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gamma.c

/* 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

/* Author:  G. Jungman */

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

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

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

#define LogRootTwoPi_  0.9189385332046727418


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

static struct {int n; double f; long i; } fact_table[GSL_SF_FACT_NMAX + 1] = {
    { 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 }
    */
};

static struct {int n; double f; long i; } doub_fact_table[GSL_SF_DOUBLEFACT_NMAX + 1] = {
  { 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 },
  { 104, 3.6325212764424704404139816015e83,       0 },
  { 105, 2.97698671513181809704837778865e84,      0 },
  { 106, 3.8504725530290186668388204976e85,       0 },
  { 107, 3.1853757851910453638417642339e86,       0 },
  { 108, 4.1585103572713401601859261374e87,       0 },
  { 109, 3.4720596058582394465875230149e88,       0 },
  { 110, 4.5743613929984741762045187512e89,       0 },
  { 111, 3.8539861625026457857121505465e90,       0 },
  { 112, 5.1232847601582910773490610013e91,       0 },
  { 113, 4.3550043636279897378547301176e92,       0 },
  { 114, 5.8405446265804518281779295415e93,       0 },
  { 115, 5.0082550181721881985329396352e94,       0 },
  { 116, 6.7750317668333241206863982681e95,       0 },
  { 117, 5.8596583712614601922835393732e96,       0 },
  { 118, 7.9945374848633224624099499564e97,       0 },
  { 119, 6.9729934618011376288174118541e98,       0 },
  { 120, 9.5934449818359869548919399477e99,       0 },
  { 121, 8.4373220887793765308690683435e100,      0 },
  { 122, 1.17040028778399040849681667362e102,       0 },
  { 123, 1.03779061691986331329689540625e103,       0 },
  { 124, 1.45129635685214810653605267528e104,       0 },
  { 125, 1.29723827114982914162111925781e105,       0 },
  { 126, 1.82863340963370661423542637086e106,       0 },
  { 127, 1.64749260436028300985882145742e107,       0 },
  { 128, 2.34065076433114446622134575470e108,       0 },
  { 129, 2.12526545962476508271787968008e109,       0 },
  { 130, 3.04284599363048780608774948111e110,       0 },
  { 131, 2.78409775210844225836042238090e111,       0 },
  { 132, 4.0165567115922439040358293151e112,        0 },
  { 133, 3.7028500103042282036193617666e113,        0 },
  { 134, 5.3821859935336068314080112822e114,        0 },
  { 135, 4.9988475139107080748861383849e115,        0 },
  { 136, 7.3197729512057052907148953438e116,        0 },
  { 137, 6.8484210940576700625940095873e117,        0 },
  { 138, 1.01012866726638733011865555744e119,       0 },
  { 139, 9.5193053207401613870056733264e119,        0 },
  { 140, 1.41418013417294226216611778042e121,       0 },
  { 141, 1.34222205022436275556779993902e122,       0 },
  { 142, 2.00813579052557801227588724819e123,       0 },
  { 143, 1.91937753182083874046195391280e124,       0 },
  { 144, 2.89171553835683233767727763739e125,       0 },
  { 145, 2.78309742114021617366983317355e126,       0 },
  { 146, 4.2219046860009752130088253506e127,        0 },
  { 147, 4.0911532090761177752946547651e128,        0 },
  { 148, 6.2484189352814433152530615189e129,        0 },
  { 149, 6.0958182815234154851890356000e130,        0 },
  { 150, 9.3726284029221649728795922783e131,        0 },
  { 151, 9.2046856051003573826354437561e132,        0 },
  { 152, 1.42463951724416907587769802630e134,       0 },
  { 153, 1.40831689758035467954322289468e135,       0 },
  { 154, 2.19394485655602037685165496051e136,       0 },
  { 155, 2.18289119124954975329199548675e137,       0 },
  { 156, 3.4225539762273917878885817384e138,        0 },
  { 157, 3.4271391702617931126684329142e139,        0 },
  { 158, 5.4076352824392790248639591467e140,        0 },
  { 159, 5.4491512807162510491428083336e141,        0 },
  { 160, 8.6522164519028464397823346347e142,        0 },
  { 161, 8.7731335619531641891199214170e143,        0 },
  { 162, 1.40165906520826112324473821082e145,       0 },
  { 163, 1.43002077059836576282654719098e146,       0 },
  { 164, 2.29872086694154824212137066574e147,       0 },
  { 165, 2.35953427148730350866380286512e148,       0 },
  { 166, 3.8158766391229700819214753051e149,        0 },
  { 167, 3.9404222333837968594685507847e150,        0 },
  { 168, 6.4106727537265897376280785126e151,        0 },
  { 169, 6.6593135744186166925018508262e152,        0 },
  { 170, 1.08981436813352025539677334714e154,       0 },
  { 171, 1.13874262122558345441781649128e155,       0 },
  { 172, 1.87448071318965483928245015709e156,       0 },
  { 173, 1.97002473472025937614282252992e157,       0 },
  { 174, 3.2615964409499994203514632733e158,        0 },
  { 175, 3.4475432857604539082499394274e159,        0 },
  { 176, 5.7404097360719989798185753611e160,        0 },
  { 177, 6.1021516157960034176023927864e161,        0 },
  { 178, 1.02179293302081581840770641427e163,       0 },
  { 179, 1.09228513922748461175082830877e164,       0 },
  { 180, 1.83922727943746847313387154568e165,       0 },
  { 181, 1.97703610200174714726899923887e166,       0 },
  { 182, 3.3473936485761926211036462131e167,        0 },
  { 183, 3.6179760666631972795022686071e168,        0 },
  { 184, 6.1592043133801944228307090322e169,        0 },
  { 185, 6.6932557233269149670791969232e170,        0 },
  { 186, 1.14561200228871616264651187999e172,       0 },
  { 187, 1.25163882026213309884380982464e173,       0 },
  { 188, 2.15375056430278638577544233437e174,       0 },
  { 189, 2.36559737029543155681480056857e175,       0 },
  { 190, 4.0921260721752941329733404353e176,        0 },
  { 191, 4.5182909772642742735162690860e177,        0 },
  { 192, 7.8568820585765647353088136358e178,        0 },
  { 193, 8.7203015861200493478863993359e179,        0 },
  { 194, 1.52423511936385355864990984535e181,       0 },
  { 195, 1.70045880929340962283784787050e182,       0 },
  { 196, 2.98750083395315297495382329688e183,       0 },
