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 "math.h"
17 #include "math_private.h"
18 
19 static const float
20 ln2 = 0.6931471805599452862268,
21 two25 =    3.355443200e+07,	/* 0x4c000000 */
22 Lg1 = 6.6666668653e-01,	/* 3F2AAAAB */
23 Lg2 = 4.0000000596e-01,	/* 3ECCCCCD */
24 Lg3 = 2.8571429849e-01, /* 3E924925 */
25 Lg4 = 2.2222198546e-01, /* 3E638E29 */
26 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
27 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
28 Lg7 = 1.4798198640e-01; /* 3E178897 */
29 
30 static const float zero   =  0.0;
31 
32 float
33 log2f(float x)
34 {
35 	float hfsq,f,s,z,R,w,t1,t2,dk;
36 	int32_t k,ix,i,j;
37 
38 	GET_FLOAT_WORD(ix,x);
39 
40 	k=0;
41 	if (ix < 0x00800000) {			/* x < 2**-126  */
42 	    if ((ix&0x7fffffff)==0)
43 		return -two25/zero;		/* log(+-0)=-inf */
44 	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
45 	    k -= 25; x *= two25; /* subnormal number, scale up x */
46 	    GET_FLOAT_WORD(ix,x);
47 	}
48 	if (ix >= 0x7f800000) return x+x;
49 	k += (ix>>23)-127;
50 	ix &= 0x007fffff;
51 	i = (ix+(0x95f64<<3))&0x800000;
52 	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
53 	k += (i>>23);
54 	dk = (float)k;
55 	f = x-(float)1.0;
56 	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
57 	    if (f==zero)
58 		    return (dk);
59 	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
60 	    return (dk-(R-f)/ln2);
61 	}
62  	s = f/((float)2.0+f);
63 	z = s*s;
64 	i = ix-(0x6147a<<3);
65 	w = z*z;
66 	j = (0x6b851<<3)-ix;
67 	t1= w*(Lg2+w*(Lg4+w*Lg6));
68 	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
69 	i |= j;
70 	R = t2+t1;
71 	if(i>0) {
72 	    hfsq=(float)0.5*f*f;
73 	    return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
74 	} else
75 		return (dk-((s*(f-R))-f)/ln2);
76 }
77