NGSolve  5.3
bessel.hpp
1 /* j0.c
2  *
3  * Bessel function of order zero
4  *
5  * thanks to Thorsten Hohage
6  *
7  *
8  * SYNOPSIS:
9  *
10  * double x, y, j0();
11  *
12  * y = j0( x );
13  *
14  *
15  *
16  * DESCRIPTION:
17  *
18  * Returns Bessel function of order zero of the argument.
19  *
20  * The domain is divided into the intervals [0, 5] and
21  * (5, infinity). In the first interval the following rational
22  * approximation is used:
23  *
24  *
25  * 2 2
26  * (w - r ) (w - r ) P (w) / Q (w)
27  * 1 2 3 8
28  *
29  * 2
30  * where w = x and the two r's are zeros of the function.
31  *
32  * In the second interval, the Hankel asymptotic expansion
33  * is employed with two rational functions of degree 6/6
34  * and 7/7.
35  *
36  *
37  *
38  * ACCURACY:
39  *
40  * Absolute error:
41  * arithmetic domain # trials peak rms
42  * DEC 0, 30 10000 4.4e-17 6.3e-18
43  * IEEE 0, 30 60000 4.2e-16 1.1e-16
44  *
45  */
46 /* y0.c
47  *
48  * Bessel function of the second kind, order zero
49  *
50  *
51  *
52  * SYNOPSIS:
53  *
54  * double x, y, y0();
55  *
56  * y = y0( x );
57  *
58  *
59  *
60  * DESCRIPTION:
61  *
62  * Returns Bessel function of the second kind, of order
63  * zero, of the argument.
64  *
65  * The domain is divided into the intervals [0, 5] and
66  * (5, infinity). In the first interval a rational approximation
67  * R(x) is employed to compute
68  * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
69  * Thus a call to j0() is required.
70  *
71  * In the second interval, the Hankel asymptotic expansion
72  * is employed with two rational functions of degree 6/6
73  * and 7/7.
74  *
75  *
76  *
77  * ACCURACY:
78  *
79  * Absolute error, when y0(x) < 1; else relative error:
80  *
81  * arithmetic domain # trials peak rms
82  * DEC 0, 30 9400 7.0e-17 7.9e-18
83  * IEEE 0, 30 30000 1.3e-15 1.6e-16
84  *
85  */
86 /*
87 Cephes Math Library Release 2.1: January, 1989
88 Copyright 1984, 1987, 1989 by Stephen L. Moshier
89 Direct inquiries to 30 Frost Street, Cambridge, MA 02140
90 */
91 
92 /* Note: all coefficients satisfy the relative error criterion
93  * except YP, YQ which are designed for absolute error. */
94 
95 //#include "mconf.h"
96 #define UNK
97 #ifdef UNK
98 static double PP[7] = {
99  7.96936729297347051624E-4,
100  8.28352392107440799803E-2,
101  1.23953371646414299388E0,
102  5.44725003058768775090E0,
103  8.74716500199817011941E0,
104  5.30324038235394892183E0,
105  9.99999999999999997821E-1,
106 };
107 static double PQ[7] = {
108  9.24408810558863637013E-4,
109  8.56288474354474431428E-2,
110  1.25352743901058953537E0,
111  5.47097740330417105182E0,
112  8.76190883237069594232E0,
113  5.30605288235394617618E0,
114  1.00000000000000000218E0,
115 };
116 #endif
117 #ifdef DEC
118 static unsigned short PP[28] = {
119 0035520,0164604,0140733,0054470,
120 0037251,0122605,0115356,0107170,
121 0040236,0124412,0071500,0056303,
122 0040656,0047737,0045720,0045263,
123 0041013,0172143,0045004,0142103,
124 0040651,0132045,0026241,0026406,
125 0040200,0000000,0000000,0000000,
126 };
127 static unsigned short PQ[28] = {
128 0035562,0052006,0070034,0134666,
129 0037257,0057055,0055242,0123424,
130 0040240,0071626,0046630,0032371,
131 0040657,0011077,0032013,0012731,
132 0041014,0030307,0050331,0006414,
133 0040651,0145457,0065021,0150304,
134 0040200,0000000,0000000,0000000,
135 };
136 #endif
137 #ifdef IBMPC
138 static unsigned short PP[28] = {
139 0x6b27,0x983b,0x1d30,0x3f4a,
140 0xd1cf,0xb35d,0x34b0,0x3fb5,
141 0x0b98,0x4e68,0xd521,0x3ff3,
142 0x0956,0xe97a,0xc9fb,0x4015,
143 0x9888,0x6940,0x7e8c,0x4021,
144 0x25a1,0xa594,0x3684,0x4015,