  { 197, 3.3499038543080169569905603049e184,        0 },
  { 198, 5.9152516512272428904085701278e185,        0 },
  { 199, 6.6663086700729537444112150067e186,        0 },
  { 200, 1.18305033024544857808171402556e188,       0 },
  { 201, 1.33992804268466370262665421635e189,       0 },
  { 202, 2.38976166709580612772506233164e190,       0 },
  { 203, 2.72005392664986731633210805920e191,       0 },
  { 204, 4.8751138008754445005591271565e192,        0 },
  { 205, 5.5761105496322279984808215214e193,        0 },
  { 206, 1.00427344298034156711518019425e195,       0 },
  { 207, 1.15425488377387119568553005492e196,       0 },
  { 208, 2.08888876139911045959957480403e197,       0 },
  { 209, 2.41239270708739079898275781478e198,       0 },
  { 210, 4.3866663989381319651591070885e199,        0 },
  { 211, 5.0901486119543945858536189892e200,        0 },
  { 212, 9.2997327657488397661373070276e201,        0 },
  { 213, 1.08420165434628604678682084470e203,       0 },
  { 214, 1.99014281187025170995338370390e204,       0 },
  { 215, 2.33103355684451500059166481610e205,       0 },
  { 216, 4.2987084736397436934993088004e206,        0 },
  { 217, 5.0583428183525975512839126509e207,        0 },
  { 218, 9.3711844725346412518284931849e208,        0 },
  { 219, 1.10777707721921886373117687056e210,       0 },
  { 220, 2.06166058395762107540226850068e211,       0 },
  { 221, 2.44818734065447368884590088393e212,       0 },
  { 222, 4.5768864963859187873930360715e213,        0 },
  { 223, 5.4594577696594763261263589712e214,        0 },
  { 224, 1.02522257519044580837604008002e216,       0 },
  { 225, 1.22837799817338217337843076851e217,       0 },
  { 226, 2.31700301993040752692985058084e218,       0 },
  { 227, 2.78841805585357753356903784452e219,       0 },
  { 228, 5.2827668854413291614000593243e220,        0 },
  { 229, 6.3854773479046925518730966640e221,        0 },
  { 230, 1.21503638365150570712201364459e223,       0 },
  { 231, 1.47504526736598397948268532937e224,       0 },
  { 232, 2.81888441007149324052307165546e225,       0 },
  { 233, 3.4368554729627426721946568174e226,        0 },
  { 234, 6.5961895195672941828239876738e227,        0 },
  { 235, 8.0766103614624452796574435210e228,        0 },
  { 236, 1.55670072661788142714646109101e230,       0 },
  { 237, 1.91415665566659953127881411447e231,       0 },
  { 238, 3.7049477293505577966085773966e232,        0 },
  { 239, 4.5748344070431728797563657336e233,        0 },
  { 240, 8.8918745504413387118605857518e234,        0 },
  { 241, 1.10253509209740466402128414180e236,       0 },
  { 242, 2.15183364120680396827026175195e237,       0 },
  { 243, 2.67916027379669333357172046456e238,       0 },
  { 244, 5.2504740845446016825794386748e239,        0 },
  { 245, 6.5639426708018986672507151382e240,        0 },
  { 246, 1.29161662479797201391454191399e242,       0 },
  { 247, 1.62129383968806897081092663913e243,       0 },
  { 248, 3.2032092294989705945080639467e244,        0 },
  { 249, 4.0370216608232917373192073314e245,        0 },
  { 250, 8.0080230737474264862701598667e246,        0 },
  { 251, 1.01329243686664622606712104019e248,       0 },
  { 252, 2.01802181458435147454008028642e249,       0 },
  { 253, 2.56362986527261495194981623168e250,       0 },
  { 254, 5.1257754090442527453318039275e251,        0 },
  { 255, 6.5372561564451681274720313908e252,        0 },
  { 256, 1.31219850471532870280494180544e254,       0 },
  { 257, 1.68007483220640820876031206743e255,       0 },
  { 258, 3.3854721421655480532367498580e256,        0 },
  { 259, 4.3513938154145972606892082546e257,        0 },
  { 260, 8.8022275696304249384155496309e258,        0 },
  { 261, 1.13571378582320988503988335446e260,       0 },
  { 262, 2.30618362324317133386487400329e261,       0 },
  { 263, 2.98692725671504199765489322224e262,       0 },
  { 264, 6.0883247653619723214032673687e263,        0 },
  { 265, 7.9153572302948612937854670389e264,        0 },
  { 266, 1.61949438758628463749326912007e266,       0 },
  { 267, 2.11340038048872796544071969939e267,       0 },
  { 268, 4.3402449587312428284819612418e268,        0 },
  { 269, 5.6850470235146782270355359914e269,        0 },
  { 270, 1.17186613885743556369012953528e271,       0 },
  { 271, 1.54064774337247779952663025366e272,       0 },
  { 272, 3.1874758976922247332371523360e273,        0 },
  { 273, 4.2059683394068643927077005925e274,        0 },
  { 274, 8.7336839596766957690697974006e275,        0 },
  { 275, 1.15664129333688770799461766294e277,       0 },
  { 276, 2.41049677287076803226326408256e278,       0 },
  { 277, 3.2038963825431789511450909263e279,        0 },
  { 278, 6.7011810285807351296918741495e280,        0 },
  { 279, 8.9388709072954692736948036845e281,        0 },
  { 280, 1.87633068800260583631372476186e283,       0 },
  { 281, 2.51182272495002686590823983534e284,       0 },
  { 282, 5.2912525401673484584047038284e285,        0 },
  { 283, 7.1084583116085760305203187340e286,        0 },
  { 284, 1.50271572140752696218693588728e288,       0 },
  { 285, 2.02591061880844416869829083919e289,       0 },
  { 286, 4.2977669632255271118546366376e290,        0 },
  { 287, 5.8143634759802347641640947085e291,        0 },
  { 288, 1.23775688540895180821413535163e293,       0 },
  { 289, 1.68035104455828784684342337075e294,       0 },
  { 290, 3.5894949676859602438209925197e295,        0 },
  { 291, 4.8898215396646176343143620089e296,        0 },
  { 292, 1.04813253056430039119572981576e298,       0 },
  { 293, 1.43271771112173296685410806860e299,       0 },
  { 294, 3.08150963985904315011544565835e300,       0 },
  { 295, 4.2265172478091122522196188024e301,        0 },
  { 296, 9.1212685339827677243417191487e302,        0 },
  { 297, 1.25527562259930633890922678431e304,       0 },
  /*
  { 298, 2.71813802312686478185383230631e305,       0 },
  { 299, 3.7532741115719259533385880851e306,        0 },
  { 300, 8.1544140693805943455614969189e307,  }
  */
};


