cast<CondBrInst>(ExitBB->getTerminator()))
+ if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
+ bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
+ if (ExitIfTrue == CI->isZero())
+ continue;
+ }
+
+ ExitLimit EL = computeExitLimit(L, ExitBB, IsOnlyExit, AllowPredicates);
+
+ assert((AllowPredicates || EL.Predicates.empty()) &&
+ "Predicated exit limit when predicates are not allowed!");
+
+ // 1. For each exit that can be computed, add an entry to ExitCounts.
+ // CouldComputeBECount is true only if all exits can be computed.
+ if (EL.ExactNotTaken != getCouldNotCompute())
+ ++NumExitCountsComputed;
+ else
+ // We couldn't compute an exact value for this exit, so
+ // we won't be able to compute an exact value for the loop.
+ CouldComputeBECount = false;
+ // Remember exit count if either exact or symbolic is known. Because
+ // Exact always implies symbolic, only check symbolic.
+ if (EL.SymbolicMaxNotTaken != getCouldNotCompute())
+ ExitCounts.emplace_back(ExitBB, EL);
+ else {
+ assert(EL.ExactNotTaken == getCouldNotCompute() &&
+ "Exact is known but symbolic isn't?");
+ ++NumExitCountsNotComputed;
+ }
+
+ // 2. Derive the loop's MaxBECount from each exit's max number of
+ // non-exiting iterations. Partition the loop exits into two kinds:
+ // LoopMustExits and LoopMayExits.
+ //
+ // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
+ // is a LoopMayExit. If any computable LoopMustExit is found, then
+ // MaxBECount is the minimum EL.ConstantMaxNotTaken of computable
+ // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
+ // EL.ConstantMaxNotTaken, where CouldNotCompute is considered greater than
+ // any
+ // computable EL.ConstantMaxNotTaken.
+ if (EL.ConstantMaxNotTaken != getCouldNotCompute() && Latch &&
+ DT.dominates(ExitBB, Latch)) {
+ if (!MustExitMaxBECount) {
+ MustExitMaxBECount = EL.ConstantMaxNotTaken;
+ MustExitMaxOrZero = EL.MaxOrZero;
+ } else {
+ MustExitMaxBECount = getUMinFromMismatchedTypes(MustExitMaxBECount,
+ EL.ConstantMaxNotTaken);
+ }
+ } else if (MayExitMaxBECount != getCouldNotCompute()) {
+ if (!MayExitMaxBECount || EL.ConstantMaxNotTaken == getCouldNotCompute())
+ MayExitMaxBECount = EL.ConstantMaxNotTaken;
+ else {
+ MayExitMaxBECount = getUMaxFromMismatchedTypes(MayExitMaxBECount,
+ EL.ConstantMaxNotTaken);
+ }
+ }
+ }
+ const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
+ (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
+ // The loop backedge will be taken the maximum or zero times if there's
+ // a single exit that must be taken the maximum or zero times.
+ bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
+
+ // Remember which SCEVs are used in exit limits for invalidation purposes.
+ // We only care about non-constant SCEVs here, so we can ignore
+ // EL.ConstantMaxNotTaken
+ // and MaxBECount, which must be SCEVConstant.
+ for (const auto &Pair : ExitCounts) {
+ if (!isa<SCEVConstant>(Pair.second.ExactNotTaken))
+ BECountUsers[Pair.second.ExactNotTaken].insert({L, AllowPredicates});
+ if (!isa<SCEVConstant>(Pair.second.SymbolicMaxNotTaken))
+ BECountUsers[Pair.second.SymbolicMaxNotTaken].insert(
+ {L, AllowPredicates});
+ }
+ return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
+ MaxBECount, MaxOrZero);
+}
+
+ScalarEvolution::ExitLimit
+ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
+ bool IsOnlyExit, bool AllowPredicates) {
+ assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
+ // If our exiting block does not dominate the latch, then its connection with
+ // loop's exit limit may be far from trivial.
+ const BasicBlock *Latch = L->getLoopLatch();
+ if (!Latch || !DT.dominates(ExitingBlock, Latch))
+ return getCouldNotCompute();
+
+ Instruction *Term = ExitingBlock->getTerminator();
+ if (CondBrInst *BI = dyn_cast<CondBrInst>(Term)) {
+ bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
+ assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
+ "It should have one successor in loop and one exit block!");
+ // Proceed to the next level to examine the exit condition expression.
+ return computeExitLimitFromCond(L, BI->getCondition(), ExitIfTrue,
+ /*ControlsOnlyExit=*/IsOnlyExit,
+ AllowPredicates);
+ }
+
+ if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
+ // For switch, make sure that there is a single exit from the loop.
+ BasicBlock *Exit = nullptr;
+ for (auto *SBB : successors(ExitingBlock))
+ if (!L->contains(SBB)) {
+ if (Exit) // Multiple exit successors.
+ return getCouldNotCompute();
+ Exit = SBB;
+ }
+ assert(Exit && "Exiting block must have at least one exit");
+ return computeExitLimitFromSingleExitSwitch(
+ L, SI, Exit, /*ControlsOnlyExit=*/IsOnlyExit);
+ }
+
+ return getCouldNotCompute();
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
+ const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsOnlyExit,
+ bool AllowPredicates) {
+ ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
+ return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
+ ControlsOnlyExit, AllowPredicates);
+}
+
+std::optional<ScalarEvolution::ExitLimit>
+ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
+ bool ExitIfTrue, bool ControlsOnlyExit,
+ bool AllowPredicates) {
+ (void)this->L;
+ (void)this->ExitIfTrue;
+ (void)this->AllowPredicates;
+
+ assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
+ this->AllowPredicates == AllowPredicates &&
+ "Variance in assumed invariant key components!");
+ auto Itr = TripCountMap.find({ExitCond, ControlsOnlyExit});
+ if (Itr == TripCountMap.end())
+ return std::nullopt;
+ return Itr->second;
+}
+
+void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
+ bool ExitIfTrue,
+ bool ControlsOnlyExit,
+ bool AllowPredicates,
+ const ExitLimit &EL) {
+ assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
+ this->AllowPredicates == AllowPredicates &&
+ "Variance in assumed invariant key components!");
+
+ auto InsertResult = TripCountMap.insert({{ExitCond, ControlsOnlyExit}, EL});
+ assert(InsertResult.second && "Expected successful insertion!");
+ (void)InsertResult;
+ (void)ExitIfTrue;
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
+ ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
+ bool ControlsOnlyExit, bool AllowPredicates) {
+
+ if (auto MaybeEL = Cache.find(L, ExitCond, ExitIfTrue, ControlsOnlyExit,
+ AllowPredicates))
+ return *MaybeEL;
+
+ ExitLimit EL = computeExitLimitFromCondImpl(
+ Cache, L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates);
+ Cache.insert(L, ExitCond, ExitIfTrue, ControlsOnlyExit, AllowPredicates, EL);
+ return EL;
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
+ ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
+ bool ControlsOnlyExit, bool AllowPredicates) {
+ // Handle BinOp conditions (And, Or).
+ if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp(
+ Cache, L, ExitCond, ExitIfTrue, AllowPredicates))
+ return *LimitFromBinOp;
+
+ // With an icmp, it may be feasible to compute an exact backedge-taken count.
+ // Proceed to the next level to examine the icmp.
+ if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
+ ExitLimit EL =
+ computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsOnlyExit);
+ if (EL.hasFullInfo() || !AllowPredicates)
+ return EL;
+
+ // Try again, but use SCEV predicates this time.
+ return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue,
+ ControlsOnlyExit,
+ /*AllowPredicates=*/true);
+ }
+
+ // Check for a constant condition. These are normally stripped out by
+ // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
+ // preserve the CFG and is temporarily leaving constant conditions
+ // in place.
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
+ if (ExitIfTrue == !CI->getZExtValue())
+ // The backedge is always taken.
+ return getCouldNotCompute();
+ // The backedge is never taken.
+ return getZero(CI->getType());
+ }
+
+ // If we're exiting based on the overflow flag of an x.with.overflow intrinsic
+ // with a constant step, we can form an equivalent icmp predicate and figure
+ // out how many iterations will be taken before we exit.
+ const WithOverflowInst *WO;
+ const APInt *C;
+ if (match(ExitCond, m_ExtractValue<1>(m_WithOverflowInst(WO))) &&
+ match(WO->getRHS(), m_APInt(C))) {
+ ConstantRange NWR =
+ ConstantRange::makeExactNoWrapRegion(WO->getBinaryOp(), *C,
+ WO->getNoWrapKind());
+ CmpInst::Predicate Pred;
+ APInt NewRHSC, Offset;
+ NWR.getEquivalentICmp(Pred, NewRHSC, Offset);
+ if (!ExitIfTrue)
+ Pred = ICmpInst::getInversePredicate(Pred);
+ auto *LHS = getSCEV(WO->getLHS());
+ if (Offset != 0)
+ LHS = getAddExpr(LHS, getConstant(Offset));
+ auto EL = computeExitLimitFromICmp(L, Pred, LHS, getConstant(NewRHSC),
+ ControlsOnlyExit, AllowPredicates);
+ if (EL.hasAnyInfo())
+ return EL;
+ }
+
+ // If it's not an integer or pointer comparison then compute it the hard way.
+ return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
+}
+
+std::optional<ScalarEvolution::ExitLimit>
+ScalarEvolution::computeExitLimitFromCondFromBinOp(ExitLimitCacheTy &Cache,
+ const Loop *L,
+ Value *ExitCond,
+ bool ExitIfTrue,
+ bool AllowPredicates) {
+ // Check if the controlling expression for this loop is an And or Or.
+ Value *Op0, *Op1;
+ bool IsAnd;
+ if (match(ExitCond, m_LogicalAnd(m_Value(Op0), m_Value(Op1))))
+ IsAnd = true;
+ else if (match(ExitCond, m_LogicalOr(m_Value(Op0), m_Value(Op1))))
+ IsAnd = false;
+ else
+ return std::nullopt;
+
+ // A sub-condition of a non-trivial binop never solely controls the exit,
+ // whether we exit always depends on both conditions.
+ ExitLimit EL0 = computeExitLimitFromCondCached(
+ Cache, L, Op0, ExitIfTrue, /*ControlsOnlyExit=*/false, AllowPredicates);
+ ExitLimit EL1 = computeExitLimitFromCondCached(
+ Cache, L, Op1, ExitIfTrue, /*ControlsOnlyExit=*/false, AllowPredicates);
+
+ // EitherMayExit is true in these two cases:
+ // br (and Op0 Op1), loop, exit
+ // br (or Op0 Op1), exit, loop
+ bool EitherMayExit = IsAnd ^ ExitIfTrue;
+
+ const SCEV *BECount = getCouldNotCompute();
+ const SCEV *ConstantMaxBECount = getCouldNotCompute();
+ const SCEV *SymbolicMaxBECount = getCouldNotCompute();
+ if (EitherMayExit) {
+ bool UseSequentialUMin = !isa<BinaryOperator>(ExitCond);
+ // Both conditions must be same for the loop to continue executing.
+ // Choose the less conservative count.
+ if (EL0.ExactNotTaken != getCouldNotCompute() &&
+ EL1.ExactNotTaken != getCouldNotCompute()) {
+ BECount = getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken,
+ UseSequentialUMin);
+ }
+ if (EL0.ConstantMaxNotTaken == getCouldNotCompute())
+ ConstantMaxBECount = EL1.ConstantMaxNotTaken;
+ else if (EL1.ConstantMaxNotTaken == getCouldNotCompute())
+ ConstantMaxBECount = EL0.ConstantMaxNotTaken;
+ else
+ ConstantMaxBECount = getUMinFromMismatchedTypes(EL0.ConstantMaxNotTaken,
+ EL1.ConstantMaxNotTaken);
+ if (EL0.SymbolicMaxNotTaken == getCouldNotCompute())
+ SymbolicMaxBECount = EL1.SymbolicMaxNotTaken;
+ else if (EL1.SymbolicMaxNotTaken == getCouldNotCompute())
+ SymbolicMaxBECount = EL0.SymbolicMaxNotTaken;
+ else
+ SymbolicMaxBECount = getUMinFromMismatchedTypes(
+ EL0.SymbolicMaxNotTaken, EL1.SymbolicMaxNotTaken, UseSequentialUMin);
+ } else {
+ // Both conditions must be same at the same time for the loop to exit.
+ // For now, be conservative.
+ if (EL0.ExactNotTaken == EL1.ExactNotTaken)
+ BECount = EL0.ExactNotTaken;
+ }
+
+ // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
+ // to be more aggressive when computing BECount than when computing
+ // ConstantMaxBECount. In these cases it is possible for EL0.ExactNotTaken
+ // and
+ // EL1.ExactNotTaken to match, but for EL0.ConstantMaxNotTaken and
+ // EL1.ConstantMaxNotTaken to not.
+ if (isa<SCEVCouldNotCompute>(ConstantMaxBECount) &&
+ !isa<SCEVCouldNotCompute>(BECount))
+ ConstantMaxBECount = getConstant(getUnsignedRangeMax(BECount));
+ if (isa<SCEVCouldNotCompute>(SymbolicMaxBECount))
+ SymbolicMaxBECount =
+ isa<SCEVCouldNotCompute>(BECount) ? ConstantMaxBECount : BECount;
+ return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, false,
+ {ArrayRef(EL0.Predicates), ArrayRef(EL1.Predicates)});
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(
+ const Loop *L, ICmpInst *ExitCond, bool ExitIfTrue, bool ControlsOnlyExit,
+ bool AllowPredicates) {
+ // If the condition was exit on true, convert the condition to exit on false
+ CmpPredicate Pred;
+ if (!ExitIfTrue)
+ Pred = ExitCond->getCmpPredicate();
+ else
+ Pred = ExitCond->getInverseCmpPredicate();
+ const ICmpInst::Predicate OriginalPred = Pred;
+
+ const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
+ const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
+
+ ExitLimit EL = computeExitLimitFromICmp(L, Pred, LHS, RHS, ControlsOnlyExit,
+ AllowPredicates);
+ if (EL.hasAnyInfo())
+ return EL;
+
+ auto *ExhaustiveCount =
+ computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
+
+ if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
+ return ExhaustiveCount;
+
+ return computeShiftCompareExitLimit(ExitCond->getOperand(0),
+ ExitCond->getOperand(1), L, OriginalPred);
+}
+ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(
+ const Loop *L, CmpPredicate Pred, SCEVUse LHS, SCEVUse RHS,
+ bool ControlsOnlyExit, bool AllowPredicates) {
+
+ // Try to evaluate any dependencies out of the loop.
+ LHS = getSCEVAtScope(LHS, L);
+ RHS = getSCEVAtScope(RHS, L);
+
+ // At this point, we would like to compute how many iterations of the
+ // loop the predicate will return true for these inputs.
+ if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
+ // If there is a loop-invariant, force it into the RHS.
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ }
+
+ bool ControllingFiniteLoop = ControlsOnlyExit && loopHasNoAbnormalExits(L) &&
+ loopIsFiniteByAssumption(L);
+ // Simplify the operands before analyzing them.
+ (void)SimplifyICmpOperands(Pred, LHS, RHS, /*Depth=*/0);
+
+ // If we have a comparison of a chrec against a constant, try to use value
+ // ranges to answer this query.
+ if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
+ if (AddRec->getLoop() == L) {
+ // Form the constant range.
+ ConstantRange CompRange =
+ ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
+
+ const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
+ if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
+ }
+
+ // If this loop must exit based on this condition (or execute undefined
+ // behaviour), see if we can improve wrap flags. This is essentially
+ // a must execute style proof.
+ if (ControllingFiniteLoop && isLoopInvariant(RHS, L)) {
+ // If we can prove the test sequence produced must repeat the same values
+ // on self-wrap of the IV, then we can infer that IV doesn't self wrap
+ // because if it did, we'd have an infinite (undefined) loop.
+ // TODO: We can peel off any functions which are invertible *in L*. Loop
+ // invariant terms are effectively constants for our purposes here.
+ SCEVUse InnerLHS = LHS;
+ if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS))
+ InnerLHS = ZExt->getOperand();
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(InnerLHS);
+ AR && !AR->hasNoSelfWrap() && AR->getLoop() == L && AR->isAffine() &&
+ isKnownToBeAPowerOfTwo(AR->getStepRecurrence(*this), /*OrZero=*/true,
+ /*OrNegative=*/true)) {
+ auto Flags = AR->getNoWrapFlags();
+ Flags = setFlags(Flags, SCEV::FlagNW);
+ SmallVector<SCEVUse> Operands{AR->operands()};
+ Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
+ }
+
+ // For a slt/ult condition with a positive step, can we prove nsw/nuw?
+ // From no-self-wrap, this follows trivially from the fact that every
+ // (un)signed-wrapped, but not self-wrapped value must be LT than the
+ // last value before (un)signed wrap. Since we know that last value
+ // didn't exit, nor will any smaller one.
+ if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_ULT) {
+ auto WrapType = Pred == ICmpInst::ICMP_SLT ? SCEV::FlagNSW : SCEV::FlagNUW;
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS);
+ AR && AR->getLoop() == L && AR->isAffine() &&
+ !AR->getNoWrapFlags(WrapType) && AR->hasNoSelfWrap() &&
+ isKnownPositive(AR->getStepRecurrence(*this))) {
+ auto Flags = AR->getNoWrapFlags();
+ Flags = setFlags(Flags, WrapType);
+ SmallVector<SCEVUse> Operands{AR->operands()};
+ Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
+ }
+ }
+ }
+
+ switch (Pred) {
+ case ICmpInst::ICMP_NE: { // while (X != Y)
+ // Convert to: while (X-Y != 0)
+ if (LHS->getType()->isPointerTy()) {
+ LHS = getPtrToAddrExpr(LHS);
+ if (isa<SCEVCouldNotCompute>(LHS))
+ return LHS;
+ }
+ if (RHS->getType()->isPointerTy()) {
+ RHS = getPtrToAddrExpr(RHS);
+ if (isa<SCEVCouldNotCompute>(RHS))
+ return RHS;
+ }
+ ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsOnlyExit,
+ AllowPredicates);
+ if (EL.hasAnyInfo())
+ return EL;
+ break;
+ }
+ case ICmpInst::ICMP_EQ: { // while (X == Y)
+ // Convert to: while (X-Y == 0)
+ if (LHS->getType()->isPointerTy()) {
+ LHS = getPtrToAddrExpr(LHS);
+ if (isa<SCEVCouldNotCompute>(LHS))
+ return LHS;
+ }
+ if (RHS->getType()->isPointerTy()) {
+ RHS = getPtrToAddrExpr(RHS);
+ if (isa<SCEVCouldNotCompute>(RHS))
+ return RHS;
+ }
+ ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
+ if (EL.hasAnyInfo()) return EL;
+ break;
+ }
+ case ICmpInst::ICMP_SLE:
+ case ICmpInst::ICMP_ULE:
+ // Since the loop is finite, an invariant RHS cannot include the boundary
+ // value, otherwise it would loop forever.
+ if (!EnableFiniteLoopControl || !ControllingFiniteLoop ||
+ !isLoopInvariant(RHS, L)) {
+ // Otherwise, perform the addition in a wider type, to avoid overflow.
+ // If the LHS is an addrec with the appropriate nowrap flag, the
+ // extension will be sunk into it and the exit count can be analyzed.
+ auto *OldType = dyn_cast<IntegerType>(LHS->getType());
+ if (!OldType)
+ break;
+ // Prefer doubling the bitwidth over adding a single bit to make it more
+ // likely that we use a legal type.
+ auto *NewType =
+ Type::getIntNTy(OldType->getContext(), OldType->getBitWidth() * 2);
+ if (ICmpInst::isSigned(Pred)) {
+ LHS = getSignExtendExpr(LHS, NewType);
+ RHS = getSignExtendExpr(RHS, NewType);
+ } else {
+ LHS = getZeroExtendExpr(LHS, NewType);
+ RHS = getZeroExtendExpr(RHS, NewType);
+ }
+ }
+ RHS = getAddExpr(getOne(RHS->getType()), RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SLT:
+ case ICmpInst::ICMP_ULT: { // while (X < Y)
+ bool IsSigned = ICmpInst::isSigned(Pred);
+ ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsOnlyExit,
+ AllowPredicates);
+ if (EL.hasAnyInfo())
+ return EL;
+ break;
+ }
+ case ICmpInst::ICMP_SGE:
+ case ICmpInst::ICMP_UGE:
+ // Since the loop is finite, an invariant RHS cannot include the boundary
+ // value, otherwise it would loop forever.
+ if (!EnableFiniteLoopControl || !ControllingFiniteLoop ||
+ !isLoopInvariant(RHS, L))
+ break;
+ RHS = getAddExpr(getMinusOne(RHS->getType()), RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SGT:
+ case ICmpInst::ICMP_UGT: { // while (X > Y)
+ bool IsSigned = ICmpInst::isSigned(Pred);
+ ExitLimit EL = howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsOnlyExit,
+ AllowPredicates);
+ if (EL.hasAnyInfo())
+ return EL;
+ break;
+ }
+ default:
+ break;
+ }
+
+ return getCouldNotCompute();
+}
+
+ScalarEvolution::ExitLimit
+ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
+ SwitchInst *Switch,
+ BasicBlock *ExitingBlock,
+ bool ControlsOnlyExit) {
+ assert(!L->contains(ExitingBlock) && "Not an exiting block!");
+
+ // Give up if the exit is the default dest of a switch.
+ if (Switch->getDefaultDest() == ExitingBlock)
+ return getCouldNotCompute();
+
+ assert(L->contains(Switch->getDefaultDest()) &&
+ "Default case must not exit the loop!");
+ const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
+ const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
+
+ // while (X != Y) --> while (X-Y != 0)
+ ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsOnlyExit);
+ if (EL.hasAnyInfo())
+ return EL;
+
+ return getCouldNotCompute();
+}
+
+static ConstantInt *
+EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
+ ScalarEvolution &SE) {
+ const SCEV *InVal = SE.getConstant(C);
+ const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
+ assert(isa<SCEVConstant>(Val) &&
+ "Evaluation of SCEV at constant didn't fold correctly?");
+ return cast<SCEVConstant>(Val)->getValue();
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
+ Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
+ ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
+ if (!RHS)
+ return getCouldNotCompute();
+
+ const BasicBlock *Latch = L->getLoopLatch();
+ if (!Latch)
+ return getCouldNotCompute();
+
+ const BasicBlock *Predecessor = L->getLoopPredecessor();
+ if (!Predecessor)
+ return getCouldNotCompute();
+
+ // Return true if V is of the form "LHS `shift_op` <positive constant>".
+ // Return LHS in OutLHS, shift_op in OutOpCode, and the shift amount in
+ // OutShiftAmt.
+ auto MatchPositiveShift = [](Value *V, Value *&OutLHS,
+ Instruction::BinaryOps &OutOpCode,
+ unsigned &OutShiftAmt) {
+ using namespace PatternMatch;
+
+ ConstantInt *ShiftAmt;
+ if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
+ OutOpCode = Instruction::LShr;
+ else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
+ OutOpCode = Instruction::AShr;
+ else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
+ OutOpCode = Instruction::Shl;
+ else
+ return false;
+
+ uint64_t Amt = ShiftAmt->getValue().getLimitedValue();
+ if (Amt == 0 || Amt >= OutLHS->getType()->getScalarSizeInBits())
+ return false;
+ OutShiftAmt = Amt;
+ return true;
+ };
+
+ // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
+ //
+ // loop:
+ // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
+ // %iv.shifted = lshr i32 %iv, <positive constant>
+ //
+ // Return true on a successful match. Return the corresponding PHI node (%iv
+ // above) in PNOut, the opcode of the shift operation in OpCodeOut, and the
+ // shift amount in ShiftAmtOut.
+ auto MatchShiftRecurrence = [&](Value *V, PHINode *&PNOut,
+ Instruction::BinaryOps &OpCodeOut,
+ unsigned &ShiftAmtOut) {
+ std::optional<Instruction::BinaryOps> PostShiftOpCode;
+
+ {
+ Instruction::BinaryOps OpC;
+ Value *V;
+ unsigned Amt;
+
+ // If we encounter a shift instruction, "peel off" the shift operation,
+ // and remember that we did so. Later when we inspect %iv's backedge
+ // value, we will make sure that the backedge value uses the same
+ // operation.
+ //
+ // Note: the peeled shift operation does not have to be the same
+ // instruction as the one feeding into the PHI's backedge value. We only
+ // really care about it being the same *kind* of shift instruction --
+ // that's all that is required for our later inferences to hold.
+ if (MatchPositiveShift(LHS, V, OpC, Amt)) {
+ PostShiftOpCode = OpC;
+ LHS = V;
+ }
+ }
+
+ PNOut = dyn_cast<PHINode>(LHS);
+ if (!PNOut || PNOut->getParent() != L->getHeader())
+ return false;
+
+ Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
+ Value *OpLHS;
+
+ return
+ // The backedge value for the PHI node must be a shift by a positive
+ // amount
+ MatchPositiveShift(BEValue, OpLHS, OpCodeOut, ShiftAmtOut) &&
+
+ // of the PHI node itself
+ OpLHS == PNOut &&
+
+ // and the kind of shift should be match the kind of shift we peeled
+ // off, if any.
+ (!PostShiftOpCode || *PostShiftOpCode == OpCodeOut);
+ };
+
+ PHINode *PN;
+ Instruction::BinaryOps OpCode;
+ unsigned ShiftAmt;
+ if (!MatchShiftRecurrence(LHS, PN, OpCode, ShiftAmt))
+ return getCouldNotCompute();
+
+ const DataLayout &DL = getDataLayout();
+
+ // The key rationale for this optimization is that for some kinds of shift
+ // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
+ // within a finite number of iterations. If the condition guarding the
+ // backedge (in the sense that the backedge is taken if the condition is true)
+ // is false for the value the shift recurrence stabilizes to, then we know
+ // that the backedge is taken only a finite number of times.
+
+ ConstantInt *StableValue = nullptr;
+ switch (OpCode) {
+ default:
+ llvm_unreachable("Impossible case!");
+
+ case Instruction::AShr: {
+ // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
+ // bitwidth(K) iterations.
+ Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
+ KnownBits Known = computeKnownBits(FirstValue, DL, &AC,
+ Predecessor->getTerminator(), &DT);
+ auto *Ty = cast<IntegerType>(RHS->getType());
+ if (Known.isNonNegative())
+ StableValue = ConstantInt::get(Ty, 0);
+ else if (Known.isNegative())
+ StableValue = ConstantInt::get(Ty, -1, true);
+ else
+ return getCouldNotCompute();
+
+ break;
+ }
+ case Instruction::LShr:
+ case Instruction::Shl:
+ // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
+ // stabilize to 0 in at most bitwidth(K) iterations.
+ StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
+ break;
+ }
+
+ auto *Result =
+ ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
+ assert(Result->getType()->isIntegerTy(1) &&
+ "Otherwise cannot be an operand to a branch instruction");
+
+ if (Result->isNullValue()) {
+ unsigned BitWidth = getTypeSizeInBits(RHS->getType());
+ unsigned MaxBTC = BitWidth;
+
+ // For right-shift recurrences (lshr/ashr with non-negative start), we can
+ // compute a tighter max backedge-taken count from the range of the start
+ // value. After k shifts of ShiftAmt, value = start >> (k * ShiftAmt).
+ // The value reaches 0 (the stable value) when k * ShiftAmt >=
+ // activeBits(start), so max BTC = ceil(activeBits(maxStart) / ShiftAmt).
+ if (OpCode == Instruction::LShr || OpCode == Instruction::AShr) {
+ Value *StartValue = PN->getIncomingValueForBlock(Predecessor);
+ const SCEV *StartSCEV = getSCEV(StartValue);
+ APInt MaxStart = getUnsignedRangeMax(StartSCEV);
+ if (MaxStart.isStrictlyPositive()) {
+ unsigned ActiveBits = MaxStart.getActiveBits();
+ unsigned RangeBTC = divideCeil(ActiveBits, ShiftAmt);
+ MaxBTC = std::min(MaxBTC, RangeBTC);
+ }
+ }
+
+ const SCEV *UpperBound =
+ getConstant(getEffectiveSCEVType(RHS->getType()), MaxBTC);
+ return ExitLimit(getCouldNotCompute(), UpperBound, UpperBound, false);
+ }
+
+ return getCouldNotCompute();
+}
+
+/// Return true if we can constant fold an instruction of the specified type,
+/// assuming that all operands were constants.
+static bool CanConstantFold(const Instruction *I) {
+ if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
+ isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
+ isa<LoadInst>(I) || isa<ExtractValueInst>(I))
+ return true;
+
+ if (const CallInst *CI = dyn_cast<CallInst>(I))
+ if (const Function *F = CI->getCalledFunction())
+ return canConstantFoldCallTo(CI, F);
+ return false;
+}
+
+/// Determine whether this instruction can constant evolve within this loop
+/// assuming its operands can all constant evolve.
+static bool canConstantEvolve(Instruction *I, const Loop *L) {
+ // An instruction outside of the loop can't be derived from a loop PHI.
+ if (!L->contains(I)) return false;
+
+ if (isa<PHINode>(I)) {
+ // We don't currently keep track of the control flow needed to evaluate
+ // PHIs, so we cannot handle PHIs inside of loops.
+ return L->getHeader() == I->getParent();
+ }
+
+ // If we won't be able to constant fold this expression even if the operands
+ // are constants, bail early.
+ return CanConstantFold(I);
+}
+
+/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
+/// recursing through each instruction operand until reaching a loop header phi.
+static PHINode *
+getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
+ DenseMap<Instruction *, PHINode *> &PHIMap,
+ unsigned Depth) {
+ if (Depth > MaxConstantEvolvingDepth)
+ return nullptr;
+
+ // Otherwise, we can evaluate this instruction if all of its operands are
+ // constant or derived from a PHI node themselves.
+ PHINode *PHI = nullptr;
+ for (Value *Op : UseInst->operands()) {
+ if (isa<Constant>(Op)) continue;
+
+ Instruction *OpInst = dyn_cast<Instruction>(Op);
+ if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
+
+ PHINode *P = dyn_cast<PHINode>(OpInst);
+ if (!P)
+ // If this operand is already visited, reuse the prior result.
+ // We may have P != PHI if this is the deepest point at which the
+ // inconsistent paths meet.
+ P = PHIMap.lookup(OpInst);
+ if (!P) {
+ // Recurse and memoize the results, whether a phi is found or not.
+ // This recursive call invalidates pointers into PHIMap.
+ P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
+ PHIMap[OpInst] = P;
+ }
+ if (!P)
+ return nullptr; // Not evolving from PHI
+ if (PHI && PHI != P)
+ return nullptr; // Evolving from multiple different PHIs.
+ PHI = P;
+ }
+ // This is a expression evolving from a constant PHI!
+ return PHI;
+}
+
+/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
+/// in the loop that V is derived from. We allow arbitrary operations along the
+/// way, but the operands of an operation must either be constants or a value
+/// derived from a constant PHI. If this expression does not fit with these
+/// constraints, return null.
+static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
+ Instruction *I = dyn_cast<Instruction>(V);
+ if (!I || !canConstantEvolve(I, L)) return nullptr;
+
+ if (PHINode *PN = dyn_cast<PHINode>(I))
+ return PN;
+
+ // Record non-constant instructions contained by the loop.
+ DenseMap<Instruction *, PHINode *> PHIMap;
+ return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
+}
+
+/// EvaluateExpression - Given an expression that passes the
+/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
+/// in the loop has the value PHIVal. If we can't fold this expression for some
+/// reason, return null.
+static Constant *EvaluateExpression(Value *V, const Loop *L,
+ DenseMap<Instruction *, Constant *> &Vals,
+ const DataLayout &DL,
+ const TargetLibraryInfo *TLI) {
+ // Convenient constant check, but redundant for recursive calls.
+ if (Constant *C = dyn_cast<Constant>(V)) return C;
+ Instruction *I = dyn_cast<Instruction>(V);
+ if (!I) return nullptr;
+
+ if (Constant *C = Vals.lookup(I)) return C;
+
+ // An instruction inside the loop depends on a value outside the loop that we
+ // weren't given a mapping for, or a value such as a call inside the loop.
+ if (!canConstantEvolve(I, L)) return nullptr;
+
+ // An unmapped PHI can be due to a branch or another loop inside this loop,
+ // or due to this not being the initial iteration through a loop where we
+ // couldn't compute the evolution of this particular PHI last time.
+ if (isa<PHINode>(I)) return nullptr;
+
+ std::vector<Constant*> Operands(I->getNumOperands());
+
+ for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
+ Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
+ if (!Operand) {
+ Operands[i] = dyn_cast<Constant>(I->getOperand(i));
+ if (!Operands[i]) return nullptr;
+ continue;
+ }
+ Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
+ Vals[Operand] = C;
+ if (!C) return nullptr;
+ Operands[i] = C;
+ }
+
+ return ConstantFoldInstOperands(I, Operands, DL, TLI,
+ /*AllowNonDeterministic=*/false);
+}
+
+
+// If every incoming value to PN except the one for BB is a specific Constant,
+// return that, else return nullptr.
+static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
+ Constant *IncomingVal = nullptr;
+
+ for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
+ if (PN->getIncomingBlock(i) == BB)
+ continue;
+
+ auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
+ if (!CurrentVal)
+ return nullptr;
+
+ if (IncomingVal != CurrentVal) {
+ if (IncomingVal)
+ return nullptr;
+ IncomingVal = CurrentVal;
+ }
+ }
+
+ return IncomingVal;
+}
+
+/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
+/// in the header of its containing loop, we know the loop executes a
+/// constant number of times, and the PHI node is just a recurrence
+/// involving constants, fold it.
+Constant *
+ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
+ const APInt &BEs,
+ const Loop *L) {
+ auto [I, Inserted] = ConstantEvolutionLoopExitValue.try_emplace(PN);
+ if (!Inserted)
+ return I->second;
+
+ if (BEs.ugt(MaxBruteForceIterations))
+ return nullptr; // Not going to evaluate it.
+
+ Constant *&RetVal = I->second;
+
+ DenseMap<Instruction *, Constant *> CurrentIterVals;
+ BasicBlock *Header = L->getHeader();
+ assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
+
+ BasicBlock *Latch = L->getLoopLatch();
+ if (!Latch)
+ return nullptr;
+
+ for (PHINode &PHI : Header->phis()) {
+ if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
+ CurrentIterVals[&PHI] = StartCST;
+ }
+ if (!CurrentIterVals.count(PN))
+ return RetVal = nullptr;
+
+ Value *BEValue = PN->getIncomingValueForBlock(Latch);
+
+ // Execute the loop symbolically to determine the exit value.
+ assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
+ "BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
+
+ unsigned NumIterations = BEs.getZExtValue(); // must be in range
+ unsigned IterationNum = 0;
+ const DataLayout &DL = getDataLayout();
+ for (; ; ++IterationNum) {
+ if (IterationNum == NumIterations)
+ return RetVal = CurrentIterVals[PN]; // Got exit value!
