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5261 libm should stop using synonyms.h
5298 fabs is 0-sized, confuses dis(1) and others
Reviewed by: Josef 'Jeff' Sipek <jeffpc@josefsipek.net>
Approved by: Gordon Ross <gwr@nexenta.com>
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--- old/usr/src/lib/libm/common/R/besself.c
+++ new/usr/src/lib/libm/common/R/besself.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
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19 19 * CDDL HEADER END
20 20 */
21 21 /*
22 22 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 23 */
24 24 /*
25 25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 26 * Use is subject to license terms.
27 27 */
28 28
29 -#pragma weak j0f = __j0f
30 -#pragma weak j1f = __j1f
31 -#pragma weak jnf = __jnf
32 -#pragma weak y0f = __y0f
33 -#pragma weak y1f = __y1f
34 -#pragma weak ynf = __ynf
29 +#pragma weak __j0f = j0f
30 +#pragma weak __j1f = j1f
31 +#pragma weak __jnf = jnf
32 +#pragma weak __y0f = y0f
33 +#pragma weak __y1f = y1f
34 +#pragma weak __ynf = ynf
35 35
36 36 #include "libm.h"
37 37 #include <float.h>
38 38
39 39 #if defined(__i386) && !defined(__amd64)
40 40 extern int __swapRP(int);
41 41 #endif
42 42
43 43 static const float
44 44 zerof = 0.0f,
45 45 onef = 1.0f;
46 46
47 47 static const double C[] = {
48 48 0.0,
49 49 -0.125,
50 50 0.25,
51 51 0.375,
52 52 0.5,
53 53 1.0,
54 54 2.0,
55 55 8.0,
56 56 0.5641895835477562869480794515607725858441, /* 1/sqrt(pi) */
57 57 0.636619772367581343075535053490057448, /* 2/pi */
58 58 1.0e9,
59 59 };
60 60
61 61 #define zero C[0]
62 62 #define neighth C[1]
63 63 #define quarter C[2]
64 64 #define three8 C[3]
65 65 #define half C[4]
66 66 #define one C[5]
67 67 #define two C[6]
68 68 #define eight C[7]
69 69 #define isqrtpi C[8]
70 70 #define tpi C[9]
71 71 #define big C[10]
72 72
73 73 static const double Cj0y0[] = {
74 74 0.4861344183386052721391238447e5, /* pr */
75 75 0.1377662549407112278133438945e6,
76 76 0.1222466364088289731869114004e6,
77 77 0.4107070084315176135583353374e5,
78 78 0.5026073801860637125889039915e4,
79 79 0.1783193659125479654541542419e3,
80 80 0.88010344055383421691677564e0,
81 81 0.4861344183386052721414037058e5, /* ps */
82 82 0.1378196632630384670477582699e6,
83 83 0.1223967185341006542748936787e6,
84 84 0.4120150243795353639995862617e5,
85 85 0.5068271181053546392490184353e4,
86 86 0.1829817905472769960535671664e3,
87 87 1.0,
88 88 -0.1731210995701068539185611951e3, /* qr */
89 89 -0.5522559165936166961235240613e3,
90 90 -0.5604935606637346590614529613e3,
91 91 -0.2200430300226009379477365011e3,
92 92 -0.323869355375648849771296746e2,
93 93 -0.14294979207907956223499258e1,
94 94 -0.834690374102384988158918e-2,
95 95 0.1107975037248683865326709645e5, /* qs */
96 96 0.3544581680627082674651471873e5,
97 97 0.3619118937918394132179019059e5,
98 98 0.1439895563565398007471485822e5,
99 99 0.2190277023344363955930226234e4,
100 100 0.106695157020407986137501682e3,
101 101 1.0,
102 102 };
103 103
104 104 #define pr Cj0y0
105 105 #define ps (Cj0y0+7)
106 106 #define qr (Cj0y0+14)
107 107 #define qs (Cj0y0+21)
108 108
109 109 static const double Cj0[] = {
