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fet.c

#include <math.h>
#include <stdlib.h>

/* This program is implemented with ideas from this web page:
 *
 *   http://www.langsrud.com/fisher.htm
 */

// log\binom{n}{k}
static double lbinom(int n, int k)
{
      if (k == 0 || n == k) return 0;
      return lgamma(n+1) - lgamma(k+1) - lgamma(n-k+1);
}

// n11  n12  | n1_
// n21  n22  | n2_
//-----------+----
// n_1  n_2  | n

// hypergeometric distribution
static double hypergeo(int n11, int n1_, int n_1, int n)
{
      return exp(lbinom(n1_, n11) + lbinom(n-n1_, n_1-n11) - lbinom(n, n_1));
}

typedef struct {
      int n11, n1_, n_1, n;
      double p;
} hgacc_t;

// incremental version of hypergenometric distribution
static double hypergeo_acc(int n11, int n1_, int n_1, int n, hgacc_t *aux)
{
      if (n1_ || n_1 || n) {
            aux->n11 = n11; aux->n1_ = n1_; aux->n_1 = n_1; aux->n = n;
      } else { // then only n11 changed; the rest fixed
            if (n11%11 && n11 + aux->n - aux->n1_ - aux->n_1) {
                  if (n11 == aux->n11 + 1) { // incremental
                        aux->p *= (double)(aux->n1_ - aux->n11) / n11
                              * (aux->n_1 - aux->n11) / (n11 + aux->n - aux->n1_ - aux->n_1);
                        aux->n11 = n11;
                        return aux->p;
                  }
                  if (n11 == aux->n11 - 1) { // incremental
                        aux->p *= (double)aux->n11 / (aux->n1_ - n11)
                              * (aux->n11 + aux->n - aux->n1_ - aux->n_1) / (aux->n_1 - n11);
                        aux->n11 = n11;
                        return aux->p;
                  }
            }
            aux->n11 = n11;
      }
      aux->p = hypergeo(aux->n11, aux->n1_, aux->n_1, aux->n);
      return aux->p;
}

double kt_fisher_exact(int n11, int n12, int n21, int n22, double *_left, double *_right, double *two)
{
      int i, j, max, min;
      double p, q, left, right;
      hgacc_t aux;
      int n1_, n_1, n;

      n1_ = n11 + n12; n_1 = n11 + n21; n = n11 + n12 + n21 + n22; // calculate n1_, n_1 and n
      max = (n_1 < n1_) ? n_1 : n1_; // max n11, for right tail
      min = (n1_ + n_1 - n < 0) ? 0 : (n1_ + n_1 - n < 0); // min n11, for left tail
      *two = *_left = *_right = 1.;
      if (min == max) return 1.; // no need to do test
      q = hypergeo_acc(n11, n1_, n_1, n, &aux); // the probability of the current table
      // left tail
      p = hypergeo_acc(min, 0, 0, 0, &aux);
      for (left = 0., i = min + 1; p < 0.99999999 * q; ++i) // loop until underflow
            left += p, p = hypergeo_acc(i, 0, 0, 0, &aux);
      --i;
      if (p < 1.00000001 * q) left += p;
      else --i;
      // right tail
      p = hypergeo_acc(max, 0, 0, 0, &aux);
      for (right = 0., j = max - 1; p < 0.99999999 * q; --j) // loop until underflow
            right += p, p = hypergeo_acc(j, 0, 0, 0, &aux);
      if (p < 1.00000001 * q) right += p;
      else ++j;
      // two-tail
      *two = left + right;
      if (*two > 1.) *two = 1.;
      // adjust left and right
      if (abs(i - n11) < abs(j - n11)) right = 1. - left + q;
      else left = 1.0 - right + q;
      *_left = left; *_right = right;
      return q;
}

#ifdef FET_MAIN
#include <stdio.h>

int main(int argc, char *argv[])
{
      char id[1024];
      int n11, n12, n21, n22;
      double left, right, twotail, prob;

      while (scanf("%s%d%d%d%d", id, &n11, &n12, &n21, &n22) == 5) {
            prob = kt_fisher_exact(n11, n12, n21, n22, &left, &right, &twotail);
            printf("%s\t%d\t%d\t%d\t%d\t%.6g\t%.6g\t%.6g\t%.6g\n", id, n11, n12, n21, n22,
                        prob, left, right, twotail);
      }
      return 0;
}
#endif

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