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11210 libm should be cstyle(1ONBLD) clean
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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
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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 *
19 19 * CDDL HEADER END
20 20 */
21 +
21 22 /*
22 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 24 */
25 +
24 26 /*
25 27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 28 * Use is subject to license terms.
27 29 */
28 30
29 31 #pragma weak __j0f = j0f
30 32 #pragma weak __j1f = j1f
31 33 #pragma weak __jnf = jnf
32 34 #pragma weak __y0f = y0f
33 35 #pragma weak __y1f = y1f
34 36 #pragma weak __ynf = ynf
35 37
36 38 #include "libm.h"
37 39 #include <float.h>
38 40
39 41 #if defined(__i386) && !defined(__amd64)
40 42 extern int __swapRP(int);
41 43 #endif
42 44
43 -static const float
44 - zerof = 0.0f,
45 - onef = 1.0f;
45 +static const float zerof = 0.0f, 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 - 0.636619772367581343075535053490057448, /* 2/pi */
57 + 0.636619772367581343075535053490057448, /* 2/pi */
58 58 1.0e9,
59 59 };
60 60
61 -#define zero C[0]
62 -#define neighth C[1]
63 -#define quarter C[2]
64 -#define three8 C[3]
65 -#define half C[4]
66 -#define one C[5]
67 -#define two C[6]
68 -#define eight C[7]
69 -#define isqrtpi C[8]
70 -#define tpi C[9]
71 -#define big C[10]
61 +#define zero C[0]
62 +#define neighth C[1]
63 +#define quarter C[2]
64 +#define three8 C[3]
65 +#define half C[4]
66 +#define one C[5]
67 +#define two C[6]
68 +#define eight C[7]
69 +#define isqrtpi C[8]
70 +#define tpi C[9]
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,
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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 -#define pr Cj0y0
105 -#define ps (Cj0y0+7)
106 -#define qr (Cj0y0+14)
107 -#define qs (Cj0y0+21)
104 +#define pr Cj0y0
105 +#define ps (Cj0y0 + 7)
106 +#define qr (Cj0y0 + 14)
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 - 1.0, /* s0 */
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 - 1.0, /* s1 */
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 -#define r0 Cj0
139 -#define s0 (Cj0+4)
140 -#define r1 (Cj0+8)
141 -#define s1 (Cj0+17)
138 +#define r0 Cj0
139 +#define s0 (Cj0 + 4)
140 +#define r1 (Cj0 + 8)
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 - 1.0, /* v0 */
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 -#define u0 Cy0
165 -#define v0 (Cy0+13)
164 +#define u0 Cy0
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,
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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 -#define pr0 Cj1y1
195 -#define ps0 (Cj1y1+6)
196 -#define qr0 (Cj1y1+12)
197 -#define qs0 (Cj1y1+18)
194 +#define pr0 Cj1y1
195 +#define ps0 (Cj1y1 + 6)
196 +#define qr0 (Cj1y1 + 12)
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 - 1.0e0, /* b0 */
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 - 1.0e0, /* b1 */
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 -#define a0 Cj1
228 -#define b0 (Cj1+4)
229 -#define a1 (Cj1+8)
