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 #if defined(ELFOBJ)
  31 #pragma weak tgammal = __tgammal
  32 #endif
  33 
  34 #include "libm.h"
  35 #include <sys/isa_defs.h>
  36 
  37 #if defined(_BIG_ENDIAN)
  38 #define H0_WORD(x)      ((unsigned *) &x)[0]
  39 #define H3_WORD(x)      ((unsigned *) &x)[3]
  40 #define CHOPPED(x)      (long double) ((double) (x))
  41 #else
  42 #define H0_WORD(x)      ((((int *) &x)[2] << 16) | \
  43                         (0x0000ffff & (((unsigned *) &x)[1] >> 15)))
  44 #define H3_WORD(x)      ((unsigned *) &x)[0]
  45 #define CHOPPED(x)      (long double) ((float) (x))
  46 #endif
  47 
  48 struct LDouble {
  49         long double h, l;
  50 };
  51 
  52 /* INDENT OFF */
  53 /* Primary interval GTi() */
  54 static const long double P1[] = {
  55         +0.709086836199777919037185741507610124611513720557L,
  56         +4.45754781206489035827915969367354835667391606951e-0001L,
  57         +3.21049298735832382311662273882632210062918153852e-0002L,
  58         -5.71296796342106617651765245858289197369688864350e-0003L,
  59         +6.04666892891998977081619174969855831606965352773e-0003L,
  60         +8.99106186996888711939627812174765258822658645168e-0004L,
  61         -6.96496846144407741431207008527018441810175568949e-0005L,
  62         +1.52597046118984020814225409300131445070213882429e-0005L,
  63         +5.68521076168495673844711465407432189190681541547e-0007L,
  64         +3.30749673519634895220582062520286565610418952979e-0008L,
  65 };
  66 static const long double Q1[] = {
  67         +1.0+0000L,
  68         +1.35806511721671070408570853537257079579490650668e+0000L,
  69         +2.97567810153429553405327140096063086994072952961e-0001L,
  70         -1.52956835982588571502954372821681851681118097870e-0001L,
  71         -2.88248519561420109768781615289082053597954521218e-0002L,
  72         +1.03475311719937405219789948456313936302378395955e-0002L,
  73         +4.12310203243891222368965360124391297374822742313e-0004L,
  74         -3.12653708152290867248931925120380729518332507388e-0004L,
  75         +2.36672170850409745237358105667757760527014332458e-0005L,
  76 };
  77 static const long double P2[] = {
  78         +0.428486815855585429730209907810650135255270600668084114L,
  79         +2.62768479103809762805691743305424077975230551176e-0001L,
  80         +3.81187532685392297608310837995193946591425896150e-0002L,
  81         +3.00063075891811043820666846129131255948527925381e-0003L,
  82         +2.47315407812279164228398470797498649142513408654e-0003L,
  83         +3.62838199917848372586173483147214880464782938664e-0004L,
  84         +3.43991105975492623982725644046473030098172692423e-0006L,
  85         +4.56902151569603272237014240794257659159045432895e-0006L,
  86         +2.13734755837595695602045100675540011352948958453e-0007L,
  87         +9.74123440547918230781670266967882492234877125358e-0009L,
  88 };
  89 static const long double Q2[] = {
  90         +1.0L,
  91         +9.18284118632506842664645516830761489700556179701e-0001L,
  92         -6.41430858837830766045202076965923776189154874947e-0003L,
  93         -1.24400885809771073213345747437964149775410921376e-0001L,
  94         +4.69803798146251757538856567522481979624746875964e-0003L,
  95         +7.18309447069495315914284705109868696262662082731e-0003L,
  96         -8.75812626987894695112722600697653425786166399105e-0004L,
  97         -1.23539972377769277995959339188431498626674835169e-0004L,
  98         +3.10019017590151598732360097849672925448587547746e-0005L,
  99         -1.77260223349332617658921874288026777465782364070e-0006L,
 100 };
 101 static const long double P3[] = {
 102         +0.3824094797345675048502747661075355640070439388902L,
 103         +3.42198093076618495415854906335908427159833377774e-0001L,
 104         +9.63828189500585568303961406863153237440702754858e-0002L,
 105         +8.76069421042696384852462044188520252156846768667e-0003L,
 106         +1.86477890389161491224872014149309015261897537488e-0003L,
 107         +8.16871354540309895879974742853701311541286944191e-0004L,
 108         +6.83783483674600322518695090864659381650125625216e-0005L,
 109         -1.10168269719261574708565935172719209272190828456e-0006L,
 110         +9.66243228508380420159234853278906717065629721016e-0007L,
 111         +2.31858885579177250541163820671121664974334728142e-0008L,
 112 };
 113 static const long double Q3[] = {
 114         +1.0L,
 115         +8.25479821168813634632437430090376252512793067339e-0001L,
 116         -1.62251363073937769739639623669295110346015576320e-0002L,
 117         -1.10621286905916732758745130629426559691187579852e-0001L,
 118         +3.48309693970985612644446415789230015515365291459e-0003L,
 119         +6.73553737487488333032431261131289672347043401328e-0003L,
 120         -7.63222008393372630162743587811004613050245128051e-0004L,
 121         -1.35792670669190631476784768961953711773073251336e-0004L,
 122         +3.19610150954223587006220730065608156460205690618e-0005L,
 123         -1.82096553862822346610109522015129585693354348322e-0006L,
 124 };
 125 
 126 static const long double
 127 #if defined(__x86)
 128 GZ1_h   =  0.938204627909682449364570100414084663498215377L,
 129 GZ1_l   =  4.518346116624229420055327632718530617227944106e-20L,
 130 GZ2_h   =  0.885603194410888700264725126309883762587560340L,
 131 GZ2_l   =  1.409077427270497062039119290776508217077297169e-20L,
 132 GZ3_h   =  0.936781411463652321613537060640553022494714241L,
 133 GZ3_l   =  5.309836440284827247897772963887219035221996813e-21L,
 134 #else
 135 GZ1_h   =  0.938204627909682449409753561580326910854647031L,
 136 GZ1_l   =  4.684412162199460089642452580902345976446297037e-35L,
 137 GZ2_h   =  0.885603194410888700278815900582588658192658794L,
 138 GZ2_l   =  7.501529273890253789219935569758713534641074860e-35L,
 139 GZ3_h   =  0.936781411463652321618846897080837818855399840L,
 140 GZ3_l   =  3.088721217404784363585591914529361687403776917e-35L,
 141 #endif
 142 TZ1     = -0.3517214357852935791015625L,
 143 TZ3     =  0.280530631542205810546875L;
 144 /* INDENT ON */
 145 
 146 /* INDENT OFF */
 147 /*
 148  * compute gamma(y=yh+yl) for y in GT1 = [1.0000, 1.2845]
 149  * ...assume yh got 53 or 24(i386) significant bits
 150  */
 151 /* INDENT ON */
 152 static struct LDouble
 153 GT1(long double yh, long double yl) {
 154         long double t3, t4, y;
 155         int i;
