ExponentialTaylerAlgorithmStrategy.java

/*
 * Copyright (c) 2009-2015
 * 	IT-Consulting Stephan Schloepke (http://www.schloepke.de/)
 * 	klemm software consulting Mirko Klemm (http://www.klemm-scs.com/)
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */
package org.jbasics.math.strategies;

import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;

import org.jbasics.math.AlgorithmStrategy;

public class ExponentialTaylerAlgorithmStrategy implements AlgorithmStrategy<BigDecimal> {
	public static final AlgorithmStrategy<BigDecimal> STRATEGY = new ExponentialTaylerAlgorithmStrategy();

	public BigDecimal calculate(MathContext mc, BigDecimal guess, BigDecimal... xn) {
		if (xn == null || xn.length == 0) {
			throw new IllegalArgumentException("must supply x as input (the xn array must contain one x)");
		}
		BigDecimal x = xn[0];
		if (x.signum() == 0) {
			return BigDecimal.ONE;
		}
		int scale = (int) Math.ceil(Math.sqrt((mc.getPrecision() + 10) * Math.log(10) / Math.log(2)));
		if (x.abs().compareTo(BigDecimal.ONE) > 0) {
			BigInteger temp = x.unscaledValue();
			int scale2 = (int) (x.scale() * (Math.log(10) / Math.log(2))) + 1;
			int precis2 = temp.bitLength();
			scale = scale + precis2 - scale2;
		} else {
			scale = scale + ((int) (x.scale() * (Math.log(10) / Math.log(2))));
		}
		BigDecimal xScaled = x.divide(new BigDecimal(BigInteger.ONE.shiftLeft(scale)));
		MathContext calcContext = new MathContext(mc.getPrecision() + (int) Math.ceil(scale * Math.log10(2)) + 1, RoundingMode.HALF_EVEN);
		BigInteger k = BigInteger.ONE;
		int n = 1;
		BigDecimal xPower = BigDecimal.ONE;
		BigDecimal result = BigDecimal.ONE;
		do {
			xPower = xPower.multiply(xScaled, calcContext);
			result = result.multiply(BigDecimal.valueOf(n)).add(xPower);
			k = k.multiply(BigInteger.valueOf(n++));
		} while (calcContext.getPrecision() - xPower.scale() + xPower.precision() > 0);
		result = result.round(calcContext).divide(new BigDecimal(k), calcContext);
		for (int i = scale; i > 0; i--) {
			result = result.multiply(result, calcContext);
		}
		return result.round(mc);
	}
}