145 0x0000,0x0000,0x0000,0x3ff0,
146 };
147 static unsigned short PQ[28] = {
148 0x9737,0xce03,0x4a80,0x3f4e,
149 0x54e3,0xab54,0xebc5,0x3fb5,
150 0x069f,0xc9b3,0x0e72,0x3ff4,
151 0x62bb,0xe681,0xe247,0x4015,
152 0x21a1,0xea1b,0x8618,0x4021,
153 0x3a19,0xed42,0x3965,0x4015,
154 0x0000,0x0000,0x0000,0x3ff0,
155 };
156 #endif
157 #ifdef MIEEE
158 static unsigned short PP[28] = {
159 0x3f4a,0x1d30,0x983b,0x6b27,
160 0x3fb5,0x34b0,0xb35d,0xd1cf,
161 0x3ff3,0xd521,0x4e68,0x0b98,
162 0x4015,0xc9fb,0xe97a,0x0956,
163 0x4021,0x7e8c,0x6940,0x9888,
164 0x4015,0x3684,0xa594,0x25a1,
165 0x3ff0,0x0000,0x0000,0x0000,
166 };
167 static unsigned short PQ[28] = {
168 0x3f4e,0x4a80,0xce03,0x9737,
169 0x3fb5,0xebc5,0xab54,0x54e3,
170 0x3ff4,0x0e72,0xc9b3,0x069f,
171 0x4015,0xe247,0xe681,0x62bb,
172 0x4021,0x8618,0xea1b,0x21a1,
173 0x4015,0x3965,0xed42,0x3a19,
174 0x3ff0,0x0000,0x0000,0x0000,
175 };
176 #endif
177 
178 #ifdef UNK
179 static double QP[8] = {
180 -1.13663838898469149931E-2,
181 -1.28252718670509318512E0,
182 -1.95539544257735972385E1,
183 -9.32060152123768231369E1,
184 -1.77681167980488050595E2,
185 -1.47077505154951170175E2,
186 -5.14105326766599330220E1,
187 -6.05014350600728481186E0,
188 };
189 static double QQ[7] = {
190 /* 1.00000000000000000000E0,*/
191  6.43178256118178023184E1,
192  8.56430025976980587198E2,
193  3.88240183605401609683E3,
194  7.24046774195652478189E3,
195  5.93072701187316984827E3,
196  2.06209331660327847417E3,
197  2.42005740240291393179E2,
198 };
199 #endif
200 #ifdef DEC
201 static unsigned short QP[32] = {
202 0136472,0035021,0142451,0141115,
203 0140244,0024731,0150620,0105642,
204 0141234,0067177,0124161,0060141,
205 0141672,0064572,0151557,0043036,
206 0142061,0127141,0003127,0043517,
207 0142023,0011727,0060271,0144544,
208 0141515,0122142,0126620,0143150,
209 0140701,0115306,0106715,0007344,
210 };
211 static unsigned short QQ[28] = {
212 /*0040200,0000000,0000000,0000000,*/
213 0041600,0121272,0004741,0026544,
214 0042526,0015605,0105654,0161771,
215 0043162,0123155,0165644,0062645,
216 0043342,0041675,0167576,0130756,
217 0043271,0052720,0165631,0154214,
218 0043000,0160576,0034614,0172024,
219 0042162,0000570,0030500,0051235,
220 };
221 #endif
222 #ifdef IBMPC
223 static unsigned short QP[32] = {
224 0x384a,0x38a5,0x4742,0xbf87,
225 0x1174,0x3a32,0x853b,0xbff4,
226 0x2c0c,0xf50e,0x8dcf,0xc033,
227 0xe8c4,0x5a6d,0x4d2f,0xc057,
228 0xe8ea,0x20ca,0x35cc,0xc066,
229 0x392d,0xec17,0x627a,0xc062,
230 0x18cd,0x55b2,0xb48c,0xc049,
231 0xa1dd,0xd1b9,0x3358,0xc018,
232 };
233 static unsigned short QQ[28] = {
234 /*0x0000,0x0000,0x0000,0x3ff0,*/
235 0x25ac,0x413c,0x1457,0x4050,
236 0x9c7f,0xb175,0xc370,0x408a,
237 0x8cb5,0xbd74,0x54cd,0x40ae,
238 0xd63e,0xbdef,0x4877,0x40bc,
239 0x3b11,0x1d73,0x2aba,0x40b7,
240 0x9e82,0xc731,0x1c2f,0x40a0,
241 0x0a54,0x0628,0x402f,0x406e,
242 };
243 #endif
244 #ifdef MIEEE
245 static unsigned short QP[32] = {
246 0xbf87,0x4742,0x38a5,0x384a,
247 0xbff4,0x853b,0x3a32,0x1174,
248 0xc033,0x8dcf,0xf50e,0x2c0c,
249 0xc057,0x4d2f,0x5a6d,0xe8c4,
250 0xc066,0x35cc,0x20ca,0xe8ea,
251 0xc062,0x627a,0xec17,0x392d,
252 0xc049,0xb48c,0x55b2,0x18cd,
253 0xc018,0x3358,0xd1b9,0xa1dd,
254 };
255 static unsigned short QQ[28] = {
256 /*0x3ff0,0x0000,0x0000,0x0000,*/
257 0x4050,0x1457,0x413c,0x25ac,
258 0x408a,0xc370,0xb175,0x9c7f,
259 0x40ae,0x54cd,0xbd74,0x8cb5,
260 0x40bc,0x4877,0xbdef,0xd63e,
261 0x40b7,0x2aba,0x1d73,0x3b11,
262 0x40a0,0x1c2f,0xc731,0x9e82,
263 0x406e,0x402f,0x0628,0x0a54,
264 };
265 #endif
266 
267 
268 #ifdef UNK
269 static double YP[8] = {
270  1.55924367855235737965E4,
271 -1.46639295903971606143E7,
