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e_lgammaf_r.c (7344B)
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1 /* e_lgammaf_r.c -- float version of e_lgamma_r.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 #ifndef lint
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_lgammaf_r.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
18 #endif
19
20 #include "math.h"
21 #include "math_private.h"
22
23 static const float
24 two23= 8.3886080000e+06, /* 0x4b000000 */
25 half= 5.0000000000e-01, /* 0x3f000000 */
26 one = 1.0000000000e+00, /* 0x3f800000 */
27 pi = 3.1415927410e+00, /* 0x40490fdb */
28 a0 = 7.7215664089e-02, /* 0x3d9e233f */
29 a1 = 3.2246702909e-01, /* 0x3ea51a66 */
30 a2 = 6.7352302372e-02, /* 0x3d89f001 */
31 a3 = 2.0580807701e-02, /* 0x3ca89915 */
32 a4 = 7.3855509982e-03, /* 0x3bf2027e */
33 a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
34 a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
35 a7 = 5.1006977446e-04, /* 0x3a05b634 */
36 a8 = 2.2086278477e-04, /* 0x39679767 */
37 a9 = 1.0801156895e-04, /* 0x38e28445 */
38 a10 = 2.5214456400e-05, /* 0x37d383a2 */
39 a11 = 4.4864096708e-05, /* 0x383c2c75 */
40 tc = 1.4616321325e+00, /* 0x3fbb16c3 */
41 tf = -1.2148628384e-01, /* 0xbdf8cdcd */
42 /* tt = -(tail of tf) */
43 tt = 6.6971006518e-09, /* 0x31e61c52 */
44 t0 = 4.8383611441e-01, /* 0x3ef7b95e */
45 t1 = -1.4758771658e-01, /* 0xbe17213c */
46 t2 = 6.4624942839e-02, /* 0x3d845a15 */
47 t3 = -3.2788541168e-02, /* 0xbd064d47 */
48 t4 = 1.7970675603e-02, /* 0x3c93373d */
49 t5 = -1.0314224288e-02, /* 0xbc28fcfe */
50 t6 = 6.1005386524e-03, /* 0x3bc7e707 */
51 t7 = -3.6845202558e-03, /* 0xbb7177fe */
52 t8 = 2.2596477065e-03, /* 0x3b141699 */
53 t9 = -1.4034647029e-03, /* 0xbab7f476 */
54 t10 = 8.8108185446e-04, /* 0x3a66f867 */
55 t11 = -5.3859531181e-04, /* 0xba0d3085 */
56 t12 = 3.1563205994e-04, /* 0x39a57b6b */
57 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
58 t14 = 3.3552918467e-04, /* 0x39afe9f7 */
59 u0 = -7.7215664089e-02, /* 0xbd9e233f */
60 u1 = 6.3282704353e-01, /* 0x3f2200f4 */
61 u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
62 u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
63 u4 = 2.2896373272e-01, /* 0x3e6a7578 */
64 u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
65 v1 = 2.4559779167e+00, /* 0x401d2ebe */
66 v2 = 2.1284897327e+00, /* 0x4008392d */
67 v3 = 7.6928514242e-01, /* 0x3f44efdf */
68 v4 = 1.0422264785e-01, /* 0x3dd572af */
69 v5 = 3.2170924824e-03, /* 0x3b52d5db */
70 s0 = -7.7215664089e-02, /* 0xbd9e233f */
71 s1 = 2.1498242021e-01, /* 0x3e5c245a */
72 s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
73 s3 = 1.4635047317e-01, /* 0x3e15dce6 */
74 s4 = 2.6642270386e-02, /* 0x3cda40e4 */
75 s5 = 1.8402845599e-03, /* 0x3af135b4 */
76 s6 = 3.1947532989e-05, /* 0x3805ff67 */
77 r1 = 1.3920053244e+00, /* 0x3fb22d3b */
78 r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
79 r3 = 1.7193385959e-01, /* 0x3e300f6e */
80 r4 = 1.8645919859e-02, /* 0x3c98bf54 */
81 r5 = 7.7794247773e-04, /* 0x3a4beed6 */
82 r6 = 7.3266842264e-06, /* 0x36f5d7bd */
83 w0 = 4.1893854737e-01, /* 0x3ed67f1d */
84 w1 = 8.3333335817e-02, /* 0x3daaaaab */
85 w2 = -2.7777778450e-03, /* 0xbb360b61 */
86 w3 = 7.9365057172e-04, /* 0x3a500cfd */
87 w4 = -5.9518753551e-04, /* 0xba1c065c */
88 w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
89 w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
90
91 static const float zero= 0.0000000000e+00;
92
93 static float sin_pif(float x)
94 {
95 float y,z;
96 int n,ix;
97
98 GET_FLOAT_WORD(ix,x);
99 ix &= 0x7fffffff;
100
101 if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
102 y = -x; /* x is assume negative */
