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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.17.0/] [newlib/] [libm/] [math/] [ef_j0.c] - Blame information for rev 158

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Line No. Rev Author Line
1 148 jeremybenn
/* ef_j0.c -- float version of e_j0.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 pzerof(float), qzerof(float);
20
#else
21
static float pzerof(), qzerof();
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, 2.00] */
34
R02  =  1.5625000000e-02, /* 0x3c800000 */
35
R03  = -1.8997929874e-04, /* 0xb947352e */
36
R04  =  1.8295404516e-06, /* 0x35f58e88 */
37
R05  = -4.6183270541e-09, /* 0xb19eaf3c */
38
S01  =  1.5619102865e-02, /* 0x3c7fe744 */
39
S02  =  1.1692678527e-04, /* 0x38f53697 */
40
S03  =  5.1354652442e-07, /* 0x3509daa6 */
41
S04  =  1.1661400734e-09; /* 0x30a045e8 */
42
 
43
#ifdef __STDC__
44
static const float zero = 0.0;
45
#else
46
static float zero = 0.0;
47
#endif
48
 
49
#ifdef __STDC__
50
        float __ieee754_j0f(float x)
51
#else
52
        float __ieee754_j0f(x)
53
        float x;
54
#endif
55
{
56
        float z, s,c,ss,cc,r,u,v;
57
        __int32_t hx,ix;
58
 
59
        GET_FLOAT_WORD(hx,x);
60
        ix = hx&0x7fffffff;
61
        if(!FLT_UWORD_IS_FINITE(ix)) return one/(x*x);
62
        x = fabsf(x);
63
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
64
                s = sinf(x);
65
                c = cosf(x);
66
                ss = s-c;
67
                cc = s+c;
68
                if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure x+x not overflow */
69
                    z = -cosf(x+x);
70
                    if ((s*c)<zero) cc = z/ss;
71
                    else            ss = z/cc;
72
                }
73
        /*
74
         * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
75
         * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
76
         */
77
                if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x);
78
                else {
79
                    u = pzerof(x); v = qzerof(x);
80
                    z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
81
                }
82
                return z;
83
        }
84
        if(ix<0x39000000) {     /* |x| < 2**-13 */
85
            if(huge+x>one) {    /* raise inexact if x != 0 */
86
                if(ix<0x32000000) return one;   /* |x|<2**-27 */
87
                else          return one - (float)0.25*x*x;
88
            }
89
        }
90
        z = x*x;
91
        r =  z*(R02+z*(R03+z*(R04+z*R05)));
92
        s =  one+z*(S01+z*(S02+z*(S03+z*S04)));
93
        if(ix < 0x3F800000) {   /* |x| < 1.00 */
94
            return one + z*((float)-0.25+(r/s));
95
        } else {
96
            u = (float)0.5*x;
97
            return((one+u)*(one-u)+z*(r/s));
98
        }
99
}
100
 
101
#ifdef __STDC__
102
static const float
103
#else
104
static float
105
#endif
106
u00  = -7.3804296553e-02, /* 0xbd9726b5 */
107
u01  =  1.7666645348e-01, /* 0x3e34e80d */
108
u02  = -1.3818567619e-02, /* 0xbc626746 */
109
u03  =  3.4745343146e-04, /* 0x39b62a69 */
110
u04  = -3.8140706238e-06, /* 0xb67ff53c */
111
u05  =  1.9559013964e-08, /* 0x32a802ba */
112
u06  = -3.9820518410e-11, /* 0xae2f21eb */
113
v01  =  1.2730483897e-02, /* 0x3c509385 */
114
v02  =  7.6006865129e-05, /* 0x389f65e0 */
115
v03  =  2.5915085189e-07, /* 0x348b216c */
116
v04  =  4.4111031494e-10; /* 0x2ff280c2 */
117
 
118
#ifdef __STDC__
119
        float __ieee754_y0f(float x)
120
#else
121
        float __ieee754_y0f(x)
122
        float x;
123
#endif
124
{
125
        float z, s,c,ss,cc,u,v;
126
        __int32_t hx,ix;
127
 
128
        GET_FLOAT_WORD(hx,x);
129
        ix = 0x7fffffff&hx;
130
    /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
131
        if(!FLT_UWORD_IS_FINITE(ix)) return  one/(x+x*x);
132
        if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
133
        if(hx<0) return zero/zero;
134
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
135
        /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
136
         * where x0 = x-pi/4
137
         *      Better formula:
138
         *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
139
         *                      =  1/sqrt(2) * (sin(x) + cos(x))
140
         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
141
         *                      =  1/sqrt(2) * (sin(x) - cos(x))
142
         * To avoid cancellation, use
143
         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
144
         * to compute the worse one.
145
         */
146
                s = sinf(x);
147
                c = cosf(x);
148
                ss = s-c;
149
                cc = s+c;
150
        /*
151
         * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
152
         * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
153
         */
154
                if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure x+x not overflow */
155
                    z = -cosf(x+x);
156
                    if ((s*c)<zero) cc = z/ss;
157
                    else            ss = z/cc;
158
                }
159
                if(ix>0x80000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
160
                else {
161
                    u = pzerof(x); v = qzerof(x);
162
                    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
163
                }
164
                return z;
165
        }
166
        if(ix<=0x32000000) {    /* x < 2**-27 */
167
            return(u00 + tpi*__ieee754_logf(x));
168
        }
169
        z = x*x;
170
        u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
171
        v = one+z*(v01+z*(v02+z*(v03+z*v04)));
172
        return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
173
}
174
 
