org.apache.commons.numbers.gamma.ErfDifference 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;
/**
* 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:
*
* - {@code Erf.value(X_CRIT) < 0.5},
* - {@code Erf.value(Math.nextUp(X_CRIT) > 0.5},
* - {@code Erfc.value(X_CRIT) = 0.5}, and
* - {@code Erfc.value(Math.nextUp(X_CRIT) < 0.5}
*
*/
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);
}
}
}
}
}