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[/] [openrisc/] [trunk/] [gnu-old/] [newlib-1.17.0/] [newlib/] [libm/] [math/] [e_j1.c] - Blame information for rev 855

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1 148 jeremybenn
 
2
/* @(#)e_j1.c 5.1 93/09/24 */
3
/*
4
 * ====================================================
5
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6
 *
7
 * Developed at SunPro, a Sun Microsystems, Inc. business.
8
 * Permission to use, copy, modify, and distribute this
9
 * software is freely granted, provided that this notice
10
 * is preserved.
11
 * ====================================================
12
 */
13
 
14
/* __ieee754_j1(x), __ieee754_y1(x)
15
 * Bessel function of the first and second kinds of order zero.
16
 * Method -- j1(x):
17
 *      1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
18
 *      2. Reduce x to |x| since j1(x)=-j1(-x),  and
19
 *         for x in (0,2)
20
 *              j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
21
 *         (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
22
 *         for x in (2,inf)
23
 *              j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
24
 *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
25
 *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
26
 *         as follow:
27
 *              cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
28
 *                      =  1/sqrt(2) * (sin(x) - cos(x))
29
 *              sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
30
 *                      = -1/sqrt(2) * (sin(x) + cos(x))
31
 *         (To avoid cancellation, use
32
 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
33
 *          to compute the worse one.)
34
 *
35
 *      3 Special cases
36
 *              j1(nan)= nan
37
 *              j1(0) = 0
38
 *              j1(inf) = 0
39
 *
40
 * Method -- y1(x):
41
 *      1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
42
 *      2. For x<2.
43
 *         Since
44
 *              y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
45
 *         therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
46
 *         We use the following function to approximate y1,
47
 *              y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
48
 *         where for x in [0,2] (abs err less than 2**-65.89)
49
 *              U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
50
 *              V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
51
 *         Note: For tiny x, 1/x dominate y1 and hence
52
 *              y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
53
 *      3. For x>=2.
54
 *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
55
 *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
56
 *         by method mentioned above.
57
 */
58
 
59
#include "fdlibm.h"
60
 
61
#ifndef _DOUBLE_IS_32BITS
62
 
63
#ifdef __STDC__
64
static double pone(double), qone(double);
65
#else
66
static double pone(), qone();
67
#endif
68
 
69
#ifdef __STDC__
70
static const double
71
#else
72
static double
73
#endif
74
huge    = 1e300,
75
one     = 1.0,
76
invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
77
tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
78
        /* R0/S0 on [0,2] */
79
r00  = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
80
r01  =  1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
81
r02  = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
82
r03  =  4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
83
s01  =  1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
84
s02  =  1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
85
s03  =  1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
86
s04  =  5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
87
s05  =  1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
88
 
89
#ifdef __STDC__
90
static const double zero    = 0.0;
91
#else
92
static double zero    = 0.0;
93
#endif
94
 
95
#ifdef __STDC__
96
        double __ieee754_j1(double x)
97
#else
98
        double __ieee754_j1(x)
99
        double x;
100
#endif
101
{
102
        double z, s,c,ss,cc,r,u,v,y;
103
        __int32_t hx,ix;
104
 
105
        GET_HIGH_WORD(hx,x);
106
        ix = hx&0x7fffffff;
107
        if(ix>=0x7ff00000) return one/x;
108
        y = fabs(x);
109
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
110
                s = sin(y);
111
                c = cos(y);
112
                ss = -s-c;
113
                cc = s-c;
114
                if(ix<0x7fe00000) {  /* make sure y+y not overflow */
115
                    z = cos(y+y);
116
                    if ((s*c)>zero) cc = z/ss;
117
                    else            ss = z/cc;
118
                }
119
        /*
120
         * j1(x) = 1/__ieee754_sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / __ieee754_sqrt(x)
121
         * y1(x) = 1/__ieee754_sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / __ieee754_sqrt(x)
122
         */
123
                if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
124
                else {
125
                    u = pone(y); v = qone(y);
126
                    z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
127
                }
128
                if(hx<0) return -z;
129
                else     return  z;
130
        }
131
        if(ix<0x3e400000) {     /* |x|<2**-27 */
132
            if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
133
        }
134
        z = x*x;
135
        r =  z*(r00+z*(r01+z*(r02+z*r03)));
136
        s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
137
        r *= x;
138
        return(x*0.5+r/s);
139
}
140
 
