[llvm] [ConstraintElim] Infer linear constraints from udiv and urem (PR #180689)
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Mon Feb 9 23:06:48 PST 2026
llvmbot wrote:
<!--LLVM PR SUMMARY COMMENT-->
@llvm/pr-subscribers-llvm-transforms
Author: Manasij Mukherjee (manasij7479)
<details>
<summary>Changes</summary>
urem x, n: result < n (remainder is always less than divisor)
urem x, n: result <= x (remainder is at most the dividend)
udiv x, n: result <= x (quotient is at most the dividend)
https://alive2.llvm.org/ce/z/ezzsjQ
---
Full diff: https://github.com/llvm/llvm-project/pull/180689.diff
2 Files Affected:
- (modified) llvm/lib/Transforms/Scalar/ConstraintElimination.cpp (+25)
- (added) llvm/test/Transforms/ConstraintElimination/urem-udiv.ll (+361)
``````````diff
diff --git a/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp b/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
index 9a743b95a2a6d..fc5ee2359a76f 100644
--- a/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
+++ b/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
@@ -1223,6 +1223,16 @@ void State::addInfoFor(BasicBlock &BB) {
break;
}
+ // Add facts from unsigned division and remainder.
+ // urem x, n: result < n and result <= x
+ // udiv x, n: result <= x
+ if (auto *BO = dyn_cast<BinaryOperator>(&I)) {
+ if ((BO->getOpcode() == Instruction::URem ||
+ BO->getOpcode() == Instruction::UDiv) &&
+ isGuaranteedNotToBePoison(BO))
+ WorkList.push_back(FactOrCheck::getInstFact(DT.getNode(&BB), BO));
+ }
+
GuaranteedToExecute &= isGuaranteedToTransferExecutionToSuccessor(&I);
}
@@ -2000,6 +2010,21 @@ static bool eliminateConstraints(Function &F, DominatorTree &DT, LoopInfo &LI,
continue;
}
+ if (auto *BO = dyn_cast<BinaryOperator>(CB.Inst)) {
+ if (BO->getOpcode() == Instruction::URem) {
+ // urem x, n: result < n (remainder is always less than divisor)
+ AddFact(CmpInst::ICMP_ULT, BO, BO->getOperand(1));
+ // urem x, n: result <= x (remainder is at most the dividend)
+ AddFact(CmpInst::ICMP_ULE, BO, BO->getOperand(0));
+ continue;
+ }
+ if (BO->getOpcode() == Instruction::UDiv) {
+ // udiv x, n: result <= x (quotient is at most the dividend)
+ AddFact(CmpInst::ICMP_ULE, BO, BO->getOperand(0));
+ continue;
+ }
+ }
+
auto &DL = F.getDataLayout();
auto AddFactsAboutIndices = [&](Value *Ptr, Type *AccessType) {
CmpPredicate Pred;
diff --git a/llvm/test/Transforms/ConstraintElimination/urem-udiv.ll b/llvm/test/Transforms/ConstraintElimination/urem-udiv.ll
new file mode 100644
index 0000000000000..c9c3260326619
--- /dev/null
+++ b/llvm/test/Transforms/ConstraintElimination/urem-udiv.ll
@@ -0,0 +1,361 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 4
+; RUN: opt -passes=constraint-elimination -S %s | FileCheck %s
+
+; n < m /\ r = urem x, n ==> r < n < m ==> r < m
+define i1 @urem_ult_divisor_bound(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @urem_ult_divisor_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: ret i1 true
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ult i32 %n, %m
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = urem i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ult i32 %r, %m
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; n <= m /\ r = urem x, n ==> r < n <= m ==> r ule m
+define i1 @urem_ule_divisor_bound(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @urem_ule_divisor_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ule i32 [[N]], [[M]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: ret i1 true
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ule i32 %n, %m
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = urem i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ule i32 %r, %m
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; x <= limit /\ r = urem x, n ==> r <= x <= limit
+define i1 @urem_ule_dividend_bound(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
+; CHECK-LABEL: define i1 @urem_ule_dividend_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: ret i1 true
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ule i32 %x, %limit
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = urem i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ule i32 %r, %limit
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; x <= limit /\ q = udiv x, n ==> q <= x <= limit
+define i1 @udiv_ule_dividend_bound(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
+; CHECK-LABEL: define i1 @udiv_ule_dividend_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[Q:%.*]] = udiv i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: ret i1 true
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ule i32 %x, %limit
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %q = udiv i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ule i32 %q, %limit
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; n < m /\ m < k /\ r = urem x, n ==> r < n < m < k ==> r < k
+define i1 @urem_chain_three_hops(i32 noundef %x, i32 noundef %n, i32 noundef %m, i32 noundef %k) {
+; CHECK-LABEL: define i1 @urem_chain_three_hops(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]], i32 noundef [[K:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[C1:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT: br i1 [[C1]], label [[BB1:%.*]], label [[OUT:%.*]]