175
/* The asymptotic expansions of pzero is
176
 *      1 - 9/128 s^2 + 11025/98304 s^4 - ...,  where s = 1/x.
177
 * For x >= 2, We approximate pzero by
178
 *      pzero(x) = 1 + (R/S)
179
 * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
180
 *        S = 1 + pS0*s^2 + ... + pS4*s^10
181
 * and
182
 *      | pzero(x)-1-R/S | <= 2  ** ( -60.26)
183
 */
184
#ifdef __STDC__
185
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
186
#else
187
static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
188
#endif
189
  0.0000000000e+00, /* 0x00000000 */
190
 -7.0312500000e-02, /* 0xbd900000 */
191
 -8.0816707611e+00, /* 0xc1014e86 */
192
 -2.5706311035e+02, /* 0xc3808814 */
193
 -2.4852163086e+03, /* 0xc51b5376 */
194
 -5.2530439453e+03, /* 0xc5a4285a */
195
};
196
#ifdef __STDC__
197
static const float pS8[5] = {
198
#else
199
static float pS8[5] = {
200
#endif
201
  1.1653436279e+02, /* 0x42e91198 */
202
  3.8337448730e+03, /* 0x456f9beb */
203
  4.0597855469e+04, /* 0x471e95db */
204
  1.1675296875e+05, /* 0x47e4087c */
205
  4.7627726562e+04, /* 0x473a0bba */
206
};
207
#ifdef __STDC__
208
static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
209
#else
210
static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
211
#endif
212
 -1.1412546255e-11, /* 0xad48c58a */
213
 -7.0312492549e-02, /* 0xbd8fffff */
214
 -4.1596107483e+00, /* 0xc0851b88 */
215
 -6.7674766541e+01, /* 0xc287597b */
216
 -3.3123129272e+02, /* 0xc3a59d9b */
217
 -3.4643338013e+02, /* 0xc3ad3779 */
218
};
219
#ifdef __STDC__
220
static const float pS5[5] = {
221
#else
222
static float pS5[5] = {
223
#endif
224
  6.0753936768e+01, /* 0x42730408 */
225
  1.0512523193e+03, /* 0x44836813 */
226
  5.9789707031e+03, /* 0x45bad7c4 */
227
  9.6254453125e+03, /* 0x461665c8 */
228
  2.4060581055e+03, /* 0x451660ee */
229
};
230
 
231
#ifdef __STDC__
232
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
233
#else
234
static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
235
#endif
236
 -2.5470459075e-09, /* 0xb12f081b */
237
 -7.0311963558e-02, /* 0xbd8fffb8 */
238
 -2.4090321064e+00, /* 0xc01a2d95 */
239
 -2.1965976715e+01, /* 0xc1afba52 */
240
 -5.8079170227e+01, /* 0xc2685112 */
241
 -3.1447946548e+01, /* 0xc1fb9565 */
242
};
243
#ifdef __STDC__
244
static const float pS3[5] = {
245
#else
246
static float pS3[5] = {
247
#endif
248
  3.5856033325e+01, /* 0x420f6c94 */
249
  3.6151397705e+02, /* 0x43b4c1ca */
250
  1.1936077881e+03, /* 0x44953373 */
251
  1.1279968262e+03, /* 0x448cffe6 */
252
  1.7358093262e+02, /* 0x432d94b8 */
253
};
254
 
255
#ifdef __STDC__
256
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
257
#else
258
static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
259
#endif
260
 -8.8753431271e-08, /* 0xb3be98b7 */
261
 -7.0303097367e-02, /* 0xbd8ffb12 */
262
 -1.4507384300e+00, /* 0xbfb9b1cc */
263
 -7.6356959343e+00, /* 0xc0f4579f */
264
 -1.1193166733e+01, /* 0xc1331736 */
265
 -3.2336456776e+00, /* 0xc04ef40d */
266
};
267
#ifdef __STDC__
268
static const float pS2[5] = {
269
#else
270
static float pS2[5] = {
271
#endif
272
  2.2220300674e+01, /* 0x41b1c32d */
273
  1.3620678711e+02, /* 0x430834f0 */
274
  2.7047027588e+02, /* 0x43873c32 */
275
  1.5387539673e+02, /* 0x4319e01a */
276
  1.4657617569e+01, /* 0x416a859a */
277
};
278
 
