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 /****************************************************************************/ 230