+
+ // Compute the value of the PHIs for the next iteration.
+ // EvaluateExpression adds non-phi values to the CurrentIterVals map.
+ DenseMap<Instruction *, Constant *> NextIterVals;
+ Constant *NextPHI =
+ EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
+ if (!NextPHI)
+ return nullptr; // Couldn't evaluate!
+ NextIterVals[PN] = NextPHI;
+
+ bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
+
+ // Also evaluate the other PHI nodes. However, we don't get to stop if we
+ // cease to be able to evaluate one of them or if they stop evolving,
+ // because that doesn't necessarily prevent us from computing PN.
+ SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
+ for (const auto &I : CurrentIterVals) {
+ PHINode *PHI = dyn_cast<PHINode>(I.first);
+ if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
+ PHIsToCompute.emplace_back(PHI, I.second);
+ }
+ // We use two distinct loops because EvaluateExpression may invalidate any
+ // iterators into CurrentIterVals.
+ for (const auto &I : PHIsToCompute) {
+ PHINode *PHI = I.first;
+ Constant *&NextPHI = NextIterVals[PHI];
+ if (!NextPHI) { // Not already computed.
+ Value *BEValue = PHI->getIncomingValueForBlock(Latch);
+ NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
+ }
+ if (NextPHI != I.second)
+ StoppedEvolving = false;
+ }
+
+ // If all entries in CurrentIterVals == NextIterVals then we can stop
+ // iterating, the loop can't continue to change.
+ if (StoppedEvolving)
+ return RetVal = CurrentIterVals[PN];
+
+ CurrentIterVals.swap(NextIterVals);
+ }
+}
+
+const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
+ Value *Cond,
+ bool ExitWhen) {
+ PHINode *PN = getConstantEvolvingPHI(Cond, L);
+ if (!PN) return getCouldNotCompute();
+
+ // If the loop is canonicalized, the PHI will have exactly two entries.
+ // That's the only form we support here.
+ if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
+
+ DenseMap<Instruction *, Constant *> CurrentIterVals;
+ BasicBlock *Header = L->getHeader();
+ assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
+
+ BasicBlock *Latch = L->getLoopLatch();
+ assert(Latch && "Should follow from NumIncomingValues == 2!");
+
+ for (PHINode &PHI : Header->phis()) {
+ if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
+ CurrentIterVals[&PHI] = StartCST;
+ }
+ if (!CurrentIterVals.count(PN))
+ return getCouldNotCompute();
+
+ // Okay, we find a PHI node that defines the trip count of this loop. Execute
+ // the loop symbolically to determine when the condition gets a value of
+ // "ExitWhen".
+ unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
+ const DataLayout &DL = getDataLayout();
+ for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
+ auto *CondVal = dyn_cast_or_null<ConstantInt>(
+ EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
+
+ // Couldn't symbolically evaluate.
+ if (!CondVal) return getCouldNotCompute();
+
+ if (CondVal->getValue() == uint64_t(ExitWhen)) {
+ ++NumBruteForceTripCountsComputed;
+ return getConstant(Type::getInt32Ty(getContext()), IterationNum);
+ }
+
+ // Update all the PHI nodes for the next iteration.
+ DenseMap<Instruction *, Constant *> NextIterVals;
+
+ // Create a list of which PHIs we need to compute. We want to do this before
+ // calling EvaluateExpression on them because that may invalidate iterators
+ // into CurrentIterVals.
+ SmallVector<PHINode *, 8> PHIsToCompute;
+ for (const auto &I : CurrentIterVals) {
+ PHINode *PHI = dyn_cast<PHINode>(I.first);
+ if (!PHI || PHI->getParent() != Header) continue;
+ PHIsToCompute.push_back(PHI);
+ }
+ for (PHINode *PHI : PHIsToCompute) {
+ Constant *&NextPHI = NextIterVals[PHI];
+ if (NextPHI) continue; // Already computed!
+
+ Value *BEValue = PHI->getIncomingValueForBlock(Latch);
+ NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
+ }
+ CurrentIterVals.swap(NextIterVals);
+ }
+
+ // Too many iterations were needed to evaluate.
+ return getCouldNotCompute();
+}
+
+const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
+ SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
+ ValuesAtScopes[V];
+ // Check to see if we've folded this expression at this loop before.
+ for (auto &LS : Values)
+ if (LS.first == L)
+ return LS.second ? LS.second : V;
+
+ Values.emplace_back(L, nullptr);
+
+ // Otherwise compute it.
+ const SCEV *C = computeSCEVAtScope(V, L);
+ for (auto &LS : reverse(ValuesAtScopes[V]))
+ if (LS.first == L) {
+ LS.second = C;
+ if (!isa<SCEVConstant>(C))
+ ValuesAtScopesUsers[C].push_back({L, V});
+ break;
+ }
+ return C;
+}
+
+/// This builds up a Constant using the ConstantExpr interface. That way, we
+/// will return Constants for objects which aren't represented by a
+/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
+/// Returns NULL if the SCEV isn't representable as a Constant.
+static Constant *BuildConstantFromSCEV(const SCEV *V) {
+ switch (V->getSCEVType()) {
+ case scCouldNotCompute:
+ case scAddRecExpr:
+ case scVScale:
+ return nullptr;
+ case scConstant:
+ return cast<SCEVConstant>(V)->getValue();
+ case scUnknown:
+ return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
+ case scPtrToAddr: {
+ const SCEVPtrToAddrExpr *P2I = cast<SCEVPtrToAddrExpr>(V);
+ if (Constant *CastOp = BuildConstantFromSCEV(P2I->getOperand()))
+ return ConstantExpr::getPtrToAddr(CastOp, P2I->getType());
+
+ return nullptr;
+ }
+ case scTruncate: {
+ const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
+ if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
+ return ConstantExpr::getTrunc(CastOp, ST->getType());
+ return nullptr;
+ }
+ case scAddExpr: {
+ const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
+ Constant *C = nullptr;
+ for (const SCEV *Op : SA->operands()) {
+ Constant *OpC = BuildConstantFromSCEV(Op);
+ if (!OpC)
+ return nullptr;
+ if (!C) {
+ C = OpC;
+ continue;
+ }
+ assert(!C->getType()->isPointerTy() &&
+ "Can only have one pointer, and it must be last");
+ if (OpC->getType()->isPointerTy()) {
+ // The offsets have been converted to bytes. We can add bytes using
+ // an i8 GEP.
+ C = ConstantExpr::getPtrAdd(OpC, C);
+ } else {
+ C = ConstantExpr::getAdd(C, OpC);
+ }
+ }
+ return C;
+ }
+ case scMulExpr:
+ case scSignExtend:
+ case scZeroExtend:
+ case scUDivExpr:
+ case scSMaxExpr:
+ case scUMaxExpr:
+ case scSMinExpr:
+ case scUMinExpr:
+ case scSequentialUMinExpr:
+ return nullptr;
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+const SCEV *ScalarEvolution::getWithOperands(const SCEV *S,
+ SmallVectorImpl<SCEVUse> &NewOps) {
+ switch (S->getSCEVType()) {
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ return getCastExpr(S->getSCEVType(), NewOps[0], S->getType());
+ case scAddRecExpr: {
+ auto *AddRec = cast<SCEVAddRecExpr>(S);
+ return getAddRecExpr(NewOps, AddRec->getLoop(), AddRec->getNoWrapFlags());
+ }
+ case scAddExpr:
+ return getAddExpr(NewOps, cast<SCEVAddExpr>(S)->getNoWrapFlags());
+ case scMulExpr:
+ return getMulExpr(NewOps, cast<SCEVMulExpr>(S)->getNoWrapFlags());
+ case scUDivExpr:
+ return getUDivExpr(NewOps[0], NewOps[1]);
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ return getMinMaxExpr(S->getSCEVType(), NewOps);
+ case scSequentialUMinExpr:
+ return getSequentialMinMaxExpr(S->getSCEVType(), NewOps);
+ case scConstant:
+ case scVScale:
+ case scUnknown:
+ return S;
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
+ switch (V->getSCEVType()) {
+ case scConstant:
+ case scVScale:
+ return V;
+ case scAddRecExpr: {
+ // If this is a loop recurrence for a loop that does not contain L, then we
+ // are dealing with the final value computed by the loop.
+ const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(V);
+ // First, attempt to evaluate each operand.
+ // Avoid performing the look-up in the common case where the specified
+ // expression has no loop-variant portions.
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
+ const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
+ if (OpAtScope == AddRec->getOperand(i))
+ continue;
+
+ // Okay, at least one of these operands is loop variant but might be
+ // foldable. Build a new instance of the folded commutative expression.
+ SmallVector<SCEVUse, 8> NewOps;
+ NewOps.reserve(AddRec->getNumOperands());
+ append_range(NewOps, AddRec->operands().take_front(i));
+ NewOps.push_back(OpAtScope);
+ for (++i; i != e; ++i)
+ NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
+
+ const SCEV *FoldedRec = getAddRecExpr(
+ NewOps, AddRec->getLoop(), AddRec->getNoWrapFlags(SCEV::FlagNW));
+ AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
+ // The addrec may be folded to a nonrecurrence, for example, if the
+ // induction variable is multiplied by zero after constant folding. Go
+ // ahead and return the folded value.
+ if (!AddRec)
+ return FoldedRec;
+ break;
+ }
+
+ // If the scope is outside the addrec's loop, evaluate it by using the
+ // loop exit value of the addrec.
+ if (!AddRec->getLoop()->contains(L)) {
+ // To evaluate this recurrence, we need to know how many times the AddRec
+ // loop iterates. Compute this now.
+ const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
+ if (BackedgeTakenCount == getCouldNotCompute())
+ return AddRec;
+
+ // Then, evaluate the AddRec.
+ return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
+ }
+
+ return AddRec;
+ }
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUDivExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr: {
+ ArrayRef<SCEVUse> Ops = V->operands();
+ // Avoid performing the look-up in the common case where the specified
+ // expression has no loop-variant portions.
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
+ const SCEV *OpAtScope = getSCEVAtScope(Ops[i].getPointer(), L);
+ if (OpAtScope != Ops[i].getPointer()) {
+ // Okay, at least one of these operands is loop variant but might be
+ // foldable. Build a new instance of the folded commutative expression.
+ SmallVector<SCEVUse, 8> NewOps;
+ NewOps.reserve(Ops.size());
+ append_range(NewOps, Ops.take_front(i));
+ NewOps.push_back(OpAtScope);
+
+ for (++i; i != e; ++i) {
+ OpAtScope = getSCEVAtScope(Ops[i].getPointer(), L);
+ NewOps.push_back(OpAtScope);
+ }
+
+ return getWithOperands(V, NewOps);
+ }
+ }
+ // If we got here, all operands are loop invariant.
+ return V;
+ }
+ case scUnknown: {
+ // If this instruction is evolved from a constant-evolving PHI, compute the
+ // exit value from the loop without using SCEVs.
+ const SCEVUnknown *SU = cast<SCEVUnknown>(V);
+ Instruction *I = dyn_cast<Instruction>(SU->getValue());
+ if (!I)
+ return V; // This is some other type of SCEVUnknown, just return it.
+
+ if (PHINode *PN = dyn_cast<PHINode>(I)) {
+ const Loop *CurrLoop = this->LI[I->getParent()];
+ // Looking for loop exit value.
+ if (CurrLoop && CurrLoop->getParentLoop() == L &&
+ PN->getParent() == CurrLoop->getHeader()) {
+ // Okay, there is no closed form solution for the PHI node. Check
+ // to see if the loop that contains it has a known backedge-taken
+ // count. If so, we may be able to force computation of the exit
+ // value.
+ const SCEV *BackedgeTakenCount = getBackedgeTakenCount(CurrLoop);
+ // This trivial case can show up in some degenerate cases where
+ // the incoming IR has not yet been fully simplified.
+ if (BackedgeTakenCount->isZero()) {
+ Value *InitValue = nullptr;
+ bool MultipleInitValues = false;
+ for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
+ if (!CurrLoop->contains(PN->getIncomingBlock(i))) {
+ if (!InitValue)
+ InitValue = PN->getIncomingValue(i);
+ else if (InitValue != PN->getIncomingValue(i)) {
+ MultipleInitValues = true;
+ break;
+ }
+ }
+ }
+ if (!MultipleInitValues && InitValue)
+ return getSCEV(InitValue);
+ }
+ // Do we have a loop invariant value flowing around the backedge
+ // for a loop which must execute the backedge?
+ if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
+ isKnownNonZero(BackedgeTakenCount) &&
+ PN->getNumIncomingValues() == 2) {
+
+ unsigned InLoopPred =
+ CurrLoop->contains(PN->getIncomingBlock(0)) ? 0 : 1;
+ Value *BackedgeVal = PN->getIncomingValue(InLoopPred);
+ if (CurrLoop->isLoopInvariant(BackedgeVal))
+ return getSCEV(BackedgeVal);
+ }
+ if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
+ // Okay, we know how many times the containing loop executes. If
+ // this is a constant evolving PHI node, get the final value at
+ // the specified iteration number.
+ Constant *RV =
+ getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), CurrLoop);
+ if (RV)
+ return getSCEV(RV);
+ }
+ }
+ }
+
+ // Okay, this is an expression that we cannot symbolically evaluate
+ // into a SCEV. Check to see if it's possible to symbolically evaluate
+ // the arguments into constants, and if so, try to constant propagate the
+ // result. This is particularly useful for computing loop exit values.
+ if (!CanConstantFold(I))
+ return V; // This is some other type of SCEVUnknown, just return it.
+
+ SmallVector<Constant *, 4> Operands;
+ Operands.reserve(I->getNumOperands());
+ bool MadeImprovement = false;
+ for (Value *Op : I->operands()) {
+ if (Constant *C = dyn_cast<Constant>(Op)) {
+ Operands.push_back(C);
+ continue;
+ }
+
+ // If any of the operands is non-constant and if they are
+ // non-integer and non-pointer, don't even try to analyze them
+ // with scev techniques.
+ if (!isSCEVable(Op->getType()))
+ return V;
+
+ const SCEV *OrigV = getSCEV(Op);
+ const SCEV *OpV = getSCEVAtScope(OrigV, L);
+ MadeImprovement |= OrigV != OpV;
+
+ Constant *C = BuildConstantFromSCEV(OpV);
+ if (!C)
+ return V;
+ assert(C->getType() == Op->getType() && "Type mismatch");
+ Operands.push_back(C);
+ }
+
+ // Check to see if getSCEVAtScope actually made an improvement.
+ if (!MadeImprovement)
+ return V; // This is some other type of SCEVUnknown, just return it.
+
+ Constant *C = nullptr;
+ const DataLayout &DL = getDataLayout();
+ C = ConstantFoldInstOperands(I, Operands, DL, &TLI,
+ /*AllowNonDeterministic=*/false);
+ if (!C)
+ return V;
+ return getSCEV(C);
+ }
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV type!");
+}
+
+const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
+ return getSCEVAtScope(getSCEV(V), L);
+}
+
+const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
+ if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
+ return stripInjectiveFunctions(ZExt->getOperand());
+ if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
+ return stripInjectiveFunctions(SExt->getOperand());
+ return S;
+}
+
+/// Finds the minimum unsigned root of the following equation:
+///
+/// A * X = B (mod N)
+///
+/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
+/// A and B isn't important.
+///
+/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
+static const SCEV *
+SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
+ SmallVectorImpl<const SCEVPredicate *> *Predicates,
+ ScalarEvolution &SE, const Loop *L) {
+ uint32_t BW = A.getBitWidth();
+ assert(BW == SE.getTypeSizeInBits(B->getType()));
+ assert(A != 0 && "A must be non-zero.");
+
+ // 1. D = gcd(A, N)
+ //
+ // The gcd of A and N may have only one prime factor: 2. The number of
+ // trailing zeros in A is its multiplicity
+ uint32_t Mult2 = A.countr_zero();
+ // D = 2^Mult2
+
+ // 2. Check if B is divisible by D.
+ //
+ // B is divisible by D if and only if the multiplicity of prime factor 2 for B
+ // is not less than multiplicity of this prime factor for D.
+ unsigned MinTZ = SE.getMinTrailingZeros(B);
+ // Try again with the terminator of the loop predecessor for context-specific
+ // result, if MinTZ s too small.
+ if (MinTZ < Mult2 && L->getLoopPredecessor())
+ MinTZ = SE.getMinTrailingZeros(B, L->getLoopPredecessor()->getTerminator());
+ if (MinTZ < Mult2) {
+ // Check if we can prove there's no remainder using URem.
+ const SCEV *URem =
+ SE.getURemExpr(B, SE.getConstant(APInt::getOneBitSet(BW, Mult2)));
+ const SCEV *Zero = SE.getZero(B->getType());
+ if (!SE.isKnownPredicate(CmpInst::ICMP_EQ, URem, Zero)) {
+ // Try to add a predicate ensuring B is a multiple of 1 << Mult2.
+ if (!Predicates)
+ return SE.getCouldNotCompute();
+
+ // Avoid adding a predicate that is known to be false.
+ if (SE.isKnownPredicate(CmpInst::ICMP_NE, URem, Zero))
+ return SE.getCouldNotCompute();
+ Predicates->push_back(SE.getEqualPredicate(URem, Zero));
+ }
+ }
+
+ // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
+ // modulo (N / D).
+ //
+ // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
+ // (N / D) in general. The inverse itself always fits into BW bits, though,
+ // so we immediately truncate it.
+ APInt AD = A.lshr(Mult2).trunc(BW - Mult2); // AD = A / D
+ APInt I = AD.multiplicativeInverse().zext(BW);
+
+ // 4. Compute the minimum unsigned root of the equation:
+ // I * (B / D) mod (N / D)
+ // To simplify the computation, we factor out the divide by D:
+ // (I * B mod N) / D
+ const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
+ return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
+}
+
+/// For a given quadratic addrec, generate coefficients of the corresponding
+/// quadratic equation, multiplied by a common value to ensure that they are
+/// integers.
+/// The returned value is a tuple { A, B, C, M, BitWidth }, where
+/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
+/// were multiplied by, and BitWidth is the bit width of the original addrec
+/// coefficients.
+/// This function returns std::nullopt if the addrec coefficients are not
+/// compile- time constants.
+static std::optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
+GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
+ assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
+ const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
+ const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
+ const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
+ LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
+ << *AddRec << '\n');
+
+ // We currently can only solve this if the coefficients are constants.
+ if (!LC || !MC || !NC) {
+ LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
+ return std::nullopt;
+ }
+
+ APInt L = LC->getAPInt();
+ APInt M = MC->getAPInt();
+ APInt N = NC->getAPInt();
+ assert(!N.isZero() && "This is not a quadratic addrec");
+
+ unsigned BitWidth = LC->getAPInt().getBitWidth();
+ unsigned NewWidth = BitWidth + 1;
+ LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
+ << BitWidth << '\n');
+ // The sign-extension (as opposed to a zero-extension) here matches the
+ // extension used in SolveQuadraticEquationWrap (with the same motivation).
+ N = N.sext(NewWidth);
+ M = M.sext(NewWidth);
+ L = L.sext(NewWidth);
+
+ // The increments are M, M+N, M+2N, ..., so the accumulated values are
+ // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
+ // L+M, L+2M+N, L+3M+3N, ...
+ // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
+ //
+ // The equation Acc = 0 is then
+ // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
+ // In a quadratic form it becomes:
+ // N n^2 + (2M-N) n + 2L = 0.
+
+ APInt A = N;
+ APInt B = 2 * M - A;
+ APInt C = 2 * L;
+ APInt T = APInt(NewWidth, 2);
+ LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
+ << "x + " << C << ", coeff bw: " << NewWidth
+ << ", multiplied by " << T << '\n');
+ return std::make_tuple(A, B, C, T, BitWidth);
+}
+
+/// Helper function to compare optional APInts:
+/// (a) if X and Y both exist, return min(X, Y),
+/// (b) if neither X nor Y exist, return std::nullopt,
+/// (c) if exactly one of X and Y exists, return that value.
+static std::optional<APInt> MinOptional(std::optional<APInt> X,
+ std::optional<APInt> Y) {
+ if (X && Y) {
+ unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
+ APInt XW = X->sext(W);
+ APInt YW = Y->sext(W);
+ return XW.slt(YW) ? *X : *Y;
+ }
+ if (!X && !Y)
+ return std::nullopt;
+ return X ? *X : *Y;
+}
+
+/// Helper function to truncate an optional APInt to a given BitWidth.
+/// When solving addrec-related equations, it is preferable to return a value
+/// that has the same bit width as the original addrec's coefficients. If the
+/// solution fits in the original bit width, truncate it (except for i1).
+/// Returning a value of a different bit width may inhibit some optimizations.
+///
+/// In general, a solution to a quadratic equation generated from an addrec
+/// may require BW+1 bits, where BW is the bit width of the addrec's
+/// coefficients. The reason is that the coefficients of the quadratic
+/// equation are BW+1 bits wide (to avoid truncation when converting from
+/// the addrec to the equation).
+static std::optional<APInt> TruncIfPossible(std::optional<APInt> X,
+ unsigned BitWidth) {
+ if (!X)
+ return std::nullopt;
+ unsigned W = X->getBitWidth();
+ if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
+ return X->trunc(BitWidth);
+ return X;
+}
+
+/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
+/// iterations. The values L, M, N are assumed to be signed, and they
+/// should all have the same bit widths.
+/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
+/// where BW is the bit width of the addrec's coefficients.
+/// If the calculated value is a BW-bit integer (for BW > 1), it will be
+/// returned as such, otherwise the bit width of the returned value may
+/// be greater than BW.
+///
+/// This function returns std::nullopt if
+/// (a) the addrec coefficients are not constant, or
+/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
+/// like x^2 = 5, no integer solutions exist, in other cases an integer
+/// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
+static std::optional<APInt>
+SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
+ APInt A, B, C, M;
+ unsigned BitWidth;
+ auto T = GetQuadraticEquation(AddRec);
+ if (!T)
+ return std::nullopt;
+
+ std::tie(A, B, C, M, BitWidth) = *T;
+ LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
+ std::optional<APInt> X =
+ APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth + 1);
+ if (!X)
+ return std::nullopt;
+
+ ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
+ ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
+ if (!V->isZero())
+ return std::nullopt;
+
+ return TruncIfPossible(X, BitWidth);
+}
+
+/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
+/// iterations. The values M, N are assumed to be signed, and they
+/// should all have the same bit widths.
+/// Find the least n such that c(n) does not belong to the given range,
+/// while c(n-1) does.
+///
+/// This function returns std::nullopt if
+/// (a) the addrec coefficients are not constant, or
+/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
+/// bounds of the range.
+static std::optional<APInt>
+SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
+ const ConstantRange &Range, ScalarEvolution &SE) {
+ assert(AddRec->getOperand(0)->isZero() &&
+ "Starting value of addrec should be 0");
+ LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
+ << Range << ", addrec " << *AddRec << '\n');
+ // This case is handled in getNumIterationsInRange. Here we can assume that
+ // we start in the range.
+ assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
+ "Addrec's initial value should be in range");
+
+ APInt A, B, C, M;
+ unsigned BitWidth;
+ auto T = GetQuadraticEquation(AddRec);
+ if (!T)
+ return std::nullopt;
+
+ // Be careful about the return value: there can be two reasons for not
+ // returning an actual number. First, if no solutions to the equations
+ // were found, and second, if the solutions don't leave the given range.
+ // The first case means that the actual solution is "unknown", the second
+ // means that it's known, but not valid. If the solution is unknown, we
+ // cannot make any conclusions.
+ // Return a pair: the optional solution and a flag indicating if the
+ // solution was found.
+ auto SolveForBoundary =
+ [&](APInt Bound) -> std::pair<std::optional<APInt>, bool> {
+ // Solve for signed overflow and unsigned overflow, pick the lower
+ // solution.
+ LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
+ << Bound << " (before multiplying by " << M << ")\n");
+ Bound *= M; // The quadratic equation multiplier.
+
+ std::optional<APInt> SO;
+ if (BitWidth > 1) {
+ LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
+ "signed overflow\n");
+ SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
+ }
+ LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
+ "unsigned overflow\n");
+ std::optional<APInt> UO =
+ APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth + 1);
+
+ auto LeavesRange = [&] (const APInt &X) {
+ ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
+ ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
+ if (Range.contains(V0->getValue()))
+ return false;
+ // X should be at least 1, so X-1 is non-negative.
+ ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
+ ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
+ if (Range.contains(V1->getValue()))
+ return true;
+ return false;
+ };
+
+ // If SolveQuadraticEquationWrap returns std::nullopt, it means that there
+ // can be a solution, but the function failed to find it. We cannot treat it
+ // as "no solution".
+ if (!SO || !UO)
+ return {std::nullopt, false};
+
+ // Check the smaller value first to see if it leaves the range.
+ // At this point, both SO and UO must have values.
+ std::optional<APInt> Min = MinOptional(SO, UO);
+ if (LeavesRange(*Min))
+ return { Min, true };
+ std::optional<APInt> Max = Min == SO ? UO : SO;
+ if (LeavesRange(*Max))
+ return { Max, true };
+
+ // Solutions were found, but were eliminated, hence the "true".
+ return {std::nullopt, true};
+ };
+
+ std::tie(A, B, C, M, BitWidth) = *T;
+ // Lower bound is inclusive, subtract 1 to represent the exiting value.
+ APInt Lower = Range.getLower().sext(A.getBitWidth()) - 1;
+ APInt Upper = Range.getUpper().sext(A.getBitWidth());
+ auto SL = SolveForBoundary(Lower);
+ auto SU = SolveForBoundary(Upper);
+ // If any of the solutions was unknown, no meaninigful conclusions can
+ // be made.
+ if (!SL.second || !SU.second)
+ return std::nullopt;
+
+ // Claim: The correct solution is not some value between Min and Max.
+ //
+ // Justification: Assuming that Min and Max are different values, one of
+ // them is when the first signed overflow happens, the other is when the
+ // first unsigned overflow happens. Crossing the range boundary is only
+ // possible via an overflow (treating 0 as a special case of it, modeling
+ // an overflow as crossing k*2^W for some k).
+ //
+ // The interesting case here is when Min was eliminated as an invalid
+ // solution, but Max was not. The argument is that if there was another
+ // overflow between Min and Max, it would also have been eliminated if
+ // it was considered.
+ //
+ // For a given boundary, it is possible to have two overflows of the same
+ // type (signed/unsigned) without having the other type in between: this
+ // can happen when the vertex of the parabola is between the iterations
+ // corresponding to the overflows. This is only possible when the two
+ // overflows cross k*2^W for the same k. In such case, if the second one
+ // left the range (and was the first one to do so), the first overflow
+ // would have to enter the range, which would mean that either we had left
+ // the range before or that we started outside of it. Both of these cases
+ // are contradictions.
+ //
+ // Claim: In the case where SolveForBoundary returns std::nullopt, the correct
+ // solution is not some value between the Max for this boundary and the
+ // Min of the other boundary.
+ //
+ // Justification: Assume that we had such Max_A and Min_B corresponding
+ // to range boundaries A and B and such that Max_A < Min_B. If there was
+ // a solution between Max_A and Min_B, it would have to be caused by an
+ // overflow corresponding to either A or B. It cannot correspond to B,
+ // since Min_B is the first occurrence of such an overflow. If it
+ // corresponded to A, it would have to be either a signed or an unsigned
+ // overflow that is larger than both eliminated overflows for A. But
+ // between the eliminated overflows and this overflow, the values would
+ // cover the entire value space, thus crossing the other boundary, which
+ // is a contradiction.
+
+ return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::howFarToZero(const SCEV *V,
+ const Loop *L,
+ bool ControlsOnlyExit,
+ bool AllowPredicates) {
+
+ // This is only used for loops with a "x != y" exit test. The exit condition
+ // is now expressed as a single expression, V = x-y. So the exit test is
+ // effectively V != 0. We know and take advantage of the fact that this
+ // expression only being used in a comparison by zero context.
+
+ SmallVector<const SCEVPredicate *> Predicates;
+ // If the value is a constant
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
+ // If the value is already zero, the branch will execute zero times.
+ if (C->getValue()->isZero()) return C;
+ return getCouldNotCompute(); // Otherwise it will loop infinitely.
+ }
+
+ const SCEVAddRecExpr *AddRec =
+ dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
+
+ if (!AddRec && AllowPredicates)
+ // Try to make this an AddRec using runtime tests, in the first X
+ // iterations of this loop, where X is the SCEV expression found by the
+ // algorithm below.
+ AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
+
+ if (!AddRec || AddRec->getLoop() != L)
+ return getCouldNotCompute();
+
+ // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
+ // the quadratic equation to solve it.
+ if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
+ // We can only use this value if the chrec ends up with an exact zero
+ // value at this index. When solving for "X*X != 5", for example, we
+ // should not accept a root of 2.
+ if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
+ const auto *R = cast<SCEVConstant>(getConstant(*S));
+ return ExitLimit(R, R, R, false, Predicates);
+ }
+ return getCouldNotCompute();
+ }
+
+ // Otherwise we can only handle this if it is affine.
+ if (!AddRec->isAffine())
+ return getCouldNotCompute();
+
+ // If this is an affine expression, the execution count of this branch is
+ // the minimum unsigned root of the following equation:
+ //
+ // Start + Step*N = 0 (mod 2^BW)
+ //
+ // equivalent to:
+ //
+ // Step*N = -Start (mod 2^BW)
+ //
+ // where BW is the common bit width of Start and Step.
+
+ // Get the initial value for the loop.
+ const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
+ const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
+
+ if (!isLoopInvariant(Step, L))
+ return getCouldNotCompute();
+
+ LoopGuards Guards = LoopGuards::collect(L, *this);
+ // Specialize step for this loop so we get context sensitive facts below.
+ const SCEV *StepWLG = applyLoopGuards(Step, Guards);
+
+ // For positive steps (counting up until unsigned overflow):
+ // N = -Start/Step (as unsigned)
+ // For negative steps (counting down to zero):
+ // N = Start/-Step
+ // First compute the unsigned distance from zero in the direction of Step.
+ bool CountDown = isKnownNegative(StepWLG);
+ if (!CountDown && !isKnownNonNegative(StepWLG))
+ return getCouldNotCompute();
+
+ const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
+ // Handle unitary steps, which cannot wraparound.
+ // 1*N = -Start; -1*N = Start (mod 2^BW), so:
+ // N = Distance (as unsigned)
+
+ if (match(Step, m_CombineOr(m_scev_One(), m_scev_AllOnes()))) {
+ APInt MaxBECount = getUnsignedRangeMax(applyLoopGuards(Distance, Guards));
+ MaxBECount = APIntOps::umin(MaxBECount, getUnsignedRangeMax(Distance));
+
+ // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
+ // we end up with a loop whose backedge-taken count is n - 1. Detect this
+ // case, and see if we can improve the bound.
+ //
+ // Explicitly handling this here is necessary because getUnsignedRange
+ // isn't context-sensitive; it doesn't know that we only care about the
+ // range inside the loop.
+ const SCEV *Zero = getZero(Distance->getType());
+ const SCEV *One = getOne(Distance->getType());
+ const SCEV *DistancePlusOne = getAddExpr(Distance, One);
+ if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
+ // If Distance + 1 doesn't overflow, we can compute the maximum distance
+ // as "unsigned_max(Distance + 1) - 1".
+ ConstantRange CR = getUnsignedRange(DistancePlusOne);
+ MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
+ }
+ return ExitLimit(Distance, getConstant(MaxBECount), Distance, false,
+ Predicates);
+ }
+
+ // If the condition controls loop exit (the loop exits only if the expression
+ // is true) and the addition is no-wrap we can use unsigned divide to
+ // compute the backedge count. In this case, the step may not divide the
+ // distance, but we don't care because if the condition is "missed" the loop
+ // will have undefined behavior due to wrapping.
+ if (ControlsOnlyExit && AddRec->hasNoSelfWrap() &&
+ loopHasNoAbnormalExits(AddRec->getLoop())) {
+
+ // If the stride is zero and the start is non-zero, the loop must be
+ // infinite. In C++, most loops are finite by assumption, in which case the
+ // step being zero implies UB must execute if the loop is entered.
+ if (!(loopIsFiniteByAssumption(L) && isKnownNonZero(Start)) &&
+ !isKnownNonZero(StepWLG))
+ return getCouldNotCompute();
+
+ const SCEV *Exact =
+ getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
+ const SCEV *ConstantMax = getCouldNotCompute();
+ if (Exact != getCouldNotCompute()) {
+ APInt MaxInt = getUnsignedRangeMax(applyLoopGuards(Exact, Guards));
+ ConstantMax =
+ getConstant(APIntOps::umin(MaxInt, getUnsignedRangeMax(Exact)));
+ }
+ const SCEV *SymbolicMax =
+ isa<SCEVCouldNotCompute>(Exact) ? ConstantMax : Exact;
+ return ExitLimit(Exact, ConstantMax, SymbolicMax, false, Predicates);
+ }
+
+ // Solve the general equation.
+ const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
+ if (!StepC || StepC->getValue()->isZero())
+ return getCouldNotCompute();
+ const SCEV *E = SolveLinEquationWithOverflow(
+ StepC->getAPInt(), getNegativeSCEV(Start),
+ AllowPredicates ? &Predicates : nullptr, *this, L);
+
+ const SCEV *M = E;
+ if (E != getCouldNotCompute()) {
+ APInt MaxWithGuards = getUnsignedRangeMax(applyLoopGuards(E, Guards));
+ M = getConstant(APIntOps::umin(MaxWithGuards, getUnsignedRangeMax(E)));
+ }
+ auto *S = isa<SCEVCouldNotCompute>(E) ? M : E;
+ return ExitLimit(E, M, S, false, Predicates);
+}
+
+ScalarEvolution::ExitLimit
+ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
+ // Loops that look like: while (X == 0) are very strange indeed. We don't
+ // handle them yet except for the trivial case. This could be expanded in the
+ // future as needed.
+
+ // If the value is a constant, check to see if it is known to be non-zero
+ // already. If so, the backedge will execute zero times.
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
+ if (!C->getValue()->isZero())
+ return getZero(C->getType());
+ return getCouldNotCompute(); // Otherwise it will loop infinitely.
+ }
+
+ // We could implement others, but I really doubt anyone writes loops like
+ // this, and if they did, they would already be constant folded.
+ return getCouldNotCompute();
+}
+
+std::pair<const BasicBlock *, const BasicBlock *>
+ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB)
+ const {
+ // If the block has a unique predecessor, then there is no path from the
+ // predecessor to the block that does not go through the direct edge
+ // from the predecessor to the block.
+ if (const BasicBlock *Pred = BB->getSinglePredecessor())
+ return {Pred, BB};
+
+ // A loop's header is defined to be a block that dominates the loop.
+ // If the header has a unique predecessor outside the loop, it must be
+ // a block that has exactly one successor that can reach the loop.
