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

[Yingwei Zheng via llvm-commits]

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@@ -350,6 +350,140 @@ 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.
+//
+// Returns unknown bits if the pattern doesn't match or constraints don't apply
+// to the given operands.
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dtcxzyw wrote:

Use `///` for header comments.

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