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389 lines
8.0 KiB
C
389 lines
8.0 KiB
C
/* gamma.c
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*
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* Gamma function
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, __tgamma_r();
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* int* sgngam;
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* y = __tgamma_r( x, sgngam );
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*
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* double x, y, tgamma();
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* y = tgamma( x)
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns gamma function of the argument. The result is
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* correctly signed. In the reentrant version the sign (+1 or -1)
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* is returned in the variable referenced by sgngam.
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*
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* Arguments |x| <= 34 are reduced by recurrence and the function
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* approximated by a rational function of degree 6/7 in the
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* interval (2,3). Large arguments are handled by Stirling's
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* formula. Large negative arguments are made positive using
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* a reflection formula.
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC -34, 34 10000 1.3e-16 2.5e-17
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* IEEE -170,-33 20000 2.3e-15 3.3e-16
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* IEEE -33, 33 20000 9.4e-16 2.2e-16
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* IEEE 33, 171.6 20000 2.3e-15 3.2e-16
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*
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* Error for arguments outside the test range will be larger
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* owing to error amplification by the exponential function.
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*
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*/
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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*/
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/*
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* 26-11-2002 Modified for mingw.
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* Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#ifndef __MINGW32__
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#include "mconf.h"
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#else
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#include "cephes_mconf.h"
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#endif
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#ifdef UNK
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static const double P[] = {
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1.60119522476751861407E-4,
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1.19135147006586384913E-3,
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1.04213797561761569935E-2,
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4.76367800457137231464E-2,
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2.07448227648435975150E-1,
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4.94214826801497100753E-1,
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9.99999999999999996796E-1
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};
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static const double Q[] = {
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-2.31581873324120129819E-5,
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5.39605580493303397842E-4,
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-4.45641913851797240494E-3,
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1.18139785222060435552E-2,
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3.58236398605498653373E-2,
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-2.34591795718243348568E-1,
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7.14304917030273074085E-2,
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1.00000000000000000320E0
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};
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#define MAXGAM 171.624376956302725
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static const double LOGPI = 1.14472988584940017414;
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#endif
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#ifdef DEC
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static const unsigned short P[] = {
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0035047,0162701,0146301,0005234,
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0035634,0023437,0032065,0176530,
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0036452,0137157,0047330,0122574,
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0037103,0017310,0143041,0017232,
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0037524,0066516,0162563,0164605,
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0037775,0004671,0146237,0014222,
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0040200,0000000,0000000,0000000
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};
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static const unsigned short Q[] = {
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0134302,0041724,0020006,0116565,
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0035415,0072121,0044251,0025634,
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0136222,0003447,0035205,0121114,
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0036501,0107552,0154335,0104271,
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0037022,0135717,0014776,0171471,
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0137560,0034324,0165024,0037021,
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0037222,0045046,0047151,0161213,
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0040200,0000000,0000000,0000000
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};
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#define MAXGAM 34.84425627277176174
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#endif
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#ifdef IBMPC
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static const unsigned short P[] = {
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0x2153,0x3998,0xfcb8,0x3f24,
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0xbfab,0xe686,0x84e3,0x3f53,
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0x14b0,0xe9db,0x57cd,0x3f85,
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0x23d3,0x18c4,0x63d9,0x3fa8,
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0x7d31,0xdcae,0x8da9,0x3fca,
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0xe312,0x3993,0xa137,0x3fdf,
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0x0000,0x0000,0x0000,0x3ff0
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};
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static const unsigned short Q[] = {
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0xd3af,0x8400,0x487a,0xbef8,
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0x2573,0x2915,0xae8a,0x3f41,
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0xb44a,0xe750,0x40e4,0xbf72,
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0xb117,0x5b1b,0x31ed,0x3f88,
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0xde67,0xe33f,0x5779,0x3fa2,
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0x87c2,0x9d42,0x071a,0xbfce,
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0x3c51,0xc9cd,0x4944,0x3fb2,
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0x0000,0x0000,0x0000,0x3ff0
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};
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#define MAXGAM 171.624376956302725
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#endif
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#ifdef MIEEE
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static const unsigned short P[] = {
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0x3f24,0xfcb8,0x3998,0x2153,
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0x3f53,0x84e3,0xe686,0xbfab,
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0x3f85,0x57cd,0xe9db,0x14b0,
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0x3fa8,0x63d9,0x18c4,0x23d3,
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0x3fca,0x8da9,0xdcae,0x7d31,
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0x3fdf,0xa137,0x3993,0xe312,
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0x3ff0,0x0000,0x0000,0x0000
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};
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static const unsigned short Q[] = {
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0xbef8,0x487a,0x8400,0xd3af,
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0x3f41,0xae8a,0x2915,0x2573,
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0xbf72,0x40e4,0xe750,0xb44a,
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0x3f88,0x31ed,0x5b1b,0xb117,
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0x3fa2,0x5779,0xe33f,0xde67,
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0xbfce,0x071a,0x9d42,0x87c2,
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0x3fb2,0x4944,0xc9cd,0x3c51,
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0x3ff0,0x0000,0x0000,0x0000
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};
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#define MAXGAM 171.624376956302725
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#endif
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/* Stirling's formula for the gamma function */
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#if UNK
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static const double STIR[5] = {
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7.87311395793093628397E-4,
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-2.29549961613378126380E-4,
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-2.68132617805781232825E-3,
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3.47222221605458667310E-3,
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8.33333333333482257126E-2,
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};
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#define MAXSTIR 143.01608
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static const double SQTPI = 2.50662827463100050242E0;
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#endif
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#if DEC
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static const unsigned short STIR[20] = {
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0035516,0061622,0144553,0112224,
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0135160,0131531,0037460,0165740,
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0136057,0134460,0037242,0077270,
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0036143,0107070,0156306,0027751,
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0037252,0125252,0125252,0146064,
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};
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#define MAXSTIR 26.77
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static const unsigned short SQT[4] = {
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0040440,0066230,0177661,0034055,
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};
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#define SQTPI *(double *)SQT
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#endif
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#if IBMPC
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static const unsigned short STIR[20] = {
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0x7293,0x592d,0xcc72,0x3f49,
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0x1d7c,0x27e6,0x166b,0xbf2e,
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0x4fd7,0x07d4,0xf726,0xbf65,
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0xc5fd,0x1b98,0x71c7,0x3f6c,
