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 /* 31 * floating point Bessel's function of the first and second kinds 32 * of order zero: j1(x),y1(x); 33 * 34 * Special cases: 35 * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; 36 * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. 37 */ 38 39 #pragma weak __j1l = j1l 40 #pragma weak __y1l = y1l 41 42 #include "libm.h" 43 #include "longdouble.h" 44 45 #define GENERIC long double 46 static const GENERIC 47 zero = 0.0L, 48 small = 1.0e-9L, 49 tiny = 1.0e-38L, 50 one = 1.0L, 51 five = 5.0L, 52 invsqrtpi= 5.641895835477562869480794515607725858441e-0001L, 53 tpi = 0.636619772367581343075535053490057448L; 54 55 static GENERIC pone(GENERIC); 56 static GENERIC qone(GENERIC); 57 58 static const GENERIC r0[7] = { 59 -6.249999999999999999999999999999999627320e-0002L, 60 1.940606727194041716205384618494641565464e-0003L, 61 -3.005630423155733701856481469986459043883e-0005L, 62 2.345586219403918667468341047369572169358e-0007L, 63 -9.976809285885253587529010109133336669724e-0010L, 64 2.218743258363623946078958783775107473381e-0012L, 65 -2.071079656218700604767650924103578046280e-0015L, 66 }; 67 static const GENERIC s0[7] = { 68 1.0e0L, 69 1.061695903156199920738051277075003059555e-0002L, 70 5.521860513111180371566951179398862692060e-0005L, 71 1.824214367413754193524107877084979441407e-0007L, 72 4.098957778439576834818838198039029353925e-0010L, 73 6.047735079699666389853240090925264056197e-0013L, 74 4.679044728878836197247923279512047035041e-0016L, 75 }; 76 77 GENERIC 78 j1l(x) GENERIC x;{ 79 GENERIC z, d, s,c,ss,cc,r; 80 int i, sgn; 81 82 if (!finitel(x)) return one/x; 83 sgn = signbitl(x); 84 x = fabsl(x); 85 if (x > 1.28L) { 86 s = sinl(x); 87 c = cosl(x); 88 /* 89 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0)) 90 * where x0 = x-3pi/4 91 * Better formula: 92 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 93 * = 1/sqrt(2) * (sin(x) - cos(x)) 94 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 95 * = -1/sqrt(2) * (cos(x) + sin(x)) 96 * To avoid cancellation, use 97 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 98 * to compute the worse one. 99 */ 100 if (x>1.0e2450L) { /* x+x may overflow */ 101 ss = -s-c; 102 cc = s-c; 103 } else if (signbitl(s) != signbitl(c)) { 104 cc = s - c; 105 ss = cosl(x+x)/cc; 106 } else { 107 ss = -s-c; 108 cc = cosl(x+x)/ss; 109 } 110 /* 111 * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss) 112 * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc) 113 */ 114 if (x>1.0e120L) return (invsqrtpi*cc)/sqrtl(x); 115 d = invsqrtpi*(pone(x)*cc-qone(x)*ss)/sqrtl(x); 116 if (sgn == 0) return d; else return -d; 117 } 118 if (x<=small) { 119 if (x<=tiny) d = 0.5L*x; 120 else d = x*(0.5L-x*x*0.125L); 121 if (sgn == 0) return d; else return -d; 122 } 123 z = x*x; 124 r = r0[6]; 125 s = s0[6]; 126 for (i=5;i>=0;i--) { 127 r = r*z + r0[i]; 128 s = s*z + s0[i]; 129 } 130 d = x*0.5L+x*(z*(r/s)); 131 if (sgn == 0) return d; else return -d; 132 } 133 134 static const GENERIC u0[7] = { 135 -1.960570906462389484060557273467558703503e-0001L, 136 5.166389353148318460304315890665450006495e-0002L, 137 -2.229699464105910913337190798743451115604e-0003L, 138 3.625437034548863342715657067759078267158e-0005L, 139 -2.689902826993117212255524537353883987171e-0007L, 140 9.304570592456930912969387719010256018466e-0010L, 141 -1.234878126794286643318321347997500346131e-0012L, 142 }; 143 static const GENERIC v0[8] = { 144 