Fastest way to multiply two 64-bit ints to 128-bit then >> to 64-bit? [duplicate]

六眼飞鱼酱① 提交于 2019-12-04 11:55:01

As a commenter on the question pointed out, this is most easily accomplished efficiently by machine-dependent code, rather than by portable code. The asker states that the main platform is x86_64, and that has a built-in instruction for performing 64 ✕ 64 → 128 bit multiplication. This is easily accessed using a small piece of inline assembly. Note that details of inline assembly may differ somewhat with compiler, the code below was built with the Intel C/C++ compiler.

#include <stdint.h>

/* compute mul_wide (a, b) >> s, for s in [0,63] */
int64_t mulshift (int64_t a, int64_t b, int s)
{
    int64_t res;
    __asm__ (
        "movq  %1, %%rax;\n\t"          // rax = a
        "movl  %3, %%ecx;\n\t"          // ecx = s
        "imulq %2;\n\t"                 // rdx:rax = a * b
        "shrdq %%cl, %%rdx, %%rax;\n\t" // rax = int64_t (rdx:rax >> s)
        "movq  %%rax, %0;\n\t"          // res = rax
        : "=rm" (res)
        : "rm"(a), "rm"(b), "rm"(s)
        : "%rax", "%rdx", "%ecx");
    return res;
}

A portable C99 equivalent to the above code is shown below. I have tested this extensively against the inline assembly version and no mismatches were found.

void umul64wide (uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo)
{
    uint64_t a_lo = (uint64_t)(uint32_t)a;
    uint64_t a_hi = a >> 32;
    uint64_t b_lo = (uint64_t)(uint32_t)b;
    uint64_t b_hi = b >> 32;

    uint64_t p0 = a_lo * b_lo;
    uint64_t p1 = a_lo * b_hi;
    uint64_t p2 = a_hi * b_lo;
    uint64_t p3 = a_hi * b_hi;

    uint32_t cy = (uint32_t)(((p0 >> 32) + (uint32_t)p1 + (uint32_t)p2) >> 32);

    *lo = p0 + (p1 << 32) + (p2 << 32);
    *hi = p3 + (p1 >> 32) + (p2 >> 32) + cy;
}

void mul64wide (int64_t a, int64_t b, int64_t *hi, int64_t *lo)
{
    umul64wide ((uint64_t)a, (uint64_t)b, (uint64_t *)hi, (uint64_t *)lo);
    if (a < 0LL) *hi -= b;
    if (b < 0LL) *hi -= a;
}

/* compute mul_wide (a, b) >> s, for s in [0,63] */
int64_t mulshift (int64_t a, int64_t b, int s)
{
    int64_t res;
    int64_t hi, lo;
    mul64wide (a, b, &hi, &lo);
    if (s) {
        res = ((uint64_t)hi << (64 - s)) | ((uint64_t)lo >> s);
    } else {
        res = lo;
    }
    return res;
}
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