]>
Commit | Line | Data |
---|---|---|
dc9dc135 XL |
1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.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::{floorf, k_cosf, k_sinf, logf}; | |
17 | ||
18 | const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */ | |
19 | const A0: f32 = 7.7215664089e-02; /* 0x3d9e233f */ | |
20 | const A1: f32 = 3.2246702909e-01; /* 0x3ea51a66 */ | |
21 | const A2: f32 = 6.7352302372e-02; /* 0x3d89f001 */ | |
22 | const A3: f32 = 2.0580807701e-02; /* 0x3ca89915 */ | |
23 | const A4: f32 = 7.3855509982e-03; /* 0x3bf2027e */ | |
24 | const A5: f32 = 2.8905137442e-03; /* 0x3b3d6ec6 */ | |
25 | const A6: f32 = 1.1927076848e-03; /* 0x3a9c54a1 */ | |
26 | const A7: f32 = 5.1006977446e-04; /* 0x3a05b634 */ | |
27 | const A8: f32 = 2.2086278477e-04; /* 0x39679767 */ | |
28 | const A9: f32 = 1.0801156895e-04; /* 0x38e28445 */ | |
29 | const A10: f32 = 2.5214456400e-05; /* 0x37d383a2 */ | |
30 | const A11: f32 = 4.4864096708e-05; /* 0x383c2c75 */ | |
31 | const TC: f32 = 1.4616321325e+00; /* 0x3fbb16c3 */ | |
32 | const TF: f32 = -1.2148628384e-01; /* 0xbdf8cdcd */ | |
33 | /* TT = -(tail of TF) */ | |
34 | const TT: f32 = 6.6971006518e-09; /* 0x31e61c52 */ | |
35 | const T0: f32 = 4.8383611441e-01; /* 0x3ef7b95e */ | |
36 | const T1: f32 = -1.4758771658e-01; /* 0xbe17213c */ | |
37 | const T2: f32 = 6.4624942839e-02; /* 0x3d845a15 */ | |
38 | const T3: f32 = -3.2788541168e-02; /* 0xbd064d47 */ | |
39 | const T4: f32 = 1.7970675603e-02; /* 0x3c93373d */ | |
40 | const T5: f32 = -1.0314224288e-02; /* 0xbc28fcfe */ | |
41 | const T6: f32 = 6.1005386524e-03; /* 0x3bc7e707 */ | |
42 | const T7: f32 = -3.6845202558e-03; /* 0xbb7177fe */ | |
43 | const T8: f32 = 2.2596477065e-03; /* 0x3b141699 */ | |
44 | const T9: f32 = -1.4034647029e-03; /* 0xbab7f476 */ | |
45 | const T10: f32 = 8.8108185446e-04; /* 0x3a66f867 */ | |
46 | const T11: f32 = -5.3859531181e-04; /* 0xba0d3085 */ | |
47 | const T12: f32 = 3.1563205994e-04; /* 0x39a57b6b */ | |
48 | const T13: f32 = -3.1275415677e-04; /* 0xb9a3f927 */ | |
49 | const T14: f32 = 3.3552918467e-04; /* 0x39afe9f7 */ | |
50 | const U0: f32 = -7.7215664089e-02; /* 0xbd9e233f */ | |
51 | const U1: f32 = 6.3282704353e-01; /* 0x3f2200f4 */ | |
52 | const U2: f32 = 1.4549225569e+00; /* 0x3fba3ae7 */ | |
53 | const U3: f32 = 9.7771751881e-01; /* 0x3f7a4bb2 */ | |
54 | const U4: f32 = 2.2896373272e-01; /* 0x3e6a7578 */ | |
55 | const U5: f32 = 1.3381091878e-02; /* 0x3c5b3c5e */ | |
56 | const V1: f32 = 2.4559779167e+00; /* 0x401d2ebe */ | |
57 | const V2: f32 = 2.1284897327e+00; /* 0x4008392d */ | |
58 | const V3: f32 = 7.6928514242e-01; /* 0x3f44efdf */ | |
59 | const V4: f32 = 1.0422264785e-01; /* 0x3dd572af */ | |
60 | const V5: f32 = 3.2170924824e-03; /* 0x3b52d5db */ | |
61 | const S0: f32 = -7.7215664089e-02; /* 0xbd9e233f */ | |
62 | const S1: f32 = 2.1498242021e-01; /* 0x3e5c245a */ | |
63 | const S2: f32 = 3.2577878237e-01; /* 0x3ea6cc7a */ | |
