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/* e_j0f.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
#ifndef lint
17
static char rcsid[] = "$\Id: e_j0f.c,v 1.2 1995/05/30 05:48:19 rgrimes Exp $";
18
#endif
19
 
20
#include "math.h"
21
#include "math_private.h"
22
 
23
#ifdef __STDC__
24
static float pzerof(float), qzerof(float);
25
#else
26
static float pzerof(), qzerof();
27
#endif
28
 
29
#ifdef __STDC__
30
static const float
31
#else
32
static float
33
#endif
34
huge    = 1e30,
35
one     = 1.0,
36
invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
37
tpi      =  6.3661974669e-01, /* 0x3f22f983 */
38
                /* R0/S0 on [0, 2.00] */
39
R02  =  1.5625000000e-02, /* 0x3c800000 */
40
R03  = -1.8997929874e-04, /* 0xb947352e */
41
R04  =  1.8295404516e-06, /* 0x35f58e88 */
42
R05  = -4.6183270541e-09, /* 0xb19eaf3c */
43
S01  =  1.5619102865e-02, /* 0x3c7fe744 */
44
S02  =  1.1692678527e-04, /* 0x38f53697 */
45
S03  =  5.1354652442e-07, /* 0x3509daa6 */
46
S04  =  1.1661400734e-09; /* 0x30a045e8 */
47
 
48
#ifdef __STDC__
49
static const float zero = 0.0;
50
#else
51
static float zero = 0.0;
52
#endif
53
 
54
#ifdef __STDC__
55
        float __ieee754_j0f(float x)
56
#else
57
        float __ieee754_j0f(x)
58
        float x;
59
#endif
60
{
61
        float z, s,c,ss,cc,r,u,v;
62
        int32_t hx,ix;
63
 
64
        GET_FLOAT_WORD(hx,x);
65
        ix = hx&0x7fffffff;
66
        if(ix>=0x7f800000) return one/(x*x);
67
        x = fabsf(x);
68
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
69
                s = sinf(x);
70
                c = cosf(x);
71
                ss = s-c;
72
                cc = s+c;
73
                if(ix<0x7f000000) {  /* make sure x+x not overflow */
74
                    z = -cosf(x+x);
75
                    if ((s*c)<zero) cc = z/ss;
76
                    else            ss = z/cc;
77
                }
78
        /*
79
         * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
80
         * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
81
         */
82
                if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
83
                else {
84
                    u = pzerof(x); v = qzerof(x);
85
                    z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
86
                }
87
                return z;
88
        }
89
        if(ix<0x39000000) {     /* |x| < 2**-13 */
90
            if(huge+x>one) {    /* raise inexact if x != 0 */
91
                if(ix<0x32000000) return one;   /* |x|<2**-27 */
92
                else          return one - (float)0.25*x*x;
93
            }
94
        }
95
        z = x*x;
96
        r =  z*(R02+z*(R03+z*(R04+z*R05)));
97
        s =  one+z*(S01+z*(S02+z*(S03+z*S04)));
98
        if(ix < 0x3F800000) {   /* |x| < 1.00 */
99
            return one + z*((float)-0.25+(r/s));
100
        } else {
101
            u = (float)0.5*x;
102
            return((one+u)*(one-u)+z*(r/s));
103
        }
104
}
105
 
106
#ifdef __STDC__
107
static const float
108
#else
109
static float
110
#endif
111
u00  = -7.3804296553e-02, /* 0xbd9726b5 */
112
u01  =  1.7666645348e-01, /* 0x3e34e80d */
113
u02  = -1.3818567619e-02, /* 0xbc626746 */
114
u03  =  3.4745343146e-04, /* 0x39b62a69 */
115
u04  = -3.8140706238e-06, /* 0xb67ff53c */
116
u05  =  1.9559013964e-08, /* 0x32a802ba */
117
u06  = -3.9820518410e-11, /* 0xae2f21eb */
118
v01  =  1.2730483897e-02, /* 0x3c509385 */
119
v02  =  7.6006865129e-05, /* 0x389f65e0 */
120
v03  =  2.5915085189e-07, /* 0x348b216c */
121
v04  =  4.4111031494e-10; /* 0x2ff280c2 */
122
 