 156         struct LDouble r;
 157 
 158         y = yh + yl;
 159         for (t4 = Q1[8], t3 = P1[8] + y * P1[9], i = 7; i >= 0; i--) {
 160                 t4 = t4 * y + Q1[i];
 161                 t3 = t3 * y + P1[i];
 162         }
 163         t3 = (y * y) * t3 / t4;
 164         t3 += (TZ1 * yl + GZ1_l);
 165         t4 = TZ1 * yh;
 166         r.h = CHOPPED((t4 + GZ1_h + t3));
 167         t3 += (t4 - (r.h - GZ1_h));
 168         r.l = t3;
 169         return (r);
 170 }
 171 
 172 /* INDENT OFF */
 173 /*
 174  * compute gamma(y=yh+yl) for y in GT2 = [1.2844, 1.6374]
 175  * ...assume yh got 53 significant bits
 176  */
 177 /* INDENT ON */
 178 static struct LDouble
 179 GT2(long double yh, long double yl) {
 180         long double t3, t4, y;
 181         int i;
 182         struct LDouble r;
 183 
 184         y = yh + yl;
 185         for (t4 = Q2[9], t3 = P2[9], i = 8; i >= 0; i--) {
 186                 t4 = t4 * y + Q2[i];
 187                 t3 = t3 * y + P2[i];
 188         }
 189         t3 = GZ2_l + (y * y) * t3 / t4;
 190         r.h = CHOPPED((GZ2_h + t3));
 191         r.l = t3 - (r.h - GZ2_h);
 192         return (r);
 193 }
 194 
 195 /* INDENT OFF */
 196 /*
 197  * compute gamma(y=yh+yl) for y in GT3 = [1.6373, 2.0000]
 198  * ...assume yh got 53 significant bits
 199  */
 200 /* INDENT ON */
 201 static struct LDouble
 202 GT3(long double yh, long double yl) {
 203         long double t3, t4, y;
 204         int i;
 205         struct LDouble r;
 206 
 207         y = yh + yl;
 208         for (t4 = Q3[9], t3 = P3[9], i = 8; i >= 0; i--) {
 209                 t4 = t4 * y + Q3[i];
 210                 t3 = t3 * y + P3[i];
 211         }
 212         t3 = (y * y) * t3 / t4;
 213         t3 += (TZ3 * yl + GZ3_l);
 214         t4 = TZ3 * yh;
 215         r.h = CHOPPED((t4 + GZ3_h + t3));
 216         t3 += (t4 - (r.h - GZ3_h));
 217         r.l = t3;
 218         return (r);
 219 }
 220 
 221 /* INDENT OFF */
 222 /* Hex value of GP[0] shoule be 3FB55555 55555555 */
 223 static const long double GP[] = {
 224         +0.083333333333333333333333333333333172839171301L,
 225         -2.77777777777777777777777777492501211999399424104e-0003L,
 226         +7.93650793650793650793635650541638236350020883243e-0004L,
 227         -5.95238095238095238057299772679324503339241961704e-0004L,
 228         +8.41750841750841696138422987977683524926142600321e-0004L,
 229         -1.91752691752686682825032547823699662178842123308e-0003L,
 230         +6.41025641022403480921891559356473451161279359322e-0003L,
 231         -2.95506535798414019189819587455577003732808185071e-0002L,
 232         +1.79644367229970031486079180060923073476568732136e-0001L,
 233         -1.39243086487274662174562872567057200255649290646e+0000L,
 234         +1.34025874044417962188677816477842265259608269775e+0001L,
 235         -1.56803713480127469414495545399982508700748274318e+0002L,
 236         +2.18739841656201561694927630335099313968924493891e+0003L,
 237         -3.55249848644100338419187038090925410976237921269e+0004L,
 238         +6.43464880437835286216768959439484376449179576452e+0005L,
 239         -1.20459154385577014992600342782821389605893904624e+0007L,
 240         +2.09263249637351298563934942349749718491071093210e+0008L,
 241         -2.96247483183169219343745316433899599834685703457e+0009L,
 242         +2.88984933605896033154727626086506756972327292981e+0010L,
 243         -1.40960434146030007732838382416230610302678063984e+0011L,      /* 19 */
 244 };
 245 
 246 static const long double T3[] = {
 247         +0.666666666666666666666666666666666634567834260213L,   /* T3[0] */
 248         +0.400000000000000000000000000040853636176634934140L,   /* T3[1] */
 249         +0.285714285714285714285696975252753987869020263448L,   /* T3[2] */
 250         +0.222222222222222225593221101192317258554772129875L,   /* T3[3] */
 251         +0.181818181817850192105847183461778186703779262916L,   /* T3[4] */
 252         +0.153846169861348633757101285952333369222567014596L,   /* T3[5] */
 253         +0.133033462889260193922261296772841229985047571265L,   /* T3[6] */
 254 };
 255 
 256 static const long double c[] = {
 257 0.0L,
 258 1.0L,
 259 2.0L,
 260 0.5L,
 261 1.0e-4930L,                                                     /* tiny */
 262 4.18937683105468750000e-01L,                                    /* hln2pim1_h */
 263 8.50099203991780329736405617639861397473637783412817152e-07L,   /* hln2pim1_l */
 264 0.418938533204672741780329736405617639861397473637783412817152L, /* hln2pim1 */
 265 2.16608493865351192653179168701171875e-02L,                     /* ln2_32hi */
 266 5.96317165397058692545083025235937919875797669127130e-12L,      /* ln2_32lo */
 267 46.16624130844682903551758979206054839765267053289554989233L,   /* invln2_32 */
 268 #if defined(__x86)
 269 1.7555483429044629170023839037639845628291e+03L,                /* overflow */
 270 #else
 271 1.7555483429044629170038892160702032034177e+03L,                /* overflow */
 272 #endif
 273 };
 274 
 275 #define zero            c[0]
 276 #define one             c[1]
 277 #define two             c[2]
 278 #define half            c[3]
 279 #define tiny            c[4]
 280 #define hln2pim1_h      c[5]
 281 #define hln2pim1_l      c[6]
 282 #define hln2pim1        c[7]
 283 #define ln2_32hi        c[8]
 284 #define ln2_32lo        c[9]
 285 #define invln2_32       c[10]
 286 #define overflow        c[11]
 287 
 288 /*
 289  * |exp(r) - (1+r+Et0*r^2+...+Et10*r^12)| <= 2^(-128.88) for |r|<=ln2/64
 290  */
 291 static const long double Et[] = {
 292         +5.0000000000000000000e-1L,
 293         +1.66666666666666666666666666666828835166292152466e-0001L,
 294         +4.16666666666666666666666666666693398646592712189e-0002L,
 295         +8.33333333333333333333331748774512601775591115951e-0003L,
 296         +1.38888888888888888888888845356011511394764753997e-0003L,
 297         +1.98412698412698413237140350092993252684198882102e-0004L,
 298         +2.48015873015873016080222025357442659895814371694e-0005L,
 299         +2.75573192239028921114572986441972140933432317798e-0006L,
 300         +2.75573192239448470555548102895526369739856219317e-0007L,
 301         +2.50521677867683935940853997995937600214167232477e-0008L,
 302         +2.08767928899010367374984448513685566514152147362e-0009L,
 303 };
 304 
 305 /*
 306  * long double precision coefficients for computing log(x)-1 in tgamma.
