summaryrefslogtreecommitdiff
path: root/libm/ldouble/gammal.c
diff options
context:
space:
mode:
Diffstat (limited to 'libm/ldouble/gammal.c')
-rw-r--r--libm/ldouble/gammal.c764
1 files changed, 0 insertions, 764 deletions
diff --git a/libm/ldouble/gammal.c b/libm/ldouble/gammal.c
deleted file mode 100644
index de7ed89a2..000000000
--- a/libm/ldouble/gammal.c
+++ /dev/null
@@ -1,764 +0,0 @@
-/* gammal.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, gammal();
- * extern int sgngam;
- *
- * y = gammal( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
- *
- * Arguments |x| <= 13 are reduced by recurrence and the function
- * approximated by a rational function of degree 7/8 in the
- * interval (2,3). Large arguments are handled by Stirling's
- * formula. Large negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -40,+40 10000 3.6e-19 7.9e-20
- * IEEE -1755,+1755 10000 4.8e-18 6.5e-19
- *
- * Accuracy for large arguments is dominated by error in powl().
- *
- */
-/* lgaml()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, lgaml();
- * extern int sgngam;
- *
- * y = lgaml( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
- *
- * For arguments greater than 33, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula using a polynomial approximation of
- * degree 4. Arguments between -33 and +33 are reduced by
- * recurrence to the interval [2,3] of a rational approximation.
- * The cosecant reflection formula is employed for arguments
- * less than -33.
- *
- * Arguments greater than MAXLGML (10^4928) return MAXNUML.
- *
- *
- *
- * ACCURACY:
- *
- *
- * arithmetic domain # trials peak rms
- * IEEE -40, 40 100000 2.2e-19 4.6e-20
- * IEEE 10^-2000,10^+2000 20000 1.6e-19 3.3e-20
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- *
- */
-
-/* gamma.c */
-/* gamma function */
-
-/*
-Copyright 1994 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-/*
-gamma(x+2) = gamma(x+2) P(x)/Q(x)
-0 <= x <= 1
-Relative error
-n=7, d=8
-Peak error = 1.83e-20
-Relative error spread = 8.4e-23
-*/
-#if UNK
-static long double P[8] = {
- 4.212760487471622013093E-5L,
- 4.542931960608009155600E-4L,
- 4.092666828394035500949E-3L,
- 2.385363243461108252554E-2L,
- 1.113062816019361559013E-1L,
- 3.629515436640239168939E-1L,
- 8.378004301573126728826E-1L,
- 1.000000000000000000009E0L,
-};
-static long double Q[9] = {
--1.397148517476170440917E-5L,
- 2.346584059160635244282E-4L,
--1.237799246653152231188E-3L,
--7.955933682494738320586E-4L,
- 2.773706565840072979165E-2L,
--4.633887671244534213831E-2L,
--2.243510905670329164562E-1L,
- 4.150160950588455434583E-1L,
- 9.999999999999999999908E-1L,
-};
-#endif
-#if IBMPC
-static short P[] = {
-0x434a,0x3f22,0x2bda,0xb0b2,0x3ff0, XPD
-0xf5aa,0xe82f,0x335b,0xee2e,0x3ff3, XPD
-0xbe6c,0x3757,0xc717,0x861b,0x3ff7, XPD
-0x7f43,0x5196,0xb166,0xc368,0x3ff9, XPD
-0x9549,0x8eb5,0x8c3a,0xe3f4,0x3ffb, XPD
-0x8d75,0x23af,0xc8e4,0xb9d4,0x3ffd, XPD
-0x29cf,0x19b3,0x16c8,0xd67a,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-static short Q[] = {
-0x5473,0x2de8,0x1268,0xea67,0xbfee, XPD
-0x334b,0xc2f0,0xa2dd,0xf60e,0x3ff2, XPD
-0xbeed,0x1853,0xa691,0xa23d,0xbff5, XPD