/* Chebyshev coefficients for Gamma*(3/4(t+1)+1/2), -1<t<1
 */
static double gstar_a_data[30] = {
  2.16786447866463034423060819465,
 -0.05533249018745584258035832802,
  0.01800392431460719960888319748,
 -0.00580919269468937714480019814,
  0.00186523689488400339978881560,
 -0.00059746524113955531852595159,
  0.00019125169907783353925426722,
 -0.00006124996546944685735909697,
  0.00001963889633130842586440945,
 -6.3067741254637180272515795142e-06,
  2.0288698405861392526872789863e-06,
 -6.5384896660838465981983750582e-07,
  2.1108698058908865476480734911e-07,
 -6.8260714912274941677892994580e-08,
  2.2108560875880560555583978510e-08,
 -7.1710331930255456643627187187e-09,
  2.3290892983985406754602564745e-09,
 -7.5740371598505586754890405359e-10,
  2.4658267222594334398525312084e-10,
 -8.0362243171659883803428749516e-11,
  2.6215616826341594653521346229e-11,
 -8.5596155025948750540420068109e-12,
  2.7970831499487963614315315444e-12,
 -9.1471771211886202805502562414e-13,
  2.9934720198063397094916415927e-13,
 -9.8026575909753445931073620469e-14,
  3.2116773667767153777571410671e-14,
 -1.0518035333878147029650507254e-14,
  3.4144405720185253938994854173e-15,
 -1.0115153943081187052322643819e-15
};
static cheb_series gstar_a_cs = {
  gstar_a_data,
  29,
  -1, 1,
  17
};


/* Chebyshev coefficients for
 * x^2(Gamma*(x) - 1 - 1/(12x)), x = 4(t+1)+2, -1 < t < 1
 */
static double gstar_b_data[] = {
  0.0057502277273114339831606096782,
  0.0004496689534965685038254147807,
 -0.0001672763153188717308905047405,
  0.0000615137014913154794776670946,
 -0.0000223726551711525016380862195,
  8.0507405356647954540694800545e-06,
 -2.8671077107583395569766746448e-06,
  1.0106727053742747568362254106e-06,
 -3.5265558477595061262310873482e-07,
  1.2179216046419401193247254591e-07,
 -4.1619640180795366971160162267e-08,
  1.4066283500795206892487241294e-08,
 -4.6982570380537099016106141654e-09,
  1.5491248664620612686423108936e-09,
 -5.0340936319394885789686867772e-10,
  1.6084448673736032249959475006e-10,
 -5.0349733196835456497619787559e-11,
  1.5357154939762136997591808461e-11,
 -4.5233809655775649997667176224e-12,
  1.2664429179254447281068538964e-12,
 -3.2648287937449326771785041692e-13,
  7.1528272726086133795579071407e-14,
 -9.4831735252566034505739531258e-15,
 -2.3124001991413207293120906691e-15,
  2.8406613277170391482590129474e-15,
 -1.7245370321618816421281770927e-15,
  8.6507923128671112154695006592e-16,
 -3.9506563665427555895391869919e-16,
  1.6779342132074761078792361165e-16,
 -6.0483153034414765129837716260e-17
};
static cheb_series gstar_b_cs = {
  gstar_b_data,
  29,
  -1, 1,
  18
};


/* coefficients for gamma=7, kmax=8  Lanczos method */
static double lanczos_7_c[9] = {
  0.99999999999980993227684700473478,
  676.520368121885098567009190444019,
 -1259.13921672240287047156078755283,
  771.3234287776530788486528258894,
 -176.61502916214059906584551354,
  12.507343278686904814458936853,
 -0.13857109526572011689554707,
  9.984369578019570859563e-6,
  1.50563273514931155834e-7
};

/* complex version of Lanczos method; this is not safe for export
 * since it becomes bad in the left half-plane
 */
static
int
lngamma_lanczos_complex(double zr, double zi, gsl_sf_result * yr, gsl_sf_result * yi)
{
  int k;
  gsl_sf_result log1_r,    log1_i;
  gsl_sf_result logAg_r,   logAg_i;
  double Ag_r, Ag_i;
  double yi_tmp_val, yi_tmp_err;

  zr -= 1.0; /* Lanczos writes z! instead of Gamma(z) */

  Ag_r = lanczos_7_c[0];
  Ag_i = 0.0;
  for(k=1; k<=8; k++) {
    double R = zr + k;
    double I = zi;
    double a = lanczos_7_c[k] / (R*R + I*I);
    Ag_r +=  a * R;
    Ag_i -=  a * I;
  }

  gsl_sf_complex_log_e(zr + 7.5, zi, &log1_r,  &log1_i);
  gsl_sf_complex_log_e(Ag_r, Ag_i,   &logAg_r, &logAg_i);

  /* (z+0.5)*log(z+7.5) - (z+7.5) + LogRootTwoPi_ + log(Ag(z)) */
  yr->val = (zr+0.5)*log1_r.val - zi*log1_i.val - (zr+7.5) + LogRootTwoPi_ + logAg_r.val;
  yi->val = zi*log1_r.val + (zr+0.5)*log1_i.val - zi + logAg_i.val;
  yr->err = 4.0 * GSL_DBL_EPSILON * fabs(yr->val);
  yi->err = 4.0 * GSL_DBL_EPSILON * fabs(yi->val);
  yi_tmp_val = yi->val;
  yi_tmp_err = yi->err;
  gsl_sf_angle_restrict_symm_err_e(yi_tmp_val, yi);
  yi->err += yi_tmp_err;
  return GSL_SUCCESS;
}


/* Lanczos method for real x > 0;
 * gamma=7, truncated at 1/(z+8) 
 * [J. SIAM Numer. Anal, Ser. B, 1 (1964) 86]
 */
static
int
lngamma_lanczos(double x, gsl_sf_result * result)
{
  int k;
  double Ag;
  double term1, term2;

  x -= 1.0; /* Lanczos writes z! instead of Gamma(z) */

  Ag = lanczos_7_c[0];
  for(k=1; k<=8; k++) { Ag += lanczos_7_c[k]/(x+k); }

  /* (x+0.5)*log(x+7.5) - (x+7.5) + LogRootTwoPi_ + log(Ag(x)) */
  term1 = (x+0.5)*log((x+7.5)/M_E);
  term2 = LogRootTwoPi_ + log(Ag);
  result->val  = term1 + (term2 - 7.0);
  result->err  = 2.0 * GSL_DBL_EPSILON * (fabs(term1) + fabs(term2) + 7.0);
  result->err += GSL_DBL_EPSILON * fabs(result->val);

  return GSL_SUCCESS;
}

/* x = eps near zero
 * gives double-precision for |eps| < 0.02
 */
static
int
lngamma_sgn_0(double eps, gsl_sf_result * lng, double * sgn)
{
  /* calculate series for g(eps) = Gamma(eps) eps - 1/(1+eps) - eps/2 */
  const double c1  = -0.07721566490153286061;
  const double c2  = -0.01094400467202744461;
  const double c3  =  0.09252092391911371098;
  const double c4  = -0.01827191316559981266;
  const double c5  =  0.01800493109685479790;
  const double c6  = -0.00685088537872380685;
  const double c7  =  0.00399823955756846603;
  const double c8  = -0.00189430621687107802;
  const double c9  =  0.00097473237804513221;
  const double c10 = -0.00048434392722255893;
  const double g6  = c6+eps*(c7+eps*(c8 + eps*(c9 + eps*c10)));
  const double g   = eps*(c1+eps*(c2+eps*(c3+eps*(c4+eps*(c5+eps*g6)))));