110 110 -2.500000000000003622131880894830476755537e-0001, /* r0 */
111 111 1.095597547334830263234433855932375353303e-0002,
112 112 -1.819734750463320921799187258987098087697e-0004,
113 113 9.977001946806131657544212501069893930846e-0007,
114 114 1.0, /* s0 */
115 115 1.867609810662950169966782360588199673741e-0002,
116 116 1.590389206181565490878430827706972074208e-0004,
117 117 6.520867386742583632375520147714499522721e-0007,
118 118 9.999999999999999942156495584397047660949e-0001, /* r1 */
119 119 -2.389887722731319130476839836908143731281e-0001,
120 120 1.293359476138939027791270393439493640570e-0002,
121 121 -2.770985642343140122168852400228563364082e-0004,
122 122 2.905241575772067678086738389169625218912e-0006,
123 123 -1.636846356264052597969042009265043251279e-0008,
124 124 5.072306160724884775085431059052611737827e-0011,
125 125 -8.187060730684066824228914775146536139112e-0014,
126 126 5.422219326959949863954297860723723423842e-0017,
127 127 1.0, /* s1 */
128 128 1.101122772686807702762104741932076228349e-0002,
129 129 6.140169310641649223411427764669143978228e-0005,
130 130 2.292035877515152097976946119293215705250e-0007,
131 131 6.356910426504644334558832036362219583789e-0010,
132 132 1.366626326900219555045096999553948891401e-0012,
133 133 2.280399586866739522891837985560481180088e-0015,
134 134 2.801559820648939665270492520004836611187e-0018,
135 135 2.073101088320349159764410261466350732968e-0021,
136 136 };
137 137
138 138 #define r0 Cj0
139 139 #define s0 (Cj0+4)
140 140 #define r1 (Cj0+8)
141 141 #define s1 (Cj0+17)
142 142
143 143 static const double Cy0[] = {
144 144 -7.380429510868722526754723020704317641941e-0002, /* u0 */
145 145 1.772607102684869924301459663049874294814e-0001,
146 146 -1.524370666542713828604078090970799356306e-0002,
147 147 4.650819100693891757143771557629924591915e-0004,
148 148 -7.125768872339528975036316108718239946022e-0006,
149 149 6.411017001656104598327565004771515257146e-0008,
150 150 -3.694275157433032553021246812379258781665e-0010,
151 151 1.434364544206266624252820889648445263842e-0012,
152 152 -3.852064731859936455895036286874139896861e-0015,
153 153 7.182052899726138381739945881914874579696e-0018,
154 154 -9.060556574619677567323741194079797987200e-0021,
155 155 7.124435467408860515265552217131230511455e-0024,
156 156 -2.709726774636397615328813121715432044771e-0027,
157 157 1.0, /* v0 */
158 158 4.678678931512549002587702477349214886475e-0003,
159 159 9.486828955529948534822800829497565178985e-0006,
160 160 1.001495929158861646659010844136682454906e-0008,
161 161 4.725338116256021660204443235685358593611e-0012,
162 162 };
163 163
164 164 #define u0 Cy0
165 165 #define v0 (Cy0+13)
166 166
167 167 static const double Cj1y1[] = {
168 168 -0.4435757816794127857114720794e7, /* pr0 */
169 169 -0.9942246505077641195658377899e7,
170 170 -0.6603373248364939109255245434e7,
171 171 -0.1523529351181137383255105722e7,
172 172 -0.1098240554345934672737413139e6,
173 173 -0.1611616644324610116477412898e4,
174 174 -0.4435757816794127856828016962e7, /* ps0 */
175 175 -0.9934124389934585658967556309e7,
176 176 -0.6585339479723087072826915069e7,
177 177 -0.1511809506634160881644546358e7,
178 178 -0.1072638599110382011903063867e6,
