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// This file is part of PLINK 1.90, copyright (C) 2005-2017 Shaun Purcell,
// Christopher Chang.
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
#include "plink_common.h"
#include "plink_stats.h"
#include "ipmpar.h"
#include "dcdflib.h"
// 2^{-40} for now, since 2^{-44} was too small on real data
#define FISHER_EPSILON 0.0000000000009094947017729282379150390625
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 calc_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;
}
double inverse_tprob(double dbl_qq, double df) {
double qq = dbl_qq * 0.5;
double pp = 1 - qq;
int32_t st = 0;
int32_t ww = 2;
double bnd = 1;
double tt;
cdft(&ww, &pp, &qq, &tt, &df, &st, &bnd);
if (st != 0) {
return -9;
}
return tt;
}
// 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: jacklam@math.uio.no
// 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 SNPHWE2(int32_t obs_hets, int32_t obs_hom1, int32_t obs_hom2, uint32_t midp) {
// This function implements an exact SNP test of Hardy-Weinberg
// Equilibrium as described in Wigginton, JE, Cutler, DJ, and
// Abecasis, GR (2005) A Note on Exact Tests of Hardy-Weinberg
// Equilibrium. American Journal of Human Genetics. 76: 000 - 000.
//
// The original version was written by Jan Wigginton.
//
// This version was written by Christopher Chang. It contains the following
// improvements over the original SNPHWE():
// - Proper handling of >64k genotypes. Previously, there was a potential
// integer overflow.
// - Detection and efficient handling of floating point overflow and
// underflow. E.g. instead of summing a tail all the way down, the loop
// stops once the latest increment underflows the partial sum's 53-bit
// precision; this results in a large speedup when max heterozygote count
// >1k.
// - No malloc() call. It's only necessary to keep track of a few partial
// sums.
// - Support for the mid-p variant of this test. See Graffelman J, Moreno V
// (2013) The mid p-value in exact tests for Hardy-Weinberg equilibrium.
//
// Note that the SNPHWE_t() function below is a lot more efficient for
// testing against a p-value inclusion threshold. SNPHWE2() should only be
// used if you need the actual p-value.
intptr_t obs_homc;
intptr_t obs_homr;
if (obs_hom1 < obs_hom2) {
obs_homc = obs_hom2;
obs_homr = obs_hom1;
} else {
obs_homc = obs_hom1;
obs_homr = obs_hom2;
}
int64_t rare_copies = 2LL * obs_homr + obs_hets;
int64_t genotypes2 = (obs_hets + obs_homc + obs_homr) * 2LL;
int32_t tie_ct = 1;
double curr_hets_t2 = obs_hets;
double curr_homr_t2 = obs_homr;
double curr_homc_t2 = obs_homc;
double tailp = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS;
double centerp = 0;
double lastp2 = tailp;
double lastp1 = tailp;
double curr_hets_t1;
double curr_homr_t1;
double curr_homc_t1;
double preaddp;
if (!genotypes2) {
if (midp) {
return 0.5;
} else {
return 1;
}
}
if (obs_hets * genotypes2 > rare_copies * (genotypes2 - rare_copies)) {
// tail 1 = upper
while (curr_hets_t2 > 1.5) {
// het_probs[curr_hets] = 1
// het_probs[curr_hets - 2] = het_probs[curr_hets] * curr_hets * (curr_hets - 1.0)
curr_homr_t2 += 1;
curr_homc_t2 += 1;
lastp2 *= (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * curr_homr_t2 * curr_homc_t2);
curr_hets_t2 -= 2;
if (lastp2 < EXACT_TEST_BIAS) {
if (lastp2 > (1 - 2 * SMALL_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
tailp += lastp2;
break;
}
centerp += lastp2;
if (centerp == INFINITY) {
return 0;
}
}
if ((centerp == 0) && (!midp)) {
return 1;
}
while (curr_hets_t2 > 1.5) {
curr_homr_t2 += 1;
curr_homc_t2 += 1;
lastp2 *= (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * curr_homr_t2 * curr_homc_t2);
curr_hets_t2 -= 2;
preaddp = tailp;
tailp += lastp2;
if (tailp <= preaddp) {
break;
}
}
curr_hets_t1 = obs_hets + 2;
curr_homr_t1 = obs_homr;
curr_homc_t1 = obs_homc;
while (curr_homr_t1 > 0.5) {
// het_probs[curr_hets + 2] = het_probs[curr_hets] * 4 * curr_homr * curr_homc / ((curr_hets + 2) * (curr_hets + 1))
lastp1 *= (4 * curr_homr_t1 * curr_homc_t1) / (curr_hets_t1 * (curr_hets_t1 - 1));
preaddp = tailp;
tailp += lastp1;
if (tailp <= preaddp) {
break;
}
curr_hets_t1 += 2;
curr_homr_t1 -= 1;
curr_homc_t1 -= 1;
}
} else {
// tail 1 = lower
while (curr_homr_t2 > 0.5) {
curr_hets_t2 += 2;
lastp2 *= (4 * curr_homr_t2 * curr_homc_t2) / (curr_hets_t2 * (curr_hets_t2 - 1));
curr_homr_t2 -= 1;
curr_homc_t2 -= 1;
if (lastp2 < EXACT_TEST_BIAS) {
if (lastp2 > (1 - 2 * SMALL_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
tailp += lastp2;
break;
}
centerp += lastp2;
if (centerp == INFINITY) {
return 0;
}
}
if ((centerp == 0) && (!midp)) {
return 1;
}
while (curr_homr_t2 > 0.5) {
curr_hets_t2 += 2;
lastp2 *= (4 * curr_homr_t2 * curr_homc_t2) / (curr_hets_t2 * (curr_hets_t2 - 1));
curr_homr_t2 -= 1;
curr_homc_t2 -= 1;
preaddp = tailp;
tailp += lastp2;
if (tailp <= preaddp) {
break;
}
}
curr_hets_t1 = obs_hets;
curr_homr_t1 = obs_homr;
curr_homc_t1 = obs_homc;
while (curr_hets_t1 > 1.5) {
curr_homr_t1 += 1;
curr_homc_t1 += 1;
lastp1 *= (curr_hets_t1 * (curr_hets_t1 - 1)) / (4 * curr_homr_t1 * curr_homc_t1);
preaddp = tailp;
tailp += lastp1;
if (tailp <= preaddp) {
break;
}
curr_hets_t1 -= 2;
}
}
if (!midp) {
return tailp / (tailp + centerp);
} else {
return (tailp - ((1 - SMALL_EPSILON) * EXACT_TEST_BIAS * 0.5) * tie_ct) / (tailp + centerp);
}
}
int32_t SNPHWE_t(int32_t obs_hets, int32_t obs_hom1, int32_t obs_hom2, double thresh) {
// Threshold-test-only version of SNPHWE2() which is usually able to exit
// from the calculation earlier. Returns 0 if these counts are close enough
// to Hardy-Weinberg equilibrium, 1 otherwise.