230 -#define b1 (Cj1+20)
227 +#define a0 Cj1
228 +#define b0 (Cj1 + 4)
229 +#define a1 (Cj1 + 8)
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 - 1.0e0, /* d0 */
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 - 1.0e0, /* d1 */
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 -#define c0 Cy1
262 -#define d0 (Cy1+4)
263 -#define c1 (Cy1+9)
264 -#define d1 (Cy1+21)
265 -
261 +#define c0 Cy1
262 +#define d0 (Cy1 + 4)
263 +#define c1 (Cy1 + 9)
264 +#define d1 (Cy1 + 21)
266 265
267 266 /* core of j0f computation; assumes fx is finite */
268 267 static double
269 268 __k_j0f(float fx)
270 269 {
271 - double x, z, s, c, ss, cc, r, t, p0, q0;
272 - int ix, i;
270 + double x, z, s, c, ss, cc, r, t, p0, q0;
271 + int ix, i;
273 272
274 273 ix = *(int *)&fx & ~0x80000000;
275 274 x = fabs((double)fx);
275 +
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 +
280 281 if (signbit(s) != signbit(c)) {
281 282 ss = s - c;
282 283 cc = -cos(x + x) / ss;
283 284 } else {
284 285 cc = s + c;
285 286 ss = -cos(x + x) / cc;
286 287 }
288 +
287 289 if (ix > 0x501502f9) {
288 290 /* x > 1.0e10 */
289 291 p0 = one;
290 292 q0 = neighth / x;
291 293 } else {
292 294 t = eight / x;
293 295 z = t * t;
294 - p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] +
295 - z * (pr[4] + z * (pr[5] + z * pr[6])))))) /
296 - (ps[0] + z * (ps[1] + z * (ps[2] + z * (ps[3] +
297 - z * (ps[4] + z * (ps[5] + z))))));
296 + p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] + z *
297 + (pr[4] + z * (pr[5] + z * pr[6])))))) / (ps[0] + z *
298 + (ps[1] + z * (ps[2] + z * (ps[3] + z * (ps[4] + z *
299 + (ps[5] + z))))));
298 300 q0 = ((qr[0] + z * (qr[1] + z * (qr[2] + z * (qr[3] +
299 - z * (qr[4] + z * (qr[5] + z * qr[6])))))) /
300 - (qs[0] + z * (qs[1] + z * (qs[2] + z * (qs[3] +
301 - z * (qs[4] + z * (qs[5] + z))))))) * t;
301 + z * (qr[4] + z * (qr[5] + z * qr[6])))))) / (qs[0] +
302 + z * (qs[1] + z * (qs[2] + z * (qs[3] + z * (qs[4] +
303 + z * (qs[5] + z))))))) * t;
302 304 }
305 +
303 306 return (isqrtpi * (p0 * cc - q0 * ss) / sqrt(x));
304 307 }
308 +
305 309 if (ix <= 0x3727c5ac) {
306 310 /* x <= 1.0e-5 */
307 - if (ix <= 0x219392ef) /* x <= 1.0e-18 */
311 + if (ix <= 0x219392ef) /* x <= 1.0e-18 */
308 312 return (one - x);
313 +
309 314 return (one - x * x * quarter);
310 315 }
316 +
311 317 z = x * x;
318 +
312 319 if (ix <= 0x3fa3d70a) {
313 320 /* x <= 1.28 */
314 321 r = r0[0] + z * (r0[1] + z * (r0[2] + z * r0[3]));
315 322 s = s0[0] + z * (s0[1] + z * (s0[2] + z * s0[3]));
316 323 return (one + z * (r / s));
317 324 }
325 +
318 326 r = r1[8];
319 327 s = s1[8];
328 +
320 329 for (i = 7; i >= 0; i--) {
321 330 r = r * z + r1[i];
322 331 s = s * z + s1[i];
323 332 }
333 +
324 334 return (r / s);
325 335 }
326 336
327 337 float
328 338 j0f(float fx)
329 339 {
330 - float f;
331 - int ix;
340 + float f;
341 + int ix;
342 +
332 343 #if defined(__i386) && !defined(__amd64)
333 - int rp;
344 + int rp;
334 345 #endif
335 346
336 347 ix = *(int *)&fx & ~0x80000000;
337 - if (ix >= 0x7f800000) { /* nan or inf */
348 +
349 + if (ix >= 0x7f800000) { /* nan or inf */
338 350 if (ix > 0x7f800000)
