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Initial import.

1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2 *
3 * ***** BEGIN LICENSE BLOCK *****
4 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
5 *
6 * The contents of this file are subject to the Mozilla Public License Version
7 * 1.1 (the "License"); you may not use this file except in compliance with
8 * the License. You may obtain a copy of the License at
9 * http://www.mozilla.org/MPL/
10 *
11 * Software distributed under the License is distributed on an "AS IS" basis,
12 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13 * for the specific language governing rights and limitations under the
14 * License.
15 *
16 * The Original Code is Mozilla Communicator client code, released
17 * March 31, 1998.
18 *
19 * The Initial Developer of the Original Code is
20 * Sun Microsystems, Inc.
21 * Portions created by the Initial Developer are Copyright (C) 1998
22 * the Initial Developer. All Rights Reserved.
23 *
24 * Contributor(s):
25 *
26 * Alternatively, the contents of this file may be used under the terms of
27 * either of the GNU General Public License Version 2 or later (the "GPL"),
28 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29 * in which case the provisions of the GPL or the LGPL are applicable instead
30 * of those above. If you wish to allow use of your version of this file only
31 * under the terms of either the GPL or the LGPL, and not to allow others to
32 * use your version of this file under the terms of the MPL, indicate your
33 * decision by deleting the provisions above and replace them with the notice
34 * and other provisions required by the GPL or the LGPL. If you do not delete
35 * the provisions above, a recipient may use your version of this file under
36 * the terms of any one of the MPL, the GPL or the LGPL.
37 *
38 * ***** END LICENSE BLOCK ***** */
39
40 /* @(#)e_j1.c 1.3 95/01/18 */
41 /*
42 * ====================================================
43 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44 *
45 * Developed at SunSoft, a Sun Microsystems, Inc. business.
46 * Permission to use, copy, modify, and distribute this
47 * software is freely granted, provided that this notice
48 * is preserved.
49 * ====================================================
50 */
51
52 /* __ieee754_j1(x), __ieee754_y1(x)
53 * Bessel function of the first and second kinds of order zero.
54 * Method -- j1(x):
55 * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
56 * 2. Reduce x to |x| since j1(x)=-j1(-x), and
57 * for x in (0,2)
58 * j1(x) = x/2 + x*z*R0/S0, where z = x*x;
59 * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
60 * for x in (2,inf)
61 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
62 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
63 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
64 * as follow:
65 * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
66 * = 1/sqrt(2) * (sin(x) - cos(x))
67 * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
68 * = -1/sqrt(2) * (sin(x) + cos(x))
69 * (To avoid cancellation, use
70 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
71 * to compute the worse one.)
72 *
73 * 3 Special cases
74 * j1(nan)= nan
75 * j1(0) = 0
76 * j1(inf) = 0
77 *
78 * Method -- y1(x):
79 * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
80 * 2. For x<2.
81 * Since
82 * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
83 * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
84 * We use the following function to approximate y1,
85 * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
86 * where for x in [0,2] (abs err less than 2**-65.89)
87 * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
88 * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
89 * Note: For tiny x, 1/x dominate y1 and hence
90 * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
91 * 3. For x>=2.
92 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
93 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
94 * by method mentioned above.