 307  *  See "algorithm" for details
 308  *
 309  *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
 310  *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
 311  *       T1(n) = T1[2n,2n+1] = n*log(2)-1,
 312  *       T2(j) = T2[2j,2j+1] = log(z[j]),
 313  *       T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + T3[2]s^7 + ... + T3[6]s^15
 314  *  Note
 315  *  (1) the leading entries are truncated to 24 binary point.
 316  *  (2) Remez error for T3(s) is bounded by 2**(-136.54)
 317  */
 318 static const long double T1[] = {
 319 -1.000000000000000000000000000000000000000000e+00L,
 320         +0.000000000000000000000000000000000000000000e+00L,
 321 -3.068528175354003906250000000000000000000000e-01L,
 322 -1.904654299957767878541823431924500011926579e-09L,
 323         +3.862943053245544433593750000000000000000000e-01L,
 324         +5.579533617547508924291635313615100141107647e-08L,
 325         +1.079441487789154052734375000000000000000000e+00L,
 326         +5.389068187551732136437452970422650211661470e-08L,
 327         +1.772588670253753662109375000000000000000000e+00L,
 328         +5.198602757555955348583270627230200282215294e-08L,
 329         +2.465735852718353271484375000000000000000000e+00L,
 330         +5.008137327560178560729088284037750352769117e-08L,
 331         +3.158883035182952880859375000000000000000000e+00L,
 332         +4.817671897564401772874905940845299849351090e-08L,
 333         +3.852030217647552490234375000000000000000000e+00L,
 334         +4.627206467568624985020723597652849919904913e-08L,
 335         +4.545177400112152099609375000000000000000000e+00L,
 336         +4.436741037572848197166541254460399990458737e-08L,
 337         +5.238324582576751708984375000000000000000000e+00L,
 338         +4.246275607577071409312358911267950061012560e-08L,
 339         +5.931471765041351318359375000000000000000000e+00L,
 340         +4.055810177581294621458176568075500131566384e-08L,
 341 };
 342 
 343 /*
 344  * T2[2i,2i+1] = log(1+i/64+1/128)
 345  */
 346 static const long double T2[] = {
 347         +7.7821016311645507812500000000000000000000e-03L,
 348         +3.8810890398166212900061136763678127453570e-08L,
 349         +2.3167014122009277343750000000000000000000e-02L,
 350         +4.5159525100885049160962289916579411752759e-08L,
 351         +3.8318812847137451171875000000000000000000e-02L,
 352         +5.1454999148021880325123797290345960518164e-08L,
 353         +5.3244471549987792968750000000000000000000e-02L,
 354         +4.2968824489897120193786528776939573415076e-08L,
 355         +6.7950606346130371093750000000000000000000e-02L,
 356         +5.5562377378300815277772629414034632394030e-08L,
 357         +8.2443654537200927734375000000000000000000e-02L,
 358         +1.4673873663533785068668307805914095366600e-08L,
 359         +9.6729576587677001953125000000000000000000e-02L,
 360         +4.9870874110342446056487463437015041543346e-08L,
 361         +1.1081433296203613281250000000000000000000e-01L,
 362         +3.3378253981382306169323211928098474801099e-08L,
 363         +1.2470346689224243164062500000000000000000e-01L,
 364         +1.1608714804222781515380863268491613205318e-08L,
 365         +1.3840228319168090820312500000000000000000e-01L,
 366         +3.9667438227482200873601649187393160823607e-08L,
 367         +1.5191602706909179687500000000000000000000e-01L,
 368         +1.4956750178196803424896884511327584958252e-08L,
 369         +1.6524952650070190429687500000000000000000e-01L,
 370         +4.6394605258578736449277240313729237989366e-08L,
 371         +1.7840760946273803710937500000000000000000e-01L,
 372         +4.8010080260010025241510941968354682199540e-08L,
 373         +1.9139480590820312500000000000000000000000e-01L,
 374         +4.7091426329609298807561308873447039132856e-08L,
 375         +2.0421552658081054687500000000000000000000e-01L,
 376         +1.4847880344628820386196239272213742113867e-08L,
 377         +2.1687388420104980468750000000000000000000e-01L,
 378         +5.4099564554931589525744347498478964801484e-08L,
 379         +2.2937405109405517578125000000000000000000e-01L,
 380         +4.9970790654210230725046139871550961365282e-08L,
 381         +2.4171990156173706054687500000000000000000e-01L,
 382         +3.5325408107597432515913513900103385655073e-08L,
 383         +2.5391519069671630859375000000000000000000e-01L,
 384         +1.9284247135543573297906606667466299224747e-08L,
 385         +2.6596349477767944335937500000000000000000e-01L,
 386         +5.3719458497979750926537543389268821141517e-08L,
 387         +2.7786844968795776367187500000000000000000e-01L,
 388         +1.3154985425144750329234012330820349974537e-09L,
 389         +2.8963327407836914062500000000000000000000e-01L,
 390         +1.8504673536253893055525668970003860369760e-08L,
 391         +3.0126130580902099609375000000000000000000e-01L,
 392         +2.4769140784919125538233755492657352680723e-08L,
 393         +3.1275570392608642578125000000000000000000e-01L,
 394         +6.0778104626049965596883190321597861455475e-09L,
 395         +3.2411944866180419921875000000000000000000e-01L,
 396         +1.9992407776871920760434987352182336158873e-08L,
 397         +3.3535552024841308593750000000000000000000e-01L,
 398         +2.1672724744319679579814166199074433006807e-08L,
 399         +3.4646672010421752929687500000000000000000e-01L,
 400         +4.7241991051621587188425772950711830538414e-08L,
 401         +3.5745584964752197265625000000000000000000e-01L,
 402         +3.9274281801569759490140904474434669956562e-08L,
 403         +3.6832553148269653320312500000000000000000e-01L,
 404         +2.9676011119845105154050398826897178765758e-08L,
 405         +3.7907832860946655273437500000000000000000e-01L,
 406         +2.4325502905656478345631019858881408009210e-08L,
 407         +3.8971674442291259765625000000000000000000e-01L,
 408         +6.7171126157142136040035208670510556529487e-09L,
 409         +4.0024316310882568359375000000000000000000e-01L,
 410         +1.0181870233355751019951311700799406124957e-09L,
 411         +4.1065990924835205078125000000000000000000e-01L,
 412         +1.5736916335153056203175822787661567534220e-08L,
 413         +4.2096924781799316406250000000000000000000e-01L,
 414         +4.6826136472066367161506795972449857268707e-08L,
 415         +4.3117344379425048828125000000000000000000e-01L,
 416         +2.1024120852577922478955594998480144051225e-08L,
 417         +4.4127452373504638671875000000000000000000e-01L,
 418         +3.7069828842770746441661301225362605528786e-08L,
 419         +4.5127463340759277343750000000000000000000e-01L,
