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 "libm_synonyms.h" 44 #include "longdouble.h" 45 #include <math.h> 46 #if defined(__SUNPRO_C) 47 #include <sunmath.h> 48 #endif 49 50 #define GENERIC long double 51 static GENERIC 52 zero = 0.0L, 53 small = 1.0e-9L, 54 tiny = 1.0e-38L, 55 one = 1.0L, 56 five = 5.0L, 57 invsqrtpi = 5.641895835477562869480794515607725858441e-0001L, 58 tpi = 0.636619772367581343075535053490057448L; 59 60 static GENERIC pone(), qone(); 61 static GENERIC r0[7] = { 62 -6.249999999999999999999999999999999627320e-0002L, 63 1.940606727194041716205384618494641565464e-0003L, 64 -3.005630423155733701856481469986459043883e-0005L, 65 2.345586219403918667468341047369572169358e-0007L, 66 -9.976809285885253587529010109133336669724e-0010L, 67 2.218743258363623946078958783775107473381e-0012L, 68 -2.071079656218700604767650924103578046280e-0015L, 69 }; 70 static GENERIC s0[7] = { 71 1.0e0L, 72 1.061695903156199920738051277075003059555e-0002L, 73 5.521860513111180371566951179398862692060e-0005L, 74 1.824214367413754193524107877084979441407e-0007L, 75 4.098957778439576834818838198039029353925e-0010L, 76 6.047735079699666389853240090925264056197e-0013L, 77 4.679044728878836197247923279512047035041e-0016L, 78 }; 79 80 GENERIC 81 j1l(x) GENERIC x; { 82 GENERIC z, d, s, c, ss, cc, r; 83 int i, sgn; 84 85 if (!finitel(x)) 86 return (one/x); 87 sgn = signbitl(x); 88 x = fabsl(x); 89 if (x > 1.28L) { 90 s = sinl(x); 91 c = cosl(x); 92 /* 93 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0)) 94 * where x0 = x-3pi/4 95 * Better formula: 96 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 97 * = 1/sqrt(2) * (sin(x) - cos(x)) 98 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 99 * = -1/sqrt(2) * (cos(x) + sin(x)) 100 * To avoid cancellation, use 101 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 102 * to compute the worse one. 103 */ 104 if (x > 1.0e2450L) { /* x+x may overflow */ 105 ss = -s-c; 106 cc = s-c; 107 } else if (signbitl(s) != signbitl(c)) { 108 cc = s - c; 109 ss = cosl(x+x)/cc; 110 } else { 111 ss = -s-c; 112 cc = cosl(x+x)/ss; 113 } 114 /* 115 * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss) 116 * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc) 117 */ 118 if (x > 1.0e120L) 119 return (invsqrtpi*cc)/sqrtl(x); 120 d = invsqrtpi*(pone(x)*cc-qone(x)*ss)/sqrtl(x); 121 if (sgn == 0) 122 return (d); 123 else 124 return (-d); 125 } 126 if (x <= small) { 127 if (x <= tiny) d = 0.5L*x; 128 else d = x*(0.5L-x*x*0.125L); 129 if (sgn == 0) 130 return (d); 131 else 132 return (-d); 133 } 134 z = x*x; 135 r = r0[6]; 136 s = s0[6]; 137 for (i = 5; i >= 0; i--) { 138 r = r*z + r0[i]; 139 s = s*z + s0[i]; 140 } 141 d = x*0.5L+x*(z*(r/s)); 142 if (sgn == 0) 143 return (d); 144 else 145 return (-d); 146 } 147 148 static GENERIC u0[7] = { 149 -1.960570906462389484060557273467558703503e-0001L, 150 5.166389353148318460304315890665450006495e-0002L, 151 -2.229699464105910913337190798743451115604e-0003L, 152 3.625437034548863342715657067759078267158e-0005L, 153 -2.689902826993117212255524537353883987171e-0007L, 154 9.304570592456930912969387719010256018466e-0010L, 155 -1.234878126794286643318321347997500346131e-0012L, 156 }; 157 static GENERIC v0[8] = { 158 1.0e0L, 159 1.369394302535807332517110204820556695644e-0002L, 160 9.508438148097659501433367062605935379588e-0005L, 161 4.399007309420092056052714797296467565655e-0007L, 162 