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wdist_stats.c
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#include "wdist_common.h"
#include "ipmpar.h"
#include "dcdflib.h"
#include "wdist_stats.h"
double chiprob_p(double xx, double df) {
int st = 0;
int ww = 1;
double bnd = 1;
double pp;
double qq;
cdfchi(&ww, &pp, &qq, &xx, &df, &st, &bnd);
if (st) {
return -9;
}
return qq;
}
double inverse_chiprob(double qq, double df) {
double pp = 1 - qq;
int32_t st = 0;
int32_t ww = 2;
double bnd = 1;
double xx;
if (qq >= 1.0) {
return 0;
}
cdfchi(&ww, &pp, &qq, &xx, &df, &st, &bnd);
if (st != 0) {
return -9;
}
return xx;
}
double tprob(double tt, double df) {
int32_t st = 0;
int32_t ww = 1;
double bnd = 1;
double pp;
double qq;
if (!realnum(tt)) {
return -9;
}
tt = fabs(tt);
cdft(&ww, &pp, &qq, &tt, &df, &st, &bnd);
if (st != 0) {
return -9;
}
return 2 * qq;
}
// Inverse normal distribution
//
// Lower tail quantile for standard normal distribution function.
//
// This function returns an approximation of the inverse cumulative
// standard normal distribution function. I.e., given P, it returns
// an approximation to the X satisfying P = Pr{Z <= X} where Z is a
// random variable from the standard normal distribution.
//
// The algorithm uses a minimax approximation by rational functions
// and the result has a relative error whose absolute value is less
// than 1.15e-9.
//
// Author: Peter J. Acklam
// Time-stamp: 2002-06-09 18:45:44 +0200
// E-mail: [email protected]
// WWW URL: http://www.math.uio.no/~jacklam
//
// C implementation adapted from Peter's Perl version
// Coefficients in rational approximations.
static const double ivn_a[] =
{
-3.969683028665376e+01,
2.209460984245205e+02,
-2.759285104469687e+02,
1.383577518672690e+02,
-3.066479806614716e+01,
2.506628277459239e+00
};
static const double ivn_b[] =
{
-5.447609879822406e+01,
1.615858368580409e+02,
-1.556989798598866e+02,
6.680131188771972e+01,
-1.328068155288572e+01
};
static const double ivn_c[] =
{
-7.784894002430293e-03,
-3.223964580411365e-01,
-2.400758277161838e+00,
-2.549732539343734e+00,
4.374664141464968e+00,
2.938163982698783e+00
};
static const double ivn_d[] =
{
7.784695709041462e-03,
3.224671290700398e-01,
2.445134137142996e+00,
3.754408661907416e+00
};
#define IVN_LOW 0.02425
#define IVN_HIGH 0.97575
double ltqnorm(double p) {
// assumes 0 < p < 1
double q, r;
if (p < IVN_LOW) {
// Rational approximation for lower region
q = sqrt(-2*log(p));
return (((((ivn_c[0]*q+ivn_c[1])*q+ivn_c[2])*q+ivn_c[3])*q+ivn_c[4])*q+ivn_c[5]) /
((((ivn_d[0]*q+ivn_d[1])*q+ivn_d[2])*q+ivn_d[3])*q+1);
} else if (p > IVN_HIGH) {
// Rational approximation for upper region
q = sqrt(-2*log(1-p));
return -(((((ivn_c[0]*q+ivn_c[1])*q+ivn_c[2])*q+ivn_c[3])*q+ivn_c[4])*q+ivn_c[5]) /
((((ivn_d[0]*q+ivn_d[1])*q+ivn_d[2])*q+ivn_d[3])*q+1);
} else {
// Rational approximation for central region
q = p - 0.5;
r = q*q;
return (((((ivn_a[0]*r+ivn_a[1])*r+ivn_a[2])*r+ivn_a[3])*r+ivn_a[4])*r+ivn_a[5])*q /
(((((ivn_b[0]*r+ivn_b[1])*r+ivn_b[2])*r+ivn_b[3])*r+ivn_b[4])*r+1);
}
}
double fisher22(uint32_t m11, uint32_t m12, uint32_t m21, uint32_t m22) {
// Basic 2x2 Fisher exact test p-value calculation.