-0x296e,0x7cb1,0x5dfd,0xd08f,0xbff4, XPD
-0x0417,0x7989,0xd7bc,0xe338,0x3ff9, XPD
-0x3295,0x3698,0xd580,0xbdcd,0xbffa, XPD
-0x75ef,0x3ab7,0x4ad3,0xe5bc,0xbffc, XPD
-0xe458,0x2ec7,0xfd57,0xd47c,0x3ffd, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-#endif
-#if MIEEE
-static long P[24] = {
-0x3ff00000,0xb0b22bda,0x3f22434a,
-0x3ff30000,0xee2e335b,0xe82ff5aa,
-0x3ff70000,0x861bc717,0x3757be6c,
-0x3ff90000,0xc368b166,0x51967f43,
-0x3ffb0000,0xe3f48c3a,0x8eb59549,
-0x3ffd0000,0xb9d4c8e4,0x23af8d75,
-0x3ffe0000,0xd67a16c8,0x19b329cf,
-0x3fff0000,0x80000000,0x00000000,
-};
-static long Q[27] = {
-0xbfee0000,0xea671268,0x2de85473,
-0x3ff20000,0xf60ea2dd,0xc2f0334b,
-0xbff50000,0xa23da691,0x1853beed,
-0xbff40000,0xd08f5dfd,0x7cb1296e,
-0x3ff90000,0xe338d7bc,0x79890417,
-0xbffa0000,0xbdcdd580,0x36983295,
-0xbffc0000,0xe5bc4ad3,0x3ab775ef,
-0x3ffd0000,0xd47cfd57,0x2ec7e458,
-0x3fff0000,0x80000000,0x00000000,
-};
-#endif
-/*
-static long double P[] = {
--3.01525602666895735709e0L,
--3.25157411956062339893e1L,
--2.92929976820724030353e2L,
--1.70730828800510297666e3L,
--7.96667499622741999770e3L,
--2.59780216007146401957e4L,
--5.99650230220855581642e4L,
--7.15743521530849602425e4L
-};
-static long double Q[] = {
- 1.00000000000000000000e0L,
--1.67955233807178858919e1L,
- 8.85946791747759881659e1L,
- 5.69440799097468430177e1L,
--1.98526250512761318471e3L,
- 3.31667508019495079814e3L,
- 1.60577839621734713377e4L,
--2.97045081369399940529e4L,
--7.15743521530849602412e4L
-};
-*/
-#define MAXGAML 1755.455L
-/*static long double LOGPI = 1.14472988584940017414L;*/
-
-/* Stirling's formula for the gamma function
-gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
-z(x) = x
-13 <= x <= 1024
-Relative error
-n=8, d=0
-Peak error = 9.44e-21
-Relative error spread = 8.8e-4
-*/
-#if UNK
-static long double STIR[9] = {
- 7.147391378143610789273E-4L,
--2.363848809501759061727E-5L,
--5.950237554056330156018E-4L,
- 6.989332260623193171870E-5L,
- 7.840334842744753003862E-4L,
--2.294719747873185405699E-4L,
--2.681327161876304418288E-3L,
- 3.472222222230075327854E-3L,
- 8.333333333333331800504E-2L,
-};
-#endif
-#if IBMPC
-static short STIR[] = {
-0x6ede,0x69f7,0x54e3,0xbb5d,0x3ff4, XPD
-0xc395,0x0295,0x4443,0xc64b,0xbfef, XPD
-0xba6f,0x7c59,0x5e47,0x9bfb,0xbff4, XPD
-0x5704,0x1a39,0xb11d,0x9293,0x3ff1, XPD
-0x30b7,0x1a21,0x98b2,0xcd87,0x3ff4, XPD
-0xbef3,0x7023,0x6a08,0xf09e,0xbff2, XPD
-0x3a1c,0x5ac8,0x3478,0xafb9,0xbff6, XPD
-0xc3c9,0x906e,0x38e3,0xe38e,0x3ff6, XPD
-0xa1d5,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
-};
-#endif
-#if MIEEE
-static long STIR[27] = {
-0x3ff40000,0xbb5d54e3,0x69f76ede,
-0xbfef0000,0xc64b4443,0x0295c395,
-0xbff40000,0x9bfb5e47,0x7c59ba6f,
-0x3ff10000,0x9293b11d,0x1a395704,
-0x3ff40000,0xcd8798b2,0x1a2130b7,
-0xbff20000,0xf09e6a08,0x7023bef3,
-0xbff60000,0xafb93478,0x5ac83a1c,
-0x3ff60000,0xe38e38e3,0x906ec3c9,
-0x3ffb0000,0xaaaaaaaa,0xaaaaa1d5,
-};
-#endif
-#define MAXSTIR 1024.0L
-static long double SQTPI = 2.50662827463100050242E0L;
-
-/* 1/gamma(x) = z P(z)
- * z(x) = 1/x
- * 0 < x < 0.03125
- * Peak relative error 4.2e-23
- */
-#if UNK
-static long double S[9] = {
--1.193945051381510095614E-3L,
