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
16use super::{cosf, fabsf, logf, sinf, sqrtf};
17
18const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */
19const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */
20
21fn 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] */
56const R00: f32 = -6.2500000000e-02; /* 0xbd800000 */
57const R01: f32 = 1.4070566976e-03; /* 0x3ab86cfd */
58const R02: f32 = -1.5995563444e-05; /* 0xb7862e36 */
59const R03: f32 = 4.9672799207e-08; /* 0x335557d2 */
60const S01: f32 = 1.9153760746e-02; /* 0x3c9ce859 */
61const S02: f32 = 1.8594678841e-04; /* 0x3942fab6 */
62const S03: f32 = 1.1771846857e-06; /* 0x359dffc2 */
63const S04: f32 = 5.0463624390e-09; /* 0x31ad6446 */
64const S05: f32 = 1.2354227016e-11; /* 0x2d59567e */
65
66/// First order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind (f32).
67#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
68pub fn j1f(x: f32) -> f32 {
69 let mut z: f32;
70 let r: f32;
71 let s: f32;
72 let mut ix: u32;
73 let sign: bool;
74
75 ix = x.to_bits();
76 sign = (ix >> 31) != 0;
77 ix &= 0x7fffffff;
78 if ix >= 0x7f800000 {
79 return 1.0 / (x * x);
80 }
81 if ix >= 0x40000000 {
82 /* |x| >= 2 */
83 return common(ix, fabsf(x), false, sign);
84 }
85 if ix >= 0x39000000 {
86 /* |x| >= 2**-13 */
87 z = x * x;
88 r = z * (R00 + z * (R01 + z * (R02 + z * R03)));
89 s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05))));
90 z = 0.5 + r / s;
91 } else {
92 z = 0.5;
93 }
94 return z * x;
95}
96
97const U0: [f32; 5] = [
98 -1.9605709612e-01, /* 0xbe48c331 */
99 5.0443872809e-02, /* 0x3d4e9e3c */
100 -1.9125689287e-03, /* 0xbafaaf2a */
101 2.3525259166e-05, /* 0x37c5581c */
102 -9.1909917899e-08, /* 0xb3c56003 */
103];
104const V0: [f32; 5] = [
105 1.9916731864e-02, /* 0x3ca3286a */
106 2.0255257550e-04, /* 0x3954644b */
107 1.3560879779e-06, /* 0x35b602d4 */
108 6.2274145840e-09, /* 0x31d5f8eb */
109 1.6655924903e-11, /* 0x2d9281cf */
110];
111
112/// First order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind (f32).
113#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
114pub fn y1f(x: f32) -> f32 {
115 let z: f32;
116 let u: f32;
117 let v: f32;
118 let ix: u32;
119
120 ix = x.to_bits();
121 if (ix & 0x7fffffff) == 0 {
122 return -1.0 / 0.0;
123 }
124 if (ix >> 31) != 0 {
125 return 0.0 / 0.0;
126 }
127 if ix >= 0x7f800000 {
128 return 1.0 / x;
129 }
130 if ix >= 0x40000000 {
131 /* |x| >= 2.0 */
132 return common(ix, x, true, false);
133 }
134 if ix < 0x33000000 {
135 /* x < 2**-25 */
136 return -TPI / x;
137 }
138 z = x * x;
139 u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4])));
140 v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4]))));
141 return x * (u / v) + TPI * (j1f(x) * logf(x) - 1.0 / x);
142}
143
144/* For x >= 8, the asymptotic expansions of pone is
145 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
146 * We approximate pone by
147 * pone(x) = 1 + (R/S)
148 * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
149 * S = 1 + ps0*s^2 + ... + ps4*s^10
150 * and
151 * | pone(x)-1-R/S | <= 2 ** ( -60.06)
152 */
153
154const PR8: [f32; 6] = [
155 /* for x in [inf, 8]=1/[0,0.125] */
156 0.0000000000e+00, /* 0x00000000 */