1.0e0L, 145 1.369394302535807332517110204820556695644e-0002L, 146 9.508438148097659501433367062605935379588e-0005L, 147 4.399007309420092056052714797296467565655e-0007L, 148 1.488083087443756398305819693177715000787e-0009L, 149 3.751609832625793536245746965768587624922e-0012L, 150 6.680926434086257291872903276124244131448e-0015L, 151 6.676602383908906988160099057991121446058e-0018L, 152 }; 153 154 GENERIC 155 y1l(x) GENERIC x;{ 156 GENERIC z, s,c,ss,cc,u,v; 157 int i; 158 159 if (isnanl(x)) return x+x; 160 if (x <= zero) { 161 if (x == zero) 162 return -one/zero; 163 else 164 return zero/zero; 165 } 166 if (x > 1.28L) { 167 if (!finitel(x)) return zero; 168 s = sinl(x); 169 c = cosl(x); 170 /* 171 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0)) 172 * where x0 = x-3pi/4 173 * Better formula: 174 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 175 * = 1/sqrt(2) * (sin(x) - cos(x)) 176 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 177 * = -1/sqrt(2) * (cos(x) + sin(x)) 178 * To avoid cancellation, use 179 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 180 * to compute the worse one. 181 */ 182 if (x>1.0e2450L) { /* x+x may overflow */ 183 ss = -s-c; 184 cc = s-c; 185 } else if (signbitl(s) != signbitl(c)) { 186 cc = s - c; 187 ss = cosl(x+x)/cc; 188 } else { 189 ss = -s-c; 190 cc = cosl(x+x)/ss; 191 } 192 /* 193 * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss) 194 * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc) 195 */ 196 if (x>1.0e91L) return (invsqrtpi*ss)/sqrtl(x); 197 return invsqrtpi*(pone(x)*ss+qone(x)*cc)/sqrtl(x); 198 } 199 if (x<=tiny) { 200 return (-tpi/x); 201 } 202 z = x*x; 203 u = u0[6]; v = v0[6]+z*v0[7]; 204 for (i=5;i>=0;i--) { 205 u = u*z + u0[i]; 206 v = v*z + v0[i]; 207 } 208 return(x*(u/v) + tpi*(j1l(x)*logl(x)-one/x)); 209 } 210 211 static const GENERIC pr0[12] = { 212 1.000000000000000000000000000000000000267e+0000L, 213 1.060717875045891455602180843276758003035e+0003L, 214 4.344347542892127024446687712181105852335e+0005L, 215 8.915680220724007016377924252717410457094e+0007L, 216 9.969502259938406062809873257569171272819e+0009L, 217 6.200290193138613035646510338707386316595e+0011L, 218 2.105978548788015119851815854422247330118e+0013L, 219 3.696635772784601239371730810311998368948e+0014L, 220 3.015913097920694682057958412534134515156e+0015L, 221 9.370298471339353098123277427328592725921e+0015L, 222 7.190349005196335967340799265074029443057e+0015L, 223 2.736097786240689996880391074927552517982e+0014L, 224 }; 225 static const GENERIC ps0[11] = { 226 1.0e0L, 227 1.060600687545891455602180843276758095107e+0003L, 228 4.343106093416975589147153906505338900961e+0005L, 229 8.910605869002176566582072242244353399059e+0007L, 230 9.959122058635087888690713917622056540190e+0009L, 231 6.188744967234948231792482949171041843894e+0011L, 232 2.098863976953783506401759873801990304907e+0013L, 233 3.672870357018063196746729751479938908450e+0014L, 234 2.975538419246824921049011529574385888420e+0015L, 235 9.063657659995043205018686029284479837091e+0015L, 236 6.401953344314747916729366441508892711691e+0015L, 237 }; 238 static const GENERIC pr1[12] = { 239 1.000000000000000000000023667524130660984e+0000L, 240 6.746154419979618754354803488126452971204e+0002L, 241 1.811210781083390154857018330296145970502e+0005L, 242 2.533098390379924268038005329095287842244e+0007L, 243 2.029683619805342145252338570875424600729e+0009L, 244 9.660859662192711465301069401598929980319e+0010L, 