+ if (const Loop *L = LI.getLoopFor(BB))
+ return {L->getLoopPredecessor(), L->getHeader()};
+
+ return {nullptr, BB};
+}
+
+/// SCEV structural equivalence is usually sufficient for testing whether two
+/// expressions are equal, however for the purposes of looking for a condition
+/// guarding a loop, it can be useful to be a little more general, since a
+/// front-end may have replicated the controlling expression.
+static bool HasSameValue(const SCEV *A, const SCEV *B) {
+ // Quick check to see if they are the same SCEV.
+ if (A == B) return true;
+
+ auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
+ // Not all instructions that are "identical" compute the same value. For
+ // instance, two distinct alloca instructions allocating the same type are
+ // identical and do not read memory; but compute distinct values.
+ return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
+ };
+
+ // Otherwise, if they're both SCEVUnknown, it's possible that they hold
+ // two different instructions with the same value. Check for this case.
+ if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
+ if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
+ if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
+ if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
+ if (ComputesEqualValues(AI, BI))
+ return true;
+
+ // Otherwise assume they may have a different value.
+ return false;
+}
+
+static bool MatchBinarySub(const SCEV *S, SCEVUse &LHS, SCEVUse &RHS) {
+ const SCEV *Op0, *Op1;
+ if (!match(S, m_scev_Add(m_SCEV(Op0), m_SCEV(Op1))))
+ return false;
+ if (match(Op0, m_scev_Mul(m_scev_AllOnes(), m_SCEV(RHS)))) {
+ LHS = Op1;
+ return true;
+ }
+ if (match(Op1, m_scev_Mul(m_scev_AllOnes(), m_SCEV(RHS)))) {
+ LHS = Op0;
+ return true;
+ }
+ return false;
+}
+
+bool ScalarEvolution::SimplifyICmpOperands(CmpPredicate &Pred, SCEVUse &LHS,
+ SCEVUse &RHS, unsigned Depth) {
+ bool Changed = false;
+ // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
+ // '0 != 0'.
+ auto TrivialCase = [&](bool TriviallyTrue) {
+ LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
+ Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
+ return true;
+ };
+ // If we hit the max recursion limit bail out.
+ if (Depth >= 3)
+ return false;
+
+ const SCEV *NewLHS, *NewRHS;
+ if (match(LHS, m_scev_c_Mul(m_SCEV(NewLHS), m_SCEVVScale())) &&
+ match(RHS, m_scev_c_Mul(m_SCEV(NewRHS), m_SCEVVScale()))) {
+ const SCEVMulExpr *LMul = cast<SCEVMulExpr>(LHS);
+ const SCEVMulExpr *RMul = cast<SCEVMulExpr>(RHS);
+
+ // (X * vscale) pred (Y * vscale) ==> X pred Y
+ // when both multiples are NSW.
+ // (X * vscale) uicmp/eq/ne (Y * vscale) ==> X uicmp/eq/ne Y
+ // when both multiples are NUW.
+ if ((LMul->hasNoSignedWrap() && RMul->hasNoSignedWrap()) ||
+ (LMul->hasNoUnsignedWrap() && RMul->hasNoUnsignedWrap() &&
+ !ICmpInst::isSigned(Pred))) {
+ LHS = NewLHS;
+ RHS = NewRHS;
+ Changed = true;
+ }
+ }
+
+ // Canonicalize a constant to the right side.
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
+ // Check for both operands constant.
+ if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
+ if (!ICmpInst::compare(LHSC->getAPInt(), RHSC->getAPInt(), Pred))
+ return TrivialCase(false);
+ return TrivialCase(true);
+ }
+ // Otherwise swap the operands to put the constant on the right.
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ Changed = true;
+ }
+
+ // (K + A) pred (K + B) --> A pred B
+ // For equality, no flags are needed.
+ // For signed, both adds must be NSW. For unsigned, both must be NUW.
+ {
+ const SCEVConstant *C = nullptr;
+ if (match(LHS, m_scev_Add(m_SCEVConstant(C), m_SCEV(NewLHS))) &&
+ match(RHS, m_scev_Add(m_scev_Specific(C), m_SCEV(NewRHS)))) {
+ const auto *LAdd = cast<SCEVAddExpr>(LHS);
+ const auto *RAdd = cast<SCEVAddExpr>(RHS);
+ if (ICmpInst::isEquality(Pred) ||
+ (ICmpInst::isSigned(Pred) && LAdd->hasNoSignedWrap() &&
+ RAdd->hasNoSignedWrap()) ||
+ (ICmpInst::isUnsigned(Pred) && LAdd->hasNoUnsignedWrap() &&
+ RAdd->hasNoUnsignedWrap())) {
+ LHS = NewLHS;
+ RHS = NewRHS;
+ Changed = true;
+ }
+ }
+ }
+
+ // (C * A) pred (C * B) --> A pred B
+ // For equality predicates, both muls must be NUW or both must be NSW
+ // (either suffices to make multiplication by C injective; C == 0 is
+ // impossible because SCEV folds 0 * X to 0).
+ // For signed ordering, C must be positive and both muls must be NSW.
+ // For unsigned ordering, both muls must be NUW.
+ {
+ const SCEVConstant *C = nullptr;
+ if (match(LHS, m_scev_Mul(m_SCEVConstant(C), m_SCEV(NewLHS))) &&
+ match(RHS, m_scev_Mul(m_scev_Specific(C), m_SCEV(NewRHS)))) {
+ const auto *LMul = cast<SCEVMulExpr>(LHS);
+ const auto *RMul = cast<SCEVMulExpr>(RHS);
+ bool BothNUW = LMul->hasNoUnsignedWrap() && RMul->hasNoUnsignedWrap();
+ bool BothNSW = LMul->hasNoSignedWrap() && RMul->hasNoSignedWrap();
+ if ((ICmpInst::isEquality(Pred) && (BothNUW || BothNSW)) ||
+ (ICmpInst::isSigned(Pred) && BothNSW &&
+ C->getAPInt().isStrictlyPositive()) ||
+ (ICmpInst::isUnsigned(Pred) && BothNUW)) {
+ LHS = NewLHS;
+ RHS = NewRHS;
+ Changed = true;
+ }
+ }
+ }
+
+ // If we're comparing an addrec with a value which is loop-invariant in the
+ // addrec's loop, put the addrec on the left. Also make a dominance check,
+ // as both operands could be addrecs loop-invariant in each other's loop.
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
+ const Loop *L = AR->getLoop();
+ if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ Changed = true;
+ }
+ }
+
+ // If there's a constant operand, canonicalize comparisons with boundary
+ // cases, and canonicalize *-or-equal comparisons to regular comparisons.
+ if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
+ const APInt &RA = RC->getAPInt();
+
+ bool SimplifiedByConstantRange = false;
+
+ if (!ICmpInst::isEquality(Pred)) {
+ ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
+ if (ExactCR.isFullSet())
+ return TrivialCase(true);
+ if (ExactCR.isEmptySet())
+ return TrivialCase(false);
+
+ APInt NewRHS;
+ CmpInst::Predicate NewPred;
+ if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
+ ICmpInst::isEquality(NewPred)) {
+ // We were able to convert an inequality to an equality.
+ Pred = NewPred;
+ RHS = getConstant(NewRHS);
+ Changed = SimplifiedByConstantRange = true;
+ }
+ }
+
+ if (!SimplifiedByConstantRange) {
+ switch (Pred) {
+ default:
+ break;
+ case ICmpInst::ICMP_EQ:
+ case ICmpInst::ICMP_NE:
+ // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
+ if (RA.isZero() && MatchBinarySub(LHS, LHS, RHS))
+ Changed = true;
+ break;
+
+ // The "Should have been caught earlier!" messages refer to the fact
+ // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
+ // should have fired on the corresponding cases, and canonicalized the
+ // check to trivial case.
+
+ case ICmpInst::ICMP_UGE:
+ assert(!RA.isMinValue() && "Should have been caught earlier!");
+ Pred = ICmpInst::ICMP_UGT;
+ RHS = getConstant(RA - 1);
+ Changed = true;
+ break;
+ case ICmpInst::ICMP_ULE:
+ assert(!RA.isMaxValue() && "Should have been caught earlier!");
+ Pred = ICmpInst::ICMP_ULT;
+ RHS = getConstant(RA + 1);
+ Changed = true;
+ break;
+ case ICmpInst::ICMP_SGE:
+ assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
+ Pred = ICmpInst::ICMP_SGT;
+ RHS = getConstant(RA - 1);
+ Changed = true;
+ break;
+ case ICmpInst::ICMP_SLE:
+ assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
+ Pred = ICmpInst::ICMP_SLT;
+ RHS = getConstant(RA + 1);
+ Changed = true;
+ break;
+ }
+ }
+ }
+
+ // Check for obvious equality.
+ if (HasSameValue(LHS, RHS)) {
+ if (ICmpInst::isTrueWhenEqual(Pred))
+ return TrivialCase(true);
+ if (ICmpInst::isFalseWhenEqual(Pred))
+ return TrivialCase(false);
+ }
+
+ // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
+ // adding or subtracting 1 from one of the operands.
+ switch (Pred) {
+ case ICmpInst::ICMP_SLE:
+ if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
+ RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
+ SCEV::FlagNSW);
+ Pred = ICmpInst::ICMP_SLT;
+ Changed = true;
+ } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
+ LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
+ SCEV::FlagNSW);
+ Pred = ICmpInst::ICMP_SLT;
+ Changed = true;
+ }
+ break;
+ case ICmpInst::ICMP_SGE:
+ if (!getSignedRangeMin(RHS).isMinSignedValue()) {
+ RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
+ SCEV::FlagNSW);
+ Pred = ICmpInst::ICMP_SGT;
+ Changed = true;
+ } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
+ LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
+ SCEV::FlagNSW);
+ Pred = ICmpInst::ICMP_SGT;
+ Changed = true;
+ }
+ break;
+ case ICmpInst::ICMP_ULE:
+ if (!getUnsignedRangeMax(RHS).isMaxValue()) {
+ RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
+ SCEV::FlagNUW);
+ Pred = ICmpInst::ICMP_ULT;
+ Changed = true;
+ } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
+ LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
+ Pred = ICmpInst::ICMP_ULT;
+ Changed = true;
+ }
+ break;
+ case ICmpInst::ICMP_UGE:
+ // If RHS is an op we can fold the -1, try that first.
+ // Otherwise prefer LHS to preserve the nuw flag.
+ if ((isa<SCEVConstant>(RHS) ||
+ (isa<SCEVAddExpr, SCEVAddRecExpr>(RHS) &&
+ isa<SCEVConstant>(cast<SCEVNAryExpr>(RHS)->getOperand(0)))) &&
+ !getUnsignedRangeMin(RHS).isMinValue()) {
+ RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
+ Pred = ICmpInst::ICMP_UGT;
+ Changed = true;
+ } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
+ LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
+ SCEV::FlagNUW);
+ Pred = ICmpInst::ICMP_UGT;
+ Changed = true;
+ } else if (!getUnsignedRangeMin(RHS).isMinValue()) {
+ RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
+ Pred = ICmpInst::ICMP_UGT;
+ Changed = true;
+ }
+ break;
+ default:
+ break;
+ }
+
+ // TODO: More simplifications are possible here.
+
+ // Recursively simplify until we either hit a recursion limit or nothing
+ // changes.
+ if (Changed)
+ (void)SimplifyICmpOperands(Pred, LHS, RHS, Depth + 1);
+
+ return Changed;
+}
+
+bool ScalarEvolution::isKnownNegative(const SCEV *S) {
+ return getSignedRangeMax(S).isNegative();
+}
+
+bool ScalarEvolution::isKnownPositive(const SCEV *S) {
+ return getSignedRangeMin(S).isStrictlyPositive();
+}
+
+bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
+ return !getSignedRangeMin(S).isNegative();
+}
+
+bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
+ return !getSignedRangeMax(S).isStrictlyPositive();
+}
+
+bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
+ // Query push down for cases where the unsigned range is
+ // less than sufficient.
+ if (const auto *SExt = dyn_cast<SCEVSignExtendExpr>(S))
+ return isKnownNonZero(SExt->getOperand(0));
+ return getUnsignedRangeMin(S) != 0;
+}
+
+bool ScalarEvolution::isKnownToBeAPowerOfTwo(const SCEV *S, bool OrZero,
+ bool OrNegative) {
+ auto NonRecursive = [OrNegative](const SCEV *S) {
+ if (auto *C = dyn_cast<SCEVConstant>(S))
+ return C->getAPInt().isPowerOf2() ||
+ (OrNegative && C->getAPInt().isNegatedPowerOf2());
+
+ // vscale is a power-of-two.
+ return isa<SCEVVScale>(S);
+ };
+
+ if (NonRecursive(S))
+ return true;
+
+ auto *Mul = dyn_cast<SCEVMulExpr>(S);
+ if (!Mul)
+ return false;
+ return all_of(Mul->operands(), NonRecursive) && (OrZero || isKnownNonZero(S));
+}
+
+bool ScalarEvolution::isKnownMultipleOf(
+ const SCEV *S, uint64_t M,
+ SmallVectorImpl<const SCEVPredicate *> &Assumptions) {
+ if (M == 0)
+ return false;
+ if (M == 1)
+ return true;
+
+ // Recursively check AddRec operands. An AddRecExpr S is a multiple of M if S
+ // starts with a multiple of M and at every iteration step S only adds
+ // multiples of M.
+ if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S))
+ return isKnownMultipleOf(AddRec->getStart(), M, Assumptions) &&
+ isKnownMultipleOf(AddRec->getStepRecurrence(*this), M, Assumptions);
+
+ // For a constant, check that "S % M == 0".
+ if (auto *Cst = dyn_cast<SCEVConstant>(S)) {
+ APInt C = Cst->getAPInt();
+ return C.urem(M) == 0;
+ }
+
+ // TODO: Also check other SCEV expressions, i.e., SCEVAddRecExpr, etc.
+
+ // Basic tests have failed.
+ // Check "S % M == 0" at compile time and record runtime Assumptions.
+ auto *STy = dyn_cast<IntegerType>(S->getType());
+ const SCEV *SmodM =
+ getURemExpr(S, getConstant(ConstantInt::get(STy, M, false)));
+ const SCEV *Zero = getZero(STy);
+
+ // Check whether "S % M == 0" is known at compile time.
+ if (isKnownPredicate(ICmpInst::ICMP_EQ, SmodM, Zero))
+ return true;
+
+ // Check whether "S % M != 0" is known at compile time.
+ if (isKnownPredicate(ICmpInst::ICMP_NE, SmodM, Zero))
+ return false;
+
+ const SCEVPredicate *P = getComparePredicate(ICmpInst::ICMP_EQ, SmodM, Zero);
+
+ // Detect redundant predicates.
+ for (auto *A : Assumptions)
+ if (A->implies(P, *this))
+ return true;
+
+ // Only record non-redundant predicates.
+ Assumptions.push_back(P);
+ return true;
+}
+
+bool ScalarEvolution::haveSameSign(const SCEV *S1, const SCEV *S2) {
+ return ((isKnownNonNegative(S1) && isKnownNonNegative(S2)) ||
+ (isKnownNegative(S1) && isKnownNegative(S2)));
+}
+
+std::pair<const SCEV *, const SCEV *>
+ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
+ // Compute SCEV on entry of loop L.
+ const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
+ if (Start == getCouldNotCompute())
+ return { Start, Start };
+ // Compute post increment SCEV for loop L.
+ const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
+ assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
+ return { Start, PostInc };
+}
+
+bool ScalarEvolution::isKnownViaInduction(CmpPredicate Pred, SCEVUse LHS,
+ SCEVUse RHS) {
+ // First collect all loops.
+ SmallPtrSet<const Loop *, 8> LoopsUsed;
+ getUsedLoops(LHS, LoopsUsed);
+ getUsedLoops(RHS, LoopsUsed);
+
+ if (LoopsUsed.empty())
+ return false;
+
+ // Domination relationship must be a linear order on collected loops.
+#ifndef NDEBUG
+ for (const auto *L1 : LoopsUsed)
+ for (const auto *L2 : LoopsUsed)
+ assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
+ DT.dominates(L2->getHeader(), L1->getHeader())) &&
+ "Domination relationship is not a linear order");
+#endif
+
+ const Loop *MDL =
+ *llvm::max_element(LoopsUsed, [&](const Loop *L1, const Loop *L2) {
+ return DT.properlyDominates(L1->getHeader(), L2->getHeader());
+ });
+
+ // Get init and post increment value for LHS.
+ auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
+ // if LHS contains unknown non-invariant SCEV then bail out.
+ if (SplitLHS.first == getCouldNotCompute())
+ return false;
+ assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
+ // Get init and post increment value for RHS.
+ auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
+ // if RHS contains unknown non-invariant SCEV then bail out.
+ if (SplitRHS.first == getCouldNotCompute())
+ return false;
+ assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
+ // It is possible that init SCEV contains an invariant load but it does
+ // not dominate MDL and is not available at MDL loop entry, so we should
+ // check it here.
+ if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
+ !isAvailableAtLoopEntry(SplitRHS.first, MDL))
+ return false;
+
+ // It seems backedge guard check is faster than entry one so in some cases
+ // it can speed up whole estimation by short circuit
+ return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
+ SplitRHS.second) &&
+ isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first);
+}
+
+bool ScalarEvolution::isKnownPredicate(CmpPredicate Pred, SCEVUse LHS,
+ SCEVUse RHS) {
+ // Canonicalize the inputs first.
+ (void)SimplifyICmpOperands(Pred, LHS, RHS);
+
+ if (isKnownViaInduction(Pred, LHS, RHS))
+ return true;
+
+ if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
+ return true;
+
+ // Otherwise see what can be done with some simple reasoning.
+ return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
+}
+
+std::optional<bool> ScalarEvolution::evaluatePredicate(CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS) {
+ if (isKnownPredicate(Pred, LHS, RHS))
+ return true;
+ if (isKnownPredicate(ICmpInst::getInverseCmpPredicate(Pred), LHS, RHS))
+ return false;
+ return std::nullopt;
+}
+
+bool ScalarEvolution::isKnownPredicateAt(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS,
+ const Instruction *CtxI) {
+ // TODO: Analyze guards and assumes from Context's block.
+ return isKnownPredicate(Pred, LHS, RHS) ||
+ isBasicBlockEntryGuardedByCond(CtxI->getParent(), Pred, LHS, RHS);
+}
+
+std::optional<bool>
+ScalarEvolution::evaluatePredicateAt(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS, const Instruction *CtxI) {
+ std::optional<bool> KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS);
+ if (KnownWithoutContext)
+ return KnownWithoutContext;
+
+ if (isBasicBlockEntryGuardedByCond(CtxI->getParent(), Pred, LHS, RHS))
+ return true;
+ if (isBasicBlockEntryGuardedByCond(
+ CtxI->getParent(), ICmpInst::getInverseCmpPredicate(Pred), LHS, RHS))
+ return false;
+ return std::nullopt;
+}
+
+bool ScalarEvolution::isKnownOnEveryIteration(CmpPredicate Pred,
+ const SCEVAddRecExpr *LHS,
+ const SCEV *RHS) {
+ const Loop *L = LHS->getLoop();
+ return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
+ isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
+}
+
+std::optional<ScalarEvolution::MonotonicPredicateType>
+ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS,
+ ICmpInst::Predicate Pred) {
+ auto Result = getMonotonicPredicateTypeImpl(LHS, Pred);
+
+#ifndef NDEBUG
+ // Verify an invariant: inverting the predicate should turn a monotonically
+ // increasing change to a monotonically decreasing one, and vice versa.
+ if (Result) {
+ auto ResultSwapped =
+ getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred));
+
+ assert(*ResultSwapped != *Result &&
+ "monotonicity should flip as we flip the predicate");
+ }
+#endif
+
+ return Result;
+}
+
+std::optional<ScalarEvolution::MonotonicPredicateType>
+ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS,
+ ICmpInst::Predicate Pred) {
+ // A zero step value for LHS means the induction variable is essentially a
+ // loop invariant value. We don't really depend on the predicate actually
+ // flipping from false to true (for increasing predicates, and the other way
+ // around for decreasing predicates), all we care about is that *if* the
+ // predicate changes then it only changes from false to true.
+ //
+ // A zero step value in itself is not very useful, but there may be places
+ // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
+ // as general as possible.
+
+ // Only handle LE/LT/GE/GT predicates.
+ if (!ICmpInst::isRelational(Pred))
+ return std::nullopt;
+
+ bool IsGreater = ICmpInst::isGE(Pred) || ICmpInst::isGT(Pred);
+ assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) &&
+ "Should be greater or less!");
+
+ // Check that AR does not wrap.
+ if (ICmpInst::isUnsigned(Pred)) {
+ if (!LHS->hasNoUnsignedWrap())
+ return std::nullopt;
+ return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
+ }
+ assert(ICmpInst::isSigned(Pred) &&
+ "Relational predicate is either signed or unsigned!");
+ if (!LHS->hasNoSignedWrap())
+ return std::nullopt;
+
+ const SCEV *Step = LHS->getStepRecurrence(*this);
+
+ if (isKnownNonNegative(Step))
+ return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
+
+ if (isKnownNonPositive(Step))
+ return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
+
+ return std::nullopt;
+}
+
+std::optional<ScalarEvolution::LoopInvariantPredicate>
+ScalarEvolution::getLoopInvariantPredicate(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS, const Loop *L,
+ const Instruction *CtxI) {
+ // If there is a loop-invariant, force it into the RHS, otherwise bail out.
+ if (!isLoopInvariant(RHS, L)) {
+ if (!isLoopInvariant(LHS, L))
+ return std::nullopt;
+
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ }
+
+ const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!ArLHS || ArLHS->getLoop() != L)
+ return std::nullopt;
+
+ auto MonotonicType = getMonotonicPredicateType(ArLHS, Pred);
+ if (!MonotonicType)
+ return std::nullopt;
+ // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
+ // true as the loop iterates, and the backedge is control dependent on
+ // "ArLHS `Pred` RHS" == true then we can reason as follows:
+ //
+ // * if the predicate was false in the first iteration then the predicate
+ // is never evaluated again, since the loop exits without taking the
+ // backedge.
+ // * if the predicate was true in the first iteration then it will
+ // continue to be true for all future iterations since it is
+ // monotonically increasing.
+ //
+ // For both the above possibilities, we can replace the loop varying
+ // predicate with its value on the first iteration of the loop (which is
+ // loop invariant).
+ //
+ // A similar reasoning applies for a monotonically decreasing predicate, by
+ // replacing true with false and false with true in the above two bullets.
+ bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing;
+ auto P = Increasing ? Pred : ICmpInst::getInverseCmpPredicate(Pred);
+
+ if (isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
+ return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(),
+ RHS);
+
+ if (!CtxI)
+ return std::nullopt;
+ // Try to prove via context.
+ // TODO: Support other cases.
+ switch (Pred) {
+ default:
+ break;
+ case ICmpInst::ICMP_ULE:
+ case ICmpInst::ICMP_ULT: {
+ assert(ArLHS->hasNoUnsignedWrap() && "Is a requirement of monotonicity!");
+ // Given preconditions
+ // (1) ArLHS does not cross the border of positive and negative parts of
+ // range because of:
+ // - Positive step; (TODO: lift this limitation)
+ // - nuw - does not cross zero boundary;
+ // - nsw - does not cross SINT_MAX boundary;
+ // (2) ArLHS <s RHS
+ // (3) RHS >=s 0
+ // we can replace the loop variant ArLHS <u RHS condition with loop
+ // invariant Start(ArLHS) <u RHS.
+ //
+ // Because of (1) there are two options:
+ // - ArLHS is always negative. It means that ArLHS <u RHS is always false;
+ // - ArLHS is always non-negative. Because of (3) RHS is also non-negative.
+ // It means that ArLHS <s RHS <=> ArLHS <u RHS.
+ // Because of (2) ArLHS <u RHS is trivially true.
+ // All together it means that ArLHS <u RHS <=> Start(ArLHS) >=s 0.
+ // We can strengthen this to Start(ArLHS) <u RHS.
+ auto SignFlippedPred = ICmpInst::getFlippedSignednessPredicate(Pred);
+ if (ArLHS->hasNoSignedWrap() && ArLHS->isAffine() &&
+ isKnownPositive(ArLHS->getStepRecurrence(*this)) &&
+ isKnownNonNegative(RHS) &&
+ isKnownPredicateAt(SignFlippedPred, ArLHS, RHS, CtxI))
+ return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(),
+ RHS);
+ }
+ }
+
+ return std::nullopt;
+}
+
+std::optional<ScalarEvolution::LoopInvariantPredicate>
+ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations(
+ CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
+ const Instruction *CtxI, const SCEV *MaxIter) {
+ if (auto LIP = getLoopInvariantExitCondDuringFirstIterationsImpl(
+ Pred, LHS, RHS, L, CtxI, MaxIter))
+ return LIP;
+ if (auto *UMin = dyn_cast<SCEVUMinExpr>(MaxIter))
+ // Number of iterations expressed as UMIN isn't always great for expressing
+ // the value on the last iteration. If the straightforward approach didn't
+ // work, try the following trick: if the a predicate is invariant for X, it
+ // is also invariant for umin(X, ...). So try to find something that works
+ // among subexpressions of MaxIter expressed as umin.
+ for (SCEVUse Op : UMin->operands())
+ if (auto LIP = getLoopInvariantExitCondDuringFirstIterationsImpl(
+ Pred, LHS, RHS, L, CtxI, Op))
+ return LIP;
+ return std::nullopt;
+}
+
+std::optional<ScalarEvolution::LoopInvariantPredicate>
+ScalarEvolution::getLoopInvariantExitCondDuringFirstIterationsImpl(
+ CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
+ const Instruction *CtxI, const SCEV *MaxIter) {
+ // Try to prove the following set of facts:
+ // - The predicate is monotonic in the iteration space.
+ // - If the check does not fail on the 1st iteration:
+ // - No overflow will happen during first MaxIter iterations;
+ // - It will not fail on the MaxIter'th iteration.
+ // If the check does fail on the 1st iteration, we leave the loop and no
+ // other checks matter.
+
+ // If there is a loop-invariant, force it into the RHS, otherwise bail out.
+ if (!isLoopInvariant(RHS, L)) {
+ if (!isLoopInvariant(LHS, L))
+ return std::nullopt;
+
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ }
+
+ auto *AR = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!AR || AR->getLoop() != L)
+ return std::nullopt;
+
+ // Even if both are valid, we need to consistently chose the unsigned or the
+ // signed predicate below, not mixtures of both. For now, prefer the unsigned
+ // predicate.
+ Pred = Pred.dropSameSign();
+
+ // The predicate must be relational (i.e. <, <=, >=, >).
+ if (!ICmpInst::isRelational(Pred))
+ return std::nullopt;
+
+ // TODO: Support steps other than +/- 1.
+ const SCEV *Step = AR->getStepRecurrence(*this);
+ auto *One = getOne(Step->getType());
+ auto *MinusOne = getNegativeSCEV(One);
+ if (Step != One && Step != MinusOne)
+ return std::nullopt;
+
+ // Type mismatch here means that MaxIter is potentially larger than max
+ // unsigned value in start type, which mean we cannot prove no wrap for the
+ // indvar.
+ if (AR->getType() != MaxIter->getType())
+ return std::nullopt;
+
+ // Value of IV on suggested last iteration.
+ const SCEV *Last = AR->evaluateAtIteration(MaxIter, *this);
+ // Does it still meet the requirement?
+ if (!isLoopBackedgeGuardedByCond(L, Pred, Last, RHS))
+ return std::nullopt;
+ // Because step is +/- 1 and MaxIter has same type as Start (i.e. it does
+ // not exceed max unsigned value of this type), this effectively proves
+ // that there is no wrap during the iteration. To prove that there is no
+ // signed/unsigned wrap, we need to check that
+ // Start <= Last for step = 1 or Start >= Last for step = -1.
+ ICmpInst::Predicate NoOverflowPred =
+ CmpInst::isSigned(Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
+ if (Step == MinusOne)
+ NoOverflowPred = ICmpInst::getSwappedPredicate(NoOverflowPred);
+ const SCEV *Start = AR->getStart();
+ if (!isKnownPredicateAt(NoOverflowPred, Start, Last, CtxI))
+ return std::nullopt;
+
+ // Everything is fine.
+ return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS);
+}
+
+bool ScalarEvolution::isKnownPredicateViaConstantRanges(CmpPredicate Pred,
+ SCEVUse LHS,
+ SCEVUse RHS) {
+ if (HasSameValue(LHS, RHS))
+ return ICmpInst::isTrueWhenEqual(Pred);
+
+ auto CheckRange = [&](bool IsSigned) {
+ auto RangeLHS = IsSigned ? getSignedRange(LHS) : getUnsignedRange(LHS);
+ auto RangeRHS = IsSigned ? getSignedRange(RHS) : getUnsignedRange(RHS);
+ return RangeLHS.icmp(Pred, RangeRHS);
+ };
+
+ // The check at the top of the function catches the case where the values are
+ // known to be equal.
+ if (Pred == CmpInst::ICMP_EQ)
+ return false;
+
+ if (Pred == CmpInst::ICMP_NE) {
+ if (CheckRange(true) || CheckRange(false))
+ return true;
+ auto *Diff = getMinusSCEV(LHS, RHS);
+ return !isa<SCEVCouldNotCompute>(Diff) && isKnownNonZero(Diff);
+ }
+
+ return CheckRange(CmpInst::isSigned(Pred));
+}
+
+bool ScalarEvolution::isKnownPredicateViaNoOverflow(CmpPredicate Pred,
+ SCEVUse LHS, SCEVUse RHS) {
+ // Match X to (A + C1)<ExpectedFlags> and Y to (A + C2)<ExpectedFlags>, where
+ // C1 and C2 are constant integers. If either X or Y are not add expressions,
+ // consider them as X + 0 and Y + 0 respectively. C1 and C2 are returned via
+ // OutC1 and OutC2.
+ auto MatchBinaryAddToConst = [this](SCEVUse X, SCEVUse Y, APInt &OutC1,
+ APInt &OutC2,
+ SCEV::NoWrapFlags ExpectedFlags) {
+ SCEVUse XNonConstOp, XConstOp;
+ SCEVUse YNonConstOp, YConstOp;
+ SCEV::NoWrapFlags XFlagsPresent;
+ SCEV::NoWrapFlags YFlagsPresent;
+
+ if (!splitBinaryAdd(X, XConstOp, XNonConstOp, XFlagsPresent)) {
+ XConstOp = getZero(X->getType());
+ XNonConstOp = X;
+ XFlagsPresent = ExpectedFlags;
+ }
+ if (!isa<SCEVConstant>(XConstOp))
+ return false;
+
+ if (!splitBinaryAdd(Y, YConstOp, YNonConstOp, YFlagsPresent)) {
+ YConstOp = getZero(Y->getType());
+ YNonConstOp = Y;
+ YFlagsPresent = ExpectedFlags;
+ }
+
+ if (YNonConstOp != XNonConstOp)
+ return false;
+
+ if (!isa<SCEVConstant>(YConstOp))
+ return false;
+
+ // When matching ADDs with NUW flags (and unsigned predicates), only the
+ // second ADD (with the larger constant) requires NUW.
+ if ((YFlagsPresent & ExpectedFlags) != ExpectedFlags)
+ return false;
+ if (ExpectedFlags != SCEV::FlagNUW &&
+ (XFlagsPresent & ExpectedFlags) != ExpectedFlags) {
+ return false;
+ }
+
+ OutC1 = cast<SCEVConstant>(XConstOp)->getAPInt();
+ OutC2 = cast<SCEVConstant>(YConstOp)->getAPInt();
+
+ return true;
+ };
+
+ APInt C1;
+ APInt C2;
+
+ switch (Pred) {
+ default:
+ break;
+
+ case ICmpInst::ICMP_SGE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SLE:
+ // (X + C1)<nsw> s<= (X + C2)<nsw> if C1 s<= C2.
+ if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.sle(C2))
+ return true;
+
+ break;
+
+ case ICmpInst::ICMP_SGT:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SLT:
+ // (X + C1)<nsw> s< (X + C2)<nsw> if C1 s< C2.
+ if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.slt(C2))
+ return true;
+
+ break;
+
+ case ICmpInst::ICMP_UGE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_ULE:
+ // (X + C1) u<= (X + C2)<nuw> for C1 u<= C2.
+ if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNUW) && C1.ule(C2))
+ return true;
+
+ break;
+
+ case ICmpInst::ICMP_UGT:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_ULT:
+ // (X + C1) u< (X + C2)<nuw> if C1 u< C2.
+ if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNUW) && C1.ult(C2))
+ return true;
+ break;
+ }
+
+ return false;
+}
+
+bool ScalarEvolution::isKnownPredicateViaSplitting(CmpPredicate Pred,
+ SCEVUse LHS, SCEVUse RHS) {
+ if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
+ return false;
+
+ // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
+ // the stack can result in exponential time complexity.
+ SaveAndRestore Restore(ProvingSplitPredicate, true);
+
+ // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
+ //
+ // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
+ // isKnownPredicate. isKnownPredicate is more powerful, but also more
+ // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
+ // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
+ // use isKnownPredicate later if needed.
+ return isKnownNonNegative(RHS) &&
+ isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
+ isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
+}
+
+bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB, CmpPredicate Pred,
+ const SCEV *LHS, const SCEV *RHS) {
+ // No need to even try if we know the module has no guards.
+ if (!HasGuards)
+ return false;
+
+ return any_of(*BB, [&](const Instruction &I) {
+ using namespace llvm::PatternMatch;
+
+ Value *Condition;
+ return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
+ m_Value(Condition))) &&
+ isImpliedCond(Pred, LHS, RHS, Condition, false);
+ });
+}
+
+/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
+/// protected by a conditional between LHS and RHS. This is used to
+/// to eliminate casts.
+bool ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
+ CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS) {
+ // Interpret a null as meaning no loop, where there is obviously no guard
+ // (interprocedural conditions notwithstanding). Do not bother about
+ // unreachable loops.
+ if (!L || !DT.isReachableFromEntry(L->getHeader()))
+ return true;
+
+ if (VerifyIR)
+ assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
+ "This cannot be done on broken IR!");
+
+
+ if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
+ return true;
+
+ BasicBlock *Latch = L->getLoopLatch();
+ if (!Latch)
+ return false;
+
+ CondBrInst *LoopContinuePredicate =
+ dyn_cast<CondBrInst>(Latch->getTerminator());
+ if (LoopContinuePredicate &&
+ isImpliedCond(Pred, LHS, RHS, LoopContinuePredicate->getCondition(),
+ LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
+ return true;
+
+ // We don't want more than one activation of the following loops on the stack
+ // -- that can lead to O(n!) time complexity.
+ if (WalkingBEDominatingConds)
+ return false;
+
+ SaveAndRestore ClearOnExit(WalkingBEDominatingConds, true);
+
+ // See if we can exploit a trip count to prove the predicate.
+ const auto &BETakenInfo = getBackedgeTakenInfo(L);
+ const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
+ if (LatchBECount != getCouldNotCompute()) {
+ // We know that Latch branches back to the loop header exactly
+ // LatchBECount times. This means the backdege condition at Latch is
+ // equivalent to "{0,+,1} u< LatchBECount".
