70 lines
1.7 KiB
C
70 lines
1.7 KiB
C
#include <stdio.h>
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#include <limits.h>
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/* Original code copied from
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http://rosettacode.org/wiki/Evaluate_binomial_coefficients
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*/
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/* We go to some effort to handle overflow situations */
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static unsigned long gcd_ui(unsigned long x, unsigned long y) {
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unsigned long t;
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if (y < x) { t = x; x = y; y = t; }
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while (y > 0) {
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t = y; y = x % y; x = t; /* y1 <- x0 % y0 ; x1 <- y0 */
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}
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return x;
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}
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unsigned long binomial(unsigned long n, unsigned long k) {
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unsigned long d, g, r = 1;
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if (k == 0) return 1;
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if (k == 1) return n;
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if (k >= n) return (k == n);
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if (k > n/2) k = n-k;
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for (d = 1; d <= k; d++) {
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if (r >= ULONG_MAX/n) { /* Possible overflow */
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unsigned long nr, dr; /* reduced numerator / denominator */
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g = gcd_ui(n, d); nr = n/g; dr = d/g;
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g = gcd_ui(r, dr); r = r/g; dr = dr/g;
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if (r >= ULONG_MAX/nr) return 0; /* Unavoidable overflow */
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r *= nr;
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r /= dr;
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n--;
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} else {
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r *= n--;
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r /= d;
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}
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}
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return r;
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}
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int main() {
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//Get test results
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printf("%lu\n", binomial(5, 3)); // 10
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printf("%lu\n", binomial(40, 19)); // 131282408400
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printf("%lu\n", binomial(67, 31)); // 11923179284862717872
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// Compute special cases for paper on TF soft-decision RS decoder:
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double a,b,c,p;
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a=(double)binomial(40, 35);
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b=(double)binomial(23, 5);
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c=(double)binomial(63, 40);
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p=a*b/c;
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printf("%e %e %e %e\n",a,b,c,p);
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a=(double)binomial(40, 36);
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b=(double)binomial(23, 4);
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c=(double)binomial(63, 40);
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p=a*b/c;
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printf("%e %e %e %e\n",a,b,c,p);
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a=(double)binomial(40, 37);
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b=(double)binomial(23, 8);
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c=(double)binomial(63, 45);
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p=a*b/c;
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printf("%e %e %e %e\n",a,b,c,p);
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return 0;
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}
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