shithub: riscv

ref: d4124d48f9c7e85fdaa50640035080174c94196e
dir: /sys/src/ape/lib/ap/math/gamma.c/

#include <math.h>
#include <errno.h>

/*
	C program for floating point log gamma function

	gamma(x) computes the log of the absolute
	value of the gamma function.
	The sign of the gamma function is returned in the
	external quantity signgam.

	The coefficients for expansion around zero
	are #5243 from Hart & Cheney; for expansion
	around infinity they are #5404.

	Calls log and sin.
*/

int	signgam;
static double goobie	= 0.9189385332046727417803297;
static double pi	= 3.1415926535897932384626434;

#define M 6
#define N 8
static double p1[] = {
	0.83333333333333101837e-1,
	-.277777777735865004e-2,
	0.793650576493454e-3,
	-.5951896861197e-3,
	0.83645878922e-3,
	-.1633436431e-2,
};
static double p2[] = {
	-.42353689509744089647e5,
	-.20886861789269887364e5,
	-.87627102978521489560e4,
	-.20085274013072791214e4,
	-.43933044406002567613e3,
	-.50108693752970953015e2,
	-.67449507245925289918e1,
	0.0,
};
static double q2[] = {
	-.42353689509744090010e5,
	-.29803853309256649932e4,
	0.99403074150827709015e4,
	-.15286072737795220248e4,
	-.49902852662143904834e3,
	0.18949823415702801641e3,
	-.23081551524580124562e2,
	0.10000000000000000000e1,
};

static double
asym(double arg)
{
	double n, argsq;
	int i;

	argsq = 1 / (arg*arg);
	n = 0;
	for(i=M-1; i>=0; i--)
		n = n*argsq + p1[i];
	return (arg-.5)*log(arg) - arg + goobie + n/arg;
}

static double
pos(double arg)
{
	double n, d, s;
	int i;

	if(arg < 2)
		return pos(arg+1)/arg;
	if(arg > 3)
		return (arg-1)*pos(arg-1);

	s = arg - 2;
	n = 0;
	d = 0;
	for(i=N-1; i>=0; i--){
		n = n*s + p2[i];
		d = d*s + q2[i];
	}
	return n/d;
}

static double
neg(double arg)
{
	double temp;

	arg = -arg;
	temp = sin(pi*arg);
	if(temp == 0) {
		errno = EDOM;
		return HUGE_VAL;
	}
	if(temp < 0)
		temp = -temp;
	else
		signgam = -1;
	return -log(arg*pos(arg)*temp/pi);
}

double
gamma(double arg)
{

	signgam = 1;
	if(arg <= 0)
		return neg(arg);
	if(arg > 8)
		return asym(arg);
	return log(pos(arg));
}