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[/] [openrisc/] [trunk/] [gnu-old/] [newlib-1.17.0/] [newlib/] [libm/] [math/] [ef_j1.c] - Blame information for rev 855

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Line No. Rev Author Line
1 148 jeremybenn
/* ef_j1.c -- float version of e_j1.c.
2
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3
 */
4
 
5
/*
6
 * ====================================================
7
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8
 *
9
 * Developed at SunPro, a Sun Microsystems, Inc. business.
10
 * Permission to use, copy, modify, and distribute this
11
 * software is freely granted, provided that this notice
12
 * is preserved.
13
 * ====================================================
14
 */
15
 
16
#include "fdlibm.h"
17
 
18
#ifdef __STDC__
19
static float ponef(float), qonef(float);
20
#else
21
static float ponef(), qonef();
22
#endif
23
 
24
#ifdef __STDC__
25
static const float
26
#else
27
static float
28
#endif
29
huge    = 1e30,
30
one     = 1.0,
31
invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
32
tpi      =  6.3661974669e-01, /* 0x3f22f983 */
33
        /* R0/S0 on [0,2] */
34
r00  = -6.2500000000e-02, /* 0xbd800000 */
35
r01  =  1.4070566976e-03, /* 0x3ab86cfd */
36
r02  = -1.5995563444e-05, /* 0xb7862e36 */
37
r03  =  4.9672799207e-08, /* 0x335557d2 */
38
s01  =  1.9153760746e-02, /* 0x3c9ce859 */
39
s02  =  1.8594678841e-04, /* 0x3942fab6 */
40
s03  =  1.1771846857e-06, /* 0x359dffc2 */
41
s04  =  5.0463624390e-09, /* 0x31ad6446 */
42
s05  =  1.2354227016e-11; /* 0x2d59567e */
43
 
44
#ifdef __STDC__
45
static const float zero    = 0.0;
46
#else
47
static float zero    = 0.0;
48
#endif
49
 
50
#ifdef __STDC__
51
        float __ieee754_j1f(float x)
52
#else
53
        float __ieee754_j1f(x)
54
        float x;
55
#endif
56
{
57
        float z, s,c,ss,cc,r,u,v,y;
58
        __int32_t hx,ix;
59
 
60
        GET_FLOAT_WORD(hx,x);
61
        ix = hx&0x7fffffff;
62
        if(!FLT_UWORD_IS_FINITE(ix)) return one/x;
63
        y = fabsf(x);
64
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
65
                s = sinf(y);
66
                c = cosf(y);
67
                ss = -s-c;
68
                cc = s-c;
69
                if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure y+y not overflow */
70
                    z = cosf(y+y);
71
                    if ((s*c)>zero) cc = z/ss;
72
                    else            ss = z/cc;
73
                }
74
        /*
75
         * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
76
         * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
77
         */
78
                if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y);
79
                else {
80
                    u = ponef(y); v = qonef(y);
81
                    z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
82
                }
83
                if(hx<0) return -z;
84
                else     return  z;
85
        }
86
        if(ix<0x32000000) {     /* |x|<2**-27 */
87
            if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
88
        }
89
        z = x*x;
90
        r =  z*(r00+z*(r01+z*(r02+z*r03)));
91
        s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
92
        r *= x;
93
        return(x*(float)0.5+r/s);
94
}
95
 
96
#ifdef __STDC__
97
static const float U0[5] = {
98
#else
99
static float U0[5] = {
100
#endif
101
 -1.9605709612e-01, /* 0xbe48c331 */
102
  5.0443872809e-02, /* 0x3d4e9e3c */
103
 -1.9125689287e-03, /* 0xbafaaf2a */
104
  2.3525259166e-05, /* 0x37c5581c */
105
 -9.1909917899e-08, /* 0xb3c56003 */
106
};
107
#ifdef __STDC__
108
static const float V0[5] = {
109
#else
110
static float V0[5] = {
111
#endif
112
  1.9916731864e-02, /* 0x3ca3286a */
113
  2.0255257550e-04, /* 0x3954644b */
114
  1.3560879779e-06, /* 0x35b602d4 */
115
  6.2274145840e-09, /* 0x31d5f8eb */
116
  1.6655924903e-11, /* 0x2d9281cf */
117
};
118
 