1.488083087443756398305819693177715000787e-0009L, 163 3.751609832625793536245746965768587624922e-0012L, 164 6.680926434086257291872903276124244131448e-0015L, 165 6.676602383908906988160099057991121446058e-0018L, 166 }; 167 168 GENERIC 169 y1l(x) GENERIC x; { 170 GENERIC z, s, c, ss, cc, u, v; 171 int i; 172 173 if (isnanl(x)) 174 return (x+x); 175 if (x <= zero) { 176 if (x == zero) 177 return (-one/zero); 178 else 179 return (zero/zero); 180 } 181 if (x > 1.28L) { 182 if (!finitel(x)) 183 return (zero); 184 s = sinl(x); 185 c = cosl(x); 186 /* 187 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0)) 188 * where x0 = x-3pi/4 189 * Better formula: 190 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 191 * = 1/sqrt(2) * (sin(x) - cos(x)) 192 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 193 * = -1/sqrt(2) * (cos(x) + sin(x)) 194 * To avoid cancellation, use 195 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 196 * to compute the worse one. 197 */ 198 if (x > 1.0e2450L) { /* x+x may overflow */ 199 ss = -s-c; 200 cc = s-c; 201 } else if (signbitl(s) != signbitl(c)) { 202 cc = s - c; 203 ss = cosl(x+x)/cc; 204 } else { 205 ss = -s-c; 206 cc = cosl(x+x)/ss; 207 } 208 /* 209 * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss) 210 * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc) 211 */ 212 if (x > 1.0e91L) 213 return (invsqrtpi*ss)/sqrtl(x); 214 return (invsqrtpi*(pone(x)*ss+qone(x)*cc)/sqrtl(x)); 215 } 216 if (x <= tiny) { 217 return (-tpi/x); 218 } 219 z = x*x; 220 u = u0[6]; v = v0[6]+z*v0[7]; 221 for (i = 5; i >= 0; i--) { 222 u = u*z + u0[i]; 223 v = v*z + v0[i]; 224 } 225 return (x*(u/v) + tpi*(j1l(x)*logl(x)-one/x)); 226 } 227 228 static GENERIC pr0[12] = { 229 1.000000000000000000000000000000000000267e+0000L, 230 1.060717875045891455602180843276758003035e+0003L, 231 4.344347542892127024446687712181105852335e+0005L, 232 8.915680220724007016377924252717410457094e+0007L, 233 9.969502259938406062809873257569171272819e+0009L, 234 6.200290193138613035646510338707386316595e+0011L, 235 2.105978548788015119851815854422247330118e+0013L, 236 3.696635772784601239371730810311998368948e+0014L, 237 3.015913097920694682057958412534134515156e+0015L, 238 9.370298471339353098123277427328592725921e+0015L, 239 7.190349005196335967340799265074029443057e+0015L, 240 2.736097786240689996880391074927552517982e+0014L, 241 }; 242 static GENERIC ps0[11] = { 243 1.0e0L, 244 1.060600687545891455602180843276758095107e+0003L, 245 4.343106093416975589147153906505338900961e+0005L, 246 8.910605869002176566582072242244353399059e+0007L, 247 9.959122058635087888690713917622056540190e+0009L, 248 6.188744967234948231792482949171041843894e+0011L, 249 2.098863976953783506401759873801990304907e+0013L, 250 3.672870357018063196746729751479938908450e+0014L, 251 2.975538419246824921049011529574385888420e+0015L, 252 9.063657659995043205018686029284479837091e+0015L, 253 6.401953344314747916729366441508892711691e+0015L, 254 }; 255 static GENERIC pr1[12] = { 256 1.000000000000000000000023667524130660984e+0000L, 257 6.746154419979618754354803488126452971204e+0002L, 258 1.811210781083390154857018330296145970502e+0005L, 259 2.533098390379924268038005329095287842244e+0007L, 260 2.029683619805342145252338570875424600729e+0009L, 261 9.660859662192711465301069401598929980319e+0010L, 262 2.743396238644831519934098967716621316316e+0012L, 263 4.553097354140854377931023170263455246288e+0013L, 264 