gamma.c

开放gsl矩阵运算

/* specfunc/gamma.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/* Author:  G. Jungman */

#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include "gsl_sf_exp.h"
#include "gsl_sf_log.h"
#include "gsl_sf_psi.h"
#include "gsl_sf_trig.h"
#include "gsl_sf_gamma.h"

#include "error.h"
#include "check.h"

#include "chebyshev.h"
#include "cheb_eval.c"

#define LogRootTwoPi_  0.9189385332046727418


/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/

#define FACT_TABLE_MAX  170
#define FACT_TABLE_SIZE (FACT_TABLE_MAX+1)
static struct {int n; double f; long i; } fact_table[FACT_TABLE_SIZE] = {
    { 0,  1.0,     1L     },
    { 1,  1.0,     1L     },
    { 2,  2.0,     2L     },
    { 3,  6.0,     6L     },
    { 4,  24.0,    24L    },
    { 5,  120.0,   120L   },
    { 6,  720.0,   720L   },
    { 7,  5040.0,  5040L  },
    { 8,  40320.0, 40320L },

    { 9,  362880.0,     362880L    },
    { 10, 3628800.0,    3628800L   },
    { 11, 39916800.0,   39916800L  },
    { 12, 479001600.0,  479001600L },

    { 13, 6227020800.0,                               0 },
    { 14, 87178291200.0,                              0 },
    { 15, 1307674368000.0,                            0 },
    { 16, 20922789888000.0,                           0 },
    { 17, 355687428096000.0,                          0 },
    { 18, 6402373705728000.0,                         0 },
    { 19, 121645100408832000.0,                       0 },
    { 20, 2432902008176640000.0,                      0 },
    { 21, 51090942171709440000.0,                     0 },
    { 22, 1124000727777607680000.0,                   0 },
    { 23, 25852016738884976640000.0,                  0 },
    { 24, 620448401733239439360000.0,                 0 },
    { 25, 15511210043330985984000000.0,               0 },
    { 26, 403291461126605635584000000.0,              0 },
    { 27, 10888869450418352160768000000.0,            0 },
    { 28, 304888344611713860501504000000.0,           0 },
    { 29, 8841761993739701954543616000000.0,          0 },
    { 30, 265252859812191058636308480000000.0,        0 },
    { 31, 8222838654177922817725562880000000.0,       0 },
    { 32, 263130836933693530167218012160000000.0,     0 },
    { 33, 8683317618811886495518194401280000000.0,    0 },
    { 34, 2.95232799039604140847618609644e38,  0 },
    { 35, 1.03331479663861449296666513375e40,  0 },
    { 36, 3.71993326789901217467999448151e41,  0 },
    { 37, 1.37637530912263450463159795816e43,  0 },
    { 38, 5.23022617466601111760007224100e44,  0 },
    { 39, 2.03978820811974433586402817399e46,  0 },
    { 40, 8.15915283247897734345611269600e47,  0 },
    { 41, 3.34525266131638071081700620534e49,  0 },
    { 42, 1.40500611775287989854314260624e51,  0 },
    { 43, 6.04152630633738356373551320685e52,  0 },
    { 44, 2.65827157478844876804362581101e54,  0 },
    { 45, 1.19622220865480194561963161496e56,  0 },
    { 46, 5.50262215981208894985030542880e57,  0 },
    { 47, 2.58623241511168180642964355154e59,  0 },
    { 48, 1.24139155925360726708622890474e61,  0 },
    { 49, 6.08281864034267560872252163321e62,  0 },
    { 50, 3.04140932017133780436126081661e64,  0 },
    { 51, 1.55111875328738228022424301647e66,  0 },
