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

This intrinsic is named __mul128.

typedef unsigned long long BIG;

// handles only the "hard" case when high bit of n is set
BIG shl_mod( BIG v, BIG n, int by )
{
    if (v > n) v -= n;
    while (by--) {
        if (v > (n-v))
            v -= n-v;
        else
            v <<= 1;
    }
    return v;
}

Now you can use shl_mod(B, n, 64)