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/* rgamma.c
*
* Reciprocal gamma function
*
*
*
* SYNOPSIS:
*
* double x, y, rgamma();
*
* y = rgamma( x );
*
*
*
* DESCRIPTION:
*
* Returns one divided by the gamma function of the argument.
*
* The function is approximated by a Chebyshev expansion in
* the interval [0,1]. Range reduction is by recurrence
* for arguments between -34.034 and +34.84425627277176174.
* 1/MAXNUM is returned for positive arguments outside this
* range. For arguments less than -34.034 the cosecant
* reflection formula is applied; lograrithms are employed
* to avoid unnecessary overflow.
*
* The reciprocal gamma function has no singularities,
* but overflow and underflow may occur for large arguments.
* These conditions return either MAXNUM or 1/MAXNUM with
* appropriate sign.
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -30,+30 4000 1.2e-16 1.8e-17
* IEEE -30,+30 30000 1.1e-15 2.0e-16
* For arguments less than -34.034 the peak error is on the
* order of 5e-15 (DEC), excepting overflow or underflow.
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1985, 1987, 2000 by Stephen L. Moshier
*/
#include <math.h>
/* Chebyshev coefficients for reciprocal gamma function
* in interval 0 to 1. Function is 1/(x gamma(x)) - 1
*/
#ifdef UNK
static double R[] = {
3.13173458231230000000E-17,
-6.70718606477908000000E-16,
2.20039078172259550000E-15,
2.47691630348254132600E-13,
-6.60074100411295197440E-12,
5.13850186324226978840E-11,
1.08965386454418662084E-9,
-3.33964630686836942556E-8,
2.68975996440595483619E-7,
2.96001177518801696639E-6,
-8.04814124978471142852E-5,
4.16609138709688864714E-4,
5.06579864028608725080E-3,
-6.41925436109158228810E-2,
-4.98558728684003594785E-3,
1.27546015610523951063E-1
};
#endif
#ifdef DEC
static unsigned short R[] = {
0022420,0066376,0176751,0071636,
0123501,0051114,0042104,0131153,
0024036,0107013,0126504,0033361,
0025613,0070040,0035174,0162316,
0126750,0037060,0077775,0122202,
0027541,0177143,0037675,0105150,
0030625,0141311,0075005,0115436,
0132017,0067714,0125033,0014721,
0032620,0063707,0105256,0152643,
0033506,0122235,0072757,0170053,
0134650,0144041,0015617,0016143,
0035332,0066125,0000776,0006215,
0036245,0177377,0137173,0131432,
0137203,0073541,0055645,0141150,
0136243,0057043,0026226,0017362,
0037402,0115554,0033441,0012310
};
#endif
#ifdef IBMPC
static unsigned short R[] = {
0x2e74,0xdfbd,0x0d9f,0x3c82,
0x964d,0x8888,0x2a49,0xbcc8,
0x86de,0x75a8,0xd1c1,0x3ce3,
0x9c9a,0x074f,0x6e04,0x3d51,
0xb490,0x0fff,0x07c6,0xbd9d,
0xb14d,0x67f7,0x3fcc,0x3dcc,
0xb364,0x2f40,0xb859,0x3e12,
0x633a,0x9543,0xedf9,0xbe61,
0xdab4,0xf155,0x0cf8,0x3e92,
0xfe05,0xaebd,0xd493,0x3ec8,
0xe38c,0x2371,0x1904,0xbf15,
0xc192,0xa03f,0x4d8a,0x3f3b,
0x7663,0xf7cf,0xbfdf,0x3f74,
0xb84d,0x2b74,0x6eec,0xbfb0,
0xc3de,0x6592,0x6bc4,0xbf74,
0x2299,0x86e4,0x536d,0x3fc0
};
#endif
#ifdef MIEEE
static unsigned short R[] = {
0x3c82,0x0d9f,0xdfbd,0x2e74,
0xbcc8,0x2a49,0x8888,0x964d,
0x3ce3,0xd1c1,0x75a8,0x86de,
0x3d51,0x6e04,0x074f,0x9c9a,
0xbd9d,0x07c6,0x0fff,0xb490,
0x3dcc,0x3fcc,0x67f7,0xb14d,
0x3e12,0xb859,0x2f40,0xb364,
0xbe61,0xedf9,0x9543,0x633a,
0x3e92,0x0cf8,0xf155,0xdab4,
0x3ec8,0xd493,0xaebd,0xfe05,
0xbf15,0x1904,0x2371,0xe38c,
0x3f3b,0x4d8a,0xa03f,0xc192,
0x3f74,0xbfdf,0xf7cf,0x7663,
0xbfb0,0x6eec,0x2b74,0xb84d,
0xbf74,0x6bc4,0x6592,0xc3de,
0x3fc0,0x536d,0x86e4,0x2299
};
#endif
static char name[] = "rgamma";
#ifdef ANSIPROT
extern double chbevl ( double, void *, int );
extern double exp ( double );
extern double log ( double );
extern double sin ( double );
extern double lgam ( double );
#else
double chbevl(), exp(), log(), sin(), lgam();
#endif
extern double PI, MAXLOG, MAXNUM;
double rgamma(x)
double x;
{
double w, y, z;
int sign;
if( x > 34.84425627277176174)
{
mtherr( name, UNDERFLOW );
return(1.0/MAXNUM);
}
if( x < -34.034 )
{
w = -x;
z = sin( PI*w );
if( z == 0.0 )
return(0.0);
if( z < 0.0 )
{
sign = 1;
z = -z;
}
else
sign = -1;
y = log( w * z ) - log(PI) + lgam(w);
if( y < -MAXLOG )
{
mtherr( name, UNDERFLOW );
return( sign * 1.0 / MAXNUM );
}
if( y > MAXLOG )
{
mtherr( name, OVERFLOW );
return( sign * MAXNUM );
}
return( sign * exp(y));
}
z = 1.0;
w = x;
while( w > 1.0 ) /* Downward recurrence */
{
w -= 1.0;
z *= w;
}
while( w < 0.0 ) /* Upward recurrence */
{
z /= w;
w += 1.0;
}
if( w == 0.0 ) /* Nonpositive integer */
return(0.0);
if( w == 1.0 ) /* Other integer */
return( 1.0/z );
y = w * ( 1.0 + chbevl( 4.0*w-2.0, R, 16 ) ) / z;
return(y);
}
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