
/*
 *  M_APM  -  mapmrsin.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.
 */

/*
 *
 *      This file contains the basic series expansion functions for
 *	the SIN / COS functions.
 */

#include "pgAdmin3.h"
#include "pgscript/utilities/mapm-lib/m_apm_lc.h"

/****************************************************************************/
/*
                                  x^3     x^5     x^7     x^9
		 sin(x)  =  x  -  ---  +  ---  -  ---  +  ---  ...
                                   3!      5!      7!      9!
*/
void	M_raw_sin(M_APM rr, int places, M_APM xx)
{
	M_APM	sum, term, tmp2, tmp7, tmp8;
	int     tolerance, flag, local_precision, dplaces;
	long	m1, m2;

	sum  = M_get_stack_var();
	term = M_get_stack_var();
	tmp2 = M_get_stack_var();
	tmp7 = M_get_stack_var();
	tmp8 = M_get_stack_var();

	m_apm_copy(sum, xx);
	m_apm_copy(term, xx);
	m_apm_multiply(tmp8, xx, xx);
	m_apm_round(tmp2, (places + 6), tmp8);

	dplaces   = (places + 8) - xx->m_apm_exponent;
	tolerance = xx->m_apm_exponent - (places + 4);

	m1   = 2L;
	flag = 0;

	while (TRUE)
	{
		m_apm_multiply(tmp8, term, tmp2);

		if ((tmp8->m_apm_exponent < tolerance) || (tmp8->m_apm_sign == 0))
			break;

		local_precision = dplaces + term->m_apm_exponent;

		if (local_precision < 20)
			local_precision = 20;

		m2 = m1 * (m1 + 1);
		m_apm_set_long(tmp7, m2);

		m_apm_divide(term, local_precision, tmp8, tmp7);

		if (flag == 0)
		{
			m_apm_subtract(tmp7, sum, term);
			m_apm_copy(sum, tmp7);
		}
		else
		{
			m_apm_add(tmp7, sum, term);
			m_apm_copy(sum, tmp7);
		}

		m1 += 2;
		flag = 1 - flag;
	}

	m_apm_round(rr, places, sum);
	M_restore_stack(5);
}
/****************************************************************************/
/*
                                  x^2     x^4     x^6     x^8
		 cos(x)  =  1  -  ---  +  ---  -  ---  +  ---  ...
                                   2!      4!      6!      8!
*/
void	M_raw_cos(M_APM rr, int places, M_APM xx)
{
	M_APM	sum, term, tmp7, tmp8, tmp9;
	int     tolerance, flag, local_precision, prev_exp;
	long	m1, m2;

	sum  = M_get_stack_var();
	term = M_get_stack_var();
	tmp7 = M_get_stack_var();
	tmp8 = M_get_stack_var();
	tmp9 = M_get_stack_var();

	m_apm_copy(sum, MM_One);
	m_apm_copy(term, MM_One);

	m_apm_multiply(tmp8, xx, xx);
	m_apm_round(tmp9, (places + 6), tmp8);

	local_precision = places + 8;
	tolerance       = -(places + 4);
	prev_exp        = 0;

	m1   = 1L;
	flag = 0;

	while (TRUE)
	{
		m2 = m1 * (m1 + 1);
		m_apm_set_long(tmp7, m2);

		m_apm_multiply(tmp8, term, tmp9);
		m_apm_divide(term, local_precision, tmp8, tmp7);

		if (flag == 0)
		{
			m_apm_subtract(tmp7, sum, term);
			m_apm_copy(sum, tmp7);
		}
		else
		{
			m_apm_add(tmp7, sum, term);
			m_apm_copy(sum, tmp7);
		}

		if ((term->m_apm_exponent < tolerance) || (term->m_apm_sign == 0))
			break;

		if (m1 != 1L)
		{
			local_precision = local_precision + term->m_apm_exponent - prev_exp;

			if (local_precision < 20)
				local_precision = 20;
		}

		prev_exp = term->m_apm_exponent;

		m1 += 2;
		flag = 1 - flag;
	}

	m_apm_round(rr, places, sum);
	M_restore_stack(5);
}
/****************************************************************************/
