1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #pragma weak __tgammal = tgammal
  31 
  32 #include "libm.h"
  33 #include <sys/isa_defs.h>
  34 
  35 #if defined(_BIG_ENDIAN)
  36 #define H0_WORD(x)      ((unsigned *) &x)[0]
  37 #define H3_WORD(x)      ((unsigned *) &x)[3]
  38 #define CHOPPED(x)      (long double) ((double) (x))
  39 #else
  40 #define H0_WORD(x)      ((((int *) &x)[2] << 16) | \
  41                         (0x0000ffff & (((unsigned *) &x)[1] >> 15)))
  42 #define H3_WORD(x)      ((unsigned *) &x)[0]
  43 #define CHOPPED(x)      (long double) ((float) (x))
  44 #endif
  45 
  46 struct LDouble {
  47         long double h, l;
  48 };
  49 
  50 /* INDENT OFF */
  51 /* Primary interval GTi() */
  52 static const long double P1[] = {
  53         +0.709086836199777919037185741507610124611513720557L,
  54         +4.45754781206489035827915969367354835667391606951e-0001L,
  55         +3.21049298735832382311662273882632210062918153852e-0002L,
  56         -5.71296796342106617651765245858289197369688864350e-0003L,
  57         +6.04666892891998977081619174969855831606965352773e-0003L,
  58         +8.99106186996888711939627812174765258822658645168e-0004L,
  59         -6.96496846144407741431207008527018441810175568949e-0005L,
  60         +1.52597046118984020814225409300131445070213882429e-0005L,
  61         +5.68521076168495673844711465407432189190681541547e-0007L,
  62         +3.30749673519634895220582062520286565610418952979e-0008L,
  63 };
  64 static const long double Q1[] = {
  65         +1.0+0000L,
  66         +1.35806511721671070408570853537257079579490650668e+0000L,
  67         +2.97567810153429553405327140096063086994072952961e-0001L,
  68         -1.52956835982588571502954372821681851681118097870e-0001L,
  69         -2.88248519561420109768781615289082053597954521218e-0002L,
  70         +1.03475311719937405219789948456313936302378395955e-0002L,
  71         +4.12310203243891222368965360124391297374822742313e-0004L,
  72         -3.12653708152290867248931925120380729518332507388e-0004L,
  73         +2.36672170850409745237358105667757760527014332458e-0005L,
  74 };
  75 static const long double P2[] = {
  76         +0.428486815855585429730209907810650135255270600668084114L,
  77         +2.62768479103809762805691743305424077975230551176e-0001L,
  78         +3.81187532685392297608310837995193946591425896150e-0002L,
  79         +3.00063075891811043820666846129131255948527925381e-0003L,
  80         +2.47315407812279164228398470797498649142513408654e-0003L,
  81         +3.62838199917848372586173483147214880464782938664e-0004L,
  82         +3.43991105975492623982725644046473030098172692423e-0006L,
  83         +4.56902151569603272237014240794257659159045432895e-0006L,
  84         +2.13734755837595695602045100675540011352948958453e-0007L,
  85         +9.74123440547918230781670266967882492234877125358e-0009L,
  86 };
  87 static const long double Q2[] = {
  88         +1.0L,
  89         +9.18284118632506842664645516830761489700556179701e-0001L,
  90         -6.41430858837830766045202076965923776189154874947e-0003L,
  91         -1.24400885809771073213345747437964149775410921376e-0001L,
  92         +4.69803798146251757538856567522481979624746875964e-0003L,
  93         +7.18309447069495315914284705109868696262662082731e-0003L,
  94         -8.75812626987894695112722600697653425786166399105e-0004L,
  95         -1.23539972377769277995959339188431498626674835169e-0004L,
  96         +3.10019017590151598732360097849672925448587547746e-0005L,
  97         -1.77260223349332617658921874288026777465782364070e-0006L,
  98 };
  99 static const long double P3[] = {
 100         +0.3824094797345675048502747661075355640070439388902L,
 101         +3.42198093076618495415854906335908427159833377774e-0001L,
 102         +9.63828189500585568303961406863153237440702754858e-0002L,
 103         +8.76069421042696384852462044188520252156846768667e-0003L,
 104         +1.86477890389161491224872014149309015261897537488e-0003L,
 105         +8.16871354540309895879974742853701311541286944191e-0004L,
 106         +6.83783483674600322518695090864659381650125625216e-0005L,
 107         -1.10168269719261574708565935172719209272190828456e-0006L,
 108         +9.66243228508380420159234853278906717065629721016e-0007L,
 109         +2.31858885579177250541163820671121664974334728142e-0008L,
 110 };
 111 static const long double Q3[] = {
 112         +1.0L,
 113         +8.25479821168813634632437430090376252512793067339e-0001L,
 114         -1.62251363073937769739639623669295110346015576320e-0002L,
 115         -1.10621286905916732758745130629426559691187579852e-0001L,
 116         +3.48309693970985612644446415789230015515365291459e-0003L,
 117         +6.73553737487488333032431261131289672347043401328e-0003L,
 118         -7.63222008393372630162743587811004613050245128051e-0004L,
 119         -1.35792670669190631476784768961953711773073251336e-0004L,
 120         +3.19610150954223587006220730065608156460205690618e-0005L,
 121         -1.82096553862822346610109522015129585693354348322e-0006L,
 122 };
 123 
 124 static const long double
 125 #if defined(__x86)
 126 GZ1_h   =  0.938204627909682449364570100414084663498215377L,
 127 GZ1_l   =  4.518346116624229420055327632718530617227944106e-20L,
 128 GZ2_h   =  0.885603194410888700264725126309883762587560340L,
 129 GZ2_l   =  1.409077427270497062039119290776508217077297169e-20L,
 130 GZ3_h   =  0.936781411463652321613537060640553022494714241L,
 131 GZ3_l   =  5.309836440284827247897772963887219035221996813e-21L,
 132 #else
 133 GZ1_h   =  0.938204627909682449409753561580326910854647031L,
 134 GZ1_l   =  4.684412162199460089642452580902345976446297037e-35L,
 135 GZ2_h   =  0.885603194410888700278815900582588658192658794L,
 136 GZ2_l   =  7.501529273890253789219935569758713534641074860e-35L,
 137 GZ3_h   =  0.936781411463652321618846897080837818855399840L,
 138 GZ3_l   =  3.088721217404784363585591914529361687403776917e-35L,
 139 #endif
 140 TZ1     = -0.3517214357852935791015625L,
 141 TZ3     =  0.280530631542205810546875L;
 142 /* INDENT ON */
 143 
 144 /* INDENT OFF */
 145 /*
 146  * compute gamma(y=yh+yl) for y in GT1 = [1.0000, 1.2845]
 147  * ...assume yh got 53 or 24(i386) significant bits
 148  */
 149 /* INDENT ON */
 150 static struct LDouble
 151 GT1(long double yh, long double yl) {
 152         long double t3, t4, y;
 153         int i;
 154         struct LDouble r;