double tprob = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS;
double cur_prob = tprob;
double cprob = 0;
uint32_t uii;
double cur11;
double cur12;
double cur21;
double cur22;
double preaddp;
// Ensure we are left of the distribution center, m11 <= m22, and m12 <= m21.
if (m12 > m21) {
uii = m12;
m12 = m21;
m21 = uii;
}
if (m11 > m22) {
uii = m11;
m11 = m22;
m22 = uii;
}
if ((((uint64_t)m11) * m22) > (((uint64_t)m12) * m21)) {
uii = m11;
m11 = m12;
m12 = uii;
uii = m21;
m21 = m22;
m22 = uii;
}
cur11 = m11;
cur12 = m12;
cur21 = m21;
cur22 = m22;
while (cur12 > 0.5) {
cur11 += 1;
cur22 += 1;
cur_prob *= (cur12 * cur21) / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
if (cur_prob == INFINITY) {
return 0;
}
if (cur_prob < EXACT_TEST_BIAS) {
tprob += cur_prob;
break;
}
cprob += cur_prob;
}
if (cprob == 0) {
return 1;
}
if (cur12 > 0.5) {
do {
cur11 += 1;
cur22 += 1;
cur_prob *= (cur12 * cur21) / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
preaddp = tprob;
tprob += cur_prob;
if (tprob <= preaddp) {
break;
}
} while (cur12 > 0.5);
}
if (m11) {
cur11 = m11;
cur12 = m12;
cur21 = m21;
cur22 = m22;
cur_prob = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS;
do {
cur12 += 1;
cur21 += 1;
cur_prob *= (cur11 * cur22) / (cur12 * cur21);
cur11 -= 1;
cur22 -= 1;
preaddp = tprob;
tprob += cur_prob;
if (tprob <= preaddp) {
return preaddp / (cprob + preaddp);
}
} while (cur11 > 0.5);
}
return tprob / (cprob + tprob);
}
double fisher22_tail_pval(uint32_t m11, uint32_t m12, uint32_t m21, uint32_t m22, uint32_t right_offset, double tot_prob_recip, double right_prob, double tail_sum, uint32_t new_m11) {
// Given that the left (w.r.t. m11) reference contingency table has
// likelihood 1/tot_prob, the contingency table with m11 increased by
// right_offset has likelihood right_prob/tot_prob, and the tails (up to but
// not including the two references) sum to tail_sum/tot_prob, this
// calculates the p-value of the given m11 (which must be on one tail).
double left_prob = 1.0;
double dxx = ((intptr_t)new_m11);
double cur11;
double cur12;
double cur21;
double cur22;
double psum;
double thresh;
if (new_m11 < m11) {
cur11 = ((intptr_t)m11);
cur12 = ((intptr_t)m12);
cur21 = ((intptr_t)m21);
cur22 = ((intptr_t)m22);
dxx += 0.5; // unnecessary (53 vs. 32 bits precision), but whatever
do {
cur12 += 1;
cur21 += 1;
left_prob *= cur11 * cur22 / (cur12 * cur21);
cur11 -= 1;
cur22 -= 1;
} while (cur11 > dxx);
if (left_prob == 0) {
return 0;
}
psum = left_prob;
thresh = left_prob * (1 + SMALLISH_EPSILON);
do {
if (cur11 < 0.5) {
break;
}
cur12 += 1;
cur21 += 1;
left_prob *= cur11 * cur22 / (cur12 * cur21);
cur11 -= 1;
cur22 -= 1;
dxx = psum;
psum += left_prob;
} while (psum > dxx);
cur11 = ((intptr_t)(m11 + right_offset));
cur12 = ((intptr_t)(m12 - right_offset));
cur21 = ((intptr_t)(m21 - right_offset));
cur22 = ((intptr_t)(m22 + right_offset));
while (right_prob > thresh) {
cur11 += 1;
cur22 += 1;
right_prob *= cur12 * cur21 / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
}
if (right_prob > 0) {
psum += right_prob;
do {
cur11 += 1;
cur22 += 1;
right_prob *= cur12 * cur21 / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
dxx = psum;
psum += right_prob;
} while (psum > dxx);
}
} else {
dxx -= 0.5;
cur11 = ((intptr_t)(m11 + right_offset));
cur12 = ((intptr_t)(m12 - right_offset));
cur21 = ((intptr_t)(m21 - right_offset));
