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("$FreeBSD$");
18 
19 #include "math.h"
20 #include "math_private.h"
21 
22 static const float
23 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
24 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
25 two25 =    3.355443200e+07,	/* 0x4c000000 */
26 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
27 Lg1 =      0xaaaaaa.0p-24,	/* 0.66666662693 */
28 Lg2 =      0xccce13.0p-25,	/* 0.40000972152 */
29 Lg3 =      0x91e9ee.0p-25,	/* 0.28498786688 */
30 Lg4 =      0xf89e26.0p-26;	/* 0.24279078841 */
31 
32 static const float zero   =  0.0;
33 static volatile float vzero = 0.0;
34 
35 float
__ieee754_logf(float x)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