* M_APM - mapm_rcp.c
*
* Copyright (C) 2000 - 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_rcp.c,v 1.7 2007/12/03 01:46:46 mike Exp $
*
* This file contains the fast division and reciprocal functions
*
* $Log: mapm_rcp.c,v $
* Revision 1.7 2007/12/03 01:46:46 mike
* Update license
*
* Revision 1.6 2003/07/21 20:20:17 mike
* Modify error messages to be in a consistent format.
*
* Revision 1.5 2003/05/01 21:58:40 mike
* remove math.h
*
* Revision 1.4 2003/03/31 22:15:49 mike
* call generic error handling function
*
* Revision 1.3 2002/11/03 21:32:09 mike
* Updated function parameters to use the modern style
*
* Revision 1.2 2000/09/26 16:27:48 mike
* add some comments
*
* Revision 1.1 2000/09/26 16:16:00 mike
* Initial revision
*/
#include "m_apm_lc.h"
void m_apm_divide(M_APM rr, int places, M_APM aa, M_APM bb)
{
M_APM tmp0, tmp1;
int sn, nexp, dplaces;
sn = aa->m_apm_sign * bb->m_apm_sign;
if (sn == 0)
{
if (bb->m_apm_sign == 0)
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_divide\', Divide by 0");
}
M_set_to_zero(rr);
return;
}
* Use the original 'Knuth' method for smaller divides. On the
* author's system, this was the *approx* break even point before
* the reciprocal method used below became faster.
*/
if (places < 250)
{
M_apm_sdivide(rr, places, aa, bb);
return;
}
nexp = aa->m_apm_exponent - bb->m_apm_exponent;
if (nexp > 0)
dplaces = nexp + places;
else
dplaces = places;
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
m_apm_reciprocal(tmp0, (dplaces + 8), bb);
m_apm_multiply(tmp1, tmp0, aa);
m_apm_round(rr, dplaces, tmp1);
M_restore_stack(2);
}
void m_apm_reciprocal(M_APM rr, int places, M_APM aa)
{
M_APM last_x, guess, tmpN, tmp1, tmp2;
char sbuf[32];
int ii, bflag, dplaces, nexp, tolerance;
if (aa->m_apm_sign == 0)
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_reciprocal\', Input = 0");
M_set_to_zero(rr);
return;
}
last_x = M_get_stack_var();
guess = M_get_stack_var();
tmpN = M_get_stack_var();
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
m_apm_absolute_value(tmpN, aa);
normalize the input number (make the exponent 0) so
the 'guess' below will not over/under flow on large
magnitude exponents.
*/
nexp = aa->m_apm_exponent;
tmpN->m_apm_exponent -= nexp;
m_apm_to_string(sbuf, 15, tmpN);
m_apm_set_double(guess, (1.0 / atof(sbuf)));
tolerance = places + 4;
dplaces = places + 16;
bflag = FALSE;
m_apm_negate(last_x, MM_Ten);
X = X * [ 2 - N * X ]
n+1
*/
ii = 0;
while (TRUE)
{
m_apm_multiply(tmp1, tmpN, guess);
m_apm_subtract(tmp2, MM_Two, tmp1);
m_apm_multiply(tmp1, tmp2, guess);
if (bflag)
break;
m_apm_round(guess, dplaces, tmp1);
if (ii != 0)
{
m_apm_subtract(tmp2, guess, last_x);
if (tmp2->m_apm_sign == 0)
break;
* if we are within a factor of 4 on the error term,
* we will be accurate enough after the *next* iteration
* is complete.
*/
if ((-4 * tmp2->m_apm_exponent) > tolerance)
bflag = TRUE;
}
m_apm_copy(last_x, guess);
ii++;
}
m_apm_round(rr, places, tmp1);
rr->m_apm_exponent -= nexp;
rr->m_apm_sign = aa->m_apm_sign;
M_restore_stack(5);
}
