pgadmin3/pgscript/utilities/m_apm/mapm_rcp.cpp

/*
 *  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.
 */

/*
 *
 *      This file contains the fast division and reciprocal functions
 *
 */

#include "pgAdmin3.h"
#include "pgscript/utilities/mapm-lib/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)                  /* one number is zero, result is zero */
	{
		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;
	}

	/* mimic the decimal place behavior of the original divide */

	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);

	/*   Use the following iteration to calculate the reciprocal :


	         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);

		/* force at least 2 iterations so 'last_x' has valid data */

		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);
}
/****************************************************************************/