//
// Suppose, for definiteness, that the number of observed hets is no less
// than expectation. (Same ideas apply for the other case.) We proceed as
// follows:
// - Sum the *relative* likelihoods of more likely smaller het counts.
// - Determine the minimum tail mass to pass the threshold.
// - The majority of the time, the tail boundary elements are enough to pass
// the threshold; we never need to sum the remainder of the tails.
// - And in the case of disequilibrium, we will often be able to immediately
// determine that the tail sum cannot possibly pass the threshold, just by
// looking at the tail boundary elements and using a geometric series to
// upper-bound the tail sums.
// - Only when neither of these conditions hold do we start traveling down
// the tails.
intptr_t obs_homc;
intptr_t obs_homr;
if (obs_hom1 < obs_hom2) {
obs_homc = obs_hom2;
obs_homr = obs_hom1;
} else {
obs_homc = obs_hom1;
obs_homr = obs_hom2;
}
int64_t rare_copies = 2LL * obs_homr + obs_hets;
int64_t genotypes2 = (obs_hets + obs_homc + obs_homr) * 2LL;
double curr_hets_t2 = obs_hets; // tail 2
double curr_homr_t2 = obs_homr;
double curr_homc_t2 = obs_homc;
// Subtract epsilon from initial probability mass, so that we can compare to
// 1 when determining tail vs. center membership without floating point error
// biting us in the ass
double tailp1 = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS;
double centerp = 0;
double lastp2 = tailp1;
double tailp2 = 0;
double tail1_ceil;
double tail2_ceil;
double lastp1;
double curr_hets_t1;
double curr_homr_t1;
double curr_homc_t1;
// Initially, if center sum reaches this, the test can immediately fail.
// Once center is summed, this is recalculated, and when tail sum has reached
// this, we've passed.
double exit_thresh;
double exit_threshx;
double ratio;
double preaddp;
if (!genotypes2) {
return 0;
}
// Convert thresh into reverse odds ratio.
thresh = (1 - thresh) / thresh;
// Expected het count:
// 2 * rarefreq * (1 - rarefreq) * genotypes
// = 2 * (rare_copies / (2 * genotypes)) * (1 - rarefreq) * genotypes
// = rare_copies * (1 - (rare_copies / (2 * genotypes)))
// = (rare_copies * (2 * genotypes - rare_copies)) / (2 * genotypes)
//
// The computational identity is
// P(nhets == n) := P(nhets == n+2) * (n+2) * (n+1) /
// (4 * homr(n) * homc(n))
// where homr() and homc() are the number of homozygous rares/commons needed
// to maintain the same allele frequencies.
// This probability is always decreasing when proceeding away from the
// expected het count.
if (obs_hets * genotypes2 > rare_copies * (genotypes2 - rare_copies)) {
// tail 1 = upper
if (obs_hets < 2) {
return 0;
}
// An initial upper bound on the tail sum is useful, since it lets us
// report test failure before summing the entire center. We use the
// trivial bound of 1 + floor(rare_copies / 2): that's the total number
// of possible het counts, and the relative probability for each count must
// be <= 1 if it's in the tail.
exit_thresh = (1 + (rare_copies / 2)) * thresh * EXACT_TEST_BIAS;
// het_probs[curr_hets] = 1
// het_probs[curr_hets - 2] = het_probs[curr_hets] * curr_hets * (curr_hets - 1) / (4 * (curr_homr + 1) * (curr_homc + 1))
do {
curr_homr_t2 += 1;
curr_homc_t2 += 1;
lastp2 *= (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * curr_homr_t2 * curr_homc_t2);
curr_hets_t2 -= 2;
if (lastp2 < EXACT_TEST_BIAS) {
tailp2 = lastp2;
break;
}
centerp += lastp2;
if (centerp > exit_thresh) {
return 1;
}
} while (curr_hets_t2 > 1.5);
exit_thresh = centerp / thresh;
if (tailp1 + tailp2 >= exit_thresh) {
return 0;
}
// c + cr + cr^2 + ... = c/(1-r), which is an upper bound for the tail sum
ratio = (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * (curr_homr_t2 + 1) * (curr_homc_t2 + 1));
tail2_ceil = tailp2 / (1 - ratio);
curr_hets_t1 = obs_hets + 2;
curr_homr_t1 = obs_homr;
curr_homc_t1 = obs_homc;
// ratio for the other tail
lastp1 = (4 * curr_homr_t1 * curr_homc_t1) / (curr_hets_t1 * (curr_hets_t1 - 1));
tail1_ceil = tailp1 / (1 - lastp1);
if (tail1_ceil + tail2_ceil < exit_thresh) {
return 1;
}
lastp1 *= tailp1;
tailp1 += lastp1;
if (obs_homr > 1) {
// het_probs[curr_hets + 2] = het_probs[curr_hets] * 4 * curr_homr * curr_homc / ((curr_hets + 2) * (curr_hets + 1))
exit_threshx = exit_thresh - tailp2;
do {
curr_hets_t1 += 2;
curr_homr_t1 -= 1;
curr_homc_t1 -= 1;
lastp1 *= (4 * curr_homr_t1 * curr_homc_t1) / (curr_hets_t1 * (curr_hets_t1 - 1));
preaddp = tailp1;
tailp1 += lastp1;
if (tailp1 > exit_threshx) {
return 0;
}
if (tailp1 <= preaddp) {
break;
}
} while (curr_homr_t1 > 1.5);
}
if (tailp1 + tail2_ceil < exit_thresh) {
return 1;
}
exit_threshx = exit_thresh - tailp1;
while (curr_hets_t2 > 1) {
curr_homr_t2 += 1;
curr_homc_t2 += 1;
lastp2 *= (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * curr_homr_t2 * curr_homc_t2);