4.210245069852219757476169864974870720374e+0014L, 265 1.987334056229596485076645967176169801727e+0015L, 266 4.067120052787096893838970455751338930462e+0015L, 267 2.486539606380406398310845264910691398133e+0015L, 268 }; 269 static GENERIC ps1[14] = { 270 1.0e0L, 271 6.744982544979618754355808680196859521782e+0002L, 272 1.810421795396966762032155290441364740350e+0005L, 273 2.530986460644310651529583759699988435573e+0007L, 274 2.026743276048023121360249288818290224145e+0009L, 275 9.637461924407405935245269407052641341836e+0010L, 276 2.732378628423766417402292797028314160831e+0012L, 277 4.522345274960527124354844364012184278488e+0013L, 278 4.160650668341743132685335758415469856545e+0014L, 279 1.943730242988858208243492424892435901211e+0015L, 280 3.880228532692127989901131618598067450001e+0015L, 281 2.178020816161154615841000173683302999728e+0015L, 282 -8.994062666842225551554346698171600634173e+0013L, 283 1.368520368508851253495764806934619574990e+0013L, 284 }; 285 static GENERIC pr2[12] = { 286 1.000000000000000006938651621840396237282e+0000L, 287 3.658416291850404981407101077037948144698e+0002L, 288 5.267073772170356547709794670602812447537e+0004L, 289 3.912012101226837463014925210735894620442e+0006L, 290 1.651295648974103957193874928714180765625e+0008L, 291 4.114901144480797609972484998142146783499e+0009L, 292 6.092524309766036681542980572526335147672e+0010L, 293 5.263913178071282616719249969074134570577e+0011L, 294 2.538408581124324223367341020538081330994e+0012L, 295 6.288607929360291027895126983015365677648e+0012L, 296 6.848330048211148419047055075386525945280e+0012L, 297 2.290309646838867941423178163991423244690e+0012L, 298 }; 299 static GENERIC ps2[14] = { 300 1.0e0L, 301 3.657244416850405086459410165762319861856e+0002L, 302 5.262802358425023243992387075861237306312e+0004L, 303 3.905896813959919648136295861661483848364e+0006L, 304 1.646791907791461220742694842108202772763e+0008L, 305 4.096132803064256022224954120208201437344e+0009L, 306 6.046665195915950447544429445730680236759e+0010L, 307 5.198061739781991313414052212328653295168e+0011L, 308 2.484233851814333966401527626421254279796e+0012L, 309 6.047868806925315879339651539434315255940e+0012L, 310 6.333103831254091652501642567294101813354e+0012L, 311 1.875143098754284994467609936924685024968e+0012L, 312 -5.238330920563392692965412762508813601534e+0010L, 313 4.656888609439364725427789198383779259957e+0009L, 314 }; 315 static GENERIC pr3[13] = { 316 1.000000000000009336887318068056137842897e+0000L, 317 2.242719942728459588488051572002835729183e+0002L, 318 1.955450611382026550266257737331095691092e+0004L, 319 8.707143293993619899395400562409175590739e+0005L, 320 2.186267894487004565948324289010954505316e+0007L, 321 3.224328510541957792360691585667502864688e+0008L, 322 2.821057355151380597331792896882741364897e+0009L, 323 1.445371387295422404365584793796028979840e+0010L, 324 4.181743160669891357783011002656658107864e+0010L, 325 6.387371088767993119325536137794535513922e+0010L, 326 4.575619999412716078064070587767416436396e+0010L, 327 1.228415651211639160620284441690503550842e+0010L, 328 7.242170349875563053436050532153112882072e+0008L, 329 }; 330 static GENERIC ps3[13] = { 331 1.0e0L, 332 2.241548067728529551049804610486061401070e+0002L, 333 1.952838216795552145132137932931237181307e+0004L, 334 8.684574926493185744628127341069974575526e+0005L, 335 2.176357771067037962940853412819852189164e+0007L, 336 3.199958682356132977319258783167122100567e+0008L, 