95 */
96
97 #include "fdlibm.h"
98
99 #ifdef __STDC__
100 static double pone(double), qone(double);
101 #else
102 static double pone(), qone();
103 #endif
104
105 #ifdef __STDC__
106 static const double
107 #else
108 static double
109 #endif
110 really_big = 1e300,
111 one = 1.0,
112 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
113 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
114 /* R0/S0 on [0,2] */
115 r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
116 r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
117 r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
118 r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
119 s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
120 s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
121 s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
122 s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
123 s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
124
125 static double zero = 0.0;
126
127 #ifdef __STDC__
128 double __ieee754_j1(double x)
129 #else
130 double __ieee754_j1(x)
131 double x;
132 #endif
133 {
134 fd_twoints un;
135 double z, s,c,ss,cc,r,u,v,y;
136 int hx,ix;
137
138 un.d = x;
139 hx = __HI(un);
140 ix = hx&0x7fffffff;
141 if(ix>=0x7ff00000) return one/x;
142 y = fd_fabs(x);
143 if(ix >= 0x40000000) { /* |x| >= 2.0 */
144 s = fd_sin(y);
145 c = fd_cos(y);
146 ss = -s-c;
147 cc = s-c;
148 if(ix<0x7fe00000) { /* make sure y+y not overflow */
149 z = fd_cos(y+y);
150 if ((s*c)>zero) cc = z/ss;
151 else ss = z/cc;
152 }
153 /*
154 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
155 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
156 */
157 if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(y);
158 else {
159 u = pone(y); v = qone(y);
160 z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(y);
161 }
162 if(hx<0) return -z;
163 else return z;
164 }
165 if(ix<0x3e400000) { /* |x|<2**-27 */
166 if(really_big+x>one) return 0.5*x;/* inexact if x!=0 necessary */
167 }
168 z = x*x;
169 r = z*(r00+z*(r01+z*(r02+z*r03)));
170 s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
171 r *= x;
172 return(x*0.5+r/s);
173 }
174
175 #ifdef __STDC__
176 static const double U0[5] = {
177 #else
178 static double U0[5] = {
179 #endif
180 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
181 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
182 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
183 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
184 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
185 };
186 #ifdef __STDC__
187 static const double V0[5] = {
188 #else
189 static double V0[5] = {
190 #endif
191 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
192 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
193 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
194 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
195 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
196 };
197
198 #ifdef __STDC__
199 double __ieee754_y1(double x)
200 #else
201 double __ieee754_y1(x)
202 double x;
203 #endif
204 {
205 fd_twoints un;
206 double z, s,c,ss,cc,u,v;
207 int hx,ix,lx;
208
209 un.d = x;
210 hx = __HI(un);
211 ix = 0x7fffffff&hx;
212 lx = __LO(un);
213 /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
214 if(ix>=0x7ff00000) return one/(x+x*x);
215 if((ix|lx)==0) return -one/zero;
216 if(hx<0) return zero/zero;
217 if(ix >= 0x40000000) { /* |x| >= 2.0 */
218 s = fd_sin(x);
219 c = fd_cos(x);
220 ss = -s-c;
221 cc = s-c;
222 if(ix<0x7fe00000) { /* make sure x+x not overflow */
223 z = fd_cos(x+x);
224 if ((s*c)>zero) cc = z/ss;
225 else ss = z/cc;
226 }
227 /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
228 * where x0 = x-3pi/4
229 * Better formula:
230 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
231 * = 1/sqrt(2) * (sin(x) - cos(x))
232 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
233 * = -1/sqrt(2) * (cos(x) + sin(x))
234 * To avoid cancellation, use
235 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
236 * to compute the worse one.
237 */
238 if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
239 else {
240 u = pone(x); v = qone(x);
241 z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
242 }
243 return z;
244 }
245 if(ix<=0x3c900000) { /* x < 2**-54 */
246 return(-tpi/x);
247 }
248 z = x*x;
249 u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
250 v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
251 return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
252 }
253
254 /* For x >= 8, the asymptotic expansions of pone is
255 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
256 * We approximate pone by
257 * pone(x) = 1 + (R/S)
258 * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
259 * S = 1 + ps0*s^2 + ... + ps4*s^10
260 * and
261 * | pone(x)-1-R/S | <= 2 ** ( -60.06)
262 */
263
264 #ifdef __STDC__
265 static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
266 #else
267 static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
268 #endif
269 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
270 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
271 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
272 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
273 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
274 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
275 };
276 #ifdef __STDC__
277 static const double ps8[5] = {
278 #else
279 static double ps8[5] = {
280 #endif
281 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
282 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
283 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
284 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
285 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
286 };
287
288 #ifdef __STDC__
289 static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
290 #else
291 static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
292 #endif
293 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
294 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
295 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
296 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
297 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
298 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
299 };
300 #ifdef __STDC__
301 static const double ps5[5] = {
302 #else
303 static double ps5[5] = {
304 #endif
305 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
306 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
307 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
308 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
309 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
310 };
311
312 #ifdef __STDC__
313 static const double pr3[6] = {
314 #else
315 static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
316 #endif
317 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
318 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
319 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
320 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