+ Type *Ty = LatchBECount->getType();
+ auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
+ const SCEV *LoopCounter =
+ getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
+ if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
+ LatchBECount))
+ return true;
+ }
+
+ // Check conditions due to any @llvm.assume intrinsics.
+ for (auto &AssumeVH : AC.assumptions()) {
+ if (!AssumeVH)
+ continue;
+ auto *CI = cast<CallInst>(AssumeVH);
+ if (!DT.dominates(CI, Latch->getTerminator()))
+ continue;
+
+ if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
+ return true;
+ }
+
+ if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
+ return true;
+
+ for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
+ DTN != HeaderDTN; DTN = DTN->getIDom()) {
+ assert(DTN && "should reach the loop header before reaching the root!");
+
+ BasicBlock *BB = DTN->getBlock();
+ if (isImpliedViaGuard(BB, Pred, LHS, RHS))
+ return true;
+
+ BasicBlock *PBB = BB->getSinglePredecessor();
+ if (!PBB)
+ continue;
+
+ CondBrInst *ContBr = dyn_cast<CondBrInst>(PBB->getTerminator());
+ if (!ContBr || ContBr->getSuccessor(0) == ContBr->getSuccessor(1))
+ continue;
+
+ // If we have an edge `E` within the loop body that dominates the only
+ // latch, the condition guarding `E` also guards the backedge. This
+ // reasoning works only for loops with a single latch.
+ // We're constructively (and conservatively) enumerating edges within the
+ // loop body that dominate the latch. The dominator tree better agree
+ // with us on this:
+ assert(DT.dominates(BasicBlockEdge(PBB, BB), Latch) && "should be!");
+ if (isImpliedCond(Pred, LHS, RHS, ContBr->getCondition(),
+ BB != ContBr->getSuccessor(0)))
+ return true;
+ }
+
+ return false;
+}
+
+bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB,
+ CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS) {
+ // Do not bother proving facts for unreachable code.
+ if (!DT.isReachableFromEntry(BB))
+ return true;
+ if (VerifyIR)
+ assert(!verifyFunction(*BB->getParent(), &dbgs()) &&
+ "This cannot be done on broken IR!");
+
+ // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
+ // the facts (a >= b && a != b) separately. A typical situation is when the
+ // non-strict comparison is known from ranges and non-equality is known from
+ // dominating predicates. If we are proving strict comparison, we always try
+ // to prove non-equality and non-strict comparison separately.
+ CmpPredicate NonStrictPredicate = ICmpInst::getNonStrictCmpPredicate(Pred);
+ const bool ProvingStrictComparison =
+ Pred != NonStrictPredicate.dropSameSign();
+ bool ProvedNonStrictComparison = false;
+ bool ProvedNonEquality = false;
+
+ auto SplitAndProve = [&](std::function<bool(CmpPredicate)> Fn) -> bool {
+ if (!ProvedNonStrictComparison)
+ ProvedNonStrictComparison = Fn(NonStrictPredicate);
+ if (!ProvedNonEquality)
+ ProvedNonEquality = Fn(ICmpInst::ICMP_NE);
+ if (ProvedNonStrictComparison && ProvedNonEquality)
+ return true;
+ return false;
+ };
+
+ if (ProvingStrictComparison) {
+ auto ProofFn = [&](CmpPredicate P) {
+ return isKnownViaNonRecursiveReasoning(P, LHS, RHS);
+ };
+ if (SplitAndProve(ProofFn))
+ return true;
+ }
+
+ // Try to prove (Pred, LHS, RHS) using isImpliedCond.
+ auto ProveViaCond = [&](const Value *Condition, bool Inverse) {
+ const Instruction *CtxI = &BB->front();
+ if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse, CtxI))
+ return true;
+ if (ProvingStrictComparison) {
+ auto ProofFn = [&](CmpPredicate P) {
+ return isImpliedCond(P, LHS, RHS, Condition, Inverse, CtxI);
+ };
+ if (SplitAndProve(ProofFn))
+ return true;
+ }
+ return false;
+ };
+
+ // Starting at the block's predecessor, climb up the predecessor chain, as long
+ // as there are predecessors that can be found that have unique successors
+ // leading to the original block.
+ const Loop *ContainingLoop = LI.getLoopFor(BB);
+ const BasicBlock *PredBB;
+ if (ContainingLoop && ContainingLoop->getHeader() == BB)
+ PredBB = ContainingLoop->getLoopPredecessor();
+ else
+ PredBB = BB->getSinglePredecessor();
+ for (std::pair<const BasicBlock *, const BasicBlock *> Pair(PredBB, BB);
+ Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
+ const CondBrInst *BlockEntryPredicate =
+ dyn_cast<CondBrInst>(Pair.first->getTerminator());
+ if (!BlockEntryPredicate)
+ continue;
+
+ if (ProveViaCond(BlockEntryPredicate->getCondition(),
+ BlockEntryPredicate->getSuccessor(0) != Pair.second))
+ return true;
+ }
+
+ // Check conditions due to any @llvm.assume intrinsics.
+ for (auto &AssumeVH : AC.assumptions()) {
+ if (!AssumeVH)
+ continue;
+ auto *CI = cast<CallInst>(AssumeVH);
+ if (!DT.dominates(CI, BB))
+ continue;
+
+ if (ProveViaCond(CI->getArgOperand(0), false))
+ return true;
+ }
+
+ // Check conditions due to any @llvm.experimental.guard intrinsics.
+ auto *GuardDecl = Intrinsic::getDeclarationIfExists(
+ F.getParent(), Intrinsic::experimental_guard);
+ if (GuardDecl)
+ for (const auto *GU : GuardDecl->users())
+ if (const auto *Guard = dyn_cast<IntrinsicInst>(GU))
+ if (Guard->getFunction() == BB->getParent() && DT.dominates(Guard, BB))
+ if (ProveViaCond(Guard->getArgOperand(0), false))
+ return true;
+ return false;
+}
+
+bool ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS) {
+ // Interpret a null as meaning no loop, where there is obviously no guard
+ // (interprocedural conditions notwithstanding).
+ if (!L)
+ return false;
+
+ // Both LHS and RHS must be available at loop entry.
+ assert(isAvailableAtLoopEntry(LHS, L) &&
+ "LHS is not available at Loop Entry");
+ assert(isAvailableAtLoopEntry(RHS, L) &&
+ "RHS is not available at Loop Entry");
+
+ if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
+ return true;
+
+ return isBasicBlockEntryGuardedByCond(L->getHeader(), Pred, LHS, RHS);
+}
+
+bool ScalarEvolution::isImpliedCond(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS,
+ const Value *FoundCondValue, bool Inverse,
+ const Instruction *CtxI) {
+ // False conditions implies anything. Do not bother analyzing it further.
+ if (FoundCondValue ==
+ ConstantInt::getBool(FoundCondValue->getContext(), Inverse))
+ return true;
+
+ if (!PendingLoopPredicates.insert(FoundCondValue).second)
+ return false;
+
+ llvm::scope_exit ClearOnExit(
+ [&]() { PendingLoopPredicates.erase(FoundCondValue); });
+
+ // Recursively handle And and Or conditions.
+ const Value *Op0, *Op1;
+ if (match(FoundCondValue, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) {
+ if (!Inverse)
+ return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, CtxI) ||
+ isImpliedCond(Pred, LHS, RHS, Op1, Inverse, CtxI);
+ } else if (match(FoundCondValue, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) {
+ if (Inverse)
+ return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, CtxI) ||
+ isImpliedCond(Pred, LHS, RHS, Op1, Inverse, CtxI);
+ }
+
+ const ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
+ if (!ICI) return false;
+
+ // Now that we found a conditional branch that dominates the loop or controls
+ // the loop latch. Check to see if it is the comparison we are looking for.
+ CmpPredicate FoundPred;
+ if (Inverse)
+ FoundPred = ICI->getInverseCmpPredicate();
+ else
+ FoundPred = ICI->getCmpPredicate();
+
+ const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
+ const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
+
+ return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, CtxI);
+}
+
+bool ScalarEvolution::isImpliedCond(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS, CmpPredicate FoundPred,
+ const SCEV *FoundLHS, const SCEV *FoundRHS,
+ const Instruction *CtxI) {
+ // Balance the types.
+ if (getTypeSizeInBits(LHS->getType()) <
+ getTypeSizeInBits(FoundLHS->getType())) {
+ // For unsigned and equality predicates, try to prove that both found
+ // operands fit into narrow unsigned range. If so, try to prove facts in
+ // narrow types.
+ if (!CmpInst::isSigned(FoundPred) && !FoundLHS->getType()->isPointerTy() &&
+ !FoundRHS->getType()->isPointerTy()) {
+ auto *NarrowType = LHS->getType();
+ auto *WideType = FoundLHS->getType();
+ auto BitWidth = getTypeSizeInBits(NarrowType);
+ const SCEV *MaxValue = getZeroExtendExpr(
+ getConstant(APInt::getMaxValue(BitWidth)), WideType);
+ if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, FoundLHS,
+ MaxValue) &&
+ isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, FoundRHS,
+ MaxValue)) {
+ const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType);
+ const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType);
+ // We cannot preserve samesign after truncation.
+ if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred.dropSameSign(),
+ TruncFoundLHS, TruncFoundRHS, CtxI))
+ return true;
+ }
+ }
+
+ if (LHS->getType()->isPointerTy() || RHS->getType()->isPointerTy())
+ return false;
+ if (CmpInst::isSigned(Pred)) {
+ LHS = getSignExtendExpr(LHS, FoundLHS->getType());
+ RHS = getSignExtendExpr(RHS, FoundLHS->getType());
+ } else {
+ LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
+ RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
+ }
+ } else if (getTypeSizeInBits(LHS->getType()) >
+ getTypeSizeInBits(FoundLHS->getType())) {
+ if (FoundLHS->getType()->isPointerTy() || FoundRHS->getType()->isPointerTy())
+ return false;
+ if (CmpInst::isSigned(FoundPred)) {
+ FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
+ FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
+ } else {
+ FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
+ FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
+ }
+ }
+ return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS,
+ FoundRHS, CtxI);
+}
+
+bool ScalarEvolution::isImpliedCondBalancedTypes(
+ CmpPredicate Pred, SCEVUse LHS, SCEVUse RHS, CmpPredicate FoundPred,
+ SCEVUse FoundLHS, SCEVUse FoundRHS, const Instruction *CtxI) {
+ assert(getTypeSizeInBits(LHS->getType()) ==
+ getTypeSizeInBits(FoundLHS->getType()) &&
+ "Types should be balanced!");
+ // Canonicalize the query to match the way instcombine will have
+ // canonicalized the comparison.
+ if (SimplifyICmpOperands(Pred, LHS, RHS))
+ if (LHS == RHS)
+ return CmpInst::isTrueWhenEqual(Pred);
+ if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
+ if (FoundLHS == FoundRHS)
+ return CmpInst::isFalseWhenEqual(FoundPred);
+
+ // Check to see if we can make the LHS or RHS match.
+ if (LHS == FoundRHS || RHS == FoundLHS) {
+ if (isa<SCEVConstant>(RHS)) {
+ std::swap(FoundLHS, FoundRHS);
+ FoundPred = ICmpInst::getSwappedCmpPredicate(FoundPred);
+ } else {
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ }
+ }
+
+ // Check whether the found predicate is the same as the desired predicate.
+ if (auto P = CmpPredicate::getMatching(FoundPred, Pred))
+ return isImpliedCondOperands(*P, LHS, RHS, FoundLHS, FoundRHS, CtxI);
+
+ // Check whether swapping the found predicate makes it the same as the
+ // desired predicate.
+ if (auto P = CmpPredicate::getMatching(
+ ICmpInst::getSwappedCmpPredicate(FoundPred), Pred)) {
+ // We can write the implication
+ // 0. LHS Pred RHS <- FoundLHS SwapPred FoundRHS
+ // using one of the following ways:
+ // 1. LHS Pred RHS <- FoundRHS Pred FoundLHS
+ // 2. RHS SwapPred LHS <- FoundLHS SwapPred FoundRHS
+ // 3. LHS Pred RHS <- ~FoundLHS Pred ~FoundRHS
+ // 4. ~LHS SwapPred ~RHS <- FoundLHS SwapPred FoundRHS
+ // Forms 1. and 2. require swapping the operands of one condition. Don't
+ // do this if it would break canonical constant/addrec ordering.
+ if (!isa<SCEVConstant>(RHS) && !isa<SCEVAddRecExpr>(LHS))
+ return isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(*P), RHS,
+ LHS, FoundLHS, FoundRHS, CtxI);
+ if (!isa<SCEVConstant>(FoundRHS) && !isa<SCEVAddRecExpr>(FoundLHS))
+ return isImpliedCondOperands(*P, LHS, RHS, FoundRHS, FoundLHS, CtxI);
+
+ // There's no clear preference between forms 3. and 4., try both. Avoid
+ // forming getNotSCEV of pointer values as the resulting subtract is
+ // not legal.
+ if (!LHS->getType()->isPointerTy() && !RHS->getType()->isPointerTy() &&
+ isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(*P),
+ getNotSCEV(LHS), getNotSCEV(RHS), FoundLHS,
+ FoundRHS, CtxI))
+ return true;
+
+ if (!FoundLHS->getType()->isPointerTy() &&
+ !FoundRHS->getType()->isPointerTy() &&
+ isImpliedCondOperands(*P, LHS, RHS, getNotSCEV(FoundLHS),
+ getNotSCEV(FoundRHS), CtxI))
+ return true;
+
+ return false;
+ }
+
+ auto IsSignFlippedPredicate = [](CmpInst::Predicate P1,
+ CmpInst::Predicate P2) {
+ assert(P1 != P2 && "Handled earlier!");
+ return CmpInst::isRelational(P2) &&
+ P1 == ICmpInst::getFlippedSignednessPredicate(P2);
+ };
+ if (IsSignFlippedPredicate(Pred, FoundPred)) {
+ // Unsigned comparison is the same as signed comparison when both the
+ // operands are non-negative or negative.
+ if (haveSameSign(FoundLHS, FoundRHS))
+ return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI);
+ // Create local copies that we can freely swap and canonicalize our
+ // conditions to "le/lt".
+ CmpPredicate CanonicalPred = Pred, CanonicalFoundPred = FoundPred;
+ const SCEV *CanonicalLHS = LHS, *CanonicalRHS = RHS,
+ *CanonicalFoundLHS = FoundLHS, *CanonicalFoundRHS = FoundRHS;
+ if (ICmpInst::isGT(CanonicalPred) || ICmpInst::isGE(CanonicalPred)) {
+ CanonicalPred = ICmpInst::getSwappedCmpPredicate(CanonicalPred);
+ CanonicalFoundPred = ICmpInst::getSwappedCmpPredicate(CanonicalFoundPred);
+ std::swap(CanonicalLHS, CanonicalRHS);
+ std::swap(CanonicalFoundLHS, CanonicalFoundRHS);
+ }
+ assert((ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) &&
+ "Must be!");
+ assert((ICmpInst::isLT(CanonicalFoundPred) ||
+ ICmpInst::isLE(CanonicalFoundPred)) &&
+ "Must be!");
+ if (ICmpInst::isSigned(CanonicalPred) && isKnownNonNegative(CanonicalRHS))
+ // Use implication:
+ // x <u y && y >=s 0 --> x <s y.
+ // If we can prove the left part, the right part is also proven.
+ return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
+ CanonicalRHS, CanonicalFoundLHS,
+ CanonicalFoundRHS);
+ if (ICmpInst::isUnsigned(CanonicalPred) && isKnownNegative(CanonicalRHS))
+ // Use implication:
+ // x <s y && y <s 0 --> x <u y.
+ // If we can prove the left part, the right part is also proven.
+ return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
+ CanonicalRHS, CanonicalFoundLHS,
+ CanonicalFoundRHS);
+ }
+
+ // Check if we can make progress by sharpening ranges.
+ if (FoundPred == ICmpInst::ICMP_NE &&
+ (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
+
+ const SCEVConstant *C = nullptr;
+ const SCEV *V = nullptr;
+
+ if (isa<SCEVConstant>(FoundLHS)) {
+ C = cast<SCEVConstant>(FoundLHS);
+ V = FoundRHS;
+ } else {
+ C = cast<SCEVConstant>(FoundRHS);
+ V = FoundLHS;
+ }
+
+ // The guarding predicate tells us that C != V. If the known range
+ // of V is [C, t), we can sharpen the range to [C + 1, t). The
+ // range we consider has to correspond to same signedness as the
+ // predicate we're interested in folding.
+
+ APInt Min = ICmpInst::isSigned(Pred) ?
+ getSignedRangeMin(V) : getUnsignedRangeMin(V);
+
+ if (Min == C->getAPInt()) {
+ // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
+ // This is true even if (Min + 1) wraps around -- in case of
+ // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
+
+ APInt SharperMin = Min + 1;
+
+ switch (Pred) {
+ case ICmpInst::ICMP_SGE:
+ case ICmpInst::ICMP_UGE:
+ // We know V `Pred` SharperMin. If this implies LHS `Pred`
+ // RHS, we're done.
+ if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(SharperMin),
+ CtxI))
+ return true;
+ [[fallthrough]];
+
+ case ICmpInst::ICMP_SGT:
+ case ICmpInst::ICMP_UGT:
+ // We know from the range information that (V `Pred` Min ||
+ // V == Min). We know from the guarding condition that !(V
+ // == Min). This gives us
+ //
+ // V `Pred` Min || V == Min && !(V == Min)
+ // => V `Pred` Min
+ //
+ // If V `Pred` Min implies LHS `Pred` RHS, we're done.
+
+ if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min), CtxI))
+ return true;
+ break;
+
+ // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively.
+ case ICmpInst::ICMP_SLE:
+ case ICmpInst::ICMP_ULE:
+ if (isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(Pred), RHS,
+ LHS, V, getConstant(SharperMin), CtxI))
+ return true;
+ [[fallthrough]];
+
+ case ICmpInst::ICMP_SLT:
+ case ICmpInst::ICMP_ULT:
+ if (isImpliedCondOperands(ICmpInst::getSwappedCmpPredicate(Pred), RHS,
+ LHS, V, getConstant(Min), CtxI))
+ return true;
+ break;
+
+ default:
+ // No change
+ break;
+ }
+ }
+ }
+
+ // Check whether the actual condition is beyond sufficient.
+ if (FoundPred == ICmpInst::ICMP_EQ)
+ if (ICmpInst::isTrueWhenEqual(Pred))
+ if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI))
+ return true;
+ if (Pred == ICmpInst::ICMP_NE)
+ if (!ICmpInst::isTrueWhenEqual(FoundPred))
+ if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS, CtxI))
+ return true;
+
+ if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS))
+ return true;
+
+ // Otherwise assume the worst.
+ return false;
+}
+
+bool ScalarEvolution::splitBinaryAdd(SCEVUse Expr, SCEVUse &L, SCEVUse &R,
+ SCEV::NoWrapFlags &Flags) {
+ if (!match(Expr, m_scev_Add(m_SCEV(L), m_SCEV(R))))
+ return false;
+
+ Flags = cast<SCEVAddExpr>(Expr)->getNoWrapFlags();
+ return true;
+}
+
+std::optional<APInt>
+ScalarEvolution::computeConstantDifference(const SCEV *More, const SCEV *Less) {
+ // We avoid subtracting expressions here because this function is usually
+ // fairly deep in the call stack (i.e. is called many times).
+
+ unsigned BW = getTypeSizeInBits(More->getType());
+ APInt Diff(BW, 0);
+ APInt DiffMul(BW, 1);
+ // Try various simplifications to reduce the difference to a constant. Limit
+ // the number of allowed simplifications to keep compile-time low.
+ for (unsigned I = 0; I < 8; ++I) {
+ if (More == Less)
+ return Diff;
+
+ // Reduce addrecs with identical steps to their start value.
+ if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
+ const auto *LAR = cast<SCEVAddRecExpr>(Less);
+ const auto *MAR = cast<SCEVAddRecExpr>(More);
+
+ if (LAR->getLoop() != MAR->getLoop())
+ return std::nullopt;
+
+ // We look at affine expressions only; not for correctness but to keep
+ // getStepRecurrence cheap.
+ if (!LAR->isAffine() || !MAR->isAffine())
+ return std::nullopt;
+
+ if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
+ return std::nullopt;
+
+ Less = LAR->getStart();
+ More = MAR->getStart();
+ continue;
+ }
+
+ // Try to match a common constant multiply.
+ auto MatchConstMul =
+ [](const SCEV *S) -> std::optional<std::pair<const SCEV *, APInt>> {
+ const APInt *C;
+ const SCEV *Op;
+ if (match(S, m_scev_Mul(m_scev_APInt(C), m_SCEV(Op))))
+ return {{Op, *C}};
+ return std::nullopt;
+ };
+ if (auto MatchedMore = MatchConstMul(More)) {
+ if (auto MatchedLess = MatchConstMul(Less)) {
+ if (MatchedMore->second == MatchedLess->second) {
+ More = MatchedMore->first;
+ Less = MatchedLess->first;
+ DiffMul *= MatchedMore->second;
+ continue;
+ }
+ }
+ }
+
+ // Try to cancel out common factors in two add expressions.
+ SmallDenseMap<const SCEV *, int, 8> Multiplicity;
+ auto Add = [&](const SCEV *S, int Mul) {
+ if (auto *C = dyn_cast<SCEVConstant>(S)) {
+ if (Mul == 1) {
+ Diff += C->getAPInt() * DiffMul;
+ } else {
+ assert(Mul == -1);
+ Diff -= C->getAPInt() * DiffMul;
+ }
+ } else
+ Multiplicity[S] += Mul;
+ };
+ auto Decompose = [&](const SCEV *S, int Mul) {
+ if (isa<SCEVAddExpr>(S)) {
+ for (const SCEV *Op : S->operands())
+ Add(Op, Mul);
+ } else
+ Add(S, Mul);
+ };
+ Decompose(More, 1);
+ Decompose(Less, -1);
+
+ // Check whether all the non-constants cancel out, or reduce to new
+ // More/Less values.
+ const SCEV *NewMore = nullptr, *NewLess = nullptr;
+ for (const auto &[S, Mul] : Multiplicity) {
+ if (Mul == 0)
+ continue;
+ if (Mul == 1) {
+ if (NewMore)
+ return std::nullopt;
+ NewMore = S;
+ } else if (Mul == -1) {
+ if (NewLess)
+ return std::nullopt;
+ NewLess = S;
+ } else
+ return std::nullopt;
+ }
+
+ // Values stayed the same, no point in trying further.
+ if (NewMore == More || NewLess == Less)
+ return std::nullopt;
+
+ More = NewMore;
+ Less = NewLess;
+
+ // Reduced to constant.
+ if (!More && !Less)
+ return Diff;
+
+ // Left with variable on only one side, bail out.
+ if (!More || !Less)
+ return std::nullopt;
+ }
+
+ // Did not reduce to constant.
+ return std::nullopt;
+}
+
+bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart(
+ CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS,
+ const SCEV *FoundRHS, const Instruction *CtxI) {
+ // Try to recognize the following pattern:
+ //
+ // FoundRHS = ...
+ // ...
+ // loop:
+ // FoundLHS = {Start,+,W}
+ // context_bb: // Basic block from the same loop
+ // known(Pred, FoundLHS, FoundRHS)
+ //
+ // If some predicate is known in the context of a loop, it is also known on
+ // each iteration of this loop, including the first iteration. Therefore, in
+ // this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to
+ // prove the original pred using this fact.
+ if (!CtxI)
+ return false;
+ const BasicBlock *ContextBB = CtxI->getParent();
+ // Make sure AR varies in the context block.
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundLHS)) {
+ const Loop *L = AR->getLoop();
+ const auto *Latch = L->getLoopLatch();
+ // Make sure that context belongs to the loop and executes on 1st iteration
+ // (if it ever executes at all).
+ if (!L->contains(ContextBB) || !Latch || !DT.dominates(ContextBB, Latch))
+ return false;
+ if (!isAvailableAtLoopEntry(FoundRHS, AR->getLoop()))
+ return false;
+ return isImpliedCondOperands(Pred, LHS, RHS, AR->getStart(), FoundRHS);
+ }
+
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundRHS)) {
+ const Loop *L = AR->getLoop();
+ const auto *Latch = L->getLoopLatch();
+ // Make sure that context belongs to the loop and executes on 1st iteration
+ // (if it ever executes at all).
+ if (!L->contains(ContextBB) || !Latch || !DT.dominates(ContextBB, Latch))
+ return false;
+ if (!isAvailableAtLoopEntry(FoundLHS, AR->getLoop()))
+ return false;
+ return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, AR->getStart());
+ }
+
+ return false;
+}
+
+bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS) {
+ if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
+ return false;
+
+ const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!AddRecLHS)
+ return false;
+
+ const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
+ if (!AddRecFoundLHS)
+ return false;
+
+ // We'd like to let SCEV reason about control dependencies, so we constrain
+ // both the inequalities to be about add recurrences on the same loop. This
+ // way we can use isLoopEntryGuardedByCond later.
+
+ const Loop *L = AddRecFoundLHS->getLoop();
+ if (L != AddRecLHS->getLoop())
+ return false;
+
+ // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
+ //
+ // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
+ // ... (2)
+ //
+ // Informal proof for (2), assuming (1) [*]:
+ //
+ // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
+ //
+ // Then
+ //
+ // FoundLHS s< FoundRHS s< INT_MIN - C
+ // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
+ // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
+ // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
+ // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
+ // <=> FoundLHS + C s< FoundRHS + C
+ //
+ // [*]: (1) can be proved by ruling out overflow.
+ //
+ // [**]: This can be proved by analyzing all the four possibilities:
+ // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
+ // (A s>= 0, B s>= 0).
+ //
+ // Note:
+ // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
+ // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
+ // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
+ // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
+ // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
+ // C)".
+
+ std::optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
+ if (!LDiff)
+ return false;
+ std::optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
+ if (!RDiff || *LDiff != *RDiff)
+ return false;
+
+ if (LDiff->isMinValue())
+ return true;
+
+ APInt FoundRHSLimit;
+
+ if (Pred == CmpInst::ICMP_ULT) {
+ FoundRHSLimit = -(*RDiff);
+ } else {
+ assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
+ FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
+ }
+
+ // Try to prove (1) or (2), as needed.
+ return isAvailableAtLoopEntry(FoundRHS, L) &&
+ isLoopEntryGuardedByCond(L, Pred, FoundRHS,
+ getConstant(FoundRHSLimit));
+}
+
+bool ScalarEvolution::isImpliedViaMerge(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS, const SCEV *FoundLHS,
+ const SCEV *FoundRHS, unsigned Depth) {
+ const PHINode *LPhi = nullptr, *RPhi = nullptr;
+
+ llvm::scope_exit ClearOnExit([&]() {
+ if (LPhi) {
+ bool Erased = PendingMerges.erase(LPhi);
+ assert(Erased && "Failed to erase LPhi!");
+ (void)Erased;
+ }
+ if (RPhi) {
+ bool Erased = PendingMerges.erase(RPhi);
+ assert(Erased && "Failed to erase RPhi!");
+ (void)Erased;
+ }
+ });
+
+ // Find respective Phis and check that they are not being pending.
+ if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
+ if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
+ if (!PendingMerges.insert(Phi).second)
+ return false;
+ LPhi = Phi;
+ }
+ if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
+ if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
+ // If we detect a loop of Phi nodes being processed by this method, for
+ // example:
+ //
+ // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
+ // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
+ //
+ // we don't want to deal with a case that complex, so return conservative
+ // answer false.
+ if (!PendingMerges.insert(Phi).second)
+ return false;
+ RPhi = Phi;
+ }
+
+ // If none of LHS, RHS is a Phi, nothing to do here.
+ if (!LPhi && !RPhi)
+ return false;
+
+ // If there is a SCEVUnknown Phi we are interested in, make it left.
+ if (!LPhi) {
+ std::swap(LHS, RHS);
+ std::swap(FoundLHS, FoundRHS);
+ std::swap(LPhi, RPhi);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ }
+
+ assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
+ const BasicBlock *LBB = LPhi->getParent();
+ const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
+
+ auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
+ return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
+ isImpliedCondOperandsViaRanges(Pred, S1, S2, Pred, FoundLHS, FoundRHS) ||
+ isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
+ };
+
+ if (RPhi && RPhi->getParent() == LBB) {
+ // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
+ // If we compare two Phis from the same block, and for each entry block
+ // the predicate is true for incoming values from this block, then the
+ // predicate is also true for the Phis.
+ for (const BasicBlock *IncBB : predecessors(LBB)) {
+ const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
+ const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
+ if (!ProvedEasily(L, R))
+ return false;
+ }
+ } else if (RAR && RAR->getLoop()->getHeader() == LBB) {
+ // Case two: RHS is also a Phi from the same basic block, and it is an
+ // AddRec. It means that there is a loop which has both AddRec and Unknown
+ // PHIs, for it we can compare incoming values of AddRec from above the loop
+ // and latch with their respective incoming values of LPhi.
+ // TODO: Generalize to handle loops with many inputs in a header.
+ if (LPhi->getNumIncomingValues() != 2) return false;
+
+ auto *RLoop = RAR->getLoop();
+ auto *Predecessor = RLoop->getLoopPredecessor();
+ assert(Predecessor && "Loop with AddRec with no predecessor?");
+ const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
+ if (!ProvedEasily(L1, RAR->getStart()))
+ return false;
+ auto *Latch = RLoop->getLoopLatch();
+ assert(Latch && "Loop with AddRec with no latch?");
+ const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
+ if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
+ return false;
+ } else {
+ // In all other cases go over inputs of LHS and compare each of them to RHS,
+ // the predicate is true for (LHS, RHS) if it is true for all such pairs.
+ // At this point RHS is either a non-Phi, or it is a Phi from some block
+ // different from LBB.
+ for (const BasicBlock *IncBB : predecessors(LBB)) {
+ // Check that RHS is available in this block.
+ if (!dominates(RHS, IncBB))
+ return false;
+ const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
+ // Make sure L does not refer to a value from a potentially previous
+ // iteration of a loop.
+ if (!properlyDominates(L, LBB))
+ return false;
+ // Addrecs are considered to properly dominate their loop, so are missed
+ // by the previous check. Discard any values that have computable
+ // evolution in this loop.
+ if (auto *Loop = LI.getLoopFor(LBB))
+ if (hasComputableLoopEvolution(L, Loop))
+ return false;
+ if (!ProvedEasily(L, RHS))
+ return false;
+ }
+ }
+ return true;
+}
+
+bool ScalarEvolution::isImpliedCondOperandsViaShift(CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS) {
+ // We want to imply LHS < RHS from LHS < (RHS >> shiftvalue). First, make
+ // sure that we are dealing with same LHS.
+ if (RHS == FoundRHS) {
+ std::swap(LHS, RHS);
+ std::swap(FoundLHS, FoundRHS);
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ }
+ if (LHS != FoundLHS)
+ return false;
+
+ auto *SUFoundRHS = dyn_cast<SCEVUnknown>(FoundRHS);
+ if (!SUFoundRHS)
+ return false;
+
+ Value *Shiftee, *ShiftValue;
+
+ using namespace PatternMatch;
+ if (match(SUFoundRHS->getValue(),
+ m_LShr(m_Value(Shiftee), m_Value(ShiftValue)))) {
+ auto *ShifteeS = getSCEV(Shiftee);
+ // Prove one of the following:
+ // LHS <u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <u RHS
+ // LHS <=u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <=u RHS
+ // LHS <s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
+ // ---> LHS <s RHS
+ // LHS <=s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
+ // ---> LHS <=s RHS
+ if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_ULE)
+ return isKnownPredicate(ICmpInst::ICMP_ULE, ShifteeS, RHS);
+ if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE)
+ if (isKnownNonNegative(ShifteeS))
+ return isKnownPredicate(ICmpInst::ICMP_SLE, ShifteeS, RHS);
+ }
+
+ return false;
+}
+
+bool ScalarEvolution::isImpliedCondOperandsViaMatchingDiff(
+ CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS,
+ const SCEV *FoundRHS) {
+ // Only valid for equality predicates: (A == B) implies (C == D) when
+ // the SCEV difference A - B equals C - D (they check the same
+ // underlying relationship at every iteration).
+ if (!ICmpInst::isEquality(Pred))
+ return false;
+
+ // Restrict to cases involving loop recurrences - that's where this
+ // pattern arises (correlated IV comparisons). This avoids calling
+ // getMinusSCEV on arbitrary non-loop expressions.
+ if ((!isa<SCEVAddRecExpr>(LHS) && !isa<SCEVAddRecExpr>(RHS)) ||
+ (!isa<SCEVAddRecExpr>(FoundLHS) && !isa<SCEVAddRecExpr>(FoundRHS)))
+ return false;
+
+ // AddRecs from different loops can never produce matching differences.
+ const SCEVAddRecExpr *QueryAddRec = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!QueryAddRec)
+ QueryAddRec = cast<SCEVAddRecExpr>(RHS);
+ const SCEVAddRecExpr *FoundAddRec = dyn_cast<SCEVAddRecExpr>(FoundLHS);
+ if (!FoundAddRec)
+ FoundAddRec = cast<SCEVAddRecExpr>(FoundRHS);
+ if (QueryAddRec->getLoop() != FoundAddRec->getLoop())
+ return false;
+
+ // If the strides differ, the differences can never match.
+ if (QueryAddRec->getStepRecurrence(*this) !=
+ FoundAddRec->getStepRecurrence(*this))
+ return false;
+
+ // Compute differences. For pointer-typed operands sharing the same base,
+ // getMinusSCEV strips the common base and returns an integer SCEV.
+ // For example, {base,+,8} - (base+8*n) = {-8n,+,8}
+ const SCEV *FoundDiff = getMinusSCEV(FoundLHS, FoundRHS);
+ if (isa<SCEVCouldNotCompute>(FoundDiff))
+ return false;
+
+ const SCEV *Diff = getMinusSCEV(LHS, RHS);
+ if (isa<SCEVCouldNotCompute>(Diff))
+ return false;
+
+ return Diff == FoundDiff;
+}
+
+bool ScalarEvolution::isImpliedCondOperands(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS,
+ const Instruction *CtxI) {
+ return isImpliedCondOperandsViaRanges(Pred, LHS, RHS, Pred, FoundLHS,
+ FoundRHS) ||
+ isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS,
+ FoundRHS) ||
+ isImpliedCondOperandsViaShift(Pred, LHS, RHS, FoundLHS, FoundRHS) ||
+ isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS,
+ CtxI) ||
+ isImpliedCondOperandsViaMatchingDiff(Pred, LHS, RHS, FoundLHS,
+ FoundRHS) ||
+ isImpliedCondOperandsHelper(Pred, LHS, RHS, FoundLHS, FoundRHS);
+}
+
+/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
+template <typename MinMaxExprType>
+static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
+ const SCEV *Candidate) {
+ const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
+ if (!MinMaxExpr)
+ return false;
+
+ return is_contained(MinMaxExpr->operands(), Candidate);
+}
+
+static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
+ CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS) {
+ // If both sides are affine addrecs for the same loop, with equal
+ // steps, and we know the recurrences don't wrap, then we only
+ // need to check the predicate on the starting values.
