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Math functions for BigDecimal.
There is a newer version: 2.3.2
package ch.obermuhlner.math.big.internal;

import static java.math.BigDecimal.ONE;

import java.math.BigDecimal;
import java.math.MathContext;
import java.util.ArrayList;
import java.util.List;

import ch.obermuhlner.math.big.BigRational;

/**
 * Utility class to calculate taylor series efficiently until the maximum error (as defined by the precision in the {@link MathContext} is reached.
 * 
 * Stores the factors of the taylor series terms so that future calculations will be faster.
 */
public abstract class SeriesCalculator {

	private boolean calculateInPairs;

	private List factors = new ArrayList<>();
	
	/**
	 * Constructs a {@link SeriesCalculator} that calculates single terms.
	 */
	protected SeriesCalculator() {
		this(false);
	}
	
	/**
	 * Constructs a {@link SeriesCalculator} with control over whether the sum terms are calculated in pairs.
	 * 
	 * Calculation of pairs is useful for taylor series where the terms alternate the sign.
	 * In these cases it is more efficient to calculate two terms at once check then whether the acceptable error has been reached.
	 * 
	 * @param calculateInPairs true to calculate the terms in pairs, false to calculate single terms
	 */
	protected SeriesCalculator(boolean calculateInPairs) {
		this.calculateInPairs = calculateInPairs;
	}
	
	/**
	 * Calculates the series for the specified value x and the precision defined in the {@link MathContext}.
	 * 
	 * @param x the value x
	 * @param mathContext the {@link MathContext}
	 * @return the calculated result
	 */
	public BigDecimal calculate(BigDecimal x, MathContext mathContext) {
		BigDecimal acceptableError = ONE.movePointLeft(mathContext.getPrecision() + 1);

		PowerIterator powerIterator = createPowerIterator(x, mathContext);
		
		BigDecimal sum = BigDecimal.ZERO;
		BigDecimal step;
		int i = 0;
		do {
			BigRational factor = getFactor(i);
			BigDecimal xToThePower  = powerIterator.getCurrentPower();
			powerIterator.calculateNextPower();
			step = factor.getNumerator().multiply(xToThePower, mathContext).divide(factor.getDenominator(), mathContext);
			i++;

			if (calculateInPairs) {
				xToThePower  = powerIterator.getCurrentPower();
				powerIterator.calculateNextPower();
				factor = getFactor(i);
				BigDecimal step2 = factor.getNumerator().multiply(xToThePower, mathContext).divide(factor.getDenominator(), mathContext);
				step = step.add(step2, mathContext);
				i++;
			}

			sum = sum.add(step, mathContext);
			//System.out.println(sum + " " + step);
		} while (step.abs().compareTo(acceptableError) > 0);
		
		return sum.round(mathContext);
	}
	
	/**
	 * Creates the {@link PowerIterator} used for this series.
	 * 
	 * @param x the value x
	 * @param mathContext the {@link MathContext}
	 * @return the {@link PowerIterator}
	 */
	protected abstract PowerIterator createPowerIterator(BigDecimal x, MathContext mathContext);

	/**
	 * Returns the factor of the term with specified index.
	 * 
	 * @param index the index (starting with 0)
	 * @return the factor of the specified term
	 */
	protected BigRational getFactor(int index) {
		while (factors.size() <= index) {
			BigRational factor = getCurrentFactor();
			factors.add(factor);
			calculateNextFactor();
		}
		return factors.get(index);
	}

	/**
	 * Returns the factor of the highest term already calculated.
	 * When called for the first time will return the factor of the first term (index 0).
	 * After this call the method {@link #calculateNextFactor()} will be called to prepare for the next term.
	 * 
	 * @return the factor of the highest term
	 */
	protected abstract BigRational getCurrentFactor();
	
	/**
	 * Calculates the factor of the next term.
	 */
	protected abstract void calculateNextFactor();
}