82 lines
2.7 KiB
C
82 lines
2.7 KiB
C
/*
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted provided
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* that: (1) source distributions retain this entire copyright notice and
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* comment, and (2) distributions including binaries display the following
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* acknowledgement: ``This product includes software developed by the
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* University of California, Berkeley and its contributors'' in the
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* documentation or other materials provided with the distribution and in
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* all advertising materials mentioning features or use of this software.
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* Neither the name of the University nor the names of its contributors may
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* be used to endorse or promote products derived from this software without
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* specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)log10.c 5.6 (Berkeley) 10/9/90";
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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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* CODED IN C BY K.C. NG, 1/20/85;
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* REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
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*
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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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* 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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* log(x) by [1/log(10)].
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*
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* Special cases:
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* log10(x) is NaN with signal if x < 0;
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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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