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/*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#ifndef lint
static char sccsid[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93";
#endif /* not lint */
/* LOG10(X)
* RETURN THE BASE 10 LOGARITHM OF x
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/20/85;
* REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
*
* Required kernel function:
* log(x)
*
* Method :
* log(x)
* log10(x) = --------- or [1/log(10)]*log(x)
* log(10)
*
* Note:
* [log(10)] rounded to 56 bits has error .0895 ulps,
* [1/log(10)] rounded to 53 bits has error .198 ulps;
* therefore, for better accuracy, in VAX D format, we divide
* log(x) by log(10), but in IEEE Double format, we multiply
* log(x) by [1/log(10)].
*
* Special cases:
* log10(x) is NaN with signal if x < 0;
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
* log10(NaN) is that NaN with no signal.
*
* Accuracy:
* log10(X) returns the exact log10(x) nearly rounded. In a test run
* with 1,536,000 random arguments on a VAX, the maximum observed
* error was 1.74 ulps (units in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#include "mathimpl.h"
vc(ln10hi, 2.3025850929940456790E0 ,5d8d,4113,a8ac,ddaa, 2, .935D8DDDAAA8AC)
ic(ivln10, 4.3429448190325181667E-1, -2, 1.BCB7B1526E50E)
#ifdef vccast
#define ln10hi vccast(ln10hi)
#endif
double log10(x)
double x;
{
#if defined(vax)||defined(tahoe)
return(log(x)/ln10hi);
#else /* defined(vax)||defined(tahoe) */
return(ivln10*log(x));
#endif /* defined(vax)||defined(tahoe) */
}
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