e_lgammaf_r.c revision 271779 
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: stable/10/lib/msun/src/e_lgammaf_r.c 271779 2014-09-18 15:10:22Z tijl $");
18
19#include "math.h"
20#include "math_private.h"
21
22static const volatile float vzero = 0;
23
24static const float
25zero=  0.0000000000e+00,
26half=  5.0000000000e-01, /* 0x3f000000 */
27one =  1.0000000000e+00, /* 0x3f800000 */
28pi  =  3.1415927410e+00, /* 0x40490fdb */
29a0  =  7.7215664089e-02, /* 0x3d9e233f */
30a1  =  3.2246702909e-01, /* 0x3ea51a66 */
31a2  =  6.7352302372e-02, /* 0x3d89f001 */
32a3  =  2.0580807701e-02, /* 0x3ca89915 */
33a4  =  7.3855509982e-03, /* 0x3bf2027e */
34a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
35a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
36a7  =  5.1006977446e-04, /* 0x3a05b634 */
37a8  =  2.2086278477e-04, /* 0x39679767 */
38a9  =  1.0801156895e-04, /* 0x38e28445 */
39a10 =  2.5214456400e-05, /* 0x37d383a2 */
40a11 =  4.4864096708e-05, /* 0x383c2c75 */
41tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
42tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
43/* tt = -(tail of tf) */
44tt  =  6.6971006518e-09, /* 0x31e61c52 */
45t0  =  4.8383611441e-01, /* 0x3ef7b95e */
46t1  = -1.4758771658e-01, /* 0xbe17213c */
47t2  =  6.4624942839e-02, /* 0x3d845a15 */
48t3  = -3.2788541168e-02, /* 0xbd064d47 */
49t4  =  1.7970675603e-02, /* 0x3c93373d */
50t5  = -1.0314224288e-02, /* 0xbc28fcfe */
51t6  =  6.1005386524e-03, /* 0x3bc7e707 */
52t7  = -3.6845202558e-03, /* 0xbb7177fe */
53t8  =  2.2596477065e-03, /* 0x3b141699 */
54t9  = -1.4034647029e-03, /* 0xbab7f476 */
55t10 =  8.8108185446e-04, /* 0x3a66f867 */
56t11 = -5.3859531181e-04, /* 0xba0d3085 */
57t12 =  3.1563205994e-04, /* 0x39a57b6b */
58t13 = -3.1275415677e-04, /* 0xb9a3f927 */
59t14 =  3.3552918467e-04, /* 0x39afe9f7 */
60u0  = -7.7215664089e-02, /* 0xbd9e233f */
61u1  =  6.3282704353e-01, /* 0x3f2200f4 */
62u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
63u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
64u4  =  2.2896373272e-01, /* 0x3e6a7578 */
65u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
66v1  =  2.4559779167e+00, /* 0x401d2ebe */
67v2  =  2.1284897327e+00, /* 0x4008392d */
68v3  =  7.6928514242e-01, /* 0x3f44efdf */
69v4  =  1.0422264785e-01, /* 0x3dd572af */
70v5  =  3.2170924824e-03, /* 0x3b52d5db */
71s0  = -7.7215664089e-02, /* 0xbd9e233f */
72s1  =  2.1498242021e-01, /* 0x3e5c245a */
73s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
74s3  =  1.4635047317e-01, /* 0x3e15dce6 */
75s4  =  2.6642270386e-02, /* 0x3cda40e4 */
76s5  =  1.8402845599e-03, /* 0x3af135b4 */
77s6  =  3.1947532989e-05, /* 0x3805ff67 */
78r1  =  1.3920053244e+00, /* 0x3fb22d3b */
79r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
80r3  =  1.7193385959e-01, /* 0x3e300f6e */
81r4  =  1.8645919859e-02, /* 0x3c98bf54 */
82r5  =  7.7794247773e-04, /* 0x3a4beed6 */
83r6  =  7.3266842264e-06, /* 0x36f5d7bd */
84w0  =  4.1893854737e-01, /* 0x3ed67f1d */
85w1  =  8.3333335817e-02, /* 0x3daaaaab */
86w2  = -2.7777778450e-03, /* 0xbb360b61 */
87w3  =  7.9365057172e-04, /* 0x3a500cfd */
88w4  = -5.9518753551e-04, /* 0xba1c065c */
89w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
90w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
91
92static float
93sin_pif(float x)
94{
95	volatile float vz;
96	float y,z;
97	int n;
98
99	y = -x;
100
101	vz = y+0x1p23F;			/* depend on 0 <= y < 0x1p23 */
102	z = vz-0x1p23F;			/* rintf(y) for the above range */
103	if (z == y)
104	    return zero;
105
106	vz = y+0x1p21F;
107	GET_FLOAT_WORD(n,vz);		/* bits for rounded y (units 0.25) */
108	z = vz-0x1p21F;			/* y rounded to a multiple of 0.25 */