123
#ifdef __STDC__
124
        float __ieee754_y0f(float x)
125
#else
126
        float __ieee754_y0f(x)
127
        float x;
128
#endif
129
{
130
        float z, s,c,ss,cc,u,v;
131
        int32_t hx,ix;
132
 
133
        GET_FLOAT_WORD(hx,x);
134
        ix = 0x7fffffff&hx;
135
    /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
136
        if(ix>=0x7f800000) return  one/(x+x*x);
137
        if(ix==0) return -one/zero;
138
        if(hx<0) return zero/zero;
139
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
140
        /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
141
         * where x0 = x-pi/4
142
         *      Better formula:
143
         *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
144
         *                      =  1/sqrt(2) * (sin(x) + cos(x))
145
         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
146
         *                      =  1/sqrt(2) * (sin(x) - cos(x))
147
         * To avoid cancellation, use
148
         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
149
         * to compute the worse one.
150
         */
151
                s = sinf(x);
152
                c = cosf(x);
153
                ss = s-c;
154
                cc = s+c;
155
        /*
156
         * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
157
         * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
158
         */
159
                if(ix<0x7f000000) {  /* make sure x+x not overflow */
160
                    z = -cosf(x+x);
161
                    if ((s*c)<zero) cc = z/ss;
162
                    else            ss = z/cc;
163
                }
164
                if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
165
                else {
166
                    u = pzerof(x); v = qzerof(x);
167
                    z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
168
                }
169
                return z;
170
        }
171
        if(ix<=0x32000000) {    /* x < 2**-27 */
172
            return(u00 + tpi*__ieee754_logf(x));
173
        }
174
        z = x*x;
175
        u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
176
        v = one+z*(v01+z*(v02+z*(v03+z*v04)));
177
        return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
178
}
179
 
180
/* The asymptotic expansions of pzero is
181
 *      1 - 9/128 s^2 + 11025/98304 s^4 - ...,  where s = 1/x.
182
 * For x >= 2, We approximate pzero by
183
 *      pzero(x) = 1 + (R/S)
184
 * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
185
 *        S = 1 + pS0*s^2 + ... + pS4*s^10
186
 * and
187
 *      | pzero(x)-1-R/S | <= 2  ** ( -60.26)
188
 */
189
#ifdef __STDC__
190
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
191
#else
192
static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
193
#endif
194
  0.0000000000e+00, /* 0x00000000 */
195
 -7.0312500000e-02, /* 0xbd900000 */
196
 -8.0816707611e+00, /* 0xc1014e86 */
197
 -2.5706311035e+02, /* 0xc3808814 */
198
 -2.4852163086e+03, /* 0xc51b5376 */
199
 -5.2530439453e+03, /* 0xc5a4285a */
200
};
201
#ifdef __STDC__
202
static const float pS8[5] = {
203
#else
204
static float pS8[5] = {
205
#endif
206
  1.1653436279e+02, /* 0x42e91198 */
207
  3.8337448730e+03, /* 0x456f9beb */
208
  4.0597855469e+04, /* 0x471e95db */
209
  1.1675296875e+05, /* 0x47e4087c */
210
  4.7627726562e+04, /* 0x473a0bba */
211
};
212
#ifdef __STDC__
213
static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
214
#else
215
static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
216
#endif
217
 -1.1412546255e-11, /* 0xad48c58a */
218
 -7.0312492549e-02, /* 0xbd8fffff */
219
 -4.1596107483e+00, /* 0xc0851b88 */
220
 -6.7674766541e+01, /* 0xc287597b */
221
 -3.3123129272e+02, /* 0xc3a59d9b */
222
 -3.4643338013e+02, /* 0xc3ad3779 */
223
};
224
#ifdef __STDC__
225
static const float pS5[5] = {
226
#else
227
static float pS5[5] = {
228
#endif
229
  6.0753936768e+01, /* 0x42730408 */
230
  1.0512523193e+03, /* 0x44836813 */
231
  5.9789707031e+03, /* 0x45bad7c4 */
232
  9.6254453125e+03, /* 0x461665c8 */
233
  2.4060581055e+03, /* 0x451660ee */
234
};
235
 