179 179 -0.1455009440190496182453565068e4,
180 180 0.3322091340985722351859704442e5, /* qr0 */
181 181 0.8514516067533570196555001171e5,
182 182 0.6617883658127083517939992166e5,
183 183 0.1849426287322386679652009819e5,
184 184 0.1706375429020768002061283546e4,
185 185 0.3526513384663603218592175580e2,
186 186 0.7087128194102874357377502472e6, /* qs0 */
187 187 0.1819458042243997298924553839e7,
188 188 0.1419460669603720892855755253e7,
189 189 0.4002944358226697511708610813e6,
190 190 0.3789022974577220264142952256e5,
191 191 0.8638367769604990967475517183e3,
192 192 };
193 193
194 194 #define pr0 Cj1y1
195 195 #define ps0 (Cj1y1+6)
196 196 #define qr0 (Cj1y1+12)
197 197 #define qs0 (Cj1y1+18)
198 198
199 199 static const double Cj1[] = {
200 200 -6.250000000000002203053200981413218949548e-0002, /* a0 */
201 201 1.600998455640072901321605101981501263762e-0003,
202 202 -1.963888815948313758552511884390162864930e-0005,
203 203 8.263917341093549759781339713418201620998e-0008,
204 204 1.0e0, /* b0 */
205 205 1.605069137643004242395356851797873766927e-0002,
206 206 1.149454623251299996428500249509098499383e-0004,
207 207 3.849701673735260970379681807910852327825e-0007,
208 208 4.999999999999999995517408894340485471724e-0001,
209 209 -6.003825028120475684835384519945468075423e-0002,
210 210 2.301719899263321828388344461995355419832e-0003,
211 211 -4.208494869238892934859525221654040304068e-0005,
212 212 4.377745135188837783031540029700282443388e-0007,
213 213 -2.854106755678624335145364226735677754179e-0009,
214 214 1.234002865443952024332943901323798413689e-0011,
215 215 -3.645498437039791058951273508838177134310e-0014,
216 216 7.404320596071797459925377103787837414422e-0017,
217 217 -1.009457448277522275262808398517024439084e-0019,
218 218 8.520158355824819796968771418801019930585e-0023,
219 219 -3.458159926081163274483854614601091361424e-0026,
220 220 1.0e0, /* b1 */
221 221 4.923499437590484879081138588998986303306e-0003,
222 222 1.054389489212184156499666953501976688452e-0005,
223 223 1.180768373106166527048240364872043816050e-0008,
224 224 5.942665743476099355323245707680648588540e-0012,
225 225 };
226 226
227 227 #define a0 Cj1
228 228 #define b0 (Cj1+4)
229 229 #define a1 (Cj1+8)
230 230 #define b1 (Cj1+20)
231 231
232 232 static const double Cy1[] = {
233 233 -1.960570906462389461018983259589655961560e-0001, /* c0 */
234 234 4.931824118350661953459180060007970291139e-0002,
235 235 -1.626975871565393656845930125424683008677e-0003,
236 236 1.359657517926394132692884168082224258360e-0005,
237 237 1.0e0, /* d0 */
238 238 2.565807214838390835108224713630901653793e-0002,
239 239 3.374175208978404268650522752520906231508e-0004,
240 240 2.840368571306070719539936935220728843177e-0006,
241 241 1.396387402048998277638900944415752207592e-0008,
242 242 -1.960570906462389473336339614647555351626e-0001, /* c1 */
243 243 5.336268030335074494231369159933012844735e-0002,
244 244 -2.684137504382748094149184541866332033280e-0003,
245 245 5.737671618979185736981543498580051903060e-0005,
246 246 -6.642696350686335339171171785557663224892e-0007,
247 247 4.692417922568160354012347591960362101664e-0009,
248 248 -2.161728635907789319335231338621412258355e-0011,