109	if (z > y) {
110	    z -= 0.25F;			/* adjust to round down */
111	    n--;
112	}
113	n &= 7;				/* octant of y mod 2 */
114	y = y - z + n * 0.25F;		/* y mod 2 */
115
116	switch (n) {
117	    case 0:   y =  __kernel_sindf(pi*y); break;
118	    case 1:
119	    case 2:   y =  __kernel_cosdf(pi*((float)0.5-y)); break;
120	    case 3:
121	    case 4:   y =  __kernel_sindf(pi*(one-y)); break;
122	    case 5:
123	    case 6:   y = -__kernel_cosdf(pi*(y-(float)1.5)); break;
124	    default:  y =  __kernel_sindf(pi*(y-(float)2.0)); break;
125	    }
126	return -y;
127}
128
129
130float
131__ieee754_lgammaf_r(float x, int *signgamp)
132{
133	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
134	int32_t hx;
135	int i,ix;
136
137	GET_FLOAT_WORD(hx,x);
138
139    /* purge off +-inf, NaN, +-0, tiny and negative arguments */
140	*signgamp = 1;
141	ix = hx&0x7fffffff;
142	if(ix>=0x7f800000) return x*x;
143	if(ix==0) return one/vzero;
144	if(ix<0x35000000) {	/* |x|<2**-21, return -log(|x|) */
145	    if(hx<0) {
146	        *signgamp = -1;
147	        return -__ieee754_logf(-x);
148	    } else return -__ieee754_logf(x);
149	}
150	if(hx<0) {
151	    if(ix>=0x4b000000) 	/* |x|>=2**23, must be -integer */
152		return one/vzero;
153	    t = sin_pif(x);
154	    if(t==zero) return one/vzero; /* -integer */
155	    nadj = __ieee754_logf(pi/fabsf(t*x));
156	    if(t<zero) *signgamp = -1;
157	    x = -x;
158	}
159
160    /* purge off 1 and 2 */
161	if (ix==0x3f800000||ix==0x40000000) r = 0;
162    /* for x < 2.0 */
163	else if(ix<0x40000000) {
164	    if(ix<=0x3f666666) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
165		r = -__ieee754_logf(x);
166		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
167		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
168	  	else {y = x; i=2;}
169	    } else {
170	  	r = zero;
171	        if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
172	        else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
173		else {y=x-one;i=2;}
174	    }
175	    switch(i) {
176	      case 0:
177		z = y*y;
178		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
179		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
180		p  = y*p1+p2;
181		r  += (p-(float)0.5*y); break;
182	      case 1:
183		z = y*y;
184		w = z*y;
185		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
186		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
187		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
188		p  = z*p1-(tt-w*(p2+y*p3));
189		r += (tf + p); break;
190	      case 2:
191		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
192		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
193		r += (-(float)0.5*y + p1/p2);
194	    }
195	}
196	else if(ix<0x41000000) { 			/* x < 8.0 */
197	    i = (int)x;
198	    y = x-(float)i;
199	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
200	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
201	    r = half*y+p/q;
202	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
203	    switch(i) {
204	    case 7: z *= (y+(float)6.0);	/* FALLTHRU */
205	    case 6: z *= (y+(float)5.0);	/* FALLTHRU */
206	    case 5: z *= (y+(float)4.0);	/* FALLTHRU */
207	    case 4: z *= (y+(float)3.0);	/* FALLTHRU */
208	    case 3: z *= (y+(float)2.0);	/* FALLTHRU */
209		    r += __ieee754_logf(z); break;
210	    }
211    /* 8.0 <= x < 2**58 */
212	} else if (ix < 0x5c800000) {
213	    t = __ieee754_logf(x);
214	    z = one/x;
215	    y = z*z;
216	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
217	    r = (x-half)*(t-one)+w;
218	} else
219    /* 2**58 <= x <= inf */
220	    r =  x*(__ieee754_logf(x)-one);
221	if(hx<0) r = nadj - r;
222	return r;
223}
224