From 9506f2257618057e4d1e296c0ba205b10555322a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=C3=89milie=20Feral?= Date: Tue, 2 Jan 2018 13:24:24 +0100 Subject: [PATCH] [apps] Probability: add erfInv function and tests --- apps/probability/Makefile | 6 ++ apps/probability/law/erf_inv.cpp | 116 ++++++++++++++++++++++++++++++ apps/probability/law/erf_inv.h | 7 ++ apps/probability/law/law.h | 2 +- apps/probability/test/erf_inv.cpp | 18 +++++ 5 files changed, 148 insertions(+), 1 deletion(-) create mode 100644 apps/probability/law/erf_inv.cpp create mode 100644 apps/probability/law/erf_inv.h create mode 100644 apps/probability/test/erf_inv.cpp diff --git a/apps/probability/Makefile b/apps/probability/Makefile index f352864b4..080071ce2 100644 --- a/apps/probability/Makefile +++ b/apps/probability/Makefile @@ -14,6 +14,7 @@ app_objs += $(addprefix apps/probability/,\ cell.o\ image_cell.o\ law/binomial_law.o\ + law/erf_inv.o\ law/exponential_law.o\ law/law.o\ law/normal_law.o\ @@ -35,6 +36,11 @@ i18n_files += $(addprefix apps/probability/,\ base.pt.i18n\ ) +tests += $(addprefix apps/probability/test/,\ + erf_inv.cpp\ +) +test_objs += $(addprefix apps/probability/law/, erf_inv.o) + app_images += apps/probability/probability_icon.png app_images += $(addprefix apps/probability/images/,\ diff --git a/apps/probability/law/erf_inv.cpp b/apps/probability/law/erf_inv.cpp new file mode 100644 index 000000000..87afdd344 --- /dev/null +++ b/apps/probability/law/erf_inv.cpp @@ -0,0 +1,116 @@ +#include "erf_inv.h" +#include "law.h" +#include +#include + +/* + * 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. + */ + +/* This implementation is described in the paper: + * Approximating the erfinv function, Mike Giles, + * Oxford-Man Institute of Quantitative Finance, + * which was published in GPU Computing Gems, volume 2, 2010. + */ + +/* The original Appache implementation has been modified to use the libc + * library. */ +double erfInv(double x) { + // beware that the logarithm argument must be + // commputed as (1.0 - x) * (1.0 + x), + // it must NOT be simplified as 1.0 - x * x as this + // would induce rounding errors near the boundaries +/-1 + double w = - std::log((1.0 - x) * (1.0 + x)); + double p; + + if (w < 6.25) { + w = 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 = std::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 (!std::isinf(w)) { + w = std::sqrt(w) - 5.0; + 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 { + // 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 = INFINITY; + } + return p * x; +} diff --git a/apps/probability/law/erf_inv.h b/apps/probability/law/erf_inv.h new file mode 100644 index 000000000..36712a693 --- /dev/null +++ b/apps/probability/law/erf_inv.h @@ -0,0 +1,7 @@ +#ifndef PROBABILITE_ERFINV_H +#define PROBABILITE_ERFINV_H + +double erfInv(double y); + +#endif + diff --git a/apps/probability/law/law.h b/apps/probability/law/law.h index 0143e19e3..e9d4c7474 100644 --- a/apps/probability/law/law.h +++ b/apps/probability/law/law.h @@ -37,8 +37,8 @@ public: virtual double cumulativeDistributiveInverseForProbability(double * probability); virtual double rightIntegralInverseForProbability(double * probability); virtual double evaluateAtDiscreteAbscissa(int k) const; -protected: constexpr static int k_maxNumberOfOperations = 1000000; +protected: static_assert(Constant::LargeNumberOfSignificantDigits == 7, "k_maxProbability is ill-defined compared to LargeNumberOfSignificantDigits"); constexpr static double k_maxProbability = 0.9999995; constexpr static float k_displayTopMarginRatio = 0.05f; diff --git a/apps/probability/test/erf_inv.cpp b/apps/probability/test/erf_inv.cpp new file mode 100644 index 000000000..35056929e --- /dev/null +++ b/apps/probability/test/erf_inv.cpp @@ -0,0 +1,18 @@ +#include +#include +#include +#include +#include +#include "../law/erf_inv.h" + +QUIZ_CASE(erf_inv) { + assert(erfInv(0.0) == 0.0); + assert(std::isinf(erfInv(1.0)) && erfInv(1.0) > 0.0); + assert(std::isinf(erfInv(-1.0)) && erfInv(-1.0) < 0.0); + assert(std::fabs(erfInv(0.5) - 0.476936276204469873381418353643130559808969749059470644703) < DBL_EPSILON); + assert(std::fabs(erfInv(0.25) - 0.225312055012178104725014013952277554782118447807246757600) < DBL_EPSILON); + assert(std::fabs(erfInv(0.999999) - 3.458910737279500022150927635957569519915669808042886747076) < 10E-6); + assert(std::fabs(erfInv(0.123456) - 0.109850294001424923867673480939041914394684494884310054922) < DBL_EPSILON); + +} +