 155 
 156         y = yh + yl;
 157         for (t4 = Q1[8], t3 = P1[8] + y * P1[9], i = 7; i >= 0; i--) {
 158                 t4 = t4 * y + Q1[i];
 159                 t3 = t3 * y + P1[i];
 160         }
 161         t3 = (y * y) * t3 / t4;
 162         t3 += (TZ1 * yl + GZ1_l);
 163         t4 = TZ1 * yh;
 164         r.h = CHOPPED((t4 + GZ1_h + t3));
 165         t3 += (t4 - (r.h - GZ1_h));
 166         r.l = t3;
 167         return (r);
 168 }
 169 
 170 /* INDENT OFF */
 171 /*
 172  * compute gamma(y=yh+yl) for y in GT2 = [1.2844, 1.6374]
 173  * ...assume yh got 53 significant bits
 174  */
 175 /* INDENT ON */
 176 static struct LDouble
 177 GT2(long double yh, long double yl) {
 178         long double t3, t4, y;
 179         int i;
 180         struct LDouble r;
 181 
 182         y = yh + yl;
 183         for (t4 = Q2[9], t3 = P2[9], i = 8; i >= 0; i--) {
 184                 t4 = t4 * y + Q2[i];
 185                 t3 = t3 * y + P2[i];
 186         }
 187         t3 = GZ2_l + (y * y) * t3 / t4;
 188         r.h = CHOPPED((GZ2_h + t3));
 189         r.l = t3 - (r.h - GZ2_h);
 190         return (r);
 191 }
 192 
 193 /* INDENT OFF */
 194 /*
 195  * compute gamma(y=yh+yl) for y in GT3 = [1.6373, 2.0000]
 196  * ...assume yh got 53 significant bits
 197  */
 198 /* INDENT ON */
 199 static struct LDouble
 200 GT3(long double yh, long double yl) {
 201         long double t3, t4, y;
 202         int i;
 203         struct LDouble r;
 204 
 205         y = yh + yl;
 206         for (t4 = Q3[9], t3 = P3[9], i = 8; i >= 0; i--) {
 207                 t4 = t4 * y + Q3[i];
 208                 t3 = t3 * y + P3[i];
 209         }
 210         t3 = (y * y) * t3 / t4;
 211         t3 += (TZ3 * yl + GZ3_l);
 212         t4 = TZ3 * yh;
 213         r.h = CHOPPED((t4 + GZ3_h + t3));
 214         t3 += (t4 - (r.h - GZ3_h));
 215         r.l = t3;
 216         return (r);
 217 }
 218 
 219 /* INDENT OFF */
 220 /* Hex value of GP[0] shoule be 3FB55555 55555555 */
 221 static const long double GP[] = {
 222         +0.083333333333333333333333333333333172839171301L,
 223         -2.77777777777777777777777777492501211999399424104e-0003L,
 224         +7.93650793650793650793635650541638236350020883243e-0004L,
 225         -5.95238095238095238057299772679324503339241961704e-0004L,
 226         +8.41750841750841696138422987977683524926142600321e-0004L,
 227         -1.91752691752686682825032547823699662178842123308e-0003L,
 228         +6.41025641022403480921891559356473451161279359322e-0003L,
 229         -2.95506535798414019189819587455577003732808185071e-0002L,
 230         +1.79644367229970031486079180060923073476568732136e-0001L,
 231         -1.39243086487274662174562872567057200255649290646e+0000L,
 232         +1.34025874044417962188677816477842265259608269775e+0001L,
 233         -1.56803713480127469414495545399982508700748274318e+0002L,
 234         +2.18739841656201561694927630335099313968924493891e+0003L,
 235         -3.55249848644100338419187038090925410976237921269e+0004L,
 236         +6.43464880437835286216768959439484376449179576452e+0005L,
 237         -1.20459154385577014992600342782821389605893904624e+0007L,
 238         +2.09263249637351298563934942349749718491071093210e+0008L,
 239         -2.96247483183169219343745316433899599834685703457e+0009L,
 240         +2.88984933605896033154727626086506756972327292981e+0010L,
 241         -1.40960434146030007732838382416230610302678063984e+0011L,      /* 19 */
 242 };
 243 
 244 static const long double T3[] = {
 245         +0.666666666666666666666666666666666634567834260213L,   /* T3[0] */
 246         +0.400000000000000000000000000040853636176634934140L,   /* T3[1] */
 247         +0.285714285714285714285696975252753987869020263448L,   /* T3[2] */
 248         +0.222222222222222225593221101192317258554772129875L,   /* T3[3] */
 249         +0.181818181817850192105847183461778186703779262916L,   /* T3[4] */
 250         +0.153846169861348633757101285952333369222567014596L,   /* T3[5] */
 251         +0.133033462889260193922261296772841229985047571265L,   /* T3[6] */
 252 };
 253 
 254 static const long double c[] = {
 255 0.0L,
 256 1.0L,
 257 2.0L,
 258 0.5L,
 259 1.0e-4930L,                                                     /* tiny */
 260 4.18937683105468750000e-01L,                                    /* hln2pim1_h */
 261 8.50099203991780329736405617639861397473637783412817152e-07L,   /* hln2pim1_l */
 262 0.418938533204672741780329736405617639861397473637783412817152L, /* hln2pim1 */
 263 2.16608493865351192653179168701171875e-02L,                     /* ln2_32hi */
 264 5.96317165397058692545083025235937919875797669127130e-12L,      /* ln2_32lo */
 265 46.16624130844682903551758979206054839765267053289554989233L,   /* invln2_32 */
 266 #if defined(__x86)
 267 1.7555483429044629170023839037639845628291e+03L,                /* overflow */
 268 #else
 269 1.7555483429044629170038892160702032034177e+03L,                /* overflow */
 270 #endif
 271 };
 272 
 273 #define zero            c[0]
 274 #define one             c[1]
 275 #define two             c[2]
 276 #define half            c[3]
 277 #define tiny            c[4]
 278 #define hln2pim1_h      c[5]
 279 #define hln2pim1_l      c[6]
 280 #define hln2pim1        c[7]
 281 #define ln2_32hi        c[8]
 282 #define ln2_32lo        c[9]
 283 #define invln2_32       c[10]
 284 #define overflow        c[11]
 285 
 286 /*
 287  * |exp(r) - (1+r+Et0*r^2+...+Et10*r^12)| <= 2^(-128.88) for |r|<=ln2/64
 288  */
 289 static const long double Et[] = {
 290         +5.0000000000000000000e-1L,
 291         +1.66666666666666666666666666666828835166292152466e-0001L,
 292         +4.16666666666666666666666666666693398646592712189e-0002L,
 293         +8.33333333333333333333331748774512601775591115951e-0003L,
 294         +1.38888888888888888888888845356011511394764753997e-0003L,
 295         +1.98412698412698413237140350092993252684198882102e-0004L,
 296         +2.48015873015873016080222025357442659895814371694e-0005L,
 297         +2.75573192239028921114572986441972140933432317798e-0006L,
 298         +2.75573192239448470555548102895526369739856219317e-0007L,
 299         +2.50521677867683935940853997995937600214167232477e-0008L,
 300         +2.08767928899010367374984448513685566514152147362e-0009L,
 301 };
 302 
 303 /*
 304  * long double precision coefficients for computing log(x)-1 in tgamma.
