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
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, 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] */
56const R02: f32 = 1.5625000000e-02; /* 0x3c800000 */
57const R03: f32 = -1.8997929874e-04; /* 0xb947352e */
58const R04: f32 = 1.8295404516e-06; /* 0x35f58e88 */
59const R05: f32 = -4.6183270541e-09; /* 0xb19eaf3c */
60const S01: f32 = 1.5619102865e-02; /* 0x3c7fe744 */
61const S02: f32 = 1.1692678527e-04; /* 0x38f53697 */
62const S03: f32 = 5.1354652442e-07; /* 0x3509daa6 */
63const S04: f32 = 1.1661400734e-09; /* 0x30a045e8 */
64
65/// Zeroth order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind (f32).
66#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
67pub fn j0f(mut x: f32) -> f32 {
68 let z: f32;
69 let r: f32;
70 let s: f32;
71 let mut ix: u32;
72
73 ix = x.to_bits();
74 ix &= 0x7fffffff;
75 if ix >= 0x7f800000 {
76 return 1.0 / (x * x);
77 }
78 x = fabsf(x);
79
80 if ix >= 0x40000000 {
81 /* |x| >= 2 */
82 /* large ulp error near zeros */
83 return common(ix, x, false);
84 }
85 if ix >= 0x3a000000 {
86 /* |x| >= 2**-11 */
87 /* up to 4ulp error near 2 */
88 z = x * x;
89 r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
90 s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
91 return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s);
92 }
93 if ix >= 0x21800000 {
94 /* |x| >= 2**-60 */
95 x = 0.25 * x * x;
96 }
97 return 1.0 - x;
98}
99
100const U00: f32 = -7.3804296553e-02; /* 0xbd9726b5 */
101const U01: f32 = 1.7666645348e-01; /* 0x3e34e80d */
102const U02: f32 = -1.3818567619e-02; /* 0xbc626746 */
103const U03: f32 = 3.4745343146e-04; /* 0x39b62a69 */
104const U04: f32 = -3.8140706238e-06; /* 0xb67ff53c */
105const U05: f32 = 1.9559013964e-08; /* 0x32a802ba */
106const U06: f32 = -3.9820518410e-11; /* 0xae2f21eb */
107const V01: f32 = 1.2730483897e-02; /* 0x3c509385 */
108const V02: f32 = 7.6006865129e-05; /* 0x389f65e0 */
109const V03: f32 = 2.5915085189e-07; /* 0x348b216c */
110const V04: f32 = 4.4111031494e-10; /* 0x2ff280c2 */
111
112/// Zeroth 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 y0f(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 /* large ulp error near zeros */
133 return common(ix, x, true);
134 }
135 if ix >= 0x39000000 {
136 /* x >= 2**-13 */
137 /* large ulp error at x ~= 0.89 */
138 z = x * x;
139 u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06)))));
140 v = 1.0 + z * (V01 + z * (V02 + z * (V03 + z * V04)));
141 return u / v + TPI * (j0f(x) * logf(x));
142 }
143 return U00 + TPI * logf(x);
144}
145
146/* The asymptotic expansions of pzero is
147 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
148 * For x >= 2, We approximate pzero by
149 * pzero(x) = 1 + (R/S)
150 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
151 * S = 1 + pS0*s^2 + ... + pS4*s^10
152 * and
153 * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
154 */
155const PR8: [f32; 6] = [
156 /* for x in [inf, 8]=1/[0,0.125] */
157 0.0000000000e+00, /* 0x00000000 */
158 -7.0312500000e-02, /* 0xbd900000 */
159 -8.0816707611e+00, /* 0xc1014e86 */
160 -2.5706311035e+02, /* 0xc3808814 */
161 -2.4852163086e+03, /* 0xc51b5376 */
162 -5.2530439453e+03, /* 0xc5a4285a */
163];
164const PS8: [f32; 5] = [
165 1.1653436279e+02, /* 0x42e91198 */
166 3.8337448730e+03, /* 0x456f9beb */
167 4.0597855469e+04, /* 0x471e95db */
168 1.1675296875e+05, /* 0x47e4087c */
169 4.7627726562e+04, /* 0x473a0bba */
170];
171const PR5: [f32; 6] = [
172 /* for x in [8,4.5454]=1/[0.125,0.22001] */
173 -1.1412546255e-11, /* 0xad48c58a */
174 -7.0312492549e-02, /* 0xbd8fffff */
175 -4.1596107483e+00, /* 0xc0851b88 */
176 -6.7674766541e+01, /* 0xc287597b */
177 -3.3123129272e+02, /* 0xc3a59d9b */
178 -3.4643338013e+02, /* 0xc3ad3779 */
179];
180const PS5: [f32; 5] = [
181 6.0753936768e+01, /* 0x42730408 */
182 1.0512523193e+03, /* 0x44836813 */
183 5.9789707031e+03, /* 0x45bad7c4 */
184 9.6254453125e+03, /* 0x461665c8 */
185 2.4060581055e+03, /* 0x451660ee */
186];
187
188const PR3: [f32; 6] = [
189 /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
190 -2.5470459075e-09, /* 0xb12f081b */
191 -7.0311963558e-02, /* 0xbd8fffb8 */
192 -2.4090321064e+00, /* 0xc01a2d95 */
193 -2.1965976715e+01, /* 0xc1afba52 */
194 -5.8079170227e+01, /* 0xc2685112 */