236
#ifdef __STDC__
237
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
238
#else
239
static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
240
#endif
241
 -2.5470459075e-09, /* 0xb12f081b */
242
 -7.0311963558e-02, /* 0xbd8fffb8 */
243
 -2.4090321064e+00, /* 0xc01a2d95 */
244
 -2.1965976715e+01, /* 0xc1afba52 */
245
 -5.8079170227e+01, /* 0xc2685112 */
246
 -3.1447946548e+01, /* 0xc1fb9565 */
247
};
248
#ifdef __STDC__
249
static const float pS3[5] = {
250
#else
251
static float pS3[5] = {
252
#endif
253
  3.5856033325e+01, /* 0x420f6c94 */
254
  3.6151397705e+02, /* 0x43b4c1ca */
255
  1.1936077881e+03, /* 0x44953373 */
256
  1.1279968262e+03, /* 0x448cffe6 */
257
  1.7358093262e+02, /* 0x432d94b8 */
258
};
259
 
260
#ifdef __STDC__
261
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
262
#else
263
static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
264
#endif
265
 -8.8753431271e-08, /* 0xb3be98b7 */
266
 -7.0303097367e-02, /* 0xbd8ffb12 */
267
 -1.4507384300e+00, /* 0xbfb9b1cc */
268
 -7.6356959343e+00, /* 0xc0f4579f */
269
 -1.1193166733e+01, /* 0xc1331736 */
270
 -3.2336456776e+00, /* 0xc04ef40d */
271
};
272
#ifdef __STDC__
273
static const float pS2[5] = {
274
#else
275
static float pS2[5] = {
276
#endif
277
  2.2220300674e+01, /* 0x41b1c32d */
278
  1.3620678711e+02, /* 0x430834f0 */
279
  2.7047027588e+02, /* 0x43873c32 */
280
  1.5387539673e+02, /* 0x4319e01a */
281
  1.4657617569e+01, /* 0x416a859a */
282
};
283
 
284
#ifdef __STDC__
285
        static float pzerof(float x)
286
#else
287
        static float pzerof(x)
288
        float x;
289
#endif
290
{
291
#ifdef __STDC__
292
        const float *p,*q;
293
#else
294
        float *p,*q;
295
#endif
296
        float z,r,s;
297
        int32_t ix;
298
        GET_FLOAT_WORD(ix,x);
299
        ix &= 0x7fffffff;
300
        if(ix>=0x41000000)     {p = pR8; q= pS8;}
301
        else if(ix>=0x40f71c58){p = pR5; q= pS5;}
302
        else if(ix>=0x4036db68){p = pR3; q= pS3;}
303
        else if(ix>=0x40000000){p = pR2; q= pS2;}
304
        z = one/(x*x);
305
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
306
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
307
        return one+ r/s;
308
}
309
 
310
 
311
/* For x >= 8, the asymptotic expansions of qzero is
312
 *      -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
313
 * We approximate pzero by
314
 *      qzero(x) = s*(-1.25 + (R/S))
315
 * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
316
 *        S = 1 + qS0*s^2 + ... + qS5*s^12
317
 * and
318
 *      | qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
319
 */
320
#ifdef __STDC__
321
static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
322
#else
323
static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
324
#endif
325
  0.0000000000e+00, /* 0x00000000 */
326
  7.3242187500e-02, /* 0x3d960000 */
327
  1.1768206596e+01, /* 0x413c4a93 */
328
  5.5767340088e+02, /* 0x440b6b19 */
329
  8.8591972656e+03, /* 0x460a6cca */
330
  3.7014625000e+04, /* 0x471096a0 */
331
};
332
#ifdef __STDC__
333
static const float qS8[6] = {
334
#else
335
static float qS8[6] = {
336
#endif
337
  1.6377603149e+02, /* 0x4323c6aa */
338
  8.0983447266e+03, /* 0x45fd12c2 */
339
  1.4253829688e+05, /* 0x480b3293 */
340
  8.0330925000e+05, /* 0x49441ed4 */
341
  8.4050156250e+05, /* 0x494d3359 */
342
 -3.4389928125e+05, /* 0xc8a7eb69 */
343
};
344
 