preaddp = tailp2;
tailp2 += lastp2;
if (tailp2 >= exit_threshx) {
return 0;
}
if (tailp2 <= preaddp) {
return 1;
}
curr_hets_t2 -= 2;
}
return 1;
} else {
// tail 1 = lower
if (!obs_homr) {
return 0;
}
exit_thresh = (1 + (rare_copies / 2)) * thresh * EXACT_TEST_BIAS;
do {
curr_hets_t2 += 2;
lastp2 *= (4 * curr_homr_t2 * curr_homc_t2) / (curr_hets_t2 * (curr_hets_t2 - 1));
curr_homr_t2 -= 1;
curr_homc_t2 -= 1;
if (lastp2 < EXACT_TEST_BIAS) {
tailp2 = lastp2;
break;
}
centerp += lastp2;
if (centerp > exit_thresh) {
return 1;
}
} while (curr_homr_t2 > 0.5);
exit_thresh = centerp / thresh;
if (tailp1 + tailp2 >= exit_thresh) {
return 0;
}
ratio = (4 * curr_homr_t2 * curr_homc_t2) / ((curr_hets_t2 + 2) * (curr_hets_t2 + 1));
tail2_ceil = tailp2 / (1 - ratio);
curr_hets_t1 = obs_hets;
curr_homr_t1 = obs_homr + 1;
curr_homc_t1 = obs_homc + 1;
lastp1 = (curr_hets_t1 * (curr_hets_t1 - 1)) / (4 * curr_homr_t1 * curr_homc_t1);
tail1_ceil = tailp1 / (1 - lastp1);
lastp1 *= tailp1;
tailp1 += lastp1;
if (tail1_ceil + tail2_ceil < exit_thresh) {
return 1;
}
if (obs_hets >= 4) {
exit_threshx = exit_thresh - tailp2;
do {
curr_hets_t1 -= 2;
curr_homr_t1 += 1;
curr_homc_t1 += 1;
lastp1 *= (curr_hets_t1 * (curr_hets_t1 - 1)) / (4 * curr_homr_t1 * curr_homc_t1);
preaddp = tailp1;
tailp1 += lastp1;
if (tailp1 > exit_threshx) {
return 0;
}
if (tailp1 <= preaddp) {
break;
}
} while (curr_hets_t1 > 3.5);
}
if (tailp1 + tail2_ceil < exit_thresh) {
return 1;
}
exit_threshx = exit_thresh - tailp1;
while (curr_homr_t2 > 0.5) {
curr_hets_t2 += 2;
lastp2 *= (4 * curr_homr_t2 * curr_homc_t2) / (curr_hets_t2 * (curr_hets_t2 - 1));
curr_homr_t2 -= 1;
curr_homc_t2 -= 1;
preaddp = tailp2;
tailp2 += lastp2;
if (tailp2 >= exit_threshx) {
return 0;
}
if (tailp2 <= preaddp) {
return 1;
}
}
return 1;
}
}
int32_t SNPHWE_midp_t(int32_t obs_hets, int32_t obs_hom1, int32_t obs_hom2, double thresh) {
// Mid-p version of SNPHWE_t(). (There are enough fiddly differences that I
// think it's better for this to be a separate function.) Assumes threshold
// is smaller than 0.5.
intptr_t obs_homc;
intptr_t obs_homr;
if (obs_hom1 < obs_hom2) {
obs_homc = obs_hom2;
obs_homr = obs_hom1;
} else {
obs_homc = obs_hom1;
obs_homr = obs_hom2;
}
int64_t rare_copies = 2LL * obs_homr + obs_hets;
int64_t genotypes2 = (obs_hets + obs_homc + obs_homr) * 2LL;
double curr_hets_t2 = obs_hets; // tail 2
double curr_homr_t2 = obs_homr;
double curr_homc_t2 = obs_homc;
double tailp1 = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS * 0.5;
double centerp = tailp1;
double lastp2 = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS;
double tailp2 = 0;
double tail1_ceil;
double tail2_ceil;
double lastp1;
double curr_hets_t1;
double curr_homr_t1;
double curr_homc_t1;
double exit_thresh;
double exit_threshx;
double ratio;
double preaddp;
if (!genotypes2) {
return 0;
}
thresh = (1 - thresh) / thresh;
if (obs_hets * genotypes2 > rare_copies * (genotypes2 - rare_copies)) {
if (obs_hets < 2) {
return 0;
}
exit_thresh = (1 + (rare_copies / 2)) * thresh * EXACT_TEST_BIAS;
do {
curr_homr_t2 += 1;
curr_homc_t2 += 1;
lastp2 *= (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * curr_homr_t2 * curr_homc_t2);
curr_hets_t2 -= 2;
if (lastp2 < EXACT_TEST_BIAS) {
if (lastp2 > (1 - 2 * SMALL_EPSILON) * EXACT_TEST_BIAS) {
// tie with original contingency table, apply mid-p correction here
// too
tailp2 = tailp1;
centerp += tailp1;
} else {
tailp2 = lastp2;
}
break;
}
centerp += lastp2;
if (centerp > exit_thresh) {
return 1;
}
} while (curr_hets_t2 > 1.5);
exit_thresh = centerp / thresh;
if (tailp1 + tailp2 >= exit_thresh) {
return 0;
}
ratio = (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * (curr_homr_t2 + 1) * (curr_homc_t2 + 1));
// this needs to work in both the tie and no-tie cases
tail2_ceil = tailp2 + lastp2 * ratio / (1 - ratio);
curr_hets_t1 = obs_hets + 2;
curr_homr_t1 = obs_homr;
curr_homc_t1 = obs_homc;
lastp1 = (4 * curr_homr_t1 * curr_homc_t1) / (curr_hets_t1 * (curr_hets_t1 - 1));
// always a tie here
tail1_ceil = tailp1 * 2 / (1 - lastp1) - tailp1;
if (tail1_ceil + tail2_ceil < exit_thresh) {
return 1;
}
lastp1 *= tailp1 * 2;
tailp1 += lastp1;
if (obs_homr > 1) {
exit_threshx = exit_thresh - tailp2;
do {
curr_hets_t1 += 2;
curr_homr_t1 -= 1;
curr_homc_t1 -= 1;
lastp1 *= (4 * curr_homr_t1 * curr_homc_t1) / (curr_hets_t1 * (curr_hets_t1 - 1));
preaddp = tailp1;
tailp1 += lastp1;
if (tailp1 > exit_threshx) {
return 0;
}
if (tailp1 <= preaddp) {
break;
}
} while (curr_homr_t1 > 1.5);
}
if (tailp1 + tail2_ceil < exit_thresh) {
return 1;
}
exit_threshx = exit_thresh - tailp1;
while (curr_hets_t2 > 1) {
curr_homr_t2 += 1;
curr_homc_t2 += 1;
lastp2 *= (curr_hets_t2 * (curr_hets_t2 - 1)) / (4 * curr_homr_t2 * curr_homc_t2);
preaddp = tailp2;
tailp2 += lastp2;