    { 52, 8.06581751709438785716606368564e67,  0 },
    { 53, 4.27488328406002556429801375339e69,  0 },
    { 54, 2.30843697339241380472092742683e71,  0 },
    { 55, 1.26964033536582759259651008476e73,  0 },
    { 56, 7.10998587804863451854045647464e74,  0 },
    { 57, 4.05269195048772167556806019054e76,  0 },
    { 58, 2.35056133128287857182947491052e78,  0 },
    { 59, 1.38683118545689835737939019720e80,  0 },
    { 60, 8.32098711274139014427634118320e81,  0 },
    { 61, 5.07580213877224798800856812177e83,  0 },
    { 62, 3.14699732603879375256531223550e85,  0 },
    { 63, 1.982608315404440064116146708360e87,  0 },
    { 64, 1.268869321858841641034333893350e89,  0 },
    { 65, 8.247650592082470666723170306800e90,  0 },
    { 66, 5.443449390774430640037292402480e92,  0 },
    { 67, 3.647111091818868528824985909660e94,  0 },
    { 68, 2.480035542436830599600990418570e96,  0 },
    { 69, 1.711224524281413113724683388810e98,  0 },
    { 70, 1.197857166996989179607278372170e100,  0 },
    { 71, 8.504785885678623175211676442400e101,  0 },
    { 72, 6.123445837688608686152407038530e103,  0 },
    { 73, 4.470115461512684340891257138130e105,  0 },
    { 74, 3.307885441519386412259530282210e107,  0 },
    { 75, 2.480914081139539809194647711660e109,  0 },
    { 76, 1.885494701666050254987932260860e111,  0 },
    { 77, 1.451830920282858696340707840860e113,  0 },
    { 78, 1.132428117820629783145752115870e115,  0 },
    { 79, 8.946182130782975286851441715400e116,  0 },
    { 80, 7.156945704626380229481153372320e118,  0 },
    { 81, 5.797126020747367985879734231580e120,  0 },
    { 82, 4.753643337012841748421382069890e122,  0 },
    { 83, 3.945523969720658651189747118010e124,  0 },
    { 84, 3.314240134565353266999387579130e126,  0 },
    { 85, 2.817104114380550276949479442260e128,  0 },
    { 86, 2.422709538367273238176552320340e130,  0 },
    { 87, 2.107757298379527717213600518700e132,  0 },
    { 88, 1.854826422573984391147968456460e134,  0 },
    { 89, 1.650795516090846108121691926250e136,  0 },
    { 90, 1.485715964481761497309522733620e138,  0 },
    { 91, 1.352001527678402962551665687590e140,  0 },
    { 92, 1.243841405464130725547532432590e142,  0 },
    { 93, 1.156772507081641574759205162310e144,  0 },
    { 94, 1.087366156656743080273652852570e146,  0 },
    { 95, 1.032997848823905926259970209940e148,  0 },
    { 96, 9.916779348709496892095714015400e149,  0 },
    { 97, 9.619275968248211985332842594960e151,  0 },
    { 98, 9.426890448883247745626185743100e153,  0 },
    { 99, 9.332621544394415268169923885600e155,  0 },
    { 100, 9.33262154439441526816992388563e157,  0 },
    { 101, 9.42594775983835942085162312450e159,  0 },
    { 102, 9.61446671503512660926865558700e161,  0 },
    { 103, 9.90290071648618040754671525458e163,  0 },
    { 104, 1.02990167451456276238485838648e166,  0 },
    { 105, 1.08139675824029090050410130580e168,  0 },
    { 106, 1.146280563734708354534347384148e170,  0 },
    { 107, 1.226520203196137939351751701040e172,  0 },
    { 108, 1.324641819451828974499891837120e174,  0 },
    { 109, 1.443859583202493582204882102460e176,  0 },
    { 110, 1.588245541522742940425370312710e178,  0 },
    { 111, 1.762952551090244663872161047110e180,  0 },
