1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.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, y1: bool, sign: bool) -> f32 { |
22 | let z: f64; |
23 | let mut s: f64; |
24 | let c: f64; |
25 | let mut ss: f64; |
26 | let mut cc: f64; |
27 | |
28 | s = sinf(x) as f64; |
29 | if y1 { |
30 | s = -s; |
31 | } |
32 | c = cosf(x) as f64; |
33 | cc = s - c; |
34 | if ix < 0x7f000000 { |
35 | ss = -s - c; |
36 | z = cosf(2.0 * x) as f64; |
37 | if s * c > 0.0 { |
38 | cc = z / ss; |
39 | } else { |
40 | ss = z / cc; |
41 | } |
42 | if ix < 0x58800000 { |
43 | if y1 { |
44 | ss = -ss; |
45 | } |
46 | cc = (ponef(x) as f64) * cc - (qonef(x) as f64) * ss; |
47 | } |
48 | } |
49 | if sign { |
50 | cc = -cc; |
51 | } |
52 | return (((INVSQRTPI as f64) * cc) / (sqrtf(x) as f64)) as f32; |
53 | } |
54 | |
55 | /* R0/S0 on [0,2] */ |
56 | const R00: f32 = -6.2500000000e-02; /* 0xbd800000 */ |
57 | const R01: f32 = 1.4070566976e-03; /* 0x3ab86cfd */ |
58 | const R02: f32 = -1.5995563444e-05; /* 0xb7862e36 */ |
59 | const R03: f32 = 4.9672799207e-08; /* 0x335557d2 */ |
60 | const S01: f32 = 1.9153760746e-02; /* 0x3c9ce859 */ |
61 | const S02: f32 = 1.8594678841e-04; /* 0x3942fab6 */ |
62 | const S03: f32 = 1.1771846857e-06; /* 0x359dffc2 */ |
63 | const S04: f32 = 5.0463624390e-09; /* 0x31ad6446 */ |
64 | const S05: f32 = 1.2354227016e-11; /* 0x2d59567e */ |
65 | |
66 | pub fn j1f(x: f32) -> f32 { |
67 | let mut z: f32; |
68 | let r: f32; |
69 | let s: f32; |
70 | let mut ix: u32; |
71 | let sign: bool; |
72 | |
73 | ix = x.to_bits(); |
74 | sign = (ix >> 31) != 0; |
75 | ix &= 0x7fffffff; |
76 | if ix >= 0x7f800000 { |
77 | return 1.0 / (x * x); |
78 | } |
79 | if ix >= 0x40000000 { |
80 | /* |x| >= 2 */ |
81 | return common(ix, fabsf(x), false, sign); |
82 | } |
83 | if ix >= 0x39000000 { |
84 | /* |x| >= 2**-13 */ |
85 | z = x * x; |
86 | r = z * (R00 + z * (R01 + z * (R02 + z * R03))); |
87 | s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05)))); |
88 | z = 0.5 + r / s; |
89 | } else { |
90 | z = 0.5; |
91 | } |
92 | return z * x; |
93 | } |
94 | |
95 | const U0: [f32; 5] = [ |
96 | -1.9605709612e-01, /* 0xbe48c331 */ |
97 | 5.0443872809e-02, /* 0x3d4e9e3c */ |
98 | -1.9125689287e-03, /* 0xbafaaf2a */ |
99 | 2.3525259166e-05, /* 0x37c5581c */ |
100 | -9.1909917899e-08, /* 0xb3c56003 */ |
101 | ]; |
102 | const V0: [f32; 5] = [ |
103 | 1.9916731864e-02, /* 0x3ca3286a */ |
104 | 2.0255257550e-04, /* 0x3954644b */ |
105 | 1.3560879779e-06, /* 0x35b602d4 */ |
106 | 6.2274145840e-09, /* 0x31d5f8eb */ |
107 | 1.6655924903e-11, /* 0x2d9281cf */ |
108 | ]; |
109 | |
110 | pub fn y1f(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 | return common(ix, x, true, false); |
129 | } |
130 | if ix < 0x33000000 { |