if (tailp2 >= exit_threshx) {
return 0;
}
if (tailp2 <= preaddp) {
return 1;
}
curr_hets_t2 -= 2;
}
return 1;
} else {
if (!obs_homr) {
return 0;
}
exit_thresh = (1 + (rare_copies / 2)) * thresh * EXACT_TEST_BIAS;
do {
curr_hets_t2 += 2;
lastp2 *= (4 * curr_homr_t2 * curr_homc_t2) / (curr_hets_t2 * (curr_hets_t2 - 1));
curr_homr_t2 -= 1;
curr_homc_t2 -= 1;
if (lastp2 < EXACT_TEST_BIAS) {
if (lastp2 > (1 - 2 * SMALL_EPSILON) * EXACT_TEST_BIAS) {
tailp2 = tailp1;
centerp += tailp1;
} else {
tailp2 = lastp2;
}
break;
}
centerp += lastp2;
if (centerp > exit_thresh) {
return 1;
}
} while (curr_homr_t2 > 0.5);
exit_thresh = centerp / thresh;
if (tailp1 + tailp2 >= exit_thresh) {
return 0;
}
ratio = (4 * curr_homr_t2 * curr_homc_t2) / ((curr_hets_t2 + 2) * (curr_hets_t2 + 1));
tail2_ceil = tailp2 + lastp2 * ratio / (1 - ratio);
curr_hets_t1 = obs_hets;
curr_homr_t1 = obs_homr + 1;
curr_homc_t1 = obs_homc + 1;
lastp1 = (curr_hets_t1 * (curr_hets_t1 - 1)) / (4 * curr_homr_t1 * curr_homc_t1);
tail1_ceil = 2 * tailp1 / (1 - lastp1) - tailp1;
lastp1 *= 2 * tailp1;
tailp1 += lastp1;
if (tail1_ceil + tail2_ceil < exit_thresh) {
return 1;
}
if (obs_hets >= 4) {
exit_threshx = exit_thresh - tailp2;
do {
curr_hets_t1 -= 2;
curr_homr_t1 += 1;
curr_homc_t1 += 1;
lastp1 *= (curr_hets_t1 * (curr_hets_t1 - 1)) / (4 * curr_homr_t1 * curr_homc_t1);
preaddp = tailp1;
tailp1 += lastp1;
if (tailp1 > exit_threshx) {
return 0;
}
if (tailp1 <= preaddp) {
break;
}
} while (curr_hets_t1 > 3.5);
}
if (tailp1 + tail2_ceil < exit_thresh) {
return 1;
}
exit_threshx = exit_thresh - tailp1;
while (curr_homr_t2 > 0.5) {
curr_hets_t2 += 2;
lastp2 *= (4 * curr_homr_t2 * curr_homc_t2) / (curr_hets_t2 * (curr_hets_t2 - 1));
curr_homr_t2 -= 1;
curr_homc_t2 -= 1;
preaddp = tailp2;
tailp2 += lastp2;
if (tailp2 >= exit_threshx) {
return 0;
}
if (tailp2 <= preaddp) {
return 1;
}
}
return 1;
}
}
double fisher22(uint32_t m11, uint32_t m12, uint32_t m21, uint32_t m22, uint32_t midp) {
// Basic 2x2 Fisher exact test p-value calculation.
double tprob = (1 - FISHER_EPSILON) * EXACT_TEST_BIAS;
double cur_prob = tprob;
double cprob = 0;
int32_t tie_ct = 1;
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) {
if (cur_prob > (1 - 2 * FISHER_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
tprob += cur_prob;
break;
}
cprob += cur_prob;
}
if ((cprob == 0) && (!midp)) {
return 1;
}
while (cur12 > 0.5) {
cur11 += 1;
cur22 += 1;
cur_prob *= (cur12 * cur21) / (cur11 * cur22);
cur12 -= 1;
cur21 -= 1;
preaddp = tprob;
tprob += cur_prob;
if (tprob <= preaddp) {
break;
}
}
if (m11) {
cur11 = m11;
cur12 = m12;
cur21 = m21;
cur22 = m22;
cur_prob = (1 - FISHER_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) {
if (!midp) {
return preaddp / (cprob + preaddp);
} else {
return (preaddp - ((1 - FISHER_EPSILON) * EXACT_TEST_BIAS * 0.5) * tie_ct) / (cprob + preaddp);
}
}
} while (cur11 > 0.5);
}
if (!midp) {
return tprob / (cprob + tprob);
} else {
return (tprob - ((1 - FISHER_EPSILON) * EXACT_TEST_BIAS * 0.5) * tie_ct) / (cprob + tprob);
}
}
double fisher22_tail_pval(uint32_t m11, uint32_t m12, uint32_t m21, uint32_t m22, int32_t right_offset, double tot_prob_recip, double right_prob, uint32_t midp, 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;
}
if (!midp) {
psum = left_prob;
} else {
psum = left_prob * 0.5;
}
thresh = left_prob * (1 + FISHER_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) {
if (midp && (right_prob < thresh * (1 - 2 * FISHER_EPSILON))) {
psum += right_prob * 0.5;
} else {
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;
}
if (!midp) {
psum = right_prob;
} else {
psum = right_prob * 0.5;
}
thresh = right_prob * (1 + FISHER_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) {
if (midp && (left_prob < thresh * (1 - 2 * FISHER_EPSILON))) {
psum += left_prob * 0.5;
} else {
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 midp, 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^{-40} 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 cmult = midp? 0.5 : 1.0;
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 - FISHER_EPSILON / 2);
threshold = pval * tot_prob * (1 + FISHER_EPSILON / 2);
lii = 0;
while (1) {
if (left_prob < right_prob * (1 - FISHER_EPSILON / 2)) {
cur_prob = tail_prob + left_prob * cmult;
if (cur_prob > threshold) {
break;
}
tail_prob += left_prob;
uii = 1;
} else if (right_prob < left_prob * (1 - FISHER_EPSILON / 2)) {
cur_prob = tail_prob + right_prob * cmult;
if (cur_prob > threshold) {
break;
}
tail_prob += right_prob;
uii = 2;
} else {
cur_prob = tail_prob + (left_prob + right_prob) * cmult;
if (cur_prob > threshold) {
if (left11 == right11) {
cur_prob = tail_prob + left_prob * cmult;
// center: left and right refer to same table. subcases:
// 1. cur_prob > threshold: center table has less extreme pval.
