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
common(ix: u32, x: f32, y1: bool, sign: bool) -> f3221 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 /// First order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind (f32).
j1f(x: f32) -> f3267 pub fn j1f(x: f32) -> f32 {
68 let mut z: f32;
69 let r: f32;
70 let s: f32;
71 let mut ix: u32;
72 let sign: bool;
73
74 ix = x.to_bits();
75 sign = (ix >> 31) != 0;
76 ix &= 0x7fffffff;
77 if ix >= 0x7f800000 {
78 return 1.0 / (x * x);
79 }
80 if ix >= 0x40000000 {
81 /* |x| >= 2 */
82 return common(ix, fabsf(x), false, sign);
83 }
84 if ix >= 0x39000000 {
85 /* |x| >= 2**-13 */
86 z = x * x;
87 r = z * (R00 + z * (R01 + z * (R02 + z * R03)));
88 s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05))));
89 z = 0.5 + r / s;
90 } else {
91 z = 0.5;
92 }
93 return z * x;
94 }
95
96 const U0: [f32; 5] = [
97 -1.9605709612e-01, /* 0xbe48c331 */
98 5.0443872809e-02, /* 0x3d4e9e3c */
99 -1.9125689287e-03, /* 0xbafaaf2a */
100 2.3525259166e-05, /* 0x37c5581c */
101 -9.1909917899e-08, /* 0xb3c56003 */
102 ];
103 const V0: [f32; 5] = [
104 1.9916731864e-02, /* 0x3ca3286a */
105 2.0255257550e-04, /* 0x3954644b */
106 1.3560879779e-06, /* 0x35b602d4 */
107 6.2274145840e-09, /* 0x31d5f8eb */
108 1.6655924903e-11, /* 0x2d9281cf */
109 ];
110
111 /// First order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind (f32).
y1f(x: f32) -> f32112 pub fn y1f(x: f32) -> f32 {
113 let z: f32;
114 let u: f32;
115 let v: f32;
116 let ix: u32;
117
118 ix = x.to_bits();
119 if (ix & 0x7fffffff) == 0 {
120 return -1.0 / 0.0;
121 }
122 if (ix >> 31) != 0 {
123 return 0.0 / 0.0;
124 }
125 if ix >= 0x7f800000 {
126 return 1.0 / x;
127 }
128 if ix >= 0x40000000 {
129 /* |x| >= 2.0 */
130 return common(ix, x, true, false);
131 }
132 if ix < 0x33000000 {
133 /* x < 2**-25 */
134 return -TPI / x;
135 }
136 z = x * x;
137 u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4])));
138 v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4]))));
139 return x * (u / v) + TPI * (j1f(x) * logf(x) - 1.0 / x);
140 }
141
142 /* For x >= 8, the asymptotic expansions of pone is
143 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
144 * We approximate pone by
145 * pone(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 * | pone(x)-1-R/S | <= 2 ** ( -60.06)
150 */
151
152 const PR8: [f32; 6] = [
153 /* for x in [inf, 8]=1/[0,0.125] */
154 0.0000000000e+00, /* 0x00000000 */
155 1.1718750000e-01, /* 0x3df00000 */
156 1.3239480972e+01, /* 0x4153d4ea */
157 4.1205184937e+02, /* 0x43ce06a3 */
158 3.8747453613e+03, /* 0x45722bed */
159 7.9144794922e+03, /* 0x45f753d6 */
160 ];
161 const PS8: [f32; 5] = [
162 1.1420736694e+02, /* 0x42e46a2c */
163 3.6509309082e+03, /* 0x45642ee5 */
164 3.6956207031e+04, /* 0x47105c35 */
165 9.7602796875e+04, /* 0x47bea166 */
166 3.0804271484e+04, /* 0x46f0a88b */
167 ];
168
169 const PR5: [f32; 6] = [
170 /* for x in [8,4.5454]=1/[0.125,0.22001] */
171 1.3199052094e-11, /* 0x2d68333f */
