* M_APM - mapmsqrt.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: mapmsqrt.c,v 1.19 2007/12/03 01:57:31 mike Exp $
*
* This file contains the SQRT function.
*
* $Log: mapmsqrt.c,v $
* Revision 1.19 2007/12/03 01:57:31 mike
* Update license
*
* Revision 1.18 2003/07/21 20:39:00 mike
* Modify error messages to be in a consistent format.
*
* Revision 1.17 2003/05/07 16:36:04 mike
* simplify 'nexp' logic
*
* Revision 1.16 2003/03/31 21:50:14 mike
* call generic error handling function
*
* Revision 1.15 2003/03/11 21:29:00 mike
* round an intermediate result for faster runtime.
*
* Revision 1.14 2002/11/03 22:00:46 mike
* Updated function parameters to use the modern style
*
* Revision 1.13 2001/07/10 22:50:31 mike
* minor optimization
*
* Revision 1.12 2000/09/26 18:32:04 mike
* use new algorithm which only uses multiply and subtract
* (avoids the slower version which used division)
*
* Revision 1.11 2000/07/11 17:56:22 mike
* make better estimate for initial precision
*
* Revision 1.10 1999/07/21 02:48:45 mike
* added some comments
*
* Revision 1.9 1999/07/19 00:25:44 mike
* adjust local precision again
*
* Revision 1.8 1999/07/19 00:09:41 mike
* adjust local precision during loop
*
* Revision 1.7 1999/07/18 22:57:08 mike
* change to dynamically changing local precision and
* change tolerance checks using integers
*
* Revision 1.6 1999/06/19 21:18:00 mike
* changed local static variables to MAPM stack variables
*
* Revision 1.5 1999/05/31 01:40:39 mike
* minor update to normalizing the exponent
*
* Revision 1.4 1999/05/31 01:21:41 mike
* optimize for large exponents
*
* Revision 1.3 1999/05/12 20:59:35 mike
* use a better 'guess' function
*
* Revision 1.2 1999/05/10 21:15:26 mike
* added some comments
*
* Revision 1.1 1999/05/10 20:56:31 mike
* Initial revision
*/
#include "m_apm_lc.h"
void m_apm_sqrt(M_APM rr, int places, M_APM aa)
{
M_APM last_x, guess, tmpN, tmp7, tmp8, tmp9;
int ii, bflag, nexp, tolerance, dplaces;
if (aa->m_apm_sign <= 0)
{
if (aa->m_apm_sign == -1)
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_sqrt\', Negative argument");
}
M_set_to_zero(rr);
return;
}
last_x = M_get_stack_var();
guess = M_get_stack_var();
tmpN = M_get_stack_var();
tmp7 = M_get_stack_var();
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
m_apm_copy(tmpN, aa);
normalize the input number (make the exponent near 0) so
the 'guess' function will not over/under flow on large
magnitude exponents.
*/
nexp = aa->m_apm_exponent / 2;
tmpN->m_apm_exponent -= 2 * nexp;
M_get_sqrt_guess(guess, tmpN);
tolerance = places + 4;
dplaces = places + 16;
bflag = FALSE;
m_apm_negate(last_x, MM_Ten);
X = 0.5 * X * [ 3 - N * X^2 ]
n+1
*/
ii = 0;
while (TRUE)
{
m_apm_multiply(tmp9, tmpN, guess);
m_apm_multiply(tmp8, tmp9, guess);
m_apm_round(tmp7, dplaces, tmp8);
m_apm_subtract(tmp9, MM_Three, tmp7);
m_apm_multiply(tmp8, tmp9, guess);
m_apm_multiply(tmp9, tmp8, MM_0_5);
if (bflag)
break;
m_apm_round(guess, dplaces, tmp9);
if (ii != 0)
{
m_apm_subtract(tmp7, guess, last_x);
if (tmp7->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. (note that the sign of the exponent on
* the error term will be a negative number).
*/
if ((-4 * tmp7->m_apm_exponent) > tolerance)
bflag = TRUE;
}
m_apm_copy(last_x, guess);
ii++;
}
* multiply by the starting number to get the final
* sqrt and then adjust the exponent since we found
* the sqrt of the normalized number.
*/
m_apm_multiply(tmp8, tmp9, tmpN);
m_apm_round(rr, places, tmp8);
rr->m_apm_exponent += nexp;
M_restore_stack(6);
}
