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 * Conversion to float fixed By Steven G. Kargl.
4 */
5
6 /*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17 #include <sys/cdefs.h>
18 __FBSDID("$FreeBSD$");
19
20 #include "math.h"
21 #include "math_private.h"
22
23 static const volatile float vzero = 0;
24
25 static const float
26 zero= 0,
27 half= 0.5,
28 one = 1,
29 pi = 3.1415927410e+00, /* 0x40490fdb */
30 /*
31 * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]:
32 * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4
33 */
34 a0 = 7.72156641e-02, /* 0x3d9e233f */
35 a1 = 3.22467119e-01, /* 0x3ea51a69 */
36 a2 = 6.73484802e-02, /* 0x3d89ee00 */
37 a3 = 2.06395667e-02, /* 0x3ca9144f */
38 a4 = 6.98275631e-03, /* 0x3be4cf9b */
39 a5 = 4.11768444e-03, /* 0x3b86eda4 */
40 /*
41 * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]:
42 * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8.
43 */
44 tc = 1.46163213e+00, /* 0x3fbb16c3 */
45 tf = -1.21486291e-01, /* 0xbdf8cdce */
46 t0 = -2.94064460e-11, /* 0xae0154b7 */
47 t1 = -2.35939837e-08, /* 0xb2caabb8 */
48 t2 = 4.83836412e-01, /* 0x3ef7b968 */
49 t3 = -1.47586212e-01, /* 0xbe1720d7 */
50 t4 = 6.46013096e-02, /* 0x3d844db1 */
51 t5 = -3.28450352e-02, /* 0xbd068884 */
52 t6 = 1.86483748e-02, /* 0x3c98c47a */
53 t7 = -9.89206228e-03, /* 0xbc221251 */
54 /*
55 * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]:
56 * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2
57 */
58 u0 = -7.72156641e-02, /* 0xbd9e233f */
59 u1 = 7.36789703e-01, /* 0x3f3c9e40 */
60 u2 = 4.95649040e-01, /* 0x3efdc5b6 */
61 v1 = 1.10958421e+00, /* 0x3f8e06db */
62 v2 = 2.10598111e-01, /* 0x3e57a708 */
63 v3 = -1.02995494e-02, /* 0xbc28bf71 */
64 /*
65 * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]:
66 * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0
67 * with y = x - 2.
68 */
69 s0 = -7.72156641e-02, /* 0xbd9e233f */
70 s1 = 2.69987404e-01, /* 0x3e8a3bca */
71 s2 = 1.42851010e-01, /* 0x3e124789 */
72 s3 = 1.19389519e-02, /* 0x3c439b98 */
73 r1 = 6.79650068e-01, /* 0x3f2dfd8c */
74 r2 = 1.16058730e-01, /* 0x3dedb033 */
75 r3 = 3.75673687e-03, /* 0x3b763396 */
76 /*
77 * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]:
78 * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6.
79 */
80 w0 = 4.18938547e-01, /* 0x3ed67f1d */
81 w1 = 8.33332464e-02, /* 0x3daaaa9f */
82 w2 = -2.76129087e-03; /* 0xbb34f6c6 */
83
84 static float
sin_pif(float x)85 sin_pif(float x)
86 {
87 volatile float vz;
88 float y,z;
89 int n;
90
91 y = -x;
92
93 vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */
94 z = vz-0x1p23F; /* rintf(y) for the above range */
95 if (z == y)
96 return zero;
97
98 vz = y+0x1p21F;
99 GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */
100 z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */
101 if (z > y) {
102 z -= 0.25F; /* adjust to round down */
103 n--;
104 }
105 n &= 7; /* octant of y mod 2 */
106 y = y - z + n * 0.25F; /* y mod 2 */
107
108 switch (n) {
109 case 0: y = __kernel_sindf(pi*y); break;
110 case 1:
111 case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break;
112 case 3:
113 case 4: y = __kernel_sindf(pi*(one-y)); break;
114 case 5:
115 case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break;
116 default: y = __kernel_sindf(pi*(y-(float)2.0)); break;
117 }
118 return -y;
119 }
120
121
122 float
__ieee754_lgammaf_r(float x,int * signgamp)123 __ieee754_lgammaf_r(float x, int *signgamp)
124 {
125 float nadj,p,p1,p2,p3,q,r,t,w,y,z;
126 int32_t hx;
127 int i,ix;
128
129 GET_FLOAT_WORD(hx,x);
130
131 /* purge +-Inf and NaNs */
132 *signgamp = 1;
133 ix = hx&0x7fffffff;
134 if(ix>=0x7f800000) return x*x;
135
136 /* purge +-0 and tiny arguments */
137 *signgamp = 1-2*((uint32_t)hx>>31);
138 if(ix<0x32000000) { /* |x|<2**-27, return -log(|x|) */
139 if(ix==0)
140 return one/vzero;
141 return -__ieee754_logf(fabsf(x));
142 }
143
144 /* purge negative integers and start evaluation for other x < 0 */
145 if(hx<0) {
146 *signgamp = 1;
147 if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
148 return one/vzero;
149 t = sin_pif(x);
150 if(t==zero) return one/vzero; /* -integer */
151 nadj = __ieee754_logf(pi/fabsf(t*x));
152 if(t<zero) *signgamp = -1;
153 x = -x;
154 }
155
156 /* purge 1 and 2 */
157 if (ix==0x3f800000||ix==0x40000000) r = 0;
158 /* for x < 2.0 */
159 else if(ix<0x40000000) {
160 if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
161 r = -__ieee754_logf(x);
162 if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
163 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
164 else {y = x; i=2;}
165 } else {
166 r = zero;
167 if(ix>=0x3fdda618) {y=2-x;i=0;} /* [1.7316,2] */
168 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
169 else {y=x-one;i=2;}
170 }
171 switch(i) {
172 case 0:
173 z = y*y;
174 p1 = a0+z*(a2+z*a4);
175 p2 = z*(a1+z*(a3+z*a5));
176 p = y*p1+p2;
177 r += p-y/2; break;
178 case 1:
179 p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7)))));
180 r += tf + p; break;
181 case 2:
182 p1 = y*(u0+y*(u1+y*u2));
183 p2 = one+y*(v1+y*(v2+y*v3));
184 r += p1/p2-y/2;
185 }
186 }
187 /* x < 8.0 */
188 else if(ix<0x41000000) {
189 i = x;
190 y = x-i;
191 p = y*(s0+y*(s1+y*(s2+y*s3)));
192 q = one+y*(r1+y*(r2+y*r3));
193 r = y/2+p/q;
194 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
195 switch(i) {
196 case 7: z *= (y+6); /* FALLTHRU */
197 case 6: z *= (y+5); /* FALLTHRU */
198 case 5: z *= (y+4); /* FALLTHRU */
199 case 4: z *= (y+3); /* FALLTHRU */
200 case 3: z *= (y+2); /* FALLTHRU */
201 r += __ieee754_logf(z); break;
202 }
203 /* 8.0 <= x < 2**27 */
204 } else if (ix < 0x4d000000) {
205 t = __ieee754_logf(x);
206 z = one/x;
207 y = z*z;
208 w = w0+z*(w1+y*w2);
209 r = (x-half)*(t-one)+w;
210 } else
211 /* 2**27 <= x <= inf */
212 r = x*(__ieee754_logf(x)-one);
213 if(hx<0) r = nadj - r;
214 return r;
215 }
216