- 7.220599478036909672331E-3L,
--9.622023360406271645744E-3L,
--4.219773360705915470089E-2L,
- 1.665386113720805206758E-1L,
--4.200263503403344054473E-2L,
--6.558780715202540684668E-1L,
- 5.772156649015328608253E-1L,
- 1.000000000000000000000E0L,
-};
-#endif
-#if IBMPC
-static short S[] = {
-0xbaeb,0xd6d3,0x25e5,0x9c7e,0xbff5, XPD
-0xfe9a,0xceb4,0xc74e,0xec9a,0x3ff7, XPD
-0x9225,0xdfef,0xb0e9,0x9da5,0xbff8, XPD
-0x10b0,0xec17,0x87dc,0xacd7,0xbffa, XPD
-0x6b8d,0x7515,0x1905,0xaa89,0x3ffc, XPD
-0xf183,0x126b,0xf47d,0xac0a,0xbffa, XPD
-0x7bf6,0x57d1,0xa013,0xa7e7,0xbffe, XPD
-0xc7a9,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-#endif
-#if MIEEE
-static long S[27] = {
-0xbff50000,0x9c7e25e5,0xd6d3baeb,
-0x3ff70000,0xec9ac74e,0xceb4fe9a,
-0xbff80000,0x9da5b0e9,0xdfef9225,
-0xbffa0000,0xacd787dc,0xec1710b0,
-0x3ffc0000,0xaa891905,0x75156b8d,
-0xbffa0000,0xac0af47d,0x126bf183,
-0xbffe0000,0xa7e7a013,0x57d17bf6,
-0x3ffe0000,0x93c467e3,0x7db0c7a9,
-0x3fff0000,0x80000000,0x00000000,
-};
-#endif
-/* 1/gamma(-x) = z P(z)
- * z(x) = 1/x
- * 0 < x < 0.03125
- * Peak relative error 5.16e-23
- * Relative error spread = 2.5e-24
- */
-#if UNK
-static long double SN[9] = {
- 1.133374167243894382010E-3L,
- 7.220837261893170325704E-3L,
- 9.621911155035976733706E-3L,
--4.219773343731191721664E-2L,
--1.665386113944413519335E-1L,
--4.200263503402112910504E-2L,
- 6.558780715202536547116E-1L,
- 5.772156649015328608727E-1L,
--1.000000000000000000000E0L,
-};
-#endif
-#if IBMPC
-static short SN[] = {
-0x5dd1,0x02de,0xb9f7,0x948d,0x3ff5, XPD
-0x989b,0xdd68,0xc5f1,0xec9c,0x3ff7, XPD
-0x2ca1,0x18f0,0x386f,0x9da5,0x3ff8, XPD
-0x783f,0x41dd,0x87d1,0xacd7,0xbffa, XPD
-0x7a5b,0xd76d,0x1905,0xaa89,0xbffc, XPD
-0x7f64,0x1234,0xf47d,0xac0a,0xbffa, XPD
-0x5e26,0x57d1,0xa013,0xa7e7,0x3ffe, XPD
-0xc7aa,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0xbfff, XPD
-};
-#endif
-#if MIEEE
-static long SN[27] = {
-0x3ff50000,0x948db9f7,0x02de5dd1,
-0x3ff70000,0xec9cc5f1,0xdd68989b,
-0x3ff80000,0x9da5386f,0x18f02ca1,
-0xbffa0000,0xacd787d1,0x41dd783f,
-0xbffc0000,0xaa891905,0xd76d7a5b,
-0xbffa0000,0xac0af47d,0x12347f64,
-0x3ffe0000,0xa7e7a013,0x57d15e26,
-0x3ffe0000,0x93c467e3,0x7db0c7aa,
-0xbfff0000,0x80000000,0x00000000,
-};
-#endif
-
-int sgngaml = 0;
-extern int sgngaml;
-extern long double MAXLOGL, MAXNUML, PIL;
-/* #define PIL 3.14159265358979323846L */
-/* #define MAXNUML 1.189731495357231765021263853E4932L */
-
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double lgaml ( long double );
-extern long double logl ( long double );
-extern long double expl ( long double );
-extern long double gammal ( long double );
-extern long double sinl ( long double );
-extern long double floorl ( long double );
-extern long double powl ( long double, long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-extern int isfinitel ( long double );
-static long double stirf ( long double );
-#else
-long double fabsl(), lgaml(), logl(), expl(), gammal(), sinl();
-long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel();
-static long double stirf();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-/* Gamma function computed by Stirling's formula.
