1 | /* |
2 | * IBM Accurate Mathematical Library |
3 | * written by International Business Machines Corp. |
4 | * Copyright (C) 2001-2018 Free Software Foundation, Inc. |
5 | * |
6 | * This program is free software; you can redistribute it and/or modify |
7 | * it under the terms of the GNU Lesser General Public License as published by |
8 | * the Free Software Foundation; either version 2.1 of the License, or |
9 | * (at your option) any later version. |
10 | * |
11 | * This program is distributed in the hope that it will be useful, |
12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
14 | * GNU Lesser General Public License for more details. |
15 | * |
16 | * You should have received a copy of the GNU Lesser General Public License |
17 | * along with this program; if not, see <http://www.gnu.org/licenses/>. |
18 | */ |
19 | /************************************************************************/ |
20 | /* */ |
21 | /* MODULE_NAME:mplog.c */ |
22 | /* */ |
23 | /* FUNCTIONS: mplog */ |
24 | /* */ |
25 | /* FILES NEEDED: endian.h mpa.h mplog.h */ |
26 | /* mpexp.c */ |
27 | /* */ |
28 | /* Multi-Precision logarithm function subroutine (for precision p >= 4, */ |
29 | /* 2**(-1024) < x < 2**1024) and x is outside of the interval */ |
30 | /* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */ |
31 | /* multi-precision value of the input and y should be set into a multi- */ |
32 | /* precision value of an approximation of log(x) with relative error */ |
33 | /* bound of at most 2**(-52). The routine improves the accuracy of y. */ |
34 | /* */ |
35 | /************************************************************************/ |
36 | #include "endian.h" |
37 | #include "mpa.h" |
38 | |
39 | void |
40 | __mplog (mp_no *x, mp_no *y, int p) |
41 | { |
42 | int i, m; |
43 | static const int mp[33] = |
44 | { |
45 | 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, |
46 | 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 |
47 | }; |
48 | mp_no mpt1, mpt2; |
49 | |
50 | /* Choose m. */ |
51 | m = mp[p]; |
52 | |
53 | /* Perform m newton iterations to solve for y: exp(y) - x = 0. The |
54 | iterations formula is: y(n + 1) = y(n) + (x * exp(-y(n)) - 1). */ |
55 | __cpy (y, &mpt1, p); |
56 | for (i = 0; i < m; i++) |
57 | { |
58 | mpt1.d[0] = -mpt1.d[0]; |
59 | __mpexp (&mpt1, &mpt2, p); |
60 | __mul (x, &mpt2, &mpt1, p); |
61 | __sub (&mpt1, &__mpone, &mpt2, p); |
62 | __add (y, &mpt2, &mpt1, p); |
63 | __cpy (&mpt1, y, p); |
64 | } |
65 | } |
66 | |