1 /* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
19 two23= 8.3886080000e+06, /* 0x4b000000 */
20 half= 5.0000000000e-01, /* 0x3f000000 */
21 one = 1.0000000000e+00, /* 0x3f800000 */
22 pi = 3.1415927410e+00, /* 0x40490fdb */
23 a0 = 7.7215664089e-02, /* 0x3d9e233f */
24 a1 = 3.2246702909e-01, /* 0x3ea51a66 */
25 a2 = 6.7352302372e-02, /* 0x3d89f001 */
26 a3 = 2.0580807701e-02, /* 0x3ca89915 */
27 a4 = 7.3855509982e-03, /* 0x3bf2027e */
28 a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
29 a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
30 a7 = 5.1006977446e-04, /* 0x3a05b634 */
31 a8 = 2.2086278477e-04, /* 0x39679767 */
32 a9 = 1.0801156895e-04, /* 0x38e28445 */
33 a10 = 2.5214456400e-05, /* 0x37d383a2 */
34 a11 = 4.4864096708e-05, /* 0x383c2c75 */
35 tc = 1.4616321325e+00, /* 0x3fbb16c3 */
36 tf = -1.2148628384e-01, /* 0xbdf8cdcd */
37 /* tt = -(tail of tf) */
38 tt = 6.6971006518e-09, /* 0x31e61c52 */
39 t0 = 4.8383611441e-01, /* 0x3ef7b95e */
40 t1 = -1.4758771658e-01, /* 0xbe17213c */
41 t2 = 6.4624942839e-02, /* 0x3d845a15 */
42 t3 = -3.2788541168e-02, /* 0xbd064d47 */
43 t4 = 1.7970675603e-02, /* 0x3c93373d */
44 t5 = -1.0314224288e-02, /* 0xbc28fcfe */
45 t6 = 6.1005386524e-03, /* 0x3bc7e707 */
46 t7 = -3.6845202558e-03, /* 0xbb7177fe */
47 t8 = 2.2596477065e-03, /* 0x3b141699 */
48 t9 = -1.4034647029e-03, /* 0xbab7f476 */
49 t10 = 8.8108185446e-04, /* 0x3a66f867 */
50 t11 = -5.3859531181e-04, /* 0xba0d3085 */
51 t12 = 3.1563205994e-04, /* 0x39a57b6b */
52 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
53 t14 = 3.3552918467e-04, /* 0x39afe9f7 */
54 u0 = -7.7215664089e-02, /* 0xbd9e233f */
55 u1 = 6.3282704353e-01, /* 0x3f2200f4 */
56 u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
57 u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
58 u4 = 2.2896373272e-01, /* 0x3e6a7578 */
59 u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
60 v1 = 2.4559779167e+00, /* 0x401d2ebe */
61 v2 = 2.1284897327e+00, /* 0x4008392d */
62 v3 = 7.6928514242e-01, /* 0x3f44efdf */
63 v4 = 1.0422264785e-01, /* 0x3dd572af */
64 v5 = 3.2170924824e-03, /* 0x3b52d5db */
65 s0 = -7.7215664089e-02, /* 0xbd9e233f */
66 s1 = 2.1498242021e-01, /* 0x3e5c245a */
67 s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
68 s3 = 1.4635047317e-01, /* 0x3e15dce6 */
69 s4 = 2.6642270386e-02, /* 0x3cda40e4 */
70 s5 = 1.8402845599e-03, /* 0x3af135b4 */
71 s6 = 3.1947532989e-05, /* 0x3805ff67 */
72 r1 = 1.3920053244e+00, /* 0x3fb22d3b */
73 r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
74 r3 = 1.7193385959e-01, /* 0x3e300f6e */
75 r4 = 1.8645919859e-02, /* 0x3c98bf54 */
76 r5 = 7.7794247773e-04, /* 0x3a4beed6 */
77 r6 = 7.3266842264e-06, /* 0x36f5d7bd */
78 w0 = 4.1893854737e-01, /* 0x3ed67f1d */
79 w1 = 8.3333335817e-02, /* 0x3daaaaab */
80 w2 = -2.7777778450e-03, /* 0xbb360b61 */
81 w3 = 7.9365057172e-04, /* 0x3a500cfd */
82 w4 = -5.9518753551e-04, /* 0xba1c065c */
83 w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
84 w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
86 static const float zero = 0.0000000000e+00;
88 static float sin_pif(float x)
93 GET_FLOAT_WORD(ix, x);
99 y = -x; /* negative x is assumed */
102 * argument reduction, make sure inexact flag not raised if input
106 if (z != y) { /* inexact anyway */
108 y = 2.0f*(y - floorf(y)); /* y = |x| mod 2.0 */
111 if (ix >= 0x4b800000) {
112 y = zero; /* y must be even */
116 z = y + two23; /* exact */
117 GET_FLOAT_WORD(n, z);
124 case 0: y = __sindf(pi*y); break;
126 case 2: y = __cosdf(pi*(0.5f - y)); break;
128 case 4: y = __sindf(pi*(one - y)); break;
130 case 6: y = -__cosdf(pi*(y - 1.5f)); break;
131 default: y = __sindf(pi*(y - 2.0f)); break;
137 float __lgammaf_r(float x, int *signgamp)
139 float t,y,z,nadj,p,p1,p2,p3,q,r,w;
143 GET_FLOAT_WORD(hx, x);
145 /* purge off +-inf, NaN, +-0, tiny and negative arguments */
147 ix = hx & 0x7fffffff;
148 if (ix >= 0x7f800000)
152 if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
160 if (ix >= 0x4b000000) /* |x| >= 2**23, must be -integer */
163 if (t == zero) /* -integer */
165 nadj = logf(pi/fabsf(t*x));
171 /* purge off 1 and 2 */
172 if (ix == 0x3f800000 || ix == 0x40000000)
175 else if (ix < 0x40000000) {
176 if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
178 if (ix >= 0x3f3b4a20) {
181 } else if (ix >= 0x3e6d3308) {
190 if (ix >= 0x3fdda618) { /* [1.7316,2] */
193 } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
204 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
205 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
212 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
213 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
214 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
215 p = z*p1-(tt-w*(p2+y*p3));
219 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
220 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
221 r += -0.5f*y + p1/p2;
223 } else if (ix < 0x41000000) { /* x < 8.0 */
226 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
227 q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
229 z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
231 case 7: z *= y + 6.0f; /* FALLTHRU */
232 case 6: z *= y + 5.0f; /* FALLTHRU */
233 case 5: z *= y + 4.0f; /* FALLTHRU */
234 case 4: z *= y + 3.0f; /* FALLTHRU */
235 case 3: z *= y + 2.0f; /* FALLTHRU */
239 } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
243 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
244 r = (x-half)*(t-one)+w;
245 } else /* 2**58 <= x <= inf */
252 weak_alias(__lgammaf_r, lgammaf_r);