Does a c/c++ compiler optimize constant divisions by power-of-two value into shifts?

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Even with g++ -O0 (yes, -O0!), this happens. Your function compiles down to:

_Z3divm:
.LFB952:
        pushq   %rbp
.LCFI0:
        movq    %rsp, %rbp
.LCFI1:
        movq    %rdi, -24(%rbp)
        movq    $64, -8(%rbp)
        movq    -24(%rbp), %rax
        shrq    $6, %rax
        leave
        ret

Note the shrq $6, which is a right shift by 6 places.

With -O1, the unnecessary junk is removed:

_Z3divm:
.LFB1023:
        movq    %rdi, %rax
        shrq    $6, %rax
        ret

Results on g++ 4.3.3, x64.

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