  /* calculate Gamma(eps) eps, a positive quantity */
  const double gee = g + 1.0/(1.0+eps) + 0.5*eps;

  lng->val = log(gee/fabs(eps));
  lng->err = 4.0 * GSL_DBL_EPSILON * fabs(lng->val);
  *sgn = GSL_SIGN(eps);

  return GSL_SUCCESS;
}


/* x near a negative integer
 * Calculates sign as well as log(|gamma(x)|).
 * x = -N + eps
 * assumes N >= 1
 */
static
int
lngamma_sgn_sing(int N, double eps, gsl_sf_result * lng, double * sgn)
{
  if(eps == 0.0) {
    lng->val = 0.0;
    lng->err = 0.0;
    *sgn = 0.0;
    GSL_ERROR ("error", GSL_EDOM);
  }
  else if(N == 1) {
    /* calculate series for
     * g = eps gamma(-1+eps) + 1 + eps/2 (1+3eps)/(1-eps^2)
     * double-precision for |eps| < 0.02
     */
    const double c0 =  0.07721566490153286061;
    const double c1 =  0.08815966957356030521;
    const double c2 = -0.00436125434555340577;
    const double c3 =  0.01391065882004640689;
    const double c4 = -0.00409427227680839100;
    const double c5 =  0.00275661310191541584;
    const double c6 = -0.00124162645565305019;
    const double c7 =  0.00065267976121802783;
    const double c8 = -0.00032205261682710437;
    const double c9 =  0.00016229131039545456;
    const double g5 = c5 + eps*(c6 + eps*(c7 + eps*(c8 + eps*c9)));
    const double g  = eps*(c0 + eps*(c1 + eps*(c2 + eps*(c3 + eps*(c4 + eps*g5)))));

    /* calculate eps gamma(-1+eps), a negative quantity */
    const double gam_e = g - 1.0 - 0.5*eps*(1.0+3.0*eps)/(1.0 - eps*eps);

    lng->val = log(fabs(gam_e)/fabs(eps));
    lng->err = 2.0 * GSL_DBL_EPSILON * fabs(lng->val);
    *sgn = ( eps > 0.0 ? -1.0 : 1.0 );
    return GSL_SUCCESS;
  }
  else {
    double g;

    /* series for sin(Pi(N+1-eps))/(Pi eps) modulo the sign
     * double-precision for |eps| < 0.02
     */
    const double cs1 = -1.6449340668482264365;
    const double cs2 =  0.8117424252833536436;
    const double cs3 = -0.1907518241220842137;
    const double cs4 =  0.0261478478176548005;
    const double cs5 = -0.0023460810354558236;
    const double e2  = eps*eps;
    const double sin_ser = 1.0 + e2*(cs1+e2*(cs2+e2*(cs3+e2*(cs4+e2*cs5))));

    /* calculate series for ln(gamma(1+N-eps))
     * double-precision for |eps| < 0.02
     */
    double aeps = fabs(eps);
    double c1, c2, c3, c4, c5, c6, c7;
    double lng_ser;
    gsl_sf_result c0;
    gsl_sf_result psi_0;
    gsl_sf_result psi_1;
    gsl_sf_result psi_2;
    gsl_sf_result psi_3;
    gsl_sf_result psi_4;
    gsl_sf_result psi_5;
    gsl_sf_result psi_6;
    psi_2.val = 0.0;
    psi_3.val = 0.0;
    psi_4.val = 0.0;
    psi_5.val = 0.0;
    psi_6.val = 0.0;
    gsl_sf_lnfact_e(N, &c0);
    gsl_sf_psi_int_e(N+1, &psi_0);
    gsl_sf_psi_1_int_e(N+1, &psi_1);
    if(aeps > 0.00001) gsl_sf_psi_n_e(2, N+1.0, &psi_2);
    if(aeps > 0.0002)  gsl_sf_psi_n_e(3, N+1.0, &psi_3);
    if(aeps > 0.001)   gsl_sf_psi_n_e(4, N+1.0, &psi_4);
    if(aeps > 0.005)   gsl_sf_psi_n_e(5, N+1.0, &psi_5);
    if(aeps > 0.01)    gsl_sf_psi_n_e(6, N+1.0, &psi_6);
    c1 = psi_0.val;
    c2 = psi_1.val/2.0;
    c3 = psi_2.val/6.0;
    c4 = psi_3.val/24.0;
    c5 = psi_4.val/120.0;
    c6 = psi_5.val/720.0;
    c7 = psi_6.val/5040.0;
    lng_ser = c0.val-eps*(c1-eps*(c2-eps*(c3-eps*(c4-eps*(c5-eps*(c6-eps*c7))))));

    /* calculate
     * g = ln(|eps gamma(-N+eps)|)
     *   = -ln(gamma(1+N-eps)) + ln(|eps Pi/sin(Pi(N+1+eps))|)
     */
    g = -lng_ser - log(sin_ser);

    lng->val = g - log(fabs(eps));
    lng->err = c0.err + 2.0 * GSL_DBL_EPSILON * (fabs(g) + fabs(lng->val));

