e_log10.c revision 15122:b211a52a7439 
1/*
2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation.  Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/* __ieee754_log10(x)
27 * Return the base 10 logarithm of x
28 *
29 * Method :
30 *      Let log10_2hi = leading 40 bits of log10(2) and
31 *          log10_2lo = log10(2) - log10_2hi,
32 *          ivln10   = 1/log(10) rounded.
33 *      Then
34 *              n = ilogb(x),
35 *              if(n<0)  n = n+1;
36 *              x = scalbn(x,-n);
37 *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
38 *
39 * Note 1:
40 *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
41 *      mode must set to Round-to-Nearest.
42 * Note 2:
43 *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
44 *      log10 is monotonic at all binary break points.
45 *
46 * Special cases:
47 *      log10(x) is NaN with signal if x < 0;
48 *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
49 *      log10(NaN) is that NaN with no signal;
50 *      log10(10**N) = N  for N=0,1,...,22.
51 *
52 * Constants:
53 * The hexadecimal values are the intended ones for the following constants.
54 * The decimal values may be used, provided that the compiler will convert
55 * from decimal to binary accurately enough to produce the hexadecimal values
56 * shown.
57 */
58
59#include "fdlibm.h"
60
61#ifdef __STDC__
62static const double
63#else
64static double
65#endif
66two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
67ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
68log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
69log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
70
71static double zero   =  0.0;
72
73#ifdef __STDC__
74        double __ieee754_log10(double x)
75#else
76        double __ieee754_log10(x)
77        double x;
78#endif
79{
80        double y,z;
81        int i,k,hx;
82        unsigned lx;
83
84        hx = __HI(x);   /* high word of x */
85        lx = __LO(x);   /* low word of x */
86
87        k=0;
88        if (hx < 0x00100000) {                  /* x < 2**-1022  */
89            if (((hx&0x7fffffff)|lx)==0)
90                return -two54/zero;             /* log(+-0)=-inf */
91            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
92            k -= 54; x *= two54; /* subnormal number, scale up x */
93            hx = __HI(x);                /* high word of x */
94        }
95        if (hx >= 0x7ff00000) return x+x;
96        k += (hx>>20)-1023;
97        i  = ((unsigned)k&0x80000000)>>31;
98        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
99        y  = (double)(k+i);
100        __HI(x) = hx;
101        z  = y*log10_2lo + ivln10*__ieee754_log(x);
102        return  z+y*log10_2hi;
103}
104