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[/] [or1k/] [trunk/] [linux/] [uClibc/] [libm/] [e_j1.c] - Blame information for rev 1765

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1 1325 phoenix
/* @(#)e_j1.c 5.1 93/09/24 */
2
/*
3
 * ====================================================
4
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5
 *
6
 * Developed at SunPro, a Sun Microsystems, Inc. business.
7
 * Permission to use, copy, modify, and distribute this
8
 * software is freely granted, provided that this notice
9
 * is preserved.
10
 * ====================================================
11
 */
12
 
13
#if defined(LIBM_SCCS) && !defined(lint)
14
static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $";
15
#endif
16
 
17
/* __ieee754_j1(x), __ieee754_y1(x)
18
 * Bessel function of the first and second kinds of order zero.
19
 * Method -- j1(x):
20
 *      1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
21
 *      2. Reduce x to |x| since j1(x)=-j1(-x),  and
22
 *         for x in (0,2)
23
 *              j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
24
 *         (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
25
 *         for x in (2,inf)
26
 *              j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
27
 *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
28
 *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
29
 *         as follow:
30
 *              cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
31
 *                      =  1/sqrt(2) * (sin(x) - cos(x))
32
 *              sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
33
 *                      = -1/sqrt(2) * (sin(x) + cos(x))
34
 *         (To avoid cancellation, use
35
 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
36
 *          to compute the worse one.)
37
 *
38
 *      3 Special cases
39
 *              j1(nan)= nan
40
 *              j1(0) = 0
41
 *              j1(inf) = 0
42
 *
43
 * Method -- y1(x):
44
 *      1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
45
 *      2. For x<2.
46
 *         Since
47
 *              y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
48
 *         therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
49
 *         We use the following function to approximate y1,
50
 *              y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
51
 *         where for x in [0,2] (abs err less than 2**-65.89)
52
 *              U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
53
 *              V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
54
 *         Note: For tiny x, 1/x dominate y1 and hence
55
 *              y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
56
 *      3. For x>=2.
57
 *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
58
 *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
59
 *         by method mentioned above.
60
 */
61
 
62
#include "math.h"
63
#include "math_private.h"
64
 
65
#ifdef __STDC__
66
static double pone(double), qone(double);
67
#else
68
static double pone(), qone();
69
#endif
70
 
71
#ifdef __STDC__
72
static const double
73
#else
74
static double
75
#endif
76
huge    = 1e300,
77
one     = 1.0,
78
invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
79
tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
80
        /* R0/S0 on [0,2] */
81
r00  = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
82
r01  =  1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
83
r02  = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
84
r03  =  4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
85
s01  =  1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
86
s02  =  1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
87
s03  =  1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
88
s04  =  5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
89
s05  =  1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
90
 
91
#ifdef __STDC__
92
static const double zero    = 0.0;
93
#else
94
static double zero    = 0.0;
95
#endif
96
 
97
#ifdef __STDC__
98
        double __ieee754_j1(double x)
99
#else
100
        double __ieee754_j1(x)
101
        double x;
102
#endif
103
{
104
        double z, s,c,ss,cc,r,u,v,y;
105
        int32_t hx,ix;
106
 
107
        GET_HIGH_WORD(hx,x);
108
        ix = hx&0x7fffffff;
109
        if(ix>=0x7ff00000) return one/x;
110
        y = fabs(x);
111
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
112
                s = sin(y);
113
                c = cos(y);
114
                ss = -s-c;
115
                cc = s-c;
116
                if(ix<0x7fe00000) {  /* make sure y+y not overflow */
117
                    z = cos(y+y);
118
                    if ((s*c)>zero) cc = z/ss;
119
                    else            ss = z/cc;
120
                }
121
        /*
122
         * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
123
         * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
124
         */
125
                if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
126
                else {
127
                    u = pone(y); v = qone(y);
128
                    z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
129
                }
130
                if(hx<0) return -z;
131
                else     return  z;
132
        }
133
        if(ix<0x3e400000) {     /* |x|<2**-27 */
134
            if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
135
        }
136
        z = x*x;
137
        r =  z*(r00+z*(r01+z*(r02+z*r03)));
138
        s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
139
        r *= x;
140
        return(x*0.5+r/s);
141
}
142
 