 420         +1.0731865811707192383079012478685922879010e-08L,
 421         +4.6117568016052246093750000000000000000000e-01L,
 422         +3.4961647705430499925597855358603099030515e-08L,
 423         +4.7097969055175781250000000000000000000000e-01L,
 424         +2.4667033200046897856056359251373510964634e-08L,
 425         +4.8068851232528686523437500000000000000000e-01L,
 426         +1.7020465042442243455448011551208861216878e-08L,
 427         +4.9030393362045288085937500000000000000000e-01L,
 428         +5.4424740957290971159645746860530583309571e-08L,
 429         +4.9982786178588867187500000000000000000000e-01L,
 430         +7.7705606579463314152470441415126573566105e-09L,
 431         +5.0926184654235839843750000000000000000000e-01L,
 432         +5.5247449548366574919228323824878565745713e-08L,
 433         +5.1860773563385009765625000000000000000000e-01L,
 434         +2.8574195534496726996364798698556235730848e-08L,
 435         +5.2786707878112792968750000000000000000000e-01L,
 436         +1.0839714455426392217778300963558522088193e-08L,
 437         +5.3704142570495605468750000000000000000000e-01L,
 438         +4.0191927599879229244153832299023744345999e-08L,
 439         +5.4613238573074340820312500000000000000000e-01L,
 440         +5.1867392242179272209231209163864971792889e-08L,
 441         +5.5514144897460937500000000000000000000000e-01L,
 442         +5.8565892217715480359515904050170125743178e-08L,
 443         +5.6407010555267333984375000000000000000000e-01L,
 444         +3.2732129626227634290090190711817681692354e-08L,
 445         +5.7291972637176513671875000000000000000000e-01L,
 446         +2.7190020372374006726626261068626400393936e-08L,
 447         +5.8169168233871459960937500000000000000000e-01L,
 448         +5.7295907882911235753725372340709967597394e-08L,
 449         +5.9038740396499633789062500000000000000000e-01L,
 450         +4.2637180036751291708123598757577783615014e-08L,
 451         +5.9900814294815063476562500000000000000000e-01L,
 452         +4.6697932764615975024461651502060474048774e-08L,
 453         +6.0755521059036254882812500000000000000000e-01L,
 454         +3.9634179246672960152791125371893149820625e-08L,
 455         +6.1602985858917236328125000000000000000000e-01L,
 456         +1.8626341656366315928196700650292529688219e-08L,
 457         +6.2443327903747558593750000000000000000000e-01L,
 458         +8.9744179151050387440546731199093039879228e-09L,
 459         +6.3276666402816772460937500000000000000000e-01L,
 460         +5.5428701049364114685035797584887586099726e-09L,
 461         +6.4103114604949951171875000000000000000000e-01L,
 462         +3.3371431779336851334405392546708949047361e-08L,
 463         +6.4922791719436645507812500000000000000000e-01L,
 464         +2.9430743363812714969905311122271269100885e-08L,
 465         +6.5735805034637451171875000000000000000000e-01L,
 466         +2.2361985518423140023245936165514147093250e-08L,
 467         +6.6542261838912963867187500000000000000000e-01L,
 468         +1.4155960810278217610006660181148303091649e-08L,
 469         +6.7342263460159301757812500000000000000000e-01L,
 470         +4.0610573702719835388801017264750843477878e-08L,
 471         +6.8135917186737060546875000000000000000000e-01L,
 472         +5.2940532463479321559568089441735584156689e-08L,
 473         +6.8923324346542358398437500000000000000000e-01L,
 474         +3.7773385396340539337814603903232796216537e-08L,
 475 };
 476 
 477 /*
 478  * S[j],S_trail[j] = 2**(j/32.) for the final computation of exp(t+w)
 479  */
 480 static const long double S[] = {
 481 #if defined(__x86)
 482         +1.0000000000000000000000000e+00L,
 483         +1.0218971486541166782081522e+00L,
 484         +1.0442737824274138402382006e+00L,
 485         +1.0671404006768236181297224e+00L,
 486         +1.0905077326652576591003302e+00L,
 487         +1.1143867425958925362894369e+00L,
 488         +1.1387886347566916536971221e+00L,
 489         +1.1637248587775775137938619e+00L,
 490         +1.1892071150027210666875674e+00L,
 491         +1.2152473599804688780476325e+00L,
 492         +1.2418578120734840485256747e+00L,
 493         +1.2690509571917332224885722e+00L,
 494         +1.2968395546510096659215822e+00L,
 495         +1.3252366431597412945939118e+00L,
 496         +1.3542555469368927282668852e+00L,
 497         +1.3839098819638319548151403e+00L,
 498         +1.4142135623730950487637881e+00L,
 499         +1.4451808069770466200253470e+00L,
 500         +1.4768261459394993113155431e+00L,
 501         +1.5091644275934227397133885e+00L,
 502         +1.5422108254079408235859630e+00L,
 503         +1.5759808451078864864006862e+00L,
 504         +1.6104903319492543080837174e+00L,
 505         +1.6457554781539648445110730e+00L,
 506         +1.6817928305074290860378350e+00L,
 507         +1.7186192981224779156032914e+00L,
 508         +1.7562521603732994831094730e+00L,
 509         +1.7947090750031071864148413e+00L,
 510         +1.8340080864093424633989166e+00L,
 511         +1.8741676341102999013002103e+00L,
 512         +1.9152065613971472938202589e+00L,
 513         +1.9571441241754002689657438e+00L,
 514 #else
 515         +1.00000000000000000000000000000000000e+00L,
 516         +1.02189714865411667823448013478329942e+00L,
 517         +1.04427378242741384032196647873992910e+00L,
 518         +1.06714040067682361816952112099280918e+00L,
 519         +1.09050773266525765920701065576070789e+00L,
 520         +1.11438674259589253630881295691960313e+00L,
 521         +1.13878863475669165370383028384151134e+00L,
 522         +1.16372485877757751381357359909218536e+00L,
 523         +1.18920711500272106671749997056047593e+00L,
 524         +1.21524735998046887811652025133879836e+00L,
 525         +1.24185781207348404859367746872659561e+00L,
 526         +1.26905095719173322255441908103233805e+00L,
 527         +1.29683955465100966593375411779245118e+00L,
 528         +1.32523664315974129462953709549872168e+00L,
 529         +1.35425554693689272829801474014070273e+00L,
 530         +1.38390988196383195487265952726519287e+00L,
 531         +1.41421356237309504880168872420969798e+00L,
 532         +1.44518080697704662003700624147167095e+00L,
 533         +1.47682614593949931138690748037404985e+00L,
 534         +1.50916442759342273976601955103319352e+00L,
 535         +1.54221082540794082361229186209073479e+00L,
 536         +1.57598084510788648645527016018190504e+00L,
 537         +1.61049033194925430817952066735740067e+00L,
 538         +1.64575547815396484451875672472582254e+00L,
 539         +1.68179283050742908606225095246642969e+00L,