157 1.1718750000e-01, /* 0x3df00000 */
158 1.3239480972e+01, /* 0x4153d4ea */
159 4.1205184937e+02, /* 0x43ce06a3 */
160 3.8747453613e+03, /* 0x45722bed */
161 7.9144794922e+03, /* 0x45f753d6 */
162];
163const PS8: [f32; 5] = [
164 1.1420736694e+02, /* 0x42e46a2c */
165 3.6509309082e+03, /* 0x45642ee5 */
166 3.6956207031e+04, /* 0x47105c35 */
167 9.7602796875e+04, /* 0x47bea166 */
168 3.0804271484e+04, /* 0x46f0a88b */
169];
170
171const PR5: [f32; 6] = [
172 /* for x in [8,4.5454]=1/[0.125,0.22001] */
173 1.3199052094e-11, /* 0x2d68333f */
174 1.1718749255e-01, /* 0x3defffff */
175 6.8027510643e+00, /* 0x40d9b023 */
176 1.0830818176e+02, /* 0x42d89dca */
177 5.1763616943e+02, /* 0x440168b7 */
178 5.2871520996e+02, /* 0x44042dc6 */
179];
180const PS5: [f32; 5] = [
181 5.9280597687e+01, /* 0x426d1f55 */
182 9.9140142822e+02, /* 0x4477d9b1 */
183 5.3532670898e+03, /* 0x45a74a23 */
184 7.8446904297e+03, /* 0x45f52586 */
185 1.5040468750e+03, /* 0x44bc0180 */
186];
187
188const PR3: [f32; 6] = [
189 3.0250391081e-09, /* 0x314fe10d */
190 1.1718686670e-01, /* 0x3defffab */
191 3.9329774380e+00, /* 0x407bb5e7 */
192 3.5119403839e+01, /* 0x420c7a45 */
193 9.1055007935e+01, /* 0x42b61c2a */
194 4.8559066772e+01, /* 0x42423c7c */
195];
196const PS3: [f32; 5] = [
197 3.4791309357e+01, /* 0x420b2a4d */
198 3.3676245117e+02, /* 0x43a86198 */
199 1.0468714600e+03, /* 0x4482dbe3 */
200 8.9081134033e+02, /* 0x445eb3ed */
201 1.0378793335e+02, /* 0x42cf936c */
202];
203
204const PR2: [f32; 6] = [
205 /* for x in [2.8570,2]=1/[0.3499,0.5] */
206 1.0771083225e-07, /* 0x33e74ea8 */
207 1.1717621982e-01, /* 0x3deffa16 */
208 2.3685150146e+00, /* 0x401795c0 */
209 1.2242610931e+01, /* 0x4143e1bc */
210 1.7693971634e+01, /* 0x418d8d41 */
211 5.0735230446e+00, /* 0x40a25a4d */
212];
213const PS2: [f32; 5] = [
214 2.1436485291e+01, /* 0x41ab7dec */
215 1.2529022980e+02, /* 0x42fa9499 */
216 2.3227647400e+02, /* 0x436846c7 */
217 1.1767937469e+02, /* 0x42eb5bd7 */
218 8.3646392822e+00, /* 0x4105d590 */
219];
220
221fn ponef(x: f32) -> f32 {
222 let p: &[f32; 6];
223 let q: &[f32; 5];
224 let z: f32;
225 let r: f32;
226 let s: f32;
227 let mut ix: u32;
228
229 ix = x.to_bits();
230 ix &= 0x7fffffff;
231 if ix >= 0x41000000 {
232 p = &PR8;
233 q = &PS8;
234 } else if ix >= 0x409173eb {
235 p = &PR5;
236 q = &PS5;
237 } else if ix >= 0x4036d917 {
238 p = &PR3;
239 q = &PS3;
240 } else
241 /*ix >= 0x40000000*/
242 {
243 p = &PR2;
244 q = &PS2;
245 }
246 z = 1.0 / (x * x);
247 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
248 s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
249 return 1.0 + r / s;
250}
251
252/* For x >= 8, the asymptotic expansions of qone is
253 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
254 * We approximate pone by
255 * qone(x) = s*(0.375 + (R/S))
256 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
257 * S = 1 + qs1*s^2 + ... + qs6*s^12
258 * and
259 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
260 */
261
262const QR8: [f32; 6] = [
263 /* for x in [inf, 8]=1/[0,0.125] */
264 0.0000000000e+00, /* 0x00000000 */
265 -1.0253906250e-01, /* 0xbdd20000 */
266 -1.6271753311e+01, /* 0xc1822c8d */
267 -7.5960174561e+02, /* 0xc43de683 */
268 -1.1849806641e+04, /* 0xc639273a */