 305  *  See "algorithm" for details
 306  *
 307  *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
 308  *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
 309  *       T1(n) = T1[2n,2n+1] = n*log(2)-1,
 310  *       T2(j) = T2[2j,2j+1] = log(z[j]),
 311  *       T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + T3[2]s^7 + ... + T3[6]s^15
 312  *  Note
 313  *  (1) the leading entries are truncated to 24 binary point.
 314  *  (2) Remez error for T3(s) is bounded by 2**(-136.54)
 315  */
 316 static const long double T1[] = {
 317 -1.000000000000000000000000000000000000000000e+00L,
 318         +0.000000000000000000000000000000000000000000e+00L,
 319 -3.068528175354003906250000000000000000000000e-01L,
 320 -1.904654299957767878541823431924500011926579e-09L,
 321         +3.862943053245544433593750000000000000000000e-01L,
 322         +5.579533617547508924291635313615100141107647e-08L,
 323         +1.079441487789154052734375000000000000000000e+00L,
 324         +5.389068187551732136437452970422650211661470e-08L,
 325         +1.772588670253753662109375000000000000000000e+00L,
 326         +5.198602757555955348583270627230200282215294e-08L,
 327         +2.465735852718353271484375000000000000000000e+00L,
 328         +5.008137327560178560729088284037750352769117e-08L,
 329         +3.158883035182952880859375000000000000000000e+00L,
 330         +4.817671897564401772874905940845299849351090e-08L,
 331         +3.852030217647552490234375000000000000000000e+00L,
 332         +4.627206467568624985020723597652849919904913e-08L,
 333         +4.545177400112152099609375000000000000000000e+00L,
 334         +4.436741037572848197166541254460399990458737e-08L,
 335         +5.238324582576751708984375000000000000000000e+00L,
 336         +4.246275607577071409312358911267950061012560e-08L,
 337         +5.931471765041351318359375000000000000000000e+00L,
 338         +4.055810177581294621458176568075500131566384e-08L,
 339 };
 340 
 341 /*
 342  * T2[2i,2i+1] = log(1+i/64+1/128)
 343  */
 344 static const long double T2[] = {
 345         +7.7821016311645507812500000000000000000000e-03L,
 346         +3.8810890398166212900061136763678127453570e-08L,
 347         +2.3167014122009277343750000000000000000000e-02L,
 348         +4.5159525100885049160962289916579411752759e-08L,
 349         +3.8318812847137451171875000000000000000000e-02L,
 350         +5.1454999148021880325123797290345960518164e-08L,
 351         +5.3244471549987792968750000000000000000000e-02L,
 352         +4.2968824489897120193786528776939573415076e-08L,
 353         +6.7950606346130371093750000000000000000000e-02L,
 354         +5.5562377378300815277772629414034632394030e-08L,
 355         +8.2443654537200927734375000000000000000000e-02L,
 356         +1.4673873663533785068668307805914095366600e-08L,
 357         +9.6729576587677001953125000000000000000000e-02L,
 358         +4.9870874110342446056487463437015041543346e-08L,
 359         +1.1081433296203613281250000000000000000000e-01L,
 360         +3.3378253981382306169323211928098474801099e-08L,
 361         +1.2470346689224243164062500000000000000000e-01L,
 362         +1.1608714804222781515380863268491613205318e-08L,
 363         +1.3840228319168090820312500000000000000000e-01L,
 364         +3.9667438227482200873601649187393160823607e-08L,
 365         +1.5191602706909179687500000000000000000000e-01L,
 366         +1.4956750178196803424896884511327584958252e-08L,
 367         +1.6524952650070190429687500000000000000000e-01L,
 368         +4.6394605258578736449277240313729237989366e-08L,
 369         +1.7840760946273803710937500000000000000000e-01L,
 370         +4.8010080260010025241510941968354682199540e-08L,
 371         +1.9139480590820312500000000000000000000000e-01L,
 372         +4.7091426329609298807561308873447039132856e-08L,
 373         +2.0421552658081054687500000000000000000000e-01L,
 374         +1.4847880344628820386196239272213742113867e-08L,
 375         +2.1687388420104980468750000000000000000000e-01L,
 376         +5.4099564554931589525744347498478964801484e-08L,
 377         +2.2937405109405517578125000000000000000000e-01L,
 378         +4.9970790654210230725046139871550961365282e-08L,
 379         +2.4171990156173706054687500000000000000000e-01L,
 380         +3.5325408107597432515913513900103385655073e-08L,
 381         +2.5391519069671630859375000000000000000000e-01L,
 382         +1.9284247135543573297906606667466299224747e-08L,
 383         +2.6596349477767944335937500000000000000000e-01L,
 384         +5.3719458497979750926537543389268821141517e-08L,
 385         +2.7786844968795776367187500000000000000000e-01L,
 386         +1.3154985425144750329234012330820349974537e-09L,
 387         +2.8963327407836914062500000000000000000000e-01L,
 388         +1.8504673536253893055525668970003860369760e-08L,
 389         +3.0126130580902099609375000000000000000000e-01L,
 390         +2.4769140784919125538233755492657352680723e-08L,
 391         +3.1275570392608642578125000000000000000000e-01L,
 392         +6.0778104626049965596883190321597861455475e-09L,
 393         +3.2411944866180419921875000000000000000000e-01L,
 394         +1.9992407776871920760434987352182336158873e-08L,
 395         +3.3535552024841308593750000000000000000000e-01L,
 396         +2.1672724744319679579814166199074433006807e-08L,
 397         +3.4646672010421752929687500000000000000000e-01L,
 398         +4.7241991051621587188425772950711830538414e-08L,
 399         +3.5745584964752197265625000000000000000000e-01L,
 400         +3.9274281801569759490140904474434669956562e-08L,
 401         +3.6832553148269653320312500000000000000000e-01L,
 402         +2.9676011119845105154050398826897178765758e-08L,
 403         +3.7907832860946655273437500000000000000000e-01L,
 404         +2.4325502905656478345631019858881408009210e-08L,
 405         +3.8971674442291259765625000000000000000000e-01L,
 406         +6.7171126157142136040035208670510556529487e-09L,
 407         +4.0024316310882568359375000000000000000000e-01L,
 408         +1.0181870233355751019951311700799406124957e-09L,
 409         +4.1065990924835205078125000000000000000000e-01L,
 410         +1.5736916335153056203175822787661567534220e-08L,
 411         +4.2096924781799316406250000000000000000000e-01L,
 412         +4.6826136472066367161506795972449857268707e-08L,
 413         +4.3117344379425048828125000000000000000000e-01L,
 414         +2.1024120852577922478955594998480144051225e-08L,
 415         +4.4127452373504638671875000000000000000000e-01L,
 416         +3.7069828842770746441661301225362605528786e-08L,
 417         +4.5127463340759277343750000000000000000000e-01L,