339 351 return (fx * fx);
352 +
340 353 return (zerof);
341 354 }
342 355
343 356 #if defined(__i386) && !defined(__amd64)
344 357 rp = __swapRP(fp_extended);
345 358 #endif
346 359 f = (float)__k_j0f(fx);
347 360 #if defined(__i386) && !defined(__amd64)
348 361 if (rp != fp_extended)
349 362 (void) __swapRP(rp);
350 363 #endif
351 364 return (f);
352 365 }
353 366
354 367 /* core of y0f computation; assumes fx is finite and positive */
355 368 static double
356 369 __k_y0f(float fx)
357 370 {
358 - double x, z, s, c, ss, cc, t, p0, q0, u, v;
359 - int ix, i;
371 + double x, z, s, c, ss, cc, t, p0, q0, u, v;
372 + int ix, i;
360 373
361 374 ix = *(int *)&fx;
362 375 x = (double)fx;
376 +
363 377 if (ix > 0x41000000) {
364 378 /* x > 8; see comments in j0.c */
365 379 s = sin(x);
366 380 c = cos(x);
381 +
367 382 if (signbit(s) != signbit(c)) {
368 383 ss = s - c;
369 384 cc = -cos(x + x) / ss;
370 385 } else {
371 386 cc = s + c;
372 387 ss = -cos(x + x) / cc;
373 388 }
389 +
374 390 if (ix > 0x501502f9) {
375 391 /* x > 1.0e10 */
376 392 p0 = one;
377 393 q0 = neighth / x;
378 394 } else {
379 395 t = eight / x;
380 396 z = t * t;
381 - p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] +
382 - z * (pr[4] + z * (pr[5] + z * pr[6])))))) /
383 - (ps[0] + z * (ps[1] + z * (ps[2] + z * (ps[3] +
384 - z * (ps[4] + z * (ps[5] + z))))));
397 + p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] + z *
398 + (pr[4] + z * (pr[5] + z * pr[6])))))) / (ps[0] + z *
399 + (ps[1] + z * (ps[2] + z * (ps[3] + z * (ps[4] + z *
400 + (ps[5] + z))))));
385 401 q0 = ((qr[0] + z * (qr[1] + z * (qr[2] + z * (qr[3] +
386 - z * (qr[4] + z * (qr[5] + z * qr[6])))))) /
387 - (qs[0] + z * (qs[1] + z * (qs[2] + z * (qs[3] +
388 - z * (qs[4] + z * (qs[5] + z))))))) * t;
402 + z * (qr[4] + z * (qr[5] + z * qr[6])))))) / (qs[0] +
403 + z * (qs[1] + z * (qs[2] + z * (qs[3] + z * (qs[4] +
404 + z * (qs[5] + z))))))) * t;
389 405 }
406 +
390 407 return (isqrtpi * (p0 * ss + q0 * cc) / sqrt(x));
391 408 }
392 - if (ix <= 0x219392ef) /* x <= 1.0e-18 */
409 +
410 + if (ix <= 0x219392ef) /* x <= 1.0e-18 */
393 411 return (u0[0] + tpi * log(x));
412 +
394 413 z = x * x;
395 414 u = u0[12];
415 +
396 416 for (i = 11; i >= 0; i--)
397 417 u = u * z + u0[i];
418 +
398 419 v = v0[0] + z * (v0[1] + z * (v0[2] + z * (v0[3] + z * v0[4])));
399 420 return (u / v + tpi * (__k_j0f(fx) * log(x)));
400 421 }
401 422
402 423 float
403 424 y0f(float fx)
404 425 {
405 - float f;
406 - int ix;
426 + float f;
427 + int ix;
428 +
407 429 #if defined(__i386) && !defined(__amd64)
408 - int rp;
430 + int rp;
409 431 #endif
410 432
411 433 ix = *(int *)&fx;
434 +
412 435 if ((ix & ~0x80000000) > 0x7f800000) /* nan */
413 436 return (fx * fx);
437 +
414 438 if (ix <= 0) { /* zero or negative */
415 439 if ((ix << 1) == 0)
416 440 return (-onef / zerof);
441 +
417 442 return (zerof / zerof);
418 443 }
419 - if (ix == 0x7f800000) /* +inf */
444 +
445 + if (ix == 0x7f800000) /* +inf */
420 446 return (zerof);
421 447
422 448 #if defined(__i386) && !defined(__amd64)
423 449 rp = __swapRP(fp_extended);
424 450 #endif
425 451 f = (float)__k_y0f(fx);
