1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.numbers.gamma;
18
19 /**
20 * <a href="https://mathworld.wolfram.com/Erfc.html">Complementary error function</a>.
21 *
22 * <p>\[ \begin{aligned} \operatorname{erfc}(z)
23 * &= 1 - \operatorname{erf}(z) \\
24 * &= \frac{2}{\sqrt\pi}\int_z^{\infty} e^{-t^2}\,dt
25 * \end{aligned} \]
26 */
27 public final class Erfc {
28 /** Private constructor. */
29 private Erfc() {
30 // intentionally empty.
31 }
32
33 /**
34 * Returns the complementary error function.
35 *
36 * <p>The value returned is always between 0 and 2 (inclusive).
37 * The appropriate extreme is returned when {@code erfc(x)} is
38 * indistinguishable from either 0 or 2 at {@code double} precision.
39 *
40 * <p>Special cases:
41 * <ul>
42 * <li>If the argument is 0, then the result is 1.
43 * <li>If the argument is {@code > 28}, then the result is 0.
44 * <li>If the argument is {@code < 6}, then the result is 2.
45 * <li>If the argument is nan, then the result is nan.
46 * </ul>
47 *
48 * @param x Value.
49 * @return the complementary error function.
50 */
51 public static double value(double x) {
52 return BoostErf.erfc(x);
53 }
54 }