    { 112, 1.974506857221074023536820372760e182,  0 },
    { 113, 2.231192748659813646596607021220e184,  0 },
    { 114, 2.543559733472187557120132004190e186,  0 },
    { 115, 2.925093693493015690688151804820e188,  0 },
    { 116, 3.393108684451898201198256093590e190,  0 },
    { 117, 3.96993716080872089540195962950e192,  0 },
    { 118, 4.68452584975429065657431236281e194,  0 },
    { 119, 5.57458576120760588132343171174e196,  0 },
    { 120, 6.68950291344912705758811805409e198,  0 },
    { 121, 8.09429852527344373968162284545e200,  0 },
    { 122, 9.87504420083360136241157987140e202,  0 },
    { 123, 1.21463043670253296757662432419e205,  0 },
    { 124, 1.50614174151114087979501416199e207,  0 },
    { 125, 1.88267717688892609974376770249e209,  0 },
    { 126, 2.37217324288004688567714730514e211,  0 },
    { 127, 3.01266001845765954480997707753e213,  0 },
    { 128, 3.85620482362580421735677065923e215,  0 },
    { 129, 4.97450422247728744039023415041e217,  0 },
    { 130, 6.46685548922047367250730439554e219,  0 },
    { 131, 8.47158069087882051098456875820e221,  0 },
    { 132, 1.11824865119600430744996307608e224,  0 },
    { 133, 1.48727070609068572890845089118e226,  0 },
    { 134, 1.99294274616151887673732419418e228,  0 },
    { 135, 2.69047270731805048359538766215e230,  0 },
    { 136, 3.65904288195254865768972722052e232,  0 },
    { 137, 5.01288874827499166103492629211e234,  0 },
    { 138, 6.91778647261948849222819828311e236,  0 },
    { 139, 9.61572319694108900419719561353e238,  0 },
    { 140, 1.34620124757175246058760738589e241,  0 },
    { 141, 1.89814375907617096942852641411e243,  0 },
    { 142, 2.69536413788816277658850750804e245,  0 },
    { 143, 3.85437071718007277052156573649e247,  0 },
    { 144, 5.55029383273930478955105466055e249,  0 },
    { 145, 8.04792605747199194484902925780e251,  0 },
    { 146, 1.17499720439091082394795827164e254,  0 },
    { 147, 1.72724589045463891120349865931e256,  0 },
    { 148, 2.55632391787286558858117801578e258,  0 },
    { 149, 3.80892263763056972698595524351e260,  0 },
    { 150, 5.71338395644585459047893286526e262,  0 },
    { 151, 8.62720977423324043162318862650e264,  0 },
    { 152, 1.31133588568345254560672467123e267,  0 },
    { 153, 2.00634390509568239477828874699e269,  0 },
    { 154, 3.08976961384735088795856467036e271,  0 },
    { 155, 4.78914290146339387633577523906e273,  0 },
    { 156, 7.47106292628289444708380937294e275,  0 },
    { 157, 1.17295687942641442819215807155e278,  0 },
    { 158, 1.85327186949373479654360975305e280,  0 },
    { 159, 2.94670227249503832650433950735e282,  0 },
    { 160, 4.71472363599206132240694321176e284,  0 },
    { 161, 7.59070505394721872907517857094e286,  0 },
    { 162, 1.22969421873944943411017892849e289,  0 },
    { 163, 2.00440157654530257759959165344e291,  0 },
    { 164, 3.28721858553429622726333031164e293,  0 },
    { 165, 5.42391066613158877498449501421e295,  0 },
    { 166, 9.00369170577843736647426172359e297,  0 },
    { 167, 1.50361651486499904020120170784e300,  0 },
    { 168, 2.52607574497319838753801886917e302,  0 },
    { 169, 4.26906800900470527493925188890e304,  0 },
    { 170, 7.25741561530799896739672821113e306,  0 },