345
#ifdef __STDC__
346
static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
347
#else
348
static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
349
#endif
350
  1.8408595828e-11, /* 0x2da1ec79 */
351
  7.3242180049e-02, /* 0x3d95ffff */
352
  5.8356351852e+00, /* 0x40babd86 */
353
  1.3511157227e+02, /* 0x43071c90 */
354
  1.0272437744e+03, /* 0x448067cd */
355
  1.9899779053e+03, /* 0x44f8bf4b */
356
};
357
#ifdef __STDC__
358
static const float qS5[6] = {
359
#else
360
static float qS5[6] = {
361
#endif
362
  8.2776611328e+01, /* 0x42a58da0 */
363
  2.0778142090e+03, /* 0x4501dd07 */
364
  1.8847289062e+04, /* 0x46933e94 */
365
  5.6751113281e+04, /* 0x475daf1d */
366
  3.5976753906e+04, /* 0x470c88c1 */
367
 -5.3543427734e+03, /* 0xc5a752be */
368
};
369
 
370
#ifdef __STDC__
371
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
372
#else
373
static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
374
#endif
375
  4.3774099900e-09, /* 0x3196681b */
376
  7.3241114616e-02, /* 0x3d95ff70 */
377
  3.3442313671e+00, /* 0x405607e3 */
378
  4.2621845245e+01, /* 0x422a7cc5 */
379
  1.7080809021e+02, /* 0x432acedf */
380
  1.6673394775e+02, /* 0x4326bbe4 */
381
};
382
#ifdef __STDC__
383
static const float qS3[6] = {
384
#else
385
static float qS3[6] = {
386
#endif
387
  4.8758872986e+01, /* 0x42430916 */
388
  7.0968920898e+02, /* 0x44316c1c */
389
  3.7041481934e+03, /* 0x4567825f */
390
  6.4604252930e+03, /* 0x45c9e367 */
391
  2.5163337402e+03, /* 0x451d4557 */
392
 -1.4924745178e+02, /* 0xc3153f59 */
393
};
394
 
395
#ifdef __STDC__
396
static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
397
#else
398
static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
399
#endif
400
  1.5044444979e-07, /* 0x342189db */
401
  7.3223426938e-02, /* 0x3d95f62a */
402
  1.9981917143e+00, /* 0x3fffc4bf */
403
  1.4495602608e+01, /* 0x4167edfd */
404
  3.1666231155e+01, /* 0x41fd5471 */
405
  1.6252708435e+01, /* 0x4182058c */
406
};
407
#ifdef __STDC__
408
static const float qS2[6] = {
409
#else
410
static float qS2[6] = {
411
#endif
412
  3.0365585327e+01, /* 0x41f2ecb8 */
413
  2.6934811401e+02, /* 0x4386ac8f */
414
  8.4478375244e+02, /* 0x44533229 */
415
  8.8293585205e+02, /* 0x445cbbe5 */
416
  2.1266638184e+02, /* 0x4354aa98 */
417
 -5.3109550476e+00, /* 0xc0a9f358 */
418
};
419
 
420
#ifdef __STDC__
421
        static float qzerof(float x)
422
#else
423
        static float qzerof(x)
424
        float x;
425
#endif
426
{
427
#ifdef __STDC__
428
        const float *p,*q;
429
#else
430
        float *p,*q;
431
#endif
432
        float s,r,z;
433
        int32_t ix;
434
        GET_FLOAT_WORD(ix,x);
435
        ix &= 0x7fffffff;
436
        if(ix>=0x41000000)     {p = qR8; q= qS8;}
437
        else if(ix>=0x40f71c58){p = qR5; q= qS5;}
438
        else if(ix>=0x4036db68){p = qR3; q= qS3;}
439
        else if(ix>=0x40000000){p = qR2; q= qS2;}
440
        z = one/(x*x);
441
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
442
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
443
        return (-(float).125 + r/s)/x;
444
}