src/libs/mapm/mapm_lg4.c

   1
   2 /*
   3  *  M_APM  -  mapm_lg4.c
   4  *
   5  *  Copyright (C) 2003 - 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_lg4.c,v 1.3 2007/12/03 01:43:32 mike Exp $
  23  *
  24  *      This file contains the LOG_NEAR_1 function.
  25  *
  26  *      $Log: mapm_lg4.c,v $
  27  *      Revision 1.3  2007/12/03 01:43:32  mike
  28  *      Update license
  29  *
  30  *      Revision 1.2  2003/06/02 18:08:45  mike
  31  *      tweak decimal places and add comments
  32  *
  33  *      Revision 1.1  2003/06/02 17:27:26  mike
  34  *      Initial revision
  35  */
  36
  37 #include "m_apm_lc.h"
  38
  39 /****************************************************************************/
  40 /*
  41         calculate log (1 + x) with the following series:
  42
  43               x
  44         y = -----      ( |y| < 1 )
  45             x + 2
  46
  47
  48             [ 1 + y ]                 y^3     y^5     y^7
  49         log [-------]  =  2 * [ y  +  ---  +  ---  +  ---  ... ]
  50             [ 1 - y ]                  3       5       7
  51
  52 */
  53 void    M_log_near_1(M_APM rr, int places, M_APM xx)
  54 {
  55 M_APM   tmp0, tmp1, tmp2, tmpS, term;
  56 int     tolerance, dplaces, local_precision;
  57 long    m1;
  58
  59 tmp0 = M_get_stack_var();
  60 tmp1 = M_get_stack_var();
  61 tmp2 = M_get_stack_var();
  62 tmpS = M_get_stack_var();
  63 term = M_get_stack_var();
  64
  65 tolerance = xx->m_apm_exponent - (places + 6);
  66 dplaces   = (places + 12) - xx->m_apm_exponent;
  67
  68 m_apm_add(tmp0, xx, MM_Two);
  69 m_apm_divide(tmpS, (dplaces + 6), xx, tmp0);
  70
  71 m_apm_copy(term, tmpS);
  72 m_apm_multiply(tmp0, tmpS, tmpS);
  73 m_apm_round(tmp2, (dplaces + 6), tmp0);
  74
  75 m1 = 3L;
  76
  77 while (TRUE)
  78   {
  79    m_apm_multiply(tmp0, term, tmp2);
  80
  81    if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0))
  82      break;
  83
  84    local_precision = dplaces + tmp0->m_apm_exponent;
  85
  86    if (local_precision < 20)
  87      local_precision = 20;
  88
  89    m_apm_set_long(tmp1, m1);
  90    m_apm_round(term, local_precision, tmp0);
  91    m_apm_divide(tmp0, local_precision, term, tmp1);
  92    m_apm_add(tmp1, tmpS, tmp0);
  93    m_apm_copy(tmpS, tmp1);
  94    m1 += 2;
  95   }
  96
  97 m_apm_multiply(tmp0, MM_Two, tmpS);
  98 m_apm_round(rr, places, tmp0);
  99
 100 M_restore_stack(5);                    /* restore the 5 locals we used here */
 101 }
 102 /****************************************************************************/