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

In this patch, we 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.

In conjunction with #165877, increases vectorization factor for lerp
loops.
3 files changed
tree: 015d91a22ba821a064b1a0f3f979d66a940d4b01
  1. .ci/
  2. .github/
  3. bolt/
  4. clang/
  5. clang-tools-extra/
  6. cmake/
  7. compiler-rt/
  8. cross-project-tests/
  9. flang/
  10. flang-rt/
  11. libc/
  12. libclc/
  13. libcxx/
  14. libcxxabi/
  15. libsycl/
  16. libunwind/
  17. lld/
  18. lldb/
  19. llvm/
  20. llvm-libgcc/
  21. mlir/
  22. offload/
  23. openmp/
  24. orc-rt/
  25. polly/
  26. runtimes/
  27. third-party/
  28. utils/
  29. .clang-format
  30. .clang-format-ignore
  31. .clang-tidy
  32. .git-blame-ignore-revs
  33. .gitattributes
  34. .gitignore
  35. .mailmap
  36. CODE_OF_CONDUCT.md
  37. CONTRIBUTING.md
  38. LICENSE.TXT
  39. pyproject.toml
  40. README.md
  41. SECURITY.md
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