cur22 = ((intptr_t)(m22 + right_offset));
do {
cur11 += 1;
cur22 += 1;
right_prob *= cur12 * cur21 / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
} while (cur11 < dxx);
if (right_prob == 0) {
return 0;
}
psum = right_prob;
thresh = right_prob * (1 + SMALLISH_EPSILON);
do {
if (cur12 < 0.5) {
break;
}
cur11 += 1;
cur22 += 1;
right_prob *= cur12 * cur21 / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
dxx = psum;
psum += right_prob;
} while (psum > dxx);
cur11 = ((intptr_t)m11);
cur12 = ((intptr_t)m12);
cur21 = ((intptr_t)m21);
cur22 = ((intptr_t)m22);
while (left_prob > thresh) {
cur12 += 1;
cur21 += 1;
left_prob *= cur11 * cur22 / (cur12 * cur21);
cur11 -= 1;
cur22 -= 1;
}
if (left_prob > 0) {
psum += left_prob;
do {
cur12 += 1;
cur21 += 1;
left_prob *= cur11 * cur22 / (cur12 * cur21);
cur11 -= 1;
cur22 -= 1;
dxx = psum;
psum += left_prob;
} while (psum > dxx);
}
}
return psum * tot_prob_recip;
}
void fisher22_precomp_pval_bounds(double pval, uint32_t row1_sum, uint32_t col1_sum, uint32_t total, uint32_t* bounds, double* tprobs) {
// bounds[0] = m11 min
// bounds[1] = m11 (max + 1)
// bounds[2] = m11 min after including ties
// bounds[3] = m11 (max + 1) after including ties
// Treating m11 as the only variable, this returns the minimum and (maximum +
// 1) values of m11 which are less extreme than the observed result, and
// notes ties (2^{-35} tolerance). Also, returns the values necessary for
// invoking fisher22_tail_pval() with
// m11 := bounds[2] and
// right_offset := bounds[3] - bounds[2] - 1
// in tprobs[0], [1], and [2] (if tprobs is not NULL).
//
// Algorithm:
// 1. Determine center.
// 2. Sum unscaled probabilities in both directions to precision limit.
// 3. Proceed further outwards to (pval * unscaled_psum) precision limit,
// fill in the remaining return values.
double tot_prob = 1.0 / EXACT_TEST_BIAS;
double left_prob = tot_prob;
double right_prob = tot_prob;
intptr_t m11_offset = 0;
double tail_prob = 0;
double dxx;
double left11;
double left12;
double left21;
double left22;
double right11;
double right12;
double right21;
double right22;
double cur_prob;
double cur11;
double cur12;
double cur21;
double cur22;
double threshold;
intptr_t lii;
uint32_t uii;
if (!total) {
// hardcode this to avoid divide-by-zero
bounds[0] = 0;
bounds[1] = 0;
bounds[2] = 0;
bounds[3] = 1;
// no need to initialize the other return values, they should never be used
return;
} else {
if (pval == 0) {
if (total >= row1_sum + col1_sum) {
bounds[0] = 0;
bounds[1] = MINV(row1_sum, col1_sum) + 1;
} else {
bounds[0] = row1_sum + col1_sum - total;
bounds[1] = total - MAXV(row1_sum, col1_sum) + 1;
}
bounds[2] = bounds[0];
bounds[3] = bounds[1];
return;
}
}
// Center must be adjacent to the x which satisfies
// (m11 + x)(m22 + x) = (m12 - x)(m21 - x), so
// x = (m12 * m21 - m11 * m22) / (m11 + m12 + m21 + m22)
if (total >= row1_sum + col1_sum) {
// m11 = 0;
// m12 = row1_sum;
// m21 = col1_sum;
// m22 = total - row1_sum - col1_sum;
lii = (((uint64_t)row1_sum) * col1_sum) / total;
left11 = lii;
left12 = row1_sum - lii;
left21 = col1_sum - lii;
left22 = (total - row1_sum - col1_sum) + lii;
} else {
// m11 = row1_sum + col1_sum - total;
// m12 = row1_sum - m11;
// m21 = col1_sum - m11;
// m22 = 0;
lii = (((uint64_t)(total - row1_sum)) * (total - col1_sum)) / total;
// Force m11 <= m22 for internal calculation, then adjust at end.