272  5.43526477051876500413E9,
273 -9.82136065717911466409E11,
274  8.75906394395366999549E13,
275 -3.46628303384729719441E15,
276  4.42733268572569800351E16,
277 -1.84950800436986690637E16,
278 };
279 static double YQ[7] = {
280 /* 1.00000000000000000000E0,*/
281  1.04128353664259848412E3,
282  6.26107330137134956842E5,
283  2.68919633393814121987E8,
284  8.64002487103935000337E10,
285  2.02979612750105546709E13,
286  3.17157752842975028269E15,
287  2.50596256172653059228E17,
288 };
289 #endif
290 #ifdef DEC
291 static unsigned short YP[32] = {
292 0043563,0120677,0042264,0046166,
293 0146137,0140371,0113444,0042260,
294 0050241,0175707,0100502,0063344,
295 0152144,0125737,0007265,0164526,
296 0053637,0051621,0163035,0060546,
297 0155105,0004416,0107306,0060023,
298 0056035,0045133,0030132,0000024,
299 0155603,0065132,0144061,0131732,
300 };
301 static unsigned short YQ[28] = {
302 /*0040200,0000000,0000000,0000000,*/
303 0042602,0024422,0135557,0162663,
304 0045030,0155665,0044075,0160135,
305 0047200,0035432,0105446,0104005,
306 0051240,0167331,0056063,0022743,
307 0053223,0127746,0025764,0012160,
308 0055064,0044206,0177532,0145545,
309 0056536,0111375,0163715,0127201,
310 };
311 #endif
312 #ifdef IBMPC
313 static unsigned short YP[32] = {
314 0x898f,0xe896,0x7437,0x40ce,
315 0x8896,0x32e4,0xf81f,0xc16b,
316 0x4cdd,0xf028,0x3f78,0x41f4,
317 0xbd2b,0xe1d6,0x957b,0xc26c,
318 0xac2d,0x3cc3,0xea72,0x42d3,
319 0xcc02,0xd1d8,0xa121,0xc328,
320 0x4003,0x660b,0xa94b,0x4363,
321 0x367b,0x5906,0x6d4b,0xc350,
322 };
323 static unsigned short YQ[28] = {
324 /*0x0000,0x0000,0x0000,0x3ff0,*/
325 0xfcb6,0x576d,0x4522,0x4090,
326 0xbc0c,0xa907,0x1b76,0x4123,
327 0xd101,0x5164,0x0763,0x41b0,
328 0x64bc,0x2b86,0x1ddb,0x4234,
329 0x828e,0xc57e,0x75fc,0x42b2,
330 0x596d,0xdfeb,0x8910,0x4326,
331 0xb5d0,0xbcf9,0xd25f,0x438b,
332 };
333 #endif
334 #ifdef MIEEE
335 static unsigned short YP[32] = {
336 0x40ce,0x7437,0xe896,0x898f,
337 0xc16b,0xf81f,0x32e4,0x8896,
338 0x41f4,0x3f78,0xf028,0x4cdd,
339 0xc26c,0x957b,0xe1d6,0xbd2b,
340 0x42d3,0xea72,0x3cc3,0xac2d,
341 0xc328,0xa121,0xd1d8,0xcc02,
342 0x4363,0xa94b,0x660b,0x4003,
343 0xc350,0x6d4b,0x5906,0x367b,
344 };
345 static unsigned short YQ[28] = {
346 /*0x3ff0,0x0000,0x0000,0x0000,*/
347 0x4090,0x4522,0x576d,0xfcb6,
348 0x4123,0x1b76,0xa907,0xbc0c,
349 0x41b0,0x0763,0x5164,0xd101,
350 0x4234,0x1ddb,0x2b86,0x64bc,
351 0x42b2,0x75fc,0xc57e,0x828e,
352 0x4326,0x8910,0xdfeb,0x596d,
353 0x438b,0xd25f,0xbcf9,0xb5d0,
354 };
355 #endif
356 
357 #ifdef UNK
358 /* 5.783185962946784521175995758455807035071 */
359 static double DR1 = 5.78318596294678452118E0;
360 /* 30.47126234366208639907816317502275584842 */
361 static double DR2 = 3.04712623436620863991E1;
362 #endif
363 
364 #ifdef DEC
365 static unsigned short R1[] = {0040671,0007734,0001061,0056734};
366 #define DR1 *(double *)R1
367 static unsigned short R2[] = {0041363,0142445,0030416,0165567};
368 #define DR2 *(double *)R2
369 #endif
370 
371 #ifdef IBMPC
372 static unsigned short R1[] = {0x2bbb,0x8046,0x21fb,0x4017};
373 #define DR1 *(double *)R1
374 static unsigned short R2[] = {0xdd6f,0xa621,0x78a4,0x403e};
375 #define DR2 *(double *)R2
376 #endif
377 
378 #ifdef MIEEE
379 static unsigned short R1[] = {0x4017,0x21fb,0x8046,0x2bbb};
380 #define DR1 *(double *)R1
381 static unsigned short R2[] = {0x403e,0x78a4,0xa621,0xdd6f};
382 #define DR2 *(double *)R2
383 #endif
384 
385 #ifdef UNK
386 static double RP[4] = {
387 -4.79443220978201773821E9,
388  1.95617491946556577543E12,
389 -2.49248344360967716204E14,
390  9.70862251047306323952E15,
391 };
392 static double RQ[8] = {
393 /* 1.00000000000000000000E0,*/