245 2.743396238644831519934098967716621316316e+0012L, 246 4.553097354140854377931023170263455246288e+0013L, 247 4.210245069852219757476169864974870720374e+0014L, 248 1.987334056229596485076645967176169801727e+0015L, 249 4.067120052787096893838970455751338930462e+0015L, 250 2.486539606380406398310845264910691398133e+0015L, 251 }; 252 static const GENERIC ps1[14] = { 253 1.0e0L, 254 6.744982544979618754355808680196859521782e+0002L, 255 1.810421795396966762032155290441364740350e+0005L, 256 2.530986460644310651529583759699988435573e+0007L, 257 2.026743276048023121360249288818290224145e+0009L, 258 9.637461924407405935245269407052641341836e+0010L, 259 2.732378628423766417402292797028314160831e+0012L, 260 4.522345274960527124354844364012184278488e+0013L, 261 4.160650668341743132685335758415469856545e+0014L, 262 1.943730242988858208243492424892435901211e+0015L, 263 3.880228532692127989901131618598067450001e+0015L, 264 2.178020816161154615841000173683302999728e+0015L, 265 -8.994062666842225551554346698171600634173e+0013L, 266 1.368520368508851253495764806934619574990e+0013L, 267 }; 268 static const GENERIC pr2[12] = { 269 1.000000000000000006938651621840396237282e+0000L, 270 3.658416291850404981407101077037948144698e+0002L, 271 5.267073772170356547709794670602812447537e+0004L, 272 3.912012101226837463014925210735894620442e+0006L, 273 1.651295648974103957193874928714180765625e+0008L, 274 4.114901144480797609972484998142146783499e+0009L, 275 6.092524309766036681542980572526335147672e+0010L, 276 5.263913178071282616719249969074134570577e+0011L, 277 2.538408581124324223367341020538081330994e+0012L, 278 6.288607929360291027895126983015365677648e+0012L, 279 6.848330048211148419047055075386525945280e+0012L, 280 2.290309646838867941423178163991423244690e+0012L, 281 }; 282 static const GENERIC ps2[14] = { 283 1.0e0L, 284 3.657244416850405086459410165762319861856e+0002L, 285 5.262802358425023243992387075861237306312e+0004L, 286 3.905896813959919648136295861661483848364e+0006L, 287 1.646791907791461220742694842108202772763e+0008L, 288 4.096132803064256022224954120208201437344e+0009L, 289 6.046665195915950447544429445730680236759e+0010L, 290 5.198061739781991313414052212328653295168e+0011L, 291 2.484233851814333966401527626421254279796e+0012L, 292 6.047868806925315879339651539434315255940e+0012L, 293 6.333103831254091652501642567294101813354e+0012L, 294 1.875143098754284994467609936924685024968e+0012L, 295 -5.238330920563392692965412762508813601534e+0010L, 296 4.656888609439364725427789198383779259957e+0009L, 297 }; 298 static const GENERIC pr3[13] = { 299 1.000000000000009336887318068056137842897e+0000L, 300 2.242719942728459588488051572002835729183e+0002L, 301 1.955450611382026550266257737331095691092e+0004L, 302 8.707143293993619899395400562409175590739e+0005L, 303 2.186267894487004565948324289010954505316e+0007L, 304 3.224328510541957792360691585667502864688e+0008L, 305 2.821057355151380597331792896882741364897e+0009L, 306 1.445371387295422404365584793796028979840e+0010L, 307 4.181743160669891357783011002656658107864e+0010L, 308 6.387371088767993119325536137794535513922e+0010L, 309 4.575619999412716078064070587767416436396e+0010L, 310 1.228415651211639160620284441690503550842e+0010L, 311 7.242170349875563053436050532153112882072e+0008L, 312 }; 313 static const GENERIC ps3[13] = { 314 1.0e0L, 315 2.241548067728529551049804610486061401070e+0002L, 316 1.952838216795552145132137932931237181307e+0004L, 317 