m11_offset = row1_sum + col1_sum - total;
left11 = lii;
left12 = total - col1_sum - lii;
left21 = total - row1_sum - lii;
left22 = m11_offset + lii;
}
// We rounded x down. Should we have rounded up instead?
if ((left11 + 1) * (left22 + 1) < left12 * left21) {
left11 += 1;
left12 -= 1;
left21 -= 1;
left22 += 1;
}
// Safe to force m12 <= m21.
if (left12 > left21) {
dxx = left12;
left12 = left21;
left21 = dxx;
}
// Sum right side to limit, then left.
right11 = left11;
right12 = left12;
right21 = left21;
right22 = left22;
do {
if (right12 < 0.5) {
break;
}
right11 += 1;
right22 += 1;
right_prob *= (right12 * right21) / (right11 * right22);
right12 -= 1;
right21 -= 1;
dxx = tot_prob;
tot_prob += right_prob;
} while (tot_prob > dxx);
do {
if (left11 < 0.5) {
break;
}
left12 += 1;
left21 += 1;
left_prob *= (left11 * left22) / (left12 * left21);
left11 -= 1;
left22 -= 1;
dxx = tot_prob;
tot_prob += left_prob;
} while (tot_prob > dxx);
// Now traverse the tails to p-value precision limit.
// Upper bound for tail sum, if current element c is included:
// (c + cr + cr^2 + ...) + (c + cs + cs^2 + ...)
// = c(1/(1 - r) + 1/(1 - s))
// Compare this to pval * tot_prob.
// I.e. compare c to pval * tot_prob * (1-r)(1-s) / (2-r-s)
dxx = 1 - (left11 * left22) / ((left12 + 1) * (left21 + 1));
threshold = 1 - (right12 * right21) / ((right11 + 1) * (right22 + 1));
threshold = pval * tot_prob * dxx * threshold / (dxx + threshold);
while (left11 > 0.5) {
if (left_prob < threshold) {
tail_prob = left_prob;
cur11 = left11;
cur12 = left12;
cur21 = left21;
cur22 = left22;
cur_prob = left_prob;
do {
cur12 += 1;
cur21 += 1;
cur_prob *= (cur11 * cur22) / (cur12 * cur21);
cur11 -= 1;
cur22 -= 1;
dxx = tail_prob;
tail_prob += cur_prob;
} while (dxx < tail_prob);
left11 += 1;
left22 += 1;
left_prob *= (left12 * left21) / (left11 * left22);
left12 -= 1;
left21 -= 1;
break;
}
left12 += 1;
left21 += 1;
left_prob *= (left11 * left22) / (left12 * left21);
left11 -= 1;
left22 -= 1;
}
while (right12 > 0.5) {
if (right_prob < threshold) {
tail_prob += right_prob;
cur11 = right11;
cur12 = right12;
cur21 = right21;
cur22 = right22;
cur_prob = right_prob;
do {
cur11 += 1;
cur22 += 1;
cur_prob *= (cur12 * cur21) / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
dxx = tail_prob;
tail_prob += cur_prob;
} while (dxx < tail_prob);
right12 += 1;
right21 += 1;
right_prob *= (right11 * right22) / (right12 * right21);
right11 -= 1;
right22 -= 1;
break;
}
right11 += 1;
right22 += 1;
right_prob *= (right12 * right21) / (right11 * right22);
right12 -= 1;
right21 -= 1;
}
dxx = pval * tot_prob * (1 - SMALL_EPSILON / 2);
threshold = pval * tot_prob * (1 + SMALL_EPSILON / 2);
lii = 0;
while (1) {
if (left_prob < right_prob * (1 - SMALL_EPSILON / 2)) {
if (tail_prob + left_prob > threshold) {
break;
}
tail_prob += left_prob;
uii = 1;
} else if (right_prob < left_prob * (1 - SMALL_EPSILON / 2)) {
if (tail_prob + right_prob > threshold) {
break;
}
tail_prob += right_prob;
uii = 2;
} else {
if (tail_prob + left_prob + right_prob > threshold) {
if (left11 == right11) {
// p=1 special case: left and right refer to the same table
if (tail_prob + left_prob < threshold) {
tail_prob += left_prob;
lii = 1;
}
}
break;
}
tail_prob += left_prob + right_prob;
uii = 3;
}
if (tail_prob > dxx) {
lii = uii;
break;
}
// if more speed is necessary, we could use a buffer to save all unscaled
// probabilities during the initial outward traversal.
