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[minix.git] / lib / libm / src / e_j0f.c
blob96d3a95b5c8968a00afa76f5a4097569c49e5bff
1 /* 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 #include <sys/cdefs.h>
17 #if defined(LIBM_SCCS) && !defined(lint)
18 __RCSID("$NetBSD: e_j0f.c,v 1.10 2007/08/20 16:01:38 drochner Exp $");
19 #endif
20
21 #include "namespace.h"
22 #include "math.h"
23 #include "math_private.h"
24
25 static float pzerof(float), qzerof(float);
26
27 static const float
28 huge = 1e30,
29 one = 1.0,
30 invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
31 tpi = 6.3661974669e-01, /* 0x3f22f983 */
32 /* R0/S0 on [0, 2.00] */
33 R02 = 1.5625000000e-02, /* 0x3c800000 */
34 R03 = -1.8997929874e-04, /* 0xb947352e */
35 R04 = 1.8295404516e-06, /* 0x35f58e88 */
36 R05 = -4.6183270541e-09, /* 0xb19eaf3c */
37 S01 = 1.5619102865e-02, /* 0x3c7fe744 */
38 S02 = 1.1692678527e-04, /* 0x38f53697 */
39 S03 = 5.1354652442e-07, /* 0x3509daa6 */
40 S04 = 1.1661400734e-09; /* 0x30a045e8 */
41
42 static const float zero = 0.0;
43
44 float
45 __ieee754_j0f(float x)
46 {
47 float z, s,c,ss,cc,r,u,v;
48 int32_t hx,ix;
49
50 GET_FLOAT_WORD(hx,x);
51 ix = hx&0x7fffffff;
52 if(ix>=0x7f800000) return one/(x*x);
53 x = fabsf(x);
54 if(ix >= 0x40000000) { /* |x| >= 2.0 */
55 s = sinf(x);
56 c = cosf(x);
57 ss = s-c;
58 cc = s+c;
59 if(ix<0x7f000000) { /* make sure x+x not overflow */
60 z = -cosf(x+x);
61 if ((s*c)<zero) cc = z/ss;
62 else ss = z/cc;
63 }
64 /*
65 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
66 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
67 */
68 #ifdef DEAD_CODE
69 if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
70 else
71 #endif
72 {
73 u = pzerof(x); v = qzerof(x);
74 z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
75 }
76 return z;
77 }
78 if(ix<0x39000000) { /* |x| < 2**-13 */
79 if(huge+x>one) { /* raise inexact if x != 0 */
80 if(ix<0x32000000) return one; /* |x|<2**-27 */
81 else return one - (float)0.25*x*x;
82 }
83 }
84 z = x*x;
85 r = z*(R02+z*(R03+z*(R04+z*R05)));
86 s = one+z*(S01+z*(S02+z*(S03+z*S04)));
87 if(ix < 0x3F800000) { /* |x| < 1.00 */
88 return one + z*((float)-0.25+(r/s));
89 } else {
90 u = (float)0.5*x;
91 return((one+u)*(one-u)+z*(r/s));
92 }
93 }
94
95 static const float
96 u00 = -7.3804296553e-02, /* 0xbd9726b5 */
97 u01 = 1.7666645348e-01, /* 0x3e34e80d */
98 u02 = -1.3818567619e-02, /* 0xbc626746 */
99 u03 = 3.4745343146e-04, /* 0x39b62a69 */
100 u04 = -3.8140706238e-06, /* 0xb67ff53c */
101 u05 = 1.9559013964e-08, /* 0x32a802ba */
102 u06 = -3.9820518410e-11, /* 0xae2f21eb */
103 v01 = 1.2730483897e-02, /* 0x3c509385 */
104 v02 = 7.6006865129e-05, /* 0x389f65e0 */
105 v03 = 2.5915085189e-07, /* 0x348b216c */
106 v04 = 4.4111031494e-10; /* 0x2ff280c2 */
107
108 float
109 __ieee754_y0f(float x)
110 {
111 float z, s,c,ss,cc,u,v;
112 int32_t hx,ix;
113
114 GET_FLOAT_WORD(hx,x);
115 ix = 0x7fffffff&hx;
116 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
117 if(ix>=0x7f800000) return one/(x+x*x);
118 if(ix==0) return -one/zero;
119 if(hx<0) return zero/zero;
120 if(ix >= 0x40000000) { /* |x| >= 2.0 */
121 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
122 * where x0 = x-pi/4
123 * Better formula:
124 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
125 * = 1/sqrt(2) * (sin(x) + cos(x))
126 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
127 * = 1/sqrt(2) * (sin(x) - cos(x))
128 * To avoid cancellation, use
129 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
130 * to compute the worse one.