119
#ifdef __STDC__
120
        float __ieee754_y1f(float x)
121
#else
122
        float __ieee754_y1f(x)
123
        float x;
124
#endif
125
{
126
        float z, s,c,ss,cc,u,v;
127
        __int32_t hx,ix;
128
 
129
        GET_FLOAT_WORD(hx,x);
130
        ix = 0x7fffffff&hx;
131
    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
132
        if(!FLT_UWORD_IS_FINITE(ix)) return one/(x+x*x);
133
        if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
134
        if(hx<0) return zero/zero;
135
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
136
                s = sinf(x);
137
                c = cosf(x);
138
                ss = -s-c;
139
                cc = s-c;
140
                if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure x+x not overflow */
141
                    z = cosf(x+x);
142
                    if ((s*c)>zero) cc = z/ss;
143
                    else            ss = z/cc;
144
                }
145
        /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
146
         * where x0 = x-3pi/4
147
         *      Better formula:
148
         *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
149
         *                      =  1/sqrt(2) * (sin(x) - cos(x))
150
         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
151
         *                      = -1/sqrt(2) * (cos(x) + sin(x))
152
         * To avoid cancellation, use
153
         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
154
         * to compute the worse one.
155
         */
156
                if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
157
                else {
158
                    u = ponef(x); v = qonef(x);
159
                    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
160
                }
161
                return z;
162
        }
163
        if(ix<=0x24800000) {    /* x < 2**-54 */
164
            return(-tpi/x);
165
        }
166
        z = x*x;
167
        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
168
        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
169
        return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
170
}
171
 
172
/* For x >= 8, the asymptotic expansions of pone is
173
 *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
174
 * We approximate pone by
175
 *      pone(x) = 1 + (R/S)
176
 * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
177
 *        S = 1 + ps0*s^2 + ... + ps4*s^10
178
 * and
179
 *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
180
 */
181
 
182
#ifdef __STDC__
183
static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
184
#else
185
static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
186
#endif
187
  0.0000000000e+00, /* 0x00000000 */
188
  1.1718750000e-01, /* 0x3df00000 */
189
  1.3239480972e+01, /* 0x4153d4ea */
190
  4.1205184937e+02, /* 0x43ce06a3 */
191
  3.8747453613e+03, /* 0x45722bed */
192
  7.9144794922e+03, /* 0x45f753d6 */
193
};
194
#ifdef __STDC__
195
static const float ps8[5] = {
196
#else
197
static float ps8[5] = {
198
#endif
199
  1.1420736694e+02, /* 0x42e46a2c */
200
  3.6509309082e+03, /* 0x45642ee5 */
201
  3.6956207031e+04, /* 0x47105c35 */
202
  9.7602796875e+04, /* 0x47bea166 */
203
  3.0804271484e+04, /* 0x46f0a88b */
204
};
205
 
206
#ifdef __STDC__
207
static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
208
#else
209
static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
210
#endif
211
  1.3199052094e-11, /* 0x2d68333f */
212
  1.1718749255e-01, /* 0x3defffff */
213
  6.8027510643e+00, /* 0x40d9b023 */
214
  1.0830818176e+02, /* 0x42d89dca */
215
  5.1763616943e+02, /* 0x440168b7 */
216
  5.2871520996e+02, /* 0x44042dc6 */
217
};
218
#ifdef __STDC__
219
static const float ps5[5] = {
220
#else
221
static float ps5[5] = {
222
#endif
223
  5.9280597687e+01, /* 0x426d1f55 */
224
  9.9140142822e+02, /* 0x4477d9b1 */
225
  5.3532670898e+03, /* 0x45a74a23 */
226
  7.8446904297e+03, /* 0x45f52586 */
227
  1.5040468750e+03, /* 0x44bc0180 */
228
};
229
 