337 2.786218931525334687844675219914201872570e+0009L, 338 1.416283776951741549631417572317916039767e+0010L, 339 4.042962659271567948735676834609348842922e+0010L, 340 6.028168462646694510083847222968444402161e+0010L, 341 4.118410226794641413833887606580085281111e+0010L, 342 9.918735736297038430744161253338202230263e+0009L, 343 4.092967198238098023219124487437130332038e+0008L, 344 }; 345 static GENERIC pr4[13] = { 346 1.000000000001509220978157399042059553390e+0000L, 347 1.437551868378147851133499996323782607787e+0002L, 348 7.911335537418177296041518061404505428004e+0003L, 349 2.193710939115317214716518908935756104804e+0005L, 350 3.390662495136730962513489796538274984382e+0006L, 351 3.048655347929348891006070609293884274789e+0007L, 352 1.613781633489496606354045161527450975195e+0008L, 353 4.975089835037230277110156150038482159988e+0008L, 354 8.636047087015115403880904418339566323264e+0008L, 355 7.918202912328366140110671223076949101509e+0008L, 356 3.423294665798984733439650311722794853294e+0008L, 357 5.621904953441963961040503934782662613621e+0007L, 358 2.086303543310240260758670404509484499793e+0006L, 359 }; 360 static GENERIC ps4[13] = { 361 1.0e0L, 362 1.436379993384532371670493319591847362304e+0002L, 363 7.894647154785430678061053848847436659499e+0003L, 364 2.184659753392097529008981741550878586174e+0005L, 365 3.366109083305465176803513738147049499361e+0006L, 366 3.011911545968996817697665866587226343186e+0007L, 367 1.582262913779689851316760148459414895301e+0008L, 368 4.819268809494937919217938589530138201770e+0008L, 369 8.201355762990450679702837123432527154830e+0008L, 370 7.268232093982510937417446421282341425212e+0008L, 371 2.950911909015572933262131323934036480462e+0008L, 372 4.242839924305934423010858966540621219396e+0007L, 373 1.064387620445090779182117666330405186866e+0006L, 374 }; 375 static GENERIC pr5[13] = { 376 1.000000000102434805241171427253847353861e+0000L, 377 9.129332257083629259060502249025963234821e+0001L, 378 3.132238483586953037576119377504557191413e+0003L, 379 5.329782528269307971278943122454171107861e+0004L, 380 4.988460157184117790692873002103052944145e+0005L, 381 2.686602071615786816147010334256047469378e+0006L, 382 8.445418526028961197703799808701268301831e+0006L, 383 1.536575358646141157475725889907900827390e+0007L, 384 1.568405818236523821796862770586544811945e+0007L, 385 8.450876239888770102387618667362302173547e+0006L, 386 2.154414900139567328424026827163203446077e+0006L, 387 2.105656926565043898888460254808062352205e+0005L, 388 4.739165011023396507022134303736862812975e+0003L, 389 }; 390 static GENERIC ps5[13] = { 391 1.0e0L, 392 9.117613509595327476509152673394703847793e+0001L, 393 3.121697972484015639301279229281770795147e+0003L, 394 5.294447222735893568040911873834576440255e+0004L, 395 4.930368882192772335798256684110887882807e+0005L, 396 2.634854685641165298302167435798357437768e+0006L, 397 8.185462775400326393555896157031818280918e+0006L, 398 1.462417423080215192609668642663030667086e+0007L, 399 1.450624993985851675982860844153954896015e+0007L, 400 7.460467647561995283219086567162006113864e+0006L, 401 1.754210981405612478869227142579056338965e+0006L, 402 1.463286721155271971526264914524746699596e+0005L, 403 2.155894725796702015341211116579827039459e+0003L, 404 }; 405 static GENERIC pr6[13] = { 406 1.000000003564855546741735920315743157129e+0000L, 407 5.734003934862540458119423509909510288366e+0001L, 408 