249 249 6.727353419738316107197644431844194668702e-0014,
250 250 -1.427502986803861372125234355906790573422e-0016,
251 251 2.020392498726806769468143219616642940371e-0019,
252 252 -1.761371948595104156753045457888272716340e-0022,
253 253 7.352828391941157905175042420249225115816e-0026,
254 254 1.0e0, /* d1 */
255 255 5.029187436727947764916247076102283399442e-0003,
256 256 1.102693095808242775074856548927801750627e-0005,
257 257 1.268035774543174837829534603830227216291e-0008,
258 258 6.579416271766610825192542295821308730206e-0012,
259 259 };
260 260
261 261 #define c0 Cy1
262 262 #define d0 (Cy1+4)
263 263 #define c1 (Cy1+9)
264 264 #define d1 (Cy1+21)
265 265
266 266
267 267 /* core of j0f computation; assumes fx is finite */
268 268 static double
269 269 __k_j0f(float fx)
270 270 {
271 271 double x, z, s, c, ss, cc, r, t, p0, q0;
272 272 int ix, i;
273 273
274 274 ix = *(int *)&fx & ~0x80000000;
275 275 x = fabs((double)fx);
276 276 if (ix > 0x41000000) {
277 277 /* x > 8; see comments in j0.c */
278 278 s = sin(x);
279 279 c = cos(x);
280 280 if (signbit(s) != signbit(c)) {
281 281 ss = s - c;
282 282 cc = -cos(x + x) / ss;
283 283 } else {
284 284 cc = s + c;
285 285 ss = -cos(x + x) / cc;
286 286 }
287 287 if (ix > 0x501502f9) {
288 288 /* x > 1.0e10 */
289 289 p0 = one;
290 290 q0 = neighth / x;
291 291 } else {
292 292 t = eight / x;
293 293 z = t * t;
294 294 p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] +
295 295 z * (pr[4] + z * (pr[5] + z * pr[6])))))) /
296 296 (ps[0] + z * (ps[1] + z * (ps[2] + z * (ps[3] +
297 297 z * (ps[4] + z * (ps[5] + z))))));
298 298 q0 = ((qr[0] + z * (qr[1] + z * (qr[2] + z * (qr[3] +
299 299 z * (qr[4] + z * (qr[5] + z * qr[6])))))) /
300 300 (qs[0] + z * (qs[1] + z * (qs[2] + z * (qs[3] +
301 301 z * (qs[4] + z * (qs[5] + z))))))) * t;
302 302 }
303 303 return (isqrtpi * (p0 * cc - q0 * ss) / sqrt(x));
304 304 }
305 305 if (ix <= 0x3727c5ac) {
306 306 /* x <= 1.0e-5 */
307 307 if (ix <= 0x219392ef) /* x <= 1.0e-18 */
308 308 return (one - x);
309 309 return (one - x * x * quarter);
310 310 }
311 311 z = x * x;
312 312 if (ix <= 0x3fa3d70a) {
313 313 /* x <= 1.28 */
314 314 r = r0[0] + z * (r0[1] + z * (r0[2] + z * r0[3]));
315 315 s = s0[0] + z * (s0[1] + z * (s0[2] + z * s0[3]));
316 316 return (one + z * (r / s));
317 317 }
318 318 r = r1[8];
319 319 s = s1[8];
320 320 for (i = 7; i >= 0; i--) {
321 321 r = r * z + r1[i];
322 322 s = s * z + s1[i];
323 323 }
324 324 return (r / s);
325 325 }
326 326
327 327 float
328 328 j0f(float fx)
329 329 {
330 330 float f;
331 331 int ix;
332 332 #if defined(__i386) && !defined(__amd64)
333 333 int rp;
334 334 #endif
335 335
336 336 ix = *(int *)&fx & ~0x80000000;
337 337 if (ix >= 0x7f800000) { /* nan or inf */
338 338 if (ix > 0x7f800000)
339 339 return (fx * fx);
340 340 return (zerof);
341 341 }
342 342
343 343 #if defined(__i386) && !defined(__amd64)
344 344 rp = __swapRP(fp_extended);
345 345 #endif
346 346 f = (float)__k_j0f(fx);
347 347 #if defined(__i386) && !defined(__amd64)
348 348 if (rp != fp_extended)
349 349 (void) __swapRP(rp);
350 350 #endif
351 351 return (f);
352 352 }
353 353