8.684574926493185744628127341069974575526e+0005L, 318 2.176357771067037962940853412819852189164e+0007L, 319 3.199958682356132977319258783167122100567e+0008L, 320 2.786218931525334687844675219914201872570e+0009L, 321 1.416283776951741549631417572317916039767e+0010L, 322 4.042962659271567948735676834609348842922e+0010L, 323 6.028168462646694510083847222968444402161e+0010L, 324 4.118410226794641413833887606580085281111e+0010L, 325 9.918735736297038430744161253338202230263e+0009L, 326 4.092967198238098023219124487437130332038e+0008L, 327 }; 328 static const GENERIC pr4[13] = { 329 1.000000000001509220978157399042059553390e+0000L, 330 1.437551868378147851133499996323782607787e+0002L, 331 7.911335537418177296041518061404505428004e+0003L, 332 2.193710939115317214716518908935756104804e+0005L, 333 3.390662495136730962513489796538274984382e+0006L, 334 3.048655347929348891006070609293884274789e+0007L, 335 1.613781633489496606354045161527450975195e+0008L, 336 4.975089835037230277110156150038482159988e+0008L, 337 8.636047087015115403880904418339566323264e+0008L, 338 7.918202912328366140110671223076949101509e+0008L, 339 3.423294665798984733439650311722794853294e+0008L, 340 5.621904953441963961040503934782662613621e+0007L, 341 2.086303543310240260758670404509484499793e+0006L, 342 }; 343 static const GENERIC ps4[13] = { 344 1.0e0L, 345 1.436379993384532371670493319591847362304e+0002L, 346 7.894647154785430678061053848847436659499e+0003L, 347 2.184659753392097529008981741550878586174e+0005L, 348 3.366109083305465176803513738147049499361e+0006L, 349 3.011911545968996817697665866587226343186e+0007L, 350 1.582262913779689851316760148459414895301e+0008L, 351 4.819268809494937919217938589530138201770e+0008L, 352 8.201355762990450679702837123432527154830e+0008L, 353 7.268232093982510937417446421282341425212e+0008L, 354 2.950911909015572933262131323934036480462e+0008L, 355 4.242839924305934423010858966540621219396e+0007L, 356 1.064387620445090779182117666330405186866e+0006L, 357 }; 358 static const GENERIC pr5[13] = { 359 1.000000000102434805241171427253847353861e+0000L, 360 9.129332257083629259060502249025963234821e+0001L, 361 3.132238483586953037576119377504557191413e+0003L, 362 5.329782528269307971278943122454171107861e+0004L, 363 4.988460157184117790692873002103052944145e+0005L, 364 2.686602071615786816147010334256047469378e+0006L, 365 8.445418526028961197703799808701268301831e+0006L, 366 1.536575358646141157475725889907900827390e+0007L, 367 1.568405818236523821796862770586544811945e+0007L, 368 8.450876239888770102387618667362302173547e+0006L, 369 2.154414900139567328424026827163203446077e+0006L, 370 2.105656926565043898888460254808062352205e+0005L, 371 4.739165011023396507022134303736862812975e+0003L, 372 }; 373 static const GENERIC ps5[13] = { 374 1.0e0L, 375 9.117613509595327476509152673394703847793e+0001L, 376 3.121697972484015639301279229281770795147e+0003L, 377 5.294447222735893568040911873834576440255e+0004L, 378 4.930368882192772335798256684110887882807e+0005L, 379 2.634854685641165298302167435798357437768e+0006L, 380 8.185462775400326393555896157031818280918e+0006L, 381 1.462417423080215192609668642663030667086e+0007L, 382 1.450624993985851675982860844153954896015e+0007L, 383 7.460467647561995283219086567162006113864e+0006L, 384 1.754210981405612478869227142579056338965e+0006L, 385 1.463286721155271971526264914524746699596e+0005L, 386 2.155894725796702015341211116579827039459e+0003L, 387 }; 388 static const GENERIC pr6[13] = { 