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#include "libm.h"
17
18static const float
19pi = 3.1415927410e+00, /* 0x40490fdb */
20a0 = 7.7215664089e-02, /* 0x3d9e233f */
21a1 = 3.2246702909e-01, /* 0x3ea51a66 */
22a2 = 6.7352302372e-02, /* 0x3d89f001 */
23a3 = 2.0580807701e-02, /* 0x3ca89915 */
24a4 = 7.3855509982e-03, /* 0x3bf2027e */
25a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
26a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
27a7 = 5.1006977446e-04, /* 0x3a05b634 */
28a8 = 2.2086278477e-04, /* 0x39679767 */
29a9 = 1.0801156895e-04, /* 0x38e28445 */
30a10 = 2.5214456400e-05, /* 0x37d383a2 */
31a11 = 4.4864096708e-05, /* 0x383c2c75 */
32tc = 1.4616321325e+00, /* 0x3fbb16c3 */
33tf = -1.2148628384e-01, /* 0xbdf8cdcd */
34/* tt = -(tail of tf) */
35tt = 6.6971006518e-09, /* 0x31e61c52 */
36t0 = 4.8383611441e-01, /* 0x3ef7b95e */
37t1 = -1.4758771658e-01, /* 0xbe17213c */
38t2 = 6.4624942839e-02, /* 0x3d845a15 */
39t3 = -3.2788541168e-02, /* 0xbd064d47 */
40t4 = 1.7970675603e-02, /* 0x3c93373d */
41t5 = -1.0314224288e-02, /* 0xbc28fcfe */
42t6 = 6.1005386524e-03, /* 0x3bc7e707 */
43t7 = -3.6845202558e-03, /* 0xbb7177fe */
44t8 = 2.2596477065e-03, /* 0x3b141699 */
45t9 = -1.4034647029e-03, /* 0xbab7f476 */
46t10 = 8.8108185446e-04, /* 0x3a66f867 */
47t11 = -5.3859531181e-04, /* 0xba0d3085 */
48t12 = 3.1563205994e-04, /* 0x39a57b6b */
49t13 = -3.1275415677e-04, /* 0xb9a3f927 */
50t14 = 3.3552918467e-04, /* 0x39afe9f7 */
51u0 = -7.7215664089e-02, /* 0xbd9e233f */
52u1 = 6.3282704353e-01, /* 0x3f2200f4 */
53u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
54u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
55u4 = 2.2896373272e-01, /* 0x3e6a7578 */
56u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
57v1 = 2.4559779167e+00, /* 0x401d2ebe */
58v2 = 2.1284897327e+00, /* 0x4008392d */
59v3 = 7.6928514242e-01, /* 0x3f44efdf */
60v4 = 1.0422264785e-01, /* 0x3dd572af */
61v5 = 3.2170924824e-03, /* 0x3b52d5db */
62s0 = -7.7215664089e-02, /* 0xbd9e233f */
63s1 = 2.1498242021e-01, /* 0x3e5c245a */
64s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
65s3 = 1.4635047317e-01, /* 0x3e15dce6 */
66s4 = 2.6642270386e-02, /* 0x3cda40e4 */
67s5 = 1.8402845599e-03, /* 0x3af135b4 */
68s6 = 3.1947532989e-05, /* 0x3805ff67 */
69r1 = 1.3920053244e+00, /* 0x3fb22d3b */
70r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
71r3 = 1.7193385959e-01, /* 0x3e300f6e */
72r4 = 1.8645919859e-02, /* 0x3c98bf54 */
73r5 = 7.7794247773e-04, /* 0x3a4beed6 */
74r6 = 7.3266842264e-06, /* 0x36f5d7bd */
75w0 = 4.1893854737e-01, /* 0x3ed67f1d */
76w1 = 8.3333335817e-02, /* 0x3daaaaab */
77w2 = -2.7777778450e-03, /* 0xbb360b61 */
78w3 = 7.9365057172e-04, /* 0x3a500cfd */
79w4 = -5.9518753551e-04, /* 0xba1c065c */
80w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
81w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
82
83/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
84static float sin_pi(float x)
85{
86 double_t y;
87 int n;
88
89 /* spurious inexact if odd int */
90 x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */
91