141
#ifdef __STDC__
142
static const double U0[5] = {
143
#else
144
static double U0[5] = {
145
#endif
146
 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
147
  5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
148
 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
149
  2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
150
 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
151
};
152
#ifdef __STDC__
153
static const double V0[5] = {
154
#else
155
static double V0[5] = {
156
#endif
157
  1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
158
  2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
159
  1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
160
  6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
161
  1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
162
};
163
 
164
#ifdef __STDC__
165
        double __ieee754_y1(double x)
166
#else
167
        double __ieee754_y1(x)
168
        double x;
169
#endif
170
{
171
        double z, s,c,ss,cc,u,v;
172
        __int32_t hx,ix,lx;
173
 
174
        EXTRACT_WORDS(hx,lx,x);
175
        ix = 0x7fffffff&hx;
176
    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
177
        if(ix>=0x7ff00000) return  one/(x+x*x);
178
        if((ix|lx)==0) return -one/zero;
179
        if(hx<0) return zero/zero;
180
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
181
                s = sin(x);
182
                c = cos(x);
183
                ss = -s-c;
184
                cc = s-c;
185
                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
186
                    z = cos(x+x);
187
                    if ((s*c)>zero) cc = z/ss;
188
                    else            ss = z/cc;
189
                }
190
        /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
191
         * where x0 = x-3pi/4
192
         *      Better formula:
193
         *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
194
         *                      =  1/sqrt(2) * (sin(x) - cos(x))
195
         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
196
         *                      = -1/sqrt(2) * (cos(x) + sin(x))
197
         * To avoid cancellation, use
198
         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
199
         * to compute the worse one.
200
         */
201
                if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
202
                else {
203
                    u = pone(x); v = qone(x);
204
                    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
205
                }
206
                return z;
207
        }
208
        if(ix<=0x3c900000) {    /* x < 2**-54 */
209
            return(-tpi/x);
210
        }
211
        z = x*x;
212
        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
213
        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
214
        return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
215
}
216
 
217
/* For x >= 8, the asymptotic expansions of pone is
218
 *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
219
 * We approximate pone by
220
 *      pone(x) = 1 + (R/S)
221
 * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
222
 *        S = 1 + ps0*s^2 + ... + ps4*s^10
223
 * and
224
 *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
225
 */
226
 
227
#ifdef __STDC__
228
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
229
#else
230
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
231
#endif
232
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
233
  1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
234
  1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
235
  4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
236
  3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
237
  7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
238
};
239
#ifdef __STDC__
240
static const double ps8[5] = {
241
#else
242
static double ps8[5] = {
243
#endif
244
  1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
245
  3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
246
  3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
247
  9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
248
  3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
249
};
250
 
251
#ifdef __STDC__
252
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
253
#else
254
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
255
#endif
256
  1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
257
  1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
258
  6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
259
  1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
260
  5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
261
  5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
262
};
263
#ifdef __STDC__
264
static const double ps5[5] = {
265
#else
266
static double ps5[5] = {
267
#endif
268
  5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
269
  9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
270
  5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
271
  7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
272
  1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
273
};
274
 
275
#ifdef __STDC__
276
static const double pr3[6] = {
277
#else
278
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
279
#endif
280
  3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
281
  1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
282
  3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
283
  3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
284
  9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
285
  4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
286
};
287
#ifdef __STDC__
288
static const double ps3[5] = {
289
#else
290
static double ps3[5] = {
291
#endif
292
  3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
293
  3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
294
  1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
295
  8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
296
  1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
297
};
298
 