- */
-static long double stirf(x)
-long double x;
-{
-long double y, w, v;
-
-w = 1.0L/x;
-/* For large x, use rational coefficients from the analytical expansion. */
-if( x > 1024.0L )
- w = (((((6.97281375836585777429E-5L * w
- + 7.84039221720066627474E-4L) * w
- - 2.29472093621399176955E-4L) * w
- - 2.68132716049382716049E-3L) * w
- + 3.47222222222222222222E-3L) * w
- + 8.33333333333333333333E-2L) * w
- + 1.0L;
-else
- w = 1.0L + w * polevll( w, STIR, 8 );
-y = expl(x);
-if( x > MAXSTIR )
- { /* Avoid overflow in pow() */
- v = powl( x, 0.5L * x - 0.25L );
- y = v * (v / y);
- }
-else
- {
- y = powl( x, x - 0.5L ) / y;
- }
-y = SQTPI * y * w;
-return( y );
-}
-
-
-
-long double gammal(x)
-long double x;
-{
-long double p, q, z;
-int i;
-
-sgngaml = 1;
-#ifdef NANS
-if( isnanl(x) )
- return(NANL);
-#endif
-#ifdef INFINITIES
-if(x == INFINITYL)
- return(INFINITYL);
-#ifdef NANS
-if(x == -INFINITYL)
- goto gamnan;
-#endif
-#endif
-q = fabsl(x);
-
-if( q > 13.0L )
- {
- if( q > MAXGAML )
- goto goverf;
- if( x < 0.0L )
- {
- p = floorl(q);
- if( p == q )
- {
-gamnan:
-#ifdef NANS
- mtherr( "gammal", DOMAIN );
- return (NANL);
-#else
- goto goverf;
-#endif
- }
- i = p;
- if( (i & 1) == 0 )
- sgngaml = -1;
- z = q - p;
- if( z > 0.5L )
- {
- p += 1.0L;
- z = q - p;
- }
- z = q * sinl( PIL * z );
- z = fabsl(z) * stirf(q);
- if( z <= PIL/MAXNUML )
- {
-goverf:
-#ifdef INFINITIES
- return( sgngaml * INFINITYL);
-#else
- mtherr( "gammal", OVERFLOW );
- return( sgngaml * MAXNUML);
-#endif
- }
- z = PIL/z;
- }
- else
- {
- z = stirf(x);
- }
- return( sgngaml * z );
- }
-
-z = 1.0L;
-while( x >= 3.0L )
- {
- x -= 1.0L;
- z *= x;
- }
-
-while( x < -0.03125L )
- {
- z /= x;
- x += 1.0L;
- }
-
-if( x <= 0.03125L )
- goto small;
-
-while( x < 2.0L )
- {
- z /= x;
- x += 1.0L;
- }
-
-if( x == 2.0L )
- return(z);
-
-x -= 2.0L;
-p = polevll( x, P, 7 );
-q = polevll( x, Q, 8 );
-return( z * p / q );
-
-small:
-if( x == 0.0L )
- {
- goto gamnan;
- }
-else
- {
- if( x < 0.0L )
- {
- x = -x;
- q = z / (x * polevll( x, SN, 8 ));
- }
- else
- q = z / (x * polevll( x, S, 8 ));
- }
-return q;
-}
-
-
-
-/* A[]: Stirling's formula expansion of log gamma
- * B[], C[]: log gamma function between 2 and 3
- */
-
-
-/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x A(1/x^2)
- * x >= 8
- * Peak relative error 1.51e-21
- * Relative spread of error peaks 5.67e-21
- */
-#if UNK
-static long double A[7] = {