// lii = 0, both intervals size 1
// 2. dxx < cur_prob < threshold: center table has equal pval.
// lii = 1, less-than interval size 0 but leq interval size 1
// 3. cur_prob < dxx: even centermost table has more extreme pval
// (only possible with mid-p adj).
// lii = 0, we increment left11 so both intervals size 0
if (cur_prob < threshold) {
if (cur_prob > dxx) {
lii = 1;
} else {
left11++;
left22++;
left_prob *= (left12 * left21) / (left11 * left22);
}
}
}
break;
}
tail_prob += left_prob + right_prob;
uii = 3;
}
if (cur_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* tie_ctp, 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;
if (cur_prob > (1 - 2 * FISHER_EPSILON) * EXACT_TEST_BIAS) {
// 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;
}
*tie_ctp += 1;
}
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 > (1 - 2 * FISHER_EPSILON) * EXACT_TEST_BIAS) {
if (cur_prob > EXACT_TEST_BIAS) {
break;
}
*tie_ctp += 1;
}
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 > (1 - 2 * FISHER_EPSILON) * EXACT_TEST_BIAS) {
if (cur_prob > EXACT_TEST_BIAS) {
// even most extreme table on this side is too probable
*totalp = 0;
return 0;
}
*tie_ctp += 1;
}
// 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, uint32_t midp) {
// 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 - FISHER_EPSILON) * EXACT_TEST_BIAS;
double tprob = cur_prob;
double cprob = 0;
double dyy = 0;
uint32_t tie_ct = 1;
uint32_t dir = 0; // 0 = forwards, 1 = backwards
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) {
if (cur_prob > (1 - 2 * FISHER_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
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) {
if (cur_prob > (1 - 2 * FISHER_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
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;
if (ukk > m22 + m23) {
ukk = m22 + m23;
}
} else {
ukk = m21;
if (ukk > m12 + m13) {
ukk = m12 + m13;
}
}
ukk++;
while (--ukk) {
if (dir) {
cur21 += 1;
if (savedl23) {
savedl13 += 1;
row_prob *= (cur11 * (savedl22 + savedl23)) / (cur21 * (savedl12 + savedl13));
base_probl *= (cur11 * savedl23) / (cur21 * savedl13);
savedl23 -= 1;
} else {
savedl12 += 1;
row_prob *= (cur11 * (savedl22 + savedl23)) / (cur21 * (savedl12 + savedl13));
base_probl *= (cur11 * savedl22) / (cur21 * savedl12);
savedl22 -= 1;
}
cur11 -= 1;
} else {
cur11 += 1;
if (savedl12) {
savedl22 += 1;
row_prob *= (cur21 * (savedl12 + savedl13)) / (cur11 * (savedl22 + savedl23));
base_probl *= (cur21 * savedl12) / (cur11 * savedl22);
savedl12 -= 1;
} else {
savedl23 += 1;
row_prob *= (cur21 * (savedl12 + savedl13)) / (cur11 * (savedl22 + savedl23));
base_probl *= (cur21 * savedl13) / (cur11 * savedl23);
savedl13 -= 1;
}
cur21 -= 1;
}
if (fisher23_tailsum(&base_probl, &savedl12, &savedl13, &savedl22, &savedl23, &dxx, &tie_ct, 0)) {
break;
}
tprob += dxx;
if (dir) {
if (savedr22) {
savedr12 += 1;
base_probr *= ((cur11 + 1) * savedr22) / (cur21 * savedr12);
savedr22 -= 1;
} else {
savedr13 += 1;
base_probr *= ((cur11 + 1) * savedr23) / (cur21 * savedr13);
savedr23 -= 1;
}
} else {
if (savedr13) {
savedr23 += 1;
base_probr *= ((cur21 + 1) * savedr13) / (cur11 * savedr23);
savedr13 -= 1;
} else {
savedr22 += 1;
base_probr *= ((cur21 + 1) * savedr12) / (cur11 * savedr22);
savedr12 -= 1;
}
}
fisher23_tailsum(&base_probr, &savedr12, &savedr13, &savedr22, &savedr23, &dyy, &tie_ct, 1);
tprob += dyy;
cprob += row_prob - dxx - dyy;
if (cprob == INFINITY) {
return 0;
}
}
if (!ukk) {
continue;
}
savedl12 += savedl13;
savedl22 += savedl23;
if (dir) {
while (1) {
preaddp = tprob;
tprob += row_prob;
if (tprob <= preaddp) {
break;
}
cur21 += 1;
savedl12 += 1;
row_prob *= (cur11 * savedl22) / (cur21 * savedl12);
cur11 -= 1;
savedl22 -= 1;
}
} else {
while (1) {
preaddp = tprob;
tprob += row_prob;
if (tprob <= preaddp) {
break;
}
cur11 += 1;
savedl22 += 1;
row_prob *= (cur21 * savedl12) / (cur11 * savedl22);
cur21 -= 1;
savedl12 -= 1;
}
}
}
if (!midp) {
return tprob / (tprob + cprob);
} else {
return (tprob - ((1 - FISHER_EPSILON) * EXACT_TEST_BIAS * 0.5) * ((int32_t)tie_ct)) / (tprob + cprob);
}
}
void chi22_get_coeffs(intptr_t row1_sum, intptr_t col1_sum, intptr_t total, double* expm11p, double* recip_sump) {
// chisq = (m11 - expm11)^2 * recip_sum
// (see discussion for chi22_precomp_val_bounds() below.)
//
// expm11 = row1_sum * col1_sum / total
// expm12 = row1_sum * col2_sum / total, etc.
