Answer by kouta-kun for What are the ways compilers recognize complex patterns?

By running gcc -O3 -fdump-tree-all-all main.c -S -march=haswell which prints out all optimization steps, we can find that this optimization is performed in main.c.036t.forwprop1:

Pass statistics of "forwprop": ----------------Applying pattern match.pd:4684, gimple-match-6.cc:4680Applying pattern match.pd:9281, gimple-match-7.cc:2488

Which in turn, by going to the match.pd file, we can see that this is in fact a hardcoded match for that popcnt implementation, constants and all:

/* 64- and 32-bits branchless implementations of popcount are detected:...(simplify (rshift  (mult   (bit_and    (plus:c     (rshift @8 INTEGER_CST@5)      (plus:c@8       (bit_and @6 INTEGER_CST@7)    (bit_and     (rshift      (minus@6 @0...  /* Check constants and optab.  */  (with { unsigned prec = TYPE_PRECISION (type);      int shift = (64 - prec) & 63;      unsigned HOST_WIDE_INT c1        = HOST_WIDE_INT_UC (0x0101010101010101) >> shift;      unsigned HOST_WIDE_INT c2        = HOST_WIDE_INT_UC (0x0F0F0F0F0F0F0F0F) >> shift;      unsigned HOST_WIDE_INT c3        = HOST_WIDE_INT_UC (0x3333333333333333) >> shift;      unsigned HOST_WIDE_INT c4        = HOST_WIDE_INT_UC (0x5555555555555555) >> shift;

In this particular case, this implementation of popcnt is probably common enough that it warrants a special case being implemented.