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 2if (~u & 1) // u is even{if (v & 1) // v is oddreturn gcd(u >> 1, v);else // both u and v are evenreturn gcd(u >> 1, v >> 1) << 1;}if (~v & 1) // u is odd, v is evenreturn gcd(u, v >> 1);// reduce larger argumentif (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 2dividing 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, theswapping is just pointer movement, and the subtractioncan 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\n", m, n, gcd(m, n));printf("gcd2: %u %u result=%u\n", m, n, gcd2(m, n));return 0;
}

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