    *sgn = ( GSL_IS_ODD(N) ? -1.0 : 1.0 ) * ( eps > 0.0 ? 1.0 : -1.0 );

    return GSL_SUCCESS;
  }
}


/* This gets bad near the negative half axis. However, this
 * region can be avoided by use of the reflection formula, as usual.
 * Only the first two terms of the series are kept.
 */
#if 0
static
int
lngamma_complex_stirling(const double zr, const double zi, double * lg_r, double * arg)
{
  double re_zinv,  im_zinv;
  double re_zinv2, im_zinv2;
  double re_zinv3, im_zinv3;
  double re_zhlnz, im_zhlnz;
  double r, lnr, theta;
  gsl_sf_complex_log_e(zr, zi, &lnr, &theta);  /* z = r e^{i theta} */
  r = exp(lnr);
  re_zinv =  (zr/r)/r;
  im_zinv = -(zi/r)/r;
  re_zinv2 = re_zinv*re_zinv - im_zinv*im_zinv;
  re_zinv2 = 2.0*re_zinv*im_zinv;
  re_zinv3 = re_zinv2*re_zinv - im_zinv2*im_zinv;
  re_zinv3 = re_zinv2*im_zinv + im_zinv2*re_zinv;
  re_zhlnz = (zr - 0.5)*lnr - zi*theta;
  im_zhlnz = zi*lnr + zr*theta;
  *lg_r = re_zhlnz - zr + 0.5*(M_LN2+M_LNPI) + re_zinv/12.0 - re_zinv3/360.0;
  *arg  = im_zhlnz - zi + 1.0/12.0*im_zinv - im_zinv3/360.0;
  return GSL_SUCCESS;
}
#endif /* 0 */


inline
static
int
lngamma_1_pade(const double eps, gsl_sf_result * result)
{
  /* Use (2,2) Pade for Log[Gamma[1+eps]]/eps
   * plus a correction series.
   */
  const double n1 = -1.0017419282349508699871138440;
  const double n2 =  1.7364839209922879823280541733;
  const double d1 =  1.2433006018858751556055436011;
  const double d2 =  5.0456274100274010152489597514;
  const double num = (eps + n1) * (eps + n2);
  const double den = (eps + d1) * (eps + d2);
  const double pade = 2.0816265188662692474880210318 * num / den;
  const double c0 =  0.004785324257581753;
  const double c1 = -0.01192457083645441;
  const double c2 =  0.01931961413960498;
  const double c3 = -0.02594027398725020;
  const double c4 =  0.03141928755021455;
  const double eps5 = eps*eps*eps*eps*eps;
  const double corr = eps5 * (c0 + eps*(c1 + eps*(c2 + eps*(c3 + c4*eps))));
  result->val = eps * (pade + corr);
  result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
  return GSL_SUCCESS;
}

inline
static
int
lngamma_2_pade(const double eps, gsl_sf_result * result)
{
  /* Use (2,2) Pade for Log[Gamma[2+eps]]/eps
   * plus a correction series.
   */
  const double n1 = 1.000895834786669227164446568;
  const double n2 = 4.209376735287755081642901277;
  const double d1 = 2.618851904903217274682578255;
  const double d2 = 10.85766559900983515322922936;
  const double num = (eps + n1) * (eps + n2);
  const double den = (eps + d1) * (eps + d2);
  const double pade = 2.85337998765781918463568869 * num/den;
  const double c0 =  0.0001139406357036744;
  const double c1 = -0.0001365435269792533;
  const double c2 =  0.0001067287169183665;
  const double c3 = -0.0000693271800931282;
  const double c4 =  0.0000407220927867950;
  const double eps5 = eps*eps*eps*eps*eps;
  const double corr = eps5 * (c0 + eps*(c1 + eps*(c2 + eps*(c3 + c4*eps))));
  result->val = eps * (pade + corr);
  result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
  return GSL_SUCCESS;
}


/* series for gammastar(x)
 * double-precision for x > 10.0
 */
static
int
gammastar_ser(const double x, gsl_sf_result * result)
{
  /* Use the Stirling series for the correction to Log(Gamma(x)),
   * which is better behaved and easier to compute than the
   * regular Stirling series for Gamma(x). 
   */
  const double y = 1.0/(x*x);
  const double c0 =  1.0/12.0;
  const double c1 = -1.0/360.0;
  const double c2 =  1.0/1260.0;
  const double c3 = -1.0/1680.0;
  const double c4 =  1.0/1188.0;
  const double c5 = -691.0/360360.0;
  const double c6 =  1.0/156.0;
  const double c7 = -3617.0/122400.0;
  const double ser = c0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*(c5 + y*(c6 + y*c7))))));
  result->val = exp(ser/x);
  result->err = 2.0 * GSL_DBL_EPSILON * result->val * GSL_MAX_DBL(1.0, ser/x);
  return GSL_SUCCESS;
}


/* Chebyshev expansion for log(gamma(x)/gamma(8))
 * 5 < x < 10
 * -1 < t < 1
 */
static double gamma_5_10_data[24] = {
 -1.5285594096661578881275075214,
  4.8259152300595906319768555035,
  0.2277712320977614992970601978,
 -0.0138867665685617873604917300,
  0.0012704876495201082588139723,
 -0.0001393841240254993658962470,
  0.0000169709242992322702260663,
 -2.2108528820210580075775889168e-06,
  3.0196602854202309805163918716e-07,
 -4.2705675000079118380587357358e-08,
  6.2026423818051402794663551945e-09,
 -9.1993973208880910416311405656e-10,
  1.3875551258028145778301211638e-10,
 -2.1218861491906788718519522978e-11,
  3.2821736040381439555133562600e-12,
 -5.1260001009953791220611135264e-13,
  8.0713532554874636696982146610e-14,
 -1.2798522376569209083811628061e-14,
  2.0417711600852502310258808643e-15,
 -3.2745239502992355776882614137e-16,
  5.2759418422036579482120897453e-17,
 -8.5354147151695233960425725513e-18,
  1.3858639703888078291599886143e-18,
 -2.2574398807738626571560124396e-19
};
static const cheb_series gamma_5_10_cs = {
  gamma_5_10_data,
  23,
  -1, 1,
  11
};


