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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2018 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
/************************************************************************/
/* */
/* MODULE_NAME:mplog.c */
/* */
/* FUNCTIONS: mplog */
/* */
/* FILES NEEDED: endian.h mpa.h mplog.h */
/* mpexp.c */
/* */
/* Multi-Precision logarithm function subroutine (for precision p >= 4, */
/* 2**(-1024) < x < 2**1024) and x is outside of the interval */
/* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */
/* multi-precision value of the input and y should be set into a multi- */
/* precision value of an approximation of log(x) with relative error */
/* bound of at most 2**(-52). The routine improves the accuracy of y. */
/* */
/************************************************************************/
#include "endian.h"
#include "mpa.h"
void
__mplog (mp_no *x, mp_no *y, int p)
{
int i, m;
static const int mp[33] =
{
0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
};
mp_no mpt1, mpt2;
/* Choose m. */
m = mp[p];
/* Perform m newton iterations to solve for y: exp(y) - x = 0. The
iterations formula is: y(n + 1) = y(n) + (x * exp(-y(n)) - 1). */
__cpy (y, &mpt1, p);
for (i = 0; i < m; i++)
{
mpt1.d[0] = -mpt1.d[0];
__mpexp (&mpt1, &mpt2, p);
__mul (x, &mpt2, &mpt1, p);
__sub (&mpt1, &__mpone, &mpt2, p);
__add (y, &mpt2, &mpt1, p);
__cpy (&mpt1, y, p);
}
}
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