389 1.000000003564855546741735920315743157129e+0000L, 390 5.734003934862540458119423509909510288366e+0001L, 391 1.209572491935850486086559692291796887976e+0003L, 392 1.243398391422281247933674779163660286838e+0004L, 393 6.930996755181437937258220998601708278787e+0004L, 394 2.198067659532757598646722249966767620099e+0005L, 395 4.033659432712058633933179115820576858455e+0005L, 396 4.257759657219008027016047206574574358678e+0005L, 397 2.511917395876004349480721277445763916389e+0005L, 398 7.813756153070623654178731651381881953552e+0004L, 399 1.152069173381127881385588092905864352891e+0004L, 400 6.548580782804088553777816037551523398082e+0002L, 401 8.668725370116906132327542766127938496880e+0000L, 402 }; 403 static const GENERIC ps6[13] = { 404 1.0e0L, 405 5.722285236357114566499221525736286205184e+0001L, 406 1.203010842878317935444582950620339570506e+0003L, 407 1.230058335378583550155825502172435371208e+0004L, 408 6.800998550607861288865300438648089894412e+0004L, 409 2.130767829599304262987769347536850885921e+0005L, 410 3.840483466643916681759936972992155310026e+0005L, 411 3.947432373459225542861819148108081160393e+0005L, 412 2.237816239393081111481588434457838526738e+0005L, 413 6.545820495124419723398946273790921540774e+0004L, 414 8.729563630320892741500726213278834737196e+0003L, 415 4.130762660291894753450174794196998813709e+0002L, 416 3.480368898672684645130335786015075595598e+0000L, 417 }; 418 static const GENERIC sixteen = 16.0L; 419 static const GENERIC eight = 8.0L; 420 static const GENERIC huge = 1.0e30L; 421 422 static GENERIC pone(x) 423 GENERIC x; 424 { 425 GENERIC s,r,t,z; 426 int i; 427 if (x>huge) return one; 428 t = one/x; z = t*t; 429 if (x>sixteen) { 430 r = z*pr0[11]+pr0[10]; s = ps0[10]; 431 for (i=9;i>=0;i--) { 432 r = z*r + pr0[i]; 433 s = z*s + ps0[i]; 434 } 435 } else if (x>eight) { 436 r = pr1[11]; s = ps1[11]+z*(ps1[12]+z*ps1[13]); 437 for (i=10;i>=0;i--) { 438 r = z*r + pr1[i]; 439 s = z*s + ps1[i]; 440 } 441 } else if (x>five) { 442 r = pr2[11]; s = ps2[11]+z*(ps2[12]+z*ps2[13]); 443 for (i=10;i>=0;i--) { 444 r = z*r + pr2[i]; 445 s = z*s + ps2[i]; 446 } 447 } else if (x>3.5L) { 448 r = pr3[12]; s = ps3[12]; 449 for (i=11;i>=0;i--) { 450 r = z*r + pr3[i]; 451 s = z*s + ps3[i]; 452 } 453 } else if (x>2.5L) { 454 r = pr4[12]; s = ps4[12]; 455 for (i=11;i>=0;i--) { 456 r = z*r + pr4[i]; 457 s = z*s + ps4[i]; 458 } 459 } else if (x> (1.0L/0.5625L)) { 460 r = pr5[12]; s = ps5[12]; 461 for (i=11;i>=0;i--) { 462 r = z*r + pr5[i]; 463 s = z*s + ps5[i]; 464 } 465 } else { /* assume x > 1.28 */ 466 r = pr6[12]; s = ps6[12]; 467 for (i=11;i>=0;i--) { 468 r = z*r + pr6[i]; 469 s = z*s + ps6[i]; 470 } 471 } 472 return r/s; 473 } 474 475 476 static const GENERIC qr0[12] = { 477 3.749999999999999999999999999999999971033e-0001L, 478 4.256726035237050601607682277433094262226e+0002L, 479 1.875976490812878489192409978945401066066e+0005L, 480 4.170314268048041914273603680317745592790e+0007L, 481 5.092750132543855817293451118974555746551e+0009L, 482 3.494749676278488654103505795794139483404e+0011L, 483 1.327062148257437316997667817096694173709e+0013L, 484 2.648993138273427226907503742066551150490e+0014L, 485 2.511695665909547412222430494473998127684e+0015L, 486 9.274694506662289043224310499164702306096e+0015L, 487 8.150904170663663829331320302911792892002e+0015L, 488 -5.001918733707662355772037829620388765122e+0014L, 489 }; 490 static const GENERIC qs0[11] = { 491 1.0e0L, 492 