140 lines
2.9 KiB
C
140 lines
2.9 KiB
C
/*
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* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
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* See the copyright notice in the ACK home directory, in the file "Copyright".
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*
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* Author: Ceriel J.H. Jacobs
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*/
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/* $Header$ */
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#include <math.h>
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#include <errno.h>
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extern int errno;
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static double
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smallpos_gamma(x)
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double x;
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{
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/* Approximation of gamma function using
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gamma(x) = P(x-2) / Q(x-2) for x in [2,3]
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*/
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/* Hart & Cheney # 5251 */
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static double p[11] = {
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-0.2983543278574342138830437659e+06,
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-0.2384953970018198872468734423e+06,
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-0.1170494760121780688403854445e+06,
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-0.3949445048301571936421824091e+05,
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-0.1046699423827521405330650531e+05,
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-0.2188218110071816359394795998e+04,
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-0.3805112208641734657584922631e+03,
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-0.5283123755635845383718978382e+02,
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-0.6128571763704498306889428212e+01,
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-0.5028018054416812467364198750e+00,
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-0.3343060322330595274515660112e-01
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};
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static double q[9] = {
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-0.2983543278574342138830438524e+06,
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-0.1123558608748644911342306408e+06,
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0.5332716689118142157485686311e+05,
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0.8571160498907043851961147763e+04,
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-0.4734865977028211706556819770e+04,
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0.1960497612885585838997039621e+03,
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0.1257733367869888645966647426e+03,
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-0.2053126153100672764513929067e+02,
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0.1000000000000000000000000000e+01
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};
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double result = 1.0;
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while (x > 3) {
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x -= 1.0;
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result *= x;
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}
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while (x < 2) {
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result /= x;
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x += 1.0;
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}
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x -= 2.0;
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return result * POLYNOM10(x, p) / POLYNOM8(x, q);
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}
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#define log_sqrt_2pi 0.91893853320467274178032973640561763
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int signgam;
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static double
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bigpos_loggamma(x)
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double x;
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{
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/* computes the log(gamma(x)) function for big arguments
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using the Stirling form
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log(gamma(x)) = (x - 0.5)log(x) - x + log(sqrt(2*pi)) + fi(x)
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where fi(x) = (1/x)*P(1/(x*x))/Q(1/(x*x)) for x in [12,1000]
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*/
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/* Hart & Cheney # 5468 */
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static double p[4] = {
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0.12398282342474941538685913e+00,
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0.67082783834332134961461700e+00,
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0.64507302912892202513890000e+00,
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0.66662907040200752600000000e-01
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};
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static double q[4] = {
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0.14877938810969929846815600e+01,
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0.80995271894897557472821400e+01,
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0.79966911236636441947720000e+01,
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0.10000000000000000000000000e+01
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};
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double rsq = 1.0/(x*x);
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extern double log();
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return (x-0.5)*log(x)-x+log_sqrt_2pi+POLYNOM3(rsq, p)/(x*POLYNOM3(rsq, q));
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}
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static double
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neg_loggamma(x)
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double x;
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{
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/* compute the log(gamma(x)) function for negative values of x,
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using the rule:
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-x*gamma(x)*gamma(-x) = pi/sin(z*pi)
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*/
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extern double sin(), log();
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double sinpix;
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x = -x;
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sinpix = sin(M_PI * x);
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if (sinpix == 0.0) {
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errno = EDOM;
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return HUGE;
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}
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if (sinpix < 0) sinpix = -sinpix;
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else signgam = -1;
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return log(M_PI/(x * smallpos_gamma(x) * sinpix));
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}
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double
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gamma(x)
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double x;
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{
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/* Wrong name; Actually computes log(gamma(x))
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*/
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extern double log();
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signgam = 1;
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if (x <= 0) {
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return neg_loggamma(x);
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}
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if (x > 12.0) {
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return bigpos_loggamma(x);
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}
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return log(smallpos_gamma(x));
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}
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