92 n = (int)(x*4);
93 n = (n+1)/2;
94 y = x - n*0.5f;
95 y *= 3.14159265358979323846;
96 switch (n) {
97 default: /* case 4: */
98 case 0: return __sindf(y);
99 case 1: return __cosdf(y);
100 case 2: return __sindf(-y);
101 case 3: return -__cosdf(y);
102 }
103}
104
105float __lgammaf_r(float x, int *signgamp)
106{
107 union {float f; uint32_t i;} u = {x};
108 float t,y,z,nadj,p,p1,p2,p3,q,r,w;
109 uint32_t ix;
110 int i,sign;
111
112 /* purge off +-inf, NaN, +-0, tiny and negative arguments */
113 *signgamp = 1;
114 sign = u.i>>31;
115 ix = u.i & 0x7fffffff;
116 if (ix >= 0x7f800000)
117 return x*x;
118 if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
119 if (sign) {
120 *signgamp = -1;
121 x = -x;
122 }
123 return -logf(x);
124 }
125 if (sign) {
126 x = -x;
127 t = sin_pi(x);
128 if (t == 0.0f) /* -integer */
129 return 1.0f/(x-x);
130 if (t > 0.0f)
131 *signgamp = -1;
132 else
133 t = -t;
134 nadj = logf(pi/(t*x));
135 }
136
137 /* purge off 1 and 2 */
138 if (ix == 0x3f800000 || ix == 0x40000000)
139 r = 0;
140 /* for x < 2.0 */
141 else if (ix < 0x40000000) {
142 if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
143 r = -logf(x);
144 if (ix >= 0x3f3b4a20) {
145 y = 1.0f - x;
146 i = 0;
147 } else if (ix >= 0x3e6d3308) {
148 y = x - (tc-1.0f);
149 i = 1;
150 } else {
151 y = x;
152 i = 2;
153 }
154 } else {
155 r = 0.0f;
156 if (ix >= 0x3fdda618) { /* [1.7316,2] */
157 y = 2.0f - x;
158 i = 0;
159 } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
160 y = x - tc;
161 i = 1;
162 } else {
163 y = x - 1.0f;
164 i = 2;
165 }
166 }
167 switch(i) {
168 case 0:
169 z = y*y;
170 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
171 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
172 p = y*p1+p2;
173 r += p - 0.5f*y;
174 break;
175 case 1:
176 z = y*y;
177 w = z*y;
178 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
179 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
180 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
181 p = z*p1-(tt-w*(p2+y*p3));
182 r += (tf + p);
183 break;
184 case 2:
185 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
186 p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
187 r += -0.5f*y + p1/p2;
188 }
189 } else if (ix < 0x41000000) { /* x < 8.0 */
190 i = (int)x;
191 y = x - (float)i;
192 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
193 q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
194 r = 0.5f*y+p/q;
195 z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */
196 switch (i) {
197 case 7: z *= y + 6.0f; /* FALLTHRU */
198 case 6: z *= y + 5.0f; /* FALLTHRU */
199 case 5: z *= y + 4.0f; /* FALLTHRU */
200 case 4: z *= y + 3.0f; /* FALLTHRU */
201 case 3: z *= y + 2.0f; /* FALLTHRU */
202 r += logf(z);
203 break;
204 }
205 } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
206 t = logf(x);
207 z = 1.0f/x;
208 y = z*z;
209 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
210 r = (x-0.5f)*(t-1.0f)+w;
211 } else /* 2**58 <= x <= inf */
212 r = x*(logf(x)-1.0f);
213 if (sign)
214 r = nadj - r;
215 return r;
216}
217
218weak_alias(__lgammaf_r, lgammaf_r);