 540         +1.71861929812247791562934437645631244e+00L,
 541         +1.75625216037329948311216061937531314e+00L,
 542         +1.79470907500310718642770324212778174e+00L,
 543         +1.83400808640934246348708318958828892e+00L,
 544         +1.87416763411029990132999894995444645e+00L,
 545         +1.91520656139714729387261127029583086e+00L,
 546         +1.95714412417540026901832225162687149e+00L,
 547 #endif
 548 };
 549 static const long double S_trail[] = {
 550 #if defined(__x86)
 551         +0.0000000000000000000000000e+00L,
 552         +2.6327965667180882569382524e-20L,
 553         +8.3765863521895191129661899e-20L,
 554         +3.9798705777454504249209575e-20L,
 555         +1.0668046596651558640993042e-19L,
 556         +1.9376009847285360448117114e-20L,
 557         +6.7081819456112953751277576e-21L,
 558         +1.9711680502629186462729727e-20L,
 559         +2.9932584438449523689104569e-20L,
 560         +6.8887754153039109411061914e-20L,
 561         +6.8002718741225378942847820e-20L,
 562         +6.5846917376975403439742349e-20L,
 563         +1.2171958727511372194876001e-20L,
 564         +3.5625253228704087115438260e-20L,
 565         +3.1129551559077560956309179e-20L,
 566         +5.7519192396164779846216492e-20L,
 567         +3.7900651177865141593101239e-20L,
 568         +1.1659262405698741798080115e-20L,
 569         +7.1364385105284695967172478e-20L,
 570         +5.2631003710812203588788949e-20L,
 571         +2.6328853788732632868460580e-20L,
 572         +5.4583950085438242788190141e-20L,
 573         +9.5803254376938269960718656e-20L,
 574         +7.6837733983874245823512279e-21L,
 575         +2.4415965910835093824202087e-20L,
 576         +2.6052966871016580981769728e-20L,
 577         +2.6876456344632553875309579e-21L,
 578         +1.2861930155613700201703279e-20L,
 579         +8.8166633394037485606572294e-20L,
 580         +2.9788615389580190940837037e-20L,
 581         +5.2352341619805098677422139e-20L,
 582         +5.2578463064010463732242363e-20L,
 583 #else
 584         +0.00000000000000000000000000000000000e+00L,
 585         +1.80506787420330954745573333054573786e-35L,
 586 -9.37452029228042742195756741973083214e-35L,
 587 -1.59696844729275877071290963023149997e-35L,
 588         +9.11249341012502297851168610167248666e-35L,
 589 -6.50422820697854828723037477525938871e-35L,
 590 -8.14846884452585113732569176748815532e-35L,
 591 -5.06621457672180031337233074514290335e-35L,
 592 -1.35983097468881697374987563824591912e-35L,
 593         +9.49742763556319647030771056643324660e-35L,
 594 -3.28317052317699860161506596533391526e-36L,
 595 -5.01723570938719041029018653045842895e-35L,
 596 -2.39147479768910917162283430160264014e-35L,
 597 -8.35057135763390881529889073794408385e-36L,
 598         +7.03675688907326504242173719067187644e-35L,
 599 -5.18248485306464645753689301856695619e-35L,
 600         +9.42224254862183206569211673639406488e-35L,
 601 -3.96750082539886230916730613021641828e-35L,
 602         +7.14352899156330061452327361509276724e-35L,
 603         +1.15987125286798512424651783410044433e-35L,
 604         +4.69693347835811549530973921320187447e-35L,
 605 -3.38651317599500471079924198499981917e-35L,
 606 -8.58731877429824706886865593510387445e-35L,
 607 -9.60595154874935050318549936224606909e-35L,
 608         +9.60973393212801278450755869714178581e-35L,
 609         +6.37839792144002843924476144978084855e-35L,
 610         +7.79243078569586424945646112516927770e-35L,
 611         +7.36133776758845652413193083663393220e-35L,
 612 -6.47299514791334723003521457561217053e-35L,
 613         +8.58747441795369869427879806229522962e-35L,
 614         +2.37181542282517483569165122830269098e-35L,
 615 -3.02689168209611877300459737342190031e-37L,
 616 #endif
 617 };
 618 /* INDENT ON */
 619 
 620 /* INDENT OFF */
 621 /*
 622  * return tgamma(x) scaled by 2**-m for 8<x<=171.62... using Stirling's formula
 623  *     log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + (1/x)*P(1/(x*x))
 624  *                = L1 + L2 + L3,
 625  */
 626 /* INDENT ON */
 627 static struct LDouble
 628 large_gam(long double x, int *m) {
 629         long double z, t1, t2, t3, z2, t5, w, y, u, r, v;
 630         long double t24 = 16777216.0L, p24 = 1.0L / 16777216.0L;
 631         int n2, j2, k, ix, j, i;
 632         struct LDouble zz;
 633         long double u2, ss_h, ss_l, r_h, w_h, w_l, t4;
 634 
 635 /* INDENT OFF */
 636 /*
 637  * compute ss = ss.h+ss.l = log(x)-1 (see tgamma_log.h for details)
 638  *
 639  *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
 640  *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
 641  *       T1(n) = T1[2n,2n+1] = n*log(2)-1,
 642  *       T2(j) = T2[2j,2j+1] = log(z[j]),
 643  *       T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + ... + T3[6]s^15
 644  *  Note
 645  *  (1) the leading entries are truncated to 24 binary point.
 646  *  (2) Remez error for T3(s) is bounded by 2**(-72.4)
 647  *                                   2**(-24)
 648  *                           _________V___________________
 649  *               T1(n):     |_________|___________________|
 650  *                             _______ ______________________
 651  *               T2(j):       |_______|______________________|
 652  *                                ____ _______________________
 653  *               2s:             |____|_______________________|
 654  *                                    __________________________
 655  *          +    T3(s)-2s:           |__________________________|
 656  *                       -------------------------------------------
 657  *                          [leading] + [Trailing]
 658  */
 659         /* INDENT ON */
 660         ix = H0_WORD(x);
 661         n2 = (ix >> 16) - 0x3fff; /* exponent of x, range:3-10 */
 662         y = scalbnl(x, -n2);    /* y = scale x to [1,2] */
 663         n2 += n2;               /* 2n */
 664         j = (ix >> 10) & 0x3f;        /* j */
 665         z = 1.0078125L + (long double) j * 0.015625L;   /* z[j]=1+j/64+1/128 */
 666         j2 = j + j;
 667         t1 = y + z;
 668         t2 = y - z;
 669         r = one / t1;
 670         u = r * t2;             /* u = (y-z)/(y+z) */
 671         t1 = CHOPPED(t1);
 672         t4 = T2[j2 + 1] + T1[n2 + 1];
 673         z2 = u * u;
 674         k = H0_WORD(u) & 0x7fffffff;
 675         t3 = T2[j2] + T1[n2];
 676         for (t5 = T3[6], i = 5; i >= 0; i--)
 677                 t5 = z2 * t5 + T3[i];
 678         if ((k >> 16) < 0x3fec) {      /* |u|<2**-19 */
 679                 t2 = t4 + u * (two + z2 * t5);
