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 } 1165