001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.numbers.gamma;
018
019/**
020 * Scaled complementary error function.
021 *
022 * <p>\[ \operatorname{erfcx}(z) = \operatorname{erfc}(z)\ e^{z^2} \]
023 *
024 * <p>For large z the value is approximately:
025 *
026 * <p>\[ \operatorname{erfcx}(z) = \frac{1}{z \sqrt{\pi}} \]
027 *
028 * @see Erfc
029 * @since 1.1
030 */
031public final class Erfcx {
032    /** Private constructor. */
033    private Erfcx() {
034        // intentionally empty.
035    }
036
037    /**
038     * Returns the scaled complementary error function.
039     *
040     * <p>Special cases:
041     * <ul>
042     * <li>If the argument is 0, then the result is 1.
043     * <li>If the argument is +infinity, then the result is 0.
044     * <li>If the argument is negative and {@code exp(x*x)} is infinite, then the result is +infinity.
045     * <li>If the argument is nan, then the result is nan.
046     * </ul>
047     *
048     * @param x Value.
049     * @return the scaled complementary error function.
050     */
051    public static double value(double x) {
052        return BoostErf.erfcx(x);
053    }
054}