/*
 * solve - solve f(x) = 0 to within the desired error value for x
 *
 * Copyright (C) 1999  David I. Bell
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 * or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * @(#) $Revision: 30.3 $
 * @(#) $Id: solve.cal,v 30.3 2013/08/11 08:41:38 chongo Exp $
 * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/solve.cal,v $
 *
 * Under source code control:	1990/02/15 01:50:37
 * File existed as early as:	before 1990
 *
 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
 */

/*
 * Solve the equation f(x) = 0 to within the desired error value for x.
 * The function 'f' must be defined outside of this routine, and the low
 * and high values are guesses which must produce values with opposite signs.
 */


define solve(low, high, epsilon)
{
	local flow, fhigh, fmid, mid, places;

	if (isnull(epsilon))
		epsilon = epsilon();
	if (epsilon <= 0)
		quit "Non-positive epsilon value";
	places = highbit(1 + int(1/epsilon)) + 1;
	flow = f(low);
	if (abs(flow) < epsilon)
		return low;
	fhigh = f(high);
	if (abs(fhigh) < epsilon)
		return high;
	if (sgn(flow) == sgn(fhigh))
		quit "Non-opposite signs";
	while (1) {
		mid = bround(high - fhigh * (high - low) / (fhigh - flow),
			     places);
		if ((mid == low) || (mid == high))
			places++;
		fmid = f(mid);
		if (abs(fmid) < epsilon)
			return mid;
		if (sgn(fmid) == sgn(flow)) {
			low = mid;
			flow = fmid;
		} else {
			high = mid;
			fhigh = fmid;
		}
	}
}