131 | /* x < 2**-25 */ |
132 | return -TPI / x; |
133 | } |
134 | z = x * x; |
135 | u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4]))); |
136 | v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4])))); |
137 | return x * (u / v) + TPI * (j1f(x) * logf(x) - 1.0 / x); |
138 | } |
139 | |
140 | /* For x >= 8, the asymptotic expansions of pone is |
141 | * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
142 | * We approximate pone by |
143 | * pone(x) = 1 + (R/S) |
144 | * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 |
145 | * S = 1 + ps0*s^2 + ... + ps4*s^10 |
146 | * and |
147 | * | pone(x)-1-R/S | <= 2 ** ( -60.06) |
148 | */ |
149 | |
150 | const PR8: [f32; 6] = [ |
151 | /* for x in [inf, 8]=1/[0,0.125] */ |
152 | 0.0000000000e+00, /* 0x00000000 */ |
153 | 1.1718750000e-01, /* 0x3df00000 */ |
154 | 1.3239480972e+01, /* 0x4153d4ea */ |
155 | 4.1205184937e+02, /* 0x43ce06a3 */ |
156 | 3.8747453613e+03, /* 0x45722bed */ |
157 | 7.9144794922e+03, /* 0x45f753d6 */ |
158 | ]; |
159 | const PS8: [f32; 5] = [ |
160 | 1.1420736694e+02, /* 0x42e46a2c */ |
161 | 3.6509309082e+03, /* 0x45642ee5 */ |
162 | 3.6956207031e+04, /* 0x47105c35 */ |
163 | 9.7602796875e+04, /* 0x47bea166 */ |
164 | 3.0804271484e+04, /* 0x46f0a88b */ |
165 | ]; |
166 | |
167 | const PR5: [f32; 6] = [ |
168 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
169 | 1.3199052094e-11, /* 0x2d68333f */ |
170 | 1.1718749255e-01, /* 0x3defffff */ |
171 | 6.8027510643e+00, /* 0x40d9b023 */ |
172 | 1.0830818176e+02, /* 0x42d89dca */ |
173 | 5.1763616943e+02, /* 0x440168b7 */ |
174 | 5.2871520996e+02, /* 0x44042dc6 */ |
175 | ]; |
176 | const PS5: [f32; 5] = [ |
177 | 5.9280597687e+01, /* 0x426d1f55 */ |
178 | 9.9140142822e+02, /* 0x4477d9b1 */ |
179 | 5.3532670898e+03, /* 0x45a74a23 */ |
180 | 7.8446904297e+03, /* 0x45f52586 */ |
181 | 1.5040468750e+03, /* 0x44bc0180 */ |
182 | ]; |
183 | |
184 | const PR3: [f32; 6] = [ |
185 | 3.0250391081e-09, /* 0x314fe10d */ |
186 | 1.1718686670e-01, /* 0x3defffab */ |
187 | 3.9329774380e+00, /* 0x407bb5e7 */ |
188 | 3.5119403839e+01, /* 0x420c7a45 */ |
189 | 9.1055007935e+01, /* 0x42b61c2a */ |
190 | 4.8559066772e+01, /* 0x42423c7c */ |
191 | ]; |
192 | const PS3: [f32; 5] = [ |
193 | 3.4791309357e+01, /* 0x420b2a4d */ |
194 | 3.3676245117e+02, /* 0x43a86198 */ |
195 | 1.0468714600e+03, /* 0x4482dbe3 */ |
196 | 8.9081134033e+02, /* 0x445eb3ed */ |
197 | 1.0378793335e+02, /* 0x42cf936c */ |
198 | ]; |
199 | |
200 | const PR2: [f32; 6] = [ |
201 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
202 | 1.0771083225e-07, /* 0x33e74ea8 */ |
203 | 1.1717621982e-01, /* 0x3deffa16 */ |
204 | 2.3685150146e+00, /* 0x401795c0 */ |
205 | 1.2242610931e+01, /* 0x4143e1bc */ |