354 354 /* core of y0f computation; assumes fx is finite and positive */
355 355 static double
356 356 __k_y0f(float fx)
357 357 {
358 358 double x, z, s, c, ss, cc, t, p0, q0, u, v;
359 359 int ix, i;
360 360
361 361 ix = *(int *)&fx;
362 362 x = (double)fx;
363 363 if (ix > 0x41000000) {
364 364 /* x > 8; see comments in j0.c */
365 365 s = sin(x);
366 366 c = cos(x);
367 367 if (signbit(s) != signbit(c)) {
368 368 ss = s - c;
369 369 cc = -cos(x + x) / ss;
370 370 } else {
371 371 cc = s + c;
372 372 ss = -cos(x + x) / cc;
373 373 }
374 374 if (ix > 0x501502f9) {
375 375 /* x > 1.0e10 */
376 376 p0 = one;
377 377 q0 = neighth / x;
378 378 } else {
379 379 t = eight / x;
380 380 z = t * t;
381 381 p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] +
382 382 z * (pr[4] + z * (pr[5] + z * pr[6])))))) /
383 383 (ps[0] + z * (ps[1] + z * (ps[2] + z * (ps[3] +
384 384 z * (ps[4] + z * (ps[5] + z))))));
385 385 q0 = ((qr[0] + z * (qr[1] + z * (qr[2] + z * (qr[3] +
386 386 z * (qr[4] + z * (qr[5] + z * qr[6])))))) /
387 387 (qs[0] + z * (qs[1] + z * (qs[2] + z * (qs[3] +
388 388 z * (qs[4] + z * (qs[5] + z))))))) * t;
389 389 }
390 390 return (isqrtpi * (p0 * ss + q0 * cc) / sqrt(x));
391 391 }
392 392 if (ix <= 0x219392ef) /* x <= 1.0e-18 */
393 393 return (u0[0] + tpi * log(x));
394 394 z = x * x;
395 395 u = u0[12];
396 396 for (i = 11; i >= 0; i--)
397 397 u = u * z + u0[i];
398 398 v = v0[0] + z * (v0[1] + z * (v0[2] + z * (v0[3] + z * v0[4])));
399 399 return (u / v + tpi * (__k_j0f(fx) * log(x)));
400 400 }
401 401
402 402 float
403 403 y0f(float fx)
404 404 {
405 405 float f;
406 406 int ix;
407 407 #if defined(__i386) && !defined(__amd64)
408 408 int rp;
409 409 #endif
410 410
411 411 ix = *(int *)&fx;
412 412 if ((ix & ~0x80000000) > 0x7f800000) /* nan */
413 413 return (fx * fx);
414 414 if (ix <= 0) { /* zero or negative */
415 415 if ((ix << 1) == 0)
416 416 return (-onef / zerof);
417 417 return (zerof / zerof);
418 418 }
419 419 if (ix == 0x7f800000) /* +inf */
420 420 return (zerof);
421 421
422 422 #if defined(__i386) && !defined(__amd64)
423 423 rp = __swapRP(fp_extended);
424 424 #endif
425 425 f = (float)__k_y0f(fx);
426 426 #if defined(__i386) && !defined(__amd64)
427 427 if (rp != fp_extended)
428 428 (void) __swapRP(rp);
429 429 #endif
430 430 return (f);
431 431 }
432 432
433 433 /* core of j1f computation; assumes fx is finite */
434 434 static double
435 435 __k_j1f(float fx)
436 436 {
437 437 double x, z, s, c, ss, cc, r, t, p1, q1;
438 438 int i, ix, sgn;
439 439
440 440 ix = *(int *)&fx;
441 441 sgn = (unsigned)ix >> 31;
442 442 ix &= ~0x80000000;
443 443 x = fabs((double)fx);
444 444 if (ix > 0x41000000) {
445 445 /* x > 8; see comments in j1.c */
446 446 s = sin(x);
447 447 c = cos(x);
448 448 if (signbit(s) != signbit(c)) {
449 449 cc = s - c;
450 450 ss = cos(x + x) / cc;
451 451 } else {
452 452 ss = -s - c;
453 453 cc = cos(x + x) / ss;
454 454 }
455 455 if (ix > 0x501502f9) {
456 456 /* x > 1.0e10 */
457 457 p1 = one;
458 458 q1 = three8 / x;
459 459 } else {
460 460 t = eight / x;
461 461 z = t * t;
462 462 p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z *
463 463 (pr0[3] + z * (pr0[4] + z * pr0[5]))))) /