+
+ if (!ICmpInst::isRelational(Pred))
+ return false;
+
+ const SCEV *LStart, *RStart, *Step;
+ const Loop *L;
+ if (!match(LHS,
+ m_scev_AffineAddRec(m_SCEV(LStart), m_SCEV(Step), m_Loop(L))) ||
+ !match(RHS, m_scev_AffineAddRec(m_SCEV(RStart), m_scev_Specific(Step),
+ m_SpecificLoop(L))))
+ return false;
+ const SCEVAddRecExpr *LAR = cast<SCEVAddRecExpr>(LHS);
+ const SCEVAddRecExpr *RAR = cast<SCEVAddRecExpr>(RHS);
+ SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
+ SCEV::FlagNSW : SCEV::FlagNUW;
+ if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
+ return false;
+
+ return SE.isKnownPredicate(Pred, LStart, RStart);
+}
+
+/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
+/// expression?
+static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE, CmpPredicate Pred,
+ const SCEV *LHS, const SCEV *RHS) {
+ switch (Pred) {
+ default:
+ return false;
+
+ case ICmpInst::ICMP_SGE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SLE:
+ return
+ // min(A, ...) <= A
+ IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
+ // A <= max(A, ...)
+ IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
+
+ case ICmpInst::ICMP_UGE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_ULE:
+ return
+ // min(A, ...) <= A
+ // FIXME: what about umin_seq?
+ IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
+ // A <= max(A, ...)
+ IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
+
+ case ICmpInst::ICMP_UGT:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_ULT:
+ // umin(Ops) u<= each Op, so proving Op u< RHS for any Op proves
+ // umin(Ops) u< RHS.
+ //
+ // Use computeConstantDifference instead of the more powerful
+ // isKnownPredicate to keep this check cheap: isKnownPredicateViaMinOrMax
+ // is called from isKnownViaNonRecursiveReasoning, so recursing into
+ // the full predicate prover would be expensive.
+ if (const auto *Min = dyn_cast<SCEVUMinExpr>(LHS)) {
+ for (SCEVUse Op : Min->operands()) {
+ std::optional<APInt> Diff = SE.computeConstantDifference(RHS, Op);
+ // When Op and RHS share a common base differing by a
+ // constant offset D (RHS - Op = D), Op u< RHS holds iff D != 0 and
+ // RHS >= D (unsigned), i.e. the subtraction doesn't underflow.
+ if (Diff && !Diff->isZero() && SE.getUnsignedRangeMin(RHS).uge(*Diff))
+ return true;
+ }
+ }
+ return false;
+ }
+
+ llvm_unreachable("covered switch fell through?!");
+}
+
+bool ScalarEvolution::isImpliedViaOperations(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS,
+ unsigned Depth) {
+ assert(getTypeSizeInBits(LHS->getType()) ==
+ getTypeSizeInBits(RHS->getType()) &&
+ "LHS and RHS have different sizes?");
+ assert(getTypeSizeInBits(FoundLHS->getType()) ==
+ getTypeSizeInBits(FoundRHS->getType()) &&
+ "FoundLHS and FoundRHS have different sizes?");
+ // We want to avoid hurting the compile time with analysis of too big trees.
+ if (Depth > MaxSCEVOperationsImplicationDepth)
+ return false;
+
+ // We only want to work with GT comparison so far.
+ if (ICmpInst::isLT(Pred)) {
+ Pred = ICmpInst::getSwappedCmpPredicate(Pred);
+ std::swap(LHS, RHS);
+ std::swap(FoundLHS, FoundRHS);
+ }
+
+ CmpInst::Predicate P = Pred.getPreferredSignedPredicate();
+
+ // For unsigned, try to reduce it to corresponding signed comparison.
+ if (P == ICmpInst::ICMP_UGT)
+ // We can replace unsigned predicate with its signed counterpart if all
+ // involved values are non-negative.
+ // TODO: We could have better support for unsigned.
+ if (isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) {
+ // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing
+ // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us
+ // use this fact to prove that LHS and RHS are non-negative.
+ const SCEV *MinusOne = getMinusOne(LHS->getType());
+ if (isImpliedCondOperands(ICmpInst::ICMP_SGT, LHS, MinusOne, FoundLHS,
+ FoundRHS) &&
+ isImpliedCondOperands(ICmpInst::ICMP_SGT, RHS, MinusOne, FoundLHS,
+ FoundRHS))
+ P = ICmpInst::ICMP_SGT;
+ }
+
+ if (P != ICmpInst::ICMP_SGT)
+ return false;
+
+ auto GetOpFromSExt = [&](const SCEV *S) -> const SCEV * {
+ if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
+ return Ext->getOperand();
+ // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
+ // the constant in some cases.
+ return S;
+ };
+
+ // Acquire values from extensions.
+ auto *OrigLHS = LHS;
+ auto *OrigFoundLHS = FoundLHS;
+ LHS = GetOpFromSExt(LHS);
+ FoundLHS = GetOpFromSExt(FoundLHS);
+
+ // Is the SGT predicate can be proved trivially or using the found context.
+ auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
+ return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
+ isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
+ FoundRHS, Depth + 1);
+ };
+
+ if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
+ // We want to avoid creation of any new non-constant SCEV. Since we are
+ // going to compare the operands to RHS, we should be certain that we don't
+ // need any size extensions for this. So let's decline all cases when the
+ // sizes of types of LHS and RHS do not match.
+ // TODO: Maybe try to get RHS from sext to catch more cases?
+ if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
+ return false;
+
+ // Should not overflow.
+ if (!LHSAddExpr->hasNoSignedWrap())
+ return false;
+
+ SCEVUse LL = LHSAddExpr->getOperand(0);
+ SCEVUse LR = LHSAddExpr->getOperand(1);
+ auto *MinusOne = getMinusOne(RHS->getType());
+
+ // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
+ auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
+ return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
+ };
+ // Try to prove the following rule:
+ // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
+ // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
+ if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
+ return true;
+ } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
+ Value *LL, *LR;
+ // FIXME: Once we have SDiv implemented, we can get rid of this matching.
+
+ using namespace llvm::PatternMatch;
+
+ if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
+ // Rules for division.
+ // We are going to perform some comparisons with Denominator and its
+ // derivative expressions. In general case, creating a SCEV for it may
+ // lead to a complex analysis of the entire graph, and in particular it
+ // can request trip count recalculation for the same loop. This would
+ // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
+ // this, we only want to create SCEVs that are constants in this section.
+ // So we bail if Denominator is not a constant.
+ if (!isa<ConstantInt>(LR))
+ return false;
+
+ auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
+
+ // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
+ // then a SCEV for the numerator already exists and matches with FoundLHS.
+ auto *Numerator = getExistingSCEV(LL);
+ if (!Numerator || Numerator->getType() != FoundLHS->getType())
+ return false;
+
+ // Make sure that the numerator matches with FoundLHS and the denominator
+ // is positive.
+ if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
+ return false;
+
+ auto *DTy = Denominator->getType();
+ auto *FRHSTy = FoundRHS->getType();
+ if (DTy->isPointerTy() != FRHSTy->isPointerTy())
+ // One of types is a pointer and another one is not. We cannot extend
+ // them properly to a wider type, so let us just reject this case.
+ // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
+ // to avoid this check.
+ return false;
+
+ // Given that:
+ // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
+ auto *WTy = getWiderType(DTy, FRHSTy);
+ auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
+ auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
+
+ // Try to prove the following rule:
+ // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
+ // For example, given that FoundLHS > 2. It means that FoundLHS is at
+ // least 3. If we divide it by Denominator < 4, we will have at least 1.
+ auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
+ if (isKnownNonPositive(RHS) &&
+ IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
+ return true;
+
+ // Try to prove the following rule:
+ // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
+ // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
+ // If we divide it by Denominator > 2, then:
+ // 1. If FoundLHS is negative, then the result is 0.
+ // 2. If FoundLHS is non-negative, then the result is non-negative.
+ // Anyways, the result is non-negative.
+ auto *MinusOne = getMinusOne(WTy);
+ auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
+ if (isKnownNegative(RHS) &&
+ IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
+ return true;
+ }
+ }
+
+ // If our expression contained SCEVUnknown Phis, and we split it down and now
+ // need to prove something for them, try to prove the predicate for every
+ // possible incoming values of those Phis.
+ if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
+ return true;
+
+ return false;
+}
+
+static bool isKnownPredicateExtendIdiom(CmpPredicate Pred, const SCEV *LHS,
+ const SCEV *RHS) {
+ // zext x u<= sext x, sext x s<= zext x
+ const SCEV *Op;
+ switch (Pred) {
+ case ICmpInst::ICMP_SGE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_SLE: {
+ // If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
+ return match(LHS, m_scev_SExt(m_SCEV(Op))) &&
+ match(RHS, m_scev_ZExt(m_scev_Specific(Op)));
+ }
+ case ICmpInst::ICMP_UGE:
+ std::swap(LHS, RHS);
+ [[fallthrough]];
+ case ICmpInst::ICMP_ULE: {
+ // If operand >=u 0 then ZExt == SExt. If operand <u 0 then ZExt <u SExt.
+ return match(LHS, m_scev_ZExt(m_SCEV(Op))) &&
+ match(RHS, m_scev_SExt(m_scev_Specific(Op)));
+ }
+ default:
+ return false;
+ };
+ llvm_unreachable("unhandled case");
+}
+
+bool ScalarEvolution::isKnownViaNonRecursiveReasoning(CmpPredicate Pred,
+ SCEVUse LHS,
+ SCEVUse RHS) {
+ return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
+ isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
+ IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
+ IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
+ isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
+}
+
+bool ScalarEvolution::isImpliedCondOperandsHelper(CmpPredicate Pred,
+ const SCEV *LHS,
+ const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS) {
+ switch (Pred) {
+ default:
+ llvm_unreachable("Unexpected CmpPredicate value!");
+ case ICmpInst::ICMP_EQ:
+ case ICmpInst::ICMP_NE:
+ if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_SLT:
+ case ICmpInst::ICMP_SLE:
+ if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
+ isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_SGT:
+ case ICmpInst::ICMP_SGE:
+ if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
+ isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_ULT:
+ case ICmpInst::ICMP_ULE:
+ if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
+ isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_UGT:
+ case ICmpInst::ICMP_UGE:
+ if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
+ isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
+ return true;
+ break;
+ }
+
+ // Maybe it can be proved via operations?
+ if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
+ return true;
+
+ return false;
+}
+
+bool ScalarEvolution::isImpliedCondOperandsViaRanges(
+ CmpPredicate Pred, const SCEV *LHS, const SCEV *RHS, CmpPredicate FoundPred,
+ const SCEV *FoundLHS, const SCEV *FoundRHS) {
+ if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
+ // The restriction on `FoundRHS` be lifted easily -- it exists only to
+ // reduce the compile time impact of this optimization.
+ return false;
+
+ std::optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
+ if (!Addend)
+ return false;
+
+ const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
+
+ // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
+ // antecedent "`FoundLHS` `FoundPred` `FoundRHS`".
+ ConstantRange FoundLHSRange =
+ ConstantRange::makeExactICmpRegion(FoundPred, ConstFoundRHS);
+
+ // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
+ ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
+
+ // We can also compute the range of values for `LHS` that satisfy the
+ // consequent, "`LHS` `Pred` `RHS`":
+ const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
+ // The antecedent implies the consequent if every value of `LHS` that
+ // satisfies the antecedent also satisfies the consequent.
+ return LHSRange.icmp(Pred, ConstRHS);
+}
+
+bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
+ bool IsSigned) {
+ assert(isKnownPositive(Stride) && "Positive stride expected!");
+
+ unsigned BitWidth = getTypeSizeInBits(RHS->getType());
+ const SCEV *One = getOne(Stride->getType());
+
+ if (IsSigned) {
+ APInt MaxRHS = getSignedRangeMax(RHS);
+ APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
+ APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
+
+ // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
+ return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
+ }
+
+ APInt MaxRHS = getUnsignedRangeMax(RHS);
+ APInt MaxValue = APInt::getMaxValue(BitWidth);
+ APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
+
+ // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
+ return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
+}
+
+bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
+ bool IsSigned) {
+
+ unsigned BitWidth = getTypeSizeInBits(RHS->getType());
+ const SCEV *One = getOne(Stride->getType());
+
+ if (IsSigned) {
+ APInt MinRHS = getSignedRangeMin(RHS);
+ APInt MinValue = APInt::getSignedMinValue(BitWidth);
+ APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
+
+ // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
+ return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
+ }
+
+ APInt MinRHS = getUnsignedRangeMin(RHS);
+ APInt MinValue = APInt::getMinValue(BitWidth);
+ APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
+
+ // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
+ return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
+}
+
+const SCEV *ScalarEvolution::getUDivCeilSCEV(const SCEV *N, const SCEV *D) {
+ // umin(N, 1) + floor((N - umin(N, 1)) / D)
+ // This is equivalent to "1 + floor((N - 1) / D)" for N != 0. The umin
+ // expression fixes the case of N=0.
+ const SCEV *MinNOne = getUMinExpr(N, getOne(N->getType()));
+ const SCEV *NMinusOne = getMinusSCEV(N, MinNOne);
+ return getAddExpr(MinNOne, getUDivExpr(NMinusOne, D));
+}
+
+const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
+ const SCEV *Stride,
+ const SCEV *End,
+ unsigned BitWidth,
+ bool IsSigned) {
+ // The logic in this function assumes we can represent a positive stride.
+ // If we can't, the backedge-taken count must be zero.
+ if (IsSigned && BitWidth == 1)
+ return getZero(Stride->getType());
+
+ // This code below only been closely audited for negative strides in the
+ // unsigned comparison case, it may be correct for signed comparison, but
+ // that needs to be established.
+ if (IsSigned && isKnownNegative(Stride))
+ return getCouldNotCompute();
+
+ // Calculate the maximum backedge count based on the range of values
+ // permitted by Start, End, and Stride.
+ APInt MinStart =
+ IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
+
+ APInt MinStride =
+ IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
+
+ // We assume either the stride is positive, or the backedge-taken count
+ // is zero. So force StrideForMaxBECount to be at least one.
+ APInt One(BitWidth, 1);
+ APInt StrideForMaxBECount = IsSigned ? APIntOps::smax(One, MinStride)
+ : APIntOps::umax(One, MinStride);
+
+ APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
+ : APInt::getMaxValue(BitWidth);
+ APInt Limit = MaxValue - (StrideForMaxBECount - 1);
+
+ // Although End can be a MAX expression we estimate MaxEnd considering only
+ // the case End = RHS of the loop termination condition. This is safe because
+ // in the other case (End - Start) is zero, leading to a zero maximum backedge
+ // taken count.
+ APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
+ : APIntOps::umin(getUnsignedRangeMax(End), Limit);
+
+ // MaxBECount = ceil((max(MaxEnd, MinStart) - MinStart) / Stride)
+ MaxEnd = IsSigned ? APIntOps::smax(MaxEnd, MinStart)
+ : APIntOps::umax(MaxEnd, MinStart);
+
+ return getUDivCeilSCEV(getConstant(MaxEnd - MinStart) /* Delta */,
+ getConstant(StrideForMaxBECount) /* Step */);
+}
+
+ScalarEvolution::ExitLimit
+ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
+ const Loop *L, bool IsSigned,
+ bool ControlsOnlyExit, bool AllowPredicates) {
+ SmallVector<const SCEVPredicate *> Predicates;
+
+ const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
+ bool PredicatedIV = false;
+ if (!IV) {
+ if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS)) {
+ const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(ZExt->getOperand());
+ if (AR && AR->getLoop() == L && AR->isAffine()) {
+ auto canProveNUW = [&]() {
+ // We can use the comparison to infer no-wrap flags only if it fully
+ // controls the loop exit.
+ if (!ControlsOnlyExit)
+ return false;
+
+ if (!isLoopInvariant(RHS, L))
+ return false;
+
+ if (!isKnownNonZero(AR->getStepRecurrence(*this)))
+ // We need the sequence defined by AR to strictly increase in the
+ // unsigned integer domain for the logic below to hold.
+ return false;
+
+ const unsigned InnerBitWidth = getTypeSizeInBits(AR->getType());
+ const unsigned OuterBitWidth = getTypeSizeInBits(RHS->getType());
+ // If RHS <=u Limit, then there must exist a value V in the sequence
+ // defined by AR (e.g. {Start,+,Step}) such that V >u RHS, and
+ // V <=u UINT_MAX. Thus, we must exit the loop before unsigned
+ // overflow occurs. This limit also implies that a signed comparison
+ // (in the wide bitwidth) is equivalent to an unsigned comparison as
+ // the high bits on both sides must be zero.
+ APInt StrideMax = getUnsignedRangeMax(AR->getStepRecurrence(*this));
+ APInt Limit = APInt::getMaxValue(InnerBitWidth) - (StrideMax - 1);
+ Limit = Limit.zext(OuterBitWidth);
+ return getUnsignedRangeMax(applyLoopGuards(RHS, L)).ule(Limit);
+ };
+ auto Flags = AR->getNoWrapFlags();
+ if (!hasFlags(Flags, SCEV::FlagNUW) && canProveNUW())
+ Flags = setFlags(Flags, SCEV::FlagNUW);
+
+ setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
+ if (AR->hasNoUnsignedWrap()) {
+ // Emulate what getZeroExtendExpr would have done during construction
+ // if we'd been able to infer the fact just above at that time.
+ const SCEV *Step = AR->getStepRecurrence(*this);
+ Type *Ty = ZExt->getType();
+ auto *S = getAddRecExpr(
+ getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 0),
+ getZeroExtendExpr(Step, Ty, 0), L, AR->getNoWrapFlags());
+ IV = dyn_cast<SCEVAddRecExpr>(S);
+ }
+ }
+ }
+ }
+
+
+ if (!IV && AllowPredicates) {
+ // Try to make this an AddRec using runtime tests, in the first X
+ // iterations of this loop, where X is the SCEV expression found by the
+ // algorithm below.
+ IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
+ PredicatedIV = true;
+ }
+
+ // Avoid weird loops
+ if (!IV || IV->getLoop() != L || !IV->isAffine())
+ return getCouldNotCompute();
+
+ // A precondition of this method is that the condition being analyzed
+ // reaches an exiting branch which dominates the latch. Given that, we can
+ // assume that an increment which violates the nowrap specification and
+ // produces poison must cause undefined behavior when the resulting poison
+ // value is branched upon and thus we can conclude that the backedge is
+ // taken no more often than would be required to produce that poison value.
+ // Note that a well defined loop can exit on the iteration which violates
+ // the nowrap specification if there is another exit (either explicit or
+ // implicit/exceptional) which causes the loop to execute before the
+ // exiting instruction we're analyzing would trigger UB.
+ auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
+ bool NoWrap = ControlsOnlyExit && any(IV->getNoWrapFlags(WrapType));
+ ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT;
+
+ const SCEV *Stride = IV->getStepRecurrence(*this);
+
+ bool PositiveStride = isKnownPositive(Stride);
+ bool IVcanOverFlowOnLT = canIVOverflowOnLT(RHS, Stride, IsSigned);
+
+ // Avoid negative or zero stride values.
+ if (!PositiveStride) {
+ // We can compute the correct backedge taken count for loops with unknown
+ // strides if we can prove that the loop is not an infinite loop with side
+ // effects. Here's the loop structure we are trying to handle -
+ //
+ // i = start
+ // do {
+ // A[i] = i;
+ // i += s;
+ // } while (i < end);
+ //
+ // The backedge taken count for such loops is evaluated as -
+ // (max(end, start + stride) - start - 1) /u stride
+ //
+ // The additional preconditions that we need to check to prove correctness
+ // of the above formula is as follows -
+ //
+ // a) IV is either nuw or nsw depending upon signedness (indicated by the
+ // NoWrap flag).
+ // b) the loop is guaranteed to be finite (e.g. is mustprogress and has
+ // no side effects within the loop)
+ // c) loop has a single static exit (with no abnormal exits)
+ //
+ // Precondition a) implies that if the stride is negative, this is a single
+ // trip loop. The backedge taken count formula reduces to zero in this case.
+ //
+ // Precondition b) and c) combine to imply that if rhs is invariant in L,
+ // then a zero stride means the backedge can't be taken without executing
+ // undefined behavior.
+ //
+ // The positive stride case is the same as isKnownPositive(Stride) returning
+ // true (original behavior of the function).
+ //
+ if (PredicatedIV || !NoWrap || !loopIsFiniteByAssumption(L) ||
+ !loopHasNoAbnormalExits(L))
+ return getCouldNotCompute();
+
+ if (!isKnownNonZero(Stride)) {
+ // If we have a step of zero, and RHS isn't invariant in L, we don't know
+ // if it might eventually be greater than start and if so, on which
+ // iteration. We can't even produce a useful upper bound.
+ if (!isLoopInvariant(RHS, L))
+ return getCouldNotCompute();
+
+ // We allow a potentially zero stride, but we need to divide by stride
+ // below. Since the loop can't be infinite and this check must control
+ // the sole exit, we can infer the exit must be taken on the first
+ // iteration (e.g. backedge count = 0) if the stride is zero. Given that,
+ // we know the numerator in the divides below must be zero, so we can
+ // pick an arbitrary non-zero value for the denominator (e.g. stride)
+ // and produce the right result.
+ // FIXME: Handle the case where Stride is poison?
+ auto wouldZeroStrideBeUB = [&]() {
+ // Proof by contradiction. Suppose the stride were zero. If we can
+ // prove that the backedge *is* taken on the first iteration, then since
+ // we know this condition controls the sole exit, we must have an
+ // infinite loop. We can't have a (well defined) infinite loop per
+ // check just above.
+ // Note: The (Start - Stride) term is used to get the start' term from
+ // (start' + stride,+,stride). Remember that we only care about the
+ // result of this expression when stride == 0 at runtime.
+ auto *StartIfZero = getMinusSCEV(IV->getStart(), Stride);
+ return isLoopEntryGuardedByCond(L, Cond, StartIfZero, RHS);
+ };
+ if (!wouldZeroStrideBeUB()) {
+ Stride = getUMaxExpr(Stride, getOne(Stride->getType()));
+ }
+ }
+ } else if (!NoWrap) {
+ // Avoid proven overflow cases: this will ensure that the backedge taken
+ // count will not generate any unsigned overflow.
+ if (IVcanOverFlowOnLT) {
+ if (!AllowPredicates)
+ return getCouldNotCompute();
+ }
+ }
+
+ // On all paths just preceeding, we established the following invariant:
+ // IV can be assumed not to overflow up to and including the exiting
+ // iteration. We proved this in one of two ways:
+ // 1) We can show overflow doesn't occur before the exiting iteration
+ // 1a) canIVOverflowOnLT, and b) step of one
+ // 2) We can show that if overflow occurs, the loop must execute UB
+ // before any possible exit.
+ // Note that we have not yet proved RHS invariant (in general).
+
+ const SCEV *Start = IV->getStart();
+
+ // Preserve pointer-typed Start/RHS to pass to isLoopEntryGuardedByCond.
+ // If we convert to integers, isLoopEntryGuardedByCond will miss some cases.
+ // Use integer-typed versions for actual computation; we can't subtract
+ // pointers in general.
+ const SCEV *OrigStart = Start;
+ const SCEV *OrigRHS = RHS;
+ if (Start->getType()->isPointerTy()) {
+ Start = getPtrToAddrExpr(Start);
+ if (isa<SCEVCouldNotCompute>(Start))
+ return Start;
+ }
+ if (RHS->getType()->isPointerTy()) {
+ RHS = getPtrToAddrExpr(RHS);
+ if (isa<SCEVCouldNotCompute>(RHS))
+ return RHS;
+ }
+
+ // Now that RHS has been converted to an integer type (if it was a pointer),
+ // we can safely build the overflow predicate. SCEVComparePredicate requires
+ // both operands to have identical LLVM types, which is guaranteed here
+ // because getConstant(Limit) uses the same BitWidth as RHS->getType().
+ if (!NoWrap && IVcanOverFlowOnLT) {
+ unsigned BitWidth = getTypeSizeInBits(RHS->getType());
+ const SCEV *One = getOne(Stride->getType());
+ const SCEV *StrideMinusOne = getMinusSCEV(Stride, One);
+
+ APInt MaxStrideMinusOne = IsSigned ? getSignedRangeMax(StrideMinusOne)
+ : getUnsignedRangeMax(StrideMinusOne);
+ APInt Limit = (IsSigned ? APInt::getSignedMaxValue(BitWidth)
+ : APInt::getMaxValue(BitWidth)) -
+ MaxStrideMinusOne;
+
+ Predicates.push_back(getComparePredicate(IsSigned ? ICmpInst::ICMP_SLE
+ : ICmpInst::ICMP_ULE,
+ RHS, getConstant(Limit)));
+ }
+
+ const SCEV *End = nullptr, *BECount = nullptr,
+ *BECountIfBackedgeTaken = nullptr;
+ if (!isLoopInvariant(RHS, L)) {
+ const auto *RHSAddRec = dyn_cast<SCEVAddRecExpr>(RHS);
+ if (PositiveStride && RHSAddRec != nullptr && RHSAddRec->getLoop() == L &&
+ any(RHSAddRec->getNoWrapFlags())) {
+ // The structure of loop we are trying to calculate backedge count of:
+ //
+ // left = left_start
+ // right = right_start
+ //
+ // while(left < right){
+ // ... do something here ...
+ // left += s1; // stride of left is s1 (s1 > 0)
+ // right += s2; // stride of right is s2 (s2 < 0)
+ // }
+ //
+
+ const SCEV *RHSStart = RHSAddRec->getStart();
+ const SCEV *RHSStride = RHSAddRec->getStepRecurrence(*this);
+
+ // If Stride - RHSStride is positive and does not overflow, we can write
+ // backedge count as ->
+ // ceil((End - Start) /u (Stride - RHSStride))
+ // Where, End = max(RHSStart, Start)
+
+ // Check if RHSStride < 0 and Stride - RHSStride will not overflow.
+ if (isKnownNegative(RHSStride) &&
+ willNotOverflow(Instruction::Sub, /*Signed=*/true, Stride,
+ RHSStride)) {
+
+ const SCEV *Denominator = getMinusSCEV(Stride, RHSStride);
+ if (isKnownPositive(Denominator)) {
+ End = IsSigned ? getSMaxExpr(RHSStart, Start)
+ : getUMaxExpr(RHSStart, Start);
+
+ // We can do this because End >= Start, as End = max(RHSStart, Start)
+ const SCEV *Delta = getMinusSCEV(End, Start);
+
+ BECount = getUDivCeilSCEV(Delta, Denominator);
+ BECountIfBackedgeTaken =
+ getUDivCeilSCEV(getMinusSCEV(RHSStart, Start), Denominator);
+ }
+ }
+ }
+ if (BECount == nullptr) {
+ // If we cannot calculate ExactBECount, we can calculate the MaxBECount,
+ // given the start, stride and max value for the end bound of the
+ // loop (RHS), and the fact that IV does not overflow (which is
+ // checked above).
+ const SCEV *MaxBECount = computeMaxBECountForLT(
+ Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
+ return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
+ MaxBECount, false /*MaxOrZero*/, Predicates);
+ }
+ } else {
+ // We use the expression (max(End,Start)-Start)/Stride to describe the
+ // backedge count, as if the backedge is taken at least once
+ // max(End,Start) is End and so the result is as above, and if not
+ // max(End,Start) is Start so we get a backedge count of zero.
+ auto *OrigStartMinusStride = getMinusSCEV(OrigStart, Stride);
+ assert(isAvailableAtLoopEntry(OrigStartMinusStride, L) && "Must be!");
+ assert(isAvailableAtLoopEntry(OrigStart, L) && "Must be!");
+ assert(isAvailableAtLoopEntry(OrigRHS, L) && "Must be!");
+ // Can we prove (max(RHS,Start) > Start - Stride?
+ if (isLoopEntryGuardedByCond(L, Cond, OrigStartMinusStride, OrigStart) &&
+ isLoopEntryGuardedByCond(L, Cond, OrigStartMinusStride, OrigRHS)) {
+ // In this case, we can use a refined formula for computing backedge
+ // taken count. The general formula remains:
+ // "End-Start /uceiling Stride" where "End = max(RHS,Start)"
+ // We want to use the alternate formula:
+ // "((End - 1) - (Start - Stride)) /u Stride"
+ // Let's do a quick case analysis to show these are equivalent under
+ // our precondition that max(RHS,Start) > Start - Stride.
+ // * For RHS <= Start, the backedge-taken count must be zero.
+ // "((End - 1) - (Start - Stride)) /u Stride" reduces to
+ // "((Start - 1) - (Start - Stride)) /u Stride" which simplies to
+ // "Stride - 1 /u Stride" which is indeed zero for all non-zero values
+ // of Stride. For 0 stride, we've use umin(1,Stride) above,
+ // reducing this to the stride of 1 case.
+ // * For RHS >= Start, the backedge count must be "RHS-Start /uceil
+ // Stride".
+ // "((End - 1) - (Start - Stride)) /u Stride" reduces to
+ // "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to
+ // "((RHS - (Start - Stride) - 1) /u Stride".
+ // Our preconditions trivially imply no overflow in that form.
+ const SCEV *MinusOne = getMinusOne(Stride->getType());
+ const SCEV *Numerator =
+ getMinusSCEV(getAddExpr(RHS, MinusOne), getMinusSCEV(Start, Stride));
+ BECount = getUDivExpr(Numerator, Stride);
+ }
+
+ if (!BECount) {
+ auto canProveRHSGreaterThanEqualStart = [&]() {
+ auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
+ const SCEV *GuardedRHS = applyLoopGuards(OrigRHS, L);
+ const SCEV *GuardedStart = applyLoopGuards(OrigStart, L);
+
+ if (isLoopEntryGuardedByCond(L, CondGE, OrigRHS, OrigStart) ||
+ isKnownPredicate(CondGE, GuardedRHS, GuardedStart))
+ return true;
+
+ // (RHS > Start - 1) implies RHS >= Start.
+ // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if
+ // "Start - 1" doesn't overflow.
+ // * For signed comparison, if Start - 1 does overflow, it's equal
+ // to INT_MAX, and "RHS >s INT_MAX" is trivially false.
+ // * For unsigned comparison, if Start - 1 does overflow, it's equal
+ // to UINT_MAX, and "RHS >u UINT_MAX" is trivially false.
+ //
+ // FIXME: Should isLoopEntryGuardedByCond do this for us?
+ auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
+ auto *StartMinusOne =
+ getAddExpr(OrigStart, getMinusOne(OrigStart->getType()));
+ return isLoopEntryGuardedByCond(L, CondGT, OrigRHS, StartMinusOne);
+ };
+
+ // If we know that RHS >= Start in the context of loop, then we know
+ // that max(RHS, Start) = RHS at this point.
+ if (canProveRHSGreaterThanEqualStart()) {
+ End = RHS;
+ } else {
+ // If RHS < Start, the backedge will be taken zero times. So in
+ // general, we can write the backedge-taken count as:
+ //
+ // RHS >= Start ? ceil(RHS - Start) / Stride : 0
+ //
+ // We convert it to the following to make it more convenient for SCEV:
+ //
+ // ceil(max(RHS, Start) - Start) / Stride
+ End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
+
+ // See what would happen if we assume the backedge is taken. This is
+ // used to compute MaxBECount.
+ BECountIfBackedgeTaken =
+ getUDivCeilSCEV(getMinusSCEV(RHS, Start), Stride);
+ }
+
+ // At this point, we know:
+ //
+ // 1. If IsSigned, Start <=s End; otherwise, Start <=u End
+ // 2. The index variable doesn't overflow.
+ //
+ // Therefore, we know N exists such that
+ // (Start + Stride * N) >= End, and computing "(Start + Stride * N)"
+ // doesn't overflow.
+ //
+ // Using this information, try to prove whether the addition in
+ // "(Start - End) + (Stride - 1)" has unsigned overflow.
+ const SCEV *One = getOne(Stride->getType());
+ bool MayAddOverflow = [&] {
+ if (isKnownToBeAPowerOfTwo(Stride)) {
+ // Suppose Stride is a power of two, and Start/End are unsigned
+ // integers. Let UMAX be the largest representable unsigned
+ // integer.
+ //
+ // By the preconditions of this function, we know
+ // "(Start + Stride * N) >= End", and this doesn't overflow.
+ // As a formula:
+ //
+ // End <= (Start + Stride * N) <= UMAX
+ //
+ // Subtracting Start from all the terms:
+ //
+ // End - Start <= Stride * N <= UMAX - Start
+ //
+ // Since Start is unsigned, UMAX - Start <= UMAX. Therefore:
+ //
+ // End - Start <= Stride * N <= UMAX
+ //
+ // Stride * N is a multiple of Stride. Therefore,
+ //
+ // End - Start <= Stride * N <= UMAX - (UMAX mod Stride)
+ //
+ // Since Stride is a power of two, UMAX + 1 is divisible by
+ // Stride. Therefore, UMAX mod Stride == Stride - 1. So we can
+ // write:
+ //
+ // End - Start <= Stride * N <= UMAX - Stride - 1
+ //
+ // Dropping the middle term:
+ //
+ // End - Start <= UMAX - Stride - 1
+ //
+ // Adding Stride - 1 to both sides:
+ //
+ // (End - Start) + (Stride - 1) <= UMAX
+ //
+ // In other words, the addition doesn't have unsigned overflow.
+ //
+ // A similar proof works if we treat Start/End as signed values.
+ // Just rewrite steps before "End - Start <= Stride * N <= UMAX"
+ // to use signed max instead of unsigned max. Note that we're
+ // trying to prove a lack of unsigned overflow in either case.
+ return false;
+ }
+ if (Start == Stride || Start == getMinusSCEV(Stride, One)) {
+ // If Start is equal to Stride, (End - Start) + (Stride - 1) == End
+ // - 1. If !IsSigned, 0 <u Stride == Start <=u End; so 0 <u End - 1
+ // <u End. If IsSigned, 0 <s Stride == Start <=s End; so 0 <s End -
+ // 1 <s End.
+ //
+ // If Start is equal to Stride - 1, (End - Start) + Stride - 1 ==
+ // End.
+ return false;
+ }
+ return true;
+ }();
+
+ const SCEV *Delta = getMinusSCEV(End, Start);
+ if (!MayAddOverflow) {
+ // floor((D + (S - 1)) / S)
+ // We prefer this formulation if it's legal because it's fewer
+ // operations.