64 | const S3: f32 = 1.4635047317e-01; /* 0x3e15dce6 */ | |
65 | const S4: f32 = 2.6642270386e-02; /* 0x3cda40e4 */ | |
66 | const S5: f32 = 1.8402845599e-03; /* 0x3af135b4 */ | |
67 | const S6: f32 = 3.1947532989e-05; /* 0x3805ff67 */ | |
68 | const R1: f32 = 1.3920053244e+00; /* 0x3fb22d3b */ | |
69 | const R2: f32 = 7.2193557024e-01; /* 0x3f38d0c5 */ | |
70 | const R3: f32 = 1.7193385959e-01; /* 0x3e300f6e */ | |
71 | const R4: f32 = 1.8645919859e-02; /* 0x3c98bf54 */ | |
72 | const R5: f32 = 7.7794247773e-04; /* 0x3a4beed6 */ | |
73 | const R6: f32 = 7.3266842264e-06; /* 0x36f5d7bd */ | |
74 | const W0: f32 = 4.1893854737e-01; /* 0x3ed67f1d */ | |
75 | const W1: f32 = 8.3333335817e-02; /* 0x3daaaaab */ | |
76 | const W2: f32 = -2.7777778450e-03; /* 0xbb360b61 */ | |
77 | const W3: f32 = 7.9365057172e-04; /* 0x3a500cfd */ | |
78 | const W4: f32 = -5.9518753551e-04; /* 0xba1c065c */ | |
79 | const W5: f32 = 8.3633989561e-04; /* 0x3a5b3dd2 */ | |
80 | const W6: f32 = -1.6309292987e-03; /* 0xbad5c4e8 */ | |
81 | ||
82 | /* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */ | |
83 | fn sin_pi(mut x: f32) -> f32 { | |
84 | let mut y: f64; | |
85 | let mut n: isize; | |
86 | ||
87 | /* spurious inexact if odd int */ | |
88 | x = 2.0 * (x * 0.5 - floorf(x * 0.5)); /* x mod 2.0 */ | |
89 | ||
90 | n = (x * 4.0) as isize; | |
91 | n = (n + 1) / 2; | |
92 | y = (x as f64) - (n as f64) * 0.5; | |
93 | y *= 3.14159265358979323846; | |
94 | match n { | |
95 | 1 => k_cosf(y), | |
96 | 2 => k_sinf(-y), | |
97 | 3 => -k_cosf(y), | |
98 | 0 | _ => k_sinf(y), | |
99 | } | |
100 | } | |
101 | ||
102 | pub fn lgammaf_r(mut x: f32) -> (f32, i32) { | |
103 | let u = x.to_bits(); | |
104 | let mut t: f32; | |
105 | let y: f32; | |
106 | let mut z: f32; | |
107 | let nadj: f32; | |
108 | let p: f32; | |
109 | let p1: f32; | |
110 | let p2: f32; | |
111 | let p3: f32; | |
112 | let q: f32; | |
113 | let mut r: f32; | |
114 | let w: f32; | |
115 | let ix: u32; | |
116 | let i: i32; | |
117 | let sign: bool; | |
118 | let mut signgam: i32; | |
119 | ||
120 | /* purge off +-inf, NaN, +-0, tiny and negative arguments */ | |
121 | signgam = 1; | |
122 | sign = (u >> 31) != 0; | |
123 | ix = u & 0x7fffffff; | |
124 | if ix >= 0x7f800000 { | |
125 | return (x * x, signgam); | |
126 | } | |
127 | if ix < 0x35000000 { | |
128 | /* |x| < 2**-21, return -log(|x|) */ | |
129 | if sign { | |
130 | signgam = -1; | |
131 | x = -x; | |
132 | } | |
133 | return (-logf(x), signgam); | |
134 | } | |
135 | if sign { | |
136 | x = -x; | |
137 | t = sin_pi(x); | |
138 | if t == 0.0 { | |
139 | /* -integer */ | |
140 | return (1.0 / (x - x), signgam); | |
141 | } | |
142 | if t > 0.0 { | |
143 | signgam = -1; | |
144 | } else { | |
145 | t = -t; | |
146 | } | |
147 | nadj = logf(PI / (t * x)); | |
148 | } else { | |
149 | nadj = 0.0; | |
150 | } | |
151 | ||
152 | /* purge off 1 and 2 */ | |
153 | if ix == 0x3f800000 || ix == 0x40000000 { | |
154 | r = 0.0; | |
155 | } | |
