1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */ |
2 | /* |
3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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 | use super::{cosf, fabsf, logf, sinf, sqrtf}; |
17 | |
18 | const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */ |
19 | const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */ |
20 | |
21 | fn common(ix: u32, x: f32, y0: bool) -> f32 { |
22 | let z: f32; |
23 | let s: f32; |
24 | let mut c: f32; |
25 | let mut ss: f32; |
26 | let mut cc: f32; |
27 | /* |
28 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
29 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
30 | */ |
31 | s = sinf(x); |
32 | c = cosf(x); |
33 | if y0 { |
34 | c = -c; |
35 | } |
36 | cc = s + c; |
37 | if ix < 0x7f000000 { |
38 | ss = s - c; |
39 | z = -cosf(2.0 * x); |
40 | if s * c < 0.0 { |
41 | cc = z / ss; |
42 | } else { |
43 | ss = z / cc; |
44 | } |
45 | if ix < 0x58800000 { |
46 | if y0 { |
47 | ss = -ss; |
48 | } |
49 | cc = pzerof(x) * cc - qzerof(x) * ss; |
50 | } |
51 | } |
52 | return INVSQRTPI * cc / sqrtf(x); |
53 | } |
54 | |
55 | /* R0/S0 on [0, 2.00] */ |
56 | const R02: f32 = 1.5625000000e-02; /* 0x3c800000 */ |
57 | const R03: f32 = -1.8997929874e-04; /* 0xb947352e */ |
58 | const R04: f32 = 1.8295404516e-06; /* 0x35f58e88 */ |
59 | const R05: f32 = -4.6183270541e-09; /* 0xb19eaf3c */ |
60 | const S01: f32 = 1.5619102865e-02; /* 0x3c7fe744 */ |
61 | const S02: f32 = 1.1692678527e-04; /* 0x38f53697 */ |
62 | const S03: f32 = 5.1354652442e-07; /* 0x3509daa6 */ |
63 | const S04: f32 = 1.1661400734e-09; /* 0x30a045e8 */ |
64 | |
65 | pub fn j0f(mut x: f32) -> f32 { |
66 | let z: f32; |
67 | let r: f32; |
68 | let s: f32; |
69 | let mut ix: u32; |
70 | |
71 | ix = x.to_bits(); |
72 | ix &= 0x7fffffff; |
73 | if ix >= 0x7f800000 { |
74 | return 1.0 / (x * x); |
75 | } |
76 | x = fabsf(x); |
77 | |
78 | if ix >= 0x40000000 { |
79 | /* |x| >= 2 */ |
80 | /* large ulp error near zeros */ |
81 | return common(ix, x, false); |
82 | } |
83 | if ix >= 0x3a000000 { |
84 | /* |x| >= 2**-11 */ |
85 | /* up to 4ulp error near 2 */ |
86 | z = x * x; |
87 | r = z * (R02 + z * (R03 + z * (R04 + z * R05))); |
88 | s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04))); |
89 | return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s); |
90 | } |
91 | if ix >= 0x21800000 { |
92 | /* |x| >= 2**-60 */ |
93 | x = 0.25 * x * x; |
94 | } |
95 | return 1.0 - x; |
96 | } |
97 | |
98 | const U00: f32 = -7.3804296553e-02; /* 0xbd9726b5 */ |
99 | const U01: f32 = 1.7666645348e-01; /* 0x3e34e80d */ |
100 | const U02: f32 = -1.3818567619e-02; /* 0xbc626746 */ |
101 | const U03: f32 = 3.4745343146e-04; /* 0x39b62a69 */ |
102 | const U04: f32 = -3.8140706238e-06; /* 0xb67ff53c */ |
103 | const U05: f32 = 1.9559013964e-08; /* 0x32a802ba */ |