 418         +1.0731865811707192383079012478685922879010e-08L,
 419         +4.6117568016052246093750000000000000000000e-01L,
 420         +3.4961647705430499925597855358603099030515e-08L,
 421         +4.7097969055175781250000000000000000000000e-01L,
 422         +2.4667033200046897856056359251373510964634e-08L,
 423         +4.8068851232528686523437500000000000000000e-01L,
 424         +1.7020465042442243455448011551208861216878e-08L,
 425         +4.9030393362045288085937500000000000000000e-01L,
 426         +5.4424740957290971159645746860530583309571e-08L,
 427         +4.9982786178588867187500000000000000000000e-01L,
 428         +7.7705606579463314152470441415126573566105e-09L,
 429         +5.0926184654235839843750000000000000000000e-01L,
 430         +5.5247449548366574919228323824878565745713e-08L,
 431         +5.1860773563385009765625000000000000000000e-01L,
 432         +2.8574195534496726996364798698556235730848e-08L,
 433         +5.2786707878112792968750000000000000000000e-01L,
 434         +1.0839714455426392217778300963558522088193e-08L,
 435         +5.3704142570495605468750000000000000000000e-01L,
 436         +4.0191927599879229244153832299023744345999e-08L,
 437         +5.4613238573074340820312500000000000000000e-01L,
 438         +5.1867392242179272209231209163864971792889e-08L,
 439         +5.5514144897460937500000000000000000000000e-01L,
 440         +5.8565892217715480359515904050170125743178e-08L,
 441         +5.6407010555267333984375000000000000000000e-01L,
 442         +3.2732129626227634290090190711817681692354e-08L,
 443         +5.7291972637176513671875000000000000000000e-01L,
 444         +2.7190020372374006726626261068626400393936e-08L,
 445         +5.8169168233871459960937500000000000000000e-01L,
 446         +5.7295907882911235753725372340709967597394e-08L,
 447         +5.9038740396499633789062500000000000000000e-01L,
 448         +4.2637180036751291708123598757577783615014e-08L,
 449         +5.9900814294815063476562500000000000000000e-01L,
 450         +4.6697932764615975024461651502060474048774e-08L,
 451         +6.0755521059036254882812500000000000000000e-01L,
 452         +3.9634179246672960152791125371893149820625e-08L,
 453         +6.1602985858917236328125000000000000000000e-01L,
 454         +1.8626341656366315928196700650292529688219e-08L,
 455         +6.2443327903747558593750000000000000000000e-01L,
 456         +8.9744179151050387440546731199093039879228e-09L,
 457         +6.3276666402816772460937500000000000000000e-01L,
 458         +5.5428701049364114685035797584887586099726e-09L,
 459         +6.4103114604949951171875000000000000000000e-01L,
 460         +3.3371431779336851334405392546708949047361e-08L,
 461         +6.4922791719436645507812500000000000000000e-01L,
 462         +2.9430743363812714969905311122271269100885e-08L,
 463         +6.5735805034637451171875000000000000000000e-01L,
 464         +2.2361985518423140023245936165514147093250e-08L,
 465         +6.6542261838912963867187500000000000000000e-01L,
 466         +1.4155960810278217610006660181148303091649e-08L,
 467         +6.7342263460159301757812500000000000000000e-01L,
 468         +4.0610573702719835388801017264750843477878e-08L,
 469         +6.8135917186737060546875000000000000000000e-01L,
 470         +5.2940532463479321559568089441735584156689e-08L,
 471         +6.8923324346542358398437500000000000000000e-01L,
 472         +3.7773385396340539337814603903232796216537e-08L,
 473 };
 474 
 475 /*
 476  * S[j],S_trail[j] = 2**(j/32.) for the final computation of exp(t+w)
 477  */
 478 static const long double S[] = {
 479 #if defined(__x86)
 480         +1.0000000000000000000000000e+00L,
 481         +1.0218971486541166782081522e+00L,
 482         +1.0442737824274138402382006e+00L,
 483         +1.0671404006768236181297224e+00L,
 484         +1.0905077326652576591003302e+00L,
 485         +1.1143867425958925362894369e+00L,
 486         +1.1387886347566916536971221e+00L,
 487         +1.1637248587775775137938619e+00L,
 488         +1.1892071150027210666875674e+00L,
 489         +1.2152473599804688780476325e+00L,
 490         +1.2418578120734840485256747e+00L,
 491         +1.2690509571917332224885722e+00L,
 492         +1.2968395546510096659215822e+00L,
 493         +1.3252366431597412945939118e+00L,
 494         +1.3542555469368927282668852e+00L,
 495         +1.3839098819638319548151403e+00L,
 496         +1.4142135623730950487637881e+00L,
 497         +1.4451808069770466200253470e+00L,
 498         +1.4768261459394993113155431e+00L,
 499         +1.5091644275934227397133885e+00L,
 500         +1.5422108254079408235859630e+00L,
 501         +1.5759808451078864864006862e+00L,
 502         +1.6104903319492543080837174e+00L,
 503         +1.6457554781539648445110730e+00L,
 504         +1.6817928305074290860378350e+00L,
 505         +1.7186192981224779156032914e+00L,
 506         +1.7562521603732994831094730e+00L,
 507         +1.7947090750031071864148413e+00L,
 508         +1.8340080864093424633989166e+00L,
 509         +1.8741676341102999013002103e+00L,
 510         +1.9152065613971472938202589e+00L,
 511         +1.9571441241754002689657438e+00L,
 512 #else
 513         +1.00000000000000000000000000000000000e+00L,
 514         +1.02189714865411667823448013478329942e+00L,
 515         +1.04427378242741384032196647873992910e+00L,
 516         +1.06714040067682361816952112099280918e+00L,
 517         +1.09050773266525765920701065576070789e+00L,
 518         +1.11438674259589253630881295691960313e+00L,
 519         +1.13878863475669165370383028384151134e+00L,
 520         +1.16372485877757751381357359909218536e+00L,
 521         +1.18920711500272106671749997056047593e+00L,
 522         +1.21524735998046887811652025133879836e+00L,
 523         +1.24185781207348404859367746872659561e+00L,
 524         +1.26905095719173322255441908103233805e+00L,
 525         +1.29683955465100966593375411779245118e+00L,
 526         +1.32523664315974129462953709549872168e+00L,
 527         +1.35425554693689272829801474014070273e+00L,
 528         +1.38390988196383195487265952726519287e+00L,
 529         +1.41421356237309504880168872420969798e+00L,
 530         +1.44518080697704662003700624147167095e+00L,
 531         +1.47682614593949931138690748037404985e+00L,
 532         +1.50916442759342273976601955103319352e+00L,
 533         +1.54221082540794082361229186209073479e+00L,
 534         +1.57598084510788648645527016018190504e+00L,
 535         +1.61049033194925430817952066735740067e+00L,
 536         +1.64575547815396484451875672472582254e+00L,
 537         +1.68179283050742908606225095246642969e+00L,