    /*
    { 171, 1.24101807021766782342484052410e309,  0 },
    { 172, 2.13455108077438865629072570146e311,  0 },
    { 173, 3.69277336973969237538295546352e313,  0 },
    { 174, 6.42542566334706473316634250653e315,  0 },
    { 175, 1.12444949108573632830410993864e318,  0 },
    { 176, 1.97903110431089593781523349201e320,  0 },
    { 177, 3.50288505463028580993296328086e322,  0 },
    { 178, 6.23513539724190874168067463993e324,  0 },
    { 179, 1.11608923610630166476084076055e327,  0 },
    { 180, 2.00896062499134299656951336898e329,  0 },
    { 181, 3.63621873123433082379081919786e331,  0 },
    { 182, 6.61791809084648209929929094011e333,  0 },
    { 183, 1.21107901062490622417177024204e336,  0 },
    { 184, 2.22838537954982745247605724535e338,  0 },
    { 185, 4.12251295216718078708070590390e340,  0 },
    { 186, 7.66787409103095626397011298130e342,  0 },
    { 187, 1.43389245502278882136241112750e345,  0 },
    { 188, 2.69571781544284298416133291969e347,  0 },
    { 189, 5.09490667118697324006491921822e349,  0 },
    { 190, 9.68032267525524915612334651460e351,  0 },
    { 191, 1.84894163097375258881955918429e354,  0 },
    { 192, 3.54996793146960497053355363384e356,  0 },
    { 193, 6.85143810773633759312975851330e358,  0 },
    { 194, 1.32917899290084949306717315158e361,  0 },
    { 195, 2.59189903615665651148098764559e363,  0 },
    { 196, 5.08012211086704676250273578535e365,  0 },
    { 197, 1.00078405584080821221303894971e368,  0 },
    { 198, 1.98155243056480026018181712043e370,  0 },
    { 199, 3.94328933682395251776181606966e372,  0 },
    { 200, 7.88657867364790503552363213932e374,  0 }
    */
};