464 464 (ps0[0] + z * (ps0[1] + z * (ps0[2] + z *
465 465 (ps0[3] + z * (ps0[4] + z * (ps0[5] + z))))));
466 466 q1 = ((qr0[0] + z * (qr0[1] + z * (qr0[2] + z *
467 467 (qr0[3] + z * (qr0[4] + z * qr0[5]))))) /
468 468 (qs0[0] + z * (qs0[1] + z * (qs0[2] + z *
469 469 (qs0[3] + z * (qs0[4] + z * (qs0[5] + z))))))) * t;
470 470 }
471 471 t = isqrtpi * (p1 * cc - q1 * ss) / sqrt(x);
472 472 return ((sgn)? -t : t);
473 473 }
474 474 if (ix <= 0x3727c5ac) {
475 475 /* x <= 1.0e-5 */
476 476 if (ix <= 0x219392ef) /* x <= 1.0e-18 */
477 477 t = half * x;
478 478 else
479 479 t = x * (half + neighth * x * x);
480 480 return ((sgn)? -t : t);
481 481 }
482 482 z = x * x;
483 483 if (ix < 0x3fa3d70a) {
484 484 /* x < 1.28 */
485 485 r = a0[0] + z * (a0[1] + z * (a0[2] + z * a0[3]));
486 486 s = b0[0] + z * (b0[1] + z * (b0[2] + z * b0[3]));
487 487 t = x * half + x * (z * (r / s));
488 488 } else {
489 489 r = a1[11];
490 490 for (i = 10; i >= 0; i--)
491 491 r = r * z + a1[i];
492 492 s = b1[0] + z * (b1[1] + z * (b1[2] + z * (b1[3] + z * b1[4])));
493 493 t = x * (r / s);
494 494 }
495 495 return ((sgn)? -t : t);
496 496 }
497 497
498 498 float
499 499 j1f(float fx)
500 500 {
501 501 float f;
502 502 int ix;
503 503 #if defined(__i386) && !defined(__amd64)
504 504 int rp;
505 505 #endif
506 506
507 507 ix = *(int *)&fx & ~0x80000000;
508 508 if (ix >= 0x7f800000) /* nan or inf */
509 509 return (onef / fx);
510 510
511 511 #if defined(__i386) && !defined(__amd64)
512 512 rp = __swapRP(fp_extended);
513 513 #endif
514 514 f = (float)__k_j1f(fx);
515 515 #if defined(__i386) && !defined(__amd64)
516 516 if (rp != fp_extended)
517 517 (void) __swapRP(rp);
518 518 #endif
519 519 return (f);
520 520 }
521 521
522 522 /* core of y1f computation; assumes fx is finite and positive */
523 523 static double
524 524 __k_y1f(float fx)
525 525 {
526 526 double x, z, s, c, ss, cc, u, v, p1, q1, t;
527 527 int i, ix;
528 528
529 529 ix = *(int *)&fx;
530 530 x = (double)fx;
531 531 if (ix > 0x41000000) {
532 532 /* x > 8; see comments in j1.c */
533 533 s = sin(x);
534 534 c = cos(x);
535 535 if (signbit(s) != signbit(c)) {
536 536 cc = s - c;
537 537 ss = cos(x + x) / cc;
538 538 } else {
539 539 ss = -s - c;
540 540 cc = cos(x + x) / ss;
541 541 }
542 542 if (ix > 0x501502f9) {
543 543 /* x > 1.0e10 */
544 544 p1 = one;
545 545 q1 = three8 / x;
546 546 } else {
547 547 t = eight / x;
548 548 z = t * t;
549 549 p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z *
550 550 (pr0[3] + z * (pr0[4] + z * pr0[5]))))) /
551 551 (ps0[0] + z * (ps0[1] + z * (ps0[2] + z *
552 552 (ps0[3] + z * (ps0[4] + z * (ps0[5] + z))))));
553 553 q1 = ((qr0[0] + z * (qr0[1] + z * (qr0[2] + z *
554 554 (qr0[3] + z * (qr0[4] + z * qr0[5]))))) /
555 555 (qs0[0] + z * (qs0[1] + z * (qs0[2] + z *
556 556 (qs0[3] + z * (qs0[4] + z * (qs0[5] + z))))))) * t;
557 557 }
558 558 return (isqrtpi * (p1 * ss + q1 * cc) / sqrt(x));
559 559 }
560 560 if (ix <= 0x219392ef) /* x <= 1.0e-18 */
561 561 return (-tpi / x);
562 562 z = x * x;
563 563 if (ix < 0x3fa3d70a) {
564 564 /* x < 1.28 */
565 565 u = c0[0] + z * (c0[1] + z * (c0[2] + z * c0[3]));