 538         +1.71861929812247791562934437645631244e+00L,
 539         +1.75625216037329948311216061937531314e+00L,
 540         +1.79470907500310718642770324212778174e+00L,
 541         +1.83400808640934246348708318958828892e+00L,
 542         +1.87416763411029990132999894995444645e+00L,
 543         +1.91520656139714729387261127029583086e+00L,
 544         +1.95714412417540026901832225162687149e+00L,
 545 #endif
 546 };
 547 static const long double S_trail[] = {
 548 #if defined(__x86)
 549         +0.0000000000000000000000000e+00L,
 550         +2.6327965667180882569382524e-20L,
 551         +8.3765863521895191129661899e-20L,
 552         +3.9798705777454504249209575e-20L,
 553         +1.0668046596651558640993042e-19L,
 554         +1.9376009847285360448117114e-20L,
 555         +6.7081819456112953751277576e-21L,
 556         +1.9711680502629186462729727e-20L,
 557         +2.9932584438449523689104569e-20L,
 558         +6.8887754153039109411061914e-20L,
 559         +6.8002718741225378942847820e-20L,
 560         +6.5846917376975403439742349e-20L,
 561         +1.2171958727511372194876001e-20L,
 562         +3.5625253228704087115438260e-20L,
 563         +3.1129551559077560956309179e-20L,
 564         +5.7519192396164779846216492e-20L,
 565         +3.7900651177865141593101239e-20L,
 566         +1.1659262405698741798080115e-20L,
 567         +7.1364385105284695967172478e-20L,
 568         +5.2631003710812203588788949e-20L,
 569         +2.6328853788732632868460580e-20L,
 570         +5.4583950085438242788190141e-20L,
 571         +9.5803254376938269960718656e-20L,
 572         +7.6837733983874245823512279e-21L,
 573         +2.4415965910835093824202087e-20L,
 574         +2.6052966871016580981769728e-20L,
 575         +2.6876456344632553875309579e-21L,
 576         +1.2861930155613700201703279e-20L,
 577         +8.8166633394037485606572294e-20L,
 578         +2.9788615389580190940837037e-20L,
 579         +5.2352341619805098677422139e-20L,
 580         +5.2578463064010463732242363e-20L,
 581 #else
 582         +0.00000000000000000000000000000000000e+00L,
 583         +1.80506787420330954745573333054573786e-35L,
 584 -9.37452029228042742195756741973083214e-35L,
 585 -1.59696844729275877071290963023149997e-35L,
 586         +9.11249341012502297851168610167248666e-35L,
 587 -6.50422820697854828723037477525938871e-35L,
 588 -8.14846884452585113732569176748815532e-35L,
 589 -5.06621457672180031337233074514290335e-35L,
 590 -1.35983097468881697374987563824591912e-35L,
 591         +9.49742763556319647030771056643324660e-35L,
 592 -3.28317052317699860161506596533391526e-36L,
 593 -5.01723570938719041029018653045842895e-35L,
 594 -2.39147479768910917162283430160264014e-35L,
 595 -8.35057135763390881529889073794408385e-36L,
 596         +7.03675688907326504242173719067187644e-35L,
 597 -5.18248485306464645753689301856695619e-35L,
 598         +9.42224254862183206569211673639406488e-35L,
 599 -3.96750082539886230916730613021641828e-35L,
 600         +7.14352899156330061452327361509276724e-35L,
 601         +1.15987125286798512424651783410044433e-35L,
 602         +4.69693347835811549530973921320187447e-35L,
 603 -3.38651317599500471079924198499981917e-35L,
 604 -8.58731877429824706886865593510387445e-35L,
 605 -9.60595154874935050318549936224606909e-35L,
 606         +9.60973393212801278450755869714178581e-35L,
 607         +6.37839792144002843924476144978084855e-35L,
 608         +7.79243078569586424945646112516927770e-35L,
 609         +7.36133776758845652413193083663393220e-35L,
 610 -6.47299514791334723003521457561217053e-35L,
 611         +8.58747441795369869427879806229522962e-35L,
 612         +2.37181542282517483569165122830269098e-35L,
 613 -3.02689168209611877300459737342190031e-37L,
 614 #endif
 615 };
 616 /* INDENT ON */
 617 
 618 /* INDENT OFF */
 619 /*
 620  * return tgamma(x) scaled by 2**-m for 8<x<=171.62... using Stirling's formula
 621  *     log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + (1/x)*P(1/(x*x))
 622  *                = L1 + L2 + L3,
 623  */
 624 /* INDENT ON */
 625 static struct LDouble
 626 large_gam(long double x, int *m) {
 627         long double z, t1, t2, t3, z2, t5, w, y, u, r, v;
 628         long double t24 = 16777216.0L, p24 = 1.0L / 16777216.0L;
 629         int n2, j2, k, ix, j, i;
 630         struct LDouble zz;
 631         long double u2, ss_h, ss_l, r_h, w_h, w_l, t4;
 632 
 633 /* INDENT OFF */
 634 /*
 635  * compute ss = ss.h+ss.l = log(x)-1 (see tgamma_log.h for details)
 636  *
 637  *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
 638  *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
 639  *       T1(n) = T1[2n,2n+1] = n*log(2)-1,
 640  *       T2(j) = T2[2j,2j+1] = log(z[j]),
 641  *       T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + ... + T3[6]s^15
 642  *  Note
 643  *  (1) the leading entries are truncated to 24 binary point.
 644  *  (2) Remez error for T3(s) is bounded by 2**(-72.4)
 645  *                                   2**(-24)
 646  *                           _________V___________________
 647  *               T1(n):     |_________|___________________|
 648  *                             _______ ______________________
 649  *               T2(j):       |_______|______________________|
 650  *                                ____ _______________________
 651  *               2s:             |____|_______________________|
 652  *                                    __________________________
 653  *          +    T3(s)-2s:           |__________________________|
 654  *                       -------------------------------------------
 655  *                          [leading] + [Trailing]
 656  */
 657         /* INDENT ON */
 658         ix = H0_WORD(x);
 659         n2 = (ix >> 16) - 0x3fff; /* exponent of x, range:3-10 */
 660         y = scalbnl(x, -n2);    /* y = scale x to [1,2] */
 661         n2 += n2;               /* 2n */
 662         j = (ix >> 10) & 0x3f;        /* j */
 663         z = 1.0078125L + (long double) j * 0.015625L;   /* z[j]=1+j/64+1/128 */
 664         j2 = j + j;
 665         t1 = y + z;
 666         t2 = y - z;
 667         r = one / t1;
 668         u = r * t2;             /* u = (y-z)/(y+z) */
 669         t1 = CHOPPED(t1);
 670         t4 = T2[j2 + 1] + T1[n2 + 1];
 671         z2 = u * u;
 672         k = H0_WORD(u) & 0x7fffffff;
 673         t3 = T2[j2] + T1[n2];
 674         for (t5 = T3[6], i = 5; i >= 0; i--)
 675                 t5 = z2 * t5 + T3[i];
 676         if ((k >> 16) < 0x3fec) {      /* |u|<2**-19 */
 677                 t2 = t4 + u * (two + z2 * t5);