321 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
322 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
323 };
324 #ifdef __STDC__
325 static const double ps3[5] = {
326 #else
327 static double ps3[5] = {
328 #endif
329 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
330 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
331 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
332 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
333 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
334 };
335
336 #ifdef __STDC__
337 static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
338 #else
339 static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
340 #endif
341 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
342 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
343 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
344 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
345 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
346 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
347 };
348 #ifdef __STDC__
349 static const double ps2[5] = {
350 #else
351 static double ps2[5] = {
352 #endif
353 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
354 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
355 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
356 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
357 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
358 };
359
360 #ifdef __STDC__
361 static double pone(double x)
362 #else
363 static double pone(x)
364 double x;
365 #endif
366 {
367 #ifdef __STDC__
368 const double *p,*q;
369 #else
370 double *p,*q;
371 #endif
372 fd_twoints un;
373 double z,r,s;
374 int ix;
375 un.d = x;
376 ix = 0x7fffffff&__HI(un);
377 if(ix>=0x40200000) {p = pr8; q= ps8;}
378 else if(ix>=0x40122E8B){p = pr5; q= ps5;}
379 else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
380 else if(ix>=0x40000000){p = pr2; q= ps2;}
381 z = one/(x*x);
382 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
383 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
384 return one+ r/s;
385 }
386
387
388 /* For x >= 8, the asymptotic expansions of qone is
389 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
390 * We approximate pone by
391 * qone(x) = s*(0.375 + (R/S))
392 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
393 * S = 1 + qs1*s^2 + ... + qs6*s^12
394 * and
395 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
396 */
397
398 #ifdef __STDC__
399 static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
400 #else
401 static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
402 #endif
403 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
404 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
405 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
406 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
407 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
408 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
409 };
410 #ifdef __STDC__
411 static const double qs8[6] = {
412 #else
413 static double qs8[6] = {
414 #endif
415 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
416 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
417 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
418 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
419 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
420 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
421 };
422
423 #ifdef __STDC__
424 static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
425 #else
426 static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
427 #endif
428 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
429 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
430 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
431 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
432 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
433 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
434 };
435 #ifdef __STDC__
436 static const double qs5[6] = {
437 #else
438 static double qs5[6] = {
439 #endif
440 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
441 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
442 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
443 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
444 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
445 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
446 };
447
448 #ifdef __STDC__
449 static const double qr3[6] = {
450 #else
451 static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
452 #endif
453 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
454 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
455 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
456 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
457 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
458 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
459 };
460 #ifdef __STDC__
461 static const double qs3[6] = {
462 #else
463 static double qs3[6] = {
464 #endif
465 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
466 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
467 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
468 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
469 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
470 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
471 };
472
473 #ifdef __STDC__
474 static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
475 #else
476 static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
477 #endif
478 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
479 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
480 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
481 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
482 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
483 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
484 };
485 #ifdef __STDC__
486 static const double qs2[6] = {
487 #else
488 static double qs2[6] = {
489 #endif
490 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
491 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
492 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
493 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
494 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
495 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
496 };
497
498 #ifdef __STDC__
499 static double qone(double x)
500 #else
501 static double qone(x)
502 double x;
503 #endif
504 {
505 #ifdef __STDC__
506 const double *p,*q;
507 #else
508 double *p,*q;
509 #endif
510 fd_twoints un;
511 double s,r,z;
512 int ix;
513 un.d = x;
514 ix = 0x7fffffff&__HI(un);
515 if(ix>=0x40200000) {p = qr8; q= qs8;}
516 else if(ix>=0x40122E8B){p = qr5; q= qs5;}
517 else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
518 else if(ix>=0x40000000){p = qr2; q= qs2;}
519 z = one/(x*x);
520 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
521 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
522 return (.375 + r/s)/x;
523 }

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