Question

I have some critical branching code inside a loop that’s run about 2^26 times. Branch prediction is not optimal because m is random. How would I remove the branching, possibly using bitwise operators?

bool m;
unsigned int a;
const unsigned int k = ...; // k >= 7
if(a == 0)
    a = (m ? (a+1) : (k));
else if(a == k)
    a = (m ?     0 : (a-1));
else
    a = (m ? (a+1) : (a-1));

And here is the relevant assembly generated by gcc -O3:

.cfi_startproc
movl    4(%esp), %edx
movb    8(%esp), %cl
movl    (%edx), %eax
testl   %eax, %eax
jne L15
cmpb    $1, %cl
sbbl    %eax, %eax
andl    $638, %eax
incl    %eax
movl    %eax, (%edx)
ret
L15:
cmpl    $639, %eax
je  L23
testb   %cl, %cl
jne L24
decl    %eax
movl    %eax, (%edx)
ret
L23:
cmpb    $1, %cl
sbbl    %eax, %eax
andl    $638, %eax
movl    %eax, (%edx)
ret
L24:
incl    %eax
movl    %eax, (%edx)
ret
.cfi_endproc

Answer 1

The branch-free division-free modulo could have been useful, but testing shows that in practice, it isn’t.

const unsigned int k = 639;
void f(bool m, unsigned int &a)
{
    a += m * 2 - 1;
    if (a == -1u)
        a = k;
    else if (a == k + 1)
        a = 0;
}

Testcase:

unsigned a = 0;
f(false, a);
assert(a == 639);
f(false, a);
assert(a == 638);
f(true, a);
assert(a == 639);
f(true, a);
assert(a == 0);
f(true, a);
assert(a == 1);
f(false, a);
assert(a == 0);

Actually timing this, using a test program:

int main()
{
    for (int i = 0; i != 10000; i++)
    {
        unsigned int a = k / 2;
        while (a != 0) f(rand() & 1, a);
    }
}

(Note: there’s no srand, so results are deterministic.)

My original answer: 5.3s

The code in the question: 4.8s

Lookup table: 4.5s (static unsigned lookup[2][k+1];)

Lookup table: 4.3s (static unsigned lookup[k+1][2];)

Eric’s answer: 4.2s

This version: 4.0s