Compute (a*b)%n FAST for 64-bit unsigned arguments in C(++) on x86-64 platforms?

Question

I\'m looking for a fast method to efficiently compute  (a⋅b) modulo n  (in the mathematical sense of that) for

Answer 1

Having no inline assembly kind of sucks. Anyway, the function call overhead is actually extremely small. Parameters are passed in volatile registers and no cleanup is needed.

I don't have an assembler, and x64 targets don't support __asm, so I had no choice but to "assemble" my function from opcodes myself.

Obviously it depends on . I'm using mpir (gmp) as a reference to show the function produces correct results.

#include "stdafx.h"

// mulmod64(a, b, m) == (a * b) % m
typedef uint64_t(__cdecl *mulmod64_fnptr_t)(uint64_t a, uint64_t b, uint64_t m);

uint8_t mulmod64_opcodes[] = {
    0x48, 0x89, 0xC8, // mov rax, rcx
    0x48, 0xF7, 0xE2, // mul rdx
    0x4C, 0x89, 0xC1, // mov rcx, r8
    0x48, 0xF7, 0xF1, // div rcx
    0x48, 0x89, 0xD0, // mov rax,rdx
    0xC3              // ret
};

mulmod64_fnptr_t mulmod64_fnptr;

void init() {
    DWORD dwOldProtect;
    VirtualProtect(
        &mulmod64_opcodes,
        sizeof(mulmod64_opcodes),
        PAGE_EXECUTE_READWRITE,
        &dwOldProtect);
    // NOTE: reinterpret byte array as a function pointer
    mulmod64_fnptr = (mulmod64_fnptr_t)(void*)mulmod64_opcodes;
}

int main() {
    init();

    uint64_t a64 = 2139018971924123ull;
    uint64_t b64 = 1239485798578921ull;
    uint64_t m64 = 8975489368910167ull;

    // reference code
    mpz_t a, b, c, m, r;
    mpz_inits(a, b, c, m, r, NULL);
    mpz_set_ui(a, a64);
    mpz_set_ui(b, b64);
    mpz_set_ui(m, m64);
    mpz_mul(c, a, b);
    mpz_mod(r, c, m);

    gmp_printf("(%Zd * %Zd) mod %Zd = %Zd\n", a, b, m, r);

    // using mulmod64
    uint64_t r64 = mulmod64_fnptr(a64, b64, m64);
    printf("(%llu * %llu) mod %llu = %llu\n", a64, b64, m64, r64);
    return 0;
}