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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_j0.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_j0(x), __ieee754_y0(x)
53 * Bessel function of the first and second kinds of order zero.
54 * Method -- j0(x):
55 * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
56 * 2. Reduce x to |x| since j0(x)=j0(-x), and
57 * for x in (0,2)
58 * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
59 * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
60 * for x in (2,inf)
61 * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
62 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
63 * as follow:
64 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
65 * = 1/sqrt(2) * (cos(x) + sin(x))
66 * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
67 * = 1/sqrt(2) * (sin(x) - cos(x))
68 * (To avoid cancellation, use
69 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
70 * to compute the worse one.)
71 *
72 * 3 Special cases
73 * j0(nan)= nan
74 * j0(0) = 1
75 * j0(inf) = 0
76 *
77 * Method -- y0(x):
78 * 1. For x<2.
79 * Since
80 * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
81 * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
82 * We use the following function to approximate y0,
83 * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
84 * where
85 * U(z) = u00 + u01*z + ... + u06*z^6
86 * V(z) = 1 + v01*z + ... + v04*z^4
87 * with absolute approximation error bounded by 2**-72.
88 * Note: For tiny x, U/V = u0 and j0(x)~1, hence
89 * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
90 * 2. For x>=2.
91 * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
92 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
93 * by the method mentioned above.
94 * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
95 */
96
97 #include "fdlibm.h"
98
99 #ifdef __STDC__
100 static double pzero(double), qzero(double);
101 #else
102 static double pzero(), qzero();
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, 2.00] */
115 R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
116 R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
117 R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
118 R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
119 S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
120 S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
121 S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
122 S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
123
124 static double zero = 0.0;
125
126 #ifdef __STDC__
127 double __ieee754_j0(double x)
128 #else
129 double __ieee754_j0(x)
130 double x;
131 #endif
132 {
133 fd_twoints un;
134 double z, s,c,ss,cc,r,u,v;
135 int hx,ix;
136
137 un.d = x;
138 hx = __HI(un);
139 ix = hx&0x7fffffff;
140 if(ix>=0x7ff00000) return one/(x*x);
141 x = fd_fabs(x);
142 if(ix >= 0x40000000) { /* |x| >= 2.0 */
143 s = fd_sin(x);
144 c = fd_cos(x);
145 ss = s-c;
146 cc = s+c;
147 if(ix<0x7fe00000) { /* make sure x+x not overflow */
148 z = -fd_cos(x+x);
149 if ((s*c)<zero) cc = z/ss;
150 else ss = z/cc;
151 }
152 /*
153 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
154 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
155 */
156 if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(x);
157 else {
158 u = pzero(x); v = qzero(x);
159 z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(x);
160 }
161 return z;
162 }
163 if(ix<0x3f200000) { /* |x| < 2**-13 */
164 if(really_big+x>one) { /* raise inexact if x != 0 */
165 if(ix<0x3e400000) return one; /* |x|<2**-27 */
166 else return one - 0.25*x*x;
167 }
168 }
169 z = x*x;
170 r = z*(R02+z*(R03+z*(R04+z*R05)));
171 s = one+z*(S01+z*(S02+z*(S03+z*S04)));
172 if(ix < 0x3FF00000) { /* |x| < 1.00 */
173 return one + z*(-0.25+(r/s));
174 } else {
175 u = 0.5*x;
176 return((one+u)*(one-u)+z*(r/s));
177 }
178 }
179
180 #ifdef __STDC__
181 static const double
182 #else
183 static double
184 #endif
185 u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
186 u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
187 u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
188 u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
189 u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
190 u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
191 u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
192 v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
193 v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
194 v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
195 v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
196
197 #ifdef __STDC__
198 double __ieee754_y0(double x)
199 #else
200 double __ieee754_y0(x)
201 double x;
202 #endif
203 {
204 fd_twoints un;
205 double z, s,c,ss,cc,u,v;
206 int hx,ix,lx;
207
208 un.d = x;
209 hx = __HI(un);
210 ix = 0x7fffffff&hx;
211 lx = __LO(un);
212 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
213 if(ix>=0x7ff00000) return one/(x+x*x);
214 if((ix|lx)==0) return -one/zero;
215 if(hx<0) return zero/zero;
216 if(ix >= 0x40000000) { /* |x| >= 2.0 */
217 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
218 * where x0 = x-pi/4
219 * Better formula:
220 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
221 * = 1/sqrt(2) * (sin(x) + cos(x))
222 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
223 * = 1/sqrt(2) * (sin(x) - cos(x))
224 * To avoid cancellation, use
225 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
226 * to compute the worse one.