156 | /* for x < 2.0 */ | |
157 | else if ix < 0x40000000 { | |
158 | if ix <= 0x3f666666 { | |
159 | /* lgamma(x) = lgamma(x+1)-log(x) */ | |
160 | r = -logf(x); | |
161 | if ix >= 0x3f3b4a20 { | |
162 | y = 1.0 - x; | |
163 | i = 0; | |
164 | } else if ix >= 0x3e6d3308 { | |
165 | y = x - (TC - 1.0); | |
166 | i = 1; | |
167 | } else { | |
168 | y = x; | |
169 | i = 2; | |
170 | } | |
171 | } else { | |
172 | r = 0.0; | |
173 | if ix >= 0x3fdda618 { | |
174 | /* [1.7316,2] */ | |
175 | y = 2.0 - x; | |
176 | i = 0; | |
177 | } else if ix >= 0x3F9da620 { | |
178 | /* [1.23,1.73] */ | |
179 | y = x - TC; | |
180 | i = 1; | |
181 | } else { | |
182 | y = x - 1.0; | |
183 | i = 2; | |
184 | } | |
185 | } | |
186 | match i { | |
187 | 0 => { | |
188 | z = y * y; | |
189 | p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10)))); | |
190 | p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11))))); | |
191 | p = y * p1 + p2; | |
192 | r += p - 0.5 * y; | |
193 | } | |
194 | 1 => { | |
195 | z = y * y; | |
196 | w = z * y; | |
197 | p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */ | |
198 | p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13))); | |
199 | p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14))); | |
200 | p = z * p1 - (TT - w * (p2 + y * p3)); | |
201 | r += TF + p; | |
202 | } | |
203 | 2 => { | |
204 | p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5))))); | |
205 | p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5)))); | |
206 | r += -0.5 * y + p1 / p2; | |
207 | } | |
60c5eb7d | 208 | #[cfg(debug_assertions)] |
dc9dc135 | 209 | _ => unreachable!(), |
60c5eb7d | 210 | #[cfg(not(debug_assertions))] |
dc9dc135 XL |
211 | _ => {} |
212 | } | |
213 | } else if ix < 0x41000000 { | |
214 | /* x < 8.0 */ | |
215 | i = x as i32; | |
216 | y = x - (i as f32); | |
217 | p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6)))))); | |
218 | q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6))))); | |
219 | r = 0.5 * y + p / q; | |
220 | z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */ | |
221 | // TODO: In C, this was implemented using switch jumps with fallthrough. | |
222 | // Does this implementation have performance problems? | |
223 | if i >= 7 { | |
224 | z *= y + 6.0; | |
225 | } | |
226 | if i >= 6 { | |
227 | z *= y + 5.0; | |
228 | } | |
229 | if i >= 5 { | |
230 | z *= y + 4.0; | |
231 | } | |
232 | if i >= 4 { | |
233 | z *= y + 3.0; | |
234 | } | |
235 | if i >= 3 { | |
236 | z *= y + 2.0; | |
237 | r += logf(z); | |
238 | } | |
239 | } else if ix < 0x5c800000 { | |
240 | /* 8.0 <= x < 2**58 */ | |
241 | t = logf(x); | |
242 | z = 1.0 / x; | |
243 | y = z * z; | |
244 | w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6))))); | |
245 | r = (x - 0.5) * (t - 1.0) + w; | |
246 | } else { | |
247 | /* 2**58 <= x <= inf */ | |
248 | r = x * (logf(x) - 1.0); | |
249 | } | |
250 | if sign { | |
251 | r = nadj - r; | |
252 | } | |
253 | return (r, signgam); | |
254 | } |