269 -4.8438511719e+04, /* 0xc73d3683 */
270];
271const QS8: [f32; 6] = [
272 1.6139537048e+02, /* 0x43216537 */
273 7.8253862305e+03, /* 0x45f48b17 */
274 1.3387534375e+05, /* 0x4802bcd6 */
275 7.1965775000e+05, /* 0x492fb29c */
276 6.6660125000e+05, /* 0x4922be94 */
277 -2.9449025000e+05, /* 0xc88fcb48 */
278];
279
280const QR5: [f32; 6] = [
281 /* for x in [8,4.5454]=1/[0.125,0.22001] */
282 -2.0897993405e-11, /* 0xadb7d219 */
283 -1.0253904760e-01, /* 0xbdd1fffe */
284 -8.0564479828e+00, /* 0xc100e736 */
285 -1.8366960144e+02, /* 0xc337ab6b */
286 -1.3731937256e+03, /* 0xc4aba633 */
287 -2.6124443359e+03, /* 0xc523471c */
288];
289const QS5: [f32; 6] = [
290 8.1276550293e+01, /* 0x42a28d98 */
291 1.9917987061e+03, /* 0x44f8f98f */
292 1.7468484375e+04, /* 0x468878f8 */
293 4.9851425781e+04, /* 0x4742bb6d */
294 2.7948074219e+04, /* 0x46da5826 */
295 -4.7191835938e+03, /* 0xc5937978 */
296];
297
298const QR3: [f32; 6] = [
299 -5.0783124372e-09, /* 0xb1ae7d4f */
300 -1.0253783315e-01, /* 0xbdd1ff5b */
301 -4.6101160049e+00, /* 0xc0938612 */
302 -5.7847221375e+01, /* 0xc267638e */
303 -2.2824453735e+02, /* 0xc3643e9a */
304 -2.1921012878e+02, /* 0xc35b35cb */
305];
306const QS3: [f32; 6] = [
307 4.7665153503e+01, /* 0x423ea91e */
308 6.7386511230e+02, /* 0x4428775e */
309 3.3801528320e+03, /* 0x45534272 */
310 5.5477290039e+03, /* 0x45ad5dd5 */
311 1.9031191406e+03, /* 0x44ede3d0 */
312 -1.3520118713e+02, /* 0xc3073381 */
313];
314
315const QR2: [f32; 6] = [
316 /* for x in [2.8570,2]=1/[0.3499,0.5] */
317 -1.7838172539e-07, /* 0xb43f8932 */
318 -1.0251704603e-01, /* 0xbdd1f475 */
319 -2.7522056103e+00, /* 0xc0302423 */
320 -1.9663616180e+01, /* 0xc19d4f16 */
321 -4.2325313568e+01, /* 0xc2294d1f */
322 -2.1371921539e+01, /* 0xc1aaf9b2 */
323];
324const QS2: [f32; 6] = [
325 2.9533363342e+01, /* 0x41ec4454 */
326 2.5298155212e+02, /* 0x437cfb47 */
327 7.5750280762e+02, /* 0x443d602e */
328 7.3939318848e+02, /* 0x4438d92a */
329 1.5594900513e+02, /* 0x431bf2f2 */
330 -4.9594988823e+00, /* 0xc09eb437 */
331];
332
333fn qonef(x: f32) -> f32 {
334 let p: &[f32; 6];
335 let q: &[f32; 6];
336 let s: f32;
337 let r: f32;
338 let z: f32;
339 let mut ix: u32;
340
341 ix = x.to_bits();
342 ix &= 0x7fffffff;
343 if ix >= 0x41000000 {
344 p = &QR8;
345 q = &QS8;
346 } else if ix >= 0x409173eb {
347 p = &QR5;
348 q = &QS5;
349 } else if ix >= 0x4036d917 {
350 p = &QR3;
351 q = &QS3;
352 } else
353 /*ix >= 0x40000000*/
354 {
355 p = &QR2;
356 q = &QS2;
357 }
358 z = 1.0 / (x * x);
359 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
360 s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
361 return (0.375 + r / s) / x;
362}
363
364// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
365#[cfg(not(target_arch = "powerpc64"))]
366#[cfg(test)]
367mod tests {
368 use super::{j1f, y1f};
369 #[test]
370 fn test_j1f_2488() {
371 // 0x401F3E49
372 assert_eq!(j1f(2.4881766_f32), 0.49999475_f32);
373 }
374 #[test]
375 fn test_y1f_2002() {
376 //allow slightly different result on x87
377 let res = y1f(2.0000002_f32);
378 if cfg!(all(target_arch = "x86", not(target_feature = "sse2"))) && (res == -0.10703231_f32)
379 {
380 return;
381 }
382 assert_eq!(res, -0.10703229_f32);
383 }
384}
385