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 <sys/cdefs.h>
17__FBSDID("$FreeBSD$");
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23two23=  8.3886080000e+06, /* 0x4b000000 */
24half=  5.0000000000e-01, /* 0x3f000000 */
25one =  1.0000000000e+00, /* 0x3f800000 */
26pi  =  3.1415927410e+00, /* 0x40490fdb */
27a0  =  7.7215664089e-02, /* 0x3d9e233f */
28a1  =  3.2246702909e-01, /* 0x3ea51a66 */
29a2  =  6.7352302372e-02, /* 0x3d89f001 */
30a3  =  2.0580807701e-02, /* 0x3ca89915 */
31a4  =  7.3855509982e-03, /* 0x3bf2027e */
32a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
33a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
34a7  =  5.1006977446e-04, /* 0x3a05b634 */
35a8  =  2.2086278477e-04, /* 0x39679767 */
36a9  =  1.0801156895e-04, /* 0x38e28445 */
37a10 =  2.5214456400e-05, /* 0x37d383a2 */
38a11 =  4.4864096708e-05, /* 0x383c2c75 */
39tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
40tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
41/* tt = -(tail of tf) */
42tt  =  6.6971006518e-09, /* 0x31e61c52 */
43t0  =  4.8383611441e-01, /* 0x3ef7b95e */
44t1  = -1.4758771658e-01, /* 0xbe17213c */
45t2  =  6.4624942839e-02, /* 0x3d845a15 */
46t3  = -3.2788541168e-02, /* 0xbd064d47 */
47t4  =  1.7970675603e-02, /* 0x3c93373d */
48t5  = -1.0314224288e-02, /* 0xbc28fcfe */
49t6  =  6.1005386524e-03, /* 0x3bc7e707 */
50t7  = -3.6845202558e-03, /* 0xbb7177fe */
51t8  =  2.2596477065e-03, /* 0x3b141699 */
52t9  = -1.4034647029e-03, /* 0xbab7f476 */
53t10 =  8.8108185446e-04, /* 0x3a66f867 */
54t11 = -5.3859531181e-04, /* 0xba0d3085 */
55t12 =  3.1563205994e-04, /* 0x39a57b6b */
56t13 = -3.1275415677e-04, /* 0xb9a3f927 */
57t14 =  3.3552918467e-04, /* 0x39afe9f7 */
58u0  = -7.7215664089e-02, /* 0xbd9e233f */
59u1  =  6.3282704353e-01, /* 0x3f2200f4 */
60u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
61u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
62u4  =  2.2896373272e-01, /* 0x3e6a7578 */
63u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
64v1  =  2.4559779167e+00, /* 0x401d2ebe */
65v2  =  2.1284897327e+00, /* 0x4008392d */
66v3  =  7.6928514242e-01, /* 0x3f44efdf */
67v4  =  1.0422264785e-01, /* 0x3dd572af */
68v5  =  3.2170924824e-03, /* 0x3b52d5db */
69s0  = -7.7215664089e-02, /* 0xbd9e233f */
70s1  =  2.1498242021e-01, /* 0x3e5c245a */
71s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
72s3  =  1.4635047317e-01, /* 0x3e15dce6 */
73s4  =  2.6642270386e-02, /* 0x3cda40e4 */
74s5  =  1.8402845599e-03, /* 0x3af135b4 */
75s6  =  3.1947532989e-05, /* 0x3805ff67 */
76r1  =  1.3920053244e+00, /* 0x3fb22d3b */
77r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
78r3  =  1.7193385959e-01, /* 0x3e300f6e */
79r4  =  1.8645919859e-02, /* 0x3c98bf54 */
80r5  =  7.7794247773e-04, /* 0x3a4beed6 */
81r6  =  7.3266842264e-06, /* 0x36f5d7bd */
82w0  =  4.1893854737e-01, /* 0x3ed67f1d */
83w1  =  8.3333335817e-02, /* 0x3daaaaab */
84w2  = -2.7777778450e-03, /* 0xbb360b61 */
85w3  =  7.9365057172e-04, /* 0x3a500cfd */
86w4  = -5.9518753551e-04, /* 0xba1c065c */
87w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
88w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
89
90static const float zero=  0.0000000000e+00;
91
92	static float sin_pif(float x)
93{
94	float y,z;
95	int n,ix;
96
97	GET_FLOAT_WORD(ix,x);
98	ix &= 0x7fffffff;
99
100	if(ix<0x3e800000) return __kernel_sindf(pi*x);
101	y = -x;		/* x is assume negative */
102
103    /*
104     * argument reduction, make sure inexact flag not raised if input
105     * is an integer
106     */
107	z = floorf(y);
108	if(z!=y) {				/* inexact anyway */
109	    y  *= (float)0.5;
110	    y   = (float)2.0*(y - floorf(y));	/* y = |x| mod 2.0 */
111	    n   = (int) (y*(float)4.0);
112	} else {
113            if(ix>=0x4b800000) {
