org.apache.commons.numbers.gamma.Erfc Maven / Gradle / Ivy
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* 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.
*
* \[ \begin{aligned} \operatorname{erfc}(z)
* &= 1 - \operatorname{erf}(z) \\
* &= \frac{2}{\sqrt\pi}\int_z^{\infty} e^{-t^2}\,dt
* \end{aligned} \]
*/
public final class Erfc {
/** Private constructor. */
private Erfc() {
// intentionally empty.
}
/**
* Returns the complementary error function.
*
*
The value returned is always between 0 and 2 (inclusive).
* The appropriate extreme is returned when {@code erfc(x)} is
* indistinguishable from either 0 or 2 at {@code double} precision.
*
*
Special cases:
*
* - If the argument is 0, then the result is 1.
*
- If the argument is {@code > 28}, then the result is 0.
*
- If the argument is {@code < 6}, then the result is 2.
*
- If the argument is nan, then the result is nan.
*
*
* @param x Value.
* @return the complementary error function.
*/
public static double value(double x) {
return BoostErf.erfc(x);
}
}