| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001-2014 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); |
| } |
| } |