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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
16use super::{floorf, k_cosf, k_sinf, logf};
17
18const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */
19const A0: f32 = 7.7215664089e-02; /* 0x3d9e233f */
20const A1: f32 = 3.2246702909e-01; /* 0x3ea51a66 */
21const A2: f32 = 6.7352302372e-02; /* 0x3d89f001 */
22const A3: f32 = 2.0580807701e-02; /* 0x3ca89915 */
23const A4: f32 = 7.3855509982e-03; /* 0x3bf2027e */
24const A5: f32 = 2.8905137442e-03; /* 0x3b3d6ec6 */
25const A6: f32 = 1.1927076848e-03; /* 0x3a9c54a1 */
26const A7: f32 = 5.1006977446e-04; /* 0x3a05b634 */
27const A8: f32 = 2.2086278477e-04; /* 0x39679767 */
28const A9: f32 = 1.0801156895e-04; /* 0x38e28445 */
29const A10: f32 = 2.5214456400e-05; /* 0x37d383a2 */
30const A11: f32 = 4.4864096708e-05; /* 0x383c2c75 */
31const TC: f32 = 1.4616321325e+00; /* 0x3fbb16c3 */
32const TF: f32 = -1.2148628384e-01; /* 0xbdf8cdcd */
33/* TT = -(tail of TF) */
34const TT: f32 = 6.6971006518e-09; /* 0x31e61c52 */
35const T0: f32 = 4.8383611441e-01; /* 0x3ef7b95e */
36const T1: f32 = -1.4758771658e-01; /* 0xbe17213c */
37const T2: f32 = 6.4624942839e-02; /* 0x3d845a15 */
38const T3: f32 = -3.2788541168e-02; /* 0xbd064d47 */
39const T4: f32 = 1.7970675603e-02; /* 0x3c93373d */
40const T5: f32 = -1.0314224288e-02; /* 0xbc28fcfe */
41const T6: f32 = 6.1005386524e-03; /* 0x3bc7e707 */
42const T7: f32 = -3.6845202558e-03; /* 0xbb7177fe */
43const T8: f32 = 2.2596477065e-03; /* 0x3b141699 */
44const T9: f32 = -1.4034647029e-03; /* 0xbab7f476 */
45const T10: f32 = 8.8108185446e-04; /* 0x3a66f867 */
46const T11: f32 = -5.3859531181e-04; /* 0xba0d3085 */
47const T12: f32 = 3.1563205994e-04; /* 0x39a57b6b */
48const T13: f32 = -3.1275415677e-04; /* 0xb9a3f927 */
49const T14: f32 = 3.3552918467e-04; /* 0x39afe9f7 */
50const U0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
51const U1: f32 = 6.3282704353e-01; /* 0x3f2200f4 */
52const U2: f32 = 1.4549225569e+00; /* 0x3fba3ae7 */
53const U3: f32 = 9.7771751881e-01; /* 0x3f7a4bb2 */
54const U4: f32 = 2.2896373272e-01; /* 0x3e6a7578 */
55const U5: f32 = 1.3381091878e-02; /* 0x3c5b3c5e */
56const V1: f32 = 2.4559779167e+00; /* 0x401d2ebe */
57const V2: f32 = 2.1284897327e+00; /* 0x4008392d */
58const V3: f32 = 7.6928514242e-01; /* 0x3f44efdf */
59const V4: f32 = 1.0422264785e-01; /* 0x3dd572af */
60const V5: f32 = 3.2170924824e-03; /* 0x3b52d5db */
61const S0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
62const S1: f32 = 2.1498242021e-01; /* 0x3e5c245a */
63const S2: f32 = 3.2577878237e-01; /* 0x3ea6cc7a */
64const S3: f32 = 1.4635047317e-01; /* 0x3e15dce6 */
65const S4: f32 = 2.6642270386e-02; /* 0x3cda40e4 */
66const S5: f32 = 1.8402845599e-03; /* 0x3af135b4 */
67const S6: f32 = 3.1947532989e-05; /* 0x3805ff67 */
68const R1: f32 = 1.3920053244e+00; /* 0x3fb22d3b */
69const R2: f32 = 7.2193557024e-01; /* 0x3f38d0c5 */
70const R3: f32 = 1.7193385959e-01; /* 0x3e300f6e */
71const R4: f32 = 1.8645919859e-02; /* 0x3c98bf54 */
72const R5: f32 = 7.7794247773e-04; /* 0x3a4beed6 */
73const R6: f32 = 7.3266842264e-06; /* 0x36f5d7bd */
74const W0: f32 = 4.1893854737e-01; /* 0x3ed67f1d */
75const W1: f32 = 8.3333335817e-02; /* 0x3daaaaab */
76const W2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
77const W3: f32 = 7.9365057172e-04; /* 0x3a500cfd */
78const W4: f32 = -5.9518753551e-04; /* 0xba1c065c */
79const W5: f32 = 8.3633989561e-04; /* 0x3a5b3dd2 */
80const W6: f32 = -1.6309292987e-03; /* 0xbad5c4e8 */
81
82/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
83fn 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
102pub 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
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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}