566 566 v = d0[0] + z * (d0[1] + z * (d0[2] + z * (d0[3] + z * d0[4])));
567 567 } else {
568 568 u = c1[11];
569 569 for (i = 10; i >= 0; i--)
570 570 u = u * z + c1[i];
571 571 v = d1[0] + z * (d1[1] + z * (d1[2] + z * (d1[3] + z * d1[4])));
572 572 }
573 573 return (x * (u / v) + tpi * (__k_j1f(fx) * log(x) - one / x));
574 574 }
575 575
576 576 float
577 577 y1f(float fx)
578 578 {
579 579 float f;
580 580 int ix;
581 581 #if defined(__i386) && !defined(__amd64)
582 582 int rp;
583 583 #endif
584 584
585 585 ix = *(int *)&fx;
586 586 if ((ix & ~0x80000000) > 0x7f800000) /* nan */
587 587 return (fx * fx);
588 588 if (ix <= 0) { /* zero or negative */
589 589 if ((ix << 1) == 0)
590 590 return (-onef / zerof);
591 591 return (zerof / zerof);
592 592 }
593 593 if (ix == 0x7f800000) /* +inf */
594 594 return (zerof);
595 595
596 596 #if defined(__i386) && !defined(__amd64)
597 597 rp = __swapRP(fp_extended);
598 598 #endif
599 599 f = (float)__k_y1f(fx);
600 600 #if defined(__i386) && !defined(__amd64)
601 601 if (rp != fp_extended)
602 602 (void) __swapRP(rp);
603 603 #endif
604 604 return (f);
605 605 }
606 606
607 607 float
608 608 jnf(int n, float fx)
609 609 {
610 610 double a, b, temp, x, z, w, t, q0, q1, h;
611 611 float f;
612 612 int i, ix, sgn, m, k;
613 613 #if defined(__i386) && !defined(__amd64)
614 614 int rp;
615 615 #endif
616 616
617 617 if (n < 0) {
618 618 n = -n;
619 619 fx = -fx;
620 620 }
621 621 if (n == 0)
622 622 return (j0f(fx));
623 623 if (n == 1)
624 624 return (j1f(fx));
625 625
626 626 ix = *(int *)&fx;
627 627 sgn = (n & 1)? ((unsigned)ix >> 31) : 0;
628 628 ix &= ~0x80000000;
629 629 if (ix >= 0x7f800000) { /* nan or inf */
630 630 if (ix > 0x7f800000)
631 631 return (fx * fx);
632 632 return ((sgn)? -zerof : zerof);
633 633 }
634 634 if ((ix << 1) == 0)
635 635 return ((sgn)? -zerof : zerof);
636 636
637 637 #if defined(__i386) && !defined(__amd64)
638 638 rp = __swapRP(fp_extended);
639 639 #endif
640 640 fx = fabsf(fx);
641 641 x = (double)fx;
642 642 if ((double)n <= x) {
643 643 /* safe to use J(n+1,x) = 2n/x * J(n,x) - J(n-1,x) */
644 644 a = __k_j0f(fx);
645 645 b = __k_j1f(fx);
646 646 for (i = 1; i < n; i++) {
647 647 temp = b;
648 648 b = b * ((double)(i + i) / x) - a;
649 649 a = temp;
650 650 }
651 651 f = (float)b;
652 652 #if defined(__i386) && !defined(__amd64)
653 653 if (rp != fp_extended)
654 654 (void) __swapRP(rp);
655 655 #endif
656 656 return ((sgn)? -f : f);
657 657 }
658 658 if (ix < 0x3089705f) {
659 659 /* x < 1.0e-9; use J(n,x) = 1/n! * (x / 2)^n */
660 660 if (n > 6)
661 661 n = 6; /* result underflows to zero for n >= 6 */
662 662 b = t = half * x;
663 663 a = one;
664 664 for (i = 2; i <= n; i++) {
665 665 b *= t;
666 666 a *= (double)i;
667 667 }
668 668 b /= a;
669 669 } else {
670 670 /*
671 671 * Use the backward recurrence:
672 672 *
673 673 * x x^2 x^2
674 674 * J(n,x)/J(n-1,x) = ---- - ------ - ------ .....
675 675 * 2n 2(n+1) 2(n+2)
676 676 *
677 677 * Let w = 2n/x and h = 2/x. Then the above quotient
678 678 * is equal to the continued fraction:
679 679 * 1
680 680 * = -----------------------
681 681 * 1
682 682 * w - -----------------
683 683 * 1
684 684 * w+h - ---------
685 685 * w+2h - ...
