1 /* erf_lgamma.c -- float version of er_lgamma.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
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
17 #define _ADD_UNDER_R_TO_FUNCS
18
19 #include "fdlibm.h"
20
21 static const float two23 = 8.3886080000e+06, /* 0x4b000000 */
22 half = 5.0000000000e-01, /* 0x3f000000 */
23 one = 1.0000000000e+00, /* 0x3f800000 */
24 pi = 3.1415927410e+00, /* 0x40490fdb */
25 a0 = 7.7215664089e-02, /* 0x3d9e233f */
26 a1 = 3.2246702909e-01, /* 0x3ea51a66 */
27 a2 = 6.7352302372e-02, /* 0x3d89f001 */
28 a3 = 2.0580807701e-02, /* 0x3ca89915 */
29 a4 = 7.3855509982e-03, /* 0x3bf2027e */
30 a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
31 a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
32 a7 = 5.1006977446e-04, /* 0x3a05b634 */
33 a8 = 2.2086278477e-04, /* 0x39679767 */
34 a9 = 1.0801156895e-04, /* 0x38e28445 */
35 a10 = 2.5214456400e-05, /* 0x37d383a2 */
36 a11 = 4.4864096708e-05, /* 0x383c2c75 */
37 tc = 1.4616321325e+00, /* 0x3fbb16c3 */
38 tf = -1.2148628384e-01, /* 0xbdf8cdcd */
39 /* tt = -(tail of tf) */
40 tt = 6.6971006518e-09, /* 0x31e61c52 */
41 t0 = 4.8383611441e-01, /* 0x3ef7b95e */
42 t1 = -1.4758771658e-01, /* 0xbe17213c */
43 t2 = 6.4624942839e-02, /* 0x3d845a15 */
44 t3 = -3.2788541168e-02, /* 0xbd064d47 */
45 t4 = 1.7970675603e-02, /* 0x3c93373d */
46 t5 = -1.0314224288e-02, /* 0xbc28fcfe */
47 t6 = 6.1005386524e-03, /* 0x3bc7e707 */
48 t7 = -3.6845202558e-03, /* 0xbb7177fe */
49 t8 = 2.2596477065e-03, /* 0x3b141699 */
50 t9 = -1.4034647029e-03, /* 0xbab7f476 */
51 t10 = 8.8108185446e-04, /* 0x3a66f867 */
52 t11 = -5.3859531181e-04, /* 0xba0d3085 */
53 t12 = 3.1563205994e-04, /* 0x39a57b6b */
54 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
55 t14 = 3.3552918467e-04, /* 0x39afe9f7 */
56 u0 = -7.7215664089e-02, /* 0xbd9e233f */
57 u1 = 6.3282704353e-01, /* 0x3f2200f4 */
58 u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
59 u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
60 u4 = 2.2896373272e-01, /* 0x3e6a7578 */
61 u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
62 v1 = 2.4559779167e+00, /* 0x401d2ebe */
63 v2 = 2.1284897327e+00, /* 0x4008392d */
64 v3 = 7.6928514242e-01, /* 0x3f44efdf */
65 v4 = 1.0422264785e-01, /* 0x3dd572af */
66 v5 = 3.2170924824e-03, /* 0x3b52d5db */
67 s0 = -7.7215664089e-02, /* 0xbd9e233f */
68 s1 = 2.1498242021e-01, /* 0x3e5c245a */
69 s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
70 s3 = 1.4635047317e-01, /* 0x3e15dce6 */
71 s4 = 2.6642270386e-02, /* 0x3cda40e4 */
72 s5 = 1.8402845599e-03, /* 0x3af135b4 */
73 s6 = 3.1947532989e-05, /* 0x3805ff67 */
74 r1 = 1.3920053244e+00, /* 0x3fb22d3b */
75 r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
76 r3 = 1.7193385959e-01, /* 0x3e300f6e */
77 r4 = 1.8645919859e-02, /* 0x3c98bf54 */
78 r5 = 7.7794247773e-04, /* 0x3a4beed6 */
79 r6 = 7.3266842264e-06, /* 0x36f5d7bd */
80 w0 = 4.1893854737e-01, /* 0x3ed67f1d */
81 w1 = 8.3333335817e-02, /* 0x3daaaaab */
82 w2 = -2.7777778450e-03, /* 0xbb360b61 */
83 w3 = 7.9365057172e-04, /* 0x3a500cfd */
84 w4 = -5.9518753551e-04, /* 0xba1c065c */
85 w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
86 w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
87
88 static const float zero = 0.0000000000e+00;
89
90 static float
sin_pif(float x)91 sin_pif(float x)
92 {
93 float y, z;
94 __int32_t n, ix;
95
96 GET_FLOAT_WORD(ix, x);
97 ix &= 0x7fffffff;
98
99 if (ix < 0x3e800000)
100 return __kernel_sinf(pi * x, zero, 0);
101 y = -x; /* x is assume negative */
102
103 /*
104 * argument reduction, make sure inexact flag not raised if input
105 * is an integer
106 */
107 z = floorf(y);
108 if (z != y) { /* inexact anyway */
109 y *= (float)0.5;
110 y = (float)2.0 * (y - floorf(y)); /* y = |x| mod 2.0 */
111 n = (__int32_t)(y * (float)4.0);
112 } else {
113 if (ix >= 0x4b800000) {
114 y = zero;
115 n = 0; /* y must be even */
116 } else {
117 if (ix < 0x4b000000)
118 z = y + two23; /* exact */
119 GET_FLOAT_WORD(n, z);
120 n &= 1;
121 y = n;
122 n <<= 2;
123 }
124 }