279
#ifdef __STDC__
280
        static float pzerof(float x)
281
#else
282
        static float pzerof(x)
283
        float x;
284
#endif
285
{
286
#ifdef __STDC__
287
        const float *p,*q;
288
#else
289
        float *p,*q;
290
#endif
291
        float z,r,s;
292
        __int32_t ix;
293
        GET_FLOAT_WORD(ix,x);
294
        ix &= 0x7fffffff;
295
        if(ix>=0x41000000)     {p = pR8; q= pS8;}
296
        else if(ix>=0x40f71c58){p = pR5; q= pS5;}
297
        else if(ix>=0x4036db68){p = pR3; q= pS3;}
298
      else {p = pR2; q= pS2;}
299
        z = one/(x*x);
300
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
301
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
302
        return one+ r/s;
303
}
304
 
305
 
306
/* For x >= 8, the asymptotic expansions of qzero is
307
 *      -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
308
 * We approximate qzero by
309
 *      qzero(x) = s*(-1.25 + (R/S))
310
 * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
311
 *        S = 1 + qS0*s^2 + ... + qS5*s^12
312
 * and
313
 *      | qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
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
  7.3242187500e-02, /* 0x3d960000 */
322
  1.1768206596e+01, /* 0x413c4a93 */
323
  5.5767340088e+02, /* 0x440b6b19 */
324
  8.8591972656e+03, /* 0x460a6cca */
325
  3.7014625000e+04, /* 0x471096a0 */
326
};
327
#ifdef __STDC__
328
static const float qS8[6] = {
329
#else
330
static float qS8[6] = {
331
#endif
332
  1.6377603149e+02, /* 0x4323c6aa */
333
  8.0983447266e+03, /* 0x45fd12c2 */
334
  1.4253829688e+05, /* 0x480b3293 */
335
  8.0330925000e+05, /* 0x49441ed4 */
336
  8.4050156250e+05, /* 0x494d3359 */
337
 -3.4389928125e+05, /* 0xc8a7eb69 */
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
  1.8408595828e-11, /* 0x2da1ec79 */
346
  7.3242180049e-02, /* 0x3d95ffff */
347
  5.8356351852e+00, /* 0x40babd86 */
348
  1.3511157227e+02, /* 0x43071c90 */
349
  1.0272437744e+03, /* 0x448067cd */
350
  1.9899779053e+03, /* 0x44f8bf4b */
351
};
352
#ifdef __STDC__
353
static const float qS5[6] = {
354
#else
355
static float qS5[6] = {
356
#endif
357
  8.2776611328e+01, /* 0x42a58da0 */
358
  2.0778142090e+03, /* 0x4501dd07 */
359
  1.8847289062e+04, /* 0x46933e94 */
360
  5.6751113281e+04, /* 0x475daf1d */
361
  3.5976753906e+04, /* 0x470c88c1 */
362
 -5.3543427734e+03, /* 0xc5a752be */
363
};
364
 
365
#ifdef __STDC__
366
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
367
#else
368
static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
369
#endif
370
  4.3774099900e-09, /* 0x3196681b */
371
  7.3241114616e-02, /* 0x3d95ff70 */
372
  3.3442313671e+00, /* 0x405607e3 */
373
  4.2621845245e+01, /* 0x422a7cc5 */
374
  1.7080809021e+02, /* 0x432acedf */
375
  1.6673394775e+02, /* 0x4326bbe4 */
376
};
377
#ifdef __STDC__
378
static const float qS3[6] = {
379
#else
380
static float qS3[6] = {
381
#endif
382
  4.8758872986e+01, /* 0x42430916 */
383
  7.0968920898e+02, /* 0x44316c1c */
384
  3.7041481934e+03, /* 0x4567825f */
385
  6.4604252930e+03, /* 0x45c9e367 */
386
  2.5163337402e+03, /* 0x451d4557 */
387
 -1.4924745178e+02, /* 0xc3153f59 */
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
  1.5044444979e-07, /* 0x342189db */
396
  7.3223426938e-02, /* 0x3d95f62a */
397
  1.9981917143e+00, /* 0x3fffc4bf */
398
  1.4495602608e+01, /* 0x4167edfd */
399
  3.1666231155e+01, /* 0x41fd5471 */
400
  1.6252708435e+01, /* 0x4182058c */
401
};
402
#ifdef __STDC__
403
static const float qS2[6] = {
404
#else
405
static float qS2[6] = {
406
#endif
407
  3.0365585327e+01, /* 0x41f2ecb8 */
408
  2.6934811401e+02, /* 0x4386ac8f */
409
  8.4478375244e+02, /* 0x44533229 */
410
  8.8293585205e+02, /* 0x445cbbe5 */
411
  2.1266638184e+02, /* 0x4354aa98 */
412
 -5.3109550476e+00, /* 0xc0a9f358 */
413
};
414
 
415
#ifdef __STDC__
416
        static float qzerof(float x)
417
#else
418
        static float qzerof(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>=0x41000000)     {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).125 + r/s)/x;
439
}

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