394  4.99563147152651017219E2,
395  1.73785401676374683123E5,
396  4.84409658339962045305E7,
397  1.11855537045356834862E10,
398  2.11277520115489217587E12,
399  3.10518229857422583814E14,
400  3.18121955943204943306E16,
401  1.71086294081043136091E18,
402 };
403 #endif
404 #ifdef DEC
405 static unsigned short RP[16] = {
406 0150216,0161235,0064344,0014450,
407 0052343,0135216,0035624,0144153,
408 0154142,0130247,0003310,0003667,
409 0055411,0173703,0047772,0176635,
410 };
411 static unsigned short RQ[32] = {
412 /*0040200,0000000,0000000,0000000,*/
413 0042371,0144025,0032265,0136137,
414 0044451,0133131,0132420,0151466,
415 0046470,0144641,0072540,0030636,
416 0050446,0126600,0045042,0044243,
417 0052365,0172633,0110301,0071063,
418 0054215,0032424,0062272,0043513,
419 0055742,0005013,0171731,0072335,
420 0057275,0170646,0036663,0013134,
421 };
422 #endif
423 #ifdef IBMPC
424 static unsigned short RP[16] = {
425 0x8325,0xad1c,0xdc53,0xc1f1,
426 0x990d,0xc772,0x7751,0x427c,
427 0x00f7,0xe0d9,0x5614,0xc2ec,
428 0x5fb4,0x69ff,0x3ef8,0x4341,
429 };
430 static unsigned short RQ[32] = {
431 /*0x0000,0x0000,0x0000,0x3ff0,*/
432 0xb78c,0xa696,0x3902,0x407f,
433 0x1a67,0x36a2,0x36cb,0x4105,
434 0x0634,0x2eac,0x1934,0x4187,
435 0x4914,0x0944,0xd5b0,0x4204,
436 0x2e46,0x7218,0xbeb3,0x427e,
437 0x48e9,0x8c97,0xa6a2,0x42f1,
438 0x2e9c,0x7e7b,0x4141,0x435c,
439 0x62cc,0xc7b6,0xbe34,0x43b7,
440 };
441 #endif
442 #ifdef MIEEE
443 static unsigned short RP[16] = {
444 0xc1f1,0xdc53,0xad1c,0x8325,
445 0x427c,0x7751,0xc772,0x990d,
446 0xc2ec,0x5614,0xe0d9,0x00f7,
447 0x4341,0x3ef8,0x69ff,0x5fb4,
448 };
449 static unsigned short RQ[32] = {
450 /*0x3ff0,0x0000,0x0000,0x0000,*/
451 0x407f,0x3902,0xa696,0xb78c,
452 0x4105,0x36cb,0x36a2,0x1a67,
453 0x4187,0x1934,0x2eac,0x0634,
454 0x4204,0xd5b0,0x0944,0x4914,
455 0x427e,0xbeb3,0x7218,0x2e46,
456 0x42f1,0xa6a2,0x8c97,0x48e9,
457 0x435c,0x4141,0x7e7b,0x2e9c,
458 0x43b7,0xbe34,0xc7b6,0x62cc,
459 };
460 #endif
461 
462 #define ANSIPROT
463 #ifndef ANSIPROT
464 double bessj0(), polevl(), p1evl(), log(), sin(), cos(), sqrt();
465 #endif
466 
467 double polevl(double x,double coef[],int N)
468 {
469 double ans;
470 int i;
471 double *p;
472 
473 p = coef;
474 ans = *p++;
475 i = N;
476 
477 do
478  ans = ans * x + *p++;
479 while( --i );
480 
481 return( ans );
482 }
483 
484 /* p1evl() */
485 /* N
486  * Evaluate polynomial when coefficient of x is 1.0.
487  * Otherwise same as polevl.
488  */
489 
490 double p1evl(double x, double coef[],int N)
491 {
492 double ans;
493 double *p;
494 int i;
495 
496 p = coef;
497 ans = x + *p++;
498 i = N-1;
499 
500 do
501  ans = ans * x + *p++;
502 while( --i );
503 
504 return( ans );
505 }
506 
507 double TWOOPI = 6.36619772367581343075535E-1; /* 2/pi */
508 double THPIO4 = 2.35619449019234492885; /* 3*pi/4 */
509 double SQ2OPI = 7.9788456080286535587989E-1; /* sqrt( 2/pi ) */
510 double PIO4 = 7.85398163397448309616E-1; /* pi/4 */
511 
512 double bessj0(double x)
513 {
514 double w, z, p, q, xn;
515 
516 if( x < 0 )
517  x = -x;
518 
519 if( x <= 5.0 )
520  {
521  z = x * x;
522  if( x < 1.0e-5 )
523  return( 1.0 - z/4.0 );
524 
525  p = (z - DR1) * (z - DR2);
526  p = p * polevl( z, RP, 3)/p1evl( z, RQ, 8 );
527  return( p );
528  }
529 
530 w = 5.0/x;
531 q = 25.0/(x*x);
532 p = polevl( q, PP, 6)/polevl( q, PQ, 6 );
533 q = polevl( q, QP, 7)/p1evl( q, QQ, 7 );
534 xn = x - PIO4;
535 p = p * cos(xn) - w * q * sin(xn);
536 return( p * SQ2OPI / sqrt(x) );
537 }
538 /* bessy0() 2 */
539 /* Bessel function of second kind, order zero */
540 
541 /* Rational approximation coefficients YP[], YQ[] are used here.