#define DOUB_FACT_TABLE_MAX  297
#define DOUB_FACT_TABLE_SIZE (DOUB_FACT_TABLE_MAX+1)
static struct {int n; double f; long i; } doub_fact_table[DOUB_FACT_TABLE_SIZE] = {
  { 0,  1.000000000000000000000000000,    1L    },
  { 1,  1.000000000000000000000000000,    1L    },
  { 2,  2.000000000000000000000000000,    2L    },
  { 3,  3.000000000000000000000000000,    3L    },
  { 4,  8.000000000000000000000000000,    8L    },
  { 5,  15.00000000000000000000000000,    15L   },
  { 6,  48.00000000000000000000000000,    48L	},
  { 7,  105.0000000000000000000000000,    105L  },
  { 8,  384.0000000000000000000000000,    384L  },
  { 9,  945.0000000000000000000000000,    945L  },
  { 10, 3840.000000000000000000000000,    3840L   },
  { 11, 10395.00000000000000000000000,    10395L  },
  { 12, 46080.00000000000000000000000,       46080L       },
  { 13, 135135.0000000000000000000000,       135135L      },
  { 14, 645120.00000000000000000000000,      645120L      },
  { 15, 2.02702500000000000000000000000e6,   2027025L     },
  { 16, 1.03219200000000000000000000000e7,   10321920L    },
  { 17, 3.4459425000000000000000000000e7,    34459425L    },
  { 18, 1.85794560000000000000000000000e8,   185794560L   },
  { 19, 6.5472907500000000000000000000e8,            0 },
  { 20, 3.7158912000000000000000000000e9,            0 },
  { 21, 1.37493105750000000000000000000e10,          0 },
  { 22, 8.1749606400000000000000000000e10,           0 },
  { 23, 3.1623414322500000000000000000e11,           0 },
  { 24, 1.96199055360000000000000000000e12,          0 },
  { 25, 7.9058535806250000000000000000e12,           0 },
  { 26, 5.1011754393600000000000000000e13,           0 },
  { 27, 2.13458046676875000000000000000e14,          0 },
  { 28, 1.42832912302080000000000000000e15,          0 },
  { 29, 6.1902833536293750000000000000e15,           0 },
  { 30, 4.2849873690624000000000000000e16,           0 },
  { 31, 1.91898783962510625000000000000e17,          0 },
  { 32, 1.37119595809996800000000000000e18,          0 },
  { 33, 6.3326598707628506250000000000e18,           0 },
  { 34, 4.6620662575398912000000000000e19,           0 },
  { 35, 2.21643095476699771875000000000e20,          0 },
  { 36, 1.67834385271436083200000000000e21,          0 },
  { 37, 8.2007945326378915593750000000e21,           0 },
  { 38, 6.3777066403145711616000000000e22,           0 },
  { 39, 3.1983098677287777081562500000e23,           0 },
  { 40, 2.55108265612582846464000000000e24,          0 },
  { 41, 1.31130704576879886034406250000e25,          0 },
  { 42, 1.07145471557284795514880000000e26,          0 },
  { 43, 5.6386202968058350994794687500e26,           0 },
  { 44, 4.7144007485205310026547200000e27,           0 },
  { 45, 2.53737913356262579476576093750e28,          0 },
  { 46, 2.16862434431944426122117120000e29,          0 },
  { 47, 1.19256819277443412353990764062e30,          0 },
  { 48, 1.04093968527333324538616217600e31,          0 },
  { 49, 5.8435841445947272053455474391e31,           0 },
  { 50, 5.2046984263666662269308108800e32,           0 },
  { 51, 2.98022791374331087472622919392e33,          0 },
  { 52, 2.70644318171066643800402165760e34,          0 },
  { 53, 1.57952079428395476360490147278e35,          0 },
  { 54, 1.46147931812375987652217169510e36,          0 },
  { 55, 8.6873643685617511998269581003e36,           0 },
  { 56, 8.1842841814930553085241614926e37,           0 },
  { 57, 4.9517976900801981839013661172e38,           0 },
  { 58, 4.7468848252659720789440136657e39,           0 },
  { 59, 2.92156063714731692850180600912e40,       0 },
  { 60, 2.84813089515958324736640819942e41,       0 },
  { 61, 1.78215198865986332638610166557e42,       0 },
  { 62, 1.76584115499894161336717308364e43,       0 },
  { 63, 1.12275575285571389562324404931e44,       0 },
  { 64, 1.13013833919932263255499077353e45,       0 },
  { 65, 7.2979123935621403215510863205e45,        0 },
  { 66, 7.4589130387155293748629391053e46,        0 },
  { 67, 4.8896013036866340154392278347e47,        0 },
  { 68, 5.0720608663265599749067985916e48,        0 },
  { 69, 3.3738248995437774706530672060e49,        0 },
  { 70, 3.5504426064285919824347590141e50,        0 },
  { 71, 2.39541567867608200416367771623e51,       0 },
  { 72, 2.55631867662858622735302649017e52,       0 },
  { 73, 1.74865344543353986303948473285e53,       0 },
  { 74, 1.89167582070515380824123960272e54,       0 },
  { 75, 1.31149008407515489727961354964e55,       0 },
  { 76, 1.43767362373591689426334209807e56,       0 },
  { 77, 1.00984736473786927090530243322e57,       0 },
  { 78, 1.12138542651401517752540683649e58,       0 },
  { 79, 7.9777941814291672401518892225e58,        0 },
  { 80, 8.9710834121121214202032546920e59,        0 },
  { 81, 6.4620132869576254645230302702e60,        0 },
  { 82, 7.3562883979319395645666688474e61,        0 },
  { 83, 5.3634710281748291355541151243e62,        0 },
  { 84, 6.1792822542628292342360018318e63,        0 },
  { 85, 4.5589503739486047652209978556e64,        0 },
  { 86, 5.3141827386660331414429615754e65,        0 },
  { 87, 3.9662868253352861457422681344e66,        0 },
  { 88, 4.6764808100261091644698061863e67,        0 },
  { 89, 3.5299952745484046697106186396e68,        0 },
  { 90, 4.2088327290234982480228255677e69,        0 },
  { 91, 3.2122956998390482494366629620e70,        0 },
  { 92, 3.8721261107016183881809995223e71,        0 },
  { 93, 2.98743500085031487197609655470e72,       0 },
  { 94, 3.6397985440595212848901395509e73,        0 },
  { 95, 2.83806325080779912837729172696e74,       0 },
  { 96, 3.4942066022971404334945339689e75,        0 },
  { 97, 2.75292135328356515452597297515e76,       0 },
  { 98, 3.4243224702511976248246432895e77,        0 },
  { 99, 2.72539213975072950298071324540e78,       0 },
  { 100, 3.4243224702511976248246432895e79,       0 },
  { 101, 2.75264606114823679801052037785e80,      0 },
  { 102, 3.4928089196562215773211361553e81,       0 },
  { 103, 2.83522544298268390195083598919e82,      0 },
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