1994-05-27 05:00:24 +00:00
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/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* LOG10(X)
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* RETURN THE BASE 10 LOGARITHM OF x
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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1995-05-30 05:51:47 +00:00
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* CODED IN C BY K.C. NG, 1/20/85;
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1994-05-27 05:00:24 +00:00
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* REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
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1995-05-30 05:51:47 +00:00
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*
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1994-05-27 05:00:24 +00:00
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* Required kernel function:
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* log(x)
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*
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* Method :
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* log(x)
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* log10(x) = --------- or [1/log(10)]*log(x)
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* log(10)
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*
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* Note:
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* [log(10)] rounded to 56 bits has error .0895 ulps,
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* [1/log(10)] rounded to 53 bits has error .198 ulps;
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1995-05-30 05:51:47 +00:00
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* therefore, for better accuracy, in VAX D format, we divide
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* log(x) by log(10), but in IEEE Double format, we multiply
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1994-05-27 05:00:24 +00:00
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* log(x) by [1/log(10)].
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*
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* Special cases:
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1995-05-30 05:51:47 +00:00
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* log10(x) is NaN with signal if x < 0;
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1994-05-27 05:00:24 +00:00
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* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
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* log10(NaN) is that NaN with no signal.
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*
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* Accuracy:
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* log10(X) returns the exact log10(x) nearly rounded. In a test run
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* with 1,536,000 random arguments on a VAX, the maximum observed
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* error was 1.74 ulps (units in the last place).
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#include "mathimpl.h"
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vc(ln10hi, 2.3025850929940456790E0 ,5d8d,4113,a8ac,ddaa, 2, .935D8DDDAAA8AC)
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ic(ivln10, 4.3429448190325181667E-1, -2, 1.BCB7B1526E50E)
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#ifdef vccast
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#define ln10hi vccast(ln10hi)
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#endif
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double log10(x)
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double x;
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{
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#if defined(vax)||defined(tahoe)
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return(log(x)/ln10hi);
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#else /* defined(vax)||defined(tahoe) */
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return(ivln10*log(x));
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#endif /* defined(vax)||defined(tahoe) */
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}
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