- 4.885026142432270781165E-3L,
--1.880801938119376907179E-3L,
- 8.412723297322498080632E-4L,
--5.952345851765688514613E-4L,
- 7.936507795855070755671E-4L,
--2.777777777750349603440E-3L,
- 8.333333333333331447505E-2L,
-};
-#endif
-#if IBMPC
-static short A[] = {
-0xd984,0xcc08,0x91c2,0xa012,0x3ff7, XPD
-0x3d91,0x0304,0x3da1,0xf685,0xbff5, XPD
-0x3bdc,0xaad1,0xd492,0xdc88,0x3ff4, XPD
-0x8b20,0x9fce,0x844e,0x9c09,0xbff4, XPD
-0xf8f2,0x30e5,0x0092,0xd00d,0x3ff4, XPD
-0x4d88,0x03a8,0x60b6,0xb60b,0xbff6, XPD
-0x9fcc,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
-};
-#endif
-#if MIEEE
-static long A[21] = {
-0x3ff70000,0xa01291c2,0xcc08d984,
-0xbff50000,0xf6853da1,0x03043d91,
-0x3ff40000,0xdc88d492,0xaad13bdc,
-0xbff40000,0x9c09844e,0x9fce8b20,
-0x3ff40000,0xd00d0092,0x30e5f8f2,
-0xbff60000,0xb60b60b6,0x03a84d88,
-0x3ffb0000,0xaaaaaaaa,0xaaaa9fcc,
-};
-#endif
-
-/* log gamma(x+2) = x B(x)/C(x)
- * 0 <= x <= 1
- * Peak relative error 7.16e-22
- * Relative spread of error peaks 4.78e-20
- */
-#if UNK
-static long double B[7] = {
--2.163690827643812857640E3L,
--8.723871522843511459790E4L,
--1.104326814691464261197E6L,
--6.111225012005214299996E6L,
--1.625568062543700591014E7L,
--2.003937418103815175475E7L,
--8.875666783650703802159E6L,
-};
-static long double C[7] = {
-/* 1.000000000000000000000E0L,*/
--5.139481484435370143617E2L,
--3.403570840534304670537E4L,
--6.227441164066219501697E5L,
--4.814940379411882186630E6L,
--1.785433287045078156959E7L,
--3.138646407656182662088E7L,
--2.099336717757895876142E7L,
-};
-#endif
-#if IBMPC
-static short B[] = {
-0x9557,0x4995,0x0da1,0x873b,0xc00a, XPD
-0xfe44,0x9af8,0x5b8c,0xaa63,0xc00f, XPD
-0x5aa8,0x7cf5,0x3684,0x86ce,0xc013, XPD
-0x259a,0x258c,0xf206,0xba7f,0xc015, XPD
-0xbe18,0x1ca3,0xc0a0,0xf80a,0xc016, XPD
-0x168f,0x2c42,0x6717,0x98e3,0xc017, XPD
-0x2051,0x9d55,0x92c8,0x876e,0xc016, XPD
-};
-static short C[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xaa77,0xcf2f,0xae76,0x807c,0xc008, XPD
-0xb280,0x0d74,0xb55a,0x84f3,0xc00e, XPD
-0xa505,0xcd30,0x81dc,0x9809,0xc012, XPD
-0x3369,0x4246,0xb8c2,0x92f0,0xc015, XPD
-0x63cf,0x6aee,0xbe6f,0x8837,0xc017, XPD
-0x26bb,0xccc7,0xb009,0xef75,0xc017, XPD
-0x462b,0xbae8,0xab96,0xa02a,0xc017, XPD
-};
-#endif
-#if MIEEE
-static long B[21] = {
-0xc00a0000,0x873b0da1,0x49959557,
-0xc00f0000,0xaa635b8c,0x9af8fe44,
-0xc0130000,0x86ce3684,0x7cf55aa8,
-0xc0150000,0xba7ff206,0x258c259a,