195 -3.1447946548e+01, /* 0xc1fb9565 */
196];
197const PS3: [f32; 5] = [
198 3.5856033325e+01, /* 0x420f6c94 */
199 3.6151397705e+02, /* 0x43b4c1ca */
200 1.1936077881e+03, /* 0x44953373 */
201 1.1279968262e+03, /* 0x448cffe6 */
202 1.7358093262e+02, /* 0x432d94b8 */
203];
204
205const PR2: [f32; 6] = [
206 /* for x in [2.8570,2]=1/[0.3499,0.5] */
207 -8.8753431271e-08, /* 0xb3be98b7 */
208 -7.0303097367e-02, /* 0xbd8ffb12 */
209 -1.4507384300e+00, /* 0xbfb9b1cc */
210 -7.6356959343e+00, /* 0xc0f4579f */
211 -1.1193166733e+01, /* 0xc1331736 */
212 -3.2336456776e+00, /* 0xc04ef40d */
213];
214const PS2: [f32; 5] = [
215 2.2220300674e+01, /* 0x41b1c32d */
216 1.3620678711e+02, /* 0x430834f0 */
217 2.7047027588e+02, /* 0x43873c32 */
218 1.5387539673e+02, /* 0x4319e01a */
219 1.4657617569e+01, /* 0x416a859a */
220];
221
222fn pzerof(x: f32) -> f32 {
223 let p: &[f32; 6];
224 let q: &[f32; 5];
225 let z: f32;
226 let r: f32;
227 let s: f32;
228 let mut ix: u32;
229
230 ix = x.to_bits();
231 ix &= 0x7fffffff;
232 if ix >= 0x41000000 {
233 p = &PR8;
234 q = &PS8;
235 } else if ix >= 0x409173eb {
236 p = &PR5;
237 q = &PS5;
238 } else if ix >= 0x4036d917 {
239 p = &PR3;
240 q = &PS3;
241 } else
242 /*ix >= 0x40000000*/
243 {
244 p = &PR2;
245 q = &PS2;
246 }
247 z = 1.0 / (x * x);
248 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
249 s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
250 return 1.0 + r / s;
251}
252
253/* For x >= 8, the asymptotic expansions of qzero is
254 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
255 * We approximate pzero by
256 * qzero(x) = s*(-1.25 + (R/S))
257 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
258 * S = 1 + qS0*s^2 + ... + qS5*s^12
259 * and
260 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
261 */
262const QR8: [f32; 6] = [
263 /* for x in [inf, 8]=1/[0,0.125] */
264 0.0000000000e+00, /* 0x00000000 */
265 7.3242187500e-02, /* 0x3d960000 */
266 1.1768206596e+01, /* 0x413c4a93 */
267 5.5767340088e+02, /* 0x440b6b19 */
268 8.8591972656e+03, /* 0x460a6cca */
269 3.7014625000e+04, /* 0x471096a0 */
270];
271const QS8: [f32; 6] = [
272 1.6377603149e+02, /* 0x4323c6aa */
273 8.0983447266e+03, /* 0x45fd12c2 */
274 1.4253829688e+05, /* 0x480b3293 */
275 8.0330925000e+05, /* 0x49441ed4 */
276 8.4050156250e+05, /* 0x494d3359 */
277 -3.4389928125e+05, /* 0xc8a7eb69 */
278];
279
280const QR5: [f32; 6] = [
281 /* for x in [8,4.5454]=1/[0.125,0.22001] */
282 1.8408595828e-11, /* 0x2da1ec79 */
283 7.3242180049e-02, /* 0x3d95ffff */
284 5.8356351852e+00, /* 0x40babd86 */
285 1.3511157227e+02, /* 0x43071c90 */
286 1.0272437744e+03, /* 0x448067cd */
287 1.9899779053e+03, /* 0x44f8bf4b */
288];
289const QS5: [f32; 6] = [
290 8.2776611328e+01, /* 0x42a58da0 */
291 2.0778142090e+03, /* 0x4501dd07 */
292 1.8847289062e+04, /* 0x46933e94 */
293 5.6751113281e+04, /* 0x475daf1d */
294 3.5976753906e+04, /* 0x470c88c1 */
295 -5.3543427734e+03, /* 0xc5a752be */
296];
297
298const QR3: [f32; 6] = [
299 /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
300 4.3774099900e-09, /* 0x3196681b */
301 7.3241114616e-02, /* 0x3d95ff70 */
302 3.3442313671e+00, /* 0x405607e3 */
303 4.2621845245e+01, /* 0x422a7cc5 */
304 1.7080809021e+02, /* 0x432acedf */
305 1.6673394775e+02, /* 0x4326bbe4 */
306];
307const QS3: [f32; 6] = [
308 4.8758872986e+01, /* 0x42430916 */
309 7.0968920898e+02, /* 0x44316c1c */
310 3.7041481934e+03, /* 0x4567825f */
311 6.4604252930e+03, /* 0x45c9e367 */
312 2.5163337402e+03, /* 0x451d4557 */
313 -1.4924745178e+02, /* 0xc3153f59 */
314];
315
316const QR2: [f32; 6] = [
317 /* 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];
325const QS2: [f32; 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
334fn qzerof(x: f32) -> f32 {
335 let p: &[f32; 6];
336 let q: &[f32; 6];
337 let s: f32;
338 let r: f32;
339 let z: f32;
340 let mut ix: u32;
341
342 ix = x.to_bits();
343 ix &= 0x7fffffff;
344 if ix >= 0x41000000 {
345 p = &QR8;
346 q = &QS8;
347 } else if ix >= 0x409173eb {
348 p = &QR5;
349 q = &QS5;
350 } else if ix >= 0x4036d917 {
351 p = &QR3;
352 q = &QS3;
353 } else
354 /*ix >= 0x40000000*/
355 {
356 p = &QR2;
357 q = &QS2;
358 }
359 z = 1.0 / (x * x);
360 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
361 s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
362 return (-0.125 + r / s) / x;
363}
364