1.209572491935850486086559692291796887976e+0003L, 409 1.243398391422281247933674779163660286838e+0004L, 410 6.930996755181437937258220998601708278787e+0004L, 411 2.198067659532757598646722249966767620099e+0005L, 412 4.033659432712058633933179115820576858455e+0005L, 413 4.257759657219008027016047206574574358678e+0005L, 414 2.511917395876004349480721277445763916389e+0005L, 415 7.813756153070623654178731651381881953552e+0004L, 416 1.152069173381127881385588092905864352891e+0004L, 417 6.548580782804088553777816037551523398082e+0002L, 418 8.668725370116906132327542766127938496880e+0000L, 419 }; 420 static GENERIC ps6[13] = { 421 1.0e0L, 422 5.722285236357114566499221525736286205184e+0001L, 423 1.203010842878317935444582950620339570506e+0003L, 424 1.230058335378583550155825502172435371208e+0004L, 425 6.800998550607861288865300438648089894412e+0004L, 426 2.130767829599304262987769347536850885921e+0005L, 427 3.840483466643916681759936972992155310026e+0005L, 428 3.947432373459225542861819148108081160393e+0005L, 429 2.237816239393081111481588434457838526738e+0005L, 430 6.545820495124419723398946273790921540774e+0004L, 431 8.729563630320892741500726213278834737196e+0003L, 432 4.130762660291894753450174794196998813709e+0002L, 433 3.480368898672684645130335786015075595598e+0000L, 434 }; 435 static GENERIC sixteen = 16.0L; 436 static GENERIC eight = 8.0L; 437 static GENERIC huge = 1.0e30L; 438 439 static GENERIC pone(x) 440 GENERIC x; 441 { 442 GENERIC s, r, t, z; 443 int i; 444 if (x > huge) 445 return (one); 446 t = one/x; z = t*t; 447 if (x > sixteen) { 448 r = z*pr0[11]+pr0[10]; s = ps0[10]; 449 for (i = 9; i >= 0; i--) { 450 r = z*r + pr0[i]; 451 s = z*s + ps0[i]; 452 } 453 } else if (x > eight) { 454 r = pr1[11]; s = ps1[11]+z*(ps1[12]+z*ps1[13]); 455 for (i = 10; i >= 0; i--) { 456 r = z*r + pr1[i]; 457 s = z*s + ps1[i]; 458 } 459 } else if (x > five) { 460 r = pr2[11]; s = ps2[11]+z*(ps2[12]+z*ps2[13]); 461 for (i = 10; i >= 0; i--) { 462 r = z*r + pr2[i]; 463 s = z*s + ps2[i]; 464 } 465 } else if (x > 3.5L) { 466 r = pr3[12]; s = ps3[12]; 467 for (i = 11; i >= 0; i--) { 468 r = z*r + pr3[i]; 469 s = z*s + ps3[i]; 470 } 471 } else if (x > 2.5L) { 472 r = pr4[12]; s = ps4[12]; 473 for (i = 11; i >= 0; i--) { 474 r = z*r + pr4[i]; 475 s = z*s + ps4[i]; 476 } 477 } else if (x > (1.0L/0.5625L)) { 478 r = pr5[12]; s = ps5[12]; 479 for (i = 11; i >= 0; i--) { 480 r = z*r + pr5[i]; 481 s = z*s + ps5[i]; 482 } 483 } else { /* assume x > 1.28 */ 484 r = pr6[12]; s = ps6[12]; 485 for (i = 11; i >= 0; i--) { 486 r = z*r + pr6[i]; 487 s = z*s + ps6[i]; 488 } 489 } 490 return (r/s); 491 } 492 493 494 static GENERIC qr0[12] = { 495 3.749999999999999999999999999999999971033e-0001L, 496 4.256726035237050601607682277433094262226e+0002L, 497 1.875976490812878489192409978945401066066e+0005L, 498 4.170314268048041914273603680317745592790e+0007L, 499 5.092750132543855817293451118974555746551e+0009L, 500 3.494749676278488654103505795794139483404e+0011L, 501 1.327062148257437316997667817096694173709e+0013L, 502 2.648993138273427226907503742066551150490e+0014L, 503 2.511695665909547412222430494473998127684e+0015L, 504 9.274694506662289043224310499164702306096e+0015L, 505 8.150904170663663829331320302911792892002e+0015L, 506 -5.001918733707662355772037829620388765122e+0014L, 507 }; 508 static GENERIC qs0[11] = { 509 1.0e0L, 510 1.135400380229880160428715273982155760093e+0003L, 511 5.005701183877126164326765545516590744360e+0005L, 