xref: /openbsd-src/lib/libm/src/e_log2.c (revision d13be5d47e4149db2549a9828e244d59dbc43f15)
1 /* @(#)e_log.c 1.3 95/01/18 */
2 /*
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  *
6  * Developed at SunSoft, a Sun Microsystems, Inc. business.
7  * Permission to use, copy, modify, and distribute this
8  * software is freely granted, provided that this notice
9  * is preserved.
10  * ====================================================
11  */
12 
13 /* LINTLIBRARY */
14 
15 #include <sys/cdefs.h>
16 #include <float.h>
17 #include <math.h>
18 
19 #include "math_private.h"
20 
21 static const double
22 ln2 = 0.6931471805599452862268,
23 two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
24 Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
25 Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
26 Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
27 Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
28 Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
29 Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
30 Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
31 
32 static const double zero   =  0.0;
33 
34 double
35 log2(double x)
36 {
37 	double hfsq,f,s,z,R,w,t1,t2,dk;
38 	int32_t k,hx,i,j;
39 	u_int32_t lx;
40 
41 	EXTRACT_WORDS(hx,lx,x);
42 
43 	k=0;
44 	if (hx < 0x00100000) {			/* x < 2**-1022  */
45 	    if (((hx&0x7fffffff)|lx)==0)
46 		return -two54/zero;		/* log(+-0)=-inf */
47 	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
48 	    k -= 54; x *= two54; /* subnormal number, scale up x */
49 	    GET_HIGH_WORD(hx,x);
50 	}
51 	if (hx >= 0x7ff00000) return x+x;
52 	k += (hx>>20)-1023;
53 	hx &= 0x000fffff;
54 	i = (hx+0x95f64)&0x100000;
55 	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
56 	k += (i>>20);
57 	f = x-1.0;
58 	dk = (double)k;
59 	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
60 	    if (f==zero)
61 		    return (dk);
62 	    R = f*f*(0.5-0.33333333333333333*f);
63 	    return (dk-(R-f)/ln2);
64 	}
65  	s = f/(2.0+f);
66 	z = s*s;
67 	i = hx-0x6147a;
68 	w = z*z;
69 	j = 0x6b851-hx;
70 	t1= w*(Lg2+w*(Lg4+w*Lg6));
71 	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
72 	i |= j;
73 	R = t2+t1;
74 	if(i>0) {
75 	    hfsq=0.5*f*f;
76 	    return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
77 	} else
78 		return (dk-((s*(f-R))-f)/ln2);
79 }
80 
81 #if	LDBL_MANT_DIG == 53
82 #ifdef	lint
83 /* PROTOLIB1 */
84 long double log2l(long double);
85 #else	/* lint */
86 __weak_alias(log2l, log2);
87 #endif	/* lint */
88 #endif	/* LDBL_MANT_DIG == 53 */
89