1
2/*
3 *  M_APM  -  mapm_log.c
4 *
5 *  Copyright (C) 1999 - 2007   Michael C. Ring
6 *
7 *  Permission to use, copy, and distribute this software and its
8 *  documentation for any purpose with or without fee is hereby granted,
9 *  provided that the above copyright notice appear in all copies and
10 *  that both that copyright notice and this permission notice appear
11 *  in supporting documentation.
12 *
13 *  Permission to modify the software is granted. Permission to distribute
14 *  the modified code is granted. Modifications are to be distributed by
15 *  using the file 'license.txt' as a template to modify the file header.
16 *  'license.txt' is available in the official MAPM distribution.
17 *
18 *  This software is provided "as is" without express or implied warranty.
19 */
20
21/*
22 *      $Id: mapm_log.c,v 1.29 2007/12/03 01:44:19 mike Exp $
23 *
24 *      This file contains the LOG and LOG10 functions.
25 *
26 *      $Log: mapm_log.c,v $
27 *      Revision 1.29  2007/12/03 01:44:19  mike
28 *      Update license
29 *
30 *      Revision 1.28  2003/07/21 20:18:06  mike
31 *      Modify error messages to be in a consistent format.
32 *
33 *      Revision 1.27  2003/06/02 17:22:46  mike
34 *      put 'log_near_1' into it's own separate module
35 *
36 *      Revision 1.26  2003/05/12 17:42:46  mike
37 *      only check for 'near 1' if exponent is 0 or 1
38 *
39 *      Revision 1.25  2003/05/04 21:08:25  mike
40 *      *** empty log message ***
41 *
42 *      Revision 1.24  2003/05/01 21:58:34  mike
43 *      remove math.h
44 *
45 *      Revision 1.23  2003/05/01 21:39:09  mike
46 *      use 'abs' call
47 *
48 *      Revision 1.22  2003/05/01 19:44:57  mike
49 *      optimize log_near_1 by calculating fewer digits
50 *      on subsequent iterations
51 *
52 *      Revision 1.21  2003/03/31 22:00:56  mike
53 *      call generic error handling function
54 *
55 *      Revision 1.20  2003/03/30 22:57:13  mike
56 *      call a new iterative log function which is cubically convergent
57 *
58 *      Revision 1.19  2002/11/03 22:14:45  mike
59 *      Updated function parameters to use the modern style
60 *
61 *      Revision 1.18  2001/07/16 19:21:16  mike
62 *      add function M_free_all_log
63 *
64 *      Revision 1.17  2000/10/22 00:24:29  mike
65 *      minor optimization
66 *
67 *      Revision 1.16  2000/10/21 16:22:50  mike
68 *      use an improved log_near_1 algorithm
69 *
70 *      Revision 1.15  2000/10/20 16:49:33  mike
71 *      update algorithm for basic log function and add new
72 *      function when input is close to '1'
73 *
74 *      Revision 1.14  2000/09/23 19:48:21  mike
75 *      change divide call to reciprocal
76 *
77 *      Revision 1.13  2000/07/11 18:58:35  mike
78 *      do it right this time
79 *
80 *      Revision 1.12  2000/07/11 18:19:27  mike
81 *      estimate a better initial precision
82 *
83 *      Revision 1.11  2000/05/19 16:14:15  mike
84 *      update some comments
85 *
86 *      Revision 1.10  2000/05/17 23:47:35  mike
87 *      recompute a local copy of log E base 10 on the fly
88 *      if more precision is needed.
89 *
90 *      Revision 1.9  2000/03/27 21:44:12  mike
91 *      determine how many iterations should be required at
92 *      run time for log
93 *
94 *      Revision 1.8  1999/07/21 02:56:18  mike
95 *      added some comments
96 *
97 *      Revision 1.7  1999/07/19 00:28:51  mike
98 *      adjust local precision again
99 *
100 *      Revision 1.6  1999/07/19 00:10:34  mike
101 *      adjust local precision during iterative loop
102 *
103 *      Revision 1.5  1999/07/18 23:15:54  mike
104 *      change local precision dynamically and change
105 *      tolerance to integers for faster iterative routine.
