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[apps] Probability: add erfInv function and tests
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Émilie Feral
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EmilieNumworks
EmilieNumworks
parent
a8b3fbbe5e
commit
9506f22576
@@ -14,6 +14,7 @@ app_objs += $(addprefix apps/probability/,\
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cell.o\
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image_cell.o\
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law/binomial_law.o\
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law/erf_inv.o\
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law/exponential_law.o\
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law/law.o\
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law/normal_law.o\
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@@ -35,6 +36,11 @@ i18n_files += $(addprefix apps/probability/,\
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base.pt.i18n\
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)
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tests += $(addprefix apps/probability/test/,\
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erf_inv.cpp\
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)
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test_objs += $(addprefix apps/probability/law/, erf_inv.o)
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app_images += apps/probability/probability_icon.png
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app_images += $(addprefix apps/probability/images/,\
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116
apps/probability/law/erf_inv.cpp
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116
apps/probability/law/erf_inv.cpp
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@@ -0,0 +1,116 @@
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#include "erf_inv.h"
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#include "law.h"
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#include <cmath>
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#include <float.h>
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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/* This implementation is described in the paper:
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* Approximating the erfinv function, Mike Giles,
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* Oxford-Man Institute of Quantitative Finance,
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* which was published in GPU Computing Gems, volume 2, 2010.
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*/
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/* The original Appache implementation has been modified to use the libc
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* library. */
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double erfInv(double x) {
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// beware that the logarithm argument must be
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// commputed as (1.0 - x) * (1.0 + x),
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// it must NOT be simplified as 1.0 - x * x as this
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// would induce rounding errors near the boundaries +/-1
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double w = - std::log((1.0 - x) * (1.0 + x));
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double p;
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if (w < 6.25) {
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w = w - 3.125;
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p = -3.6444120640178196996e-21;
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p = -1.685059138182016589e-19 + p * w;
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p = 1.2858480715256400167e-18 + p * w;
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p = 1.115787767802518096e-17 + p * w;
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p = -1.333171662854620906e-16 + p * w;
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p = 2.0972767875968561637e-17 + p * w;
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p = 6.6376381343583238325e-15 + p * w;
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p = -4.0545662729752068639e-14 + p * w;
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p = -8.1519341976054721522e-14 + p * w;
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p = 2.6335093153082322977e-12 + p * w;
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p = -1.2975133253453532498e-11 + p * w;
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p = -5.4154120542946279317e-11 + p * w;
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p = 1.051212273321532285e-09 + p * w;
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p = -4.1126339803469836976e-09 + p * w;
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p = -2.9070369957882005086e-08 + p * w;
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p = 4.2347877827932403518e-07 + p * w;
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p = -1.3654692000834678645e-06 + p * w;
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p = -1.3882523362786468719e-05 + p * w;
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p = 0.0001867342080340571352 + p * w;
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p = -0.00074070253416626697512 + p * w;
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p = -0.0060336708714301490533 + p * w;
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p = 0.24015818242558961693 + p * w;
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p = 1.6536545626831027356 + p * w;
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} else if (w < 16.0) {
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w = std::sqrt(w) - 3.25;
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p = 2.2137376921775787049e-09;
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p = 9.0756561938885390979e-08 + p * w;
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p = -2.7517406297064545428e-07 + p * w;
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p = 1.8239629214389227755e-08 + p * w;
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p = 1.5027403968909827627e-06 + p * w;
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p = -4.013867526981545969e-06 + p * w;
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p = 2.9234449089955446044e-06 + p * w;
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p = 1.2475304481671778723e-05 + p * w;
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p = -4.7318229009055733981e-05 + p * w;
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p = 6.8284851459573175448e-05 + p * w;
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p = 2.4031110387097893999e-05 + p * w;
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p = -0.0003550375203628474796 + p * w;