if (uii & 1) {
left11 += 1;
left22 += 1;
left_prob *= (left12 * left21) / (left11 * left22);
left12 -= 1;
left21 -= 1;
}
if (uii & 2) {
right12 += 1;
right21 += 1;
right_prob *= (right11 * right22) / (right12 * right21);
right11 -= 1;
right22 -= 1;
}
}
bounds[2] = m11_offset + ((intptr_t)left11);
bounds[3] = m11_offset + ((intptr_t)right11) + 1;
bounds[0] = bounds[2] + (lii & 1);
bounds[1] = bounds[3] - (lii >> 1);
if (!tprobs) {
return;
}
dxx = 1.0 / left_prob;
tprobs[0] = left_prob / tot_prob;
tprobs[1] = right_prob * dxx;
if (lii & 1) {
tail_prob -= left_prob;
}
if (lii >> 1) {
tail_prob -= right_prob;
}
tprobs[2] = tail_prob * dxx;
}
int32_t fisher23_tailsum(double* base_probp, double* saved12p, double* saved13p, double* saved22p, double* saved23p, double *totalp, uint32_t right_side) {
double total = 0;
double cur_prob = *base_probp;
double tmp12 = *saved12p;
double tmp13 = *saved13p;
double tmp22 = *saved22p;
double tmp23 = *saved23p;
double tmps12;
double tmps13;
double tmps22;
double tmps23;
double prev_prob;
// identify beginning of tail
if (right_side) {
if (cur_prob > EXACT_TEST_BIAS) {
prev_prob = tmp13 * tmp22;
while (prev_prob > 0.5) {
tmp12 += 1;
tmp23 += 1;
cur_prob *= prev_prob / (tmp12 * tmp23);
tmp13 -= 1;
tmp22 -= 1;
if (cur_prob <= EXACT_TEST_BIAS) {
break;
}
prev_prob = tmp13 * tmp22;
}
*base_probp = cur_prob;
tmps12 = tmp12;
tmps13 = tmp13;
tmps22 = tmp22;
tmps23 = tmp23;
} else {
tmps12 = tmp12;
tmps13 = tmp13;
tmps22 = tmp22;
tmps23 = tmp23;
while (1) {
prev_prob = cur_prob;
tmp13 += 1;
tmp22 += 1;
cur_prob *= (tmp12 * tmp23) / (tmp13 * tmp22);
if (cur_prob < prev_prob) {
return 1;
}
tmp12 -= 1;
tmp23 -= 1;
// throw in extra (1 - SMALL_EPSILON) multiplier to prevent rounding
// errors from causing this to keep going when the left-side test
// stopped
if (cur_prob > (1 - SMALL_EPSILON) * EXACT_TEST_BIAS) {
break;
}
total += cur_prob;
}
prev_prob = cur_prob;
cur_prob = *base_probp;
*base_probp = prev_prob;
}
} else {
if (cur_prob > EXACT_TEST_BIAS) {
prev_prob = tmp12 * tmp23;
while (prev_prob > 0.5) {
tmp13 += 1;
tmp22 += 1;
cur_prob *= prev_prob / (tmp13 * tmp22);
tmp12 -= 1;
tmp23 -= 1;
if (cur_prob <= EXACT_TEST_BIAS) {
break;
}
prev_prob = tmp12 * tmp23;
}
*base_probp = cur_prob;
tmps12 = tmp12;
tmps13 = tmp13;
tmps22 = tmp22;
tmps23 = tmp23;
} else {
tmps12 = tmp12;
tmps13 = tmp13;
tmps22 = tmp22;
tmps23 = tmp23;
while (1) {
prev_prob = cur_prob;
tmp12 += 1;
tmp23 += 1;
cur_prob *= (tmp13 * tmp22) / (tmp12 * tmp23);
if (cur_prob < prev_prob) {
return 1;
}
tmp13 -= 1;
tmp22 -= 1;
if (cur_prob > EXACT_TEST_BIAS) {
