pgadmin3/pgscript/utilities/m_apm/mapm_exp.cpp

/*
 *  M_APM  -  mapm_exp.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 EXP function.
 *
 */

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

static  M_APM  MM_exp_log2R;
static  M_APM  MM_exp_512R;
static	int    MM_firsttime1 = TRUE;

/****************************************************************************/
void	M_free_all_exp()
{
	if (MM_firsttime1 == FALSE)
	{
		m_apm_free(MM_exp_log2R);
		m_apm_free(MM_exp_512R);

		MM_firsttime1 = TRUE;
	}
}
/****************************************************************************/
void	m_apm_exp(M_APM r, int places, M_APM x)
{
	M_APM   tmp7, tmp8, tmp9;
	int	dplaces, nn, ii;

	if (MM_firsttime1)
	{
		MM_firsttime1 = FALSE;

		MM_exp_log2R = m_apm_init();
		MM_exp_512R  = m_apm_init();

		m_apm_set_string(MM_exp_log2R, "1.44269504089");   /* ~ 1 / log(2) */
		m_apm_set_string(MM_exp_512R,  "1.953125E-3");     /*   1 / 512    */
	}

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

	if (x->m_apm_sign == 0)		/* if input == 0, return '1' */
	{
		m_apm_copy(r, MM_One);
		M_restore_stack(3);
		return;
	}

	if (x->m_apm_exponent <= -3)  /* already small enough so call _raw directly */
	{
		M_raw_exp(tmp9, (places + 6), x);
		m_apm_round(r, places, tmp9);
		M_restore_stack(3);
		return;
	}

	/*
	    From David H. Bailey's MPFUN Fortran package :

	    exp (t) =  (1 + r + r^2 / 2! + r^3 / 3! + r^4 / 4! ...) ^ q * 2 ^ n

	    where q = 256, r = t' / q, t' = t - n Log(2) and where n is chosen so
	    that -0.5 Log(2) < t' <= 0.5 Log(2).  Reducing t mod Log(2) and
	    dividing by 256 insures that -0.001 < r <= 0.001, which accelerates
	    convergence in the above series.

	    I use q = 512 and also limit how small 'r' can become. The 'r' used
	    here is limited in magnitude from 1.95E-4 < |r| < 1.35E-3. Forcing
	    'r' into a narrow range keeps the algorithm 'well behaved'.

	    ( the range is [0.1 / 512] to [log(2) / 512] )
	*/

	if (M_exp_compute_nn(&nn, tmp7, x) != 0)
	{
		M_apm_log_error_msg(M_APM_RETURN,
		                    "\'m_apm_exp\', Input too large, Overflow");

		M_set_to_zero(r);
		M_restore_stack(3);
		return;
	}

	dplaces = places + 8;

	/* check to make sure our log(2) is accurate enough */

	M_check_log_places(dplaces);

	m_apm_multiply(tmp8, tmp7, MM_lc_log2);
	m_apm_subtract(tmp7, x, tmp8);

	/*
	 *     guarantee that |tmp7| is between 0.1 and 0.9999999....
	 *     (in practice, the upper limit only reaches log(2), 0.693... )
	 */

	while (TRUE)
	{
		if (tmp7->m_apm_sign != 0)
		{
			if (tmp7->m_apm_exponent == 0)
				break;
		}

		if (tmp7->m_apm_sign >= 0)
		{
			nn++;
			m_apm_subtract(tmp8, tmp7, MM_lc_log2);
			m_apm_copy(tmp7, tmp8);
		}
		else
		{
			nn--;
			m_apm_add(tmp8, tmp7, MM_lc_log2);
			m_apm_copy(tmp7, tmp8);
		}
	}

	m_apm_multiply(tmp9, tmp7, MM_exp_512R);

	/* perform the series expansion ... */

	M_raw_exp(tmp8, dplaces, tmp9);

	/*
	 *   raise result to the 512 power
	 *
	 *   note : x ^ 512  =  (((x ^ 2) ^ 2) ^ 2) ... 9 times
	 */

	ii = 9;

	while (TRUE)
	{
		m_apm_multiply(tmp9, tmp8, tmp8);
		m_apm_round(tmp8, dplaces, tmp9);

		if (--ii == 0)
			break;
	}

	/* now compute 2 ^ N */

	m_apm_integer_pow(tmp7, dplaces, MM_Two, nn);

	m_apm_multiply(tmp9, tmp7, tmp8);
	m_apm_round(r, places, tmp9);

	M_restore_stack(3);                    /* restore the 3 locals we used here */
}
/****************************************************************************/
/*
	compute  int *n  = round_to_nearest_int(a / log(2))
	         M_APM b = MAPM version of *n

        returns      0: OK
		 -1, 1: failure
*/
int	M_exp_compute_nn(int *n, M_APM b, M_APM a)
{
	M_APM	tmp0, tmp1;
	void	*vp;
	char    *cp, sbuf[48];
	int	kk;

	*n   = 0;
	vp   = NULL;
	cp   = sbuf;
	tmp0 = M_get_stack_var();
	tmp1 = M_get_stack_var();

	/* find 'n' and convert it to a normal C int            */
	/* we just need an approx 1/log(2) for this calculation */

	m_apm_multiply(tmp1, a, MM_exp_log2R);

	/* round to the nearest int */

	if (tmp1->m_apm_sign >= 0)
	{
		m_apm_add(tmp0, tmp1, MM_0_5);
		m_apm_floor(tmp1, tmp0);
	}
	else
	{
		m_apm_subtract(tmp0, tmp1, MM_0_5);
		m_apm_ceil(tmp1, tmp0);
	}

	kk = tmp1->m_apm_exponent;
	if (kk >= 42)
	{
		if ((vp = (void *)MAPM_MALLOC((kk + 16) * sizeof(char))) == NULL)
		{
			/* fatal, this does not return */

			M_apm_log_error_msg(M_APM_FATAL, "\'M_exp_compute_nn\', Out of memory");
		}

		cp = (char *)vp;
	}

	m_apm_to_integer_string(cp, tmp1);
	*n = atoi(cp);

	m_apm_set_long(b, (long)(*n));

	kk = m_apm_compare(b, tmp1);

	if (vp != NULL)
		MAPM_FREE(vp);

	M_restore_stack(2);
	return(kk);
}
/****************************************************************************/
/*
	calculate the exponential function using the following series :

                              x^2     x^3     x^4     x^5
	exp(x) == 1  +  x  +  ---  +  ---  +  ---  +  ---  ...
                               2!      3!      4!      5!

*/
void	M_raw_exp(M_APM rr, int places, M_APM xx)
{
	M_APM   tmp0, digit, term;
	int	tolerance,  local_precision, prev_exp;
	long    m1;

	tmp0  = M_get_stack_var();
	term  = M_get_stack_var();
	digit = M_get_stack_var();

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

	m_apm_add(rr, MM_One, xx);
	m_apm_copy(term, xx);

	m1 = 2L;

	while (TRUE)
	{
		m_apm_set_long(digit, m1);
		m_apm_multiply(tmp0, term, xx);
		m_apm_divide(term, local_precision, tmp0, digit);
		m_apm_add(tmp0, rr, term);
		m_apm_copy(rr, tmp0);

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

		if (m1 != 2L)
		{
			local_precision = local_precision + term->m_apm_exponent - prev_exp;

			if (local_precision < 20)
				local_precision = 20;
		}

		prev_exp = term->m_apm_exponent;
		m1++;
	}

	M_restore_stack(3);                    /* restore the 3 locals we used here */
}
/****************************************************************************/