| /* |
| * 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; |
| |
| /** |
| * Inverse of the <a href="http://mathworld.wolfram.com/Erf.html">error function</a>. |
| * <p> |
| * This implementation is described in the paper: |
| * <a href="http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf">Approximating |
| * the erfinv function</a> by Mike Giles, Oxford-Man Institute of Quantitative Finance, |
| * which was published in GPU Computing Gems, volume 2, 2010. |
| * The source code is available <a href="http://gpucomputing.net/?q=node/1828">here</a>. |
| * </p> |
| */ |
| public final class InverseErf { |
| /** Private constructor. */ |
| private InverseErf() { |
| // intentionally empty. |
| } |
| |
| /** |
| * Returns the inverse error function. |
| * |
| * @param x Value. |
| * @return t such that {@code x =} {@link Erf#value(double) Erf.value(t)}. |
| */ |
| public static double value(final double x) { |
| // Beware that the logarithm argument must be |
| // computed as (1 - x) * (1 + x), |
| // it must NOT be simplified as 1 - x * x as this |
| // would induce rounding errors near the boundaries +/-1 |
| double w = -Math.log((1 - x) * (1 + x)); |
| double p; |
| |
| if (w < 6.25) { |
| w -= 3.125; |
| p = -3.6444120640178196996e-21; |
| p = -1.685059138182016589e-19 + p * w; |
| p = 1.2858480715256400167e-18 + p * w; |
| p = 1.115787767802518096e-17 + p * w; |
| p = -1.333171662854620906e-16 + p * w; |
| p = 2.0972767875968561637e-17 + p * w; |
| p = 6.6376381343583238325e-15 + p * w; |
| p = -4.0545662729752068639e-14 + p * w; |
| p = -8.1519341976054721522e-14 + p * w; |
| p = 2.6335093153082322977e-12 + p * w; |
| p = -1.2975133253453532498e-11 + p * w; |
| p = -5.4154120542946279317e-11 + p * w; |
| p = 1.051212273321532285e-09 + p * w; |
| p = -4.1126339803469836976e-09 + p * w; |
| p = -2.9070369957882005086e-08 + p * w; |
| p = 4.2347877827932403518e-07 + p * w; |
| p = -1.3654692000834678645e-06 + p * w; |
| p = -1.3882523362786468719e-05 + p * w; |
| p = 0.0001867342080340571352 + p * w; |
| p = -0.00074070253416626697512 + p * w; |
| p = -0.0060336708714301490533 + p * w; |
| p = 0.24015818242558961693 + p * w; |
| p = 1.6536545626831027356 + p * w; |
| } else if (w < 16.0) { |
| w = Math.sqrt(w) - 3.25; |
| p = 2.2137376921775787049e-09; |
| p = 9.0756561938885390979e-08 + p * w; |
| p = -2.7517406297064545428e-07 + p * w; |
| p = 1.8239629214389227755e-08 + p * w; |
| p = 1.5027403968909827627e-06 + p * w; |
| p = -4.013867526981545969e-06 + p * w; |
| p = 2.9234449089955446044e-06 + p * w; |
| p = 1.2475304481671778723e-05 + p * w; |
| p = -4.7318229009055733981e-05 + p * w; |
| p = 6.8284851459573175448e-05 + p * w; |
| p = 2.4031110387097893999e-05 + p * w; |
| p = -0.0003550375203628474796 + p * w; |
| p = 0.00095328937973738049703 + p * w; |
| p = -0.0016882755560235047313 + p * w; |
| p = 0.0024914420961078508066 + p * w; |
| p = -0.0037512085075692412107 + p * w; |
| p = 0.005370914553590063617 + p * w; |
| p = 1.0052589676941592334 + p * w; |
| p = 3.0838856104922207635 + p * w; |
| } else if (w < Double.POSITIVE_INFINITY) { |
| w = Math.sqrt(w) - 5; |
| p = -2.7109920616438573243e-11; |
| p = -2.5556418169965252055e-10 + p * w; |
| p = 1.5076572693500548083e-09 + p * w; |
| p = -3.7894654401267369937e-09 + p * w; |
| p = 7.6157012080783393804e-09 + p * w; |
| p = -1.4960026627149240478e-08 + p * w; |
| p = 2.9147953450901080826e-08 + p * w; |
| p = -6.7711997758452339498e-08 + p * w; |
| p = 2.2900482228026654717e-07 + p * w; |
| p = -9.9298272942317002539e-07 + p * w; |
| p = 4.5260625972231537039e-06 + p * w; |
| p = -1.9681778105531670567e-05 + p * w; |
| p = 7.5995277030017761139e-05 + p * w; |
| p = -0.00021503011930044477347 + p * w; |
| p = -0.00013871931833623122026 + p * w; |
| p = 1.0103004648645343977 + p * w; |
| p = 4.8499064014085844221 + p * w; |
| } else if (w == Double.POSITIVE_INFINITY) { |
| // this branch does not appears in the original code, it |
| // was added because the previous branch does not handle |
| // x = +/-1 correctly. In this case, w is positive infinity |
| // and as the first coefficient (-2.71e-11) is negative. |
| // Once the first multiplication is done, p becomes negative |
| // infinity and remains so throughout the polynomial evaluation. |
| // So the branch above incorrectly returns negative infinity |
| // instead of the correct positive infinity. |
| p = Double.POSITIVE_INFINITY; |
| } else { |
| // this branch does not appears in the original code, it |
| // occurs when the input is NaN or not in the range [-1, 1]. |
| return Double.NaN; |
| } |
| |
| return p * x; |
| } |
| } |
| |