/* gamma(x) for x >= 1/2
 * assumes x >= 1/2
 */
static
int
gamma_xgthalf(const double x, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(x == 0.5) {
    result->val = 1.77245385090551602729817;
    result->err = GSL_DBL_EPSILON * result->val;
    return GSL_SUCCESS;
  } else if (x <= (GSL_SF_FACT_NMAX + 1.0) && x == floor(x)) {
    int n = (int) floor (x);
    result->val = fact_table[n - 1].f;
    result->err = GSL_DBL_EPSILON * result->val;
    return GSL_SUCCESS;
  }    
  else if(fabs(x - 1.0) < 0.01) {
    /* Use series for Gamma[1+eps] - 1/(1+eps).
     */
    const double eps = x - 1.0;
    const double c1 =  0.4227843350984671394;
    const double c2 = -0.01094400467202744461;
    const double c3 =  0.09252092391911371098;
    const double c4 = -0.018271913165599812664;
    const double c5 =  0.018004931096854797895;
    const double c6 = -0.006850885378723806846;
    const double c7 =  0.003998239557568466030;
    result->val = 1.0/x + eps*(c1+eps*(c2+eps*(c3+eps*(c4+eps*(c5+eps*(c6+eps*c7))))));
    result->err = GSL_DBL_EPSILON;
    return GSL_SUCCESS;
  }
  else if(fabs(x - 2.0) < 0.01) {
    /* Use series for Gamma[1 + eps].
     */
    const double eps = x - 2.0;
    const double c1 =  0.4227843350984671394;
    const double c2 =  0.4118403304264396948;
    const double c3 =  0.08157691924708626638;
    const double c4 =  0.07424901075351389832;
    const double c5 = -0.00026698206874501476832;
    const double c6 =  0.011154045718130991049;
    const double c7 = -0.002852645821155340816;
    const double c8 =  0.0021039333406973880085;
    result->val = 1.0 + eps*(c1+eps*(c2+eps*(c3+eps*(c4+eps*(c5+eps*(c6+eps*(c7+eps*c8)))))));
    result->err = GSL_DBL_EPSILON;
    return GSL_SUCCESS;
  }
  else if(x < 5.0) {
    /* Exponentiating the logarithm is fine, as
     * long as the exponential is not so large
     * that it greatly amplifies the error.
     */
    gsl_sf_result lg;
    lngamma_lanczos(x, &lg);
    result->val = exp(lg.val);
    result->err = result->val * (lg.err + 2.0 * GSL_DBL_EPSILON);
    return GSL_SUCCESS;
  }
  else if(x < 10.0) {
    /* This is a sticky area. The logarithm
     * is too large and the gammastar series
     * is not good.
     */
    const double gamma_8 = 5040.0;
    const double t = (2.0*x - 15.0)/5.0;
    gsl_sf_result c;
    cheb_eval_e(&gamma_5_10_cs, t, &c);
    result->val  = exp(c.val) * gamma_8;
    result->err  = result->val * c.err;
    result->err += 2.0 * GSL_DBL_EPSILON * result->val;
    return GSL_SUCCESS;
  }
  else if(x < GSL_SF_GAMMA_XMAX) {
    /* We do not want to exponentiate the logarithm
     * if x is large because of the inevitable
     * inflation of the error. So we carefully
     * use pow() and exp() with exact quantities.
     */
    double p = pow(x, 0.5*x);
    double e = exp(-x);
    double q = (p * e) * p;
    double pre = M_SQRT2 * M_SQRTPI * q/sqrt(x);
    gsl_sf_result gstar;
    int stat_gs = gammastar_ser(x, &gstar);
    result->val = pre * gstar.val;
    result->err = (x + 2.5) * GSL_DBL_EPSILON * result->val;
    return stat_gs;
  }
  else {
    OVERFLOW_ERROR(result);
  }
}


/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/


int gsl_sf_lngamma_e(double x, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(fabs(x - 1.0) < 0.01) {
    /* Note that we must amplify the errors
     * from the Pade evaluations because of
     * the way we must pass the argument, i.e.
     * writing (1-x) is a loss of precision
     * when x is near 1.
     */
    int stat = lngamma_1_pade(x - 1.0, result);
    result->err *= 1.0/(GSL_DBL_EPSILON + fabs(x - 1.0));
    return stat;
  }
  else if(fabs(x - 2.0) < 0.01) {
    int stat = lngamma_2_pade(x - 2.0, result);
    result->err *= 1.0/(GSL_DBL_EPSILON + fabs(x - 2.0));
    return stat;
  }
  else if(x >= 0.5) {
    return lngamma_lanczos(x, result);
  }
  else if(x == 0.0) {
    DOMAIN_ERROR(result);
  }
  else if(fabs(x) < 0.02) {
    double sgn;
    return lngamma_sgn_0(x, result, &sgn);
  }
  else if(x > -0.5/(GSL_DBL_EPSILON*M_PI)) {
    /* Try to extract a fractional
     * part from x.
     */
    double z  = 1.0 - x;
    double s  = sin(M_PI*z);
    double as = fabs(s);
    if(s == 0.0) {
      DOMAIN_ERROR(result);
    }
    else if(as < M_PI*0.015) {
      /* x is near a negative integer, -N */
      if(x < INT_MIN + 2.0) {
        result->val = 0.0;
        result->err = 0.0;
        GSL_ERROR ("error", GSL_EROUND);
      }
      else {
        int N = -(int)(x - 0.5);
        double eps = x + N;
        double sgn;
        return lngamma_sgn_sing(N, eps, result, &sgn);
      }
    }
    else {
      gsl_sf_result lg_z;
      lngamma_lanczos(z, &lg_z);
      result->val = M_LNPI - (log(as) + lg_z.val);
      result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) + lg_z.err;
      return GSL_SUCCESS;
    }
  }
  else {
    /* |x| was too large to extract any fractional part */
    result->val = 0.0;
    result->err = 0.0;
    GSL_ERROR ("error", GSL_EROUND);
  }
}


int gsl_sf_lngamma_sgn_e(double x, gsl_sf_result * result_lg, double * sgn)
{
  if(fabs(x - 1.0) < 0.01) {
    int stat = lngamma_1_pade(x - 1.0, result_lg);
    result_lg->err *= 1.0/(GSL_DBL_EPSILON + fabs(x - 1.0));
    *sgn = 1.0;
    return stat;
  }
  else if(fabs(x - 2.0) < 0.01) {
   int stat = lngamma_2_pade(x - 2.0, result_lg);
    result_lg->err *= 1.0/(GSL_DBL_EPSILON + fabs(x - 2.0));
    *sgn = 1.0;
    return stat;
  }
  else if(x >= 0.5) {
    *sgn = 1.0;
    return lngamma_lanczos(x, result_lg);
  }
  else if(x == 0.0) {
    *sgn = 0.0;
    DOMAIN_ERROR(result_lg);
  }
  else if(fabs(x) < 0.02) {
    return lngamma_sgn_0(x, result_lg, sgn);
  }
  else if(x > -0.5/(GSL_DBL_EPSILON*M_PI)) {
   /* Try to extract a fractional
     * part from x.
     */
    double z = 1.0 - x;
    double s = sin(M_PI*x);
    double as = fabs(s);
    if(s == 0.0) {
      *sgn = 0.0;
      DOMAIN_ERROR(result_lg);
    }
    else if(as < M_PI*0.015) {
      /* x is near a negative integer, -N */
      if(x < INT_MIN + 2.0) {
        result_lg->val = 0.0;
        result_lg->err = 0.0;
        *sgn = 0.0;
        GSL_ERROR ("error", GSL_EROUND);
      }
      else {
        int N = -(int)(x - 0.5);
        double eps = x + N;
        return lngamma_sgn_sing(N, eps, result_lg, sgn);
      }
    }
    else {
      gsl_sf_result lg_z;
      lngamma_lanczos(z, &lg_z);
      *sgn = (s > 0.0 ? 1.0 : -1.0);
      result_lg->val = M_LNPI - (log(as) + lg_z.val);
      result_lg->err = 2.0 * GSL_DBL_EPSILON * fabs(result_lg->val) + lg_z.err;
      return GSL_SUCCESS;
    }
  }
  else {
    /* |x| was too large to extract any fractional part */
    result_lg->val = 0.0;
    result_lg->err = 0.0;
    *sgn = 0.0;
    GSL_ERROR ("error", GSL_EROUND);
  }
}


