66 lines
2.7 KiB
C
66 lines
2.7 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2013 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/************************************************************************/
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/* */
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/* MODULE_NAME:mplog.c */
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/* */
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/* FUNCTIONS: mplog */
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/* */
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/* FILES NEEDED: endian.h mpa.h mplog.h */
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/* mpexp.c */
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/* */
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/* Multi-Precision logarithm function subroutine (for precision p >= 4, */
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/* 2**(-1024) < x < 2**1024) and x is outside of the interval */
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/* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */
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/* multi-precision value of the input and y should be set into a multi- */
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/* precision value of an approximation of log(x) with relative error */
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/* bound of at most 2**(-52). The routine improves the accuracy of y. */
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/* */
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/************************************************************************/
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#include "endian.h"
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#include "mpa.h"
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void
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__mplog (mp_no *x, mp_no *y, int p)
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{
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int i, m;
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static const int mp[33] =
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{
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0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
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4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
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};
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mp_no mpt1, mpt2;
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/* Choose m. */
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m = mp[p];
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/* Perform m newton iterations to solve for y: exp(y) - x = 0. The
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iterations formula is: y(n + 1) = y(n) + (x * exp(-y(n)) - 1). */
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__cpy (y, &mpt1, p);
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for (i = 0; i < m; i++)
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{
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mpt1.d[0] = -mpt1.d[0];
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__mpexp (&mpt1, &mpt2, p);
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__mul (x, &mpt2, &mpt1, p);
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__sub (&mpt1, &mpone, &mpt2, p);
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__add (y, &mpt2, &mpt1, p);
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__cpy (&mpt1, y, p);
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}
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}
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