-0xc0160000,0xf80ac0a0,0x1ca3be18,
-0xc0170000,0x98e36717,0x2c42168f,
-0xc0160000,0x876e92c8,0x9d552051,
-};
-static long C[21] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0080000,0x807cae76,0xcf2faa77,
-0xc00e0000,0x84f3b55a,0x0d74b280,
-0xc0120000,0x980981dc,0xcd30a505,
-0xc0150000,0x92f0b8c2,0x42463369,
-0xc0170000,0x8837be6f,0x6aee63cf,
-0xc0170000,0xef75b009,0xccc726bb,
-0xc0170000,0xa02aab96,0xbae8462b,
-};
-#endif
-
-/* log( sqrt( 2*pi ) ) */
-static long double LS2PI = 0.91893853320467274178L;
-#define MAXLGM 1.04848146839019521116e+4928L
-
-
-/* Logarithm of gamma function */
-
-
-long double lgaml(x)
-long double x;
-{
-long double p, q, w, z, f, nx;
-int i;
-
-sgngaml = 1;
-#ifdef NANS
-if( isnanl(x) )
- return(NANL);
-#endif
-#ifdef INFINITIES
-if( !isfinitel(x) )
- return(INFINITYL);
-#endif
-if( x < -34.0L )
- {
- q = -x;
- w = lgaml(q); /* note this modifies sgngam! */
- p = floorl(q);
- if( p == q )
- {
-#ifdef INFINITIES
- mtherr( "lgaml", SING );
- return (INFINITYL);
-#else
- goto loverf;
-#endif
- }
- i = p;
- if( (i & 1) == 0 )
- sgngaml = -1;
- else
- sgngaml = 1;
- z = q - p;
- if( z > 0.5L )
- {
- p += 1.0L;
- z = p - q;
- }
- z = q * sinl( PIL * z );
- if( z == 0.0L )
- goto loverf;
-/* z = LOGPI - logl( z ) - w; */
- z = logl( PIL/z ) - w;
- return( z );
- }
-
-if( x < 13.0L )
- {
- z = 1.0L;
- nx = floorl( x + 0.5L );
- f = x - nx;
- while( x >= 3.0L )
- {
- nx -= 1.0L;
- x = nx + f;
- z *= x;
- }
- while( x < 2.0L )
- {
- if( fabsl(x) <= 0.03125 )
- goto lsmall;
- z /= nx + f;
- nx += 1.0L;
- x = nx + f;
- }
- if( z < 0.0L )
- {
- sgngaml = -1;
- z = -z;
- }
- else
- sgngaml = 1;
- if( x == 2.0L )
- return( logl(z) );
- x = (nx - 2.0L) + f;
- p = x * polevll( x, B, 6 ) / p1evll( x, C, 7);
- return( logl(z) + p );
- }
-
-if( x > MAXLGM )
- {
-loverf:
-#ifdef INFINITIES
- return( sgngaml * INFINITYL );
-#else
- mtherr( "lgaml", OVERFLOW );
- return( sgngaml * MAXNUML );
-#endif
- }
-
-q = ( x - 0.5L ) * logl(x) - x + LS2PI;
-if( x > 1.0e10L )
- return(q);
-p = 1.0L/(x*x);
-q += polevll( p, A, 6 ) / x;
-return( q );
-
-
-lsmall:
-if( x == 0.0L )
- goto loverf;
-if( x < 0.0L )
- {
- x = -x;
- q = z / (x * polevll( x, SN, 8 ));
- }
-else
- q = z / (x * polevll( x, S, 8 ));
-if( q < 0.0L )
- {
- sgngaml = -1;
- q = -q;
- }
-else
- sgngaml = 1;
-q = logl( q );
-return(q);
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-04-24 11:44:48 +0000