src/libs/mapm/mapm_log.c

   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 /****************************************************************************/