686 686 *
687 687 * To determine how many terms are needed, run the
688 688 * recurrence
689 689 *
690 690 * Q(0) = w,
691 691 * Q(1) = w(w+h) - 1,
692 692 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2).
693 693 *
694 694 * Then when Q(k) > 1e4, k is large enough for single
695 695 * precision.
696 696 */
697 697 /* XXX NOT DONE - rework this */
698 698 w = (n + n) / x;
699 699 h = two / x;
700 700 q0 = w;
701 701 z = w + h;
702 702 q1 = w * z - one;
703 703 k = 1;
704 704 while (q1 < big) {
705 705 k++;
706 706 z += h;
707 707 temp = z * q1 - q0;
708 708 q0 = q1;
709 709 q1 = temp;
710 710 }
711 711 m = n + n;
712 712 t = zero;
713 713 for (i = (n + k) << 1; i >= m; i -= 2)
714 714 t = one / ((double)i / x - t);
715 715 a = t;
716 716 b = one;
717 717 /*
718 718 * estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
719 719 * hence, if n*(log(2n/x)) > ...
720 720 * single 8.8722839355e+01
721 721 * double 7.09782712893383973096e+02
722 722 * then recurrent value may overflow and the result is
723 723 * likely underflow to zero
724 724 */
725 725 temp = (double)n;
726 726 temp *= log((two / x) * temp);
727 727 if (temp < 7.09782712893383973096e+02) {
728 728 for (i = n - 1; i > 0; i--) {
729 729 temp = b;
730 730 b = b * ((double)(i + i) / x) - a;
731 731 a = temp;
732 732 }
733 733 } else {
734 734 for (i = n - 1; i > 0; i--) {
735 735 temp = b;
736 736 b = b * ((double)(i + i) / x) - a;
737 737 a = temp;
738 738 if (b > 1.0e100) {
739 739 a /= b;
740 740 t /= b;
741 741 b = one;
742 742 }
743 743 }
744 744 }
745 745 b = (t * __k_j0f(fx) / b);
746 746 }
747 747 f = (float)b;
748 748 #if defined(__i386) && !defined(__amd64)
749 749 if (rp != fp_extended)
750 750 (void) __swapRP(rp);
751 751 #endif
752 752 return ((sgn)? -f : f);
753 753 }
754 754
755 755 float
756 756 ynf(int n, float fx)
757 757 {
758 758 double a, b, temp, x;
759 759 float f;
760 760 int i, sign, ix;
761 761 #if defined(__i386) && !defined(__amd64)
762 762 int rp;
763 763 #endif
764 764
765 765 sign = 0;
766 766 if (n < 0) {
767 767 n = -n;
768 768 if (n & 1)
769 769 sign = 1;
770 770 }
771 771 if (n == 0)
772 772 return (y0f(fx));
773 773 if (n == 1)
774 774 return ((sign)? -y1f(fx) : y1f(fx));
775 775
776 776 ix = *(int *)&fx;
777 777 if ((ix & ~0x80000000) > 0x7f800000) /* nan */
778 778 return (fx * fx);
779 779 if (ix <= 0) { /* zero or negative */
780 780 if ((ix << 1) == 0)
781 781 return (-onef / zerof);
782 782 return (zerof / zerof);
783 783 }
784 784 if (ix == 0x7f800000) /* +inf */
785 785 return (zerof);
786 786
787 787 #if defined(__i386) && !defined(__amd64)
788 788 rp = __swapRP(fp_extended);
789 789 #endif
790 790 a = __k_y0f(fx);
791 791 b = __k_y1f(fx);
792 792 x = (double)fx;
793 793 for (i = 1; i < n; i++) {
794 794 temp = b;
795 795 b *= (double)(i + i) / x;
796 796 if (b <= -DBL_MAX)
797 797 break;
798 798 b -= a;
799 799 a = temp;
800 800 }
801 801 f = (float)b;
802 802 #if defined(__i386) && !defined(__amd64)
803 803 if (rp != fp_extended)
804 804 (void) __swapRP(rp);
805 805 #endif
806 806 return ((sign)? -f : f);
807 807 }
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