206 | 1.7693971634e+01, /* 0x418d8d41 */ |
207 | 5.0735230446e+00, /* 0x40a25a4d */ |
208 | ]; |
209 | const PS2: [f32; 5] = [ |
210 | 2.1436485291e+01, /* 0x41ab7dec */ |
211 | 1.2529022980e+02, /* 0x42fa9499 */ |
212 | 2.3227647400e+02, /* 0x436846c7 */ |
213 | 1.1767937469e+02, /* 0x42eb5bd7 */ |
214 | 8.3646392822e+00, /* 0x4105d590 */ |
215 | ]; |
216 | |
217 | fn ponef(x: f32) -> f32 { |
218 | let p: &[f32; 6]; |
219 | let q: &[f32; 5]; |
220 | let z: f32; |
221 | let r: f32; |
222 | let s: f32; |
223 | let mut ix: u32; |
224 | |
225 | ix = x.to_bits(); |
226 | ix &= 0x7fffffff; |
227 | if ix >= 0x41000000 { |
228 | p = &PR8; |
229 | q = &PS8; |
230 | } else if ix >= 0x409173eb { |
231 | p = &PR5; |
232 | q = &PS5; |
233 | } else if ix >= 0x4036d917 { |
234 | p = &PR3; |
235 | q = &PS3; |
236 | } else |
237 | /*ix >= 0x40000000*/ |
238 | { |
239 | p = &PR2; |
240 | q = &PS2; |
241 | } |
242 | z = 1.0 / (x * x); |
243 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
244 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); |
245 | return 1.0 + r / s; |
246 | } |
247 | |
248 | /* For x >= 8, the asymptotic expansions of qone is |
249 | * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
250 | * We approximate pone by |
251 | * qone(x) = s*(0.375 + (R/S)) |
252 | * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
253 | * S = 1 + qs1*s^2 + ... + qs6*s^12 |
254 | * and |
255 | * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
256 | */ |
257 | |
258 | const QR8: [f32; 6] = [ |
259 | /* for x in [inf, 8]=1/[0,0.125] */ |
260 | 0.0000000000e+00, /* 0x00000000 */ |
261 | -1.0253906250e-01, /* 0xbdd20000 */ |
262 | -1.6271753311e+01, /* 0xc1822c8d */ |
263 | -7.5960174561e+02, /* 0xc43de683 */ |
264 | -1.1849806641e+04, /* 0xc639273a */ |
265 | -4.8438511719e+04, /* 0xc73d3683 */ |
266 | ]; |
267 | const QS8: [f32; 6] = [ |
268 | 1.6139537048e+02, /* 0x43216537 */ |
269 | 7.8253862305e+03, /* 0x45f48b17 */ |
270 | 1.3387534375e+05, /* 0x4802bcd6 */ |
271 | 7.1965775000e+05, /* 0x492fb29c */ |
272 | 6.6660125000e+05, /* 0x4922be94 */ |
273 | -2.9449025000e+05, /* 0xc88fcb48 */ |
274 | ]; |
275 | |
276 | const QR5: [f32; 6] = [ |
277 | /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
278 | -2.0897993405e-11, /* 0xadb7d219 */ |
279 | -1.0253904760e-01, /* 0xbdd1fffe */ |
280 | -8.0564479828e+00, /* 0xc100e736 */ |
281 | -1.8366960144e+02, /* 0xc337ab6b */ |
282 | -1.3731937256e+03, /* 0xc4aba633 */ |
283 | -2.6124443359e+03, /* 0xc523471c */ |
284 | ]; |
285 | const QS5: [f32; 6] = [ |
286 | 8.1276550293e+01, /* 0x42a28d98 */ |
287 | 1.9917987061e+03, /* 0x44f8f98f */ |
288 | 1.7468484375e+04, /* 0x468878f8 */ |
289 | 4.9851425781e+04, /* 0x4742bb6d */ |
290 | 2.7948074219e+04, /* 0x46da5826 */ |
