| /* |
| * 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; |
| |
| /** |
| * Computes the difference between {@link Erf error function values}. |
| */ |
| public final class ErfDifference { |
| /** |
| * This number solves {@code erf(x) = 0.5} within 1 ulp. |
| * More precisely, the current implementations of |
| * {@link Erf#value(double)} and {@link Erfc#value(double)} satisfy: |
| * <ul> |
| * <li>{@code Erf.value(X_CRIT) < 0.5},</li> |
| * <li>{@code Erf.value(Math.nextUp(X_CRIT) > 0.5},</li> |
| * <li>{@code Erfc.value(X_CRIT) = 0.5}, and</li> |
| * <li>{@code Erfc.value(Math.nextUp(X_CRIT) < 0.5}</li> |
| * </ul> |
| */ |
| private static final double X_CRIT = 0.4769362762044697; |
| |
| /** Private constructor. */ |
| private ErfDifference() { |
| // intentionally empty. |
| } |
| |
| /** |
| * The implementation uses either {@link Erf} or {@link Erfc}, |
| * depending on which provides the most precise result. |
| * |
| * @param x1 First value. |
| * @param x2 Second value. |
| * @return {@link Erf#value(double) Erf.value(x2) - Erf.value(x1)}. |
| * @throws ArithmeticException if the algorithm fails to converge. |
| */ |
| public static double value(double x1, |
| double x2) { |
| if (x1 > x2) { |
| return -value(x2, x1); |
| } else { |
| if (x1 < -X_CRIT) { |
| if (x2 < 0) { |
| return Erfc.value(-x2) - Erfc.value(-x1); |
| } else { |
| return Erf.value(x2) - Erf.value(x1); |
| } |
| } else { |
| if (x2 > X_CRIT && |
| x1 > 0) { |
| return Erfc.value(x1) - Erfc.value(x2); |
| } else { |
| return Erf.value(x2) - Erf.value(x1); |
| } |
| } |
| } |
| } |
| } |