[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.

0 files changed, 0 insertions, 0 deletions