512 1.113444200113712167984337603933040102987e+0008L, 513 1.361074819925223062778717565699039471124e+0010L, 514 9.355750985802849484438933905325982809653e+0011L, 515 3.563462786008988825003965543857998084828e+0013L, 516 7.155145113900094163648726863803802910454e+0014L, 517 6.871266835834472758055559013851843654113e+0015L, 518 2.622030899226736712644974988157345234092e+0016L, 519 2.602912729172876330650077021706139707746e+0016L, 520 }; 521 static GENERIC qr1[12] = { 522 3.749999999999999999997762458207284405806e-0001L, 523 2.697883998881706839929255517498189980485e+0002L, 524 7.755195925781028489386938870473834411019e+0004L, 525 1.166777762104017777198211072895528968355e+0007L, 526 1.011504772984321168320010084520261069362e+0009L, 527 5.246007703574156853577754571720205550010e+0010L, 528 1.637692549885592683166116551691266537647e+0012L, 529 3.022303623698185669912990310925039382495e+0013L, 530 3.154769927290655684846107030265909987946e+0014L, 531 1.715819913441554770089730934808123360921e+0015L, 532 4.165044355759732622273534445131736188510e+0015L, 533 3.151381420874174705643100381708086287596e+0015L, 534 }; 535 static GENERIC qs1[14] = { 536 1.0e0L, 537 7.197091705351218239785633172408276982828e+0002L, 538 2.070012799599548685544883041297609861055e+0005L, 539 3.117014815317656221871840152778458754516e+0007L, 540 2.705719678902554974863325877025902971727e+0009L, 541 1.406113614727345726925060648750867264098e+0011L, 542 4.403777536067131320363005978631674817359e+0012L, 543 8.170725690209322283061499386703167242894e+0013L, 544 8.609458844975495289227794126964431210566e+0014L, 545 4.766766367015473481257280600694952920204e+0015L, 546 1.202286587943342194863557940888115641650e+0016L, 547 1.012474328306200909525063936061756024120e+0016L, 548 6.183552022678917858273222879615824070703e+0014L, 549 -9.756731548558226997573737400988225722740e+0013L, 550 }; 551 static GENERIC qr2[12] = { 552 3.749999999999999481245647262226994293189e-0001L, 553 1.471366807289771354491181140167359026735e+0002L, 554 2.279432486768448220142080962843526951250e+0004L, 555 1.828943048523771225163804043356958285893e+0006L, 556 8.379828388647823135832220596417725010837e+0007L, 557 2.279814029335044024585393671278378022053e+0009L, 558 3.711653952257118120832817785271466441420e+0010L, 559 3.557650914518554549916730572553105048068e+0011L, 560 1.924583483146095896259774329498934160650e+0012L, 561 5.424386256063736390759567088291887140278e+0012L, 562 6.839325621241776786206509704671746841737e+0012L, 563 2.702169563144001166291686452305436313971e+0012L, 564 }; 565 static GENERIC qs2[14] = { 566 1.0e0L, 567 3.926379194439388135703211933895203191089e+0002L, 568 6.089148804106598297488336063007609312276e+0004L, 569 4.893546162973278583711376356041614150645e+0006L, 570 2.247571119114497845046388801813832219404e+0008L, 571 6.137635663350177751290469334200757872645e+0009L, 572 1.005115019784102856424493519524998953678e+0011L, 573 9.725664462014503832860151384604677240620e+0011L, 574 5.345525100485511116148634192844434636072e+0012L, 575 1.549944007398946691720862738173956994779e+0013L, 576 2.067148441178952625710302124163264760362e+0013L, 577 9.401565402641963611295119487242595462301e+0012L, 578 3.548217088622398274748837287769709374385e+0011L, 579 -2.934470341719047120076509938432417352365e+0010L, 580 }; 581 static GENERIC qr3[13] = { 582 3.749999999999412724084579833297451472091e-0001L, 583 9.058478580291706212422978492938435582527e+0001L, 