ref: 2ebb6ad371f312e8d15fd8ce385f558a98eb0868
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));
}