106 *
107 *      Revision 1.4  1999/06/19 21:08:32  mike
108 *      changed local static variables to MAPM stack variables
109 *
110 *      Revision 1.3  1999/05/15 01:34:50  mike
111 *      add check for number of decimal places
112 *
113 *      Revision 1.2  1999/05/10 21:42:32  mike
114 *      added some comments
115 *
116 *      Revision 1.1  1999/05/10 20:56:31  mike
117 *      Initial revision
118 */
119
120#include "m_apm_lc.h"
121
122/****************************************************************************/
123/*
124        Calls the LOG function. The formula used is :
125
126        log10(x)  =  A * log(x) where A = log  (e)  [0.43429448190325...]
127                                             10
128*/
129void	m_apm_log10(M_APM rr, int places, M_APM aa)
130{
131int     dplaces;
132M_APM   tmp8, tmp9;
133
134tmp8 = M_get_stack_var();
135tmp9 = M_get_stack_var();
136
137dplaces = places + 4;
138M_check_log_places(dplaces + 45);
139
140m_apm_log(tmp9, dplaces, aa);
141m_apm_multiply(tmp8, tmp9, MM_lc_log10R);
142m_apm_round(rr, places, tmp8);
143M_restore_stack(2);                    /* restore the 2 locals we used here */
144}
145/****************************************************************************/
146void	m_apm_log(M_APM r, int places, M_APM a)
147{
148M_APM   tmp0, tmp1, tmp2;
149int	mexp, dplaces;
150
151if (a->m_apm_sign <= 0)
152  {
153   M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_log\', Negative argument");
154   M_set_to_zero(r);
155   return;
156  }
157
158tmp0 = M_get_stack_var();
159tmp1 = M_get_stack_var();
160tmp2 = M_get_stack_var();
161
162dplaces = places + 8;
163
164/*
165 *    if the input is real close to 1, use the series expansion
166 *    to compute the log.
167 *
168 *    0.9999 < a < 1.0001
169 */
170
171mexp = a->m_apm_exponent;
172
173if (mexp == 0 || mexp == 1)
174  {
175   m_apm_subtract(tmp0, a, MM_One);
176
177   if (tmp0->m_apm_sign == 0)    /* is input exactly 1 ?? */
178     {                           /* if so, result is 0    */
179      M_set_to_zero(r);
180      M_restore_stack(3);
181      return;
182     }
183
184   if (tmp0->m_apm_exponent <= -4)
185     {
186      M_log_near_1(r, places, tmp0);
187      M_restore_stack(3);
188      return;
189     }
190  }
191
192/* make sure our log(10) is accurate enough for this calculation */
193/* (and log(2) which is called from M_log_basic_iteration) */
194
195M_check_log_places(dplaces + 25);
196
197if (abs(mexp) <= 3)
198  {
199   M_log_basic_iteration(r, places, a);
200  }
201else
202  {
203   /*
204    *  use log (x * y) = log(x) + log(y)
205    *
206    *  here we use y = exponent of our base 10 number.
207    *
208    *  let 'C' = log(10) = 2.3025850929940....
209    *
210    *  then log(x * y) = log(x) + ( C * base_10_exponent )
211    */
212
213   m_apm_copy(tmp2, a);
214
215   mexp = tmp2->m_apm_exponent - 2;
216   tmp2->m_apm_exponent = 2;              /* force number between 10 & 100 */
217
218   M_log_basic_iteration(tmp0, dplaces, tmp2);
219
220   m_apm_set_long(tmp1, (long)mexp);
221   m_apm_multiply(tmp2, tmp1, MM_lc_log10);
222   m_apm_add(tmp1, tmp2, tmp0);
223
224   m_apm_round(r, places, tmp1);
225  }
226
227M_restore_stack(3);                    /* restore the 3 locals we used here */
228}
229/****************************************************************************/
230