125 switch (n) {
126 case 0:
127 y = __kernel_sinf(pi * y, zero, 0);
128 break;
129 case 1:
130 case 2:
131 y = __kernel_cosf(pi * ((float)0.5 - y), zero);
132 break;
133 case 3:
134 case 4:
135 y = __kernel_sinf(pi * (one - y), zero, 0);
136 break;
137 case 5:
138 case 6:
139 y = -__kernel_cosf(pi * (y - (float)1.5), zero);
140 break;
141 default:
142 y = __kernel_sinf(pi * (y - (float)2.0), zero, 0);
143 break;
144 }
145 return -y;
146 }
147
148 float
__math_lgammaf_r(float x,int * signgamp,int * divzero)149 __math_lgammaf_r(float x, int *signgamp, int *divzero)
150 {
151 float t, y, z, nadj = 0.0, p, p1, p2, p3, q, r, w;
152 __int32_t i, hx, ix;
153
154 GET_FLOAT_WORD(hx, x);
155
156 /* purge off +-inf, NaN, +-0, and negative arguments */
157 *signgamp = 1;
158 ix = hx & 0x7fffffff;
159 if (ix >= 0x7f800000)
160 return fabsf(x+x);
161 if (ix == 0) {
162 if (hx < 0)
163 *signgamp = -1;
164 *divzero = 1;
165 return __math_divzerof(0);
166 }
167 if (ix < 0x1c800000) { /* |x|<2**-70, return -log(|x|) */
168 if (hx < 0) {
169 *signgamp = -1;
170 return -logf(-x);
171 } else
172 return -logf(x);
173 }
174 if (hx < 0) {
175 if (ix >= 0x4b000000) { /* |x|>=2**23, must be -integer */
176 *divzero = 1;
177 return __math_divzerof(0);
178 }
179 t = sin_pif(x);
180 if (t == zero) {
181 *divzero = 1;
182 return __math_divzerof(0);
183 }
184 nadj = logf(pi / fabsf(t * x));
185 if (t < zero)
186 *signgamp = -1;
187 x = -x;
188 }
189
190 /* purge off 1 and 2 */
191 if (ix == 0x3f800000 || ix == 0x40000000)
192 r = 0;
193 /* for x < 2.0 */
194 else if (ix < 0x40000000) {
195 if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
196 r = -logf(x);
197 if (ix >= 0x3f3b4a20) {
198 y = one - x;
199 i = 0;
200 } else if (ix >= 0x3e6d3308) {
201 y = x - (tc - one);
202 i = 1;
203 } else {
204 y = x;
205 i = 2;
206 }
207 } else {
208 r = zero;
209 if (ix >= 0x3fdda618) {
210 y = (float)2.0 - x;
211 i = 0;
212 } /* [1.7316,2] */
213 else if (ix >= 0x3F9da620) {
214 y = x - tc;
215 i = 1;
216 } /* [1.23,1.73] */
217 else {
218 y = x - one;
219 i = 2;
220 }
221 }
222 switch (i) {
223 case 0:
224 z = y * y;
225 p1 = a0 + z * (a2 + z * (a4 + z * (a6 + z * (a8 + z * a10))));
226 p2 = z * (a1 + z * (a3 + z * (a5 + z * (a7 + z * (a9 + z * a11)))));
227 p = y * p1 + p2;
228 r += (p - (float)0.5 * y);
229 break;
230 case 1:
231 z = y * y;
232 w = z * y;
233 p1 = t0 +
234 w * (t3 + w * (t6 + w * (t9 + w * t12))); /* parallel comp */
235 p2 = t1 + w * (t4 + w * (t7 + w * (t10 + w * t13)));
236 p3 = t2 + w * (t5 + w * (t8 + w * (t11 + w * t14)));
237 p = z * p1 - (tt - w * (p2 + y * p3));
238 r += (tf + p);
239 break;
240 case 2:
241 p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * u5)))));
242 p2 = one + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * v5))));
243 r += (-(float)0.5 * y + p1 / p2);
244 }
245 } else if (ix < 0x41000000) { /* x < 8.0 */
246 i = (__int32_t)x;
247 t = zero;
248 y = x - (float)i;
249 p = y * (s0 +
250 y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
251 q = one + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * r6)))));
252 r = half * y + p / q;
253 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
254 switch (i) {
255 case 7:
256 z *= (y + (float)6.0); /* FALLTHRU */
257 case 6:
258 z *= (y + (float)5.0); /* FALLTHRU */
259 case 5:
260 z *= (y + (float)4.0); /* FALLTHRU */
261 case 4:
262 z *= (y + (float)3.0); /* FALLTHRU */
263 case 3:
264 z *= (y + (float)2.0); /* FALLTHRU */
265 r += logf(z);
266 break;
267 }
268 /* 8.0 <= x < 2**58 */
269 } else if (ix < 0x5c800000) {
270 t = logf(x);
271 z = one / x;
272 y = z * z;
273 w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * w6)))));
274 r = (x - half) * (t - one) + w;
275 } else
276 /* 2**58 <= x <= inf */
277 r = x * (logf(x) - one);
278 if (hx < 0)
279 r = nadj - r;
280 return check_oflowf(r);
281 }
282
283 float
lgammaf_r(float x,int * signgamp)284 lgammaf_r(float x, int *signgamp)
285 {
286 int divzero = 0;
287 return __math_lgammaf_r(x, signgamp, &divzero);
288 }
289
290 _MATH_ALIAS_f_fI(lgamma)
291