230
#ifdef __STDC__
231
static const float pr3[6] = {
232
#else
233
static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
234
#endif
235
  3.0250391081e-09, /* 0x314fe10d */
236
  1.1718686670e-01, /* 0x3defffab */
237
  3.9329774380e+00, /* 0x407bb5e7 */
238
  3.5119403839e+01, /* 0x420c7a45 */
239
  9.1055007935e+01, /* 0x42b61c2a */
240
  4.8559066772e+01, /* 0x42423c7c */
241
};
242
#ifdef __STDC__
243
static const float ps3[5] = {
244
#else
245
static float ps3[5] = {
246
#endif
247
  3.4791309357e+01, /* 0x420b2a4d */
248
  3.3676245117e+02, /* 0x43a86198 */
249
  1.0468714600e+03, /* 0x4482dbe3 */
250
  8.9081134033e+02, /* 0x445eb3ed */
251
  1.0378793335e+02, /* 0x42cf936c */
252
};
253
 
254
#ifdef __STDC__
255
static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
256
#else
257
static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
258
#endif
259
  1.0771083225e-07, /* 0x33e74ea8 */
260
  1.1717621982e-01, /* 0x3deffa16 */
261
  2.3685150146e+00, /* 0x401795c0 */
262
  1.2242610931e+01, /* 0x4143e1bc */
263
  1.7693971634e+01, /* 0x418d8d41 */
264
  5.0735230446e+00, /* 0x40a25a4d */
265
};
266
#ifdef __STDC__
267
static const float ps2[5] = {
268
#else
269
static float ps2[5] = {
270
#endif
271
  2.1436485291e+01, /* 0x41ab7dec */
272
  1.2529022980e+02, /* 0x42fa9499 */
273
  2.3227647400e+02, /* 0x436846c7 */
274
  1.1767937469e+02, /* 0x42eb5bd7 */
275
  8.3646392822e+00, /* 0x4105d590 */
276
};
277
 
278
#ifdef __STDC__
279
        static float ponef(float x)
280
#else
281
        static float ponef(x)
282
        float x;
283
#endif
284
{
285
#ifdef __STDC__
286
        const float *p,*q;
287
#else
288
        float *p,*q;
289
#endif
290
        float z,r,s;
291
        __int32_t ix;
292
        GET_FLOAT_WORD(ix,x);
293
        ix &= 0x7fffffff;
294
        if(ix>=0x41000000)     {p = pr8; q= ps8;}
295
        else if(ix>=0x40f71c58){p = pr5; q= ps5;}
296
        else if(ix>=0x4036db68){p = pr3; q= ps3;}
297
        else {p = pr2; q= ps2;}
298
        z = one/(x*x);
299
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
300
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
301
        return one+ r/s;
302
}
303
 
304
 
305
/* For x >= 8, the asymptotic expansions of qone is
306
 *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
307
 * We approximate qone by
308
 *      qone(x) = s*(0.375 + (R/S))
309
 * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
310
 *        S = 1 + qs1*s^2 + ... + qs6*s^12
311
 * and
312
 *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
313
 */
314
 
315
#ifdef __STDC__
316
static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
317
#else
318
static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
319
#endif
320
  0.0000000000e+00, /* 0x00000000 */
321
 -1.0253906250e-01, /* 0xbdd20000 */
322
 -1.6271753311e+01, /* 0xc1822c8d */
323
 -7.5960174561e+02, /* 0xc43de683 */
324
 -1.1849806641e+04, /* 0xc639273a */
325
 -4.8438511719e+04, /* 0xc73d3683 */
326
};
327
#ifdef __STDC__
328
static const float qs8[6] = {
329
#else
330
static float qs8[6] = {
331
#endif
332
  1.6139537048e+02, /* 0x43216537 */
333
  7.8253862305e+03, /* 0x45f48b17 */
334
  1.3387534375e+05, /* 0x4802bcd6 */
335
  7.1965775000e+05, /* 0x492fb29c */
336
  6.6660125000e+05, /* 0x4922be94 */
337
 -2.9449025000e+05, /* 0xc88fcb48 */
338
};
339
 