// recip_sum = 1 / expm11 + 1 / expm12 + 1 / expm21 + 1 / expm22
// = total * (1 / (row1_sum * col1_sum) + 1 / (row1_sum * col2_sum) +
// 1 / (row2_sum * col1_sum) + 1 / (row2_sum * col2_sum))
// = total^3 / (row1_sum * col1_sum * row2_sum * col2_sum)
double m11_numer = ((uint64_t)row1_sum) * ((uint64_t)col1_sum);
double denom = m11_numer * (((uint64_t)(total - row1_sum)) * ((uint64_t)(total - col1_sum)));
double dxx;
if (denom != 0) {
dxx = total;
*expm11p = m11_numer / dxx;
*recip_sump = dxx * dxx * dxx / denom;
} else {
// since an entire row or column is zero, either m11 or m22 is zero
// row1_sum + col1_sum - total = m11 - m22
if (row1_sum + col1_sum < total) {
*expm11p = 0;
} else {
*expm11p = row1_sum + col1_sum - total;
}
*recip_sump = 0;
}
}
double chi22_eval(intptr_t m11, intptr_t row1_sum, intptr_t col1_sum, intptr_t total) {
double expm11_numer = ((uint64_t)row1_sum) * ((uint64_t)col1_sum);
double denom = expm11_numer * (((uint64_t)(total - row1_sum)) * ((uint64_t)(total - col1_sum)));
double dxx;
double dyy;
if (denom != 0) {
dxx = total;
dyy = m11 * dxx - expm11_numer; // total * (m11 - expm11)
return (dyy * dyy * dxx) / denom;
} else {
return 0;
}
}
double chi22_evalx(intptr_t m11, intptr_t row1_sum, intptr_t col1_sum, intptr_t total) {
// PLINK emulation. returns -9 instead of 0 if row1_sum, row2_sum, col1_sum,
// or col2_sum is zero, for identical "NA" reporting.
double expm11_numer = ((uint64_t)row1_sum) * ((uint64_t)col1_sum);
double denom = expm11_numer * (((uint64_t)(total - row1_sum)) * ((uint64_t)(total - col1_sum)));
double dxx;
double dyy;
if (denom != 0) {
dxx = total;
dyy = m11 * dxx - expm11_numer; // total * (m11 - expm11)
return (dyy * dyy * dxx) / denom;
} else {
return -9;
}
}
void chi22_precomp_val_bounds(double chisq, intptr_t row1_sum, intptr_t col1_sum, intptr_t total, uint32_t* bounds, double* coeffs) {
// Treating m11 as the only variable, this returns the minimum and (maximum +
// 1) values of m11 which produce smaller chisq statistics than given in
// bounds[0] and bounds[1] respectively, and smaller-or-equal interval
// bounds in bounds[2] and bounds[3].
double expm11;
double recip_sum;
double cur11;
double dxx;
intptr_t ceil11;
intptr_t lii;
chi22_get_coeffs(row1_sum, col1_sum, total, &expm11, &recip_sum);
if (coeffs) {
coeffs[0] = expm11;
coeffs[1] = recip_sum;
}
if (recip_sum == 0) {
// sum-0 row or column, no freedom at all
bounds[0] = (intptr_t)expm11;
bounds[1] = bounds[0];
bounds[2] = bounds[0];
if (chisq == 0) {
bounds[3] = bounds[0] + 1;
} else {
bounds[3] = bounds[0];
}
return;
}
// double cur_stat = (cur11 - exp11) * (cur11 - exp11) * recipx11 + (cur12 - exp12) * (cur12 - exp12) * recipx12 + (cur21 - exp21) * (cur21 - exp21) * recipx21 + (cur22 - exp22) * (cur22 - exp22) * recipx22;
// However, we have
// cur11 - exp11 = -(cur12 - exp12) = -(cur21 - exp21) = cur22 - exp22
// So the chisq statistic reduces to
// (cur11 - exp11)^2 * (recipx11 + recipx12 + recipx21 + recipx22).
ceil11 = MINV(row1_sum, col1_sum);
// chisq = (cur11 - expm11)^2 * recip_sum
// -> expm11 +/- sqrt(chisq / recip_sum) = cur11
recip_sum = sqrt(chisq / recip_sum);
cur11 = expm11 - recip_sum;
dxx = cur11 + 1 - BIG_EPSILON;
if (dxx < 0) {
bounds[0] = 0;
bounds[2] = 0;
} else {
lii = (intptr_t)dxx;
bounds[2] = lii;
if (lii == (intptr_t)(cur11 + BIG_EPSILON)) {
bounds[0] = lii + 1;
} else {
bounds[0] = lii;
}
}
cur11 = expm11 + recip_sum;
if (cur11 > ceil11 + BIG_EPSILON) {
bounds[1] = ceil11 + 1;
bounds[3] = bounds[1];
} else {
dxx = cur11 + 1 - BIG_EPSILON;
lii = (intptr_t)dxx;
bounds[1] = lii;
if (lii == (intptr_t)(cur11 + BIG_EPSILON)) {
bounds[3] = lii + 1;
} else {
bounds[3] = lii;
}
}
}
double chi23_eval(intptr_t m11, intptr_t m12, intptr_t row1_sum, intptr_t col1_sum, intptr_t col2_sum, intptr_t total) {
// assumes no sum-zero row
intptr_t m13 = row1_sum - m11 - m12;
intptr_t col3_sum = total - col1_sum - col2_sum;
double col1_sumd;
double col2_sumd;
double col3_sumd;
double tot_recip;
double dxx;
double expect;
double delta;
double chisq;
col1_sumd = col1_sum;
col2_sumd = col2_sum;
col3_sumd = col3_sum;
tot_recip = 1.0 / ((double)total);
dxx = row1_sum * tot_recip;
expect = dxx * col1_sumd;
delta = m11 - expect;
chisq = delta * delta / expect;
expect = dxx * col2_sumd;
delta = m12 - expect;
chisq += delta * delta / expect;
expect = dxx * col3_sumd;
delta = m13 - expect;
chisq += delta * delta / expect;
dxx = (total - row1_sum) * tot_recip;
expect = dxx * col1_sumd;
delta = (col1_sum - m11) - expect;
chisq += delta * delta / expect;
expect = dxx * col2_sumd;
delta = (col2_sum - m12) - expect;
chisq += delta * delta / expect;
expect = dxx * col3_sumd;
delta = (col3_sum - m13) - expect;
chisq += delta * delta / expect;
if (chisq < (SMALL_EPSILON * SMALL_EPSILON)) {
return 0;
}
return chisq;
}
void chi23_evalx(intptr_t m11, intptr_t m12, intptr_t m13, intptr_t m21, intptr_t m22, intptr_t m23, double* chip, uint32_t* dfp) {
// Slightly different from PLINK calculation, since it detects lone nonzero
// columns.