 680         } else {
 681                 t5 = t4 + (u * z2) * t5;
 682                 u2 = u + u;
 683                 v = (long double) ((int) (u2 * t24)) * p24;
 684                 t2 = t5 + r * ((two * t2 - v * t1) - v * (y - (t1 - z)));
 685                 t3 += v;
 686         }
 687         ss_h = CHOPPED((t2 + t3));
 688         ss_l = t2 - (ss_h - t3);
 689 /* INDENT OFF */
 690 /*
 691  * compute ww = (x-.5)*(log(x)-1) + .5*(log(2pi)-1) + 1/x*(P(1/x^2)))
 692  * where ss = log(x) - 1 in already in extra precision
 693  */
 694         /* INDENT ON */
 695         z = one / x;
 696         r = x - half;
 697         r_h = CHOPPED((r));
 698         w_h = r_h * ss_h + hln2pim1_h;
 699         z2 = z * z;
 700         w = (r - r_h) * ss_h + r * ss_l;
 701         t1 = GP[19];
 702         for (i = 18; i > 0; i--)
 703                 t1 = z2 * t1 + GP[i];
 704         w += hln2pim1_l;
 705         w_l = z * (GP[0] + z2 * t1) + w;
 706         k = (int) ((w_h + w_l) * invln2_32 + half);
 707 
 708         /* compute the exponential of w_h+w_l */
 709 
 710         j = k & 0x1f;
 711         *m = k >> 5;
 712         t3 = (long double) k;
 713 
 714         /* perform w - k*ln2_32 (represent as w_h - w_l) */
 715         t1 = w_h - t3 * ln2_32hi;
 716         t2 = t3 * ln2_32lo;
 717         w = t2 - w_l;
 718         w_h = t1 - w;
 719         w_l = w - (t1 - w_h);
 720 
 721         /* compute exp(w_h-w_l) */
 722         z = w_h - w_l;
 723         for (t1 = Et[10], i = 9; i >= 0; i--)
 724                 t1 = z * t1 + Et[i];
 725         t3 = w_h - (w_l - (z * z) * t1);        /* t3 = expm1(z) */
 726         zz.l = S_trail[j] * (one + t3) + S[j] * t3;
 727         zz.h = S[j];
 728         return (zz);
 729 }
 730 
 731 /* INDENT OFF */
 732 /*
 733  * kpsin(x)= sin(pi*x)/pi
 734  *                 3        5        7        9        11                27
 735  *      = x+ks[0]*x +ks[1]*x +ks[2]*x +ks[3]*x +ks[4]*x  + ... + ks[12]*x
 736  */
 737 static const long double ks[] = {
 738         -1.64493406684822643647241516664602518705158902870e+0000L,
 739         +8.11742425283353643637002772405874238094995726160e-0001L,
 740         -1.90751824122084213696472111835337366232282723933e-0001L,
 741         +2.61478478176548005046532613563241288115395517084e-0002L,
 742         -2.34608103545582363750893072647117829448016479971e-0003L,
 743         +1.48428793031071003684606647212534027556262040158e-0004L,
 744         -6.97587366165638046518462722252768122615952898698e-0006L,
 745         +2.53121740413702536928659271747187500934840057929e-0007L,
 746         -7.30471182221385990397683641695766121301933621956e-0009L,
 747         +1.71653847451163495739958249695549313987973589884e-0010L,
 748         -3.34813314714560776122245796929054813458341420565e-0012L,
 749         +5.50724992262622033449487808306969135431411753047e-0014L,
 750         -7.67678132753577998601234393215802221104236979928e-0016L,
 751 };
 752 /* INDENT ON */
 753 
 754 /*
 755  * assume x is not tiny and positive
 756  */
 757 static struct LDouble
 758 kpsin(long double x) {
 759         long double z, t1, t2;
 760         struct LDouble xx;
 761         int i;
 762 
 763         z = x * x;
 764         xx.h = x;
 765         for (t2 = ks[12], i = 11; i > 0; i--)
 766                 t2 = z * t2 + ks[i];
 767         t1 = z * x;
 768         t2 *= z * t1;
 769         xx.l = t1 * ks[0] + t2;
 770         return (xx);
 771 }
 772 
 773 /* INDENT OFF */
 774 /*
 775  * kpcos(x)= cos(pi*x)/pi
 776  *                     2        4        6        8        10        12
 777  *      = 1/pi +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x +kc[4]*x  +kc[5]*x
 778  *
 779  *                     2        4        6        8        10            22
 780  *      = 1/pi - pi/2*x +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x  +...+kc[9]*x
 781  *
 782  * -pi/2*x*x = (npi_2_h + npi_2_l) * (x_f+x_l)*(x_f+x_l)
 783  *         =  npi_2_h*(x_f+x_l)*(x_f+x_l) + npi_2_l*x*x
 784  *         =  npi_2_h*x_f*x_f + npi_2_h*(x*x-x_f*x_f) + npi_2_l*x*x
 785  *         =  npi_2_h*x_f*x_f + npi_2_h*(x+x_f)*(x-x_f) + npi_2_l*x*x
 786  * Here x_f = (long double) (float)x
 787  * Note that pi/2(in hex) =
 788  *  1.921FB54442D18469898CC51701B839A252049C1114CF98E804177D4C76273644A29
 789  * npi_2_h = -pi/2 chopped to 25 bits = -1.921FB50000000000000000000000000 =
 790  *  -1.570796310901641845703125000000000 and
 791  * npi_2_l =
 792  *  -0.0000004442D18469898CC51701B839A252049C1114CF98E804177D4C76273644A29 =
 793  *  -.0000000158932547735281966916397514420985846996875529104874722961539 =
 794  *  -1.5893254773528196691639751442098584699687552910487472296153e-8
 795  * 1/pi(in hex) =
 796  *  .517CC1B727220A94FE13ABE8FA9A6EE06DB14ACC9E21C820FF28B1D5EF5DE2B
 797  * will be splitted into:
 798  *  one_pi_h = 1/pi chopped to 48 bits = .517CC1B727220000000000...  and
 799  *  one_pi_l = .0000000000000A94FE13ABE8FA9A6EE06DB14ACC9E21C820FF28B1D5EF5DE2B
 800  */
 801 
 802 static const long double
 803 #if defined(__x86)
 804 one_pi_h = 0.3183098861481994390487670898437500L,       /* 31 bits */
 805 one_pi_l = 3.559123248900043690127872406891929148e-11L,
 806 #else
 807 one_pi_h = 0.31830988618379052468299050815403461456298828125L,
 808 one_pi_l = 1.46854777018590994109505931010230912897495334688117e-16L,
 809 #endif
 810 npi_2_h = -1.570796310901641845703125000000000L,
 811 npi_2_l = -1.5893254773528196691639751442098584699687552910e-8L;
 812 
 813 static const long double kc[] = {
 814         +1.29192819501249250731151312779548918765320728489e+0000L,
 815         -4.25027339979557573976029596929319207009444090366e-0001L,
 816         +7.49080661650990096109672954618317623888421628613e-0002L,
 817         -8.21458866111282287985539464173976555436050215120e-0003L,
 818         +6.14202578809529228503205255165761204750211603402e-0004L,
 819         -3.33073432691149607007217330302595267179545908740e-0005L,
 820         +1.36970959047832085796809745461530865597993680204e-0006L,
 821         -4.41780774262583514450246512727201806217271097336e-0008L,
 822         +1.14741409212381858820016567664488123478660705759e-0009L,
 823         -2.44261236114707374558437500654381006300502749632e-0011L,
 824 };
 825 /* INDENT ON */
 826 
 827 /*
 828  * assume x is not tiny and positive
 829  */
 830 static struct LDouble
 831 kpcos(long double x) {
 832         long double z, t1, t2, t3, t4, x4, x8;
 833         int i;
 834         struct LDouble xx;
 835 
 836         z = x * x;
 837         xx.h = one_pi_h;
 838         t1 = (long double) ((float) x);
 839         x4 = z * z;