 678         } else {
 679                 t5 = t4 + (u * z2) * t5;
 680                 u2 = u + u;
 681                 v = (long double) ((int) (u2 * t24)) * p24;
 682                 t2 = t5 + r * ((two * t2 - v * t1) - v * (y - (t1 - z)));
 683                 t3 += v;
 684         }
 685         ss_h = CHOPPED((t2 + t3));
 686         ss_l = t2 - (ss_h - t3);
 687 /* INDENT OFF */
 688 /*
 689  * compute ww = (x-.5)*(log(x)-1) + .5*(log(2pi)-1) + 1/x*(P(1/x^2)))
 690  * where ss = log(x) - 1 in already in extra precision
 691  */
 692         /* INDENT ON */
 693         z = one / x;
 694         r = x - half;
 695         r_h = CHOPPED((r));
 696         w_h = r_h * ss_h + hln2pim1_h;
 697         z2 = z * z;
 698         w = (r - r_h) * ss_h + r * ss_l;
 699         t1 = GP[19];
 700         for (i = 18; i > 0; i--)
 701                 t1 = z2 * t1 + GP[i];
 702         w += hln2pim1_l;
 703         w_l = z * (GP[0] + z2 * t1) + w;
 704         k = (int) ((w_h + w_l) * invln2_32 + half);
 705 
 706         /* compute the exponential of w_h+w_l */
 707 
 708         j = k & 0x1f;
 709         *m = k >> 5;
 710         t3 = (long double) k;
 711 
 712         /* perform w - k*ln2_32 (represent as w_h - w_l) */
 713         t1 = w_h - t3 * ln2_32hi;
 714         t2 = t3 * ln2_32lo;
 715         w = t2 - w_l;
 716         w_h = t1 - w;
 717         w_l = w - (t1 - w_h);
 718 
 719         /* compute exp(w_h-w_l) */
 720         z = w_h - w_l;
 721         for (t1 = Et[10], i = 9; i >= 0; i--)
 722                 t1 = z * t1 + Et[i];
 723         t3 = w_h - (w_l - (z * z) * t1);        /* t3 = expm1(z) */
 724         zz.l = S_trail[j] * (one + t3) + S[j] * t3;
 725         zz.h = S[j];
 726         return (zz);
 727 }
 728 
 729 /* INDENT OFF */
 730 /*
 731  * kpsin(x)= sin(pi*x)/pi
 732  *                 3        5        7        9        11                27
 733  *      = x+ks[0]*x +ks[1]*x +ks[2]*x +ks[3]*x +ks[4]*x  + ... + ks[12]*x
 734  */
 735 static const long double ks[] = {
 736         -1.64493406684822643647241516664602518705158902870e+0000L,
 737         +8.11742425283353643637002772405874238094995726160e-0001L,
 738         -1.90751824122084213696472111835337366232282723933e-0001L,
 739         +2.61478478176548005046532613563241288115395517084e-0002L,
 740         -2.34608103545582363750893072647117829448016479971e-0003L,
 741         +1.48428793031071003684606647212534027556262040158e-0004L,
 742         -6.97587366165638046518462722252768122615952898698e-0006L,
 743         +2.53121740413702536928659271747187500934840057929e-0007L,
 744         -7.30471182221385990397683641695766121301933621956e-0009L,
 745         +1.71653847451163495739958249695549313987973589884e-0010L,
 746         -3.34813314714560776122245796929054813458341420565e-0012L,
 747         +5.50724992262622033449487808306969135431411753047e-0014L,
 748         -7.67678132753577998601234393215802221104236979928e-0016L,
 749 };
 750 /* INDENT ON */
 751 
 752 /*
 753  * assume x is not tiny and positive
 754  */
 755 static struct LDouble
 756 kpsin(long double x) {
 757         long double z, t1, t2;
 758         struct LDouble xx;
 759         int i;
 760 
 761         z = x * x;
 762         xx.h = x;
 763         for (t2 = ks[12], i = 11; i > 0; i--)
 764                 t2 = z * t2 + ks[i];
 765         t1 = z * x;
 766         t2 *= z * t1;
 767         xx.l = t1 * ks[0] + t2;
 768         return (xx);
 769 }
 770 
 771 /* INDENT OFF */
 772 /*
 773  * kpcos(x)= cos(pi*x)/pi
 774  *                     2        4        6        8        10        12
 775  *      = 1/pi +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x +kc[4]*x  +kc[5]*x
 776  *
 777  *                     2        4        6        8        10            22
 778  *      = 1/pi - pi/2*x +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x  +...+kc[9]*x
 779  *
 780  * -pi/2*x*x = (npi_2_h + npi_2_l) * (x_f+x_l)*(x_f+x_l)
 781  *         =  npi_2_h*(x_f+x_l)*(x_f+x_l) + npi_2_l*x*x
 782  *         =  npi_2_h*x_f*x_f + npi_2_h*(x*x-x_f*x_f) + npi_2_l*x*x
 783  *         =  npi_2_h*x_f*x_f + npi_2_h*(x+x_f)*(x-x_f) + npi_2_l*x*x
 784  * Here x_f = (long double) (float)x
 785  * Note that pi/2(in hex) =
 786  *  1.921FB54442D18469898CC51701B839A252049C1114CF98E804177D4C76273644A29
 787  * npi_2_h = -pi/2 chopped to 25 bits = -1.921FB50000000000000000000000000 =
 788  *  -1.570796310901641845703125000000000 and
 789  * npi_2_l =
 790  *  -0.0000004442D18469898CC51701B839A252049C1114CF98E804177D4C76273644A29 =
 791  *  -.0000000158932547735281966916397514420985846996875529104874722961539 =
 792  *  -1.5893254773528196691639751442098584699687552910487472296153e-8
 793  * 1/pi(in hex) =
 794  *  .517CC1B727220A94FE13ABE8FA9A6EE06DB14ACC9E21C820FF28B1D5EF5DE2B
 795  * will be splitted into:
 796  *  one_pi_h = 1/pi chopped to 48 bits = .517CC1B727220000000000...  and
 797  *  one_pi_l = .0000000000000A94FE13ABE8FA9A6EE06DB14ACC9E21C820FF28B1D5EF5DE2B
 798  */
 799 
 800 static const long double
 801 #if defined(__x86)
 802 one_pi_h = 0.3183098861481994390487670898437500L,       /* 31 bits */
 803 one_pi_l = 3.559123248900043690127872406891929148e-11L,
 804 #else
 805 one_pi_h = 0.31830988618379052468299050815403461456298828125L,
 806 one_pi_l = 1.46854777018590994109505931010230912897495334688117e-16L,
 807 #endif
 808 npi_2_h = -1.570796310901641845703125000000000L,
 809 npi_2_l = -1.5893254773528196691639751442098584699687552910e-8L;
 810 
 811 static const long double kc[] = {
 812         +1.29192819501249250731151312779548918765320728489e+0000L,
 813         -4.25027339979557573976029596929319207009444090366e-0001L,
 814         +7.49080661650990096109672954618317623888421628613e-0002L,
 815         -8.21458866111282287985539464173976555436050215120e-0003L,
 816         +6.14202578809529228503205255165761204750211603402e-0004L,
 817         -3.33073432691149607007217330302595267179545908740e-0005L,
 818         +1.36970959047832085796809745461530865597993680204e-0006L,
 819         -4.41780774262583514450246512727201806217271097336e-0008L,
 820         +1.14741409212381858820016567664488123478660705759e-0009L,
 821         -2.44261236114707374558437500654381006300502749632e-0011L,
 822 };
 823 /* INDENT ON */
 824 
 825 /*
 826  * assume x is not tiny and positive
 827  */
 828 static struct LDouble
 829 kpcos(long double x) {
 830         long double z, t1, t2, t3, t4, x4, x8;
 831         int i;
 832         struct LDouble xx;
 833 
 834         z = x * x;
 835         xx.h = one_pi_h;
 836         t1 = (long double) ((float) x);
 837         x4 = z * z;