114                y = zero; n = 0;                 /* y must be even */
115            } else {
116                if(ix<0x4b000000) z = y+two23;	/* exact */
117		GET_FLOAT_WORD(n,z);
118		n &= 1;
119                y  = n;
120                n<<= 2;
121            }
122        }
123	switch (n) {
124	    case 0:   y =  __kernel_sindf(pi*y); break;
125	    case 1:
126	    case 2:   y =  __kernel_cosdf(pi*((float)0.5-y)); break;
127	    case 3:
128	    case 4:   y =  __kernel_sindf(pi*(one-y)); break;
129	    case 5:
130	    case 6:   y = -__kernel_cosdf(pi*(y-(float)1.5)); break;
131	    default:  y =  __kernel_sindf(pi*(y-(float)2.0)); break;
132	    }
133	return -y;
134}
135
136
137float
138__ieee754_lgammaf_r(float x, int *signgamp)
139{
140	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
141	int32_t hx;
142	int i,ix;
143
144	GET_FLOAT_WORD(hx,x);
145
146    /* purge off +-inf, NaN, +-0, tiny and negative arguments */
147	*signgamp = 1;
148	ix = hx&0x7fffffff;
149	if(ix>=0x7f800000) return x*x;
150	if(ix==0) return one/zero;
151	if(ix<0x35000000) {	/* |x|<2**-21, return -log(|x|) */
152	    if(hx<0) {
153	        *signgamp = -1;
154	        return -__ieee754_logf(-x);
155	    } else return -__ieee754_logf(x);
156	}
157	if(hx<0) {
158	    if(ix>=0x4b000000) 	/* |x|>=2**23, must be -integer */
159		return one/zero;
160	    t = sin_pif(x);
161	    if(t==zero) return one/zero; /* -integer */
162	    nadj = __ieee754_logf(pi/fabsf(t*x));
163	    if(t<zero) *signgamp = -1;
164	    x = -x;
165	}
166
167    /* purge off 1 and 2 */
168	if (ix==0x3f800000||ix==0x40000000) r = 0;
169    /* for x < 2.0 */
170	else if(ix<0x40000000) {
171	    if(ix<=0x3f666666) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
172		r = -__ieee754_logf(x);
173		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
174		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
175	  	else {y = x; i=2;}
176	    } else {
177	  	r = zero;
178	        if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
179	        else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
180		else {y=x-one;i=2;}
181	    }
182	    switch(i) {
183	      case 0:
184		z = y*y;
185		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
186		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
187		p  = y*p1+p2;
188		r  += (p-(float)0.5*y); break;
189	      case 1:
190		z = y*y;
191		w = z*y;
192		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
193		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
194		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
195		p  = z*p1-(tt-w*(p2+y*p3));
196		r += (tf + p); break;
197	      case 2:
198		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
199		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
200		r += (-(float)0.5*y + p1/p2);
201	    }
202	}
203	else if(ix<0x41000000) { 			/* x < 8.0 */
204	    i = (int)x;
205	    y = x-(float)i;
206	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
207	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
208	    r = half*y+p/q;
209	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
210	    switch(i) {
211	    case 7: z *= (y+(float)6.0);	/* FALLTHRU */
212	    case 6: z *= (y+(float)5.0);	/* FALLTHRU */
213	    case 5: z *= (y+(float)4.0);	/* FALLTHRU */
214	    case 4: z *= (y+(float)3.0);	/* FALLTHRU */
215	    case 3: z *= (y+(float)2.0);	/* FALLTHRU */
216		    r += __ieee754_logf(z); break;
217	    }
218    /* 8.0 <= x < 2**58 */
219	} else if (ix < 0x5c800000) {
220	    t = __ieee754_logf(x);
221	    z = one/x;
222	    y = z*z;
223	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
224	    r = (x-half)*(t-one)+w;
225	} else
226    /* 2**58 <= x <= inf */
227	    r =  x*(__ieee754_logf(x)-one);
228	if(hx<0) r = nadj - r;
229	return r;
230}
231