+; CHECK: bb1:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: [[C2:%.*]] = icmp ult i32 [[M]], [[K]]
+; CHECK-NEXT: br i1 [[C2]], label [[BB2:%.*]], label [[OUT]]
+; CHECK: bb2:
+; CHECK-NEXT: ret i1 true
+; CHECK: out:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %c1 = icmp ult i32 %n, %m
+ br i1 %c1, label %bb1, label %out
+
+bb1:
+ %r = urem i32 %x, %n
+ %c2 = icmp ult i32 %m, %k
+ br i1 %c2, label %bb2, label %out
+
+bb2:
+ %v = icmp ult i32 %r, %k
+ ret i1 %v
+
+out:
+ ret i1 false
+}
+
+define i1 @udiv_urem_combined(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
+; CHECK-LABEL: define i1 @udiv_urem_combined(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
+; CHECK-NEXT: [[CMP1:%.*]] = icmp ult i32 [[N]], [[LIMIT]]
+; CHECK-NEXT: [[CMP2:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT: [[AND:%.*]] = and i1 [[CMP1]], [[CMP2]]
+; CHECK-NEXT: br i1 [[AND]], label [[THEN:%.*]], label [[ELSE:%.*]]
+; CHECK: then:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: [[Q:%.*]] = udiv i32 [[X]], [[N]]
+; CHECK-NEXT: [[RES:%.*]] = and i1 true, true
+; CHECK-NEXT: ret i1 [[RES]]
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+ %cmp1 = icmp ult i32 %n, %limit
+ %cmp2 = icmp ule i32 %x, %limit
+ %and = and i1 %cmp1, %cmp2
+ br i1 %and, label %then, label %else
+
+then:
+ %r = urem i32 %x, %n
+ %q = udiv i32 %x, %n
+ %cmp3 = icmp ule i32 %r, %limit
+ %cmp4 = icmp ule i32 %q, %limit
+ %res = and i1 %cmp3, %cmp4
+ ret i1 %res
+
+else:
+ ret i1 false
+}
+
+define i1 @urem_i64(i64 noundef %x, i64 noundef %n, i64 noundef %m) {
+; CHECK-LABEL: define i1 @urem_i64(
+; CHECK-SAME: i64 noundef [[X:%.*]], i64 noundef [[N:%.*]], i64 noundef [[M:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ult i64 [[N]], [[M]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = urem i64 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: ret i1 true
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ult i64 %n, %m
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = urem i64 %x, %n
+ br label %check
+
+check:
+ %v = icmp ult i64 %r, %m
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; Without noundef, isGuaranteedNotToBePoison may fail; don't add facts.
+define i1 @neg_urem_no_noundef(i32 %x, i32 %n, i32 %m) {
+; CHECK-LABEL: define i1 @neg_urem_no_noundef(
+; CHECK-SAME: i32 [[X:%.*]], i32 [[N:%.*]], i32 [[M:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT: ret i1 [[V]]
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ult i32 %n, %m
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = urem i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ult i32 %r, %m
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+define i1 @neg_udiv_no_noundef(i32 %x, i32 %n, i32 %limit) {
+; CHECK-LABEL: define i1 @neg_udiv_no_noundef(
+; CHECK-SAME: i32 [[X:%.*]], i32 [[N:%.*]], i32 [[LIMIT:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[Q:%.*]] = udiv i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: [[V:%.*]] = icmp ule i32 [[Q]], [[LIMIT]]
+; CHECK-NEXT: ret i1 [[V]]
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ule i32 %x, %limit
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %q = udiv i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ule i32 %q, %limit
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; srem/sdiv are NOT handled.
+define i1 @neg_srem_not_handled(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @neg_srem_not_handled(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = srem i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT: ret i1 [[V]]
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ult i32 %n, %m
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = srem i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ult i32 %r, %m
+ ret i1 %v
+
+else:
+ ret i1 false
+}
+
+; No dominating constraint relating n to m; can't simplify.
+define i1 @neg_no_dominating_fact(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @neg_no_dominating_fact(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT: ret i1 [[V]]
+;
+ %r = urem i32 %x, %n
+ %v = icmp ult i32 %r, %m
+ ret i1 %v
+}
+
+; Wrong direction: m < n, r < n, but r < m is NOT implied.
+define i1 @neg_wrong_direction(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @neg_wrong_direction(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT: entry:
+; CHECK-NEXT: [[CMP:%.*]] = icmp ult i32 [[M]], [[N]]
+; CHECK-NEXT: br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK: mid:
+; CHECK-NEXT: [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT: br label [[CHECK:%.*]]
+; CHECK: check:
+; CHECK-NEXT: [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT: ret i1 [[V]]
+; CHECK: else:
+; CHECK-NEXT: ret i1 false
+;
+entry:
+ %cmp = icmp ult i32 %m, %n
+ br i1 %cmp, label %mid, label %else
+
+mid:
+ %r = urem i32 %x, %n
+ br label %check
+
+check:
+ %v = icmp ult i32 %r, %m
+ ret i1 %v
+
+else:
+ ret i1 false
+}
``````````
</details>
https://github.com/llvm/llvm-project/pull/180689
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