Subversion Repositories shark

Rev

Rev 1618 | Details | Compare with Previous | Last modification | View Log | RSS feed

Rev Author Line No. Line
2 pj 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
14
static char rcsid[] = "$\Id: e_log10.c,v 1.3.6.1 1997/02/23 11:03:06 joerg Exp $";
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
 
53
#ifdef __STDC__
54
static const double
55
#else
56
static double
57
#endif
58
two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
59
ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
60
log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
61
log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
62
 
63
#ifdef __STDC__
64
static const double zero   =  0.0;
65
#else
66
static double zero   =  0.0;
67
#endif
68
 
69
#ifdef __STDC__
70
        double __generic___ieee754_log10(double x)
71
#else
72
        double __generic___ieee754_log10(x)
73
        double x;
74
#endif
75
{
76
        double y,z;
77
        int32_t i,k,hx;
78
        u_int32_t lx;
79
 
80
        EXTRACT_WORDS(hx,lx,x);
81
 
82
        k=0;
83
        if (hx < 0x00100000) {                  /* x < 2**-1022  */
84
            if (((hx&0x7fffffff)|lx)==0)
85
                return -two54/zero;             /* log(+-0)=-inf */
86
            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
87
            k -= 54; x *= two54; /* subnormal number, scale up x */
88
            GET_HIGH_WORD(hx,x);
89
        }
90
        if (hx >= 0x7ff00000) return x+x;
91
        k += (hx>>20)-1023;
92
        i  = ((u_int32_t)k&0x80000000)>>31;
93
        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
94
        y  = (double)(k+i);
95
        SET_HIGH_WORD(x,hx);
96
        z  = y*log10_2lo + ivln10*__ieee754_log(x);
97
        return  z+y*log10_2hi;
98
}