xref: /minix3/lib/libm/src/e_log2.c (revision 2fe8fb192fe7e8720e3e7a77f928da545e872a6a)
1 
2 /* @(#)e_log.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 #include <sys/cdefs.h>
15 #if defined(LIBM_SCCS) && !defined(lint)
16 __RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
17 #endif
18 
19 #include "math.h"
20 #include "math_private.h"
21 
22 static const double
23 ln2 = 0.6931471805599452862268,
24 two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
25 Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
26 Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
27 Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
28 Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
29 Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
30 Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
31 Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
32 
33 static const double zero   =  0.0;
34 
35 double
__ieee754_log2(double x)36 __ieee754_log2(double x)
37 {
38 	double hfsq,f,s,z,R,w,t1,t2,dk;
39 	int32_t k,hx,i,j;
40 	u_int32_t lx;
41 
42 	EXTRACT_WORDS(hx,lx,x);
43 
44 	k=0;
45 	if (hx < 0x00100000) {			/* x < 2**-1022  */
46 	    if (((hx&0x7fffffff)|lx)==0)
47 		return -two54/zero;		/* log(+-0)=-inf */
48 	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
49 	    k -= 54; x *= two54; /* subnormal number, scale up x */
50 	    GET_HIGH_WORD(hx,x);
51 	}
52 	if (hx >= 0x7ff00000) return x+x;
53 	k += (hx>>20)-1023;
54 	hx &= 0x000fffff;
55 	i = (hx+0x95f64)&0x100000;
56 	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
57 	k += (i>>20);
58 	f = x-1.0;
59 	dk = (double)k;
60 	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
61 	    if (f==zero)
62 		    return (dk);
63 	    R = f*f*(0.5-0.33333333333333333*f);
64 	    return (dk-(R-f)/ln2);
65 	}
66  	s = f/(2.0+f);
67 	z = s*s;
68 	i = hx-0x6147a;
69 	w = z*z;
70 	j = 0x6b851-hx;
71 	t1= w*(Lg2+w*(Lg4+w*Lg6));
72 	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
73 	i |= j;
74 	R = t2+t1;
75 	if(i>0) {
76 	    hfsq=0.5*f*f;
77 	    return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
78 	} else
79 		return (dk-((s*(f-R))-f)/ln2);
80 }
81