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p = 0.00095328937973738049703 + p * w;
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p = -0.0016882755560235047313 + p * w;
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p = 0.0024914420961078508066 + p * w;
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p = -0.0037512085075692412107 + p * w;
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p = 0.005370914553590063617 + p * w;
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p = 1.0052589676941592334 + p * w;
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p = 3.0838856104922207635 + p * w;
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} else if (!std::isinf(w)) {
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w = std::sqrt(w) - 5.0;
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p = -2.7109920616438573243e-11;
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p = -2.5556418169965252055e-10 + p * w;
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p = 1.5076572693500548083e-09 + p * w;
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p = -3.7894654401267369937e-09 + p * w;
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p = 7.6157012080783393804e-09 + p * w;
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p = -1.4960026627149240478e-08 + p * w;
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p = 2.9147953450901080826e-08 + p * w;
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p = -6.7711997758452339498e-08 + p * w;
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p = 2.2900482228026654717e-07 + p * w;
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p = -9.9298272942317002539e-07 + p * w;
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p = 4.5260625972231537039e-06 + p * w;
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p = -1.9681778105531670567e-05 + p * w;
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p = 7.5995277030017761139e-05 + p * w;
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p = -0.00021503011930044477347 + p * w;
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p = -0.00013871931833623122026 + p * w;
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p = 1.0103004648645343977 + p * w;
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p = 4.8499064014085844221 + p * w;
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} else {
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// this branch does not appears in the original code, it
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// was added because the previous branch does not handle
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// x = +/-1 correctly. In this case, w is positive infinity
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// and as the first coefficient (-2.71e-11) is negative.
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// Once the first multiplication is done, p becomes negative
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// infinity and remains so throughout the polynomial evaluation.
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// So the branch above incorrectly returns negative infinity
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// instead of the correct positive infinity.
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p = INFINITY;
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}
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return p * x;
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}
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7
apps/probability/law/erf_inv.h
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7
apps/probability/law/erf_inv.h
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@@ -0,0 +1,7 @@
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#ifndef PROBABILITE_ERFINV_H
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#define PROBABILITE_ERFINV_H
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double erfInv(double y);
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#endif
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@@ -37,8 +37,8 @@ public:
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virtual double cumulativeDistributiveInverseForProbability(double * probability);
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virtual double rightIntegralInverseForProbability(double * probability);
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virtual double evaluateAtDiscreteAbscissa(int k) const;
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protected:
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constexpr static int k_maxNumberOfOperations = 1000000;
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protected:
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static_assert(Constant::LargeNumberOfSignificantDigits == 7, "k_maxProbability is ill-defined compared to LargeNumberOfSignificantDigits");
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constexpr static double k_maxProbability = 0.9999995;
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constexpr static float k_displayTopMarginRatio = 0.05f;
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18
apps/probability/test/erf_inv.cpp
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18
apps/probability/test/erf_inv.cpp
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@@ -0,0 +1,18 @@
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#include <quiz.h>
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#include <string.h>
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#include <assert.h>
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#include <float.h>
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#include <cmath>
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#include "../law/erf_inv.h"
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QUIZ_CASE(erf_inv) {
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assert(erfInv(0.0) == 0.0);
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assert(std::isinf(erfInv(1.0)) && erfInv(1.0) > 0.0);
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assert(std::isinf(erfInv(-1.0)) && erfInv(-1.0) < 0.0);
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assert(std::fabs(erfInv(0.5) - 0.476936276204469873381418353643130559808969749059470644703) < DBL_EPSILON);
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assert(std::fabs(erfInv(0.25) - 0.225312055012178104725014013952277554782118447807246757600) < DBL_EPSILON);
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assert(std::fabs(erfInv(0.999999) - 3.458910737279500022150927635957569519915669808042886747076) < 10E-6);
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assert(std::fabs(erfInv(0.123456) - 0.109850294001424923867673480939041914394684494884310054922) < DBL_EPSILON);
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}
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