103
104 /*
105 * argument reduction, make sure inexact flag not raised if input
106 * is an integer
107 */
108 z = floorf(y);
109 if(z!=y) { /* inexact anyway */
110 y *= (float)0.5;
111 y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
112 n = (int) (y*(float)4.0);
113 } else {
114 if(ix>=0x4b800000) {
115 y = zero; n = 0; /* y must be even */
116 } else {
117 if(ix<0x4b000000) z = y+two23; /* exact */
118 GET_FLOAT_WORD(n,z);
119 n &= 1;
120 y = n;
121 n<<= 2;
122 }
123 }
124 switch (n) {
125 case 0: y = __kernel_sinf(pi*y,zero,0); break;
126 case 1:
127 case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
128 case 3:
129 case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
130 case 5:
131 case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
132 default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
133 }
134 return -y;
135 }
136
137
138 float
139 __ieee754_lgammaf_r(float x, int *signgamp)
140 {
141 float t,y,z,nadj,p,p1,p2,p3,q,r,w;
142 int i,hx,ix;
143
144 GET_FLOAT_WORD(hx,x);
145
146 /* purge off +-inf, NaN, +-0, and negative arguments */
147 *signgamp = 1;
148 ix = hx&0x7fffffff;
149 if(ix>=0x7f800000) return x*x;
150 if(ix==0) return one/zero;
151 if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */
152 if(hx<0) {
153 *signgamp = -1;
154 return -__ieee754_logf(-x);
155 } else return -__ieee754_logf(x);
156 }
157 if(hx<0) {
158 if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
159 return one/zero;
160 t = sin_pif(x);
161 if(t==zero) return one/zero; /* -integer */
162 nadj = __ieee754_logf(pi/fabsf(t*x));
163 if(t<zero) *signgamp = -1;
164 x = -x;
165 }
166
167 /* purge off 1 and 2 */
168 if (ix==0x3f800000||ix==0x40000000) r = 0;
169 /* for x < 2.0 */
170 else if(ix<0x40000000) {
171 if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
172 r = -__ieee754_logf(x);
173 if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
174 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
175 else {y = x; i=2;}
176 } else {
177 r = zero;
178 if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
179 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
180 else {y=x-one;i=2;}
181 }
182 switch(i) {
183 case 0:
184 z = y*y;
185 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
186 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
187 p = y*p1+p2;
188 r += (p-(float)0.5*y); break;
189 case 1:
190 z = y*y;
191 w = z*y;
192 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
193 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
194 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
195 p = z*p1-(tt-w*(p2+y*p3));
196 r += (tf + p); break;
197 case 2:
198 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
199 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
200 r += (-(float)0.5*y + p1/p2);
201 }
202 }
203 else if(ix<0x41000000) { /* x < 8.0 */
204 i = (int)x;
205 t = zero;
206 y = x-(float)i;
207 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
208 q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
209 r = half*y+p/q;
210 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
211 switch(i) {
212 case 7: z *= (y+(float)6.0); /* FALLTHRU */
213 case 6: z *= (y+(float)5.0); /* FALLTHRU */
214 case 5: z *= (y+(float)4.0); /* FALLTHRU */
215 case 4: z *= (y+(float)3.0); /* FALLTHRU */
216 case 3: z *= (y+(float)2.0); /* FALLTHRU */
217 r += __ieee754_logf(z); break;
218 }
219 /* 8.0 <= x < 2**58 */
220 } else if (ix < 0x5c800000) {
221 t = __ieee754_logf(x);
222 z = one/x;
223 y = z*z;
224 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
225 r = (x-half)*(t-one)+w;
226 } else
227 /* 2**58 <= x <= inf */
228 r = x*(__ieee754_logf(x)-one);
229 if(hx<0) r = nadj - r;
230 return r;
231 }