/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.special;

import org.apache.commons.math.MathException;

/**
 * This is a utility class that provides computation methods related to the
 * error functions.
 *
 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
 */
public class Erf {

    /**
     * Default constructor.  Prohibit instantiation.
     */
    private Erf() {
        super();
    }

    /**
     * Returns the error function erf(x).
     * <p/>
     * The implementation of this method is based on:
     * <ul>
     * <li>
     * <a href="http://mathworld.wolfram.com/Erf.html">
     * Erf</a>, equation (3).</li>
     * </ul>
     *
     * @param x the value.
     * @return the error function erf(x)
     * @throws MathException if the algorithm fails to converge.
     */
    public static double erf(double x) throws MathException {
        double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000);
        if (x < 0) {
            ret = -ret;
        }
        return ret;
    }
    
    // fractional error in math formula less than 1.2 * 10 ^ -7.
    // although subject to catastrophic cancellation when z in very close to 0
    // from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2
    public static double erfAlternative(double z) throws MathException {
        double t = 1.0 / (1.0 + 0.5 * Math.abs(z));

        // use Horner's method
        double ans = 1 - t * Math.exp( -z*z   -   1.26551223 +
                                            t * ( 1.00002368 +
                                            t * ( 0.37409196 + 
                                            t * ( 0.09678418 + 
                                            t * (-0.18628806 + 
                                            t * ( 0.27886807 + 
                                            t * (-1.13520398 + 
                                            t * ( 1.48851587 + 
                                            t * (-0.82215223 + 
                                            t * ( 0.17087277))))))))));
        if (z >= 0) return  ans;
        else        return -ans;
    }
    
}