426 452 #if defined(__i386) && !defined(__amd64)
427 453 if (rp != fp_extended)
428 454 (void) __swapRP(rp);
429 455 #endif
430 456 return (f);
431 457 }
432 458
433 459 /* core of j1f computation; assumes fx is finite */
434 460 static double
435 461 __k_j1f(float fx)
436 462 {
437 - double x, z, s, c, ss, cc, r, t, p1, q1;
438 - int i, ix, sgn;
463 + double x, z, s, c, ss, cc, r, t, p1, q1;
464 + int i, ix, sgn;
439 465
440 466 ix = *(int *)&fx;
441 467 sgn = (unsigned)ix >> 31;
442 468 ix &= ~0x80000000;
443 469 x = fabs((double)fx);
470 +
444 471 if (ix > 0x41000000) {
445 472 /* x > 8; see comments in j1.c */
446 473 s = sin(x);
447 474 c = cos(x);
475 +
448 476 if (signbit(s) != signbit(c)) {
449 477 cc = s - c;
450 478 ss = cos(x + x) / cc;
451 479 } else {
452 480 ss = -s - c;
453 481 cc = cos(x + x) / ss;
454 482 }
483 +
455 484 if (ix > 0x501502f9) {
456 485 /* x > 1.0e10 */
457 486 p1 = one;
458 487 q1 = three8 / x;
459 488 } else {
460 489 t = eight / x;
461 490 z = t * t;
462 - p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z *
463 - (pr0[3] + z * (pr0[4] + z * pr0[5]))))) /
464 - (ps0[0] + z * (ps0[1] + z * (ps0[2] + z *
465 - (ps0[3] + z * (ps0[4] + z * (ps0[5] + z))))));
491 + p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z * (pr0[3] +
492 + z * (pr0[4] + z * pr0[5]))))) / (ps0[0] + z *
493 + (ps0[1] + z * (ps0[2] + z * (ps0[3] + z * (ps0[4] +
494 + z * (ps0[5] + z))))));
466 495 q1 = ((qr0[0] + z * (qr0[1] + z * (qr0[2] + z *
467 - (qr0[3] + z * (qr0[4] + z * qr0[5]))))) /
468 - (qs0[0] + z * (qs0[1] + z * (qs0[2] + z *
469 - (qs0[3] + z * (qs0[4] + z * (qs0[5] + z))))))) * t;
496 + (qr0[3] + z * (qr0[4] + z * qr0[5]))))) / (qs0[0] +
497 + z * (qs0[1] + z * (qs0[2] + z * (qs0[3] + z *
498 + (qs0[4] + z * (qs0[5] + z))))))) * t;
470 499 }
500 +
471 501 t = isqrtpi * (p1 * cc - q1 * ss) / sqrt(x);
472 - return ((sgn)? -t : t);
502 + return ((sgn) ? -t : t);
473 503 }
504 +
474 505 if (ix <= 0x3727c5ac) {
475 506 /* x <= 1.0e-5 */
476 - if (ix <= 0x219392ef) /* x <= 1.0e-18 */
507 + if (ix <= 0x219392ef) /* x <= 1.0e-18 */
477 508 t = half * x;
478 509 else
479 510 t = x * (half + neighth * x * x);
480 - return ((sgn)? -t : t);
511 +
512 + return ((sgn) ? -t : t);
481 513 }
514 +
482 515 z = x * x;
516 +
483 517 if (ix < 0x3fa3d70a) {
484 518 /* x < 1.28 */
485 519 r = a0[0] + z * (a0[1] + z * (a0[2] + z * a0[3]));
486 520 s = b0[0] + z * (b0[1] + z * (b0[2] + z * b0[3]));
487 521 t = x * half + x * (z * (r / s));
488 522 } else {
489 523 r = a1[11];
524 +
490 525 for (i = 10; i >= 0; i--)
491 526 r = r * z + a1[i];
527 +
492 528 s = b1[0] + z * (b1[1] + z * (b1[2] + z * (b1[3] + z * b1[4])));
493 529 t = x * (r / s);
494 530 }
495 - return ((sgn)? -t : t);
531 +
532 + return ((sgn) ? -t : t);
496 533 }
497 534
498 535 float
499 536 j1f(float fx)
500 537 {
501 - float f;
502 - int ix;
538 + float f;
539 + int ix;
540 +
503 541 #if defined(__i386) && !defined(__amd64)
504 - int rp;
542 + int rp;
505 543 #endif
506 544
507 545 ix = *(int *)&fx & ~0x80000000;
508 - if (ix >= 0x7f800000) /* nan or inf */
546 +
547 + if (ix >= 0x7f800000) /* nan or inf */