542  * The function computed is bessy0(x) - 2 * log(x) * bessj0(x) / PI,
543  * whose value at x = 0 is 2 * ( log(0.5) + EUL ) / PI
544  * = 0.073804295108687225.
545  */
546 
547 
548 double bessy0(double x)
549 {
550 double w, z, p, q, xn;
551 
552 if( x <= 5.0 )
553  {
554  if( x <= 0.0 )
555  throw Exception ("arg<=0 in bessy0");
556  z = x * x;
557  w = polevl( z, YP, 7) / p1evl( z, YQ, 7 );
558  w += TWOOPI * log(x) * bessj0(x);
559  return( w );
560  }
561 
562 w = 5.0/x;
563 z = 25.0 / (x * x);
564 p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
565 q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
566 xn = x - PIO4;
567 p = p * sin(xn) + w * q * cos(xn);
568 return( p * SQ2OPI / sqrt(x) );
569 }
570 
571 /* j1.c
572  *
573  * Bessel function of order one
574  *
575  *
576  *
577  * SYNOPSIS:
578  *
579  * double x, y, j1();
580  *
581  * y = j1( x );
582  *
583  *
584  *
585  * DESCRIPTION:
586  *
587  * Returns Bessel function of order one of the argument.
588  *
589  * The domain is divided into the intervals [0, 8] and
590  * (8, infinity). In the first interval a 24 term Chebyshev
591  * expansion is used. In the second, the asymptotic
592  * trigonometric representation is employed using two
593  * rational functions of degree 5/5.
594  *
595  *
596  *
597  * ACCURACY:
598  *
599  * Absolute error:
600  * arithmetic domain # trials peak rms
601  * DEC 0, 30 10000 4.0e-17 1.1e-17
602  * IEEE 0, 30 30000 2.6e-16 1.1e-16
603  *
604  *
605  */
606 /* y1.c
607  *
608  * Bessel function of second kind of order one
609  *
610  *
611  *
612  * SYNOPSIS:
613  *
614  * double x, y, y1();
615  *
616  * y = y1( x );
617  *
618  *
619  *
620  * DESCRIPTION:
621  *
622  * Returns Bessel function of the second kind of order one
623  * of the argument.
624  *
625  * The domain is divided into the intervals [0, 8] and
626  * (8, infinity). In the first interval a 25 term Chebyshev
627  * expansion is used, and a call to j1() is required.
628  * In the second, the asymptotic trigonometric representation
629  * is employed using two rational functions of degree 5/5.
630  *
631  *
632  *
633  * ACCURACY:
634  *
635  * Absolute error:
636  * arithmetic domain # trials peak rms
637  * DEC 0, 30 10000 8.6e-17 1.3e-17
638  * IEEE 0, 30 30000 1.0e-15 1.3e-16
639  *
640  * (error criterion relative when |y1| > 1).
641  *
642  */
643 /*
644 Cephes Math Library Release 2.1: January, 1989
645 Copyright 1984, 1987, 1989 by Stephen L. Moshier
646 Direct inquiries to 30 Frost Street, Cambridge, MA 02140
647 */
648 
649 #define PIO4 .78539816339744830962
650 #define THPIO4 2.35619449019234492885
651 #define SQ2OPI .79788456080286535588
652 
653 // #include "mconf.h"
654 
655 #ifdef UNK
656 static double RP1[4] = {
657 -8.99971225705559398224E8,
658  4.52228297998194034323E11,
659 -7.27494245221818276015E13,
660  3.68295732863852883286E15,
661 };
662 static double RQ1[8] = {
663 /* 1.00000000000000000000E0,*/
664  6.20836478118054335476E2,
665  2.56987256757748830383E5,
666  8.35146791431949253037E7,
667  2.21511595479792499675E10,
668  4.74914122079991414898E12,
669  7.84369607876235854894E14,
670  8.95222336184627338078E16,
671  5.32278620332680085395E18,
672 };
673 #endif
674 #ifdef DEC
675 static unsigned short RP1[16] = {
676 0147526,0110742,0063322,0077052,
677 0051722,0112720,0065034,0061530,
678 0153604,0052227,0033147,0105650,
679 0055121,0055025,0032276,0022015,
680 };
681 static unsigned short RQ1[32] = {
682 /*0040200,0000000,0000000,0000000,*/
683 0042433,0032610,0155604,0033473,
684 0044572,0173320,0067270,0006616,
