[llvm] [ValueTracking] Refine known bits for linear interpolation patterns (PR #166378)

[Yingwei Zheng via llvm-commits]

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@@ -350,6 +350,139 @@ unsigned llvm::ComputeMaxSignificantBits(const Value *V, const DataLayout &DL,
   return V->getType()->getScalarSizeInBits() - SignBits + 1;
 }
 
+/// Try to detect the lerp pattern: a * (b - c) + c * d
+/// where a >= 0, b >= 0, c >= 0, d >= 0, and b >= c.
+///
+/// In that particular case, we can use the following chain of reasoning:
+///
+///   a * (b - c) + c * d <= a' * (b - c) + a' * c = a' * b where a' = max(a, d)
+///
+/// Since that is true for arbitrary a, b, c and d within our constraints, we
+/// can conclude that:
+///
+///   max(a * (b - c) + c * d) <= max(max(a), max(d)) * max(b) = U
+///
+/// Considering that any result of the lerp would be less or equal to U, it
+/// would have at least the number of leading 0s as in U.
+///
+/// While being quite a specific situation, it is fairly common in computer
+/// graphics in the shape of alpha blending.
+///
+/// Modifies given KnownOut in-place with the inferred information.
+static void computeKnownBitsFromLerpPattern(const Value *Op0, const Value *Op1,
+                                            const APInt &DemandedElts,
+                                            KnownBits &KnownOut,
+                                            const SimplifyQuery &Q,
+                                            unsigned Depth) {
+
+  Type *Ty = Op0->getType();
+  const unsigned BitWidth = Ty->getScalarSizeInBits();
+
+  // Only handle scalar types for now
+  if (Ty->isVectorTy())
+    return;
+
+  // Try to match: a * (b - c) + c * d.
+  // When a == 1 => A == nullptr, the same applies to d/D as well.
+  const Value *A = nullptr, *B = nullptr, *C = nullptr, *D = nullptr;
+  const Instruction *SubBC = nullptr;
+
+  const auto MatchSubBC = [&]() {
+    // (b - c) can have two forms that interest us:
+    //
+    //   1. sub nuw %b, %c
+    //   2. xor %c, %b
+    //
+    // For the first case, nuw flag guarantees our requirement b >= c.
+    //
+    // The second case might happen when the analysis can infer that b is a mask
+    // for c and we can transform sub operation into xor (that is usually true
+    // for constant b's). Even though xor is symmetrical, canonicalization
+    // ensures that the constant will be the RHS. We have additional checks
+    // later on to ensure that this xor operation is equivalent to subtraction.
+    return m_Instruction(SubBC, m_CombineOr(m_NUWSub(m_Value(B), m_Value(C)),
+                                            m_Xor(m_Value(C), m_Value(B))));
----------------
dtcxzyw wrote:

We may fail to match when both b and c are non-constants and c is a subset of b. But I think it is fair enough to handle the constant RHS case first.


https://github.com/llvm/llvm-project/pull/166378