break;
}
total += cur_prob;
}
prev_prob = cur_prob;
cur_prob = *base_probp;
*base_probp = prev_prob;
}
}
*saved12p = tmp12;
*saved13p = tmp13;
*saved22p = tmp22;
*saved23p = tmp23;
if (cur_prob > EXACT_TEST_BIAS) {
*totalp = 0;
return 0;
}
// sum tail to floating point precision limit
if (right_side) {
prev_prob = total;
total += cur_prob;
while (total > prev_prob) {
tmps12 += 1;
tmps23 += 1;
cur_prob *= (tmps13 * tmps22) / (tmps12 * tmps23);
tmps13 -= 1;
tmps22 -= 1;
prev_prob = total;
total += cur_prob;
}
} else {
prev_prob = total;
total += cur_prob;
while (total > prev_prob) {
tmps13 += 1;
tmps22 += 1;
cur_prob *= (tmps12 * tmps23) / (tmps13 * tmps22);
tmps12 -= 1;
tmps23 -= 1;
prev_prob = total;
total += cur_prob;
}
}
*totalp = total;
return 0;
}
double fisher23(uint32_t m11, uint32_t m12, uint32_t m13, uint32_t m21, uint32_t m22, uint32_t m23) {
// 2x3 Fisher-Freeman-Halton exact test p-value calculation.
// The number of tables involved here is still small enough that the network
// algorithm (and the improved variants thereof that I've seen) are
// suboptimal; a 2-dimensional version of the SNPHWE2 strategy has higher
// performance.
// 2x4, 2x5, and 3x3 should also be practical with this method, but beyond
// that I doubt it's worth the trouble.
// Complexity of approach is O(n^{df/2}), where n is number of observations.
double cur_prob = (1 - SMALLISH_EPSILON) * EXACT_TEST_BIAS;
double tprob = cur_prob;
double cprob = 0;
uint32_t dir = 0; // 0 = forwards, 1 = backwards
double dyy = 0;
double base_probl;
double base_probr;
double orig_base_probl;
double orig_base_probr;
double orig_row_prob;
double row_prob;
uint32_t uii;
uint32_t ujj;
uint32_t ukk;
double cur11;
double cur21;
double savedl12;
double savedl13;
double savedl22;
double savedl23;
double savedr12;
double savedr13;
double savedr22;
double savedr23;
double orig_savedl12;
double orig_savedl13;
double orig_savedl22;
double orig_savedl23;
double orig_savedr12;
double orig_savedr13;
double orig_savedr22;
double orig_savedr23;
double tmp12;
double tmp13;
double tmp22;
double tmp23;
double dxx;
double preaddp;
// Ensure m11 + m21 <= m12 + m22 <= m13 + m23.
uii = m11 + m21;
ujj = m12 + m22;
if (uii > ujj) {
ukk = m11;
m11 = m12;
m12 = ukk;
ukk = m21;
m21 = m22;
m22 = ukk;
ukk = uii;
uii = ujj;
ujj = ukk;
}
ukk = m13 + m23;
if (ujj > ukk) {
ujj = ukk;
ukk = m12;
m12 = m13;
m13 = ukk;
ukk = m22;
m22 = m23;
m23 = ukk;
}
if (uii > ujj) {
ukk = m11;
m11 = m12;
m12 = ukk;
ukk = m21;
m21 = m22;
m22 = ukk;
}
// Ensure majority of probability mass is in front of m11.
