e_logf.c revision 251024 
1/* e_logf.c -- float version of e_log.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: head/lib/msun/src/e_logf.c 251024 2013-05-27 08:50:10Z das $");
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
24ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
25two25 =    3.355443200e+07,	/* 0x4c000000 */
26/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
27Lg1 =      0xaaaaaa.0p-24,	/* 0.66666662693 */
28Lg2 =      0xccce13.0p-25,	/* 0.40000972152 */
29Lg3 =      0x91e9ee.0p-25,	/* 0.28498786688 */
30Lg4 =      0xf89e26.0p-26;	/* 0.24279078841 */
31
32static const float zero   =  0.0;
33static volatile float vzero = 0.0;
34
35float
36__ieee754_logf(float x)
37{
38	float hfsq,f,s,z,R,w,t1,t2,dk;
39	int32_t k,ix,i,j;
40
41	GET_FLOAT_WORD(ix,x);
42
43	k=0;
44	if (ix < 0x00800000) {			/* x < 2**-126  */
45	    if ((ix&0x7fffffff)==0)
46		return -two25/vzero;		/* log(+-0)=-inf */
47	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
48	    k -= 25; x *= two25; /* subnormal number, scale up x */
49	    GET_FLOAT_WORD(ix,x);
50	}
51	if (ix >= 0x7f800000) return x+x;
52	k += (ix>>23)-127;
53	ix &= 0x007fffff;
54	i = (ix+(0x95f64<<3))&0x800000;
55	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
56	k += (i>>23);
57	f = x-(float)1.0;
58	if((0x007fffff&(0x8000+ix))<0xc000) {	/* -2**-9 <= f < 2**-9 */
59	    if(f==zero) {
60		if(k==0) {
61		    return zero;
62		} else {
63		    dk=(float)k;
64		    return dk*ln2_hi+dk*ln2_lo;
65		}
66	    }
67	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
68	    if(k==0) return f-R; else {dk=(float)k;
69	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
70	}
71 	s = f/((float)2.0+f);
72	dk = (float)k;
73	z = s*s;
74	i = ix-(0x6147a<<3);
75	w = z*z;
76	j = (0x6b851<<3)-ix;
77	t1= w*(Lg2+w*Lg4);
78	t2= z*(Lg1+w*Lg3);
79	i |= j;
80	R = t2+t1;
81	if(i>0) {
82	    hfsq=(float)0.5*f*f;
83	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
84		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
85	} else {
86	    if(k==0) return f-s*(f-R); else
87		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
88	}
89}
90