509 548 return (onef / fx);
510 549
511 550 #if defined(__i386) && !defined(__amd64)
512 551 rp = __swapRP(fp_extended);
513 552 #endif
514 553 f = (float)__k_j1f(fx);
515 554 #if defined(__i386) && !defined(__amd64)
516 555 if (rp != fp_extended)
517 556 (void) __swapRP(rp);
518 557 #endif
519 558 return (f);
520 559 }
521 560
522 561 /* core of y1f computation; assumes fx is finite and positive */
523 562 static double
524 563 __k_y1f(float fx)
525 564 {
526 - double x, z, s, c, ss, cc, u, v, p1, q1, t;
527 - int i, ix;
565 + double x, z, s, c, ss, cc, u, v, p1, q1, t;
566 + int i, ix;
528 567
529 568 ix = *(int *)&fx;
530 569 x = (double)fx;
570 +
531 571 if (ix > 0x41000000) {
532 572 /* x > 8; see comments in j1.c */
533 573 s = sin(x);
534 574 c = cos(x);
575 +
535 576 if (signbit(s) != signbit(c)) {
536 577 cc = s - c;
537 578 ss = cos(x + x) / cc;
538 579 } else {
539 580 ss = -s - c;
540 581 cc = cos(x + x) / ss;
541 582 }
583 +
542 584 if (ix > 0x501502f9) {
543 585 /* x > 1.0e10 */
544 586 p1 = one;
545 587 q1 = three8 / x;
546 588 } else {
547 589 t = eight / x;
548 590 z = t * t;
549 - p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z *
550 - (pr0[3] + z * (pr0[4] + z * pr0[5]))))) /
551 - (ps0[0] + z * (ps0[1] + z * (ps0[2] + z *
552 - (ps0[3] + z * (ps0[4] + z * (ps0[5] + z))))));
591 + p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z * (pr0[3] +
592 + z * (pr0[4] + z * pr0[5]))))) / (ps0[0] + z *
593 + (ps0[1] + z * (ps0[2] + z * (ps0[3] + z * (ps0[4] +
594 + z * (ps0[5] + z))))));
553 595 q1 = ((qr0[0] + z * (qr0[1] + z * (qr0[2] + z *
554 - (qr0[3] + z * (qr0[4] + z * qr0[5]))))) /
555 - (qs0[0] + z * (qs0[1] + z * (qs0[2] + z *
556 - (qs0[3] + z * (qs0[4] + z * (qs0[5] + z))))))) * t;
596 + (qr0[3] + z * (qr0[4] + z * qr0[5]))))) / (qs0[0] +
597 + z * (qs0[1] + z * (qs0[2] + z * (qs0[3] + z *
598 + (qs0[4] + z * (qs0[5] + z))))))) * t;
557 599 }
600 +
558 601 return (isqrtpi * (p1 * ss + q1 * cc) / sqrt(x));
559 602 }
560 - if (ix <= 0x219392ef) /* x <= 1.0e-18 */
603 +
604 + if (ix <= 0x219392ef) /* x <= 1.0e-18 */
561 605 return (-tpi / x);
606 +
562 607 z = x * x;
608 +
563 609 if (ix < 0x3fa3d70a) {
564 610 /* x < 1.28 */
565 611 u = c0[0] + z * (c0[1] + z * (c0[2] + z * c0[3]));
566 612 v = d0[0] + z * (d0[1] + z * (d0[2] + z * (d0[3] + z * d0[4])));
567 613 } else {
568 614 u = c1[11];
615 +
569 616 for (i = 10; i >= 0; i--)
570 617 u = u * z + c1[i];
618 +
571 619 v = d1[0] + z * (d1[1] + z * (d1[2] + z * (d1[3] + z * d1[4])));
572 620 }
621 +
573 622 return (x * (u / v) + tpi * (__k_j1f(fx) * log(x) - one / x));
574 623 }
575 624
576 625 float
577 626 y1f(float fx)
578 627 {
579 - float f;
580 - int ix;
628 + float f;
629 + int ix;
630 +
581 631 #if defined(__i386) && !defined(__amd64)
582 - int rp;
632 + int rp;
583 633 #endif
584 634
585 635 ix = *(int *)&fx;
636 +
586 637 if ((ix & ~0x80000000) > 0x7f800000) /* nan */
587 638 return (fx * fx);
639 +
588 640 if (ix <= 0) { /* zero or negative */
589 641 if ((ix << 1) == 0)
590 642 return (-onef / zerof);
643 +
591 644 return (zerof / zerof);
592 645 }
593 - if (ix == 0x7f800000) /* +inf */
646 +