1.135400380229880160428715273982155760093e+0003L, 493 5.005701183877126164326765545516590744360e+0005L, 494 1.113444200113712167984337603933040102987e+0008L, 495 1.361074819925223062778717565699039471124e+0010L, 496 9.355750985802849484438933905325982809653e+0011L, 497 3.563462786008988825003965543857998084828e+0013L, 498 7.155145113900094163648726863803802910454e+0014L, 499 6.871266835834472758055559013851843654113e+0015L, 500 2.622030899226736712644974988157345234092e+0016L, 501 2.602912729172876330650077021706139707746e+0016L, 502 }; 503 static const GENERIC qr1[12] = { 504 3.749999999999999999997762458207284405806e-0001L, 505 2.697883998881706839929255517498189980485e+0002L, 506 7.755195925781028489386938870473834411019e+0004L, 507 1.166777762104017777198211072895528968355e+0007L, 508 1.011504772984321168320010084520261069362e+0009L, 509 5.246007703574156853577754571720205550010e+0010L, 510 1.637692549885592683166116551691266537647e+0012L, 511 3.022303623698185669912990310925039382495e+0013L, 512 3.154769927290655684846107030265909987946e+0014L, 513 1.715819913441554770089730934808123360921e+0015L, 514 4.165044355759732622273534445131736188510e+0015L, 515 3.151381420874174705643100381708086287596e+0015L, 516 }; 517 static const GENERIC qs1[14] = { 518 1.0e0L, 519 7.197091705351218239785633172408276982828e+0002L, 520 2.070012799599548685544883041297609861055e+0005L, 521 3.117014815317656221871840152778458754516e+0007L, 522 2.705719678902554974863325877025902971727e+0009L, 523 1.406113614727345726925060648750867264098e+0011L, 524 4.403777536067131320363005978631674817359e+0012L, 525 8.170725690209322283061499386703167242894e+0013L, 526 8.609458844975495289227794126964431210566e+0014L, 527 4.766766367015473481257280600694952920204e+0015L, 528 1.202286587943342194863557940888115641650e+0016L, 529 1.012474328306200909525063936061756024120e+0016L, 530 6.183552022678917858273222879615824070703e+0014L, 531 -9.756731548558226997573737400988225722740e+0013L, 532 }; 533 static const GENERIC qr2[12] = { 534 3.749999999999999481245647262226994293189e-0001L, 535 1.471366807289771354491181140167359026735e+0002L, 536 2.279432486768448220142080962843526951250e+0004L, 537 1.828943048523771225163804043356958285893e+0006L, 538 8.379828388647823135832220596417725010837e+0007L, 539 2.279814029335044024585393671278378022053e+0009L, 540 3.711653952257118120832817785271466441420e+0010L, 541 3.557650914518554549916730572553105048068e+0011L, 542 1.924583483146095896259774329498934160650e+0012L, 543 5.424386256063736390759567088291887140278e+0012L, 544 6.839325621241776786206509704671746841737e+0012L, 545 2.702169563144001166291686452305436313971e+0012L, 546 }; 547 static const GENERIC qs2[14] = { 548 1.0e0L, 549 3.926379194439388135703211933895203191089e+0002L, 550 6.089148804106598297488336063007609312276e+0004L, 551 4.893546162973278583711376356041614150645e+0006L, 552 2.247571119114497845046388801813832219404e+0008L, 553 6.137635663350177751290469334200757872645e+0009L, 554 1.005115019784102856424493519524998953678e+0011L, 555 9.725664462014503832860151384604677240620e+0011L, 556 5.345525100485511116148634192844434636072e+0012L, 557 1.549944007398946691720862738173956994779e+0013L, 558 2.067148441178952625710302124163264760362e+0013L, 559 9.401565402641963611295119487242595462301e+0012L, 560 3.548217088622398274748837287769709374385e+0011L, 561 -2.934470341719047120076509938432417352365e+0010L, 562 }; 563 static const GENERIC qr3[13] = { 564 