584 8.524056033161038750461083666711724381171e+0003L, 585 4.105967158629109427753434569223631014730e+0005L, 586 1.118326603378531348259783091972623333657e+0007L, 587 1.794636683403578918528064904714132329343e+0008L, 588 1.714314157463635959556133236004368896724e+0009L, 589 9.622092032236084846572067257267661456030e+0009L, 590 3.057759524485859159957762858780768355020e+0010L, 591 5.129306780754798531609621454415938890020e+0010L, 592 3.999122002794961070680636194346316041352e+0010L, 593 1.122298454643493485989721564358100345388e+0010L, 594 5.603981987645989709668830968522362582221e+0008L, 595 }; 596 static GENERIC qs3[13] = { 597 1.0e0L, 598 2.418328663076578169836155170053634419922e+0002L, 599 2.279620205900121042587523541281272875520e+0004L, 600 1.100984222585729521470129014992217092794e+0006L, 601 3.010743223679247091004262516286654516282e+0007L, 602 4.860925542827367817289619265215599433996e+0008L, 603 4.686668111035348691982715864307839581243e+0009L, 604 2.668701788405102017427214705946730894074e+0010L, 605 8.677395746106802640390580944836650584903e+0010L, 606 1.511936455574951790658498795945106643036e+0011L, 607 1.260845604432623478002018696873608353093e+0011L, 608 4.052692278419853853911440231600864589805e+0010L, 609 2.965516519212226064983267822243329694729e+0009L, 610 }; 611 static GENERIC qr4[13] = { 612 3.749999999919234164154669754440123072618e-0001L, 613 5.844218580776819864791168253485055101858e+0001L, 614 3.489273514092912982675669411371435670220e+0003L, 615 1.050523637774575684509663430018995479594e+0005L, 616 1.764549172059701565500717319792780115289e+0006L, 617 1.725532438844133795028063102681497371154e+0007L, 618 9.938114847359778539965140247590176334874e+0007L, 619 3.331710808184595545396883770200772842314e+0008L, 620 6.271970557641881511609560444872797282698e+0008L, 621 6.188529798677357075020774923903737913285e+0008L, 622 2.821905302742849974509982167877885011629e+0008L, 623 4.615467358646911976773290256984329814896e+0007L, 624 1.348140608731546467396685802693380693275e+0006L, 625 }; 626 static GENERIC qs4[13] = { 627 1.0e0L, 628 1.561192663112345185261418296389902133372e+0002L, 629 9.346678031144098270547225423124213083072e+0003L, 630 2.825851246482293547838023847601704751590e+0005L, 631 4.776572711622156091710902891124911556293e+0006L, 632 4.715106953717135402977938048006267859302e+0007L, 633 2.753962350894311316439652227611209035193e+0008L, 634 9.428501434615463207768964787500411575223e+0008L, 635 1.832650858775206787088236896454141572617e+0009L, 636 1.901697378939743226948920874296595242257e+0009L, 637 9.433322226854293780627188599226380812725e+0008L, 638 1.808520540608671608680284520798858587370e+0008L, 639 7.983342331736662753157217446919462398008e+0006L, 640 }; 641 static GENERIC qr5[13] = { 642 3.749999995331364437028988850515190446719e-0001L, 643 3.739356381766559882677514593041627547911e+0001L, 644 1.399562500629413529355265462912819802551e+0003L, 645 2.594154053098947925345332218062210111753e+0004L, 646 2.640149879297408640394163979394594318371e+0005L, 647 1.542471854873199142031889093591449397995e+0006L, 648 5.242272868972053374067572098992335425895e+0006L, 649 1.025834487769410221329633071426044839935e+0007L, 650 1.116553924239448940142230579060124209622e+0007L, 651 6.318076065595910176374916303525884653514e+0006L, 652 1.641218086168640408527639735915512881785e+0006L, 653 1.522369793529178644168813882912134706444e+0005L, 