 840         t2 = npi_2_l * z + npi_2_h * (x + t1) * (x - t1);
 841         for (i = 8, t3 = kc[9]; i >= 0; i--)
 842                 t3 = z * t3 + kc[i];
 843         t3 = one_pi_l + x4 * t3;
 844         t4 = t1 * t1 * npi_2_h;
 845         x8 = t2 + t3;
 846         xx.l = x8 + t4;
 847         return (xx);
 848 }
 849 
 850 /* INDENT OFF */
 851 static const long double
 852         /* 0.13486180573279076968979393577465291700642511139552429398233 */
 853 #if defined(__x86)
 854 t0z1   =  0.1348618057327907696779385054997035808810L,
 855 t0z1_l =  1.1855430274949336125392717150257379614654e-20L,
 856 #else
 857 t0z1   =  0.1348618057327907696897939357746529168654L,
 858 t0z1_l =  1.4102088588676879418739164486159514674310e-37L,
 859 #endif
 860         /* 0.46163214496836234126265954232572132846819620400644635129599 */
 861 #if defined(__x86)
 862 t0z2   =  0.4616321449683623412538115843295472018326L,
 863 t0z2_l =  8.84795799617412663558532305039261747030640e-21L,
 864 #else
 865 t0z2   =  0.46163214496836234126265954232572132343318L,
 866 t0z2_l =  5.03501162329616380465302666480916271611101e-36L,
 867 #endif
 868         /* 0.81977310110050060178786870492160699631174407846245179119586 */
 869 #if defined(__x86)
 870 t0z3   =  0.81977310110050060178773362329351925836817L,
 871 t0z3_l =  1.350816280877379435658077052534574556256230e-22L
 872 #else
 873 t0z3   =  0.8197731011005006017878687049216069516957449L,
 874 t0z3_l =  4.461599916947014419045492615933551648857380e-35L
 875 #endif
 876 ;
 877 /* INDENT ON */
 878 
 879 /*
 880  * gamma(x+i) for 0 <= x < 1
 881  */
 882 static struct LDouble
 883 gam_n(int i, long double x) {
 884         struct LDouble rr, yy;
 885         long double r1, r2, t2, z, xh, xl, yh, yl, zh, z1, z2, zl, x5, wh, wl;
 886 
 887         /* compute yy = gamma(x+1) */
 888         if (x > 0.2845L) {
 889                 if (x > 0.6374L) {
 890                         r1 = x - t0z3;
 891                         r2 = CHOPPED((r1 - t0z3_l));
 892                         t2 = r1 - r2;
 893                         yy = GT3(r2, t2 - t0z3_l);
 894                 } else {
 895                         r1 = x - t0z2;
 896                         r2 = CHOPPED((r1 - t0z2_l));
 897                         t2 = r1 - r2;
 898                         yy = GT2(r2, t2 - t0z2_l);
 899                 }
 900         } else {
 901                 r1 = x - t0z1;
 902                 r2 = CHOPPED((r1 - t0z1_l));
 903                 t2 = r1 - r2;
 904                 yy = GT1(r2, t2 - t0z1_l);
 905         }
 906         /* compute gamma(x+i) = (x+i-1)*...*(x+1)*yy, 0<i<8 */
 907         switch (i) {
 908         case 0:         /* yy/x */
 909                 r1 = one / x;
 910                 xh = CHOPPED((x));      /* x is not tiny */
 911                 rr.h = CHOPPED(((yy.h + yy.l) * r1));
 912                 rr.l = r1 * (yy.h - rr.h * xh) - ((r1 * rr.h) * (x - xh) -
 913                         r1 * yy.l);
 914                 break;
 915         case 1:         /* yy */
 916                 rr.h = yy.h;
 917                 rr.l = yy.l;
 918                 break;
 919         case 2:         /* (x+1)*yy */
 920                 z = x + one;    /* may not be exact */
 921                 zh = CHOPPED((z));
 922                 rr.h = zh * yy.h;
 923                 rr.l = z * yy.l + (x - (zh - one)) * yy.h;
 924                 break;
 925         case 3:         /* (x+2)*(x+1)*yy */
 926                 z1 = x + one;
 927                 z2 = x + 2.0L;
 928                 z = z1 * z2;
 929                 xh = CHOPPED((z));
 930                 zh = CHOPPED((z1));
 931                 xl = (x - (zh - one)) * (z2 + zh) - (xh - zh * (zh + one));
 932 
 933                 rr.h = xh * yy.h;
 934                 rr.l = z * yy.l + xl * yy.h;
 935                 break;
 936 
 937         case 4:         /* (x+1)*(x+3)*(x+2)*yy */
 938                 z1 = x + 2.0L;
 939                 z2 = (x + one) * (x + 3.0L);
 940                 zh = CHOPPED(z1);
 941                 zl = x - (zh - 2.0L);
 942                 xh = CHOPPED(z2);
 943                 xl = zl * (zh + z1) - (xh - (zh * zh - one));
 944 
 945                 /* wh+wl=(x+2)*yy */
 946                 wh = CHOPPED((z1 * (yy.h + yy.l)));
 947                 wl = (zl * yy.h + z1 * yy.l) - (wh - zh * yy.h);
 948 
 949                 rr.h = xh * wh;
 950                 rr.l = z2 * wl + xl * wh;
 951 
 952                 break;
 953         case 5:         /* ((x+1)*(x+4)*(x+2)*(x+3))*yy */
 954                 z1 = x + 2.0L;
 955                 z2 = x + 3.0L;
 956                 z = z1 * z2;
 957                 zh = CHOPPED((z1));
 958                 yh = CHOPPED((z));
 959                 yl = (x - (zh - 2.0L)) * (z2 + zh) - (yh - zh * (zh + one));
 960                 z2 = z - 2.0L;
 961                 z *= z2;
 962                 xh = CHOPPED((z));
 963                 xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
 964                 rr.h = xh * yy.h;
 965                 rr.l = z * yy.l + xl * yy.h;
 966                 break;
 967         case 6:         /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5))*yy */
 968                 z1 = x + 2.0L;
 969                 z2 = x + 3.0L;
 970                 z = z1 * z2;
 971                 zh = CHOPPED((z1));
 972                 yh = CHOPPED((z));
 973                 z1 = x - (zh - 2.0L);
 974                 yl = z1 * (z2 + zh) - (yh - zh * (zh + one));
 975                 z2 = z - 2.0L;
 976                 x5 = x + 5.0L;
 977                 z *= z2;
 978                 xh = CHOPPED(z);
 979                 zh += 3.0;
 980                 xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
 981                                                 /* xh+xl=(x+1)*...*(x+4) */
 982                 /* wh+wl=(x+5)*yy */
 983                 wh = CHOPPED((x5 * (yy.h + yy.l)));
 984                 wl = (z1 * yy.h + x5 * yy.l) - (wh - zh * yy.h);
 985                 rr.h = wh * xh;
 986                 rr.l = z * wl + xl * wh;
 987                 break;
 988         case 7:         /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5)*(x+6))*yy */
 989                 z1 = x + 3.0L;
 990                 z2 = x + 4.0L;
 991                 z = z2 * z1;
 992                 zh = CHOPPED((z1));
 993                 yh = CHOPPED((z));      /* yh+yl = (x+3)(x+4) */
 994                 yl = (x - (zh - 3.0L)) * (z2 + zh) - (yh - (zh * (zh + one)));
 995                 z1 = x + 6.0L;
 996                 z2 = z - 2.0L;  /* z2 = (x+2)*(x+5) */