143
#ifdef __STDC__
144
static const double U0[5] = {
145
#else
146
static double U0[5] = {
147
#endif
148
 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
149
  5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
150
 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
151
  2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
152
 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
153
};
154
#ifdef __STDC__
155
static const double V0[5] = {
156
#else
157
static double V0[5] = {
158
#endif
159
  1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
160
  2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
161
  1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
162
  6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
163
  1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
164
};
165
 
166
#ifdef __STDC__
167
        double __ieee754_y1(double x)
168
#else
169
        double __ieee754_y1(x)
170
        double x;
171
#endif
172
{
173
        double z, s,c,ss,cc,u,v;
174
        int32_t hx,ix,lx;
175
 
176
        EXTRACT_WORDS(hx,lx,x);
177
        ix = 0x7fffffff&hx;
178
    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
179
        if(ix>=0x7ff00000) return  one/(x+x*x);
180
        if((ix|lx)==0) return -one/zero;
181
        if(hx<0) return zero/zero;
182
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
183
                s = sin(x);
184
                c = cos(x);
185
                ss = -s-c;
186
                cc = s-c;
187
                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
188
                    z = cos(x+x);
189
                    if ((s*c)>zero) cc = z/ss;
190
                    else            ss = z/cc;
191
                }
192
        /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
193
         * where x0 = x-3pi/4
194
         *      Better formula:
195
         *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
196
         *                      =  1/sqrt(2) * (sin(x) - cos(x))
197
         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
198
         *                      = -1/sqrt(2) * (cos(x) + sin(x))
199
         * To avoid cancellation, use
200
         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
201
         * to compute the worse one.
202
         */
203
                if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
204
                else {
205
                    u = pone(x); v = qone(x);
206
                    z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
207
                }
208
                return z;
209
        }
210
        if(ix<=0x3c900000) {    /* x < 2**-54 */
211
            return(-tpi/x);
212
        }
213
        z = x*x;
214
        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
215
        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
216
        return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
217
}
218
 
219
/* For x >= 8, the asymptotic expansions of pone is
220
 *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
221
 * We approximate pone by
222
 *      pone(x) = 1 + (R/S)
223
 * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
224
 *        S = 1 + ps0*s^2 + ... + ps4*s^10
225
 * and
226
 *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
227
 */
228
 
229
#ifdef __STDC__
230
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
231
#else
232
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
233
#endif
234
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
235
  1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
236
  1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
237
  4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
238
  3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
239
  7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
240
};
241
#ifdef __STDC__
242
static const double ps8[5] = {
243
#else
244
static double ps8[5] = {
245
#endif
246
  1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
247
  3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
248
  3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
249
  9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
250
  3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
251
};
252
 
253
#ifdef __STDC__
254
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
255
#else
256
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
257
#endif
258
  1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
259
  1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
260
  6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
261
  1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
262
  5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
263
  5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
264
};
265
#ifdef __STDC__
266
static const double ps5[5] = {
267
#else
268
static double ps5[5] = {
269
#endif
270
  5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
271
  9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
272
  5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
273
  7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
274
  1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
275
};
276
 
277
#ifdef __STDC__
278
static const double pr3[6] = {
279
#else
280
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
281
#endif
282
  3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
283
  1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
284
  3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
285
  3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
286
  9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
287
  4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
288
};
289
#ifdef __STDC__
290
static const double ps3[5] = {
291
#else
292
static double ps3[5] = {
293
#endif
294
  3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
295
  3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
296
  1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
297
  8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
298
  1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
299
};
300
 