685 0046637,0045246,0162225,0006606,
686 0050645,0004773,0157577,0053004,
687 0052612,0033734,0001667,0176501,
688 0054462,0054121,0173147,0121367,
689 0056237,0002777,0121451,0176007,
690 0057623,0136253,0131601,0044710,
691 };
692 #endif
693 #ifdef IBMPC
694 static unsigned short RP1[16] = {
695 0x4fc5,0x4cda,0xd23c,0xc1ca,
696 0x8c6b,0x0d43,0x52ba,0x425a,
697 0xf175,0xe6cc,0x8a92,0xc2d0,
698 0xc482,0xa697,0x2b42,0x432a,
699 };
700 static unsigned short RQ1[32] = {
701 /*0x0000,0x0000,0x0000,0x3ff0,*/
702 0x86e7,0x1b70,0x66b1,0x4083,
703 0x01b2,0x0dd7,0x5eda,0x410f,
704 0xa1b1,0xdc92,0xe954,0x4193,
705 0xeac1,0x7bef,0xa13f,0x4214,
706 0xffa8,0x8076,0x46fb,0x4291,
707 0xf45f,0x3ecc,0x4b0a,0x4306,
708 0x3f81,0xf465,0xe0bf,0x4373,
709 0x2939,0x7670,0x7795,0x43d2,
710 };
711 #endif
712 #ifdef MIEEE
713 static unsigned short RP1[16] = {
714 0xc1ca,0xd23c,0x4cda,0x4fc5,
715 0x425a,0x52ba,0x0d43,0x8c6b,
716 0xc2d0,0x8a92,0xe6cc,0xf175,
717 0x432a,0x2b42,0xa697,0xc482,
718 };
719 static unsigned short RQ1[32] = {
720 /*0x3ff0,0x0000,0x0000,0x0000,*/
721 0x4083,0x66b1,0x1b70,0x86e7,
722 0x410f,0x5eda,0x0dd7,0x01b2,
723 0x4193,0xe954,0xdc92,0xa1b1,
724 0x4214,0xa13f,0x7bef,0xeac1,
725 0x4291,0x46fb,0x8076,0xffa8,
726 0x4306,0x4b0a,0x3ecc,0xf45f,
727 0x4373,0xe0bf,0xf465,0x3f81,
728 0x43d2,0x7795,0x7670,0x2939,
729 };
730 #endif
731 
732 #ifdef UNK
733 static double PP1[7] = {
734  7.62125616208173112003E-4,
735  7.31397056940917570436E-2,
736  1.12719608129684925192E0,
737  5.11207951146807644818E0,
738  8.42404590141772420927E0,
739  5.21451598682361504063E0,
740  1.00000000000000000254E0,
741 };
742 static double PQ1[7] = {
743  5.71323128072548699714E-4,
744  6.88455908754495404082E-2,
745  1.10514232634061696926E0,
746  5.07386386128601488557E0,
747  8.39985554327604159757E0,
748  5.20982848682361821619E0,
749  9.99999999999999997461E-1,
750 };
751 #endif
752 #ifdef DEC
753 static unsigned short PP1[28] = {
754 0035507,0144542,0061543,0024326,
755 0037225,0145105,0017766,0022661,
756 0040220,0043766,0010254,0133255,
757 0040643,0113047,0142611,0151521,
758 0041006,0144344,0055351,0074261,
759 0040646,0156520,0120574,0006416,
760 0040200,0000000,0000000,0000000,
761 };
762 static unsigned short PQ1[28] = {
763 0035425,0142330,0115041,0165514,
764 0037214,0177352,0145105,0052026,
765 0040215,0072515,0141207,0073255,
766 0040642,0056427,0137222,0106405,
767 0041006,0062716,0166427,0165450,
768 0040646,0133352,0035425,0123304,
769 0040200,0000000,0000000,0000000,
770 };
771 #endif
772 #ifdef IBMPC
773 static unsigned short PP1[28] = {
774 0x651b,0x4c6c,0xf92c,0x3f48,
775 0xc4b6,0xa3fe,0xb948,0x3fb2,
776 0x96d6,0xc215,0x08fe,0x3ff2,
777 0x3a6a,0xf8b1,0x72c4,0x4014,
778 0x2f16,0x8b5d,0xd91c,0x4020,
779 0x81a2,0x142f,0xdbaa,0x4014,
780 0x0000,0x0000,0x0000,0x3ff0,
781 };
782 static unsigned short PQ1[28] = {
783 0x3d69,0x1344,0xb89b,0x3f42,
784 0xaa83,0x5948,0x9fdd,0x3fb1,
785 0xeed6,0xb850,0xaea9,0x3ff1,
786 0x51a1,0xf7d2,0x4ba2,0x4014,
787 0xfd65,0xdda2,0xccb9,0x4020,
788 0xb4d9,0x4762,0xd6dd,0x4014,
789 0x0000,0x0000,0x0000,0x3ff0,
790 };
791 #endif
792 #ifdef MIEEE
793 static unsigned short PP1[28] = {
794 0x3f48,0xf92c,0x4c6c,0x651b,
795 0x3fb2,0xb948,0xa3fe,0xc4b6,
796 0x3ff2,0x08fe,0xc215,0x96d6,
797 0x4014,0x72c4,0xf8b1,0x3a6a,
798 0x4020,0xd91c,0x8b5d,0x2f16,
799 0x4014,0xdbaa,0x142f,0x81a2,
800 0x3ff0,0x0000,0x0000,0x0000,
801 };
802 static unsigned short PQ1[28] = {
803 0x3f42,0xb89b,0x1344,0x3d69,
804 0x3fb1,0x9fdd,0x5948,0xaa83,
805 0x3ff1,0xaea9,0xb850,0xeed6,
806 0x4014,0x4ba2,0xf7d2,0x51a1,
807 0x4020,0xccb9,0xdda2,0xfd65,
808 0x4014,0xd6dd,0x4762,0xb4d9,
