Answer by Eldritch Conundrum for What are the ways compilers recognize complex patterns?

As an aside to @kouta-kun's answer for gcc, I searched what llvm does.

I found popcnt being generated in LoopIdiomRecognize.cpp, a pass that recognizes idioms and transforms simple loops into a non-loop form.The recognizePopcount and the detectPopcountIdiom functions only recognizes popcnt implementations that look like this:

for (popcount=0; x; popcount++)    x &= x - 1;

However, I could not find a detection for the branchless version.

But how would a compiler be able to figure that out, besides hardcoding numerous possible implementations and then comparing until there is a match?

Rather than comparing directly to multiple possible implementations, it's more like pattern matching. Here we detect if the loop:

• is small enough,
• has only one block,
• has only one backedge,
• contains instructions corresponding to "x2 = x1 & (x1 - 1)",
• has the cnt2 = cnt1 + 1 increment... And so on.

Do compilers have a way of 'simulating' the possible inputs and outputs of a function, and determining that they will match the result of a specific assembly instruction?

That would quickly become extremely slow to perform during compilation, just for the sake of detecting this very specific optimization.