+ BECount =
+ getUDivExpr(getAddExpr(Delta, getMinusSCEV(Stride, One)), Stride);
+ } else {
+ BECount = getUDivCeilSCEV(Delta, Stride);
+ }
+ }
+ }
+
+ const SCEV *ConstantMaxBECount;
+ bool MaxOrZero = false;
+ if (isa<SCEVConstant>(BECount)) {
+ ConstantMaxBECount = BECount;
+ } else if (BECountIfBackedgeTaken &&
+ isa<SCEVConstant>(BECountIfBackedgeTaken)) {
+ // If we know exactly how many times the backedge will be taken if it's
+ // taken at least once, then the backedge count will either be that or
+ // zero.
+ ConstantMaxBECount = BECountIfBackedgeTaken;
+ MaxOrZero = true;
+ } else {
+ ConstantMaxBECount = computeMaxBECountForLT(
+ Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
+ }
+
+ if (isa<SCEVCouldNotCompute>(ConstantMaxBECount) &&
+ !isa<SCEVCouldNotCompute>(BECount))
+ ConstantMaxBECount = getConstant(getUnsignedRangeMax(BECount));
+
+ const SCEV *SymbolicMaxBECount =
+ isa<SCEVCouldNotCompute>(BECount) ? ConstantMaxBECount : BECount;
+ return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, MaxOrZero,
+ Predicates);
+}
+
+ScalarEvolution::ExitLimit ScalarEvolution::howManyGreaterThans(
+ const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned,
+ bool ControlsOnlyExit, bool AllowPredicates) {
+ SmallVector<const SCEVPredicate *> Predicates;
+ // We handle only IV > Invariant
+ if (!isLoopInvariant(RHS, L))
+ return getCouldNotCompute();
+
+ const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!IV && AllowPredicates)
+ // Try to make this an AddRec using runtime tests, in the first X
+ // iterations of this loop, where X is the SCEV expression found by the
+ // algorithm below.
+ IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
+
+ // Avoid weird loops
+ if (!IV || IV->getLoop() != L || !IV->isAffine())
+ return getCouldNotCompute();
+
+ auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
+ bool NoWrap = ControlsOnlyExit && any(IV->getNoWrapFlags(WrapType));
+ ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
+
+ const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
+
+ // Avoid negative or zero stride values
+ if (!isKnownPositive(Stride))
+ return getCouldNotCompute();
+
+ // Avoid proven overflow cases: this will ensure that the backedge taken count
+ // will not generate any unsigned overflow. Relaxed no-overflow conditions
+ // exploit NoWrapFlags, allowing to optimize in presence of undefined
+ // behaviors like the case of C language.
+ if (!Stride->isOne() && !NoWrap)
+ if (canIVOverflowOnGT(RHS, Stride, IsSigned))
+ return getCouldNotCompute();
+
+ const SCEV *Start = IV->getStart();
+ const SCEV *End = RHS;
+ if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
+ // If we know that Start >= RHS in the context of loop, then we know that
+ // min(RHS, Start) = RHS at this point.
+ if (isLoopEntryGuardedByCond(
+ L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS))
+ End = RHS;
+ else
+ End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
+ }
+
+ if (Start->getType()->isPointerTy()) {
+ Start = getPtrToAddrExpr(Start);
+ if (isa<SCEVCouldNotCompute>(Start))
+ return Start;
+ }
+ if (End->getType()->isPointerTy()) {
+ End = getPtrToAddrExpr(End);
+ if (isa<SCEVCouldNotCompute>(End))
+ return End;
+ }
+
+ // Compute ((Start - End) + (Stride - 1)) / Stride.
+ // FIXME: This can overflow. Holding off on fixing this for now;
+ // howManyGreaterThans will hopefully be gone soon.
+ const SCEV *One = getOne(Stride->getType());
+ const SCEV *BECount = getUDivExpr(
+ getAddExpr(getMinusSCEV(Start, End), getMinusSCEV(Stride, One)), Stride);
+
+ APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
+ : getUnsignedRangeMax(Start);
+
+ APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
+ : getUnsignedRangeMin(Stride);
+
+ unsigned BitWidth = getTypeSizeInBits(LHS->getType());
+ APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
+ : APInt::getMinValue(BitWidth) + (MinStride - 1);
+
+ // Although End can be a MIN expression we estimate MinEnd considering only
+ // the case End = RHS. This is safe because in the other case (Start - End)
+ // is zero, leading to a zero maximum backedge taken count.
+ APInt MinEnd =
+ IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
+ : APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
+
+ const SCEV *ConstantMaxBECount =
+ isa<SCEVConstant>(BECount)
+ ? BECount
+ : getUDivCeilSCEV(getConstant(MaxStart - MinEnd),
+ getConstant(MinStride));
+
+ if (isa<SCEVCouldNotCompute>(ConstantMaxBECount))
+ ConstantMaxBECount = BECount;
+ const SCEV *SymbolicMaxBECount =
+ isa<SCEVCouldNotCompute>(BECount) ? ConstantMaxBECount : BECount;
+
+ return ExitLimit(BECount, ConstantMaxBECount, SymbolicMaxBECount, false,
+ Predicates);
+}
+
+const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
+ ScalarEvolution &SE) const {
+ if (Range.isFullSet()) // Infinite loop.
+ return SE.getCouldNotCompute();
+
+ // If the start is a non-zero constant, shift the range to simplify things.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
+ if (!SC->getValue()->isZero()) {
+ SmallVector<SCEVUse, 4> Operands(operands());
+ Operands[0] = SE.getZero(SC->getType());
+ const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
+ getNoWrapFlags(FlagNW));
+ if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
+ return ShiftedAddRec->getNumIterationsInRange(
+ Range.subtract(SC->getAPInt()), SE);
+ // This is strange and shouldn't happen.
+ return SE.getCouldNotCompute();
+ }
+
+ // The only time we can solve this is when we have all constant indices.
+ // Otherwise, we cannot determine the overflow conditions.
+ if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
+ return SE.getCouldNotCompute();
+
+ // Okay at this point we know that all elements of the chrec are constants and
+ // that the start element is zero.
+
+ // First check to see if the range contains zero. If not, the first
+ // iteration exits.
+ unsigned BitWidth = SE.getTypeSizeInBits(getType());
+ if (!Range.contains(APInt(BitWidth, 0)))
+ return SE.getZero(getType());
+
+ if (isAffine()) {
+ // If this is an affine expression then we have this situation:
+ // Solve {0,+,A} in Range === Ax in Range
+
+ // We know that zero is in the range. If A is positive then we know that
+ // the upper value of the range must be the first possible exit value.
+ // If A is negative then the lower of the range is the last possible loop
+ // value. Also note that we already checked for a full range.
+ APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
+ APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
+
+ // The exit value should be (End+A)/A.
+ APInt ExitVal = (End + A).udiv(A);
+ ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
+
+ // Evaluate at the exit value. If we really did fall out of the valid
+ // range, then we computed our trip count, otherwise wrap around or other
+ // things must have happened.
+ ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
+ if (Range.contains(Val->getValue()))
+ return SE.getCouldNotCompute(); // Something strange happened
+
+ // Ensure that the previous value is in the range.
+ assert(Range.contains(
+ EvaluateConstantChrecAtConstant(this,
+ ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
+ "Linear scev computation is off in a bad way!");
+ return SE.getConstant(ExitValue);
+ }
+
+ if (isQuadratic()) {
+ if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
+ return SE.getConstant(*S);
+ }
+
+ return SE.getCouldNotCompute();
+}
+
+const SCEVAddRecExpr *
+SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
+ assert(getNumOperands() > 1 && "AddRec with zero step?");
+ // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
+ // but in this case we cannot guarantee that the value returned will be an
+ // AddRec because SCEV does not have a fixed point where it stops
+ // simplification: it is legal to return ({rec1} + {rec2}). For example, it
+ // may happen if we reach arithmetic depth limit while simplifying. So we
+ // construct the returned value explicitly.
+ SmallVector<SCEVUse, 3> Ops;
+ // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
+ // (this + Step) is {A+B,+,B+C,+...,+,N}.
+ for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
+ Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
+ // We know that the last operand is not a constant zero (otherwise it would
+ // have been popped out earlier). This guarantees us that if the result has
+ // the same last operand, then it will also not be popped out, meaning that
+ // the returned value will be an AddRec.
+ const SCEV *Last = getOperand(getNumOperands() - 1);
+ assert(!Last->isZero() && "Recurrency with zero step?");
+ Ops.push_back(Last);
+ return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
+ SCEV::FlagAnyWrap));
+}
+
+// Return true when S contains at least an undef value.
+bool ScalarEvolution::containsUndefs(const SCEV *S) const {
+ return SCEVExprContains(
+ S, [](const SCEV *S) { return match(S, m_scev_UndefOrPoison()); });
+}
+
+// Return true when S contains a value that is a nullptr.
+bool ScalarEvolution::containsErasedValue(const SCEV *S) const {
+ return SCEVExprContains(S, [](const SCEV *S) {
+ if (const auto *SU = dyn_cast<SCEVUnknown>(S))
+ return SU->getValue() == nullptr;
+ return false;
+ });
+}
+
+/// Return the size of an element read or written by Inst.
+const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
+ Type *Ty;
+ Type *PtrTy;
+ if (StoreInst *Store = dyn_cast<StoreInst>(Inst)) {
+ Ty = Store->getValueOperand()->getType();
+ PtrTy = Store->getPointerOperandType();
+ } else if (LoadInst *Load = dyn_cast<LoadInst>(Inst)) {
+ Ty = Load->getType();
+ PtrTy = Load->getPointerOperandType();
+ } else {
+ return nullptr;
+ }
+
+ Type *ETy = getEffectiveSCEVType(PtrTy);
+ return getSizeOfExpr(ETy, Ty);
+}
+
+//===----------------------------------------------------------------------===//
+// SCEVCallbackVH Class Implementation
+//===----------------------------------------------------------------------===//
+
+void ScalarEvolution::SCEVCallbackVH::deleted() {
+ assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
+ if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ SE->eraseValueFromMap(getValPtr());
+ // this now dangles!
+}
+
+void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
+ assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
+
+ // Forget all the expressions associated with users of the old value,
+ // so that future queries will recompute the expressions using the new
+ // value.
+ SE->forgetValue(getValPtr());
+ // this now dangles!
+}
+
+ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
+ : CallbackVH(V), SE(se) {}
+
+//===----------------------------------------------------------------------===//
+// ScalarEvolution Class Implementation
+//===----------------------------------------------------------------------===//
+
+ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
+ AssumptionCache &AC, DominatorTree &DT,
+ LoopInfo &LI)
+ : F(F), DL(F.getDataLayout()), TLI(TLI), AC(AC), DT(DT), LI(LI),
+ CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
+ LoopDispositions(64), BlockDispositions(64) {
+ // To use guards for proving predicates, we need to scan every instruction in
+ // relevant basic blocks, and not just terminators. Doing this is a waste of
+ // time if the IR does not actually contain any calls to
+ // @llvm.experimental.guard, so do a quick check and remember this beforehand.
+ //
+ // This pessimizes the case where a pass that preserves ScalarEvolution wants
+ // to _add_ guards to the module when there weren't any before, and wants
+ // ScalarEvolution to optimize based on those guards. For now we prefer to be
+ // efficient in lieu of being smart in that rather obscure case.
+
+ auto *GuardDecl = Intrinsic::getDeclarationIfExists(
+ F.getParent(), Intrinsic::experimental_guard);
+ HasGuards = GuardDecl && !GuardDecl->use_empty();
+}
+
+ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
+ : F(Arg.F), DL(Arg.DL), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC),
+ DT(Arg.DT), LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
+ ValueExprMap(std::move(Arg.ValueExprMap)),
+ PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
+ PendingMerges(std::move(Arg.PendingMerges)),
+ ConstantMultipleCache(std::move(Arg.ConstantMultipleCache)),
+ BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
+ PredicatedBackedgeTakenCounts(
+ std::move(Arg.PredicatedBackedgeTakenCounts)),
+ BECountUsers(std::move(Arg.BECountUsers)),
+ ConstantEvolutionLoopExitValue(
+ std::move(Arg.ConstantEvolutionLoopExitValue)),
+ ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
+ ValuesAtScopesUsers(std::move(Arg.ValuesAtScopesUsers)),
+ LoopDispositions(std::move(Arg.LoopDispositions)),
+ LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
+ BlockDispositions(std::move(Arg.BlockDispositions)),
+ SCEVUsers(std::move(Arg.SCEVUsers)),
+ UnsignedRanges(std::move(Arg.UnsignedRanges)),
+ SignedRanges(std::move(Arg.SignedRanges)),
+ UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
+ UniquePreds(std::move(Arg.UniquePreds)),
+ SCEVAllocator(std::move(Arg.SCEVAllocator)),
+ ConstantSCEVs(std::move(Arg.ConstantSCEVs)),
+ LoopUsers(std::move(Arg.LoopUsers)),
+ PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
+ FirstUnknown(Arg.FirstUnknown) {
+ Arg.FirstUnknown = nullptr;
+}
+
+ScalarEvolution::~ScalarEvolution() {
+ // Iterate through all the SCEVUnknown instances and call their
+ // destructors, so that they release their references to their values.
+ for (SCEVUnknown *U = FirstUnknown; U;) {
+ SCEVUnknown *Tmp = U;
+ U = U->Next;
+ Tmp->~SCEVUnknown();
+ }
+ FirstUnknown = nullptr;
+
+ ExprValueMap.clear();
+ ValueExprMap.clear();
+ HasRecMap.clear();
+ BackedgeTakenCounts.clear();
+ PredicatedBackedgeTakenCounts.clear();
+
+ assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
+ assert(PendingMerges.empty() && "isImpliedViaMerge garbage");
+ assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
+ assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
+}
+
+bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
+ return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
+}
+
+/// When printing a top-level SCEV for trip counts, it's helpful to include
+/// a type for constants which are otherwise hard to disambiguate.
+static void PrintSCEVWithTypeHint(raw_ostream &OS, const SCEV* S) {
+ if (isa<SCEVConstant>(S))
+ OS << *S->getType() << " ";
+ OS << *S;
+}
+
+static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
+ const Loop *L) {
+ // Print all inner loops first
+ for (Loop *I : *L)
+ PrintLoopInfo(OS, SE, I);
+
+ OS << "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+
+ SmallVector<BasicBlock *, 8> ExitingBlocks;
+ L->getExitingBlocks(ExitingBlocks);
+ if (ExitingBlocks.size() != 1)
+ OS << "<multiple exits> ";
+
+ auto *BTC = SE->getBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(BTC)) {
+ OS << "backedge-taken count is ";
+ PrintSCEVWithTypeHint(OS, BTC);
+ } else
+ OS << "Unpredictable backedge-taken count.";
+ OS << "\n";
+
+ if (ExitingBlocks.size() > 1)
+ for (BasicBlock *ExitingBlock : ExitingBlocks) {
+ OS << " exit count for " << ExitingBlock->getName() << ": ";
+ const SCEV *EC = SE->getExitCount(L, ExitingBlock);
+ PrintSCEVWithTypeHint(OS, EC);
+ if (isa<SCEVCouldNotCompute>(EC)) {
+ // Retry with predicates.
+ SmallVector<const SCEVPredicate *> Predicates;
+ EC = SE->getPredicatedExitCount(L, ExitingBlock, &Predicates);
+ if (!isa<SCEVCouldNotCompute>(EC)) {
+ OS << "\n predicated exit count for " << ExitingBlock->getName()
+ << ": ";
+ PrintSCEVWithTypeHint(OS, EC);
+ OS << "\n Predicates:\n";
+ for (const auto *P : Predicates)
+ P->print(OS, 4);
+ }
+ }
+ OS << "\n";
+ }
+
+ OS << "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+
+ auto *ConstantBTC = SE->getConstantMaxBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(ConstantBTC)) {
+ OS << "constant max backedge-taken count is ";
+ PrintSCEVWithTypeHint(OS, ConstantBTC);
+ if (SE->isBackedgeTakenCountMaxOrZero(L))
+ OS << ", actual taken count either this or zero.";
+ } else {
+ OS << "Unpredictable constant max backedge-taken count. ";
+ }
+
+ OS << "\n"
+ "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+
+ auto *SymbolicBTC = SE->getSymbolicMaxBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(SymbolicBTC)) {
+ OS << "symbolic max backedge-taken count is ";
+ PrintSCEVWithTypeHint(OS, SymbolicBTC);
+ if (SE->isBackedgeTakenCountMaxOrZero(L))
+ OS << ", actual taken count either this or zero.";
+ } else {
+ OS << "Unpredictable symbolic max backedge-taken count. ";
+ }
+ OS << "\n";
+
+ if (ExitingBlocks.size() > 1)
+ for (BasicBlock *ExitingBlock : ExitingBlocks) {
+ OS << " symbolic max exit count for " << ExitingBlock->getName() << ": ";
+ auto *ExitBTC = SE->getExitCount(L, ExitingBlock,
+ ScalarEvolution::SymbolicMaximum);
+ PrintSCEVWithTypeHint(OS, ExitBTC);
+ if (isa<SCEVCouldNotCompute>(ExitBTC)) {
+ // Retry with predicates.
+ SmallVector<const SCEVPredicate *> Predicates;
+ ExitBTC = SE->getPredicatedExitCount(L, ExitingBlock, &Predicates,
+ ScalarEvolution::SymbolicMaximum);
+ if (!isa<SCEVCouldNotCompute>(ExitBTC)) {
+ OS << "\n predicated symbolic max exit count for "
+ << ExitingBlock->getName() << ": ";
+ PrintSCEVWithTypeHint(OS, ExitBTC);
+ OS << "\n Predicates:\n";
+ for (const auto *P : Predicates)
+ P->print(OS, 4);
+ }
+ }
+ OS << "\n";
+ }
+
+ SmallVector<const SCEVPredicate *, 4> Preds;
+ auto *PBT = SE->getPredicatedBackedgeTakenCount(L, Preds);
+ if (PBT != BTC) {
+ OS << "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+ if (!isa<SCEVCouldNotCompute>(PBT)) {
+ OS << "Predicated backedge-taken count is ";
+ PrintSCEVWithTypeHint(OS, PBT);
+ } else
+ OS << "Unpredictable predicated backedge-taken count.";
+ OS << "\n";
+ OS << " Predicates:\n";
+ for (const auto *P : Preds)
+ P->print(OS, 4);
+ }
+ Preds.clear();
+
+ auto *PredConstantMax =
+ SE->getPredicatedConstantMaxBackedgeTakenCount(L, Preds);
+ if (PredConstantMax != ConstantBTC) {
+ OS << "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+ if (!isa<SCEVCouldNotCompute>(PredConstantMax)) {
+ OS << "Predicated constant max backedge-taken count is ";
+ PrintSCEVWithTypeHint(OS, PredConstantMax);
+ } else
+ OS << "Unpredictable predicated constant max backedge-taken count.";
+ OS << "\n";
+ OS << " Predicates:\n";
+ for (const auto *P : Preds)
+ P->print(OS, 4);
+ }
+ Preds.clear();
+
+ auto *PredSymbolicMax =
+ SE->getPredicatedSymbolicMaxBackedgeTakenCount(L, Preds);
+ if (SymbolicBTC != PredSymbolicMax) {
+ OS << "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+ if (!isa<SCEVCouldNotCompute>(PredSymbolicMax)) {
+ OS << "Predicated symbolic max backedge-taken count is ";
+ PrintSCEVWithTypeHint(OS, PredSymbolicMax);
+ } else
+ OS << "Unpredictable predicated symbolic max backedge-taken count.";
+ OS << "\n";
+ OS << " Predicates:\n";
+ for (const auto *P : Preds)
+ P->print(OS, 4);
+ }
+
+ if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
+ OS << "Loop ";
+ L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": ";
+ OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
+ }
+}
+
+namespace llvm {
+// Note: these overloaded operators need to be in the llvm namespace for them
+// to be resolved correctly. If we put them outside the llvm namespace, the
+//
+// OS << ": " << SE.getLoopDisposition(SV, InnerL);
+//
+// code below "breaks" and start printing raw enum values as opposed to the
+// string values.
+static raw_ostream &operator<<(raw_ostream &OS,
+ ScalarEvolution::LoopDisposition LD) {
+ switch (LD) {
+ case ScalarEvolution::LoopVariant:
+ OS << "Variant";
+ break;
+ case ScalarEvolution::LoopInvariant:
+ OS << "Invariant";
+ break;
+ case ScalarEvolution::LoopUniform:
+ OS << "Uniform";
+ break;
+ case ScalarEvolution::LoopComputable:
+ OS << "Computable";
+ break;
+ }
+ return OS;
+}
+
+static raw_ostream &operator<<(raw_ostream &OS,
+ llvm::ScalarEvolution::BlockDisposition BD) {
+ switch (BD) {
+ case ScalarEvolution::DoesNotDominateBlock:
+ OS << "DoesNotDominate";
+ break;
+ case ScalarEvolution::DominatesBlock:
+ OS << "Dominates";
+ break;
+ case ScalarEvolution::ProperlyDominatesBlock:
+ OS << "ProperlyDominates";
+ break;
+ }
+ return OS;
+}
+} // namespace llvm
+
+void ScalarEvolution::print(raw_ostream &OS) const {
+ // ScalarEvolution's implementation of the print method is to print
+ // out SCEV values of all instructions that are interesting. Doing
+ // this potentially causes it to create new SCEV objects though,
+ // which technically conflicts with the const qualifier. This isn't
+ // observable from outside the class though, so casting away the
+ // const isn't dangerous.
+ ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
+
+ if (ClassifyExpressions) {
+ OS << "Classifying expressions for: ";
+ F.printAsOperand(OS, /*PrintType=*/false);
+ OS << "\n";
+ for (Instruction &I : instructions(F))
+ if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
+ OS << I << '\n';
+ OS << " --> ";
+ const SCEV *SV = SE.getSCEV(&I);
+ SV->print(OS);
+ if (!isa<SCEVCouldNotCompute>(SV)) {
+ OS << " U: ";
+ SE.getUnsignedRange(SV).print(OS);
+ OS << " S: ";
+ SE.getSignedRange(SV).print(OS);
+ }
+
+ const Loop *L = LI.getLoopFor(I.getParent());
+
+ const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
+ if (AtUse != SV) {
+ OS << " --> ";
+ AtUse->print(OS);
+ if (!isa<SCEVCouldNotCompute>(AtUse)) {
+ OS << " U: ";
+ SE.getUnsignedRange(AtUse).print(OS);
+ OS << " S: ";
+ SE.getSignedRange(AtUse).print(OS);
+ }
+ }
+
+ if (L) {
+ OS << "\t\t" "Exits: ";
+ const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
+ if (!SE.isLoopInvariant(ExitValue, L)) {
+ OS << "<<Unknown>>";
+ } else {
+ OS << *ExitValue;
+ }
+
+ ListSeparator LS(", ", "\t\tLoopDispositions: { ");
+ for (const auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
+ OS << LS;
+ Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": " << SE.getLoopDisposition(SV, Iter);
+ }
+
+ for (const auto *InnerL : depth_first(L)) {
+ if (InnerL == L)
+ continue;
+ OS << LS;
+ InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
+ OS << ": " << SE.getLoopDisposition(SV, InnerL);
+ }
+
+ OS << " }";
+ }
+
+ OS << "\n";
+ }
+ }
+
+ OS << "Determining loop execution counts for: ";
+ F.printAsOperand(OS, /*PrintType=*/false);
+ OS << "\n";
+ for (Loop *I : LI)
+ PrintLoopInfo(OS, &SE, I);
+}
+
+ScalarEvolution::LoopDisposition
+ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
+ auto &Values = LoopDispositions[S];
+ for (auto &V : Values) {
+ if (V.getPointer() == L)
+ return V.getInt();
+ }
+ Values.emplace_back(L, LoopVariant);
+ LoopDisposition D = computeLoopDisposition(S, L);
+ auto &Values2 = LoopDispositions[S];
+ for (auto &V : llvm::reverse(Values2)) {
+ if (V.getPointer() == L) {
+ V.setInt(D);
+ break;
+ }
+ }
+ return D;
+}
+
+ScalarEvolution::LoopDisposition
+ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
+ switch (S->getSCEVType()) {
+ case scConstant:
+ case scVScale:
+ return LoopInvariant;
+ case scAddRecExpr: {
+ const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
+
+ // If L is the addrec's loop, it's computable.
+ if (AR->getLoop() == L)
+ return LoopComputable;
+
+ // Add recurrences are never invariant in the function-body (null loop).
+ if (!L)
+ return LoopVariant;
+
+ // Everything that is not defined at loop entry is variant.
+ if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader())) {
+ if (L->contains(AR->getLoop()) &&
+ llvm::all_of(AR->operands(),
+ [&](const SCEV *Op) { return isLoopUniform(Op, L); }))
+ return LoopUniform;
+
+ return LoopVariant;
+ }
+ assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
+ " dominate the contained loop's header?");
+
+ // This recurrence is invariant w.r.t. L if AR's loop contains L.
+ if (AR->getLoop()->contains(L))
+ return LoopInvariant;
+
+ // This recurrence is variant w.r.t. L if any of its operands
+ // are variant.
+ for (SCEVUse Op : AR->operands())
+ if (!isLoopInvariant(Op, L))
+ return LoopVariant;
+
+ // Otherwise it's loop-invariant.
+ return LoopInvariant;
+ }
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUDivExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr: {
+ bool HasVarying = false;
+ bool HasUniform = false;
+ for (SCEVUse Op : S->operands()) {
+ LoopDisposition D = getLoopDisposition(Op, L);
+ if (D == LoopVariant)
+ return LoopVariant;
+ if (D == LoopComputable)
+ HasVarying = true;
+ if (D == LoopUniform)
+ HasUniform = true;
+ }
+ return HasVarying ? (HasUniform ? LoopVariant : LoopComputable)
+ : (HasUniform ? LoopUniform : LoopInvariant);
+ }
+ case scUnknown:
+ // All non-instruction values are loop invariant. All instructions are loop
+ // invariant if they are not contained in the specified loop.
+ // Instructions are never considered invariant in the function body
+ // (null loop) because they are defined within the "loop".
+ if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
+ return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
+ return LoopInvariant;
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+bool ScalarEvolution::isLoopUniform(const SCEV *S, const Loop *L) {
+ LoopDisposition D = getLoopDisposition(S, L);
+ return D == LoopUniform || D == LoopInvariant;
+}
+
+bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
+ return getLoopDisposition(S, L) == LoopInvariant;
+}
+
+bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
+ return getLoopDisposition(S, L) == LoopComputable;
+}
+
+ScalarEvolution::BlockDisposition
+ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
+ auto &Values = BlockDispositions[S];
+ for (auto &V : Values) {
+ if (V.getPointer() == BB)
+ return V.getInt();
+ }
+ Values.emplace_back(BB, DoesNotDominateBlock);
+ BlockDisposition D = computeBlockDisposition(S, BB);
+ auto &Values2 = BlockDispositions[S];
+ for (auto &V : llvm::reverse(Values2)) {
+ if (V.getPointer() == BB) {
+ V.setInt(D);
+ break;
+ }
+ }
+ return D;
+}
+
+ScalarEvolution::BlockDisposition
+ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
+ switch (S->getSCEVType()) {
+ case scConstant:
+ case scVScale:
+ return ProperlyDominatesBlock;
+ case scAddRecExpr: {
+ // This uses a "dominates" query instead of "properly dominates" query
+ // to test for proper dominance too, because the instruction which
+ // produces the addrec's value is a PHI, and a PHI effectively properly
+ // dominates its entire containing block.
+ const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
+ if (!DT.dominates(AR->getLoop()->getHeader(), BB))
+ return DoesNotDominateBlock;
+
+ // Fall through into SCEVNAryExpr handling.
+ [[fallthrough]];
+ }
+ case scTruncate:
+ case scZeroExtend:
+ case scSignExtend:
+ case scPtrToAddr:
+ case scAddExpr:
+ case scMulExpr:
+ case scUDivExpr:
+ case scUMaxExpr:
+ case scSMaxExpr:
+ case scUMinExpr:
+ case scSMinExpr:
+ case scSequentialUMinExpr: {
+ bool Proper = true;
+ for (const SCEV *NAryOp : S->operands()) {
+ BlockDisposition D = getBlockDisposition(NAryOp, BB);
+ if (D == DoesNotDominateBlock)
+ return DoesNotDominateBlock;
+ if (D == DominatesBlock)
+ Proper = false;
+ }
+ return Proper ? ProperlyDominatesBlock : DominatesBlock;
+ }
+ case scUnknown:
+ if (Instruction *I =
+ dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
+ if (I->getParent() == BB)
+ return DominatesBlock;
+ if (DT.properlyDominates(I->getParent(), BB))
+ return ProperlyDominatesBlock;
+ return DoesNotDominateBlock;
+ }
+ return ProperlyDominatesBlock;
+ case scCouldNotCompute:
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ }
+ llvm_unreachable("Unknown SCEV kind!");
+}
+
+bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
+ return getBlockDisposition(S, BB) >= DominatesBlock;
+}
+
+bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
+ return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
+}
+
+bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
+ return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
+}
+
+void ScalarEvolution::forgetBackedgeTakenCounts(const Loop *L,
+ bool Predicated) {
+ auto &BECounts =
+ Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
+ auto It = BECounts.find(L);
+ if (It != BECounts.end()) {
+ for (const ExitNotTakenInfo &ENT : It->second.ExitNotTaken) {
+ for (const SCEV *S : {ENT.ExactNotTaken, ENT.SymbolicMaxNotTaken}) {
+ if (!isa<SCEVConstant>(S)) {
+ auto UserIt = BECountUsers.find(S);
+ assert(UserIt != BECountUsers.end());
+ UserIt->second.erase({L, Predicated});
+ }
+ }
+ }
+ BECounts.erase(It);
+ }
+}
+
+void ScalarEvolution::forgetMemoizedResults(ArrayRef<SCEVUse> SCEVs) {
+ SmallPtrSet<const SCEV *, 8> ToForget(llvm::from_range, SCEVs);
+ SmallVector<SCEVUse, 8> Worklist(ToForget.begin(), ToForget.end());
+
+ while (!Worklist.empty()) {
+ const SCEV *Curr = Worklist.pop_back_val();
+ auto Users = SCEVUsers.find(Curr);
+ if (Users != SCEVUsers.end())
+ for (const auto *User : Users->second)
+ if (ToForget.insert(User).second)
+ Worklist.push_back(User);
+ }
+
+ for (const auto *S : ToForget)
+ forgetMemoizedResultsImpl(S);
+
+ PredicatedSCEVRewrites.remove_if(
+ [&](const auto &Entry) { return ToForget.count(Entry.first.first); });
+}
+
+void ScalarEvolution::forgetMemoizedResultsImpl(const SCEV *S) {
+ LoopDispositions.erase(S);
+ BlockDispositions.erase(S);
+ UnsignedRanges.erase(S);
+ SignedRanges.erase(S);
+ HasRecMap.erase(S);
+ ConstantMultipleCache.erase(S);
+
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(S)) {
+ UnsignedWrapViaInductionTried.erase(AR);
+ SignedWrapViaInductionTried.erase(AR);
+ }
+
+ auto ExprIt = ExprValueMap.find(S);
+ if (ExprIt != ExprValueMap.end()) {
+ for (Value *V : ExprIt->second) {
+ auto ValueIt = ValueExprMap.find_as(V);
+ if (ValueIt != ValueExprMap.end())
+ ValueExprMap.erase(ValueIt);
+ }
+ ExprValueMap.erase(ExprIt);
+ }
+
+ auto ScopeIt = ValuesAtScopes.find(S);
+ if (ScopeIt != ValuesAtScopes.end()) {
+ for (const auto &Pair : ScopeIt->second)
+ if (!isa_and_nonnull<SCEVConstant>(Pair.second))
+ llvm::erase(ValuesAtScopesUsers[Pair.second],
+ std::make_pair(Pair.first, S));
+ ValuesAtScopes.erase(ScopeIt);
+ }
+
+ auto ScopeUserIt = ValuesAtScopesUsers.find(S);
+ if (ScopeUserIt != ValuesAtScopesUsers.end()) {
+ for (const auto &Pair : ScopeUserIt->second)
+ llvm::erase(ValuesAtScopes[Pair.second], std::make_pair(Pair.first, S));
+ ValuesAtScopesUsers.erase(ScopeUserIt);
+ }
+
+ auto BEUsersIt = BECountUsers.find(S);
+ if (BEUsersIt != BECountUsers.end()) {
+ // Work on a copy, as forgetBackedgeTakenCounts() will modify the original.
+ auto Copy = BEUsersIt->second;
+ for (const auto &Pair : Copy)
+ forgetBackedgeTakenCounts(Pair.getPointer(), Pair.getInt());
+ BECountUsers.erase(BEUsersIt);
+ }
+
+ auto FoldUser = FoldCacheUser.find(S);
+ if (FoldUser != FoldCacheUser.end())
+ for (auto &KV : FoldUser->second)
+ FoldCache.erase(KV);
+ FoldCacheUser.erase(S);
+}
+
+void
+ScalarEvolution::getUsedLoops(const SCEV *S,
+ SmallPtrSetImpl<const Loop *> &LoopsUsed) {
+ struct FindUsedLoops {
+ FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
+ : LoopsUsed(LoopsUsed) {}
+ SmallPtrSetImpl<const Loop *> &LoopsUsed;
+ bool follow(const SCEV *S) {
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
+ LoopsUsed.insert(AR->getLoop());
+ return true;
+ }
+
+ bool isDone() const { return false; }
+ };
+
+ FindUsedLoops F(LoopsUsed);
+ SCEVTraversal<FindUsedLoops>(F).visitAll(S);
+}
+
+void ScalarEvolution::getReachableBlocks(
+ SmallPtrSetImpl<BasicBlock *> &Reachable, Function &F) {
+ SmallVector<BasicBlock *> Worklist;
+ Worklist.push_back(&F.getEntryBlock());
+ while (!Worklist.empty()) {
+ BasicBlock *BB = Worklist.pop_back_val();
+ if (!Reachable.insert(BB).second)
+ continue;
+
+ Value *Cond;
+ BasicBlock *TrueBB, *FalseBB;
+ if (match(BB->getTerminator(), m_Br(m_Value(Cond), m_BasicBlock(TrueBB),
+ m_BasicBlock(FalseBB)))) {
+ if (auto *C = dyn_cast<ConstantInt>(Cond)) {
+ Worklist.push_back(C->isOne() ? TrueBB : FalseBB);
+ continue;
+ }
+
+ if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) {
+ const SCEV *L = getSCEV(Cmp->getOperand(0));
+ const SCEV *R = getSCEV(Cmp->getOperand(1));
+ if (isKnownPredicateViaConstantRanges(Cmp->getCmpPredicate(), L, R)) {
+ Worklist.push_back(TrueBB);
+ continue;
+ }
+ if (isKnownPredicateViaConstantRanges(Cmp->getInverseCmpPredicate(), L,
+ R)) {
+ Worklist.push_back(FalseBB);
+ continue;
+ }
+ }
+ }
+
+ append_range(Worklist, successors(BB));
+ }
+}
+
+void ScalarEvolution::verify() const {
+ ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
+ ScalarEvolution SE2(F, TLI, AC, DT, LI);
+
+ SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
+
+ // Map's SCEV expressions from one ScalarEvolution "universe" to another.
+ struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
+ SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
+
+ const SCEV *visitConstant(const SCEVConstant *Constant) {
+ return SE.getConstant(Constant->getAPInt());
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ return SE.getUnknown(Expr->getValue());
+ }
+
+ const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
+ return SE.getCouldNotCompute();
+ }
+ };
+
+ SCEVMapper SCM(SE2);
+ SmallPtrSet<BasicBlock *, 16> ReachableBlocks;
+ SE2.getReachableBlocks(ReachableBlocks, F);
+
+ auto GetDelta = [&](const SCEV *Old, const SCEV *New) -> const SCEV * {
+ if (containsUndefs(Old) || containsUndefs(New)) {
+ // SCEV treats "undef" as an unknown but consistent value (i.e. it does
+ // not propagate undef aggressively). This means we can (and do) fail
+ // verification in cases where a transform makes a value go from "undef"
+ // to "undef+1" (say). The transform is fine, since in both cases the
+ // result is "undef", but SCEV thinks the value increased by 1.
+ return nullptr;
+ }
+
+ // Unless VerifySCEVStrict is set, we only compare constant deltas.
+ const SCEV *Delta = SE2.getMinusSCEV(Old, New);
+ if (!VerifySCEVStrict && !isa<SCEVConstant>(Delta))
+ return nullptr;
+
+ return Delta;
+ };
+
+ while (!LoopStack.empty()) {
+ auto *L = LoopStack.pop_back_val();
+ llvm::append_range(LoopStack, *L);
+
+ // Only verify BECounts in reachable loops. For an unreachable loop,
+ // any BECount is legal.
+ if (!ReachableBlocks.contains(L->getHeader()))
+ continue;
+
+ // Only verify cached BECounts. Computing new BECounts may change the
+ // results of subsequent SCEV uses.
+ auto It = BackedgeTakenCounts.find(L);
+ if (It == BackedgeTakenCounts.end())
+ continue;
+
+ auto *CurBECount =
+ SCM.visit(It->second.getExact(L, const_cast<ScalarEvolution *>(this)));
+ auto *NewBECount = SE2.getBackedgeTakenCount(L);
+
+ if (CurBECount == SE2.getCouldNotCompute() ||
+ NewBECount == SE2.getCouldNotCompute()) {
+ // NB! This situation is legal, but is very suspicious -- whatever pass
+ // change the loop to make a trip count go from could not compute to
+ // computable or vice-versa *should have* invalidated SCEV. However, we
+ // choose not to assert here (for now) since we don't want false
+ // positives.
+ continue;
+ }
+
+ if (SE.getTypeSizeInBits(CurBECount->getType()) >
+ SE.getTypeSizeInBits(NewBECount->getType()))
+ NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
+ else if (SE.getTypeSizeInBits(CurBECount->getType()) <
+ SE.getTypeSizeInBits(NewBECount->getType()))
+ CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
+
+ const SCEV *Delta = GetDelta(CurBECount, NewBECount);
+ if (Delta && !Delta->isZero()) {
+ dbgs() << "Trip Count for " << *L << " Changed!\n";
+ dbgs() << "Old: " << *CurBECount << "\n";
+ dbgs() << "New: " << *NewBECount << "\n";
+ dbgs() << "Delta: " << *Delta << "\n";
+ std::abort();
+ }
+ }
+
+ // Collect all valid loops currently in LoopInfo.
+ SmallPtrSet<Loop *, 32> ValidLoops;
+ SmallVector<Loop *, 32> Worklist(LI.begin(), LI.end());
+ while (!Worklist.empty()) {
+ Loop *L = Worklist.pop_back_val();
+ if (ValidLoops.insert(L).second)
+ Worklist.append(L->begin(), L->end());
+ }
+ for (const auto &KV : ValueExprMap) {
+#ifndef NDEBUG
+ // Check for SCEV expressions referencing invalid/deleted loops.
+ if (auto *AR = dyn_cast<SCEVAddRecExpr>(KV.second)) {
+ assert(ValidLoops.contains(AR->getLoop()) &&
+ "AddRec references invalid loop");
+ }
+#endif
+
+ // Check that the value is also part of the reverse map.
+ auto It = ExprValueMap.find(KV.second);
+ if (It == ExprValueMap.end() || !It->second.contains(KV.first)) {
+ dbgs() << "Value " << *KV.first
+ << " is in ValueExprMap but not in ExprValueMap\n";
+ std::abort();
+ }
+
+ if (auto *I = dyn_cast<Instruction>(&*KV.first)) {
+ if (!ReachableBlocks.contains(I->getParent()))
+ continue;
+ const SCEV *OldSCEV = SCM.visit(KV.second);
+ const SCEV *NewSCEV = SE2.getSCEV(I);
+ const SCEV *Delta = GetDelta(OldSCEV, NewSCEV);
+ if (Delta && !Delta->isZero()) {
+ dbgs() << "SCEV for value " << *I << " changed!\n"
+ << "Old: " << *OldSCEV << "\n"
+ << "New: " << *NewSCEV << "\n"
+ << "Delta: " << *Delta << "\n";
+ std::abort();
+ }
+ }
+ }
+
+ for (const auto &KV : ExprValueMap) {
+ for (Value *V : KV.second) {
+ const SCEV *S = ValueExprMap.lookup(V);
+ if (!S) {
+ dbgs() << "Value " << *V
+ << " is in ExprValueMap but not in ValueExprMap\n";
+ std::abort();
+ }
+ if (S != KV.first) {
+ dbgs() << "Value " << *V << " mapped to " << *S << " rather than "
+ << *KV.first << "\n";
+ std::abort();
+ }
+ }
+ }
+
+ // Verify integrity of SCEV users.
+ for (const auto &S : UniqueSCEVs) {
+ for (SCEVUse Op : S.operands()) {
+ // We do not store dependencies of constants.
+ if (isa<SCEVConstant>(Op))
+ continue;
+ auto It = SCEVUsers.find(Op);
+ if (It != SCEVUsers.end() && It->second.count(&S))
+ continue;
+ dbgs() << "Use of operand " << *Op << " by user " << S
+ << " is not being tracked!\n";
+ std::abort();
+ }
+ }
+
+ // Verify integrity of ValuesAtScopes users.
+ for (const auto &ValueAndVec : ValuesAtScopes) {
+ const SCEV *Value = ValueAndVec.first;
+ for (const auto &LoopAndValueAtScope : ValueAndVec.second) {
+ const Loop *L = LoopAndValueAtScope.first;
+ const SCEV *ValueAtScope = LoopAndValueAtScope.second;
+ if (!isa<SCEVConstant>(ValueAtScope)) {
+ auto It = ValuesAtScopesUsers.find(ValueAtScope);
+ if (It != ValuesAtScopesUsers.end() &&
+ is_contained(It->second, std::make_pair(L, Value)))
+ continue;
+ dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
+ << *ValueAtScope << " missing in ValuesAtScopesUsers\n";
+ std::abort();
+ }
+ }
+ }
+
+ for (const auto &ValueAtScopeAndVec : ValuesAtScopesUsers) {
+ const SCEV *ValueAtScope = ValueAtScopeAndVec.first;
+ for (const auto &LoopAndValue : ValueAtScopeAndVec.second) {
+ const Loop *L = LoopAndValue.first;
+ const SCEV *Value = LoopAndValue.second;
+ assert(!isa<SCEVConstant>(Value));
+ auto It = ValuesAtScopes.find(Value);
+ if (It != ValuesAtScopes.end() &&
+ is_contained(It->second, std::make_pair(L, ValueAtScope)))
+ continue;
+ dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
+ << *ValueAtScope << " missing in ValuesAtScopes\n";
+ std::abort();
+ }
+ }
+
+ // Verify integrity of BECountUsers.
+ auto VerifyBECountUsers = [&](bool Predicated) {
+ auto &BECounts =
+ Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
+ for (const auto &LoopAndBEInfo : BECounts) {
+ for (const ExitNotTakenInfo &ENT : LoopAndBEInfo.second.ExitNotTaken) {
+ for (const SCEV *S : {ENT.ExactNotTaken, ENT.SymbolicMaxNotTaken}) {
+ if (!isa<SCEVConstant>(S)) {
+ auto UserIt = BECountUsers.find(S);
+ if (UserIt != BECountUsers.end() &&
+ UserIt->second.contains({ LoopAndBEInfo.first, Predicated }))
+ continue;
+ dbgs() << "Value " << *S << " for loop " << *LoopAndBEInfo.first
+ << " missing from BECountUsers\n";
+ std::abort();
+ }
+ }
+ }
+ }
+ };
+ VerifyBECountUsers(/* Predicated */ false);
+ VerifyBECountUsers(/* Predicated */ true);
+
+ // Verify intergity of loop disposition cache.
+ for (auto &[S, Values] : LoopDispositions) {
+ for (auto [Loop, CachedDisposition] : Values) {
+ const auto RecomputedDisposition = SE2.getLoopDisposition(S, Loop);
+ if (CachedDisposition != RecomputedDisposition) {
+ dbgs() << "Cached disposition of " << *S << " for loop " << *Loop
+ << " is incorrect: cached " << CachedDisposition << ", actual "
+ << RecomputedDisposition << "\n";
+ std::abort();
+ }
+ }
+ }
+
+ // Verify integrity of the block disposition cache.
+ for (auto &[S, Values] : BlockDispositions) {
+ for (auto [BB, CachedDisposition] : Values) {
+ const auto RecomputedDisposition = SE2.getBlockDisposition(S, BB);
+ if (CachedDisposition != RecomputedDisposition) {
+ dbgs() << "Cached disposition of " << *S << " for block %"
+ << BB->getName() << " is incorrect: cached " << CachedDisposition
+ << ", actual " << RecomputedDisposition << "\n";
+ std::abort();
+ }
+ }
+ }
+
+ // Verify FoldCache/FoldCacheUser caches.
+ for (auto [FoldID, Expr] : FoldCache) {
+ auto I = FoldCacheUser.find(Expr);
+ if (I == FoldCacheUser.end()) {
+ dbgs() << "Missing entry in FoldCacheUser for cached expression " << *Expr
+ << "!\n";
+ std::abort();
+ }
+ if (!is_contained(I->second, FoldID)) {
+ dbgs() << "Missing FoldID in cached users of " << *Expr << "!\n";
+ std::abort();
+ }
+ }
+ for (auto [Expr, IDs] : FoldCacheUser) {
+ for (auto &FoldID : IDs) {
+ const SCEV *S = FoldCache.lookup(FoldID);
+ if (!S) {
+ dbgs() << "Missing entry in FoldCache for expression " << *Expr
+ << "!\n";
+ std::abort();
+ }
+ if (S != Expr) {
+ dbgs() << "Entry in FoldCache doesn't match FoldCacheUser: " << *S
+ << " != " << *Expr << "!\n";
+ std::abort();
+ }
+ }
+ }
+
+ // Verify that ConstantMultipleCache computations are correct. We check that
+ // cached multiples and recomputed multiples are multiples of each other to
+ // verify correctness. It is possible that a recomputed multiple is different
+ // from the cached multiple due to strengthened no wrap flags or changes in
+ // KnownBits computations.
+ for (auto [S, Multiple] : ConstantMultipleCache) {
+ APInt RecomputedMultiple = SE2.getConstantMultiple(S);
+ if ((Multiple != 0 && RecomputedMultiple != 0 &&
+ Multiple.urem(RecomputedMultiple) != 0 &&
+ RecomputedMultiple.urem(Multiple) != 0)) {
+ dbgs() << "Incorrect cached computation in ConstantMultipleCache for "
+ << *S << " : Computed " << RecomputedMultiple
+ << " but cache contains " << Multiple << "!\n";
+ std::abort();
+ }
+ }
+}
+
+bool ScalarEvolution::invalidate(
+ Function &F, const PreservedAnalyses &PA,
+ FunctionAnalysisManager::Invalidator &Inv) {
+ // Invalidate the ScalarEvolution object whenever it isn't preserved or one
+ // of its dependencies is invalidated.
+ auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
+ return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
+ Inv.invalidate<AssumptionAnalysis>(F, PA) ||
+ Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
+ Inv.invalidate<LoopAnalysis>(F, PA);
+}
+
+AnalysisKey ScalarEvolutionAnalysis::Key;
+
+ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
+ FunctionAnalysisManager &AM) {
+ auto &TLI = AM.getResult<TargetLibraryAnalysis>(F);
+ auto &AC = AM.getResult<AssumptionAnalysis>(F);
+ auto &DT = AM.getResult<DominatorTreeAnalysis>(F);
+ auto &LI = AM.getResult<LoopAnalysis>(F);
+ return ScalarEvolution(F, TLI, AC, DT, LI);
+}
+
+PreservedAnalyses
+ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
+ AM.getResult<ScalarEvolutionAnalysis>(F).verify();
+ return PreservedAnalyses::all();
+}
+
+PreservedAnalyses
+ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
+ // For compatibility with opt's -analyze feature under legacy pass manager
+ // which was not ported to NPM. This keeps tests using
+ // update_analyze_test_checks.py working.
+ OS << "Printing analysis 'Scalar Evolution Analysis' for function '"
+ << F.getName() << "':\n";
+ AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
+ return PreservedAnalyses::all();
+}
+
+INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
+ "Scalar Evolution Analysis", false, true)
+INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
+INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
+INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
+INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
+INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
+ "Scalar Evolution Analysis", false, true)
+
+char ScalarEvolutionWrapperPass::ID = 0;
+
+ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {}
+
+bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
+ SE.reset(new ScalarEvolution(
+ F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
+ getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
+ getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
+ getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
+ return false;
+}
+
+void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
+
+void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
+ SE->print(OS);
+}
+
+void ScalarEvolutionWrapperPass::verifyAnalysis() const {
+ if (!VerifySCEV)
+ return;
+
+ SE->verify();
+}
+
+void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
+ AU.setPreservesAll();
+ AU.addRequiredTransitive<AssumptionCacheTracker>();
+ AU.addRequiredTransitive<LoopInfoWrapperPass>();
+ AU.addRequiredTransitive<DominatorTreeWrapperPass>();
+ AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
+}
+
+const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
+ const SCEV *RHS) {
+ return getComparePredicate(ICmpInst::ICMP_EQ, LHS, RHS);
+}
+
+const SCEVPredicate *
+ScalarEvolution::getComparePredicate(const ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS) {
+ FoldingSetNodeID ID;
+ assert(LHS->getType() == RHS->getType() &&
+ "Type mismatch between LHS and RHS");
+ // Unique this node based on the arguments
+ ID.AddInteger(SCEVPredicate::P_Compare);
+ ID.AddInteger(Pred);
+ ID.AddPointer(LHS);
+ ID.AddPointer(RHS);
+ void *IP = nullptr;
+ if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
+ return S;
+ SCEVComparePredicate *Eq = new (SCEVAllocator)
+ SCEVComparePredicate(ID.Intern(SCEVAllocator), Pred, LHS, RHS);
+ UniquePreds.InsertNode(Eq, IP);
+ return Eq;
+}
+
+const SCEVPredicate *ScalarEvolution::getWrapPredicate(
+ const SCEVAddRecExpr *AR,
+ SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
+ FoldingSetNodeID ID;
+ // Unique this node based on the arguments
+ ID.AddInteger(SCEVPredicate::P_Wrap);
+ ID.AddPointer(AR);
+ ID.AddInteger(AddedFlags);
+ void *IP = nullptr;
+ if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
+ return S;
+ auto *OF = new (SCEVAllocator)
+ SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
+ UniquePreds.InsertNode(OF, IP);
+ return OF;
+}
+
+namespace {
+
+class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
+public:
+
+ /// Rewrites \p S in the context of a loop L and the SCEV predication
+ /// infrastructure.
+ ///
+ /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
+ /// equivalences present in \p Pred.
+ ///
+ /// If \p NewPreds is non-null, rewrite is free to add further predicates to
+ /// \p NewPreds such that the result will be an AddRecExpr.
+ static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
+ SmallVectorImpl<const SCEVPredicate *> *NewPreds,
+ const SCEVPredicate *Pred) {
+ SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
+ return Rewriter.visit(S);
+ }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ if (Pred) {
+ if (auto *U = dyn_cast<SCEVUnionPredicate>(Pred)) {
+ for (const auto *Pred : U->getPredicates())
+ if (const auto *IPred = dyn_cast<SCEVComparePredicate>(Pred))
+ if (IPred->getLHS() == Expr &&
+ IPred->getPredicate() == ICmpInst::ICMP_EQ)
+ return IPred->getRHS();
+ } else if (const auto *IPred = dyn_cast<SCEVComparePredicate>(Pred)) {
+ if (IPred->getLHS() == Expr &&
+ IPred->getPredicate() == ICmpInst::ICMP_EQ)
+ return IPred->getRHS();
+ }
+ }
+ return convertToAddRecWithPreds(Expr);
+ }
+
+ const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
+ const SCEV *Operand = visit(Expr->getOperand());
+ const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
+ if (AR && AR->getLoop() == L && AR->isAffine()) {
+ // This couldn't be folded because the operand didn't have the nuw
+ // flag. Add the nusw flag as an assumption that we could make.
+ const SCEV *Step = AR->getStepRecurrence(SE);
+ Type *Ty = Expr->getType();
+ if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
+ return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
+ SE.getSignExtendExpr(Step, Ty), L,
+ AR->getNoWrapFlags());
+ }
+ return SE.getZeroExtendExpr(Operand, Expr->getType());
+ }
+
+ const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
+ const SCEV *Operand = visit(Expr->getOperand());
+ const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
+ if (AR && AR->getLoop() == L && AR->isAffine()) {
+ // This couldn't be folded because the operand didn't have the nsw
+ // flag. Add the nssw flag as an assumption that we could make.
+ const SCEV *Step = AR->getStepRecurrence(SE);
+ Type *Ty = Expr->getType();
+ if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
+ return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
+ SE.getSignExtendExpr(Step, Ty), L,
+ AR->getNoWrapFlags());
+ }
+ return SE.getSignExtendExpr(Operand, Expr->getType());
+ }
+
+private:
+ explicit SCEVPredicateRewriter(
+ const Loop *L, ScalarEvolution &SE,
+ SmallVectorImpl<const SCEVPredicate *> *NewPreds,
+ const SCEVPredicate *Pred)
+ : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
+
+ bool addOverflowAssumption(const SCEVPredicate *P) {
+ if (!NewPreds) {
+ // Check if we've already made this assumption.
+ return Pred && Pred->implies(P, SE);
+ }
+ NewPreds->push_back(P);
+ return true;
+ }
+
+ bool addOverflowAssumption(const SCEVAddRecExpr *AR,
+ SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
+ auto *A = SE.getWrapPredicate(AR, AddedFlags);
+ return addOverflowAssumption(A);
+ }
+
+ // If \p Expr represents a PHINode, we try to see if it can be represented
+ // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
+ // to add this predicate as a runtime overflow check, we return the AddRec.
+ // If \p Expr does not meet these conditions (is not a PHI node, or we
+ // couldn't create an AddRec for it, or couldn't add the predicate), we just
+ // return \p Expr.
+ const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
+ if (!isa<PHINode>(Expr->getValue()))
+ return Expr;
+ std::optional<
+ std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
+ if (!PredicatedRewrite)
+ return Expr;
+ for (const auto *P : PredicatedRewrite->second){
+ // Wrap predicates from outer loops are not supported.
+ if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
+ if (L != WP->getExpr()->getLoop())
+ return Expr;
+ }
+ if (!addOverflowAssumption(P))
+ return Expr;
+ }
+ return PredicatedRewrite->first;
+ }
+
+ SmallVectorImpl<const SCEVPredicate *> *NewPreds;
+ const SCEVPredicate *Pred;
+ const Loop *L;
+};
+
+} // end anonymous namespace
+
+const SCEV *
+ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
+ const SCEVPredicate &Preds) {
+ return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
+}
+
+const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
+ const SCEV *S, const Loop *L,
+ SmallVectorImpl<const SCEVPredicate *> &Preds) {
+ SmallVector<const SCEVPredicate *> TransformPreds;
+ S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
+ auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
+
+ if (!AddRec)
+ return nullptr;
+
+ // Check if any of the transformed predicates is known to be false. In that
+ // case, it doesn't make sense to convert to a predicated AddRec, as the
+ // versioned loop will never execute.
+ for (const SCEVPredicate *Pred : TransformPreds) {
+ auto *WrapPred = dyn_cast<SCEVWrapPredicate>(Pred);
+ if (!WrapPred || WrapPred->getFlags() != SCEVWrapPredicate::IncrementNSSW)
+ continue;
+
+ const SCEVAddRecExpr *AddRecToCheck = WrapPred->getExpr();
+ const SCEV *ExitCount = getBackedgeTakenCount(AddRecToCheck->getLoop());
+ if (isa<SCEVCouldNotCompute>(ExitCount))
+ continue;
+
+ const SCEV *Step = AddRecToCheck->getStepRecurrence(*this);
+ if (!Step->isOne())
+ continue;
+
+ ExitCount = getTruncateOrSignExtend(ExitCount, Step->getType());
+ const SCEV *Add = getAddExpr(AddRecToCheck->getStart(), ExitCount);
+ if (isKnownPredicate(CmpInst::ICMP_SLT, Add, AddRecToCheck->getStart()))
+ return nullptr;
+ }
+
+ // Since the transformation was successful, we can now transfer the SCEV
+ // predicates.
+ Preds.append(TransformPreds.begin(), TransformPreds.end());
+
+ return AddRec;
+}
+
+/// SCEV predicates
+SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
+ SCEVPredicateKind Kind)
+ : FastID(ID), Kind(Kind) {}
+
+SCEVComparePredicate::SCEVComparePredicate(const FoldingSetNodeIDRef ID,
+ const ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS)
+ : SCEVPredicate(ID, P_Compare), Pred(Pred), LHS(LHS), RHS(RHS) {
+ assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
+ assert(LHS != RHS && "LHS and RHS are the same SCEV");
+}
+
+bool SCEVComparePredicate::implies(const SCEVPredicate *N,
+ ScalarEvolution &SE) const {
+ const auto *Op = dyn_cast<SCEVComparePredicate>(N);
+
+ if (!Op)
+ return false;
+
+ if (Pred != ICmpInst::ICMP_EQ)
+ return false;
+
+ return Op->LHS == LHS && Op->RHS == RHS;
+}
+
+bool SCEVComparePredicate::isAlwaysTrue() const { return false; }
+
+void SCEVComparePredicate::print(raw_ostream &OS, unsigned Depth) const {
+ if (Pred == ICmpInst::ICMP_EQ)
+ OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
+ else
+ OS.indent(Depth) << "Compare predicate: " << *LHS << " " << Pred << ") "
+ << *RHS << "\n";
+
+}
+
+SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
+ const SCEVAddRecExpr *AR,
+ IncrementWrapFlags Flags)
+ : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
+
+const SCEVAddRecExpr *SCEVWrapPredicate::getExpr() const { return AR; }
+
+bool SCEVWrapPredicate::implies(const SCEVPredicate *N,
+ ScalarEvolution &SE) const {
+ const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
+ if (!Op || setFlags(Flags, Op->Flags) != Flags)
+ return false;
+
+ if (Op->AR == AR)
+ return true;
+
+ if (Flags != SCEVWrapPredicate::IncrementNSSW &&
+ Flags != SCEVWrapPredicate::IncrementNUSW)
+ return false;
+
+ const SCEV *Start = AR->getStart();
+ const SCEV *OpStart = Op->AR->getStart();
+ if (Start->getType()->isPointerTy() != OpStart->getType()->isPointerTy())
+ return false;
+
+ // Reject pointers to different address spaces.
+ if (Start->getType()->isPointerTy() && Start->getType() != OpStart->getType())
+ return false;
+
+ // NUSW/NSSW on a wider-type AddRec does not imply the same on a
+ // narrower-type AddRec.
+ if (SE.getTypeSizeInBits(AR->getType()) >
+ SE.getTypeSizeInBits(Op->AR->getType()))
+ return false;
+
+ const SCEV *Step = AR->getStepRecurrence(SE);
+ const SCEV *OpStep = Op->AR->getStepRecurrence(SE);
+ if (!SE.isKnownPositive(Step) || !SE.isKnownPositive(OpStep))
+ return false;
+
+ // If both steps are positive, this implies N, if N's start and step are
+ // ULE/SLE (for NSUW/NSSW) than this'.
+ Type *WiderTy = SE.getWiderType(Step->getType(), OpStep->getType());
+ Step = SE.getNoopOrZeroExtend(Step, WiderTy);
+ OpStep = SE.getNoopOrZeroExtend(OpStep, WiderTy);
+
+ bool IsNUW = Flags == SCEVWrapPredicate::IncrementNUSW;
+ OpStart = IsNUW ? SE.getNoopOrZeroExtend(OpStart, WiderTy)
+ : SE.getNoopOrSignExtend(OpStart, WiderTy);
+ Start = IsNUW ? SE.getNoopOrZeroExtend(Start, WiderTy)
+ : SE.getNoopOrSignExtend(Start, WiderTy);
+ CmpInst::Predicate Pred = IsNUW ? CmpInst::ICMP_ULE : CmpInst::ICMP_SLE;
+ return SE.isKnownPredicate(Pred, OpStep, Step) &&
+ SE.isKnownPredicate(Pred, OpStart, Start);
+}
+
+bool SCEVWrapPredicate::isAlwaysTrue() const {
+ SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
+ IncrementWrapFlags IFlags = Flags;
+
+ if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
+ IFlags = clearFlags(IFlags, IncrementNSSW);
+
+ return IFlags == IncrementAnyWrap;
+}
+
+void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
+ OS.indent(Depth) << *getExpr() << " Added Flags: ";
+ if (SCEVWrapPredicate::IncrementNUSW & getFlags())
+ OS << "<nusw>";
+ if (SCEVWrapPredicate::IncrementNSSW & getFlags())
+ OS << "<nssw>";
+ OS << "\n";
+}
+
+SCEVWrapPredicate::IncrementWrapFlags
+SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
+ ScalarEvolution &SE) {
+ IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
+ SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
+
+ // We can safely transfer the NSW flag as NSSW.
+ if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
+ ImpliedFlags = IncrementNSSW;
+
+ if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
+ // If the increment is positive, the SCEV NUW flag will also imply the
+ // WrapPredicate NUSW flag.
+ if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
+ if (Step->getValue()->getValue().isNonNegative())
+ ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
+ }
+
+ return ImpliedFlags;
+}
+
+/// Union predicates don't get cached so create a dummy set ID for it.
+SCEVUnionPredicate::SCEVUnionPredicate(ArrayRef<const SCEVPredicate *> Preds,
+ ScalarEvolution &SE)
+ : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {
+ for (const auto *P : Preds)
+ add(P, SE);
+}
+
+bool SCEVUnionPredicate::isAlwaysTrue() const {
+ return all_of(Preds,
+ [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
+}
+
+bool SCEVUnionPredicate::implies(const SCEVPredicate *N,
+ ScalarEvolution &SE) const {
+ if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
+ return all_of(Set->Preds, [this, &SE](const SCEVPredicate *I) {
+ return this->implies(I, SE);
+ });
+
+ if (any_of(Preds,
+ [N, &SE](const SCEVPredicate *I) { return I->implies(N, SE); }))
+ return true;
+
+ // A wrap predicate may be implied by a wrap predicate in Preds after applying
+ // equal predicates.
+ const auto *NWrap = dyn_cast<SCEVWrapPredicate>(N);
+ if (!NWrap)
+ return false;
+ const Loop *L = NWrap->getExpr()->getLoop();
+ return any_of(Preds, [&](const SCEVPredicate *I) {
+ const auto *IWrap = dyn_cast<SCEVWrapPredicate>(I);
+ if (!IWrap)
+ return false;
+ const auto *RewrittenAR = dyn_cast<SCEVAddRecExpr>(
+ SE.rewriteUsingPredicate(IWrap->getExpr(), L, *this));
+ return RewrittenAR &&
+ SE.getWrapPredicate(RewrittenAR, IWrap->getFlags())->implies(N, SE);
+ });
+}
+
+void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
+ for (const auto *Pred : Preds)
+ Pred->print(OS, Depth);
+}
+
+void SCEVUnionPredicate::add(const SCEVPredicate *N, ScalarEvolution &SE) {
+ if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
+ for (const auto *Pred : Set->Preds)
+ add(Pred, SE);
+ return;
+ }
+
+ // Implication checks are quadratic in the number of predicates. Stop doing
+ // them if there are many predicates, as they should be too expensive to use
+ // anyway at that point.
+ bool CheckImplies = Preds.size() < 16;
+
+ // Only add predicate if it is not already implied by this union predicate.
+ if (CheckImplies && implies(N, SE))
+ return;
+
+ // Build a new vector containing the current predicates, except the ones that
+ // are implied by the new predicate N.
+ SmallVector<const SCEVPredicate *> PrunedPreds;
+ for (auto *P : Preds) {
+ if (CheckImplies && N->implies(P, SE))
+ continue;
+ PrunedPreds.push_back(P);
+ }
+ Preds = std::move(PrunedPreds);
+ Preds.push_back(N);
+}
+
+PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
+ Loop &L)
+ : SE(SE), L(L) {
+ SmallVector<const SCEVPredicate*, 4> Empty;
+ Preds = std::make_unique<SCEVUnionPredicate>(Empty, SE);
+}
+
+void ScalarEvolution::registerUser(const SCEV *User,
+ ArrayRef<const SCEV *> Ops) {
+ for (const auto *Op : Ops)
+ // We do not expect that forgetting cached data for SCEVConstants will ever
+ // open any prospects for sharpening or introduce any correctness issues,
+ // so we don't bother storing their dependencies.
+ if (!isa<SCEVConstant>(Op))
+ SCEVUsers[Op].insert(User);
+}
+
+void ScalarEvolution::registerUser(const SCEV *User, ArrayRef<SCEVUse> Ops) {
+ for (const SCEV *Op : Ops)
+ // We do not expect that forgetting cached data for SCEVConstants will ever
+ // open any prospects for sharpening or introduce any correctness issues,
+ // so we don't bother storing their dependencies.
+ if (!isa<SCEVConstant>(Op))
+ SCEVUsers[Op].insert(User);
+}
+
+const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
+ const SCEV *Expr = SE.getSCEV(V);
+ return getPredicatedSCEV(Expr);
+}
+
+const SCEV *PredicatedScalarEvolution::getPredicatedSCEV(const SCEV *Expr) {
+ RewriteEntry &Entry = RewriteMap[Expr];
+
+ // If we already have an entry and the version matches, return it.
+ if (Entry.second && Generation == Entry.first)
+ return Entry.second;
+
+ // We found an entry but it's stale. Rewrite the stale entry
+ // according to the current predicate.
+ if (Entry.second)
+ Expr = Entry.second;
+
+ const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, *Preds);
+ Entry = {Generation, NewSCEV};
+
+ return NewSCEV;
+}
+
+const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
+ if (!BackedgeCount) {
+ SmallVector<const SCEVPredicate *, 4> Preds;
+ BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, Preds);
+ for (const auto *P : Preds)
+ addPredicate(*P);
+ }
+ return BackedgeCount;
+}
+
+const SCEV *PredicatedScalarEvolution::getSymbolicMaxBackedgeTakenCount() {
+ if (!SymbolicMaxBackedgeCount) {
+ SmallVector<const SCEVPredicate *, 4> Preds;
+ SymbolicMaxBackedgeCount =
+ SE.getPredicatedSymbolicMaxBackedgeTakenCount(&L, Preds);
+ for (const auto *P : Preds)
+ addPredicate(*P);
+ }
+ return SymbolicMaxBackedgeCount;
+}
+
+unsigned PredicatedScalarEvolution::getSmallConstantMaxTripCount() {
+ if (!SmallConstantMaxTripCount) {
+ SmallVector<const SCEVPredicate *, 4> Preds;
+ SmallConstantMaxTripCount = SE.getSmallConstantMaxTripCount(&L, &Preds);
+ for (const auto *P : Preds)
+ addPredicate(*P);
+ }
+ return *SmallConstantMaxTripCount;
+}
+
+void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
+ if (Preds->implies(&Pred, SE))
+ return;
+
+ SmallVector<const SCEVPredicate *, 4> NewPreds(Preds->getPredicates());
+ NewPreds.push_back(&Pred);
+ Preds = std::make_unique<SCEVUnionPredicate>(NewPreds, SE);
+ updateGeneration();
+}
+
+void PredicatedScalarEvolution::addPredicates(
+ ArrayRef<const SCEVPredicate *> Preds) {
+ for (const SCEVPredicate *P : Preds)
+ addPredicate(*P);
+}
+
+const SCEVPredicate &PredicatedScalarEvolution::getPredicate() const {
+ return *Preds;
+}
+
+void PredicatedScalarEvolution::updateGeneration() {
+ // If the generation number wrapped recompute everything.
+ if (++Generation == 0) {
+ for (auto &II : RewriteMap) {
+ const SCEV *Rewritten = II.second.second;
+ II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, *Preds)};
+ }
+ }
+}
+
+bool PredicatedScalarEvolution::hasNoOverflow(
+ Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
+ const auto *AR = dyn_cast<SCEVAddRecExpr>(getSCEV(V));
+ if (!AR)
+ return false;
+
+ Flags = SCEVWrapPredicate::clearFlags(
+ Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
+
+ return Flags == SCEVWrapPredicate::IncrementAnyWrap;
+}
+
+const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(
+ Value *V, SmallVectorImpl<const SCEVPredicate *> *ExtraPreds) {
+ const SCEV *Expr = this->getSCEV(V);
+ SmallVector<const SCEVPredicate *, 4> NewPreds;
+ auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
+
+ if (!New)
+ return nullptr;
+
+ if (ExtraPreds) {
+ ExtraPreds->append(NewPreds);
+ return New;
+ }
+
+ addPredicates(NewPreds);
+
+ RewriteMap[SE.getSCEV(V)] = {Generation, New};
+ return New;
+}
+
+PredicatedScalarEvolution::PredicatedScalarEvolution(
+ const PredicatedScalarEvolution &Init)
+ : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L),
+ Preds(std::make_unique<SCEVUnionPredicate>(Init.Preds->getPredicates(),
+ SE)),
+ Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {}
+
+void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
+ // For each block.
+ for (auto *BB : L.getBlocks())
+ for (auto &I : *BB) {
+ if (!SE.isSCEVable(I.getType()))
+ continue;
+
+ auto *Expr = SE.getSCEV(&I);
+ auto II = RewriteMap.find(Expr);
+
+ if (II == RewriteMap.end())
+ continue;
+
+ // Don't print things that are not interesting.
