* M_APM - mapm_lg4.c
*
* Copyright (C) 2003 - 2007 Michael C. Ring
*
* Permission to use, copy, and distribute this software and its
* documentation for any purpose with or without fee is hereby granted,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation.
*
* Permission to modify the software is granted. Permission to distribute
* the modified code is granted. Modifications are to be distributed by
* using the file 'license.txt' as a template to modify the file header.
* 'license.txt' is available in the official MAPM distribution.
*
* This software is provided "as is" without express or implied warranty.
*/
* $Id: mapm_lg4.c,v 1.3 2007/12/03 01:43:32 mike Exp $
*
* This file contains the LOG_NEAR_1 function.
*
* $Log: mapm_lg4.c,v $
* Revision 1.3 2007/12/03 01:43:32 mike
* Update license
*
* Revision 1.2 2003/06/02 18:08:45 mike
* tweak decimal places and add comments
*
* Revision 1.1 2003/06/02 17:27:26 mike
* Initial revision
*/
#include "m_apm_lc.h"
calculate log (1 + x) with the following series:
x
y = ----- ( |y| < 1 )
x + 2
[ 1 + y ] y^3 y^5 y^7
log [-------] = 2 * [ y + --- + --- + --- ... ]
[ 1 - y ] 3 5 7
*/
void M_log_near_1(M_APM rr, int places, M_APM xx)
{
M_APM tmp0, tmp1, tmp2, tmpS, term;
int tolerance, dplaces, local_precision;
long m1;
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
tmpS = M_get_stack_var();
term = M_get_stack_var();
tolerance = xx->m_apm_exponent - (places + 6);
dplaces = (places + 12) - xx->m_apm_exponent;
m_apm_add(tmp0, xx, MM_Two);
m_apm_divide(tmpS, (dplaces + 6), xx, tmp0);
m_apm_copy(term, tmpS);
m_apm_multiply(tmp0, tmpS, tmpS);
m_apm_round(tmp2, (dplaces + 6), tmp0);
m1 = 3L;
while (TRUE)
{
m_apm_multiply(tmp0, term, tmp2);
if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0))
break;
local_precision = dplaces + tmp0->m_apm_exponent;
if (local_precision < 20)
local_precision = 20;
m_apm_set_long(tmp1, m1);
m_apm_round(term, local_precision, tmp0);
m_apm_divide(tmp0, local_precision, term, tmp1);
m_apm_add(tmp1, tmpS, tmp0);
m_apm_copy(tmpS, tmp1);
m1 += 2;
}
m_apm_multiply(tmp0, MM_Two, tmpS);
m_apm_round(rr, places, tmp0);
M_restore_stack(5);
}
