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1 siliconforks 2 /* -*- 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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