340
#ifdef __STDC__
341
static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
342
#else
343
static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
344
#endif
345
 -2.0897993405e-11, /* 0xadb7d219 */
346
 -1.0253904760e-01, /* 0xbdd1fffe */
347
 -8.0564479828e+00, /* 0xc100e736 */
348
 -1.8366960144e+02, /* 0xc337ab6b */
349
 -1.3731937256e+03, /* 0xc4aba633 */
350
 -2.6124443359e+03, /* 0xc523471c */
351
};
352
#ifdef __STDC__
353
static const float qs5[6] = {
354
#else
355
static float qs5[6] = {
356
#endif
357
  8.1276550293e+01, /* 0x42a28d98 */
358
  1.9917987061e+03, /* 0x44f8f98f */
359
  1.7468484375e+04, /* 0x468878f8 */
360
  4.9851425781e+04, /* 0x4742bb6d */
361
  2.7948074219e+04, /* 0x46da5826 */
362
 -4.7191835938e+03, /* 0xc5937978 */
363
};
364
 
365
#ifdef __STDC__
366
static const float qr3[6] = {
367
#else
368
static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
369
#endif
370
 -5.0783124372e-09, /* 0xb1ae7d4f */
371
 -1.0253783315e-01, /* 0xbdd1ff5b */
372
 -4.6101160049e+00, /* 0xc0938612 */
373
 -5.7847221375e+01, /* 0xc267638e */
374
 -2.2824453735e+02, /* 0xc3643e9a */
375
 -2.1921012878e+02, /* 0xc35b35cb */
376
};
377
#ifdef __STDC__
378
static const float qs3[6] = {
379
#else
380
static float qs3[6] = {
381
#endif
382
  4.7665153503e+01, /* 0x423ea91e */
383
  6.7386511230e+02, /* 0x4428775e */
384
  3.3801528320e+03, /* 0x45534272 */
385
  5.5477290039e+03, /* 0x45ad5dd5 */
386
  1.9031191406e+03, /* 0x44ede3d0 */
387
 -1.3520118713e+02, /* 0xc3073381 */
388
};
389
 
390
#ifdef __STDC__
391
static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
392
#else
393
static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
394
#endif
395
 -1.7838172539e-07, /* 0xb43f8932 */
396
 -1.0251704603e-01, /* 0xbdd1f475 */
397
 -2.7522056103e+00, /* 0xc0302423 */
398
 -1.9663616180e+01, /* 0xc19d4f16 */
399
 -4.2325313568e+01, /* 0xc2294d1f */
400
 -2.1371921539e+01, /* 0xc1aaf9b2 */
401
};
402
#ifdef __STDC__
403
static const float qs2[6] = {
404
#else
405
static float qs2[6] = {
406
#endif
407
  2.9533363342e+01, /* 0x41ec4454 */
408
  2.5298155212e+02, /* 0x437cfb47 */
409
  7.5750280762e+02, /* 0x443d602e */
410
  7.3939318848e+02, /* 0x4438d92a */
411
  1.5594900513e+02, /* 0x431bf2f2 */
412
 -4.9594988823e+00, /* 0xc09eb437 */
413
};
414
 
415
#ifdef __STDC__
416
        static float qonef(float x)
417
#else
418
        static float qonef(x)
419
        float x;
420
#endif
421
{
422
#ifdef __STDC__
423
        const float *p,*q;
424
#else
425
        float *p,*q;
426
#endif
427
        float  s,r,z;
428
        __int32_t ix;
429
        GET_FLOAT_WORD(ix,x);
430
        ix &= 0x7fffffff;
431
        if(ix>=0x40200000)     {p = qr8; q= qs8;}
432
        else if(ix>=0x40f71c58){p = qr5; q= qs5;}
433
        else if(ix>=0x4036db68){p = qr3; q= qs3;}
434
      else {p = qr2; q= qs2;}
435
        z = one/(x*x);
436
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
437
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
438
        return ((float).375 + r/s)/x;
439
}

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