* M_APM - mapm_log.c
*
* Copyright (C) 1999 - 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_log.c,v 1.29 2007/12/03 01:44:19 mike Exp $
*
* This file contains the LOG and LOG10 functions.
*
* $Log: mapm_log.c,v $
* Revision 1.29 2007/12/03 01:44:19 mike
* Update license
*
* Revision 1.28 2003/07/21 20:18:06 mike
* Modify error messages to be in a consistent format.
*
* Revision 1.27 2003/06/02 17:22:46 mike
* put 'log_near_1' into it's own separate module
*
* Revision 1.26 2003/05/12 17:42:46 mike
* only check for 'near 1' if exponent is 0 or 1
*
* Revision 1.25 2003/05/04 21:08:25 mike
* *** empty log message ***
*
* Revision 1.24 2003/05/01 21:58:34 mike
* remove math.h
*
* Revision 1.23 2003/05/01 21:39:09 mike
* use 'abs' call
*
* Revision 1.22 2003/05/01 19:44:57 mike
* optimize log_near_1 by calculating fewer digits
* on subsequent iterations
*
* Revision 1.21 2003/03/31 22:00:56 mike
* call generic error handling function
*
* Revision 1.20 2003/03/30 22:57:13 mike
* call a new iterative log function which is cubically convergent
*
* Revision 1.19 2002/11/03 22:14:45 mike
* Updated function parameters to use the modern style
*
* Revision 1.18 2001/07/16 19:21:16 mike
* add function M_free_all_log
*
* Revision 1.17 2000/10/22 00:24:29 mike
* minor optimization
*
* Revision 1.16 2000/10/21 16:22:50 mike
* use an improved log_near_1 algorithm
*
* Revision 1.15 2000/10/20 16:49:33 mike
* update algorithm for basic log function and add new
* function when input is close to '1'
*
* Revision 1.14 2000/09/23 19:48:21 mike
* change divide call to reciprocal
*
* Revision 1.13 2000/07/11 18:58:35 mike
* do it right this time
*
* Revision 1.12 2000/07/11 18:19:27 mike
* estimate a better initial precision
*
* Revision 1.11 2000/05/19 16:14:15 mike
* update some comments
*
* Revision 1.10 2000/05/17 23:47:35 mike
* recompute a local copy of log E base 10 on the fly
* if more precision is needed.
*
* Revision 1.9 2000/03/27 21:44:12 mike
* determine how many iterations should be required at
* run time for log
*
* Revision 1.8 1999/07/21 02:56:18 mike
* added some comments
*
* Revision 1.7 1999/07/19 00:28:51 mike
* adjust local precision again
*
* Revision 1.6 1999/07/19 00:10:34 mike
* adjust local precision during iterative loop
*
* Revision 1.5 1999/07/18 23:15:54 mike
* change local precision dynamically and change
* tolerance to integers for faster iterative routine.
*
* Revision 1.4 1999/06/19 21:08:32 mike
* changed local static variables to MAPM stack variables
*
* Revision 1.3 1999/05/15 01:34:50 mike
* add check for number of decimal places
*
* Revision 1.2 1999/05/10 21:42:32 mike
* added some comments
*
* Revision 1.1 1999/05/10 20:56:31 mike
* Initial revision
*/
#include "m_apm_lc.h"
Calls the LOG function. The formula used is :
log10(x) = A * log(x) where A = log (e) [0.43429448190325...]
10
*/
void m_apm_log10(M_APM rr, int places, M_APM aa)
{
int dplaces;
M_APM tmp8, tmp9;
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
dplaces = places + 4;
M_check_log_places(dplaces + 45);
m_apm_log(tmp9, dplaces, aa);
m_apm_multiply(tmp8, tmp9, MM_lc_log10R);
m_apm_round(rr, places, tmp8);
M_restore_stack(2);
}
void m_apm_log(M_APM r, int places, M_APM a)
{
M_APM tmp0, tmp1, tmp2;
int mexp, dplaces;
if (a->m_apm_sign <= 0)
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_log\', Negative argument");
M_set_to_zero(r);
return;
}
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
dplaces = places + 8;
* if the input is real close to 1, use the series expansion
* to compute the log.
*
* 0.9999 < a < 1.0001
*/
mexp = a->m_apm_exponent;
if (mexp == 0 || mexp == 1)
{
m_apm_subtract(tmp0, a, MM_One);
if (tmp0->m_apm_sign == 0)
{
M_set_to_zero(r);
M_restore_stack(3);
return;
}
if (tmp0->m_apm_exponent <= -4)
{
M_log_near_1(r, places, tmp0);
M_restore_stack(3);
return;
}
}
M_check_log_places(dplaces + 25);
if (abs(mexp) <= 3)
{
M_log_basic_iteration(r, places, a);
}
else
{
* use log (x * y) = log(x) + log(y)
*
* here we use y = exponent of our base 10 number.
*
* let 'C' = log(10) = 2.3025850929940....
*
* then log(x * y) = log(x) + ( C * base_10_exponent )
*/
m_apm_copy(tmp2, a);
mexp = tmp2->m_apm_exponent - 2;
tmp2->m_apm_exponent = 2;
M_log_basic_iteration(tmp0, dplaces, tmp2);
m_apm_set_long(tmp1, (long)mexp);
m_apm_multiply(tmp2, tmp1, MM_lc_log10);
m_apm_add(tmp1, tmp2, tmp0);
m_apm_round(r, places, tmp1);
}
M_restore_stack(3);
}