647 + if (ix == 0x7f800000) /* +inf */
594 648 return (zerof);
595 649
596 650 #if defined(__i386) && !defined(__amd64)
597 651 rp = __swapRP(fp_extended);
598 652 #endif
599 653 f = (float)__k_y1f(fx);
600 654 #if defined(__i386) && !defined(__amd64)
601 655 if (rp != fp_extended)
602 656 (void) __swapRP(rp);
603 657 #endif
604 658 return (f);
605 659 }
606 660
607 661 float
608 662 jnf(int n, float fx)
609 663 {
610 - double a, b, temp, x, z, w, t, q0, q1, h;
611 - float f;
612 - int i, ix, sgn, m, k;
664 + double a, b, temp, x, z, w, t, q0, q1, h;
665 + float f;
666 + int i, ix, sgn, m, k;
667 +
613 668 #if defined(__i386) && !defined(__amd64)
614 - int rp;
669 + int rp;
615 670 #endif
616 671
617 672 if (n < 0) {
618 673 n = -n;
619 674 fx = -fx;
620 675 }
676 +
621 677 if (n == 0)
622 678 return (j0f(fx));
679 +
623 680 if (n == 1)
624 681 return (j1f(fx));
625 682
626 683 ix = *(int *)&fx;
627 - sgn = (n & 1)? ((unsigned)ix >> 31) : 0;
684 + sgn = (n & 1) ? ((unsigned)ix >> 31) : 0;
628 685 ix &= ~0x80000000;
686 +
629 687 if (ix >= 0x7f800000) { /* nan or inf */
630 688 if (ix > 0x7f800000)
631 689 return (fx * fx);
632 - return ((sgn)? -zerof : zerof);
690 +
691 + return ((sgn) ? -zerof : zerof);
633 692 }
693 +
634 694 if ((ix << 1) == 0)
635 - return ((sgn)? -zerof : zerof);
695 + return ((sgn) ? -zerof : zerof);
636 696
637 697 #if defined(__i386) && !defined(__amd64)
638 698 rp = __swapRP(fp_extended);
639 699 #endif
640 700 fx = fabsf(fx);
641 701 x = (double)fx;
702 +
642 703 if ((double)n <= x) {
643 704 /* safe to use J(n+1,x) = 2n/x * J(n,x) - J(n-1,x) */
644 705 a = __k_j0f(fx);
645 706 b = __k_j1f(fx);
707 +
646 708 for (i = 1; i < n; i++) {
647 709 temp = b;
648 710 b = b * ((double)(i + i) / x) - a;
649 711 a = temp;
650 712 }
713 +
651 714 f = (float)b;
652 715 #if defined(__i386) && !defined(__amd64)
653 716 if (rp != fp_extended)
654 717 (void) __swapRP(rp);
655 718 #endif
656 - return ((sgn)? -f : f);
719 + return ((sgn) ? -f : f);
657 720 }
721 +
658 722 if (ix < 0x3089705f) {
659 723 /* x < 1.0e-9; use J(n,x) = 1/n! * (x / 2)^n */
660 724 if (n > 6)
661 725 n = 6; /* result underflows to zero for n >= 6 */
726 +
662 727 b = t = half * x;
663 728 a = one;
729 +
664 730 for (i = 2; i <= n; i++) {
665 731 b *= t;
666 732 a *= (double)i;
667 733 }
734 +
668 735 b /= a;
669 736 } else {
737 + /* BEGIN CSTYLED */
670 738 /*
671 739 * Use the backward recurrence:
672 740 *
673 - * x x^2 x^2
741 + * x x^2 x^2
674 742 * J(n,x)/J(n-1,x) = ---- - ------ - ------ .....
675 743 * 2n 2(n+1) 2(n+2)
676 744 *
677 745 * Let w = 2n/x and h = 2/x. Then the above quotient
678 746 * is equal to the continued fraction:
679 747 * 1
680 748 * = -----------------------
681 749 * 1
682 750 * w - -----------------
683 751 * 1
684 - * w+h - ---------
752 + * w+h - ---------
685 753 * w+2h - ...
686 754 *
687 755 * To determine how many terms are needed, run the
688 756 * recurrence
689 757 *
690 758 * Q(0) = w,
691 759 * Q(1) = w(w+h) - 1,
692 760 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2).
693 761 *
694 762 * Then when Q(k) > 1e4, k is large enough for single
695 763 * precision.
