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/Erf.html">Error function</a>.
21 *
22 * <p>\[ \operatorname{erf}(z) = \frac{2}{\sqrt\pi}\int_0^z e^{-t^2}\,dt \]
23 */
24 public final class Erf {
25 /** Private constructor. */
26 private Erf() {
27 // intentionally empty.
28 }
29
30 /**
31 * Returns the error function.
32 *
33 * <p>The returned value is always between -1 and 1 (inclusive).
34 * The appropriate extreme is returned when {@code erf(x)} is
35 * indistinguishable from either -1 or 1 at {@code double} precision.
36 *
37 * <p>Special cases:
38 * <ul>
39 * <li>If the argument is 0, then the result is 0.
40 * <li>If the argument is {@code > 6}, then the result is 1.
41 * <li>If the argument is {@code < 6}, then the result is -1.
42 * <li>If the argument is nan, then the result is nan.
43 * </ul>
44 *
45 * @param x the value.
46 * @return the error function.
47 */
48 public static double value(double x) {
49 return BoostErf.erf(x);
50 }
51 }