104 | const U06: f32 = -3.9820518410e-11; /* 0xae2f21eb */ |
105 | const V01: f32 = 1.2730483897e-02; /* 0x3c509385 */ |
106 | const V02: f32 = 7.6006865129e-05; /* 0x389f65e0 */ |
107 | const V03: f32 = 2.5915085189e-07; /* 0x348b216c */ |
108 | const V04: f32 = 4.4111031494e-10; /* 0x2ff280c2 */ |
109 | |
110 | pub fn y0f(x: f32) -> f32 { |
111 | let z: f32; |
112 | let u: f32; |
113 | let v: f32; |
114 | let ix: u32; |
115 | |
116 | ix = x.to_bits(); |
117 | if (ix & 0x7fffffff) == 0 { |
118 | return -1.0 / 0.0; |
119 | } |
120 | if (ix >> 31) != 0 { |
121 | return 0.0 / 0.0; |
122 | } |
123 | if ix >= 0x7f800000 { |
124 | return 1.0 / x; |
125 | } |
126 | if ix >= 0x40000000 { |
127 | /* |x| >= 2.0 */ |
128 | /* large ulp error near zeros */ |
129 | return common(ix, x, true); |
130 | } |
131 | if ix >= 0x39000000 { |
132 | /* x >= 2**-13 */ |
133 | /* large ulp error at x ~= 0.89 */ |
134 | z = x * x; |
135 | u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06))))); |
136 | v = 1.0 + z * (V01 + z * (V02 + z * (V03 + z * V04))); |
137 | return u / v + TPI * (j0f(x) * logf(x)); |
138 | } |
139 | return U00 + TPI * logf(x); |
140 | } |
141 | |
142 | /* The asymptotic expansions of pzero is |
143 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
144 | * For x >= 2, We approximate pzero by |
145 | * pzero(x) = 1 + (R/S) |
146 | * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
147 | * S = 1 + pS0*s^2 + ... + pS4*s^10 |
148 | * and |
149 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
150 | */ |
151 | const PR8: [f32; 6] = [ |
152 | /* for x in [inf, 8]=1/[0,0.125] */ |
153 | 0.0000000000e+00, /* 0x00000000 */ |
154 | -7.0312500000e-02, /* 0xbd900000 */ |
155 | -8.0816707611e+00, /* 0xc1014e86 */ |
156 | -2.5706311035e+02, /* 0xc3808814 */ |
157 | -2.4852163086e+03, /* 0xc51b5376 */ |
158 | -5.2530439453e+03, /* 0xc5a4285a */ |
159 | ]; |
160 | const PS8: [f32; 5] = [ |
161 | 1.1653436279e+02, /* 0x42e91198 */ |
162 | 3.8337448730e+03, /* 0x456f9beb */ |
163 | 4.0597855469e+04, /* 0x471e95db */ |
164 | 1.1675296875e+05, /* 0x47e4087c */ |
165 | 4.7627726562e+04, /* 0x473a0bba */ |
166 | ]; |
167 | const PR5: [f32; 6] = [ |
168 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
169 | -1.1412546255e-11, /* 0xad48c58a */ |
170 | -7.0312492549e-02, /* 0xbd8fffff */ |
171 | -4.1596107483e+00, /* 0xc0851b88 */ |
172 | -6.7674766541e+01, /* 0xc287597b */ |
173 | -3.3123129272e+02, /* 0xc3a59d9b */ |
174 | -3.4643338013e+02, /* 0xc3ad3779 */ |
175 | ]; |
176 | const PS5: [f32; 5] = [ |
177 | 6.0753936768e+01, /* 0x42730408 */ |
178 | 1.0512523193e+03, /* 0x44836813 */ |
179 | 5.9789707031e+03, /* 0x45bad7c4 */ |
180 | 9.6254453125e+03, /* 0x461665c8 */ |
181 | 2.4060581055e+03, /* 0x451660ee */ |
182 | ]; |
183 | |
184 | const PR3: [f32; 6] = [ |
185 | /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