172 1.1718749255e-01, /* 0x3defffff */
173 6.8027510643e+00, /* 0x40d9b023 */
174 1.0830818176e+02, /* 0x42d89dca */
175 5.1763616943e+02, /* 0x440168b7 */
176 5.2871520996e+02, /* 0x44042dc6 */
177 ];
178 const PS5: [f32; 5] = [
179 5.9280597687e+01, /* 0x426d1f55 */
180 9.9140142822e+02, /* 0x4477d9b1 */
181 5.3532670898e+03, /* 0x45a74a23 */
182 7.8446904297e+03, /* 0x45f52586 */
183 1.5040468750e+03, /* 0x44bc0180 */
184 ];
185
186 const PR3: [f32; 6] = [
187 3.0250391081e-09, /* 0x314fe10d */
188 1.1718686670e-01, /* 0x3defffab */
189 3.9329774380e+00, /* 0x407bb5e7 */
190 3.5119403839e+01, /* 0x420c7a45 */
191 9.1055007935e+01, /* 0x42b61c2a */
192 4.8559066772e+01, /* 0x42423c7c */
193 ];
194 const PS3: [f32; 5] = [
195 3.4791309357e+01, /* 0x420b2a4d */
196 3.3676245117e+02, /* 0x43a86198 */
197 1.0468714600e+03, /* 0x4482dbe3 */
198 8.9081134033e+02, /* 0x445eb3ed */
199 1.0378793335e+02, /* 0x42cf936c */
200 ];
201
202 const PR2: [f32; 6] = [
203 /* for x in [2.8570,2]=1/[0.3499,0.5] */
204 1.0771083225e-07, /* 0x33e74ea8 */
205 1.1717621982e-01, /* 0x3deffa16 */
206 2.3685150146e+00, /* 0x401795c0 */
207 1.2242610931e+01, /* 0x4143e1bc */
208 1.7693971634e+01, /* 0x418d8d41 */
209 5.0735230446e+00, /* 0x40a25a4d */
210 ];
211 const PS2: [f32; 5] = [
212 2.1436485291e+01, /* 0x41ab7dec */
213 1.2529022980e+02, /* 0x42fa9499 */
214 2.3227647400e+02, /* 0x436846c7 */
215 1.1767937469e+02, /* 0x42eb5bd7 */
216 8.3646392822e+00, /* 0x4105d590 */
217 ];
218
ponef(x: f32) -> f32219 fn ponef(x: f32) -> f32 {
220 let p: &[f32; 6];
221 let q: &[f32; 5];
222 let z: f32;
223 let r: f32;
224 let s: f32;
225 let mut ix: u32;
226
227 ix = x.to_bits();
228 ix &= 0x7fffffff;
229 if ix >= 0x41000000 {
230 p = &PR8;
231 q = &PS8;
232 } else if ix >= 0x409173eb {
233 p = &PR5;
234 q = &PS5;
235 } else if ix >= 0x4036d917 {
236 p = &PR3;
237 q = &PS3;
238 } else
239 /*ix >= 0x40000000*/
240 {
241 p = &PR2;
242 q = &PS2;
243 }
244 z = 1.0 / (x * x);
245 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
246 s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
247 return 1.0 + r / s;
248 }
249
250 /* For x >= 8, the asymptotic expansions of qone is
251 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
252 * We approximate pone by
253 * qone(x) = s*(0.375 + (R/S))
254 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
255 * S = 1 + qs1*s^2 + ... + qs6*s^12
256 * and
257 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
258 */
259
260 const QR8: [f32; 6] = [
261 /* for x in [inf, 8]=1/[0,0.125] */
262 0.0000000000e+00, /* 0x00000000 */
263 -1.0253906250e-01, /* 0xbdd20000 */
264 -1.6271753311e+01, /* 0xc1822c8d */
265 -7.5960174561e+02, /* 0xc43de683 */
266 -1.1849806641e+04, /* 0xc639273a */
267 -4.8438511719e+04, /* 0xc73d3683 */
268 ];
269 const QS8: [f32; 6] = [
270 1.6139537048e+02, /* 0x43216537 */
271 7.8253862305e+03, /* 0x45f48b17 */
272 1.3387534375e+05, /* 0x4802bcd6 */
273 7.1965775000e+05, /* 0x492fb29c */
274 6.6660125000e+05, /* 0x4922be94 */
