Binary GCD algorithm

基于二进制计算最大公约数的算法。

程序来自维基百科。

#include <stdio.h>

// Recursive version in C
unsigned int gcd(unsigned int u, unsigned int v)
{
    // simple cases (termination)
    if (u == v)
        return u;

    if (u == 0)
        return v;

    if (v == 0)
        return u;

    // look for factors of 2
    if (~u & 1) // u is even
    {
        if (v & 1) // v is odd
            return gcd(u >> 1, v);
        else // both u and v are even
            return gcd(u >> 1, v >> 1) << 1;
    }

    if (~v & 1) // u is odd, v is even
        return gcd(u, v >> 1);

    // reduce larger argument
    if (u > v)
        return gcd((u - v) >> 1, v);

    return gcd((v - u) >> 1, u);
}

// Iterative version in C
unsigned int gcd2(unsigned int u, unsigned int v)
{
  int shift;

  /* GCD(0,v) == v; GCD(u,0) == u, GCD(0,0) == 0 */
  if (u == 0) return v;
  if (v == 0) return u;

  /* Let shift := lg K, where K is the greatest power of 2
        dividing both u and v. */
  for (shift = 0; ((u | v) & 1) == 0; ++shift) {
         u >>= 1;
         v >>= 1;
  }

  while ((u & 1) == 0)
    u >>= 1;

  /* From here on, u is always odd. */
  do {
       /* remove all factors of 2 in v -- they are not common */
       /*   note: v is not zero, so while will terminate */
       while ((v & 1) == 0)  /* Loop X */
           v >>= 1;

       /* Now u and v are both odd. Swap if necessary so u <= v,
          then set v = v - u (which is even). For bignums, the
          swapping is just pointer movement, and the subtraction
          can be done in-place. */
       if (u > v) {
         unsigned int t = v; v = u; u = t;}  // Swap u and v.
       v = v - u;                       // Here v >= u.
     } while (v != 0);

  /* restore common factors of 2 */
  return u << shift;
}

int main(void)
{
    unsigned m = 140, n = 42;

    printf("gcd1: %u %u result=%u
", m, n, gcd(m, n));
    printf("gcd2: %u %u result=%u
", m, n, gcd2(m, n));

    return 0;
}