if ((((uint64_t)m11) * (m22 + m23)) > (((uint64_t)m21) * (m12 + m13))) {
ukk = m11;
m11 = m21;
m21 = ukk;
ukk = m12;
m12 = m22;
m22 = ukk;
ukk = m13;
m13 = m23;
m23 = ukk;
}
if ((((uint64_t)m12) * m23) > (((uint64_t)m13) * m22)) {
base_probr = cur_prob;
savedr12 = m12;
savedr13 = m13;
savedr22 = m22;
savedr23 = m23;
tmp12 = savedr12;
tmp13 = savedr13;
tmp22 = savedr22;
tmp23 = savedr23;
// m12 and m23 must be nonzero
dxx = tmp12 * tmp23;
do {
tmp13 += 1;
tmp22 += 1;
cur_prob *= dxx / (tmp13 * tmp22);
tmp12 -= 1;
tmp23 -= 1;
if (cur_prob <= EXACT_TEST_BIAS) {
tprob += cur_prob;
break;
}
cprob += cur_prob;
if (cprob == INFINITY) {
return 0;
}
dxx = tmp12 * tmp23;
// must enforce tmp12 >= 0 and tmp23 >= 0 since we're saving these
} while (dxx > 0.5);
savedl12 = tmp12;
savedl13 = tmp13;
savedl22 = tmp22;
savedl23 = tmp23;
base_probl = cur_prob;
do {
tmp13 += 1;
tmp22 += 1;
cur_prob *= (tmp12 * tmp23) / (tmp13 * tmp22);
tmp12 -= 1;
tmp23 -= 1;
preaddp = tprob;
tprob += cur_prob;
} while (tprob > preaddp);
tmp12 = savedr12;
tmp13 = savedr13;
tmp22 = savedr22;
tmp23 = savedr23;
cur_prob = base_probr;
do {
tmp12 += 1;
tmp23 += 1;
cur_prob *= (tmp13 * tmp22) / (tmp12 * tmp23);
tmp13 -= 1;
tmp22 -= 1;
preaddp = tprob;
tprob += cur_prob;
} while (tprob > preaddp);
} else {
base_probl = cur_prob;
savedl12 = m12;
savedl13 = m13;
savedl22 = m22;
savedl23 = m23;
if (!((((uint64_t)m12) * m23) + (((uint64_t)m13) * m22))) {
base_probr = cur_prob;
savedr12 = savedl12;
savedr13 = savedl13;
savedr22 = savedl22;
savedr23 = savedl23;
} else {
tmp12 = savedl12;
tmp13 = savedl13;
tmp22 = savedl22;
tmp23 = savedl23;
dxx = tmp13 * tmp22;
do {
tmp12 += 1;
tmp23 += 1;
cur_prob *= dxx / (tmp12 * tmp23);
tmp13 -= 1;
tmp22 -= 1;
if (cur_prob <= EXACT_TEST_BIAS) {
tprob += cur_prob;
break;
}
cprob += cur_prob;
if (cprob == INFINITY) {
return 0;
}
dxx = tmp13 * tmp22;
} while (dxx > 0.5);
savedr12 = tmp12;
savedr13 = tmp13;
savedr22 = tmp22;
savedr23 = tmp23;
base_probr = cur_prob;
do {
tmp12 += 1;
tmp23 += 1;
cur_prob *= (tmp13 * tmp22) / (tmp12 * tmp23);
tmp13 -= 1;
tmp22 -= 1;
preaddp = tprob;
tprob += cur_prob;
} while (tprob > preaddp);
tmp12 = savedl12;
tmp13 = savedl13;
tmp22 = savedl22;
tmp23 = savedl23;
cur_prob = base_probl;
do {
tmp13 += 1;
tmp22 += 1;
cur_prob *= (tmp12 * tmp23) / (tmp13 * tmp22);
tmp12 -= 1;
tmp23 -= 1;
preaddp = tprob;
tprob += cur_prob;
} while (tprob > preaddp);
}
}
row_prob = tprob + cprob;
orig_base_probl = base_probl;
orig_base_probr = base_probr;
orig_row_prob = row_prob;
orig_savedl12 = savedl12;
orig_savedl13 = savedl13;
orig_savedl22 = savedl22;
orig_savedl23 = savedl23;
orig_savedr12 = savedr12;
orig_savedr13 = savedr13;
orig_savedr22 = savedr22;
orig_savedr23 = savedr23;
for (; dir < 2; dir++) {
cur11 = m11;
cur21 = m21;
if (dir) {
base_probl = orig_base_probl;
base_probr = orig_base_probr;
row_prob = orig_row_prob;
savedl12 = orig_savedl12;
savedl13 = orig_savedl13;
savedl22 = orig_savedl22;
savedl23 = orig_savedl23;
savedr12 = orig_savedr12;
savedr13 = orig_savedr13;
savedr22 = orig_savedr22;
savedr23 = orig_savedr23;
ukk = m11;