696 764 */
765 + /* END CSTYLED */
697 766 /* XXX NOT DONE - rework this */
698 767 w = (n + n) / x;
699 768 h = two / x;
700 769 q0 = w;
701 770 z = w + h;
702 771 q1 = w * z - one;
703 772 k = 1;
773 +
704 774 while (q1 < big) {
705 775 k++;
706 776 z += h;
707 777 temp = z * q1 - q0;
708 778 q0 = q1;
709 779 q1 = temp;
710 780 }
781 +
711 782 m = n + n;
712 783 t = zero;
784 +
713 785 for (i = (n + k) << 1; i >= m; i -= 2)
714 786 t = one / ((double)i / x - t);
787 +
715 788 a = t;
716 789 b = one;
790 +
717 791 /*
718 792 * estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
719 793 * hence, if n*(log(2n/x)) > ...
720 794 * single 8.8722839355e+01
721 795 * double 7.09782712893383973096e+02
722 796 * then recurrent value may overflow and the result is
723 797 * likely underflow to zero
724 798 */
725 799 temp = (double)n;
726 800 temp *= log((two / x) * temp);
801 +
727 802 if (temp < 7.09782712893383973096e+02) {
728 803 for (i = n - 1; i > 0; i--) {
729 804 temp = b;
730 805 b = b * ((double)(i + i) / x) - a;
731 806 a = temp;
732 807 }
733 808 } else {
734 809 for (i = n - 1; i > 0; i--) {
735 810 temp = b;
736 811 b = b * ((double)(i + i) / x) - a;
737 812 a = temp;
813 +
738 814 if (b > 1.0e100) {
739 815 a /= b;
740 816 t /= b;
741 817 b = one;
742 818 }
743 819 }
744 820 }
821 +
745 822 b = (t * __k_j0f(fx) / b);
746 823 }
824 +
747 825 f = (float)b;
748 826 #if defined(__i386) && !defined(__amd64)
749 827 if (rp != fp_extended)
750 828 (void) __swapRP(rp);
751 829 #endif
752 - return ((sgn)? -f : f);
830 + return ((sgn) ? -f : f);
753 831 }
754 832
755 833 float
756 834 ynf(int n, float fx)
757 835 {
758 - double a, b, temp, x;
759 - float f;
760 - int i, sign, ix;
836 + double a, b, temp, x;
837 + float f;
838 + int i, sign, ix;
839 +
761 840 #if defined(__i386) && !defined(__amd64)
762 - int rp;
841 + int rp;
763 842 #endif
764 843
765 844 sign = 0;
845 +
766 846 if (n < 0) {
767 847 n = -n;
848 +
768 849 if (n & 1)
769 850 sign = 1;
770 851 }
852 +
771 853 if (n == 0)
772 854 return (y0f(fx));
855 +
773 856 if (n == 1)
774 - return ((sign)? -y1f(fx) : y1f(fx));
857 + return ((sign) ? -y1f(fx) : y1f(fx));
775 858
776 859 ix = *(int *)&fx;
860 +
777 861 if ((ix & ~0x80000000) > 0x7f800000) /* nan */
778 862 return (fx * fx);
863 +
779 864 if (ix <= 0) { /* zero or negative */
780 865 if ((ix << 1) == 0)
781 866 return (-onef / zerof);
867 +
782 868 return (zerof / zerof);
783 869 }
784 - if (ix == 0x7f800000) /* +inf */
870 +
871 + if (ix == 0x7f800000) /* +inf */
785 872 return (zerof);
786 873
787 874 #if defined(__i386) && !defined(__amd64)
788 875 rp = __swapRP(fp_extended);
789 876 #endif
790 877 a = __k_y0f(fx);
791 878 b = __k_y1f(fx);
792 879 x = (double)fx;
880 +
793 881 for (i = 1; i < n; i++) {
794 882 temp = b;
795 883 b *= (double)(i + i) / x;
884 +
796 885 if (b <= -DBL_MAX)
797 886 break;
887 +
798 888 b -= a;
799 889 a = temp;
800 890 }
891 +
801 892 f = (float)b;
802 893 #if defined(__i386) && !defined(__amd64)
803 894 if (rp != fp_extended)
804 895 (void) __swapRP(rp);
805 896 #endif
806 - return ((sign)? -f : f);
897 + return ((sign) ? -f : f);
807 898 }
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