 997                 z *= z2;
 998                 xh = CHOPPED((z));
 999                 xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
1000                                                 /* xh+xl=(x+2)*...*(x+5) */
1001                 /* wh+wl=(x+1)(x+6)*yy */
1002                 z2 -= 4.0L;     /* z2 = (x+1)(x+6) */
1003                 wh = CHOPPED((z2 * (yy.h + yy.l)));
1004                 wl = (z2 * yy.l + yl * yy.h) - (wh - (yh - 6.0L) * yy.h);
1005                 rr.h = wh * xh;
1006                 rr.l = z * wl + xl * wh;
1007         }
1008         return (rr);
1009 }
1010 
1011 long double
1012 tgammal(long double x) {
1013         struct LDouble ss, ww;
1014         long double t, t1, t2, t3, t4, t5, w, y, z, z1, z2, z3, z5;
1015         int i, j, m, ix, hx, xk;
1016         unsigned lx;
1017 
1018         hx = H0_WORD(x);
1019         lx = H3_WORD(x);
1020         ix = hx & 0x7fffffff;
1021         y = x;
1022         if (ix < 0x3f8e0000) {       /* x < 2**-113 */
1023                 return (one / x);
1024         }
1025         if (ix >= 0x7fff0000)
1026                 return (x * ((hx < 0)? zero : x));   /* Inf or NaN */
1027         if (x > overflow)    /* overflow threshold */
1028                 return (x * 1.0e4932L);
1029         if (hx >= 0x40020000) {      /* x >= 8 */
1030                 ww = large_gam(x, &m);
1031                 w = ww.h + ww.l;
1032                 return (scalbnl(w, m));
1033         }
1034 
1035         if (hx > 0) {                /* x from 0 to 8 */
1036                 i = (int) x;
1037                 ww = gam_n(i, x - (long double) i);
1038                 return (ww.h + ww.l);
1039         }
1040         /* INDENT OFF */
1041         /* negative x */
1042         /*
1043          * compute xk =
1044          *      -2 ... x is an even int (-inf is considered an even #)
1045          *      -1 ... x is an odd int
1046          *      +0 ... x is not an int but chopped to an even int
1047          *      +1 ... x is not an int but chopped to an odd int
1048          */
1049         /* INDENT ON */
1050         xk = 0;
1051 #if defined(__x86)
1052         if (ix >= 0x403e0000) {      /* x >= 2**63 } */
1053                 if (ix >= 0x403f0000)
1054                         xk = -2;
1055                 else
1056                         xk = -2 + (lx & 1);
1057 #else
1058         if (ix >= 0x406f0000) {      /* x >= 2**112 */
1059                 if (ix >= 0x40700000)
1060                         xk = -2;
1061                 else
1062                         xk = -2 + (lx & 1);
1063 #endif
1064         } else if (ix >= 0x3fff0000) {
1065                 w = -x;
1066                 t1 = floorl(w);
1067                 t2 = t1 * half;
1068                 t3 = floorl(t2);
1069                 if (t1 == w) {
1070                         if (t2 == t3)
1071                                 xk = -2;
1072                         else
1073                                 xk = -1;
1074                 } else {
1075                         if (t2 == t3)
1076                                 xk = 0;
1077                         else
1078                                 xk = 1;
1079                 }
1080         }
1081 
1082         if (xk < 0) {
1083                 /* return NaN. Ideally gamma(-n)= (-1)**(n+1) * inf */
1084                 return (x - x) / (x - x);
1085         }
1086 
1087         /*
1088          * negative underflow thresold -(1774+9ulp)
1089          */
1090         if (x < -1774.0000000000000000000000000000017749370L) {
1091                 z = tiny / x;
1092                 if (xk == 1)
1093                         z = -z;
1094                 return (z * tiny);
1095         }
1096 
1097         /* INDENT OFF */
1098         /*
1099          * now compute gamma(x) by  -1/((sin(pi*y)/pi)*gamma(1+y)), y = -x
1100          */
1101         /*
1102          * First compute ss = -sin(pi*y)/pi so that
1103          * gamma(x) = 1/(ss*gamma(1+y))
1104          */
1105         /* INDENT ON */
1106         y = -x;
1107         j = (int) y;
1108         z = y - (long double) j;
1109         if (z > 0.3183098861837906715377675L)
1110                 if (z > 0.6816901138162093284622325L)
1111                         ss = kpsin(one - z);
1112                 else
1113                         ss = kpcos(0.5L - z);
1114         else
1115                 ss = kpsin(z);
1116         if (xk == 0) {
1117                 ss.h = -ss.h;
1118                 ss.l = -ss.l;
1119         }
1120 
1121         /* Then compute ww = gamma(1+y), note that result scale to 2**m */
1122         m = 0;
1123         if (j < 7) {
1124                 ww = gam_n(j + 1, z);
1125         } else {
1126                 w = y + one;
1127                 if ((lx & 1) == 0) {        /* y+1 exact (note that y<184) */
1128                         ww = large_gam(w, &m);
1129                 } else {
1130                         t = w - one;
1131                         if (t == y) {   /* y+one exact */
1132                                 ww = large_gam(w, &m);
1133                         } else {        /* use y*gamma(y) */
1134                                 if (j == 7)
1135                                         ww = gam_n(j, z);
1136                                 else
1137                                         ww = large_gam(y, &m);
1138                                 t4 = ww.h + ww.l;
1139                                 t1 = CHOPPED((y));
1140                                 t2 = CHOPPED((t4));
1141                                                 /* t4 will not be too large */
1142                                 ww.l = y * (ww.l - (t2 - ww.h)) + (y - t1) * t2;
1143                                 ww.h = t1 * t2;
1144                         }
1145                 }
1146         }
1147 
1148         /* compute 1/(ss*ww) */
1149         t3 = ss.h + ss.l;
1150         t4 = ww.h + ww.l;
1151         t1 = CHOPPED((t3));
1152         t2 = CHOPPED((t4));
1153         z1 = ss.l - (t1 - ss.h);        /* (t1,z1) = ss */
1154         z2 = ww.l - (t2 - ww.h);        /* (t2,z2) = ww */
1155         t3 = t3 * t4;                   /* t3 = ss*ww */
1156         z3 = one / t3;                  /* z3 = 1/(ss*ww) */
1157         t5 = t1 * t2;
1158         z5 = z1 * t4 + t1 * z2;         /* (t5,z5) = ss*ww */
1159         t1 = CHOPPED((t3));             /* (t1,z1) = ss*ww */
1160         z1 = z5 - (t1 - t5);
1161         t2 = CHOPPED((z3));             /* leading 1/(ss*ww) */
1162         z2 = z3 * (t2 * z1 - (one - t2 * t1));
1163         z = t2 - z2;
1164 
1165         return (scalbnl(z, -m));
1166 }