org.apache.commons.numbers.gamma.Erfc Maven / Gradle / Ivy
/*
* 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.numbers.gamma;
/**
* Complementary error function.
*/
public final class Erfc {
/** The threshold value for returning the extreme value. */
private static final double EXTREME_VALUE_BOUND = 40;
/** Private constructor. */
private Erfc() {
// intentionally empty.
}
/**
*
* This implementation computes erfc(x) using the
* {@link RegularizedGamma.Q#value(double, double, double, int) regularized gamma function},
* following Erf, equation (3).
*
*
*
* The value returned is always between 0 and 2 (inclusive).
* If {@code abs(x) > 40}, then {@code erf(x)} is indistinguishable from
* either 0 or 2 at {@code double} precision, so the appropriate extreme
* value is returned.
*
*
* @param x Value.
* @return the complementary error function.
* @throws ArithmeticException if the algorithm fails to converge.
*
* @see RegularizedGamma.Q#value(double, double, double, int)
*/
public static double value(double x) {
if (Math.abs(x) > EXTREME_VALUE_BOUND) {
return x > 0 ? 0 : 2;
}
final double ret = RegularizedGamma.Q.value(0.5, x * x, 1e-15, 10000);
return x < 0 ?
2 - ret :
ret;
}
}