299
#ifdef __STDC__
300
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
301
#else
302
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
303
#endif
304
  1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
305
  1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
306
  2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
307
  1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
308
  1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
309
  5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
310
};
311
#ifdef __STDC__
312
static const double ps2[5] = {
313
#else
314
static double ps2[5] = {
315
#endif
316
  2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
317
  1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
318
  2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
319
  1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
320
  8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
321
};
322
 
323
#ifdef __STDC__
324
        static double pone(double x)
325
#else
326
        static double pone(x)
327
        double x;
328
#endif
329
{
330
#ifdef __STDC__
331
        const double *p,*q;
332
#else
333
        double *p,*q;
334
#endif
335
        double z,r,s;
336
        __int32_t ix;
337
        GET_HIGH_WORD(ix,x);
338
        ix &= 0x7fffffff;
339
        if(ix>=0x40200000)     {p = pr8; q= ps8;}
340
        else if(ix>=0x40122E8B){p = pr5; q= ps5;}
341
        else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
342
        else {p = pr2; q= ps2;}
343
        z = one/(x*x);
344
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
345
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
346
        return one+ r/s;
347
}
348
 
349
 
350
/* For x >= 8, the asymptotic expansions of qone is
351
 *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
352
 * We approximate qone by
353
 *      qone(x) = s*(0.375 + (R/S))
354
 * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
355
 *        S = 1 + qs1*s^2 + ... + qs6*s^12
356
 * and
357
 *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
358
 */
359
 
360
#ifdef __STDC__
361
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
362
#else
363
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
364
#endif
365
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
366
 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
367
 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
368
 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
369
 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
370
 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
371
};
372
#ifdef __STDC__
373
static const double qs8[6] = {
374
#else
375
static double qs8[6] = {
376
#endif
377
  1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
378
  7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
379
  1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
380
  7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
381
  6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
382
 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
383
};
384
 
385
#ifdef __STDC__
386
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
387
#else
388
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
389
#endif
390
 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
391
 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
392
 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
393
 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
394
 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
395
 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
396
};
397
#ifdef __STDC__
398
static const double qs5[6] = {
399
#else
400
static double qs5[6] = {
401
#endif
402
  8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
403
  1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
404
  1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
405
  4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
406
  2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
407
 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
408
};
409
 
410
#ifdef __STDC__
411
static const double qr3[6] = {
412
#else
413
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
414
#endif
415
 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
416
 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
417
 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
418
 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
419
 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
420
 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
421
};
422
#ifdef __STDC__
423
static const double qs3[6] = {
424
#else
425
static double qs3[6] = {
426
#endif
427
  4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
428
  6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
429
  3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
430
  5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
431
  1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
432
 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
433
};
434
 
435
#ifdef __STDC__
436
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
437
#else
438
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
439
#endif
440
 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
441
 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
442
 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
443
 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
444
 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
445
 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
446
};
447
#ifdef __STDC__
448
static const double qs2[6] = {
449
#else
450
static double qs2[6] = {
451
#endif
452
  2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
453
  2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
454
  7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
455
  7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
456
  1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
457
 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
458
};
459
 
460
#ifdef __STDC__
461
        static double qone(double x)
462
#else
463
        static double qone(x)
464
        double x;
465
#endif
466
{
467
#ifdef __STDC__
468
        const double *p,*q;
469
#else
470
        double *p,*q;
471
#endif
472
        double  s,r,z;
473
        __int32_t ix;
474
        GET_HIGH_WORD(ix,x);
475
        ix &= 0x7fffffff;
476
        if(ix>=0x40200000)     {p = qr8; q= qs8;}
477
        else if(ix>=0x40122E8B){p = qr5; q= qs5;}
478
        else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
479
      else {p = qr2; q= qs2;}
480
        z = one/(x*x);
481
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
482
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
483
        return (.375 + r/s)/x;
484
}
485
 
486
#endif /* defined(_DOUBLE_IS_32BITS) */

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