int
gsl_sf_gamma_e(const double x, gsl_sf_result * result)
{
  if(x < 0.5) {
    int rint_x = (int)floor(x+0.5);
    double f_x = x - rint_x;
    double sgn_gamma = ( GSL_IS_EVEN(rint_x) ? 1.0 : -1.0 );
    double sin_term = sgn_gamma * sin(M_PI * f_x) / M_PI;

    if(sin_term == 0.0) {
      DOMAIN_ERROR(result);
    }
    else if(x > -169.0) {
      gsl_sf_result g;
      gamma_xgthalf(1.0-x, &g);
      if(fabs(sin_term) * g.val * GSL_DBL_MIN < 1.0) {
        result->val  = 1.0/(sin_term * g.val);
        result->err  = fabs(g.err/g.val) * fabs(result->val);
        result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
        return GSL_SUCCESS;
      }
      else {
        UNDERFLOW_ERROR(result);
      }
    }
    else {
      /* It is hard to control it here.
       * We can only exponentiate the
       * logarithm and eat the loss of
       * precision.
       */
      gsl_sf_result lng;
      double sgn;
      int stat_lng = gsl_sf_lngamma_sgn_e(x, &lng, &sgn);
      int stat_e   = gsl_sf_exp_mult_err_e(lng.val, lng.err, sgn, 0.0, result);
      return GSL_ERROR_SELECT_2(stat_e, stat_lng);
    }
  }
  else {
    return gamma_xgthalf(x, result);
  }
}


int
gsl_sf_gammastar_e(const double x, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(x <= 0.0) {
    DOMAIN_ERROR(result);
  }
  else if(x < 0.5) {
    gsl_sf_result lg;
    const int stat_lg = gsl_sf_lngamma_e(x, &lg);
    const double lx = log(x);
    const double c  = 0.5*(M_LN2+M_LNPI);
    const double lnr_val = lg.val - (x-0.5)*lx + x - c;
    const double lnr_err = lg.err + 2.0 * GSL_DBL_EPSILON *((x+0.5)*fabs(lx) + c);
    const int stat_e  = gsl_sf_exp_err_e(lnr_val, lnr_err, result);
    return GSL_ERROR_SELECT_2(stat_lg, stat_e);
  }
  else if(x < 2.0) {
    const double t = 4.0/3.0*(x-0.5) - 1.0;
    return cheb_eval_e(&gstar_a_cs, t, result);
  }
  else if(x < 10.0) {
    const double t = 0.25*(x-2.0) - 1.0;
    gsl_sf_result c;
    cheb_eval_e(&gstar_b_cs, t, &c);
    result->val  = c.val/(x*x) + 1.0 + 1.0/(12.0*x);
    result->err  = c.err/(x*x);
    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
  else if(x < 1.0/GSL_ROOT4_DBL_EPSILON) {
    return gammastar_ser(x, result);
  }
  else if(x < 1.0/GSL_DBL_EPSILON) {
    /* Use Stirling formula for Gamma(x).
     */
    const double xi = 1.0/x;
    result->val = 1.0 + xi/12.0*(1.0 + xi/24.0*(1.0 - xi*(139.0/180.0 + 571.0/8640.0*xi)));
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
  else {
    result->val = 1.0;
    result->err = 1.0/x;
    return GSL_SUCCESS;
  }
}


int
gsl_sf_gammainv_e(const double x, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if (x <= 0.0 && x == floor(x)) { /* negative integer */
    result->val = 0.0;
    result->err = 0.0;
    return GSL_SUCCESS;
  } else if(x < 0.5) {
    gsl_sf_result lng;
    double sgn;
    int stat_lng = gsl_sf_lngamma_sgn_e(x, &lng, &sgn);
    if(stat_lng == GSL_EDOM) {
      result->val = 0.0;
      result->err = 0.0;
      return GSL_SUCCESS;
    }
    else if(stat_lng != GSL_SUCCESS) {
      result->val = 0.0;
      result->err = 0.0;
      return stat_lng;
    }
    else {
      return gsl_sf_exp_mult_err_e(-lng.val, lng.err, sgn, 0.0, result);
    }
  }
  else {
    gsl_sf_result g;
    int stat_g = gamma_xgthalf(x, &g);
    if(stat_g == GSL_EOVRFLW) {
      UNDERFLOW_ERROR(result);
    }
    else {
      result->val  = 1.0/g.val;
      result->err  = fabs(g.err/g.val) * fabs(result->val);
      result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
      CHECK_UNDERFLOW(result);
      return GSL_SUCCESS;
    }
  }
}


int
gsl_sf_lngamma_complex_e(double zr, double zi, gsl_sf_result * lnr, gsl_sf_result * arg)
{
  if(zr <= 0.5) {
    /* Transform to right half plane using reflection;
     * in fact we do a little better by stopping at 1/2.
     */
    double x = 1.0-zr;
    double y = -zi;
    gsl_sf_result a, b;
    gsl_sf_result lnsin_r, lnsin_i;

    int stat_l = lngamma_lanczos_complex(x, y, &a, &b);
    int stat_s = gsl_sf_complex_logsin_e(M_PI*zr, M_PI*zi, &lnsin_r, &lnsin_i);

    if(stat_s == GSL_SUCCESS) {
      int stat_r;
      lnr->val = M_LNPI - lnsin_r.val - a.val;
      lnr->err = lnsin_r.err + a.err + 2.0 * GSL_DBL_EPSILON * fabs(lnr->val);
      arg->val = -lnsin_i.val - b.val;
      arg->err = lnsin_i.err + b.err + 2.0 * GSL_DBL_EPSILON * fabs(arg->val);
      stat_r = gsl_sf_angle_restrict_symm_e(&(arg->val));
      return GSL_ERROR_SELECT_2(stat_r, stat_l);
    }
    else {
      DOMAIN_ERROR_2(lnr,arg);
    }
  }
  else {
    /* otherwise plain vanilla Lanczos */
    return lngamma_lanczos_complex(zr, zi, lnr, arg);
  }
}


