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/* __ieee754_log10(x)
15 * Return the base 10 logarithm of x
16 *
17 * Method :
18 *	Let log10_2hi = leading 40 bits of ieee_log10(2) and
19 *	    log10_2lo = ieee_log10(2) - log10_2hi,
20 *	    ivln10   = 1/ieee_log(10) rounded.
21 *	Then
22 *		n = ieee_ilogb(x),
23 *		if(n<0)  n = n+1;
24 *		x = ieee_scalbn(x,-n);
25 *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*ieee_log(x))
26 *
27 * Note 1:
28 *	To guarantee ieee_log10(10**n)=n, where 10**n is normal, the rounding
29 *	mode must set to Round-to-Nearest.
30 * Note 2:
31 *	[1/ieee_log(10)] rounded to 53 bits has error  .198   ulps;
32 *	log10 is monotonic at all binary break points.
33 *
34 * Special cases:
35 *	log10(x) is NaN with signal if x < 0;
36 *	log10(+INF) is +INF with no signal; ieee_log10(0) is -INF with signal;
37 *	log10(NaN) is that NaN with no signal;
38 *	log10(10**N) = N  for N=0,1,...,22.
39 *
40 * Constants:
41 * The hexadecimal values are the intended ones for the following constants.
42 * The decimal values may be used, provided that the compiler will convert
43 * from decimal to binary accurately enough to produce the hexadecimal values
44 * shown.
45 */
46
47#include "fdlibm.h"
48
49#ifdef __STDC__
50static const double
51#else
52static double
53#endif
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 double zero   =  0.0;
60
61#ifdef __STDC__
62	double __ieee754_log10(double x)
63#else
64	double __ieee754_log10(x)
65	double x;
66#endif
67{
68	double y,z;
69	int i,k,hx;
70	unsigned lx;
71
72	hx = __HI(x);	/* high word of x */
73	lx = __LO(x);	/* low word of x */
74
75        k=0;
76        if (hx < 0x00100000) {                  /* x < 2**-1022  */
77            if (((hx&0x7fffffff)|lx)==0)
78                return -two54/zero;             /* ieee_log(+-0)=-inf */
79            if (hx<0) return (x-x)/zero;        /* ieee_log(-#) = NaN */
80            k -= 54; x *= two54; /* subnormal number, scale up x */
81            hx = __HI(x);                /* high word of x */
82        }
83	if (hx >= 0x7ff00000) return x+x;
84	k += (hx>>20)-1023;
85	i  = ((unsigned)k&0x80000000)>>31;
86        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
87        y  = (double)(k+i);
88        __HI(x) = hx;
89	z  = y*log10_2lo + ivln10*__ieee754_log(x);
90	return  z+y*log10_2hi;
91}
92