275 -2.9449025000e+05, /* 0xc88fcb48 */
276 ];
277
278 const QR5: [f32; 6] = [
279 /* for x in [8,4.5454]=1/[0.125,0.22001] */
280 -2.0897993405e-11, /* 0xadb7d219 */
281 -1.0253904760e-01, /* 0xbdd1fffe */
282 -8.0564479828e+00, /* 0xc100e736 */
283 -1.8366960144e+02, /* 0xc337ab6b */
284 -1.3731937256e+03, /* 0xc4aba633 */
285 -2.6124443359e+03, /* 0xc523471c */
286 ];
287 const QS5: [f32; 6] = [
288 8.1276550293e+01, /* 0x42a28d98 */
289 1.9917987061e+03, /* 0x44f8f98f */
290 1.7468484375e+04, /* 0x468878f8 */
291 4.9851425781e+04, /* 0x4742bb6d */
292 2.7948074219e+04, /* 0x46da5826 */
293 -4.7191835938e+03, /* 0xc5937978 */
294 ];
295
296 const QR3: [f32; 6] = [
297 -5.0783124372e-09, /* 0xb1ae7d4f */
298 -1.0253783315e-01, /* 0xbdd1ff5b */
299 -4.6101160049e+00, /* 0xc0938612 */
300 -5.7847221375e+01, /* 0xc267638e */
301 -2.2824453735e+02, /* 0xc3643e9a */
302 -2.1921012878e+02, /* 0xc35b35cb */
303 ];
304 const QS3: [f32; 6] = [
305 4.7665153503e+01, /* 0x423ea91e */
306 6.7386511230e+02, /* 0x4428775e */
307 3.3801528320e+03, /* 0x45534272 */
308 5.5477290039e+03, /* 0x45ad5dd5 */
309 1.9031191406e+03, /* 0x44ede3d0 */
310 -1.3520118713e+02, /* 0xc3073381 */
311 ];
312
313 const QR2: [f32; 6] = [
314 /* for x in [2.8570,2]=1/[0.3499,0.5] */
315 -1.7838172539e-07, /* 0xb43f8932 */
316 -1.0251704603e-01, /* 0xbdd1f475 */
317 -2.7522056103e+00, /* 0xc0302423 */
318 -1.9663616180e+01, /* 0xc19d4f16 */
319 -4.2325313568e+01, /* 0xc2294d1f */
320 -2.1371921539e+01, /* 0xc1aaf9b2 */
321 ];
322 const QS2: [f32; 6] = [
323 2.9533363342e+01, /* 0x41ec4454 */
324 2.5298155212e+02, /* 0x437cfb47 */
325 7.5750280762e+02, /* 0x443d602e */
326 7.3939318848e+02, /* 0x4438d92a */
327 1.5594900513e+02, /* 0x431bf2f2 */
328 -4.9594988823e+00, /* 0xc09eb437 */
329 ];
330
qonef(x: f32) -> f32331 fn qonef(x: f32) -> f32 {
332 let p: &[f32; 6];
333 let q: &[f32; 6];
334 let s: f32;
335 let r: f32;
336 let z: f32;
337 let mut ix: u32;
338
339 ix = x.to_bits();
340 ix &= 0x7fffffff;
341 if ix >= 0x41000000 {
342 p = &QR8;
343 q = &QS8;
344 } else if ix >= 0x409173eb {
345 p = &QR5;
346 q = &QS5;
347 } else if ix >= 0x4036d917 {
348 p = &QR3;
349 q = &QS3;
350 } else
351 /*ix >= 0x40000000*/
352 {
353 p = &QR2;
354 q = &QS2;
355 }
356 z = 1.0 / (x * x);
357 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
358 s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
359 return (0.375 + r / s) / x;
360 }
361
362 // PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
363 #[cfg(not(target_arch = "powerpc64"))]
364 #[cfg(test)]
365 mod tests {
366 use super::{j1f, y1f};
367 #[test]
test_j1f_2488()368 fn test_j1f_2488() {
369 // 0x401F3E49
370 assert_eq!(j1f(2.4881766_f32), 0.49999475_f32);
371 }
372 #[test]
test_y1f_2002()373 fn test_y1f_2002() {
374 //allow slightly different result on x87
375 let res = y1f(2.0000002_f32);
376 if cfg!(all(target_arch = "x86", not(target_feature = "sse2"))) && (res == -0.10703231_f32)
377 {
378 return;
379 }
380 assert_eq!(res, -0.10703229_f32);
381 }
382 }
383