intptr_t row1_sum = m11 + m12 + m13;
intptr_t row2_sum = m21 + m22 + m23;
intptr_t col1_sum = m11 + m21;
intptr_t col2_sum = m12 + m22;
intptr_t col3_sum = m13 + m23;
intptr_t total;
double col1_sumd;
double col2_sumd;
double col3_sumd;
double tot_recip;
double dxx;
double expect;
double delta;
double chisq;
if ((!row1_sum) || (!row2_sum)) {
*chip = -9;
*dfp = 0;
return;
}
total = row1_sum + row2_sum;
if (!col1_sum) {
*chip = chi22_evalx(m12, row1_sum, col2_sum, total);
if (*chip != -9) {
*dfp = 1;
} else {
*dfp = 0;
}
return;
} else if ((!col2_sum) || (!col3_sum)) {
*chip = chi22_evalx(m11, row1_sum, col1_sum, total);
if (*chip != -9) {
*dfp = 1;
} else {
*dfp = 0;
}
return;
}
col1_sumd = col1_sum;
col2_sumd = col2_sum;
col3_sumd = col3_sum;
tot_recip = 1.0 / ((double)total);
dxx = row1_sum * tot_recip;
expect = dxx * col1_sumd;
delta = m11 - expect;
chisq = delta * delta / expect;
expect = dxx * col2_sumd;
delta = m12 - expect;
chisq += delta * delta / expect;
expect = dxx * col3_sumd;
delta = m13 - expect;
chisq += delta * delta / expect;
dxx = row2_sum * tot_recip;
expect = dxx * col1_sumd;
delta = m21 - expect;
chisq += delta * delta / expect;
expect = dxx * col2_sumd;
delta = m22 - expect;
chisq += delta * delta / expect;
expect = dxx * col3_sumd;
delta = m23 - expect;
chisq += delta * delta / expect;
if (chisq < (SMALL_EPSILON * SMALL_EPSILON)) {
chisq = 0;
}
*chip = chisq;
*dfp = 2;
}
double ca_trend_eval(intptr_t case_dom_ct, intptr_t case_ct, intptr_t het_ct, intptr_t homdom_ct, intptr_t total) {
// case_dom_ct is an allele count (2 * homa2 + het), while other inputs are
// observation counts.
//
// If case_missing_ct is fixed,
// row1_sum = case ct
// col1_sum = A2 ct
// case_ct * ctrl_ct * REC_ct * DOM_ct
// REC_ct = 2 * obs_11 + obs_12
// DOM_ct = 2 * obs_22 + obs_12
// CA = (obs_U / obs_T) * (case REC ct) - (obs_A / obs_T) * (ctrl DOM ct)
// = (case A2) * (obs_U / obs_T) - (obs_A / obs_T) * (DOM ct - case DOM)
// = (case A2) * (obs_U / obs_T) + (case DOM) * (obs_A / obs_T) - DOM*(A/T)
// = (case A2 ct) - total A2 ct * (A/T)
// CAT = CA * obs_T
// varCA_recip = obs_T * obs_T * obs_T /
// (obs_A * obs_U * (obs_T * (obs_12 + 4 * obs_22) - DOMct * DOMct))
// trend statistic = CAT * CAT * [varCA_recip / obs_T^2]
double dom_ct = het_ct + 2 * homdom_ct;
double totald = total;
double case_ctd = case_ct;
double cat = case_dom_ct * totald - dom_ct * case_ctd;
double dxx = totald * (het_ct + 4 * ((int64_t)homdom_ct)) - dom_ct * dom_ct;
// This should never be called with dxx == 0 (which happens when two columns
// are all-zero). Use ca_trend_evalx() to check for that.
dxx *= case_ctd * (totald - case_ctd);
return cat * cat * totald / dxx;
}
double ca_trend_evalx(intptr_t case_dom_ct, intptr_t case_ct, intptr_t het_ct, intptr_t homdom_ct, intptr_t total) {
double dom_ct = het_ct + 2 * homdom_ct;
double totald = total;
double case_ctd = case_ct;
double cat = case_dom_ct * totald - dom_ct * case_ctd;
double dxx = totald * (het_ct + 4 * ((int64_t)homdom_ct)) - dom_ct * dom_ct;
if (dxx != 0) {
dxx *= case_ctd * (totald - case_ctd);
return cat * cat * totald / dxx;
} else {
return -9;
}
}
void ca_trend_precomp_val_bounds(double chisq, intptr_t case_ct, intptr_t het_ct, intptr_t homdom_ct, intptr_t total, uint32_t* bounds, double* coeffs) {
// If case_missing_ct is fixed,
// row1_sum = case ct
// col1_sum = DOM ct
// case_ct * ctrl_ct * REC_ct * DOM_ct
// REC_ct = 2 * obs_11 + obs_12
// DOM_ct = 2 * obs_22 + obs_12
// CA = (obs_U / obs_T) * (case DOM ct) - (obs_A / obs_T) * (ctrl DOM ct)
// = (case DOM) * (obs_U / obs_T) - (obs_A / obs_T) * (DOM ct - case DOM)
// = (case DOM) * (obs_U / obs_T) + (case DOM) * (obs_A / obs_T) - DOM*(A/T)
// = (case DOM ct) - total DOM ct * (A/T)
// varCA_recip = obs_T * obs_T * obs_T /
// (obs_A * obs_U * (obs_T * (obs_12 + 4 * obs_22) - DOMct * DOMct))
// trend statistic = CA * CA * varCA_recip
intptr_t dom_ct = het_ct + 2 * homdom_ct;
double dom_ctd = dom_ct;
double totald = total;
double case_ctd = case_ct;
double tot_recip = 1.0 / totald;
double expm11 = dom_ctd * case_ctd * tot_recip;
double dxx = case_ctd * (totald - case_ctd) * (totald * (het_ct + 4 * ((int64_t)homdom_ct)) - dom_ctd * dom_ctd);
double varca_recip;
double cur11;
intptr_t ceil11;
intptr_t lii;
if (dxx == 0) {
// bounds/coefficients should never be referenced in this case
return;
}
varca_recip = totald * totald * totald / dxx;
if (coeffs) {
coeffs[0] = expm11;
coeffs[1] = varca_recip;
}
// statistic: (cur11 - expm11)^2 * varca_recip
ceil11 = case_ct * 2;
if (dom_ct < ceil11) {
ceil11 = dom_ct;
}
// chisq = (cur11 - expm11)^2 * varca_recip
// -> expm11 +/- sqrt(chisq / varca_recip) = cur11
varca_recip = sqrt(chisq / varca_recip);
cur11 = expm11 - varca_recip;
dxx = cur11 + 1 - BIG_EPSILON;
if (dxx < 0) {
bounds[0] = 0;
bounds[2] = 0;
} else {
lii = (intptr_t)dxx;
bounds[2] = lii;
if (lii == (intptr_t)(cur11 + BIG_EPSILON)) {
bounds[0] = lii + 1;
} else {
bounds[0] = lii;
}
}
cur11 = expm11 + varca_recip;
if (cur11 > ceil11 + BIG_EPSILON) {
bounds[1] = ceil11 + 1;
bounds[3] = bounds[1];
} else {
dxx = cur11 + 1 - BIG_EPSILON;
lii = (intptr_t)dxx;
bounds[1] = lii;
if (lii == (intptr_t)(cur11 + BIG_EPSILON)) {
bounds[3] = lii + 1;
} else {
bounds[3] = lii;
}
}
}
uint32_t linear_hypothesis_chisq(uintptr_t constraint_ct, uintptr_t param_ct, double* constraints_con_major, double* coef, double* cov_matrix, double* param_df_buf, double* param_df_buf2, double* df_df_buf, MATRIX_INVERT_BUF1_TYPE* mi_buf, double* df_buf, double* chisq_ptr) {
// See PLINK model.cpp Model::linearHypothesis().
