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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 */
129 void m_apm_log10(M_APM rr, int places, M_APM aa)
130 {
131 int dplaces;
132 M_APM tmp8, tmp9;
133
134 tmp8 = M_get_stack_var();
135 tmp9 = M_get_stack_var();
136
137 dplaces = places + 4;
138 M_check_log_places(dplaces + 45);
139
140 m_apm_log(tmp9, dplaces, aa);
141 m_apm_multiply(tmp8, tmp9, MM_lc_log10R);
142 m_apm_round(rr, places, tmp8);
143 M_restore_stack(2); /* restore the 2 locals we used here */
144 }
145 /****************************************************************************/
146 void m_apm_log(M_APM r, int places, M_APM a)
147 {
148 M_APM tmp0, tmp1, tmp2;
149 int mexp, dplaces;
150
151 if (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
158 tmp0 = M_get_stack_var();
159 tmp1 = M_get_stack_var();
160 tmp2 = M_get_stack_var();
161
162 dplaces = 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
171 mexp = a->m_apm_exponent;
172
173 if (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
195 M_check_log_places(dplaces + 25);
196
197 if (abs(mexp) <= 3)
198 {
199 M_log_basic_iteration(r, places, a);
200 }
201 else
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
227 M_restore_stack(3); /* restore the 3 locals we used here */
228 }
229 /****************************************************************************/