131 */
132 s = sinf(x);
133 c = cosf(x);
134 ss = s-c;
135 cc = s+c;
136 /*
137 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
138 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
139 */
140 if(ix<0x7f000000) { /* 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 #ifdef DEAD_CODE
146 if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
147 else
148 #endif
149 {
150 u = pzerof(x); v = qzerof(x);
151 z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
152 }
153 return z;
154 }
155 if(ix<=0x32000000) { /* x < 2**-27 */
156 return(u00 + tpi*__ieee754_logf(x));
157 }
158 z = x*x;
159 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
160 v = one+z*(v01+z*(v02+z*(v03+z*v04)));
161 return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
162 }
163
164 /* The asymptotic expansions of pzero is
165 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
166 * For x >= 2, We approximate pzero by
167 * pzero(x) = 1 + (R/S)
168 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
169 * S = 1 + pS0*s^2 + ... + pS4*s^10
170 * and
171 * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
172 */
173 static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
174 0.0000000000e+00, /* 0x00000000 */
175 -7.0312500000e-02, /* 0xbd900000 */
176 -8.0816707611e+00, /* 0xc1014e86 */
177 -2.5706311035e+02, /* 0xc3808814 */
178 -2.4852163086e+03, /* 0xc51b5376 */
179 -5.2530439453e+03, /* 0xc5a4285a */
180 };
181 static const float pS8[5] = {
182 1.1653436279e+02, /* 0x42e91198 */
183 3.8337448730e+03, /* 0x456f9beb */
184 4.0597855469e+04, /* 0x471e95db */
185 1.1675296875e+05, /* 0x47e4087c */
186 4.7627726562e+04, /* 0x473a0bba */
187 };
188 static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
189 -1.1412546255e-11, /* 0xad48c58a */
190 -7.0312492549e-02, /* 0xbd8fffff */
191 -4.1596107483e+00, /* 0xc0851b88 */
192 -6.7674766541e+01, /* 0xc287597b */
193 -3.3123129272e+02, /* 0xc3a59d9b */
194 -3.4643338013e+02, /* 0xc3ad3779 */
195 };
196 static const float pS5[5] = {
197 6.0753936768e+01, /* 0x42730408 */
198 1.0512523193e+03, /* 0x44836813 */
199 5.9789707031e+03, /* 0x45bad7c4 */
200 9.6254453125e+03, /* 0x461665c8 */
201 2.4060581055e+03, /* 0x451660ee */
202 };
203
204 static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
205 -2.5470459075e-09, /* 0xb12f081b */
206 -7.0311963558e-02, /* 0xbd8fffb8 */
207 -2.4090321064e+00, /* 0xc01a2d95 */
208 -2.1965976715e+01, /* 0xc1afba52 */
209 -5.8079170227e+01, /* 0xc2685112 */
210 -3.1447946548e+01, /* 0xc1fb9565 */
211 };
212 static const float pS3[5] = {
213 3.5856033325e+01, /* 0x420f6c94 */
214 3.6151397705e+02, /* 0x43b4c1ca */
215 1.1936077881e+03, /* 0x44953373 */
216 1.1279968262e+03, /* 0x448cffe6 */
217 1.7358093262e+02, /* 0x432d94b8 */
218 };
219
220 static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
221 -8.8753431271e-08, /* 0xb3be98b7 */
222 -7.0303097367e-02, /* 0xbd8ffb12 */
223 -1.4507384300e+00, /* 0xbfb9b1cc */
224 -7.6356959343e+00, /* 0xc0f4579f */
225 -1.1193166733e+01, /* 0xc1331736 */
226 -3.2336456776e+00, /* 0xc04ef40d */
227 };
228 static const float pS2[5] = {
229 2.2220300674e+01, /* 0x41b1c32d */
230 1.3620678711e+02, /* 0x430834f0 */
231 2.7047027588e+02, /* 0x43873c32 */
232 1.5387539673e+02, /* 0x4319e01a */
233 1.4657617569e+01, /* 0x416a859a */
234 };
235
236 static float
237 pzerof(float x)
238 {
239 const float *p,*q;
240 float z,r,s;
241 int32_t ix;
242
243 p = q = 0;
244 GET_FLOAT_WORD(ix,x);
245 ix &= 0x7fffffff;
246 if(ix>=0x41000000) {p = pR8; q= pS8;}
