e_log10.c revision 117912 
1/* @(#)e_log10.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, 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#ifndef lint
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_log10.c 117912 2003-07-23 04:53:47Z peter $";
15#endif
16
17/* __ieee754_log10(x)
18 * Return the base 10 logarithm of x
19 *
20 * Method :
21 *	Let log10_2hi = leading 40 bits of log10(2) and
22 *	    log10_2lo = log10(2) - log10_2hi,
23 *	    ivln10   = 1/log(10) rounded.
24 *	Then
25 *		n = ilogb(x),
26 *		if(n<0)  n = n+1;
27 *		x = scalbn(x,-n);
28 *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
29 *
30 * Note 1:
31 *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
32 *	mode must set to Round-to-Nearest.
33 * Note 2:
34 *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
35 *	log10 is monotonic at all binary break points.
36 *
37 * Special cases:
38 *	log10(x) is NaN with signal if x < 0;
39 *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
40 *	log10(NaN) is that NaN with no signal;
41 *	log10(10**N) = N  for N=0,1,...,22.
42 *
43 * Constants:
44 * The hexadecimal values are the intended ones for the following constants.
45 * The decimal values may be used, provided that the compiler will convert
46 * from decimal to binary accurately enough to produce the hexadecimal values
47 * shown.
48 */
49
50#include "math.h"
51#include "math_private.h"
52
53static const double
54two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
55ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
56log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
57log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
58
59static const double zero   =  0.0;
60
61double
62__ieee754_log10(double x)
63{
64	double y,z;
65	int32_t i,k,hx;
66	u_int32_t lx;
67
68	EXTRACT_WORDS(hx,lx,x);
69
70        k=0;
71        if (hx < 0x00100000) {                  /* x < 2**-1022  */
72            if (((hx&0x7fffffff)|lx)==0)
73                return -two54/zero;             /* log(+-0)=-inf */
74            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
75            k -= 54; x *= two54; /* subnormal number, scale up x */
76	    GET_HIGH_WORD(hx,x);
77        }
78	if (hx >= 0x7ff00000) return x+x;
79	k += (hx>>20)-1023;
80	i  = ((u_int32_t)k&0x80000000)>>31;
81        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
82        y  = (double)(k+i);
83	SET_HIGH_WORD(x,hx);
84	z  = y*log10_2lo + ivln10*__ieee754_log(x);
85	return  z+y*log10_2hi;
86}
87