Annotation of src/lib/libm/src/e_lgammaf_r.c, Revision 1.6
1.1 jtc 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
1.5 simonb 11: * software is freely granted, provided that this notice
1.1 jtc 12: * is preserved.
13: * ====================================================
14: */
15:
1.4 lukem 16: #include <sys/cdefs.h>
1.2 jtc 17: #if defined(LIBM_SCCS) && !defined(lint)
1.6 ! wiz 18: __RCSID("$NetBSD: e_lgammaf_r.c,v 1.5 1999/07/02 15:37:40 simonb Exp $");
1.1 jtc 19: #endif
20:
21: #include "math.h"
22: #include "math_private.h"
23:
1.5 simonb 24: static const float
1.1 jtc 25: two23= 8.3886080000e+06, /* 0x4b000000 */
26: half= 5.0000000000e-01, /* 0x3f000000 */
27: one = 1.0000000000e+00, /* 0x3f800000 */
28: pi = 3.1415927410e+00, /* 0x40490fdb */
29: a0 = 7.7215664089e-02, /* 0x3d9e233f */
30: a1 = 3.2246702909e-01, /* 0x3ea51a66 */
31: a2 = 6.7352302372e-02, /* 0x3d89f001 */
32: a3 = 2.0580807701e-02, /* 0x3ca89915 */
33: a4 = 7.3855509982e-03, /* 0x3bf2027e */
34: a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
35: a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
36: a7 = 5.1006977446e-04, /* 0x3a05b634 */
37: a8 = 2.2086278477e-04, /* 0x39679767 */
38: a9 = 1.0801156895e-04, /* 0x38e28445 */
39: a10 = 2.5214456400e-05, /* 0x37d383a2 */
40: a11 = 4.4864096708e-05, /* 0x383c2c75 */
41: tc = 1.4616321325e+00, /* 0x3fbb16c3 */
42: tf = -1.2148628384e-01, /* 0xbdf8cdcd */
43: /* tt = -(tail of tf) */
44: tt = 6.6971006518e-09, /* 0x31e61c52 */
45: t0 = 4.8383611441e-01, /* 0x3ef7b95e */
46: t1 = -1.4758771658e-01, /* 0xbe17213c */
47: t2 = 6.4624942839e-02, /* 0x3d845a15 */
48: t3 = -3.2788541168e-02, /* 0xbd064d47 */
49: t4 = 1.7970675603e-02, /* 0x3c93373d */
50: t5 = -1.0314224288e-02, /* 0xbc28fcfe */
51: t6 = 6.1005386524e-03, /* 0x3bc7e707 */
52: t7 = -3.6845202558e-03, /* 0xbb7177fe */
53: t8 = 2.2596477065e-03, /* 0x3b141699 */
54: t9 = -1.4034647029e-03, /* 0xbab7f476 */
55: t10 = 8.8108185446e-04, /* 0x3a66f867 */
56: t11 = -5.3859531181e-04, /* 0xba0d3085 */
57: t12 = 3.1563205994e-04, /* 0x39a57b6b */
58: t13 = -3.1275415677e-04, /* 0xb9a3f927 */
59: t14 = 3.3552918467e-04, /* 0x39afe9f7 */
60: u0 = -7.7215664089e-02, /* 0xbd9e233f */
61: u1 = 6.3282704353e-01, /* 0x3f2200f4 */
62: u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
63: u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
64: u4 = 2.2896373272e-01, /* 0x3e6a7578 */
65: u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
66: v1 = 2.4559779167e+00, /* 0x401d2ebe */
67: v2 = 2.1284897327e+00, /* 0x4008392d */
68: v3 = 7.6928514242e-01, /* 0x3f44efdf */
69: v4 = 1.0422264785e-01, /* 0x3dd572af */
70: v5 = 3.2170924824e-03, /* 0x3b52d5db */
71: s0 = -7.7215664089e-02, /* 0xbd9e233f */
72: s1 = 2.1498242021e-01, /* 0x3e5c245a */
73: s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
74: s3 = 1.4635047317e-01, /* 0x3e15dce6 */
75: s4 = 2.6642270386e-02, /* 0x3cda40e4 */
76: s5 = 1.8402845599e-03, /* 0x3af135b4 */
77: s6 = 3.1947532989e-05, /* 0x3805ff67 */
78: r1 = 1.3920053244e+00, /* 0x3fb22d3b */
79: r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
80: r3 = 1.7193385959e-01, /* 0x3e300f6e */
81: r4 = 1.8645919859e-02, /* 0x3c98bf54 */
82: r5 = 7.7794247773e-04, /* 0x3a4beed6 */
83: r6 = 7.3266842264e-06, /* 0x36f5d7bd */
84: w0 = 4.1893854737e-01, /* 0x3ed67f1d */
85: w1 = 8.3333335817e-02, /* 0x3daaaaab */
86: w2 = -2.7777778450e-03, /* 0xbb360b61 */
87: w3 = 7.9365057172e-04, /* 0x3a500cfd */
88: w4 = -5.9518753551e-04, /* 0xba1c065c */
89: w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
90: w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
91:
92: static const float zero= 0.0000000000e+00;
93:
1.6 ! wiz 94: static float
! 95: sin_pif(float x)
1.1 jtc 96: {
97: float y,z;
98: int n,ix;
99:
100: GET_FLOAT_WORD(ix,x);
101: ix &= 0x7fffffff;
102:
103: if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
104: y = -x; /* x is assume negative */
105:
106: /*
107: * argument reduction, make sure inexact flag not raised if input