291 | -4.7191835938e+03, /* 0xc5937978 */ |
292 | ]; |
293 | |
294 | const QR3: [f32; 6] = [ |
295 | -5.0783124372e-09, /* 0xb1ae7d4f */ |
296 | -1.0253783315e-01, /* 0xbdd1ff5b */ |
297 | -4.6101160049e+00, /* 0xc0938612 */ |
298 | -5.7847221375e+01, /* 0xc267638e */ |
299 | -2.2824453735e+02, /* 0xc3643e9a */ |
300 | -2.1921012878e+02, /* 0xc35b35cb */ |
301 | ]; |
302 | const QS3: [f32; 6] = [ |
303 | 4.7665153503e+01, /* 0x423ea91e */ |
304 | 6.7386511230e+02, /* 0x4428775e */ |
305 | 3.3801528320e+03, /* 0x45534272 */ |
306 | 5.5477290039e+03, /* 0x45ad5dd5 */ |
307 | 1.9031191406e+03, /* 0x44ede3d0 */ |
308 | -1.3520118713e+02, /* 0xc3073381 */ |
309 | ]; |
310 | |
311 | const QR2: [f32; 6] = [ |
312 | /* for x in [2.8570,2]=1/[0.3499,0.5] */ |
313 | -1.7838172539e-07, /* 0xb43f8932 */ |
314 | -1.0251704603e-01, /* 0xbdd1f475 */ |
315 | -2.7522056103e+00, /* 0xc0302423 */ |
316 | -1.9663616180e+01, /* 0xc19d4f16 */ |
317 | -4.2325313568e+01, /* 0xc2294d1f */ |
318 | -2.1371921539e+01, /* 0xc1aaf9b2 */ |
319 | ]; |
320 | const QS2: [f32; 6] = [ |
321 | 2.9533363342e+01, /* 0x41ec4454 */ |
322 | 2.5298155212e+02, /* 0x437cfb47 */ |
323 | 7.5750280762e+02, /* 0x443d602e */ |
324 | 7.3939318848e+02, /* 0x4438d92a */ |
325 | 1.5594900513e+02, /* 0x431bf2f2 */ |
326 | -4.9594988823e+00, /* 0xc09eb437 */ |
327 | ]; |
328 | |
329 | fn qonef(x: f32) -> f32 { |
330 | let p: &[f32; 6]; |
331 | let q: &[f32; 6]; |
332 | let s: f32; |
333 | let r: f32; |
334 | let z: f32; |
335 | let mut ix: u32; |
336 | |
337 | ix = x.to_bits(); |
338 | ix &= 0x7fffffff; |
339 | if ix >= 0x41000000 { |
340 | p = &QR8; |
341 | q = &QS8; |
342 | } else if ix >= 0x409173eb { |
343 | p = &QR5; |
344 | q = &QS5; |
345 | } else if ix >= 0x4036d917 { |
346 | p = &QR3; |
347 | q = &QS3; |
348 | } else |
349 | /*ix >= 0x40000000*/ |
350 | { |
351 | p = &QR2; |
352 | q = &QS2; |
353 | } |
354 | z = 1.0 / (x * x); |
355 | r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); |
356 | s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); |
357 | return (0.375 + r / s) / x; |
358 | } |
359 | |
360 | // PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520 |
361 | #[cfg (not(target_arch = "powerpc64" ))] |
362 | #[cfg (test)] |
363 | mod tests { |
364 | use super::{j1f, y1f}; |
365 | #[test ] |
366 | fn test_j1f_2488() { |
367 | // 0x401F3E49 |
368 | assert_eq!(j1f(2.4881766_f32), 0.49999475_f32); |
369 | } |
370 | #[test ] |
371 | fn test_y1f_2002() { |
372 | //allow slightly different result on x87 |
373 | let res = y1f(2.0000002_f32); |
374 | if cfg!(all(target_arch = "x86" , not(target_feature = "sse2" ))) && (res == -0.10703231_f32) |
375 | { |
376 | return; |
377 | } |
378 | assert_eq!(res, -0.10703229_f32); |
379 | } |
380 | } |
381 | |