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0x5986,0x5555,0x5555,0x3fb5,
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};
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#define MAXSTIR 143.01608
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static const union
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{
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unsigned short s[4];
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double d;
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} sqt = {{0x2706,0x1ff6,0x0d93,0x4004}};
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#define SQTPI (sqt.d)
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#endif
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#if MIEEE
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static const unsigned short STIR[20] = {
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0x3f49,0xcc72,0x592d,0x7293,
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0xbf2e,0x166b,0x27e6,0x1d7c,
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0xbf65,0xf726,0x07d4,0x4fd7,
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0x3f6c,0x71c7,0x1b98,0xc5fd,
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0x3fb5,0x5555,0x5555,0x5986,
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};
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#define MAXSTIR 143.01608
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static const unsigned short SQT[4] = {
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0x4004,0x0d93,0x1ff6,0x2706,
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};
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#define SQTPI *(double *)SQT
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#endif
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#ifndef __MINGW32__
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int sgngam = 0;
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extern int sgngam;
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extern double MAXLOG, MAXNUM, PI;
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#ifdef ANSIPROT
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extern double pow ( double, double );
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extern double log ( double );
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extern double exp ( double );
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extern double sin ( double );
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double floor ( double );
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extern double fabs ( double );
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extern int isnan ( double );
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extern int isfinite ( double );
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static double stirf ( double );
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double lgam ( double );
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#else
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double pow(), log(), exp(), sin(), polevl(), p1evl(), floor(), fabs();
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int isnan(), isfinite();
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static double stirf();
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double lgam();
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#endif
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#ifdef INFINITIES
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extern double INFINITY;
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#endif
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#ifdef NANS
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extern double NAN;
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#endif
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#else /* __MINGW32__ */
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static double stirf ( double );
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#endif
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/* Gamma function computed by Stirling's formula.
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* The polynomial STIR is valid for 33 <= x <= 172.
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*/
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static double stirf(x)
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double x;
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{
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double y, w, v;
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w = 1.0/x;
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w = 1.0 + w * polevl( w, STIR, 4 );
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y = exp(x);
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if( x > MAXSTIR )
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{ /* Avoid overflow in pow() */
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v = pow( x, 0.5 * x - 0.25 );
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y = v * (v / y);
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}
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else
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{
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y = pow( x, x - 0.5 ) / y;
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}
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y = SQTPI * y * w;
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return( y );
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}
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double __tgamma_r(double x, int* sgngam)
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{
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double p, q, z;
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int i;
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*sgngam = 1;
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#ifdef NANS
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if( isnan(x) )
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return(x);
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#endif
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#ifdef INFINITIES
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#ifdef NANS
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if( x == INFINITY )
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return(x);
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if( x == -INFINITY )
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return(NAN);
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#else
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if( !isfinite(x) )
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return(x);
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#endif
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#endif
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q = fabs(x);
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if( q > 33.0 )
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{
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if( x < 0.0 )
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{
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p = floor(q);
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if( p == q )
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{
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gsing:
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_SET_ERRNO(EDOM);
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mtherr( "tgamma", SING );
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#ifdef INFINITIES
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return (INFINITY);
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#else
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return (MAXNUM);
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#endif
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}
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i = p;
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if( (i & 1) == 0 )
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*sgngam = -1;
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z = q - p;
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if( z > 0.5 )
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{
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p += 1.0;
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z = q - p;
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}
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z = q * sin( PI * z );
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if( z == 0.0 )
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{
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_SET_ERRNO(ERANGE);
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mtherr( "tgamma", OVERFLOW );
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#ifdef INFINITIES
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return( *sgngam * INFINITY);
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#else
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return( *sgngam * MAXNUM);
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#endif
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}
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z = fabs(z);
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z = PI/(z * stirf(q) );
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}
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else
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{
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z = stirf(x);
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}
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return( *sgngam * z );
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}
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z = 1.0;
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while( x >= 3.0 )
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{
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x -= 1.0;
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z *= x;
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}
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while( x < 0.0 )
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{
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if( x > -1.E-9 )
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goto Small;
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z /= x;
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x += 1.0;
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}
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while( x < 2.0 )
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{
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if( x < 1.e-9 )
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goto Small;
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z /= x;
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x += 1.0;
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}
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if( x == 2.0 )
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return(z);
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x -= 2.0;
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p = polevl( x, P, 6 );
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q = polevl( x, Q, 7 );
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return( z * p / q );
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Small:
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if( x == 0.0 )
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{
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goto gsing;
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}
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else
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return( z/((1.0 + 0.5772156649015329 * x) * x) );
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}
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/* This is the C99 version */
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double tgamma(double x)
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{
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int local_sgngam=0;
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return (__tgamma_r(x, &local_sgngam));
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}
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