108: * is an integer
109: */
110: z = floorf(y);
111: if(z!=y) { /* inexact anyway */
112: y *= (float)0.5;
113: y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
114: n = (int) (y*(float)4.0);
115: } else {
116: if(ix>=0x4b800000) {
117: y = zero; n = 0; /* y must be even */
118: } else {
119: if(ix<0x4b000000) z = y+two23; /* exact */
120: GET_FLOAT_WORD(n,z);
121: n &= 1;
122: y = n;
123: n<<= 2;
124: }
125: }
126: switch (n) {
127: case 0: y = __kernel_sinf(pi*y,zero,0); break;
1.5 simonb 128: case 1:
1.1 jtc 129: case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
1.5 simonb 130: case 3:
1.1 jtc 131: case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
132: case 5:
133: case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
134: default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
135: }
136: return -y;
137: }
138:
139:
1.6 ! wiz 140: float
! 141: __ieee754_lgammaf_r(float x, int *signgamp)
1.1 jtc 142: {
143: float t,y,z,nadj,p,p1,p2,p3,q,r,w;
144: int i,hx,ix;
145:
1.4 lukem 146: nadj = 0;
1.1 jtc 147: GET_FLOAT_WORD(hx,x);
148:
149: /* purge off +-inf, NaN, +-0, and negative arguments */
150: *signgamp = 1;
151: ix = hx&0x7fffffff;
152: if(ix>=0x7f800000) return x*x;
153: if(ix==0) return one/zero;
154: if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */
155: if(hx<0) {
156: *signgamp = -1;
157: return -__ieee754_logf(-x);
158: } else return -__ieee754_logf(x);
159: }
160: if(hx<0) {
161: if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
162: return one/zero;
163: t = sin_pif(x);
164: if(t==zero) return one/zero; /* -integer */
165: nadj = __ieee754_logf(pi/fabsf(t*x));
166: if(t<zero) *signgamp = -1;
167: x = -x;
168: }
169:
170: /* purge off 1 and 2 */
171: if (ix==0x3f800000||ix==0x40000000) r = 0;
172: /* for x < 2.0 */
173: else if(ix<0x40000000) {
174: if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
175: r = -__ieee754_logf(x);
176: if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
177: else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
178: else {y = x; i=2;}
179: } else {
180: r = zero;
181: if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
182: else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
183: else {y=x-one;i=2;}
184: }
185: switch(i) {
186: case 0:
187: z = y*y;
188: p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
189: p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
190: p = y*p1+p2;
191: r += (p-(float)0.5*y); break;
192: case 1:
193: z = y*y;
194: w = z*y;
195: p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
196: p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
197: p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
198: p = z*p1-(tt-w*(p2+y*p3));
199: r += (tf + p); break;
1.5 simonb 200: case 2:
1.1 jtc 201: p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
202: p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
203: r += (-(float)0.5*y + p1/p2);
204: }
205: }
206: else if(ix<0x41000000) { /* x < 8.0 */
207: i = (int)x;
208: t = zero;
209: y = x-(float)i;
210: p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
211: q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
212: r = half*y+p/q;
213: z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
214: switch(i) {
215: case 7: z *= (y+(float)6.0); /* FALLTHRU */
216: case 6: z *= (y+(float)5.0); /* FALLTHRU */
217: case 5: z *= (y+(float)4.0); /* FALLTHRU */
218: case 4: z *= (y+(float)3.0); /* FALLTHRU */
219: case 3: z *= (y+(float)2.0); /* FALLTHRU */
220: r += __ieee754_logf(z); break;
221: }
222: /* 8.0 <= x < 2**58 */
223: } else if (ix < 0x5c800000) {
224: t = __ieee754_logf(x);
225: z = one/x;
226: y = z*z;
227: w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
228: r = (x-half)*(t-one)+w;
1.5 simonb 229: } else
1.1 jtc 230: /* 2**58 <= x <= inf */
231: r = x*(__ieee754_logf(x)-one);
232: if(hx<0) r = nadj - r;
233: return r;
234: }
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