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
19static const float
20two23=  8.3886080000e+06, /* 0x4b000000 */
21half=  5.0000000000e-01, /* 0x3f000000 */
22one =  1.0000000000e+00, /* 0x3f800000 */
23pi  =  3.1415927410e+00, /* 0x40490fdb */
24a0  =  7.7215664089e-02, /* 0x3d9e233f */
25a1  =  3.2246702909e-01, /* 0x3ea51a66 */
26a2  =  6.7352302372e-02, /* 0x3d89f001 */
27a3  =  2.0580807701e-02, /* 0x3ca89915 */
28a4  =  7.3855509982e-03, /* 0x3bf2027e */
29a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
30a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
31a7  =  5.1006977446e-04, /* 0x3a05b634 */
32a8  =  2.2086278477e-04, /* 0x39679767 */
33a9  =  1.0801156895e-04, /* 0x38e28445 */
34a10 =  2.5214456400e-05, /* 0x37d383a2 */
35a11 =  4.4864096708e-05, /* 0x383c2c75 */
36tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
37tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
38/* tt = -(tail of tf) */
39tt  =  6.6971006518e-09, /* 0x31e61c52 */
40t0  =  4.8383611441e-01, /* 0x3ef7b95e */
41t1  = -1.4758771658e-01, /* 0xbe17213c */
42t2  =  6.4624942839e-02, /* 0x3d845a15 */
43t3  = -3.2788541168e-02, /* 0xbd064d47 */
44t4  =  1.7970675603e-02, /* 0x3c93373d */
45t5  = -1.0314224288e-02, /* 0xbc28fcfe */
46t6  =  6.1005386524e-03, /* 0x3bc7e707 */
47t7  = -3.6845202558e-03, /* 0xbb7177fe */
48t8  =  2.2596477065e-03, /* 0x3b141699 */
49t9  = -1.4034647029e-03, /* 0xbab7f476 */
50t10 =  8.8108185446e-04, /* 0x3a66f867 */
51t11 = -5.3859531181e-04, /* 0xba0d3085 */
52t12 =  3.1563205994e-04, /* 0x39a57b6b */
53t13 = -3.1275415677e-04, /* 0xb9a3f927 */
54t14 =  3.3552918467e-04, /* 0x39afe9f7 */
55u0  = -7.7215664089e-02, /* 0xbd9e233f */
56u1  =  6.3282704353e-01, /* 0x3f2200f4 */
57u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
58u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
59u4  =  2.2896373272e-01, /* 0x3e6a7578 */
60u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
61v1  =  2.4559779167e+00, /* 0x401d2ebe */
62v2  =  2.1284897327e+00, /* 0x4008392d */
63v3  =  7.6928514242e-01, /* 0x3f44efdf */
64v4  =  1.0422264785e-01, /* 0x3dd572af */
65v5  =  3.2170924824e-03, /* 0x3b52d5db */
66s0  = -7.7215664089e-02, /* 0xbd9e233f */
67s1  =  2.1498242021e-01, /* 0x3e5c245a */
68s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
69s3  =  1.4635047317e-01, /* 0x3e15dce6 */
70s4  =  2.6642270386e-02, /* 0x3cda40e4 */
71s5  =  1.8402845599e-03, /* 0x3af135b4 */
72s6  =  3.1947532989e-05, /* 0x3805ff67 */
73r1  =  1.3920053244e+00, /* 0x3fb22d3b */
74r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
75r3  =  1.7193385959e-01, /* 0x3e300f6e */
76r4  =  1.8645919859e-02, /* 0x3c98bf54 */
77r5  =  7.7794247773e-04, /* 0x3a4beed6 */
78r6  =  7.3266842264e-06, /* 0x36f5d7bd */
79w0  =  4.1893854737e-01, /* 0x3ed67f1d */
80w1  =  8.3333335817e-02, /* 0x3daaaaab */
81w2  = -2.7777778450e-03, /* 0xbb360b61 */
82w3  =  7.9365057172e-04, /* 0x3a500cfd */
83w4  = -5.9518753551e-04, /* 0xba1c065c */
84w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
85w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
86
87static const float zero=  0.0000000000e+00;
88
89static float
90sin_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
135float
136lgammaf_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}
233DEF_NONSTD(lgammaf_r);
234