/* $NetBSD: n_log10.c,v 1.8 2024/07/16 14:52:50 riastradh Exp $ */
/*
* 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. 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
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* SUCH DAMAGE.
*/
/* 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.
*/