3.749999999999412724084579833297451472091e-0001L, 565 9.058478580291706212422978492938435582527e+0001L, 566 8.524056033161038750461083666711724381171e+0003L, 567 4.105967158629109427753434569223631014730e+0005L, 568 1.118326603378531348259783091972623333657e+0007L, 569 1.794636683403578918528064904714132329343e+0008L, 570 1.714314157463635959556133236004368896724e+0009L, 571 9.622092032236084846572067257267661456030e+0009L, 572 3.057759524485859159957762858780768355020e+0010L, 573 5.129306780754798531609621454415938890020e+0010L, 574 3.999122002794961070680636194346316041352e+0010L, 575 1.122298454643493485989721564358100345388e+0010L, 576 5.603981987645989709668830968522362582221e+0008L, 577 }; 578 static const GENERIC qs3[13] = { 579 1.0e0L, 580 2.418328663076578169836155170053634419922e+0002L, 581 2.279620205900121042587523541281272875520e+0004L, 582 1.100984222585729521470129014992217092794e+0006L, 583 3.010743223679247091004262516286654516282e+0007L, 584 4.860925542827367817289619265215599433996e+0008L, 585 4.686668111035348691982715864307839581243e+0009L, 586 2.668701788405102017427214705946730894074e+0010L, 587 8.677395746106802640390580944836650584903e+0010L, 588 1.511936455574951790658498795945106643036e+0011L, 589 1.260845604432623478002018696873608353093e+0011L, 590 4.052692278419853853911440231600864589805e+0010L, 591 2.965516519212226064983267822243329694729e+0009L, 592 }; 593 static const GENERIC qr4[13] = { 594 3.749999999919234164154669754440123072618e-0001L, 595 5.844218580776819864791168253485055101858e+0001L, 596 3.489273514092912982675669411371435670220e+0003L, 597 1.050523637774575684509663430018995479594e+0005L, 598 1.764549172059701565500717319792780115289e+0006L, 599 1.725532438844133795028063102681497371154e+0007L, 600 9.938114847359778539965140247590176334874e+0007L, 601 3.331710808184595545396883770200772842314e+0008L, 602 6.271970557641881511609560444872797282698e+0008L, 603 6.188529798677357075020774923903737913285e+0008L, 604 2.821905302742849974509982167877885011629e+0008L, 605 4.615467358646911976773290256984329814896e+0007L, 606 1.348140608731546467396685802693380693275e+0006L, 607 }; 608 static const GENERIC qs4[13] = { 609 1.0e0L, 610 1.561192663112345185261418296389902133372e+0002L, 611 9.346678031144098270547225423124213083072e+0003L, 612 2.825851246482293547838023847601704751590e+0005L, 613 4.776572711622156091710902891124911556293e+0006L, 614 4.715106953717135402977938048006267859302e+0007L, 615 2.753962350894311316439652227611209035193e+0008L, 616 9.428501434615463207768964787500411575223e+0008L, 617 1.832650858775206787088236896454141572617e+0009L, 618 1.901697378939743226948920874296595242257e+0009L, 619 9.433322226854293780627188599226380812725e+0008L, 620 1.808520540608671608680284520798858587370e+0008L, 621 7.983342331736662753157217446919462398008e+0006L, 622 }; 623 static const GENERIC qr5[13] = { 624 3.749999995331364437028988850515190446719e-0001L, 625 3.739356381766559882677514593041627547911e+0001L, 626 1.399562500629413529355265462912819802551e+0003L, 627 2.594154053098947925345332218062210111753e+0004L, 628 2.640149879297408640394163979394594318371e+0005L, 629 1.542471854873199142031889093591449397995e+0006L, 630 5.242272868972053374067572098992335425895e+0006L, 631 1.025834487769410221329633071426044839935e+0007L, 632 1.116553924239448940142230579060124209622e+0007L, 633 6.318076065595910176374916303525884653514e+0006L, 634 1.641218086168640408527639735915512881785e+0006L, 