186 | -2.5470459075e-09, /* 0xb12f081b */ |
187 | -7.0311963558e-02, /* 0xbd8fffb8 */ |
188 | -2.4090321064e+00, /* 0xc01a2d95 */ |
189 | -2.1965976715e+01, /* 0xc1afba52 */ |
190 | -5.8079170227e+01, /* 0xc2685112 */ |
191 | -3.1447946548e+01, /* 0xc1fb9565 */ |
192 | ]; |
193 | const PS3: [f32; 5] = [ |
194 | 3.5856033325e+01, /* 0x420f6c94 */ |
195 | 3.6151397705e+02, /* 0x43b4c1ca */ |
196 | 1.1936077881e+03, /* 0x44953373 */ |
197 | 1.1279968262e+03, /* 0x448cffe6 */ |
198 | 1.7358093262e+02, /* 0x432d94b8 */ |
199 | ]; |
200 | |
201 | const PR2: [f32; 6] = [ |
202 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
203 | -8.8753431271e-08, /* 0xb3be98b7 */ |
204 | -7.0303097367e-02, /* 0xbd8ffb12 */ |
205 | -1.4507384300e+00, /* 0xbfb9b1cc */ |
206 | -7.6356959343e+00, /* 0xc0f4579f */ |
207 | -1.1193166733e+01, /* 0xc1331736 */ |
208 | -3.2336456776e+00, /* 0xc04ef40d */ |
209 | ]; |
210 | const PS2: [f32; 5] = [ |
211 | 2.2220300674e+01, /* 0x41b1c32d */ |
212 | 1.3620678711e+02, /* 0x430834f0 */ |
213 | 2.7047027588e+02, /* 0x43873c32 */ |
214 | 1.5387539673e+02, /* 0x4319e01a */ |
215 | 1.4657617569e+01, /* 0x416a859a */ |
216 | ]; |
217 | |
218 | fn pzerof(x: f32) -> f32 { |
219 | let p: &[f32; 6]; |
220 | let q: &[f32; 5]; |
221 | let z: f32; |
222 | let r: f32; |
223 | let s: f32; |
224 | let mut ix: u32; |
225 | |
226 | ix = x.to_bits(); |
227 | ix &= 0x7fffffff; |
228 | if ix >= 0x41000000 { |
229 | p = &PR8; |
230 | q = &PS8; |
231 | } else if ix >= 0x409173eb { |
232 | p = &PR5; |
233 | q = &PS5; |
234 | } else if ix >= 0x4036d917 { |
235 | p = &PR3; |
236 | q = &PS3; |
237 | } else |
238 | /*ix >= 0x40000000*/ |
239 | { |
240 | p = &PR2; |
241 | q = &PS2; |
242 | } |
243 | z = 1.0 / (x * x); |
244 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
245 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); |
246 | return 1.0 + r / s; |
247 | } |
248 | |
249 | /* For x >= 8, the asymptotic expansions of qzero is |
250 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
251 | * We approximate pzero by |
252 | * qzero(x) = s*(-1.25 + (R/S)) |
253 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
254 | * S = 1 + qS0*s^2 + ... + qS5*s^12 |
255 | * and |
256 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
257 | */ |
258 | const QR8: [f32; 6] = [ |
259 | /* for x in [inf, 8]=1/[0,0.125] */ |
260 | 0.0000000000e+00, /* 0x00000000 */ |
261 | 7.3242187500e-02, /* 0x3d960000 */ |
262 | 1.1768206596e+01, /* 0x413c4a93 */ |
263 | 5.5767340088e+02, /* 0x440b6b19 */ |
264 | 8.8591972656e+03, /* 0x460a6cca */ |
265 | 3.7014625000e+04, /* 0x471096a0 */ |
266 | ]; |
267 | const QS8: [f32; 6] = [ |
268 | 1.6377603149e+02, /* 0x4323c6aa */ |
269 | 8.0983447266e+03, /* 0x45fd12c2 */ |
270 | 1.4253829688e+05, /* 0x480b3293 */ |
271 | 8.0330925000e+05, /* 0x49441ed4 */ |