int gsl_sf_taylorcoeff_e(const int n, const double x, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(x < 0.0 || n < 0) {
    DOMAIN_ERROR(result);
  }
  else if(n == 0) {
    result->val = 1.0;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else if(n == 1) {
    result->val = x;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else if(x == 0.0) {
    result->val = 0.0;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else {
    const double log2pi = M_LNPI + M_LN2;
    const double ln_test = n*(log(x)+1.0) + 1.0 - (n+0.5)*log(n+1.0) + 0.5*log2pi;

    if(ln_test < GSL_LOG_DBL_MIN+1.0) {
      UNDERFLOW_ERROR(result);
    }
    else if(ln_test > GSL_LOG_DBL_MAX-1.0) {
      OVERFLOW_ERROR(result);
    }
    else {
      double product = 1.0;
      int k;
      for(k=1; k<=n; k++) {
        product *= (x/k);
      }
      result->val = product;
      result->err = n * GSL_DBL_EPSILON * product;
      CHECK_UNDERFLOW(result);
      return GSL_SUCCESS;
    }    
  }
}


int gsl_sf_fact_e(const unsigned int n, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(n < 18) {
    result->val = fact_table[n].f;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else if(n <= GSL_SF_FACT_NMAX){
    result->val = fact_table[n].f;
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
  else {
    OVERFLOW_ERROR(result);
  }
}


int gsl_sf_doublefact_e(const unsigned int n, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(n < 26) {
    result->val = doub_fact_table[n].f;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else if(n <= GSL_SF_DOUBLEFACT_NMAX){
    result->val = doub_fact_table[n].f;
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
  else {
    OVERFLOW_ERROR(result);
  }
}


int gsl_sf_lnfact_e(const unsigned int n, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(n <= GSL_SF_FACT_NMAX){
    result->val = log(fact_table[n].f);
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
  else {
    gsl_sf_lngamma_e(n+1.0, result);
    return GSL_SUCCESS;
  }
}


int gsl_sf_lndoublefact_e(const unsigned int n, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(n <= GSL_SF_DOUBLEFACT_NMAX){
    result->val = log(doub_fact_table[n].f);
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
  else if(GSL_IS_ODD(n)) {
    gsl_sf_result lg;
    gsl_sf_lngamma_e(0.5*(n+2.0), &lg);
    result->val = 0.5*(n+1.0) * M_LN2 - 0.5*M_LNPI + lg.val;
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) + lg.err;
    return GSL_SUCCESS;
  }
  else {
    gsl_sf_result lg;
    gsl_sf_lngamma_e(0.5*n+1.0, &lg);
    result->val = 0.5*n*M_LN2 + lg.val;
    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) + lg.err;
    return GSL_SUCCESS;
  }
}


int gsl_sf_lnchoose_e(unsigned int n, unsigned int m, gsl_sf_result * result)
{
  /* CHECK_POINTER(result) */

  if(m > n) {
    DOMAIN_ERROR(result);
  }
  else if(m == n || m == 0) {
    result->val = 0.0;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else {
    gsl_sf_result nf;
    gsl_sf_result mf;
    gsl_sf_result nmmf;
    if(m*2 > n) m = n-m;
    gsl_sf_lnfact_e(n, &nf);
    gsl_sf_lnfact_e(m, &mf);
    gsl_sf_lnfact_e(n-m, &nmmf);
    result->val  = nf.val - mf.val - nmmf.val;
    result->err  = nf.err + mf.err + nmmf.err;
    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  }
}


int gsl_sf_choose_e(unsigned int n, unsigned int m, gsl_sf_result * result)
{
  if(m > n) {
    DOMAIN_ERROR(result);
  }
  else if(m == n || m == 0) {
    result->val = 1.0;
    result->err = 0.0;
    return GSL_SUCCESS;
  }
  else if (n <= GSL_SF_FACT_NMAX) {
    result->val = (fact_table[n].f / fact_table[m].f) / fact_table[n-m].f;
    result->err = 6.0 * GSL_DBL_EPSILON * fabs(result->val);
    return GSL_SUCCESS;
  } else {
    if(m*2 < n) m = n-m;

    if (n - m < 64)  /* compute product for a manageable number of terms */
      {
        double prod = 1.0;
        unsigned int k;
        
        for(k=n; k>=m+1; k--) {
          double tk = (double)k / (double)(k-m);
          if(tk > GSL_DBL_MAX/prod) {
            OVERFLOW_ERROR(result);
          }
          prod *= tk;
        }
        result->val = prod;
        result->err = 2.0 * GSL_DBL_EPSILON * prod * fabs(n-m);
        return GSL_SUCCESS;
      }
    else
      {
        gsl_sf_result lc;
        const int stat_lc = gsl_sf_lnchoose_e (n, m, &lc);
        const int stat_e  = gsl_sf_exp_err_e(lc.val, lc.err, result);
        return GSL_ERROR_SELECT_2(stat_lc, stat_e);
      }
  }
}


/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/

#include "eval.h"

double gsl_sf_fact(const unsigned int n)
{
  EVAL_RESULT(gsl_sf_fact_e(n, &result));
}

double gsl_sf_lnfact(const unsigned int n)
{
  EVAL_RESULT(gsl_sf_lnfact_e(n, &result));
}

double gsl_sf_doublefact(const unsigned int n)
{
  EVAL_RESULT(gsl_sf_doublefact_e(n, &result));
}

double gsl_sf_lndoublefact(const unsigned int n)
{
  EVAL_RESULT(gsl_sf_lndoublefact_e(n, &result));
}

double gsl_sf_lngamma(const double x)
{
  EVAL_RESULT(gsl_sf_lngamma_e(x, &result));
}

double gsl_sf_gamma(const double x)
{
  EVAL_RESULT(gsl_sf_gamma_e(x, &result));
}

double gsl_sf_gammastar(const double x)
{
  EVAL_RESULT(gsl_sf_gammastar_e(x, &result));
}

double gsl_sf_gammainv(const double x)
{
  EVAL_RESULT(gsl_sf_gammainv_e(x, &result));
}

double gsl_sf_taylorcoeff(const int n, const double x)
{
  EVAL_RESULT(gsl_sf_taylorcoeff_e(n, x, &result));
}

double gsl_sf_choose(unsigned int n, unsigned int m)
{
  EVAL_RESULT(gsl_sf_choose_e(n, m, &result));
}

double gsl_sf_lnchoose(unsigned int n, unsigned int m)
{
  EVAL_RESULT(gsl_sf_lnchoose_e(n, m, &result));
}

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