GAMMA.cpp
1.98 KB
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// gamma.cpp -- computation of gamma function.
// Algorithms and coefficient values from "Computation of Special
// Functions", Zhang and Jin, John Wiley and Sons, 1996.
//
// (C) 2003, C. Bond. All rights reserved.
//
// Returns gamma function of argument 'x'.
//
// NOTE: Returns 1e308 if argument is a negative integer or 0,
// or if argument exceeds 171.
//
#define _USE_MATH_DEFINES
#include <math.h>
double gamma(double x)
{
int i,k,m;
double ga,gr,r,z;
static double g[] = {
1.0,
0.5772156649015329,
-0.6558780715202538,
-0.420026350340952e-1,
0.1665386113822915,
-0.421977345555443e-1,
-0.9621971527877e-2,
0.7218943246663e-2,
-0.11651675918591e-2,
-0.2152416741149e-3,
0.1280502823882e-3,
-0.201348547807e-4,
-0.12504934821e-5,
0.1133027232e-5,
-0.2056338417e-6,
0.6116095e-8,
0.50020075e-8,
-0.11812746e-8,
0.1043427e-9,
0.77823e-11,
-0.36968e-11,
0.51e-12,
-0.206e-13,
-0.54e-14,
0.14e-14};
if (x > 171.0) return 1e308; // This value is an overflow flag.
if (x == (int)x) {
if (x > 0.0) {
ga = 1.0; // use factorial
for (i=2;i<x;i++) {
ga *= i;
}
}
else
ga = 1e308;
}
else {
if (fabs(x) > 1.0) {
z = fabs(x);
m = (int)z;
r = 1.0;
for (k=1;k<=m;k++) {
r *= (z-k);
}
z -= m;
}
else
z = x;
gr = g[24];
for (k=23;k>=0;k--) {
gr = gr*z+g[k];
}
ga = 1.0/(gr*z);
if (fabs(x) > 1.0) {
ga *= r;
if (x < 0.0) {
ga = -M_PI/(x*ga*sin(M_PI*x));
}
}
}
return ga;
}