 838         t2 = npi_2_l * z + npi_2_h * (x + t1) * (x - t1);
 839         for (i = 8, t3 = kc[9]; i >= 0; i--)
 840                 t3 = z * t3 + kc[i];
 841         t3 = one_pi_l + x4 * t3;
 842         t4 = t1 * t1 * npi_2_h;
 843         x8 = t2 + t3;
 844         xx.l = x8 + t4;
 845         return (xx);
 846 }
 847 
 848 /* INDENT OFF */
 849 static const long double
 850         /* 0.13486180573279076968979393577465291700642511139552429398233 */
 851 #if defined(__x86)
 852 t0z1   =  0.1348618057327907696779385054997035808810L,
 853 t0z1_l =  1.1855430274949336125392717150257379614654e-20L,
 854 #else
 855 t0z1   =  0.1348618057327907696897939357746529168654L,
 856 t0z1_l =  1.4102088588676879418739164486159514674310e-37L,
 857 #endif
 858         /* 0.46163214496836234126265954232572132846819620400644635129599 */
 859 #if defined(__x86)
 860 t0z2   =  0.4616321449683623412538115843295472018326L,
 861 t0z2_l =  8.84795799617412663558532305039261747030640e-21L,
 862 #else
 863 t0z2   =  0.46163214496836234126265954232572132343318L,
 864 t0z2_l =  5.03501162329616380465302666480916271611101e-36L,
 865 #endif
 866         /* 0.81977310110050060178786870492160699631174407846245179119586 */
 867 #if defined(__x86)
 868 t0z3   =  0.81977310110050060178773362329351925836817L,
 869 t0z3_l =  1.350816280877379435658077052534574556256230e-22L
 870 #else
 871 t0z3   =  0.8197731011005006017878687049216069516957449L,
 872 t0z3_l =  4.461599916947014419045492615933551648857380e-35L
 873 #endif
 874 ;
 875 /* INDENT ON */
 876 
 877 /*
 878  * gamma(x+i) for 0 <= x < 1
 879  */
 880 static struct LDouble
 881 gam_n(int i, long double x) {
 882         struct LDouble rr = {0.0L, 0.0L}, yy;
 883         long double r1, r2, t2, z, xh, xl, yh, yl, zh, z1, z2, zl, x5, wh, wl;
 884 
 885         /* compute yy = gamma(x+1) */
 886         if (x > 0.2845L) {
 887                 if (x > 0.6374L) {
 888                         r1 = x - t0z3;
 889                         r2 = CHOPPED((r1 - t0z3_l));
 890                         t2 = r1 - r2;
 891                         yy = GT3(r2, t2 - t0z3_l);
 892                 } else {
 893                         r1 = x - t0z2;
 894                         r2 = CHOPPED((r1 - t0z2_l));
 895                         t2 = r1 - r2;
 896                         yy = GT2(r2, t2 - t0z2_l);
 897                 }
 898         } else {
 899                 r1 = x - t0z1;
 900                 r2 = CHOPPED((r1 - t0z1_l));
 901                 t2 = r1 - r2;
 902                 yy = GT1(r2, t2 - t0z1_l);
 903         }
 904         /* compute gamma(x+i) = (x+i-1)*...*(x+1)*yy, 0<i<8 */
 905         switch (i) {
 906         case 0:         /* yy/x */
 907                 r1 = one / x;
 908                 xh = CHOPPED((x));      /* x is not tiny */
 909                 rr.h = CHOPPED(((yy.h + yy.l) * r1));
 910                 rr.l = r1 * (yy.h - rr.h * xh) - ((r1 * rr.h) * (x - xh) -
 911                         r1 * yy.l);
 912                 break;
 913         case 1:         /* yy */
 914                 rr.h = yy.h;
 915                 rr.l = yy.l;
 916                 break;
 917         case 2:         /* (x+1)*yy */
 918                 z = x + one;    /* may not be exact */
 919                 zh = CHOPPED((z));
 920                 rr.h = zh * yy.h;
 921                 rr.l = z * yy.l + (x - (zh - one)) * yy.h;
 922                 break;
 923         case 3:         /* (x+2)*(x+1)*yy */
 924                 z1 = x + one;
 925                 z2 = x + 2.0L;
 926                 z = z1 * z2;
 927                 xh = CHOPPED((z));
 928                 zh = CHOPPED((z1));
 929                 xl = (x - (zh - one)) * (z2 + zh) - (xh - zh * (zh + one));
 930 
 931                 rr.h = xh * yy.h;
 932                 rr.l = z * yy.l + xl * yy.h;
 933                 break;
 934 
 935         case 4:         /* (x+1)*(x+3)*(x+2)*yy */
 936                 z1 = x + 2.0L;
 937                 z2 = (x + one) * (x + 3.0L);
 938                 zh = CHOPPED(z1);
 939                 zl = x - (zh - 2.0L);
 940                 xh = CHOPPED(z2);
 941                 xl = zl * (zh + z1) - (xh - (zh * zh - one));
 942 
 943                 /* wh+wl=(x+2)*yy */
 944                 wh = CHOPPED((z1 * (yy.h + yy.l)));
 945                 wl = (zl * yy.h + z1 * yy.l) - (wh - zh * yy.h);
 946 
 947                 rr.h = xh * wh;
 948                 rr.l = z2 * wl + xl * wh;
 949 
 950                 break;
 951         case 5:         /* ((x+1)*(x+4)*(x+2)*(x+3))*yy */
 952                 z1 = x + 2.0L;
 953                 z2 = x + 3.0L;
 954                 z = z1 * z2;
 955                 zh = CHOPPED((z1));
 956                 yh = CHOPPED((z));
 957                 yl = (x - (zh - 2.0L)) * (z2 + zh) - (yh - zh * (zh + one));
 958                 z2 = z - 2.0L;
 959                 z *= z2;
 960                 xh = CHOPPED((z));
 961                 xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
 962                 rr.h = xh * yy.h;
 963                 rr.l = z * yy.l + xl * yy.h;
 964                 break;
 965         case 6:         /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5))*yy */
 966                 z1 = x + 2.0L;
 967                 z2 = x + 3.0L;
 968                 z = z1 * z2;
 969                 zh = CHOPPED((z1));
 970                 yh = CHOPPED((z));
 971                 z1 = x - (zh - 2.0L);
 972                 yl = z1 * (z2 + zh) - (yh - zh * (zh + one));
 973                 z2 = z - 2.0L;
 974                 x5 = x + 5.0L;
 975                 z *= z2;
 976                 xh = CHOPPED(z);
 977                 zh += 3.0;
 978                 xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
 979                                                 /* xh+xl=(x+1)*...*(x+4) */
 980                 /* wh+wl=(x+5)*yy */
 981                 wh = CHOPPED((x5 * (yy.h + yy.l)));
 982                 wl = (z1 * yy.h + x5 * yy.l) - (wh - zh * yy.h);
 983                 rr.h = wh * xh;
 984                 rr.l = z * wl + xl * wh;
 985                 break;
 986         case 7:         /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5)*(x+6))*yy */
 987                 z1 = x + 3.0L;
 988                 z2 = x + 4.0L;
 989                 z = z2 * z1;
 990                 zh = CHOPPED((z1));
 991                 yh = CHOPPED((z));      /* yh+yl = (x+3)(x+4) */
 992                 yl = (x - (zh - 3.0L)) * (z2 + zh) - (yh - (zh * (zh + one)));
 993                 z1 = x + 6.0L;
 994                 z2 = z - 2.0L;  /* z2 = (x+2)*(x+5) */
