
/*
 *  M_APM  -  mapmasin.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 'ARC' family of functions; ARC-SIN, ARC-COS,
 *	ARC-TAN, and ARC-TAN2.
 *
 */

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

/****************************************************************************/
void	m_apm_arctan2(M_APM rr, int places, M_APM yy, M_APM xx)
{
	M_APM   tmp5, tmp6, tmp7;
	int	ix, iy;

	iy = yy->m_apm_sign;
	ix = xx->m_apm_sign;

	if (ix == 0)       /* x == 0 */
	{
		if (iy == 0)    /* y == 0 */
		{
			M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arctan2\', Both Inputs = 0");
			M_set_to_zero(rr);
			return;
		}

		M_check_PI_places(places);
		m_apm_round(rr, places, MM_lc_HALF_PI);
		rr->m_apm_sign = iy;
		return;
	}

	if (iy == 0)
	{
		if (ix == 1)
		{
			M_set_to_zero(rr);
		}
		else
		{
			M_check_PI_places(places);
			m_apm_round(rr, places, MM_lc_PI);
		}

		return;
	}

	/*
	 *    the special cases have been handled, now do the real work
	 */

	tmp5 = M_get_stack_var();
	tmp6 = M_get_stack_var();
	tmp7 = M_get_stack_var();

	m_apm_divide(tmp6, (places + 6), yy, xx);
	m_apm_arctan(tmp5, (places + 6), tmp6);

	if (ix == 1)         /* 'x' is positive */
	{
		m_apm_round(rr, places, tmp5);
	}
	else                 /* 'x' is negative */
	{
		M_check_PI_places(places);

		if (iy == 1)      /* 'y' is positive */
		{
			m_apm_add(tmp7, tmp5, MM_lc_PI);
			m_apm_round(rr, places, tmp7);
		}
		else              /* 'y' is negative */
		{
			m_apm_subtract(tmp7, tmp5, MM_lc_PI);
			m_apm_round(rr, places, tmp7);
		}
	}

	M_restore_stack(3);
}
/****************************************************************************/
/*
        Calculate arctan using the identity :

                                      x
        arctan (x) == arcsin [ --------------- ]
                                sqrt(1 + x^2)

*/
void	m_apm_arctan(M_APM rr, int places, M_APM xx)
{
	M_APM   tmp8, tmp9;

	if (xx->m_apm_sign == 0)			/* input == 0 ?? */
	{
		M_set_to_zero(rr);
		return;
	}

	if (xx->m_apm_exponent <= -4)			/* input close to 0 ?? */
	{
		M_arctan_near_0(rr, places, xx);
		return;
	}

	if (xx->m_apm_exponent >= 4)			/* large input */
	{
		M_arctan_large_input(rr, places, xx);
		return;
	}

	tmp8 = M_get_stack_var();
	tmp9 = M_get_stack_var();

	m_apm_multiply(tmp9, xx, xx);
	m_apm_add(tmp8, tmp9, MM_One);
	m_apm_sqrt(tmp9, (places + 6), tmp8);
	m_apm_divide(tmp8, (places + 6), xx, tmp9);
	m_apm_arcsin(rr, places, tmp8);
	M_restore_stack(2);
}
/****************************************************************************/
/*

	for large input values use :

	arctan(x) =  (PI / 2) - arctan(1 / |x|)

	and sign of result = sign of original input

*/
void	M_arctan_large_input(M_APM rr, int places, M_APM xx)
{
	M_APM	tmp1, tmp2;

	tmp1 = M_get_stack_var();
	tmp2 = M_get_stack_var();

	M_check_PI_places(places);

	m_apm_divide(tmp1, (places + 6), MM_One, xx);   	   /*  1 / xx       */
	tmp1->m_apm_sign = 1;					   /* make positive */
	m_apm_arctan(tmp2, (places + 6), tmp1);
	m_apm_subtract(tmp1, MM_lc_HALF_PI, tmp2);
	m_apm_round(rr, places, tmp1);

	rr->m_apm_sign = xx->m_apm_sign;			  /* fix final sign */

	M_restore_stack(2);
}
/****************************************************************************/
void	m_apm_arcsin(M_APM r, int places, M_APM x)
{
	M_APM   tmp0, tmp1, tmp2, tmp3, current_x;
	int	ii, maxiter, maxp, tolerance, local_precision;

	current_x = M_get_stack_var();
	tmp0      = M_get_stack_var();
	tmp1      = M_get_stack_var();
	tmp2      = M_get_stack_var();
	tmp3      = M_get_stack_var();

	m_apm_absolute_value(tmp0, x);

	ii = m_apm_compare(tmp0, MM_One);

	if (ii == 1)       /* |x| > 1 */
	{
		M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arcsin\', |Argument| > 1");
		M_set_to_zero(r);
		M_restore_stack(5);
		return;
	}

	if (ii == 0)       /* |x| == 1, arcsin = +/- PI / 2 */
	{
		M_check_PI_places(places);
		m_apm_round(r, places, MM_lc_HALF_PI);
		r->m_apm_sign = x->m_apm_sign;

		M_restore_stack(5);
		return;
	}

	if (m_apm_compare(tmp0, MM_0_85) == 1)        /* check if > 0.85 */
	{
		M_cos_to_sin(tmp2, (places + 4), x);
		m_apm_arccos(r, places, tmp2);
		r->m_apm_sign = x->m_apm_sign;

