#include <limits.h>
#include <assert.h>
#include <stdlib.h>

int signed_high_prod(int x, int y) {
  long long p = (long long) x * y;
  return p >> 32;
}

unsigned unsigned_high_prod(unsigned x, unsigned y) {
  int w = sizeof(int) << 3;
  return signed_high_prod(x, y) + (((int) y >> (w - 1)) & x) + (((int) x >> (w - 1)) & y);
}

unsigned randu() {
  if (rand() & 1) {
    return rand();
  } else {
    return ~rand();
  }
}

int main() {
  assert(RAND_MAX == INT_MAX);

  const int test_cases = 1e8;
  for (int i = 0; i < test_cases; i++) {
    unsigned x = randu(), y = randu();
    assert((unsigned long long) x * y == ((unsigned long long) unsigned_high_prod(x, y) << 32) + x * y);
  }
}