 995                 z *= z2;
 996                 xh = CHOPPED((z));
 997                 xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
 998                                                 /* xh+xl=(x+2)*...*(x+5) */
 999                 /* wh+wl=(x+1)(x+6)*yy */
1000                 z2 -= 4.0L;     /* z2 = (x+1)(x+6) */
1001                 wh = CHOPPED((z2 * (yy.h + yy.l)));
1002                 wl = (z2 * yy.l + yl * yy.h) - (wh - (yh - 6.0L) * yy.h);
1003                 rr.h = wh * xh;
1004                 rr.l = z * wl + xl * wh;
1005         }
1006         return (rr);
1007 }
1008 
1009 long double
1010 tgammal(long double x) {
1011         struct LDouble ss, ww;
1012         long double t, t1, t2, t3, t4, t5, w, y, z, z1, z2, z3, z5;
1013         int i, j, m, ix, hx, xk;
1014         unsigned lx;
1015 
1016         hx = H0_WORD(x);
1017         lx = H3_WORD(x);
1018         ix = hx & 0x7fffffff;
1019         y = x;
1020         if (ix < 0x3f8e0000) {       /* x < 2**-113 */
1021                 return (one / x);
1022         }
1023         if (ix >= 0x7fff0000)
1024                 return (x * ((hx < 0)? zero : x));   /* Inf or NaN */
1025         if (x > overflow)    /* overflow threshold */
1026                 return (x * 1.0e4932L);
1027         if (hx >= 0x40020000) {      /* x >= 8 */
1028                 ww = large_gam(x, &m);
1029                 w = ww.h + ww.l;
1030                 return (scalbnl(w, m));
1031         }
1032 
1033         if (hx > 0) {                /* 0 < x < 8 */
1034                 i = (int) x;
1035                 ww = gam_n(i, x - (long double) i);
1036                 return (ww.h + ww.l);
1037         }
1038         /* INDENT OFF */
1039         /* negative x */
1040         /*
1041          * compute xk =
1042          *      -2 ... x is an even int (-inf is considered an even #)
1043          *      -1 ... x is an odd int
1044          *      +0 ... x is not an int but chopped to an even int
1045          *      +1 ... x is not an int but chopped to an odd int
1046          */
1047         /* INDENT ON */
1048         xk = 0;
1049 #if defined(__x86)
1050         if (ix >= 0x403e0000) {      /* x >= 2**63 } */
1051                 if (ix >= 0x403f0000)
1052                         xk = -2;
1053                 else
1054                         xk = -2 + (lx & 1);
1055 #else
1056         if (ix >= 0x406f0000) {      /* x >= 2**112 */
1057                 if (ix >= 0x40700000)
1058                         xk = -2;
1059                 else
1060                         xk = -2 + (lx & 1);
1061 #endif
1062         } else if (ix >= 0x3fff0000) {
1063                 w = -x;
1064                 t1 = floorl(w);
1065                 t2 = t1 * half;
1066                 t3 = floorl(t2);
1067                 if (t1 == w) {
1068                         if (t2 == t3)
1069                                 xk = -2;
1070                         else
1071                                 xk = -1;
1072                 } else {
1073                         if (t2 == t3)
1074                                 xk = 0;
1075                         else
1076                                 xk = 1;
1077                 }
1078         }
1079 
1080         if (xk < 0) {
1081                 /* return NaN. Ideally gamma(-n)= (-1)**(n+1) * inf */
1082                 return (x - x) / (x - x);
1083         }
1084 
1085         /*
1086          * negative underflow thresold -(1774+9ulp)
1087          */
1088         if (x < -1774.0000000000000000000000000000017749370L) {
1089                 z = tiny / x;
1090                 if (xk == 1)
1091                         z = -z;
1092                 return (z * tiny);
1093         }
1094 
1095         /* INDENT OFF */
1096         /*
1097          * now compute gamma(x) by  -1/((sin(pi*y)/pi)*gamma(1+y)), y = -x
1098          */
1099         /*
1100          * First compute ss = -sin(pi*y)/pi so that
1101          * gamma(x) = 1/(ss*gamma(1+y))
1102          */
1103         /* INDENT ON */
1104         y = -x;
1105         j = (int) y;
1106         z = y - (long double) j;
1107         if (z > 0.3183098861837906715377675L)
1108                 if (z > 0.6816901138162093284622325L)
1109                         ss = kpsin(one - z);
1110                 else
1111                         ss = kpcos(0.5L - z);
1112         else
1113                 ss = kpsin(z);
1114         if (xk == 0) {
1115                 ss.h = -ss.h;
1116                 ss.l = -ss.l;
1117         }
1118 
1119         /* Then compute ww = gamma(1+y), note that result scale to 2**m */
1120         m = 0;
1121         if (j < 7) {
1122                 ww = gam_n(j + 1, z);
1123         } else {
1124                 w = y + one;
1125                 if ((lx & 1) == 0) {        /* y+1 exact (note that y<184) */
1126                         ww = large_gam(w, &m);
1127                 } else {
1128                         t = w - one;
1129                         if (t == y) {   /* y+one exact */
1130                                 ww = large_gam(w, &m);
1131                         } else {        /* use y*gamma(y) */
1132                                 if (j == 7)
1133                                         ww = gam_n(j, z);
1134                                 else
1135                                         ww = large_gam(y, &m);
1136                                 t4 = ww.h + ww.l;
1137                                 t1 = CHOPPED((y));
1138                                 t2 = CHOPPED((t4));
1139                                                 /* t4 will not be too large */
1140                                 ww.l = y * (ww.l - (t2 - ww.h)) + (y - t1) * t2;
1141                                 ww.h = t1 * t2;
1142                         }
1143                 }
1144         }
1145 
1146         /* compute 1/(ss*ww) */
1147         t3 = ss.h + ss.l;
1148         t4 = ww.h + ww.l;
1149         t1 = CHOPPED((t3));
1150         t2 = CHOPPED((t4));
1151         z1 = ss.l - (t1 - ss.h);        /* (t1,z1) = ss */
1152         z2 = ww.l - (t2 - ww.h);        /* (t2,z2) = ww */
1153         t3 = t3 * t4;                   /* t3 = ss*ww */
1154         z3 = one / t3;                  /* z3 = 1/(ss*ww) */
1155         t5 = t1 * t2;
1156         z5 = z1 * t4 + t1 * z2;         /* (t5,z5) = ss*ww */
1157         t1 = CHOPPED((t3));             /* (t1,z1) = ss*ww */
1158         z1 = z5 - (t1 - t5);
1159         t2 = CHOPPED((z3));             /* leading 1/(ss*ww) */
1160         z2 = z3 * (t2 * z1 - (one - t2 * t1));
1161         z = t2 - z2;
1162 
1163         return (scalbnl(z, -m));
1164 }