809 0x3ff0,0x0000,0x0000,0x0000,
810 };
811 #endif
812 
813 #ifdef UNK
814 static double QP1[8] = {
815  5.10862594750176621635E-2,
816  4.98213872951233449420E0,
817  7.58238284132545283818E1,
818  3.66779609360150777800E2,
819  7.10856304998926107277E2,
820  5.97489612400613639965E2,
821  2.11688757100572135698E2,
822  2.52070205858023719784E1,
823 };
824 static double QQ1[7] = {
825 /* 1.00000000000000000000E0,*/
826  7.42373277035675149943E1,
827  1.05644886038262816351E3,
828  4.98641058337653607651E3,
829  9.56231892404756170795E3,
830  7.99704160447350683650E3,
831  2.82619278517639096600E3,
832  3.36093607810698293419E2,
833 };
834 #endif
835 #ifdef DEC
836 static unsigned short QP1[32] = {
837 0037121,0037723,0055605,0151004,
838 0040637,0066656,0031554,0077264,
839 0041627,0122714,0153170,0161466,
840 0042267,0061712,0036520,0140145,
841 0042461,0133315,0131573,0071176,
842 0042425,0057525,0147500,0013201,
843 0042123,0130122,0061245,0154131,
844 0041311,0123772,0064254,0172650,
845 };
846 static unsigned short QQ1[28] = {
847 /*0040200,0000000,0000000,0000000,*/
848 0041624,0074603,0002112,0101670,
849 0042604,0007135,0010162,0175565,
850 0043233,0151510,0157757,0172010,
851 0043425,0064506,0112006,0104276,
852 0043371,0164125,0032271,0164242,
853 0043060,0121425,0122750,0136013,
854 0042250,0005773,0053472,0146267,
855 };
856 #endif
857 #ifdef IBMPC
858 static unsigned short QP1[32] = {
859 0xba40,0x6b70,0x27fa,0x3faa,
860 0x8fd6,0xc66d,0xedb5,0x4013,
861 0x1c67,0x9acf,0xf4b9,0x4052,
862 0x180d,0x47aa,0xec79,0x4076,
863 0x6e50,0xb66f,0x36d9,0x4086,
864 0x02d0,0xb9e8,0xabea,0x4082,
865 0xbb0b,0x4c54,0x760a,0x406a,
866 0x9eb5,0x4d15,0x34ff,0x4039,
867 };
868 static unsigned short QQ1[28] = {
869 /*0x0000,0x0000,0x0000,0x3ff0,*/
870 0x5077,0x6089,0x8f30,0x4052,
871 0x5f6f,0xa20e,0x81cb,0x4090,
872 0xfe81,0x1bfd,0x7a69,0x40b3,
873 0xd118,0xd280,0xad28,0x40c2,
874 0x3d14,0xa697,0x3d0a,0x40bf,
875 0x1781,0xb4bd,0x1462,0x40a6,
876 0x5997,0x6ae7,0x017f,0x4075,
877 };
878 #endif
879 #ifdef MIEEE
880 static unsigned short QP1[32] = {
881 0x3faa,0x27fa,0x6b70,0xba40,
882 0x4013,0xedb5,0xc66d,0x8fd6,
883 0x4052,0xf4b9,0x9acf,0x1c67,
884 0x4076,0xec79,0x47aa,0x180d,
885 0x4086,0x36d9,0xb66f,0x6e50,
886 0x4082,0xabea,0xb9e8,0x02d0,
887 0x406a,0x760a,0x4c54,0xbb0b,
888 0x4039,0x34ff,0x4d15,0x9eb5,
889 };
890 static unsigned short QQ1[28] = {
891 /*0x3ff0,0x0000,0x0000,0x0000,*/
892 0x4052,0x8f30,0x6089,0x5077,
893 0x4090,0x81cb,0xa20e,0x5f6f,
894 0x40b3,0x7a69,0x1bfd,0xfe81,
895 0x40c2,0xad28,0xd280,0xd118,
896 0x40bf,0x3d0a,0xa697,0x3d14,
897 0x40a6,0x1462,0xb4bd,0x1781,
898 0x4075,0x017f,0x6ae7,0x5997,
899 };
900 #endif
901 
902 #ifdef UNK
903 static double YP1[6] = {
904  1.26320474790178026440E9,
905 -6.47355876379160291031E11,
906  1.14509511541823727583E14,
907 -8.12770255501325109621E15,
908  2.02439475713594898196E17,
909 -7.78877196265950026825E17,
910 };
911 static double YQ1[8] = {
912 /* 1.00000000000000000000E0,*/
913  5.94301592346128195359E2,
914  2.35564092943068577943E5,
915  7.34811944459721705660E7,
916  1.87601316108706159478E10,
917  3.88231277496238566008E12,
918  6.20557727146953693363E14,
919  6.87141087355300489866E16,
920  3.97270608116560655612E18,
921 };
922 #endif
923 #ifdef DEC
924 static unsigned short YP1[24] = {
925 0047626,0112763,0013715,0133045,
926 0152026,0134552,0142033,0024411,
927 0053720,0045245,0102210,0077565,
928 0155347,0000321,0136415,0102031,
929 0056463,0146550,0055633,0032605,
930 0157054,0171012,0167361,0054265,
931 };
932 static unsigned short YQ1[32] = {
933 /*0040200,0000000,0000000,0000000,*/
