1 /* $NetBSD: n_log10.c,v 1.7 2014/03/06 10:57:44 martin Exp $ */
2 /*
3 * Copyright (c) 1985, 1993
4 * The Regents of the University of California. All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 * may be used to endorse or promote products derived from this software
16 * without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 */
30
31 #ifndef lint
32 #if 0
33 static char sccsid[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93";
34 #endif
35 #endif /* not lint */
36
37 /* LOG10(X)
38 * RETURN THE BASE 10 LOGARITHM OF x
39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
40 * CODED IN C BY K.C. NG, 1/20/85;
41 * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
42 *
43 * Required kernel function:
44 * log(x)
45 *
46 * Method :
47 * log(x)
48 * log10(x) = --------- or [1/log(10)]*log(x)
49 * log(10)
50 *
51 * Note:
52 * [log(10)] rounded to 56 bits has error .0895 ulps,
53 * [1/log(10)] rounded to 53 bits has error .198 ulps;
54 * therefore, for better accuracy, in VAX D format, we divide
55 * log(x) by log(10), but in IEEE Double format, we multiply
56 * log(x) by [1/log(10)].
57 *
58 * Special cases:
59 * log10(x) is NaN with signal if x < 0;
60 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
61 * log10(NaN) is that NaN with no signal.
62 *
63 * Accuracy:
64 * log10(X) returns the exact log10(x) nearly rounded. In a test run
65 * with 1,536,000 random arguments on a VAX, the maximum observed
66 * error was 1.74 ulps (units in the last place).
67 *
68 * Constants:
69 * The hexadecimal values are the intended ones for the following constants.
70 * The decimal values may be used, provided that the compiler will convert
71 * from decimal to binary accurately enough to produce the hexadecimal values
72 * shown.
73 */
74
75 #define _LIBM_STATIC
76 #include "mathimpl.h"
77
78 vc(ln10hi, 2.3025850929940456790E0 ,5d8d,4113,a8ac,ddaa, 2, .935D8DDDAAA8AC)
79
80 ic(ivln10, 4.3429448190325181667E-1, -2, 1.BCB7B1526E50E)
81
82 #ifdef vccast
83 #define ln10hi vccast(ln10hi)
84 #endif
85
86
87 double
log10(double x)88 log10(double x)
89 {
90 #if defined(__vax__)||defined(tahoe)
91 return(log(x)/ln10hi);
92 #else /* defined(__vax__)||defined(tahoe) */
93 return(ivln10*log(x));
94 #endif /* defined(__vax__)||defined(tahoe) */
95 }
96
97 float
log10f(float x)98 log10f(float x)
99 {
100 #if defined(__vax__)||defined(tahoe)
101 return(logf(x)/ln10hi);
102 #else /* defined(__vax__)||defined(tahoe) */
103 return(ivln10*log(x));
104 #endif /* defined(__vax__)||defined(tahoe) */
105 }
106