654 2.526530541062297200914180060208669584055e+0003L, 655 }; 656 static GENERIC qs5[13] = { 657 1.0e0L, 658 9.998960735935075380397545659016287506660e+0001L, 659 3.758767417842043742686475060540416737562e+0003L, 660 7.013652806952306520121959742519780781653e+0004L, 661 7.208949808818615099246529616211730446850e+0005L, 662 4.272753927109614455417836186072202009252e+0006L, 663 1.482524411356470699336129814111025434703e+0007L, 664 2.988750366665678233425279237627700803473e+0007L, 665 3.396957890261080492694709150553619185065e+0007L, 666 2.050652487738593004111578091156304540386e+0007L, 667 5.900504120811732547616511555946279451316e+0006L, 668 6.563391409260160897024498082273183468347e+0005L, 669 1.692629845012790205348966731477187041419e+0004L, 670 }; 671 static GENERIC qr6[13] = { 672 3.749999861516664133157566870858975421296e-0001L, 673 2.367863756747764863120797431599473468918e+0001L, 674 5.476715802114976248882067325630793143777e+0002L, 675 6.143190357869842894025012945444096170251e+0003L, 676 3.716250534677997850513733595140463851730e+0004L, 677 1.270883463823876752138326905022875657430e+0005L, 678 2.495301449636814481646371665429083801388e+0005L, 679 2.789578988212952248340486296254398601942e+0005L, 680 1.718247946911109055931819087137397324634e+0005L, 681 5.458973214011665714330326732204106364229e+0004L, 682 7.912102686687948786048943339759596652813e+0003L, 683 4.077961006160866935722030715149087938091e+0002L, 684 3.765206972770245085551057237882528510428e+0000L, 685 }; 686 static GENERIC qs6[13] = { 687 1.0e0L, 688 6.341646532940517305641893852673926809601e+0001L, 689 1.477058277414040790932597537920671025359e+0003L, 690 1.674406564031044491436044253393536487604e+0004L, 691 1.028516501369755949895050806908994650768e+0005L, 692 3.593620042532885295087463507733285434207e+0005L, 693 7.267924991381020915185873399453724799625e+0005L, 694 8.462277510768818399961191426205006083088e+0005L, 695 5.514399892230892163373611895645500250514e+0005L, 696 1.898084241009259353540620272932188102299e+0005L, 697 3.102941242117739015721984123081026253068e+0004L, 698 1.958971184431466907681440650181421086143e+0003L, 699 2.878853357310495087181721613889455121867e+0001L, 700 }; 701 static GENERIC qone(x) 702 GENERIC x; 703 { 704 GENERIC s, r, t, z; 705 int i; 706 if (x > huge) 707 return (0.375L/x); 708 t = one/x; z = t*t; 709 if (x > sixteen) { 710 r = z*qr0[11]+qr0[10]; s = qs0[10]; 711 for (i = 9; i >= 0; i--) { 712 r = z*r + qr0[i]; 713 s = z*s + qs0[i]; 714 } 715 } else if (x > eight) { 716 r = qr1[11]; s = qs1[11]+z*(qs1[12]+z*qs1[13]); 717 for (i = 10; i >= 0; i--) { 718 r = z*r + qr1[i]; 719 s = z*s + qs1[i]; 720 } 721 } else if (x > five) { /* x > 5.0 */ 722 r = qr2[11]; s = qs2[11]+z*(qs2[12]+z*qs2[13]); 723 for (i = 10; i >= 0; i--) { 724 r = z*r + qr2[i]; 725 s = z*s + qs2[i]; 726 } 727 } else if (x > 3.5L) { 728 r = qr3[12]; s = qs3[12]; 729 for (i = 11; i >= 0; i--) { 730 r = z*r + qr3[i]; 731 s = z*s + qs3[i]; 732 } 733 } else if (x > 2.5L) { 734 r = qr4[12]; s = qs4[12]; 735 for (i = 11; i >= 0; i--) { 736 r = z*r + qr4[i]; 737 s = z*s + qs4[i]; 738 } 739 } else if (x > (1.0L/0.5625L)) { 740 r = qr5[12]; s = qs5[12]; 741 for (i = 11; i >= 0; i--) { 742 r = z*r + qr5[i]; 743 s = z*s + qs5[i]; 744 } 745 } else { /* assume x > 1.28 */ 746 r = qr6[12]; s = qs6[12]; 747 for (i = 11; i >= 0; i--) { 748 r = z*r + qr6[i]; 749 s = z*s + qs6[i]; 750 } 751 } 752 return (t*(r/s)); 753 } 754