301
#ifdef __STDC__
302
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
303
#else
304
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
305
#endif
306
  1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
307
  1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
308
  2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
309
  1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
310
  1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
311
  5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
312
};
313
#ifdef __STDC__
314
static const double ps2[5] = {
315
#else
316
static double ps2[5] = {
317
#endif
318
  2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
319
  1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
320
  2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
321
  1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
322
  8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
323
};
324
 
325
#ifdef __STDC__
326
        static double pone(double x)
327
#else
328
        static double pone(x)
329
        double x;
330
#endif
331
{
332
#ifdef __STDC__
333
        const double *p=0,*q=0;
334
#else
335
        double *p,*q;
336
#endif
337
        double z,r,s;
338
        int32_t ix;
339
        GET_HIGH_WORD(ix,x);
340
        ix &= 0x7fffffff;
341
        if(ix>=0x40200000)     {p = pr8; q= ps8;}
342
        else if(ix>=0x40122E8B){p = pr5; q= ps5;}
343
        else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
344
        else if(ix>=0x40000000){p = pr2; q= ps2;}
345
        z = one/(x*x);
346
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
347
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
348
        return one+ r/s;
349
}
350
 
351
 
352
/* For x >= 8, the asymptotic expansions of qone is
353
 *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
354
 * We approximate pone by
355
 *      qone(x) = s*(0.375 + (R/S))
356
 * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
357
 *        S = 1 + qs1*s^2 + ... + qs6*s^12
358
 * and
359
 *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
360
 */
361
 
362
#ifdef __STDC__
363
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
364
#else
365
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
366
#endif
367
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
368
 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
369
 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
370
 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
371
 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
372
 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
373
};
374
#ifdef __STDC__
375
static const double qs8[6] = {
376
#else
377
static double qs8[6] = {
378
#endif
379
  1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
380
  7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
381
  1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
382
  7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
383
  6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
384
 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
385
};
386
 
387
#ifdef __STDC__
388
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
389
#else
390
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
391
#endif
392
 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
393
 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
394
 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
395
 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
396
 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
397
 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
398
};
399
#ifdef __STDC__
400
static const double qs5[6] = {
401
#else
402
static double qs5[6] = {
403
#endif
404
  8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
405
  1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
406
  1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
407
  4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
408
  2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
409
 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
410
};
411
 
412
#ifdef __STDC__
413
static const double qr3[6] = {
414
#else
415
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
416
#endif
417
 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
418
 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
419
 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
420
 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
421
 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
422
 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
423
};
424
#ifdef __STDC__
425
static const double qs3[6] = {
426
#else
427
static double qs3[6] = {
428
#endif
429
  4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
430
  6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
431
  3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
432
  5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
433
  1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
434
 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
435
};
436
 
437
#ifdef __STDC__
438
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
439
#else
440
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
441
#endif
442
 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
443
 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
444
 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
445
 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
446
 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
447
 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
448
};
449
#ifdef __STDC__
450
static const double qs2[6] = {
451
#else
452
static double qs2[6] = {
453
#endif
454
  2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
455
  2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
456
  7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
457
  7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
458
  1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
459
 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
460
};
461
 
462
#ifdef __STDC__
463
        static double qone(double x)
464
#else
465
        static double qone(x)
466
        double x;
467
#endif
468
{
469
#ifdef __STDC__
470
        const double *p=0,*q=0;
471
#else
472
        double *p,*q;
473
#endif
474
        double  s,r,z;
475
        int32_t ix;
476
        GET_HIGH_WORD(ix,x);
477
        ix &= 0x7fffffff;
478
        if(ix>=0x40200000)     {p = qr8; q= qs8;}
479
        else if(ix>=0x40122E8B){p = qr5; q= qs5;}
480
        else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
481
        else if(ix>=0x40000000){p = qr2; q= qs2;}
482
        z = one/(x*x);
483
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
484
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
485
        return (.375 + r/s)/x;
486
}

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