1 /* $NetBSD: n_log10.c,v 1.7 2014/03/06 10:57:44 martin Exp $ */
3 * Copyright (c) 1985, 1993
4 * The Regents of the University of California. All rights reserved.
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7 * modification, are permitted provided that the following conditions
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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.
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
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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
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33 static char sccsid
[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93";
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.
43 * Required kernel function:
48 * log10(x) = --------- or [1/log(10)]*log(x)
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)].
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.
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).
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
78 vc(ln10hi
, 2.3025850929940456790E0
,5d8d
,4113,a8ac
,ddaa
, 2, .935D8DDDAAA8AC
)
80 ic(ivln10
, 4.3429448190325181667E-1, -2, 1.BCB7B1526E50E
)
83 #define ln10hi vccast(ln10hi)
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) */
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) */