source: trunk/sys/libm/e_log10.c @ 1

Last change on this file since 1 was 1, checked in by alain, 5 years ago

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1
2/* @(#)e_log10.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, 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 log10(2) and
19 *          log10_2lo = log10(2) - log10_2hi,
20 *          ivln10   = 1/log(10) rounded.
21 *      Then
22 *              n = ilogb(x),
23 *              if(n<0)  n = n+1;
24 *              x = scalbn(x,-n);
25 *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
26 *
27 * Note 1:
28 *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
29 *      mode must set to Round-to-Nearest.
30 * Note 2:
31 *      [1/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; 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 <libm/fdlibm.h>
48
49#ifdef __STDC__
50static const double
51#else
52static double
53#endif
54one       = 1.0,
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 double zero   =  0.0;
61
62#ifdef __STDC__
63        double __ieee754_log10(double x)
64#else
65        double __ieee754_log10(x)
66        double x;
67#endif
68{
69        double y,z;
70        int i,k,n0,hx;
71        unsigned lx;
72
73        n0 = ((*(int*)&one)>>29)^1;     /* high word index */
74        hx = *(n0+(unsigned*)&x);       /* high word of x */
75        lx = *(1-n0+(unsigned*)&x);     /* low word of x */
76
77        k=0;
78        if (hx < 0x00100000) {                  /* x < 2**-1022  */
79            if (((hx&0x7fffffff)|lx)==0)
80                return -two54/zero;             /* log(+-0)=-inf */
81            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
82            k -= 54; x *= two54; /* subnormal number, scale up x */
83            hx = *(n0+(int*)&x);                /* high word of x */
84        }
85        if (hx >= 0x7ff00000) return x+x;
86        k += (hx>>20)-1023;
87        i  = ((unsigned)k&0x80000000)>>31;
88        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
89        y  = (double)(k+i);
90        *(n0+(int*)&x) = hx;
91        z  = y*log10_2lo + ivln10*__ieee754_log(x);
92        return  z+y*log10_2hi;
93}
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