934 0042424,0111515,0044773,0153014,
935 0044546,0005405,0171307,0075774,
936 0046614,0023575,0047105,0063556,
937 0050613,0143034,0101533,0156026,
938 0052541,0175367,0166514,0114257,
939 0054415,0014466,0134350,0171154,
940 0056164,0017436,0025075,0022101,
941 0057534,0103614,0103663,0121772,
942 };
943 #endif
944 #ifdef IBMPC
945 static unsigned short YP1[24] = {
946 0xb6c5,0x62f9,0xd2be,0x41d2,
947 0x6521,0x5883,0xd72d,0xc262,
948 0x0fef,0xb091,0x0954,0x42da,
949 0xb083,0x37a1,0xe01a,0xc33c,
950 0x66b1,0x0b73,0x79ad,0x4386,
951 0x2b17,0x5dde,0x9e41,0xc3a5,
952 };
953 static unsigned short YQ1[32] = {
954 /*0x0000,0x0000,0x0000,0x3ff0,*/
955 0x7ac2,0xa93f,0x9269,0x4082,
956 0xef7f,0xbe58,0xc160,0x410c,
957 0xacee,0xa9c8,0x84ef,0x4191,
958 0x7b83,0x906b,0x78c3,0x4211,
959 0x9316,0xfda9,0x3f5e,0x428c,
960 0x1e4e,0xd71d,0xa326,0x4301,
961 0xa488,0xc547,0x83e3,0x436e,
962 0x747f,0x90f6,0x90f1,0x43cb,
963 };
964 #endif
965 #ifdef MIEEE
966 static unsigned short YP1[24] = {
967 0x41d2,0xd2be,0x62f9,0xb6c5,
968 0xc262,0xd72d,0x5883,0x6521,
969 0x42da,0x0954,0xb091,0x0fef,
970 0xc33c,0xe01a,0x37a1,0xb083,
971 0x4386,0x79ad,0x0b73,0x66b1,
972 0xc3a5,0x9e41,0x5dde,0x2b17,
973 };
974 static unsigned short YQ1[32] = {
975 /*0x3ff0,0x0000,0x0000,0x0000,*/
976 0x4082,0x9269,0xa93f,0x7ac2,
977 0x410c,0xc160,0xbe58,0xef7f,
978 0x4191,0x84ef,0xa9c8,0xacee,
979 0x4211,0x78c3,0x906b,0x7b83,
980 0x428c,0x3f5e,0xfda9,0x9316,
981 0x4301,0xa326,0xd71d,0x1e4e,
982 0x436e,0x83e3,0xc547,0xa488,
983 0x43cb,0x90f1,0x90f6,0x747f,
984 };
985 #endif
986 
987 
988 #ifdef UNK
989 static double Z1 = 1.46819706421238932572E1;
990 static double Z2 = 4.92184563216946036703E1;
991 #endif
992 
993 #ifdef DEC
994 static unsigned short DZ1[] = {0041152,0164532,0006114,0010540};
995 static unsigned short DZ2[] = {0041504,0157663,0001625,0020621};
996 #define Z1 (*(double *)DZ1)
997 #define Z2 (*(double *)DZ2)
998 #endif
999 
1000 #ifdef IBMPC
1001 static unsigned short DZ1[] = {0x822c,0x4189,0x5d2b,0x402d};
1002 static unsigned short DZ2[] = {0xa432,0x6072,0x9bf6,0x4048};
1003 #define Z1 (*(double *)DZ1)
1004 #define Z2 (*(double *)DZ2)
1005 #endif
1006 
1007 #ifdef MIEEE
1008 static unsigned short DZ1[] = {0x402d,0x5d2b,0x4189,0x822c};
1009 static unsigned short DZ2[] = {0x4048,0x9bf6,0x6072,0xa432};
1010 #define Z1 (*(double *)DZ1)
1011 #define Z2 (*(double *)DZ2)
1012 #endif
1013 
1014 #ifndef ANSIPROT
1015 double bessj1(), polevl(), p1evl(), log(), sin(), cos(), sqrt();
1016 #endif
1017 
1018 double bessj1(double x)
1019 {
1020 double w, z, p, q, xn;
1021 
1022 w = x;
1023 if( x < 0 )
1024  w = -x;
1025 
1026 if( w <= 5.0 )
1027  {
1028  z = x * x;
1029  w = polevl( z, RP1, 3 ) / p1evl( z, RQ1, 8 );
1030  w = w * x * (z - Z1) * (z - Z2);
1031  return( w );
1032  }
1033 
1034 w = 5.0/x;
1035 z = w * w;
1036 p = polevl( z, PP1, 6)/polevl( z, PQ1, 6 );
1037 q = polevl( z, QP1, 7)/p1evl( z, QQ1, 7 );
1038 xn = x - THPIO4;
1039 p = p * cos(xn) - w * q * sin(xn);
1040 return( p * SQ2OPI / sqrt(x) );
1041 }
1042 
1043 double bessy1(double x)
1044 {
1045 double w, z, p, q, xn;
1046 
1047 if( x <= 5.0 )
1048  {
1049  if( x <= 0.0 )
1050  throw Exception("arg<=0 in bessy1");
1051  z = x * x;
1052  w = x * (polevl( z, YP1, 5 ) / p1evl( z, YQ1, 8 ));
1053  w += TWOOPI * ( bessj1(x) * log(x) - 1.0/x );
1054  return( w );
1055  }
1056 
1057 w = 5.0/x;
1058 z = w * w;
1059 p = polevl( z, PP1, 6)/polevl( z, PQ1, 6 );
1060 q = polevl( z, QP1, 7)/p1evl( z, QQ1, 7 );
1061 xn = x - THPIO4;
1062 p = p * sin(xn) + w * q * cos(xn);
1063 return( p * SQ2OPI / sqrt(x) );
1064 }