227 */
228 s = fd_sin(x);
229 c = fd_cos(x);
230 ss = s-c;
231 cc = s+c;
232 /*
233 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
234 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
235 */
236 if(ix<0x7fe00000) { /* make sure x+x not overflow */
237 z = -fd_cos(x+x);
238 if ((s*c)<zero) cc = z/ss;
239 else ss = z/cc;
240 }
241 if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
242 else {
243 u = pzero(x); v = qzero(x);
244 z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
245 }
246 return z;
247 }
248 if(ix<=0x3e400000) { /* x < 2**-27 */
249 return(u00 + tpi*__ieee754_log(x));
250 }
251 z = x*x;
252 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
253 v = one+z*(v01+z*(v02+z*(v03+z*v04)));
254 return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
255 }
256
257 /* The asymptotic expansions of pzero is
258 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
259 * For x >= 2, We approximate pzero by
260 * pzero(x) = 1 + (R/S)
261 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
262 * S = 1 + pS0*s^2 + ... + pS4*s^10
263 * and
264 * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
265 */
266 #ifdef __STDC__
267 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
268 #else
269 static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
270 #endif
271 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
272 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
273 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
274 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
275 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
276 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
277 };
278 #ifdef __STDC__
279 static const double pS8[5] = {
280 #else
281 static double pS8[5] = {
282 #endif
283 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
284 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
285 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
286 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
287 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
288 };
289
290 #ifdef __STDC__
291 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
292 #else
293 static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
294 #endif
295 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
296 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
297 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
298 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
299 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
300 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
301 };
302 #ifdef __STDC__
303 static const double pS5[5] = {
304 #else
305 static double pS5[5] = {
306 #endif
307 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
308 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
309 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
310 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
311 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
312 };
313
314 #ifdef __STDC__
315 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
316 #else
317 static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
318 #endif
319 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
320 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
321 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
322 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
323 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
324 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
325 };
326 #ifdef __STDC__
327 static const double pS3[5] = {
328 #else
329 static double pS3[5] = {
330 #endif
331 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
332 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
333 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
334 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
335 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
336 };
337
338 #ifdef __STDC__
339 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
340 #else
341 static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
342 #endif
343 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
344 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
345 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
346 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
347 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
348 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
349 };
350 #ifdef __STDC__
351 static const double pS2[5] = {
352 #else
353 static double pS2[5] = {
354 #endif
355 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
356 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
357 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
358 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
359 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
360 };
361
362 #ifdef __STDC__
363 static double pzero(double x)
364 #else
365 static double pzero(x)
366 double x;
367 #endif
368 {
369 #ifdef __STDC__
370 const double *p,*q;
371 #else
372 double *p,*q;
373 #endif
374 fd_twoints u;
375 double z,r,s;
376 int ix;
377 u.d = x;
378 ix = 0x7fffffff&__HI(u);
379 if(ix>=0x40200000) {p = pR8; q= pS8;}
380 else if(ix>=0x40122E8B){p = pR5; q= pS5;}
381 else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
382 else if(ix>=0x40000000){p = pR2; q= pS2;}
383 z = one/(x*x);
384 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
385 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
386 return one+ r/s;
387 }
388
389
390 /* For x >= 8, the asymptotic expansions of qzero is
391 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
392 * We approximate pzero by
393 * qzero(x) = s*(-1.25 + (R/S))
394 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
395 * S = 1 + qS0*s^2 + ... + qS5*s^12
396 * and
397 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
398 */
399 #ifdef __STDC__
400 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
401 #else
402 static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
403 #endif
404 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
405 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
406 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
407 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
408 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
409 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
410 };
411 #ifdef __STDC__
412 static const double qS8[6] = {
413 #else
414 static double qS8[6] = {
415 #endif
416 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
417 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
418 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
419 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
420 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
421 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
422 };
423
424 #ifdef __STDC__
425 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
426 #else
427 static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
428 #endif
429 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
430 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
431 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
432 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
433 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
434 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
435 };
436 #ifdef __STDC__
437 static const double qS5[6] = {
438 #else
439 static double qS5[6] = {
440 #endif
441 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
442 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
443 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
444 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
445 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
446 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
447 };
448
449 #ifdef __STDC__
450 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
451 #else
452 static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
453 #endif
454 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
455 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
456 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
457 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
458 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
459 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
460 };
461 #ifdef __STDC__
462 static const double qS3[6] = {
463 #else
464 static double qS3[6] = {
465 #endif
466 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
467 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
468 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
469 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
470 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
471 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
472 };
473
474 #ifdef __STDC__
475 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
476 #else
477 static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
478 #endif
479 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
480 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
481 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
482 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
483 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
484 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
485 };
486 #ifdef __STDC__
487 static const double qS2[6] = {
488 #else
489 static double qS2[6] = {
490 #endif
491 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
492 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
493 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
494 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
495 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
496 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
497 };
498
499 #ifdef __STDC__
500 static double qzero(double x)
501 #else
502 static double qzero(x)
503 double x;
504 #endif
505 {
506 #ifdef __STDC__
507 const double *p,*q;
508 #else
509 double *p,*q;
510 #endif
511 fd_twoints u;
512 double s,r,z;
513 int ix;
514 u.d = x;
515 ix = 0x7fffffff&__HI(u);
516 if(ix>=0x40200000) {p = qR8; q= qS8;}
517 else if(ix>=0x40122E8B){p = qR5; q= qS5;}
518 else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
519 else if(ix>=0x40000000){p = qR2; q= qS2;}
520 z = one/(x*x);
521 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
522 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
523 return (-.125 + r/s)/x;
524 }

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