272 | 8.4050156250e+05, /* 0x494d3359 */ |
273 | -3.4389928125e+05, /* 0xc8a7eb69 */ |
274 | ]; |
275 | |
276 | const QR5: [f32; 6] = [ |
277 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
278 | 1.8408595828e-11, /* 0x2da1ec79 */ |
279 | 7.3242180049e-02, /* 0x3d95ffff */ |
280 | 5.8356351852e+00, /* 0x40babd86 */ |
281 | 1.3511157227e+02, /* 0x43071c90 */ |
282 | 1.0272437744e+03, /* 0x448067cd */ |
283 | 1.9899779053e+03, /* 0x44f8bf4b */ |
284 | ]; |
285 | const QS5: [f32; 6] = [ |
286 | 8.2776611328e+01, /* 0x42a58da0 */ |
287 | 2.0778142090e+03, /* 0x4501dd07 */ |
288 | 1.8847289062e+04, /* 0x46933e94 */ |
289 | 5.6751113281e+04, /* 0x475daf1d */ |
290 | 3.5976753906e+04, /* 0x470c88c1 */ |
291 | -5.3543427734e+03, /* 0xc5a752be */ |
292 | ]; |
293 | |
294 | const QR3: [f32; 6] = [ |
295 | /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
296 | 4.3774099900e-09, /* 0x3196681b */ |
297 | 7.3241114616e-02, /* 0x3d95ff70 */ |
298 | 3.3442313671e+00, /* 0x405607e3 */ |
299 | 4.2621845245e+01, /* 0x422a7cc5 */ |
300 | 1.7080809021e+02, /* 0x432acedf */ |
301 | 1.6673394775e+02, /* 0x4326bbe4 */ |
302 | ]; |
303 | const QS3: [f32; 6] = [ |
304 | 4.8758872986e+01, /* 0x42430916 */ |
305 | 7.0968920898e+02, /* 0x44316c1c */ |
306 | 3.7041481934e+03, /* 0x4567825f */ |
307 | 6.4604252930e+03, /* 0x45c9e367 */ |
308 | 2.5163337402e+03, /* 0x451d4557 */ |
309 | -1.4924745178e+02, /* 0xc3153f59 */ |
310 | ]; |
311 | |
312 | const QR2: [f32; 6] = [ |
313 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
314 | 1.5044444979e-07, /* 0x342189db */ |
315 | 7.3223426938e-02, /* 0x3d95f62a */ |
316 | 1.9981917143e+00, /* 0x3fffc4bf */ |
317 | 1.4495602608e+01, /* 0x4167edfd */ |
318 | 3.1666231155e+01, /* 0x41fd5471 */ |
319 | 1.6252708435e+01, /* 0x4182058c */ |
320 | ]; |
321 | const QS2: [f32; 6] = [ |
322 | 3.0365585327e+01, /* 0x41f2ecb8 */ |
323 | 2.6934811401e+02, /* 0x4386ac8f */ |
324 | 8.4478375244e+02, /* 0x44533229 */ |
325 | 8.8293585205e+02, /* 0x445cbbe5 */ |
326 | 2.1266638184e+02, /* 0x4354aa98 */ |
327 | -5.3109550476e+00, /* 0xc0a9f358 */ |
328 | ]; |
329 | |
330 | fn qzerof(x: f32) -> f32 { |
331 | let p: &[f32; 6]; |
332 | let q: &[f32; 6]; |
333 | let s: f32; |
334 | let r: f32; |
335 | let z: f32; |
336 | let mut ix: u32; |
337 | |
338 | ix = x.to_bits(); |
339 | ix &= 0x7fffffff; |
340 | if ix >= 0x41000000 { |
341 | p = &QR8; |
342 | q = &QS8; |
343 | } else if ix >= 0x409173eb { |
344 | p = &QR5; |
345 | q = &QS5; |
346 | } else if ix >= 0x4036d917 { |
347 | p = &QR3; |
348 | q = &QS3; |
349 | } else |
350 | /*ix >= 0x40000000*/ |
351 | { |
352 | p = &QR2; |
353 | q = &QS2; |
354 | } |
355 | z = 1.0 / (x * x); |
356 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
357 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); |
358 | return (-0.125 + r / s) / x; |
359 | } |
360 | |