cosmopolitan/libc/tinymath/poz.c

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2020-06-15 14:18:57 +00:00
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:4;tab-width:4;coding:utf-8 -*-│
vi: set et ft=c ts=4 sts=4 sw=4 fenc=utf-8 :vi
*/
/* clang-format off */
/*
Compute probability of measured Chi Square value.
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This code was developed by Gary Perlman of the Wang
Institute (full citation below) and has been minimally
modified for use in this program.
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*/
#include "libc/math.h"
/*HEADER
Module: z.c
Purpose: compute approximations to normal z distribution probabilities
Programmer: Gary Perlman
Organization: Wang Institute, Tyngsboro, MA 01879
Copyright: none
Tabstops: 4
*/
#define Z_MAX 6.0 /* maximum meaningful z value */
/*FUNCTION poz: probability of normal z value */
/*ALGORITHM
Adapted from a polynomial approximation in:
Ibbetson D, Algorithm 209
Collected Algorithms of the CACM 1963 p. 616
Note:
This routine has six digit accuracy, so it is only useful for absolute
z values < 6. For z values >= to 6.0, poz() returns 0.0.
*/
static double /*VAR returns cumulative probability from -oo to z */
poz(const double z) /*VAR normal z value */
{
double y, x, w;
if (z == 0.0) {
x = 0.0;
} else {
y = 0.5 * fabs(z);
if (y >= (Z_MAX * 0.5)) {
x = 1.0;
} else if (y < 1.0) {
w = y * y;
x = ((((((((0.000124818987 * w
-0.001075204047) * w +0.005198775019) * w
-0.019198292004) * w +0.059054035642) * w
-0.151968751364) * w +0.319152932694) * w
-0.531923007300) * w +0.797884560593) * y * 2.0;
} else {
y -= 2.0;
x = (((((((((((((-0.000045255659 * y
+0.000152529290) * y -0.000019538132) * y
-0.000676904986) * y +0.001390604284) * y
-0.000794620820) * y -0.002034254874) * y
+0.006549791214) * y -0.010557625006) * y
+0.011630447319) * y -0.009279453341) * y
+0.005353579108) * y -0.002141268741) * y
+0.000535310849) * y +0.999936657524;
}
}
return (z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5));
}
/*
Module: chisq.c
Purpose: compute approximations to chisquare distribution probabilities
Contents: pochisq()
Uses: poz() in z.c (Algorithm 209)
Programmer: Gary Perlman
Organization: Wang Institute, Tyngsboro, MA 01879
Copyright: none
Tabstops: 4
*/
#define LOG_SQRT_PI 0.5723649429247000870717135 /* log (sqrt (pi)) */
#define I_SQRT_PI 0.5641895835477562869480795 /* 1 / sqrt (pi) */
#define BIGX 20.0 /* max value to represent exp (x) */
#define ex(x) (((x) < -BIGX) ? 0.0 : exp(x))
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/*FUNCTION pochisq: probability of chi square value */
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/*ALGORITHM Compute probability of chi square value.
Adapted from:
Hill, I. D. and Pike, M. C. Algorithm 299
Collected Algorithms for the CACM 1967 p. 243
Updated for rounding errors based on remark in
ACM TOMS June 1985, page 185
*/
double pochisq(
const double ax, /* obtained chi-square value */
const int df /* degrees of freedom */
)
{
double x = ax;
double a, y, s;
double e, c, z;
int even; /* true if df is an even number */
y = 0.0; /* XXX: blind modification due to GCC error */
if (x <= 0.0 || df < 1) {
return 1.0;
}
a = 0.5 * x;
even = (2 * (df / 2)) == df;
if (df > 1) {
y = ex(-a);
}
s = (even ? y : (2.0 * poz(-sqrt(x))));
if (df > 2) {
x = 0.5 * (df - 1.0);
z = (even ? 1.0 : 0.5);
if (a > BIGX) {
e = (even ? 0.0 : LOG_SQRT_PI);
c = log(a);
while (z <= x) {
e = log(z) + e;
s += ex(c * z - a - e);
z += 1.0;
}
return (s);
} else {
e = (even ? 1.0 : (I_SQRT_PI / sqrt(a)));
c = 0.0;
while (z <= x) {
e = e * (a / z);
c = c + e;
z += 1.0;
}
return (c * y + s);
}
} else {
return s;
}
}