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