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