		M_restore_stack(5);
		return;
	}

	if (x->m_apm_sign == 0)			      /* input == 0 ?? */
	{
		M_set_to_zero(r);
		M_restore_stack(5);
		return;
	}

	if (x->m_apm_exponent <= -4)		      /* input close to 0 ?? */
	{
		M_arcsin_near_0(r, places, x);
		M_restore_stack(5);
		return;
	}

	tolerance       = -(places + 4);
	maxp            = places + 8 - x->m_apm_exponent;
	local_precision = 20 - x->m_apm_exponent;

	/*
	 *      compute the maximum number of iterations
	 *	that should be needed to calculate to
	 *	the desired accuracy.  [ constant below ~= 1 / log(2) ]
	 */

	maxiter = (int)(log((double)(places + 2)) * 1.442695) + 3;

	if (maxiter < 5)
		maxiter = 5;

	M_get_asin_guess(current_x, x);

	/*    Use the following iteration to solve for arc-sin :

	                      sin(X) - N
	      X     =  X  -  ------------
	       n+1              cos(X)
	*/

	ii = 0;

	while (TRUE)
	{
		M_4x_cos(tmp1, local_precision, current_x);

		M_cos_to_sin(tmp2, local_precision, tmp1);
		if (tmp2->m_apm_sign != 0)
			tmp2->m_apm_sign = current_x->m_apm_sign;

		m_apm_subtract(tmp3, tmp2, x);
		m_apm_divide(tmp0, local_precision, tmp3, tmp1);

		m_apm_subtract(tmp2, current_x, tmp0);
		m_apm_copy(current_x, tmp2);

		if (ii != 0)
		{
			if (((2 * tmp0->m_apm_exponent) < tolerance) || (tmp0->m_apm_sign == 0))
				break;
		}

		if (++ii == maxiter)
		{
			M_apm_log_error_msg(M_APM_RETURN,
			                    "\'m_apm_arcsin\', max iteration count reached");
			break;
		}

		local_precision *= 2;

		if (local_precision > maxp)
			local_precision = maxp;
	}

	m_apm_round(r, places, current_x);
	M_restore_stack(5);
}
/****************************************************************************/
void	m_apm_arccos(M_APM r, int places, M_APM x)
{
	M_APM   tmp0, tmp1, tmp2, tmp3, current_x;
	int	ii, maxiter, maxp, tolerance, local_precision;

	current_x = M_get_stack_var();
	tmp0      = M_get_stack_var();
	tmp1      = M_get_stack_var();
	tmp2      = M_get_stack_var();
	tmp3      = M_get_stack_var();

	m_apm_absolute_value(tmp0, x);

	ii = m_apm_compare(tmp0, MM_One);

	if (ii == 1)       /* |x| > 1 */
	{
		M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arccos\', |Argument| > 1");
		M_set_to_zero(r);
		M_restore_stack(5);
		return;
	}

	if (ii == 0)       /* |x| == 1, arccos = 0, PI */
	{
		if (x->m_apm_sign == 1)
		{
			M_set_to_zero(r);
		}
		else
		{
			M_check_PI_places(places);
			m_apm_round(r, places, MM_lc_PI);
		}

		M_restore_stack(5);
		return;
	}

	if (m_apm_compare(tmp0, MM_0_85) == 1)        /* check if > 0.85 */
	{
		M_cos_to_sin(tmp2, (places + 4), x);

		if (x->m_apm_sign == 1)
		{
			m_apm_arcsin(r, places, tmp2);
		}
		else
		{
			M_check_PI_places(places);
			m_apm_arcsin(tmp3, (places + 4), tmp2);
			m_apm_subtract(tmp1, MM_lc_PI, tmp3);
			m_apm_round(r, places, tmp1);
		}

		M_restore_stack(5);
		return;
	}

	if (x->m_apm_sign == 0)			      /* input == 0 ?? */
	{
		M_check_PI_places(places);
		m_apm_round(r, places, MM_lc_HALF_PI);
		M_restore_stack(5);
		return;
	}

	if (x->m_apm_exponent <= -4)		      /* input close to 0 ?? */
	{
		M_arccos_near_0(r, places, x);
		M_restore_stack(5);
		return;
	}

	tolerance       = -(places + 4);
	maxp            = places + 8;
	local_precision = 18;

	/*
	 *      compute the maximum number of iterations
	 *	that should be needed to calculate to
	 *	the desired accuracy.  [ constant below ~= 1 / log(2) ]
	 */

	maxiter = (int)(log((double)(places + 2)) * 1.442695) + 3;

	if (maxiter < 5)
		maxiter = 5;

	M_get_acos_guess(current_x, x);

	/*    Use the following iteration to solve for arc-cos :

	                      cos(X) - N
	      X     =  X  +  ------------
	       n+1              sin(X)
	*/

	ii = 0;

	while (TRUE)
	{
		M_4x_cos(tmp1, local_precision, current_x);

		M_cos_to_sin(tmp2, local_precision, tmp1);
		if (tmp2->m_apm_sign != 0)
			tmp2->m_apm_sign = current_x->m_apm_sign;

		m_apm_subtract(tmp3, tmp1, x);
		m_apm_divide(tmp0, local_precision, tmp3, tmp2);

		m_apm_add(tmp2, current_x, tmp0);
		m_apm_copy(current_x, tmp2);

		if (ii != 0)
		{
			if (((2 * tmp0->m_apm_exponent) < tolerance) || (tmp0->m_apm_sign == 0))
				break;
		}

		if (++ii == maxiter)
		{
			M_apm_log_error_msg(M_APM_RETURN,
			                    "\'m_apm_arccos\', max iteration count reached");
			break;
		}

		local_precision *= 2;

		if (local_precision > maxp)
			local_precision = maxp;
	}

	m_apm_round(r, places, current_x);
	M_restore_stack(5);
}
/****************************************************************************/