//
// outer = df_buf
// inner = df_df_buf
// tmp = param_df_buf
// mi_buf only needs to be of length constraint_ct
//
// Since no PLINK function ever calls this with nonzero h[] values, this just
// takes a df parameter for now; it's trivial to switch to the more general
// interface later.
double* dptr = constraints_con_major;
double* dptr2;
uintptr_t constraint_idx;
uintptr_t constraint_idx2;
uintptr_t param_idx;
double dxx;
double dyy;
for (constraint_idx = 0; constraint_idx < constraint_ct; constraint_idx++) {
dxx = 0;
dptr2 = coef;
for (param_idx = 0; param_idx < param_ct; param_idx++) {
dxx += (*dptr++) * (*dptr2++);
}
df_buf[constraint_idx] = dxx;
}
// temporarily set param_df_buf2[][] to H-transpose
transpose_copy(constraint_ct, param_ct, constraints_con_major, param_df_buf2);
col_major_matrix_multiply(constraint_ct, param_ct, param_ct, param_df_buf2, cov_matrix, param_df_buf);
// tmp[][] is now param-major
col_major_matrix_multiply(constraint_ct, constraint_ct, param_ct, param_df_buf, constraints_con_major, df_df_buf);
if (invert_matrix((uint32_t)constraint_ct, df_df_buf, mi_buf, param_df_buf2)) {
return 1;
}
dxx = 0; // result
dptr = df_df_buf;
for (constraint_idx = 0; constraint_idx < constraint_ct; constraint_idx++) {
dyy = 0; // tmp2[c]
dptr2 = df_buf;
for (constraint_idx2 = 0; constraint_idx2 < constraint_ct; constraint_idx2++) {
dyy += (*dptr++) * (*dptr2++);
}
dxx += dyy * df_buf[constraint_idx];
}
*chisq_ptr = dxx;
return 0;
}
double binom_2sided(uint32_t succ, uint32_t obs, uint32_t midp) {
// straightforward to generalize this to any success probability
double cur_succ_t2 = (int32_t)succ;
double cur_fail_t2 = (int32_t)(obs - succ);
double tailp = (1 - SMALL_EPSILON) * EXACT_TEST_BIAS;
double centerp = 0;
double lastp2 = tailp;
double lastp1 = tailp;
int32_t tie_ct = 1;
// double rate_mult_incr = rate / (1 - rate);
// double rate_mult_decr = (1 - rate) / rate;
double cur_succ_t1;
double cur_fail_t1;
double preaddp;
if (!obs) {
return midp? 0.5 : 1;
}
if (obs < succ * 2) {
// if (obs * rate < succ) {
while (cur_succ_t2 > 0.5) {
cur_fail_t2 += 1;
lastp2 *= cur_succ_t2 / cur_fail_t2;
// lastp2 *= rate_mult_decr * cur_succ_t2 / cur_fail_t2;
cur_succ_t2 -= 1;
if (lastp2 < EXACT_TEST_BIAS) {
if (lastp2 > (1 - 2 * SMALL_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
tailp += lastp2;
break;
}
centerp += lastp2;
if (centerp == INFINITY) {
return 0;
}
}
if ((centerp == 0) && (!midp)) {
return 1;
}
while (cur_succ_t2 > 0.5) {
cur_fail_t2 += 1;
lastp2 *= cur_succ_t2 / cur_fail_t2;
// lastp2 *= rate_mult_decr * cur_succ_t2 / cur_fail_t2;
cur_succ_t2 -= 1;
preaddp = tailp;
tailp += lastp2;
if (tailp <= preaddp) {
break;
}
}
cur_succ_t1 = (int32_t)(succ + 1);
cur_fail_t1 = (int32_t)(obs - succ);
while (cur_fail_t1 > 0.5) {
lastp1 *= cur_fail_t1 / cur_succ_t1;
// lastp1 *= rate_mult_incr * cur_fail_t1 / cur_succ_t1;
preaddp = tailp;
tailp += lastp1;
if (tailp <= preaddp) {
break;
}
cur_succ_t1 += 1;
cur_fail_t1 -= 1;
}
} else {
while (cur_fail_t2 > 0.5) {
cur_succ_t2++;
lastp2 *= cur_fail_t2 / cur_succ_t2;
// lastp2 *= rate_mult_incr * cur_fail_t2 / cur_succ_t2;
cur_fail_t2--;
if (lastp2 < EXACT_TEST_BIAS) {
if (lastp2 > (1 - 2 * SMALL_EPSILON) * EXACT_TEST_BIAS) {
tie_ct++;
}
tailp += lastp2;
break;
}
centerp += lastp2;
if (centerp == INFINITY) {
return 0;
}
}
if ((centerp == 0) && (!midp)) {
return 1;
}
while (cur_fail_t2 > 0.5) {
cur_succ_t2 += 1;
lastp2 *= cur_fail_t2 / cur_succ_t2;
// lastp2 *= rate_mult_incr * cur_fail_t2 / cur_succ_t2;
cur_fail_t2 -= 1;
preaddp = tailp;
tailp += lastp2;
if (tailp <= preaddp) {
break;
}
}
cur_succ_t1 = (int32_t)succ;
cur_fail_t1 = (int32_t)(obs - succ);
while (cur_succ_t1 > 0.5) {
cur_fail_t1 += 1;
lastp1 *= cur_succ_t1 / cur_fail_t1;
// lastp1 *= rate_mult_decr * cur_succ_t1 / cur_fail_t1;
preaddp = tailp;
tailp += lastp1;
if (tailp <= preaddp) {
break;
}
cur_succ_t1 -= 1;
}
}
if (!midp) {
return tailp / (tailp + centerp);
} else {
return (tailp - ((1 - SMALL_EPSILON) * EXACT_TEST_BIAS * 0.5) * tie_ct) / (tailp + centerp);
}
}
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