635 1.522369793529178644168813882912134706444e+0005L, 636 2.526530541062297200914180060208669584055e+0003L, 637 }; 638 static const GENERIC qs5[13] = { 639 1.0e0L, 640 9.998960735935075380397545659016287506660e+0001L, 641 3.758767417842043742686475060540416737562e+0003L, 642 7.013652806952306520121959742519780781653e+0004L, 643 7.208949808818615099246529616211730446850e+0005L, 644 4.272753927109614455417836186072202009252e+0006L, 645 1.482524411356470699336129814111025434703e+0007L, 646 2.988750366665678233425279237627700803473e+0007L, 647 3.396957890261080492694709150553619185065e+0007L, 648 2.050652487738593004111578091156304540386e+0007L, 649 5.900504120811732547616511555946279451316e+0006L, 650 6.563391409260160897024498082273183468347e+0005L, 651 1.692629845012790205348966731477187041419e+0004L, 652 }; 653 static const GENERIC qr6[13] = { 654 3.749999861516664133157566870858975421296e-0001L, 655 2.367863756747764863120797431599473468918e+0001L, 656 5.476715802114976248882067325630793143777e+0002L, 657 6.143190357869842894025012945444096170251e+0003L, 658 3.716250534677997850513733595140463851730e+0004L, 659 1.270883463823876752138326905022875657430e+0005L, 660 2.495301449636814481646371665429083801388e+0005L, 661 2.789578988212952248340486296254398601942e+0005L, 662 1.718247946911109055931819087137397324634e+0005L, 663 5.458973214011665714330326732204106364229e+0004L, 664 7.912102686687948786048943339759596652813e+0003L, 665 4.077961006160866935722030715149087938091e+0002L, 666 3.765206972770245085551057237882528510428e+0000L, 667 }; 668 static const GENERIC qs6[13] = { 669 1.0e0L, 670 6.341646532940517305641893852673926809601e+0001L, 671 1.477058277414040790932597537920671025359e+0003L, 672 1.674406564031044491436044253393536487604e+0004L, 673 1.028516501369755949895050806908994650768e+0005L, 674 3.593620042532885295087463507733285434207e+0005L, 675 7.267924991381020915185873399453724799625e+0005L, 676 8.462277510768818399961191426205006083088e+0005L, 677 5.514399892230892163373611895645500250514e+0005L, 678 1.898084241009259353540620272932188102299e+0005L, 679 3.102941242117739015721984123081026253068e+0004L, 680 1.958971184431466907681440650181421086143e+0003L, 681 2.878853357310495087181721613889455121867e+0001L, 682 }; 683 static GENERIC qone(x) 684 GENERIC x; 685 { 686 GENERIC s,r,t,z; 687 int i; 688 if (x>huge) return 0.375L/x; 689 t = one/x; z = t*t; 690 if (x>sixteen) { 691 r = z*qr0[11]+qr0[10]; s = qs0[10]; 692 for (i=9;i>=0;i--) { 693 r = z*r + qr0[i]; 694 s = z*s + qs0[i]; 695 } 696 } else if (x>eight) { 697 r = qr1[11]; s = qs1[11]+z*(qs1[12]+z*qs1[13]); 698 for (i=10;i>=0;i--) { 699 r = z*r + qr1[i]; 700 s = z*s + qs1[i]; 701 } 702 } else if (x>five) { /* x > 5.0 */ 703 r = qr2[11]; s = qs2[11]+z*(qs2[12]+z*qs2[13]); 704 for (i=10;i>=0;i--) { 705 r = z*r + qr2[i]; 706 s = z*s + qs2[i]; 707 } 708 } else if (x>3.5L) { 709 r = qr3[12]; s = qs3[12]; 710 for (i=11;i>=0;i--) { 711 r = z*r + qr3[i]; 712 s = z*s + qs3[i]; 713 } 714 } else if (x>2.5L) { 715 r = qr4[12]; s = qs4[12]; 716 for (i=11;i>=0;i--) { 717 r = z*r + qr4[i]; 718 s = z*s + qs4[i]; 719 } 720 } else if (x> (1.0L/0.5625L)) { 721 r = qr5[12]; s = qs5[12]; 722 for (i=11;i>=0;i--) { 723 r = z*r + qr5[i]; 724 s = z*s + qs5[i]; 725 } 726 } else { /* assume x > 1.28 */ 727 r = qr6[12]; s = qs6[12]; 728 for (i=11;i>=0;i--) { 729 r = z*r + qr6[i]; 730 s = z*s + qs6[i]; 731 } 732 } 733 return t*(r/s); 734 } 735