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

7 years later, I got a solution working in Visual Studio 2019

#include 
#include 
#pragma intrinsic(_umul128)
#pragma intrinsic(_udiv128)

// compute (a*b)%n with 128-bit intermediary result
// assumes n>0  and  a*b < n * 2**64 (always the case when a<=n || b<=n )
inline uint64_t mulmod(uint64_t a, uint64_t b, uint64_t n) {
  uint64_t r, s = _umul128(a, b, &r);
  (void)_udiv128(r, s, n, &r);
  return r;
}

// compute (a*b)%n with 128-bit intermediary result
// assumes n>0, works including if a*b >= n * 2**64
inline uint64_t mulmod1(uint64_t a, uint64_t b, uint64_t n) {
  uint64_t r, s = _umul128(a % n, b, &r);
  (void)_udiv128(r, s, n, &r);
  return r;
}