247 else if(ix>=0x40f71c58){p = pR5; q= pS5;}
248 else if(ix>=0x4036db68){p = pR3; q= pS3;}
249 else if(ix>=0x40000000){p = pR2; q= pS2;}
250 z = one/(x*x);
251 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
252 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
253 return one+ r/s;
254 }
255
256
257 /* For x >= 8, the asymptotic expansions of qzero is
258 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
259 * We approximate pzero by
260 * qzero(x) = s*(-1.25 + (R/S))
261 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
262 * S = 1 + qS0*s^2 + ... + qS5*s^12
263 * and
264 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
265 */
266 static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
267 0.0000000000e+00, /* 0x00000000 */
268 7.3242187500e-02, /* 0x3d960000 */
269 1.1768206596e+01, /* 0x413c4a93 */
270 5.5767340088e+02, /* 0x440b6b19 */
271 8.8591972656e+03, /* 0x460a6cca */
272 3.7014625000e+04, /* 0x471096a0 */
273 };
274 static const float qS8[6] = {
275 1.6377603149e+02, /* 0x4323c6aa */
276 8.0983447266e+03, /* 0x45fd12c2 */
277 1.4253829688e+05, /* 0x480b3293 */
278 8.0330925000e+05, /* 0x49441ed4 */
279 8.4050156250e+05, /* 0x494d3359 */
280 -3.4389928125e+05, /* 0xc8a7eb69 */
281 };
282
283 static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
284 1.8408595828e-11, /* 0x2da1ec79 */
285 7.3242180049e-02, /* 0x3d95ffff */
286 5.8356351852e+00, /* 0x40babd86 */
287 1.3511157227e+02, /* 0x43071c90 */
288 1.0272437744e+03, /* 0x448067cd */
289 1.9899779053e+03, /* 0x44f8bf4b */
290 };
291 static const float qS5[6] = {
292 8.2776611328e+01, /* 0x42a58da0 */
293 2.0778142090e+03, /* 0x4501dd07 */
294 1.8847289062e+04, /* 0x46933e94 */
295 5.6751113281e+04, /* 0x475daf1d */
296 3.5976753906e+04, /* 0x470c88c1 */
297 -5.3543427734e+03, /* 0xc5a752be */
298 };
299
300 static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
301 4.3774099900e-09, /* 0x3196681b */
302 7.3241114616e-02, /* 0x3d95ff70 */
303 3.3442313671e+00, /* 0x405607e3 */
304 4.2621845245e+01, /* 0x422a7cc5 */
305 1.7080809021e+02, /* 0x432acedf */
306 1.6673394775e+02, /* 0x4326bbe4 */
307 };
308 static const float qS3[6] = {
309 4.8758872986e+01, /* 0x42430916 */
310 7.0968920898e+02, /* 0x44316c1c */
311 3.7041481934e+03, /* 0x4567825f */
312 6.4604252930e+03, /* 0x45c9e367 */
313 2.5163337402e+03, /* 0x451d4557 */
314 -1.4924745178e+02, /* 0xc3153f59 */
315 };
316
317 static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
318 1.5044444979e-07, /* 0x342189db */
319 7.3223426938e-02, /* 0x3d95f62a */
320 1.9981917143e+00, /* 0x3fffc4bf */
321 1.4495602608e+01, /* 0x4167edfd */
322 3.1666231155e+01, /* 0x41fd5471 */
323 1.6252708435e+01, /* 0x4182058c */
324 };
325 static const float qS2[6] = {
326 3.0365585327e+01, /* 0x41f2ecb8 */
327 2.6934811401e+02, /* 0x4386ac8f */
328 8.4478375244e+02, /* 0x44533229 */
329 8.8293585205e+02, /* 0x445cbbe5 */
330 2.1266638184e+02, /* 0x4354aa98 */
331 -5.3109550476e+00, /* 0xc0a9f358 */
332 };
333
334 static float
335 qzerof(float x)
336 {
337 const float *p,*q;
338 float s,r,z;
339 int32_t ix;
340
341 p = q = 0;
342 GET_FLOAT_WORD(ix,x);
343 ix &= 0x7fffffff;
344 if(ix>=0x41000000) {p = qR8; q= qS8;}
345 else if(ix>=0x40f71c58){p = qR5; q= qS5;}
346 else if(ix>=0x4036db68){p = qR3; q= qS3;}
347 else if(ix>=0x40000000){p = qR2; q= qS2;}
348 z = one/(x*x);
349 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
350 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
351 return (-(float).125 + r/s)/x;
352 }
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