+ if (II->second.second == Expr)
+ continue;
+
+ OS.indent(Depth) << "[PSE]" << I << ":\n";
+ OS.indent(Depth + 2) << *Expr << "\n";
+ OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
+ }
+}
+
+ScalarEvolution::LoopGuards
+ScalarEvolution::LoopGuards::collect(const Loop *L, ScalarEvolution &SE) {
+ BasicBlock *Header = L->getHeader();
+ BasicBlock *Pred = L->getLoopPredecessor();
+ LoopGuards Guards(SE);
+ if (!Pred)
+ return Guards;
+ SmallPtrSet<const BasicBlock *, 8> VisitedBlocks;
+ collectFromBlock(SE, Guards, Header, Pred, VisitedBlocks);
+ return Guards;
+}
+
+void ScalarEvolution::LoopGuards::collectFromPHI(
+ ScalarEvolution &SE, ScalarEvolution::LoopGuards &Guards,
+ const PHINode &Phi, SmallPtrSetImpl<const BasicBlock *> &VisitedBlocks,
+ SmallDenseMap<const BasicBlock *, LoopGuards> &IncomingGuards,
+ unsigned Depth) {
+ if (!SE.isSCEVable(Phi.getType()))
+ return;
+
+ using MinMaxPattern = std::pair<const SCEVConstant *, SCEVTypes>;
+ auto GetMinMaxConst = [&](unsigned IncomingIdx) -> MinMaxPattern {
+ const BasicBlock *InBlock = Phi.getIncomingBlock(IncomingIdx);
+ if (!VisitedBlocks.insert(InBlock).second)
+ return {nullptr, scCouldNotCompute};
+
+ // Avoid analyzing unreachable blocks so that we don't get trapped
+ // traversing cycles with ill-formed dominance or infinite cycles
+ if (!SE.DT.isReachableFromEntry(InBlock))
+ return {nullptr, scCouldNotCompute};
+
+ auto [G, Inserted] = IncomingGuards.try_emplace(InBlock, LoopGuards(SE));
+ if (Inserted)
+ collectFromBlock(SE, G->second, Phi.getParent(), InBlock, VisitedBlocks,
+ Depth + 1);
+ auto &RewriteMap = G->second.RewriteMap;
+ if (RewriteMap.empty())
+ return {nullptr, scCouldNotCompute};
+ auto S = RewriteMap.find(SE.getSCEV(Phi.getIncomingValue(IncomingIdx)));
+ if (S == RewriteMap.end())
+ return {nullptr, scCouldNotCompute};
+ auto *SM = dyn_cast_if_present<SCEVMinMaxExpr>(S->second);
+ if (!SM)
+ return {nullptr, scCouldNotCompute};
+ if (const SCEVConstant *C0 = dyn_cast<SCEVConstant>(SM->getOperand(0)))
+ return {C0, SM->getSCEVType()};
+ return {nullptr, scCouldNotCompute};
+ };
+ auto MergeMinMaxConst = [](MinMaxPattern P1,
+ MinMaxPattern P2) -> MinMaxPattern {
+ auto [C1, T1] = P1;
+ auto [C2, T2] = P2;
+ if (!C1 || !C2 || T1 != T2)
+ return {nullptr, scCouldNotCompute};
+ switch (T1) {
+ case scUMaxExpr:
+ return {C1->getAPInt().ult(C2->getAPInt()) ? C1 : C2, T1};
+ case scSMaxExpr:
+ return {C1->getAPInt().slt(C2->getAPInt()) ? C1 : C2, T1};
+ case scUMinExpr:
+ return {C1->getAPInt().ugt(C2->getAPInt()) ? C1 : C2, T1};
+ case scSMinExpr:
+ return {C1->getAPInt().sgt(C2->getAPInt()) ? C1 : C2, T1};
+ default:
+ llvm_unreachable("Trying to merge non-MinMaxExpr SCEVs.");
+ }
+ };
+ auto P = GetMinMaxConst(0);
+ for (unsigned int In = 1; In < Phi.getNumIncomingValues(); In++) {
+ if (!P.first)
+ break;
+ P = MergeMinMaxConst(P, GetMinMaxConst(In));
+ }
+ if (P.first) {
+ const SCEV *LHS = SE.getSCEV(const_cast<PHINode *>(&Phi));
+ SmallVector<SCEVUse, 2> Ops({P.first, LHS});
+ const SCEV *RHS = SE.getMinMaxExpr(P.second, Ops);
+ Guards.RewriteMap.insert({LHS, RHS});
+ }
+}
+
+// Return a new SCEV that modifies \p Expr to the closest number divides by
+// \p Divisor and less or equal than Expr. For now, only handle constant
+// Expr.
+static const SCEV *getPreviousSCEVDivisibleByDivisor(const SCEV *Expr,
+ const APInt &DivisorVal,
+ ScalarEvolution &SE) {
+ const APInt *ExprVal;
+ if (!match(Expr, m_scev_APInt(ExprVal)) || ExprVal->isNegative() ||
+ DivisorVal.isNonPositive())
+ return Expr;
+ APInt Rem = ExprVal->urem(DivisorVal);
+ // return the SCEV: Expr - Expr % Divisor
+ return SE.getConstant(*ExprVal - Rem);
+}
+
+// Return a new SCEV that modifies \p Expr to the closest number divides by
+// \p Divisor and greater or equal than Expr. For now, only handle constant
+// Expr.
+static const SCEV *getNextSCEVDivisibleByDivisor(const SCEV *Expr,
+ const APInt &DivisorVal,
+ ScalarEvolution &SE) {
+ const APInt *ExprVal;
+ if (!match(Expr, m_scev_APInt(ExprVal)) || ExprVal->isNegative() ||
+ DivisorVal.isNonPositive())
+ return Expr;
+ APInt Rem = ExprVal->urem(DivisorVal);
+ if (Rem.isZero())
+ return Expr;
+ // return the SCEV: Expr + Divisor - Expr % Divisor
+ return SE.getConstant(*ExprVal + DivisorVal - Rem);
+}
+
+static bool collectDivisibilityInformation(
+ ICmpInst::Predicate Predicate, const SCEV *LHS, const SCEV *RHS,
+ DenseMap<const SCEV *, const SCEV *> &DivInfo,
+ DenseMap<const SCEV *, APInt> &Multiples, ScalarEvolution &SE) {
+ // If we have LHS == 0, check if LHS is computing a property of some unknown
+ // SCEV %v which we can rewrite %v to express explicitly.
+ if (Predicate != CmpInst::ICMP_EQ || !match(RHS, m_scev_Zero()))
+ return false;
+ // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to
+ // explicitly express that.
+ const SCEVUnknown *URemLHS = nullptr;
+ const SCEV *URemRHS = nullptr;
+ if (!match(LHS, m_scev_URem(m_SCEVUnknown(URemLHS), m_SCEV(URemRHS), SE)))
+ return false;
+
+ const SCEV *Multiple =
+ SE.getMulExpr(SE.getUDivExpr(URemLHS, URemRHS), URemRHS);
+ DivInfo[URemLHS] = Multiple;
+ if (auto *C = dyn_cast<SCEVConstant>(URemRHS))
+ Multiples[URemLHS] = C->getAPInt();
+ return true;
+}
+
+// Check if the condition is a divisibility guard (A % B == 0).
+static bool isDivisibilityGuard(const SCEV *LHS, const SCEV *RHS,
+ ScalarEvolution &SE) {
+ const SCEV *X, *Y;
+ return match(LHS, m_scev_URem(m_SCEV(X), m_SCEV(Y), SE)) && RHS->isZero();
+}
+
+// Apply divisibility by \p Divisor on MinMaxExpr with constant values,
+// recursively. This is done by aligning up/down the constant value to the
+// Divisor.
+static const SCEV *applyDivisibilityOnMinMaxExpr(const SCEV *MinMaxExpr,
+ APInt Divisor,
+ ScalarEvolution &SE) {
+ // Return true if \p Expr is a MinMax SCEV expression with a non-negative
+ // constant operand. If so, return in \p SCTy the SCEV type and in \p RHS
+ // the non-constant operand and in \p LHS the constant operand.
+ auto IsMinMaxSCEVWithNonNegativeConstant =
+ [&](const SCEV *Expr, SCEVTypes &SCTy, const SCEV *&LHS,
+ const SCEV *&RHS) {
+ if (auto *MinMax = dyn_cast<SCEVMinMaxExpr>(Expr)) {
+ if (MinMax->getNumOperands() != 2)
+ return false;
+ if (auto *C = dyn_cast<SCEVConstant>(MinMax->getOperand(0))) {
+ if (C->getAPInt().isNegative())
+ return false;
+ SCTy = MinMax->getSCEVType();
+ LHS = MinMax->getOperand(0);
+ RHS = MinMax->getOperand(1);
+ return true;
+ }
+ }
+ return false;
+ };
+
+ const SCEV *MinMaxLHS = nullptr, *MinMaxRHS = nullptr;
+ SCEVTypes SCTy;
+ if (!IsMinMaxSCEVWithNonNegativeConstant(MinMaxExpr, SCTy, MinMaxLHS,
+ MinMaxRHS))
+ return MinMaxExpr;
+ auto IsMin = isa<SCEVSMinExpr>(MinMaxExpr) || isa<SCEVUMinExpr>(MinMaxExpr);
+ assert(SE.isKnownNonNegative(MinMaxLHS) && "Expected non-negative operand!");
+ auto *DivisibleExpr =
+ IsMin ? getPreviousSCEVDivisibleByDivisor(MinMaxLHS, Divisor, SE)
+ : getNextSCEVDivisibleByDivisor(MinMaxLHS, Divisor, SE);
+ SmallVector<SCEVUse> Ops = {
+ applyDivisibilityOnMinMaxExpr(MinMaxRHS, Divisor, SE), DivisibleExpr};
+ return SE.getMinMaxExpr(SCTy, Ops);
+}
+
+void ScalarEvolution::LoopGuards::collectFromBlock(
+ ScalarEvolution &SE, ScalarEvolution::LoopGuards &Guards,
+ const BasicBlock *Block, const BasicBlock *Pred,
+ SmallPtrSetImpl<const BasicBlock *> &VisitedBlocks, unsigned Depth) {
+
+ assert(SE.DT.isReachableFromEntry(Block) && SE.DT.isReachableFromEntry(Pred));
+
+ SmallVector<SCEVUse> ExprsToRewrite;
+ auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS,
+ const SCEV *RHS,
+ DenseMap<const SCEV *, const SCEV *> &RewriteMap,
+ const LoopGuards &DivGuards) {
+ // WARNING: It is generally unsound to apply any wrap flags to the proposed
+ // replacement SCEV which isn't directly implied by the structure of that
+ // SCEV. In particular, using contextual facts to imply flags is *NOT*
+ // legal. See the scoping rules for flags in the header to understand why.
+
+ // Puts rewrite rule \p From -> \p To into the rewrite map. Also if \p From
+ // and \p FromRewritten are the same (i.e. there has been no rewrite
+ // registered for \p From), then puts this value in the list of rewritten
+ // expressions.
+ auto AddRewrite = [&](const SCEV *From, const SCEV *FromRewritten,
+ const SCEV *To) {
+ if (From == FromRewritten)
+ ExprsToRewrite.push_back(From);
+ RewriteMap[From] = To;
+ };
+
+ // Checks whether \p S has already been rewritten. In that case returns the
+ // existing rewrite because we want to chain further rewrites onto the
+ // already rewritten value. Otherwise returns \p S.
+ auto GetMaybeRewritten = [&](const SCEV *S) {
+ return RewriteMap.lookup_or(S, S);
+ };
+
+ // Check for a condition of the form (-C1 + X < C2). InstCombine will
+ // create this form when combining two checks of the form (X u< C2 + C1) and
+ // (X >=u C1).
+ auto MatchRangeCheckIdiom = [&](ICmpInst::Predicate Pred,
+ const SCEV *MatchLHS,
+ const SCEV *MatchRHS) {
+ const SCEVConstant *C1;
+ const SCEVUnknown *LHSUnknown;
+ auto *C2 = dyn_cast<SCEVConstant>(MatchRHS);
+ if (!match(MatchLHS,
+ m_scev_Add(m_SCEVConstant(C1), m_SCEVUnknown(LHSUnknown))) ||
+ !C2)
+ return false;
+
+ auto ExactRegion =
+ ConstantRange::makeExactICmpRegion(Pred, C2->getAPInt())
+ .sub(C1->getAPInt());
+
+ // Tighten the raw range with what we already know about LHSUnknown
+ // from prior guards recorded in RewriteMap, or from SCEV's own range
+ // analysis.
+ const SCEV *RewrittenLHS = GetMaybeRewritten(LHSUnknown);
+ ExactRegion = ExactRegion.intersectWith(SE.getUnsignedRange(RewrittenLHS),
+ ConstantRange::Unsigned);
+
+ // Bail if the guard is inconsistent with prior facts, or if the range
+ // is still not a monotonic non-wrapping interval after tightening.
+ if (ExactRegion.isEmptySet() || ExactRegion.isWrappedSet() ||
+ ExactRegion.isFullSet())
+ return false;
+
+ const SCEV *RegionMin = SE.getConstant(ExactRegion.getUnsignedMin());
+ const SCEV *RegionMax = SE.getConstant(ExactRegion.getUnsignedMax());
+ const SCEV *ClampedLHS =
+ SE.getUMaxExpr(RegionMin, SE.getUMinExpr(RewrittenLHS, RegionMax));
+ AddRewrite(LHSUnknown, RewrittenLHS, ClampedLHS);
+ return true;
+ };
+ if (MatchRangeCheckIdiom(Predicate, LHS, RHS))
+ return;
+
+ // Do not apply information for constants or if RHS contains an AddRec.
+ if (isa<SCEVConstant>(LHS) || SE.containsAddRecurrence(RHS))
+ return;
+
+ // If RHS is SCEVUnknown, make sure the information is applied to it.
+ if (!isa<SCEVUnknown>(LHS) && isa<SCEVUnknown>(RHS)) {
+ std::swap(LHS, RHS);
+ Predicate = CmpInst::getSwappedPredicate(Predicate);
+ }
+
+ const SCEV *RewrittenLHS = GetMaybeRewritten(LHS);
+ // Apply divisibility information when computing the constant multiple.
+ const APInt &DividesBy =
+ SE.getConstantMultiple(DivGuards.rewrite(RewrittenLHS));
+
+ // Collect rewrites for LHS and its transitive operands based on the
+ // condition.
+ // For min/max expressions, also apply the guard to its operands:
+ // 'min(a, b) >= c' -> '(a >= c) and (b >= c)',
+ // 'min(a, b) > c' -> '(a > c) and (b > c)',
+ // 'max(a, b) <= c' -> '(a <= c) and (b <= c)',
+ // 'max(a, b) < c' -> '(a < c) and (b < c)'.
+
+ // We cannot express strict predicates in SCEV, so instead we replace them
+ // with non-strict ones against plus or minus one of RHS depending on the
+ // predicate.
+ const SCEV *One = SE.getOne(RHS->getType());
+ switch (Predicate) {
+ case CmpInst::ICMP_ULT:
+ if (RHS->getType()->isPointerTy())
+ return;
+ RHS = SE.getUMaxExpr(RHS, One);
+ [[fallthrough]];
+ case CmpInst::ICMP_SLT: {
+ RHS = SE.getMinusSCEV(RHS, One);
+ RHS = getPreviousSCEVDivisibleByDivisor(RHS, DividesBy, SE);
+ break;
+ }
+ case CmpInst::ICMP_UGT:
+ case CmpInst::ICMP_SGT:
+ RHS = SE.getAddExpr(RHS, One);
+ RHS = getNextSCEVDivisibleByDivisor(RHS, DividesBy, SE);
+ break;
+ case CmpInst::ICMP_ULE:
+ case CmpInst::ICMP_SLE:
+ RHS = getPreviousSCEVDivisibleByDivisor(RHS, DividesBy, SE);
+ break;
+ case CmpInst::ICMP_UGE:
+ case CmpInst::ICMP_SGE:
+ RHS = getNextSCEVDivisibleByDivisor(RHS, DividesBy, SE);
+ break;
+ default:
+ break;
+ }
+
+ SmallVector<SCEVUse, 16> Worklist(1, LHS);
+ SmallPtrSet<const SCEV *, 16> Visited;
+
+ auto EnqueueOperands = [&Worklist](const SCEVNAryExpr *S) {
+ append_range(Worklist, S->operands());
+ };
+
+ while (!Worklist.empty()) {
+ const SCEV *From = Worklist.pop_back_val();
+ if (isa<SCEVConstant>(From))
+ continue;
+ if (!Visited.insert(From).second)
+ continue;
+ const SCEV *FromRewritten = GetMaybeRewritten(From);
+ const SCEV *To = nullptr;
+
+ switch (Predicate) {
+ case CmpInst::ICMP_ULT:
+ case CmpInst::ICMP_ULE:
+ To = SE.getUMinExpr(FromRewritten, RHS);
+ if (auto *UMax = dyn_cast<SCEVUMaxExpr>(FromRewritten))
+ EnqueueOperands(UMax);
+ break;
+ case CmpInst::ICMP_SLT:
+ case CmpInst::ICMP_SLE:
+ To = SE.getSMinExpr(FromRewritten, RHS);
+ if (auto *SMax = dyn_cast<SCEVSMaxExpr>(FromRewritten))
+ EnqueueOperands(SMax);
+ break;
+ case CmpInst::ICMP_UGT:
+ case CmpInst::ICMP_UGE:
+ To = SE.getUMaxExpr(FromRewritten, RHS);
+ if (auto *UMin = dyn_cast<SCEVUMinExpr>(FromRewritten))
+ EnqueueOperands(UMin);
+ break;
+ case CmpInst::ICMP_SGT:
+ case CmpInst::ICMP_SGE:
+ To = SE.getSMaxExpr(FromRewritten, RHS);
+ if (auto *SMin = dyn_cast<SCEVSMinExpr>(FromRewritten))
+ EnqueueOperands(SMin);
+ break;
+ case CmpInst::ICMP_EQ:
+ if (isa<SCEVConstant>(RHS))
+ To = RHS;
+ break;
+ case CmpInst::ICMP_NE:
+ if (match(RHS, m_scev_Zero())) {
+ const SCEV *OneAlignedUp =
+ getNextSCEVDivisibleByDivisor(One, DividesBy, SE);
+ To = SE.getUMaxExpr(FromRewritten, OneAlignedUp);
+ } else {
+ // LHS != RHS can be rewritten as (LHS - RHS) = UMax(1, LHS - RHS),
+ // but creating the subtraction eagerly is expensive. Track the
+ // inequalities in a separate map, and materialize the rewrite lazily
+ // when encountering a suitable subtraction while re-writing.
+ if (LHS->getType()->isPointerTy()) {
+ LHS = SE.getPtrToAddrExpr(LHS);
+ RHS = SE.getPtrToAddrExpr(RHS);
+ if (isa<SCEVCouldNotCompute>(LHS) || isa<SCEVCouldNotCompute>(RHS))
+ break;
+ }
+ const SCEVConstant *C;
+ const SCEV *A, *B;
+ if (match(RHS, m_scev_Add(m_SCEVConstant(C), m_SCEV(A))) &&
+ match(LHS, m_scev_Add(m_scev_Specific(C), m_SCEV(B)))) {
+ RHS = A;
+ LHS = B;
+ }
+ if (LHS > RHS)
+ std::swap(LHS, RHS);
+ Guards.NotEqual.insert({LHS, RHS});
+ continue;
+ }
+ break;
+ default:
+ break;
+ }
+
+ if (To)
+ AddRewrite(From, FromRewritten, To);
+ }
+ };
+
+ SmallVector<PointerIntPair<Value *, 1, bool>> Terms;
+ // First, collect information from assumptions dominating the loop.
+ for (auto &AssumeVH : SE.AC.assumptions()) {
+ if (!AssumeVH)
+ continue;
+ auto *AssumeI = cast<CallInst>(AssumeVH);
+ if (!SE.DT.dominates(AssumeI, Block))
+ continue;
+ Terms.emplace_back(AssumeI->getOperand(0), true);
+ }
+
+ // Second, collect information from llvm.experimental.guards dominating the loop.
+ auto *GuardDecl = Intrinsic::getDeclarationIfExists(
+ SE.F.getParent(), Intrinsic::experimental_guard);
+ if (GuardDecl)
+ for (const auto *GU : GuardDecl->users())
+ if (const auto *Guard = dyn_cast<IntrinsicInst>(GU))
+ if (Guard->getFunction() == Block->getParent() &&
+ SE.DT.dominates(Guard, Block))
+ Terms.emplace_back(Guard->getArgOperand(0), true);
+
+ // Third, collect conditions from dominating branches. Starting at the loop
+ // predecessor, climb up the predecessor chain, as long as there are
+ // predecessors that can be found that have unique successors leading to the
+ // original header.
+ // TODO: share this logic with isLoopEntryGuardedByCond.
+ unsigned NumCollectedConditions = 0;
+ VisitedBlocks.insert(Block);
+ std::pair<const BasicBlock *, const BasicBlock *> Pair(Pred, Block);
+ for (; Pair.first;
+ Pair = SE.getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
+ VisitedBlocks.insert(Pair.second);
+ const CondBrInst *LoopEntryPredicate =
+ dyn_cast<CondBrInst>(Pair.first->getTerminator());
+ if (!LoopEntryPredicate)
+ continue;
+
+ Terms.emplace_back(LoopEntryPredicate->getCondition(),
+ LoopEntryPredicate->getSuccessor(0) == Pair.second);
+ NumCollectedConditions++;
+
+ // If we are recursively collecting guards stop after 2
+ // conditions to limit compile-time impact for now.
+ if (Depth > 0 && NumCollectedConditions == 2)
+ break;
+ }
+ // Finally, if we stopped climbing the predecessor chain because
+ // there wasn't a unique one to continue, try to collect conditions
+ // for PHINodes by recursively following all of their incoming
+ // blocks and try to merge the found conditions to build a new one
+ // for the Phi.
+ if (Pair.second->hasNPredecessorsOrMore(2) &&
+ Depth < MaxLoopGuardCollectionDepth) {
+ SmallDenseMap<const BasicBlock *, LoopGuards> IncomingGuards;
+ for (auto &Phi : Pair.second->phis())
+ collectFromPHI(SE, Guards, Phi, VisitedBlocks, IncomingGuards, Depth);
+ }
+
+ // Now apply the information from the collected conditions to
+ // Guards.RewriteMap. Conditions are processed in reverse order, so the
+ // earliest conditions is processed first, except guards with divisibility
+ // information, which are moved to the back. This ensures the SCEVs with the
+ // shortest dependency chains are constructed first.
+ SmallVector<std::tuple<CmpInst::Predicate, const SCEV *, const SCEV *>>
+ GuardsToProcess;
+ for (auto [Term, EnterIfTrue] : reverse(Terms)) {
+ SmallVector<Value *, 8> Worklist;
+ SmallPtrSet<Value *, 8> Visited;
+ Worklist.push_back(Term);
+ while (!Worklist.empty()) {
+ Value *Cond = Worklist.pop_back_val();
+ if (!Visited.insert(Cond).second)
+ continue;
+
+ if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) {
+ auto Predicate =
+ EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate();
+ const auto *LHS = SE.getSCEV(Cmp->getOperand(0));
+ const auto *RHS = SE.getSCEV(Cmp->getOperand(1));
+ // If LHS is a constant, apply information to the other expression.
+ // TODO: If LHS is not a constant, check if using CompareSCEVComplexity
+ // can improve results.
+ if (isa<SCEVConstant>(LHS)) {
+ std::swap(LHS, RHS);
+ Predicate = CmpInst::getSwappedPredicate(Predicate);
+ }
+ GuardsToProcess.emplace_back(Predicate, LHS, RHS);
+ continue;
+ }
+
+ Value *L, *R;
+ if (EnterIfTrue ? match(Cond, m_LogicalAnd(m_Value(L), m_Value(R)))
+ : match(Cond, m_LogicalOr(m_Value(L), m_Value(R)))) {
+ Worklist.push_back(L);
+ Worklist.push_back(R);
+ }
+ }
+ }
+
+ // Process divisibility guards in reverse order to populate DivGuards early.
+ DenseMap<const SCEV *, APInt> Multiples;
+ LoopGuards DivGuards(SE);
+ for (const auto &[Predicate, LHS, RHS] : GuardsToProcess) {
+ if (!isDivisibilityGuard(LHS, RHS, SE))
+ continue;
+ collectDivisibilityInformation(Predicate, LHS, RHS, DivGuards.RewriteMap,
+ Multiples, SE);
+ }
+
+ for (const auto &[Predicate, LHS, RHS] : GuardsToProcess)
+ CollectCondition(Predicate, LHS, RHS, Guards.RewriteMap, DivGuards);
+
+ // Apply divisibility information last. This ensures it is applied to the
+ // outermost expression after other rewrites for the given value.
+ for (const auto &[K, Divisor] : Multiples) {
+ const SCEV *DivisorSCEV = SE.getConstant(Divisor);
+ Guards.RewriteMap[K] =
+ SE.getMulExpr(SE.getUDivExpr(applyDivisibilityOnMinMaxExpr(
+ Guards.rewrite(K), Divisor, SE),
+ DivisorSCEV),
+ DivisorSCEV);
+ ExprsToRewrite.push_back(K);
+ }
+
+ // Let the rewriter preserve NUW/NSW flags if the unsigned/signed ranges of
+ // the replacement expressions are contained in the ranges of the replaced
+ // expressions.
+ Guards.PreserveNUW = true;
+ Guards.PreserveNSW = true;
+ for (const SCEV *Expr : ExprsToRewrite) {
+ const SCEV *RewriteTo = Guards.RewriteMap[Expr];
+ Guards.PreserveNUW &=
+ SE.getUnsignedRange(Expr).contains(SE.getUnsignedRange(RewriteTo));
+ Guards.PreserveNSW &=
+ SE.getSignedRange(Expr).contains(SE.getSignedRange(RewriteTo));
+ }
+
+ // Now that all rewrite information is collect, rewrite the collected
+ // expressions with the information in the map. This applies information to
+ // sub-expressions.
+ if (ExprsToRewrite.size() > 1) {
+ for (const SCEV *Expr : ExprsToRewrite) {
+ const SCEV *RewriteTo = Guards.RewriteMap[Expr];
+ Guards.RewriteMap.erase(Expr);
+ Guards.RewriteMap.insert({Expr, Guards.rewrite(RewriteTo)});
+ }
+ }
+}
+
+const SCEV *ScalarEvolution::LoopGuards::rewrite(const SCEV *Expr) const {
+ /// A rewriter to replace SCEV expressions in Map with the corresponding entry
+ /// in the map. It skips AddRecExpr because we cannot guarantee that the
+ /// replacement is loop invariant in the loop of the AddRec.
+ class SCEVLoopGuardRewriter
+ : public SCEVRewriteVisitor<SCEVLoopGuardRewriter> {
+ const DenseMap<const SCEV *, const SCEV *> ⤅
+ const SmallDenseSet<std::pair<const SCEV *, const SCEV *>> ≠
+
+ SCEV::NoWrapFlags FlagMask = SCEV::FlagAnyWrap;
+
+ public:
+ SCEVLoopGuardRewriter(ScalarEvolution &SE,
+ const ScalarEvolution::LoopGuards &Guards)
+ : SCEVRewriteVisitor(SE), Map(Guards.RewriteMap),
+ NotEqual(Guards.NotEqual) {
+ if (Guards.PreserveNUW)
+ FlagMask = ScalarEvolution::setFlags(FlagMask, SCEV::FlagNUW);
+ if (Guards.PreserveNSW)
+ FlagMask = ScalarEvolution::setFlags(FlagMask, SCEV::FlagNSW);
+ }
+
+ const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }
+
+ const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+ return Map.lookup_or(Expr, Expr);
+ }
+
+ const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
+ if (const SCEV *S = Map.lookup(Expr))
+ return S;
+
+ // If we didn't find the extact ZExt expr in the map, check if there's
+ // an entry for a smaller ZExt we can use instead.
+ Type *Ty = Expr->getType();
+ const SCEV *Op = Expr->getOperand(0);
+ unsigned Bitwidth = Ty->getScalarSizeInBits() / 2;
+ while (Bitwidth % 8 == 0 && Bitwidth >= 8 &&
+ Bitwidth > Op->getType()->getScalarSizeInBits()) {
+ Type *NarrowTy = IntegerType::get(SE.getContext(), Bitwidth);
+ auto *NarrowExt = SE.getZeroExtendExpr(Op, NarrowTy);
+ if (const SCEV *S = Map.lookup(NarrowExt))
+ return SE.getZeroExtendExpr(S, Ty);
+ Bitwidth = Bitwidth / 2;
+ }
+
+ return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitZeroExtendExpr(
+ Expr);
+ }
+
+ const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
+ if (const SCEV *S = Map.lookup(Expr))
+ return S;
+ return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitSignExtendExpr(
+ Expr);
+ }
+
+ const SCEV *visitUMinExpr(const SCEVUMinExpr *Expr) {
+ if (const SCEV *S = Map.lookup(Expr))
+ return S;
+ return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitUMinExpr(Expr);
+ }
+
+ const SCEV *visitSMinExpr(const SCEVSMinExpr *Expr) {
+ if (const SCEV *S = Map.lookup(Expr))
+ return S;
+ return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitSMinExpr(Expr);
+ }
+
+ const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
+ if (const SCEV *S = Map.lookup(Expr))
+ return S;
+
+ // Helper to check if S is a subtraction (A - B) where A != B, and if so,
+ // return UMax(S, 1).
+ auto RewriteSubtraction = [&](const SCEV *S) -> const SCEV * {
+ SCEVUse LHS, RHS;
+ if (MatchBinarySub(S, LHS, RHS)) {
+ if (LHS > RHS)
+ std::swap(LHS, RHS);
+ if (NotEqual.contains({LHS, RHS})) {
+ const SCEV *OneAlignedUp = getNextSCEVDivisibleByDivisor(
+ SE.getOne(S->getType()), SE.getConstantMultiple(S), SE);
+ return SE.getUMaxExpr(OneAlignedUp, S);
+ }
+ }
+ return nullptr;
+ };
+
+ // Check if Expr itself is a subtraction pattern with guard info.
+ if (const SCEV *Rewritten = RewriteSubtraction(Expr))
+ return Rewritten;
+
+ // Trip count expressions sometimes consist of adding 3 operands, i.e.
+ // (Const + A + B). There may be guard info for A + B, and if so, apply
+ // it.
+ // TODO: Could more generally apply guards to Add sub-expressions.
+ if (isa<SCEVConstant>(Expr->getOperand(0))) {
+ if (Expr->getNumOperands() == 3) {
+ const SCEV *Add =
+ SE.getAddExpr(Expr->getOperand(1), Expr->getOperand(2));
+ if (const SCEV *Rewritten = RewriteSubtraction(Add))
+ return SE.getAddExpr(
+ Expr->getOperand(0), Rewritten,
+ ScalarEvolution::maskFlags(Expr->getNoWrapFlags(), FlagMask));
+ if (const SCEV *S = Map.lookup(Add))
+ return SE.getAddExpr(Expr->getOperand(0), S);
+ }
+
+ // For expressions of the form (Const + A), check if we have guard info
+ // for (Const + 1 + A), and rewrite to ((Const + 1 + A) - 1). This makes
+ // sure we don't lose information when rewriting expressions based on
+ // back-edge taken counts in some cases.
+ if (Expr->getNumOperands() == 2) {
+ const SCEV *S = nullptr;
+ // Handle (-1 + 1 + A) without constructing SCEVs.
+ if (match(Expr->getOperand(0), m_scev_AllOnes())) {
+ S = Map.lookup(Expr->getOperand(1));
+ } else {
+ const SCEV *NewC =
+ SE.getAddExpr(Expr->getOperand(0), SE.getOne(Expr->getType()));
+ S = Map.lookup(SE.getAddExpr(NewC, Expr->getOperand(1)));
+ }
+ if (S)
+ return SE.getAddExpr(S, SE.getMinusOne(Expr->getType()));
+ }
+ }
+ SmallVector<SCEVUse, 2> Operands;
+ bool Changed = false;
+ for (SCEVUse Op : Expr->operands()) {
+ Operands.push_back(
+ SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visit(Op));
+ Changed |= Op != Operands.back();
+ }
+ // We are only replacing operands with equivalent values, so transfer the
+ // flags from the original expression.
+ return !Changed ? Expr
+ : SE.getAddExpr(Operands,
+ ScalarEvolution::maskFlags(
+ Expr->getNoWrapFlags(), FlagMask));
+ }
+
+ const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
+ SmallVector<SCEVUse, 2> Operands;
+ bool Changed = false;
+ for (SCEVUse Op : Expr->operands()) {
+ Operands.push_back(
+ SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visit(Op));
+ Changed |= Op != Operands.back();
+ }
+ // We are only replacing operands with equivalent values, so transfer the
+ // flags from the original expression.
+ return !Changed ? Expr
+ : SE.getMulExpr(Operands,
+ ScalarEvolution::maskFlags(
+ Expr->getNoWrapFlags(), FlagMask));
+ }
+ };
+
+ if (RewriteMap.empty() && NotEqual.empty())
+ return Expr;
+
+ SCEVLoopGuardRewriter Rewriter(SE, *this);
+ return Rewriter.visit(Expr);
+}
+
+const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) {
+ return applyLoopGuards(Expr, LoopGuards::collect(L, *this));
+}
+
+const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr,
+ const LoopGuards &Guards) {
+ return Guards.rewrite(Expr);
+}
diff --git a/llvm/unittests/Analysis/ScalarEvolutionTest.cpp b/llvm/unittests/Analysis/ScalarEvolutionTest.cpp
index cf048408baf8d..fc57af1f26f85 100644
--- a/llvm/unittests/Analysis/ScalarEvolutionTest.cpp
+++ b/llvm/unittests/Analysis/ScalarEvolutionTest.cpp
@@ -1538,19 +1538,19 @@ TEST_F(ScalarEvolutionsTest, ImpliedCond) {
TEST_F(ScalarEvolutionsTest, PredicatedBackedgeTakenCountForOverflowingStride) {
LLVMContext C;
SMDiagnostic Err;
- std::unique_ptr<Module> M = parseAssemblyString(
- "define void @foo(i32 %n) { "
- "entry: "
- " br label %loop "
- "loop: "
- " %iv = phi i32 [ 0, %entry ], [ %iv.next, %loop ] "
- " %iv.next = add i32 %iv, 3 "
- " %cmp = icmp slt i32 %iv, %n "
- " br i1 %cmp, label %loop, label %exit "
- "exit: "
- " ret void "
- "}",
- Err, C);
+std::unique_ptr<Module> M =
+ parseAssemblyString("define void @foo(i32 %n) { "
+ "entry: "
+ " br label %loop "
+ "loop: "
+ " %iv = phi i32 [ 0, %entry ], [ %iv.next, %loop ] "
+ " %iv.next = add i32 %iv, 3 "
+ " %cmp = icmp slt i32 %iv, %n "
+ " br i1 %cmp, label %loop, label %exit "
+ "exit: "
+ " ret void "
+ "}",
+ Err, C);
ASSERT_TRUE(M && "Could not parse module?");
ASSERT_TRUE(!verifyModule(*M) && "Must have been well formed!");
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