1
2/* @(#)e_log10.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#ifndef lint
15static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.11 2005/02/04 18:26:06 das Exp $";
16#endif
17
18/* __ieee754_log10(x)
19 * Return the base 10 logarithm of x
20 *
21 * Method :
22 *	Let log10_2hi = leading 40 bits of log10(2) and
23 *	    log10_2lo = log10(2) - log10_2hi,
24 *	    ivln10   = 1/log(10) rounded.
25 *	Then
26 *		n = ilogb(x),
27 *		if(n<0)  n = n+1;
28 *		x = scalbn(x,-n);
29 *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
30 *
31 * Note 1:
32 *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
33 *	mode must set to Round-to-Nearest.
34 * Note 2:
35 *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
36 *	log10 is monotonic at all binary break points.
37 *
38 * Special cases:
39 *	log10(x) is NaN with signal if x < 0;
40 *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
41 *	log10(NaN) is that NaN with no signal;
42 *	log10(10**N) = N  for N=0,1,...,22.
43 *
44 * Constants:
45 * The hexadecimal values are the intended ones for the following constants.
46 * The decimal values may be used, provided that the compiler will convert
47 * from decimal to binary accurately enough to produce the hexadecimal values
48 * shown.
49 */
50
51#include "math.h"
52#include "math_private.h"
53
54static const double
55two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
56ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
57log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
58log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
59
60static const double zero   =  0.0;
61
62double
63__ieee754_log10(double x)
64{
65	double y,z;
66	int32_t i,k,hx;
67	u_int32_t lx;
68
69	EXTRACT_WORDS(hx,lx,x);
70
71        k=0;
72        if (hx < 0x00100000) {                  /* x < 2**-1022  */
73            if (((hx&0x7fffffff)|lx)==0)
74                return -two54/zero;             /* log(+-0)=-inf */
75            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
76            k -= 54; x *= two54; /* subnormal number, scale up x */
77	    GET_HIGH_WORD(hx,x);
78        }
79	if (hx >= 0x7ff00000) return x+x;
80	k += (hx>>20)-1023;
81	i  = ((u_int32_t)k&0x80000000)>>31;
82        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
83        y  = (double)(k+i);
84	SET_HIGH_WORD(x,hx);
85	z  = y*log10_2lo + ivln10*__ieee754_log(x);
86	return  z+y*log10_2hi;
87}
88