third_party/cephes/inverse_gaussian_cdf_test.cc - third_party/github.com/google/differential-privacy - Git at Google

 // Distributed under 3-clause BSD license with permission from the author,
 //   see https://lists.debian.org/debian-legal/2004/12/msg00295.html
 //
 //   Cephes Math Library Release 2.8:  June, 2000
 //
 //   Copyright 1984, 1995, 2000 by Stephen L. Moshier
 //
 //   This software is derived from the Cephes Math Library and is
 //   incorporated herein by permission of the author.
 //
 //   All rights reserved.
 //
 //   Redistribution and use in source and binary forms, with or without
 //   modification, are permitted provided that the following conditions are met:
 //
 //       * Redistributions of source code must retain the above copyright
 //         notice, this list of conditions and the following disclaimer.
 //       * Redistributions in binary form must reproduce the above copyright
 //         notice, this list of conditions and the following disclaimer in the
 //        documentation and/or other materials provided with the distribution.
 //       * Neither the name of the <organization> nor the
 //         names of its contributors may be used to endorse or promote products
 //         derived from this software without specific prior written permission.
 //
 //   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 //   AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 //   IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 //   ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
 //   DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 //   (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 //   SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 //   CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 //   LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 //   OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
 //   DAMAGE.
 //
 // Note: The file inverse_gaussian_cdf.cc is a rewrite of the implementation
 // of the ndtri function in the cephes library. It is not a copy; modification
 // was permitted by the author under the above license. The original file can be
 // found here: https://netlib.org/cephes/doubldoc.html#ndtri
 #include "third_party/cephes/inverse_gaussian_cdf.h"

 #include <cstdlib>
 #include <limits>

 #include "gtest/gtest.h"

 namespace differential_privacy::third_party::cephes {
 namespace {

 TEST(InverseCdfStandardGaussianTest, InputZeroReturnsNagativeInfinity) {
   EXPECT_EQ(InverseCdfStandardGaussian(0.0),
             -std::numeric_limits<double>::infinity());
 }

 TEST(InverseCdfStandardGaussianTest, InputOneReturnsInfinity) {
   EXPECT_EQ(InverseCdfStandardGaussian(1.0),
             std::numeric_limits<double>::infinity());
 }

 TEST(InverseCdfStandardGaussianTest, VerifiesThatMedianOfGaussianIsZero) {
   EXPECT_NEAR(InverseCdfStandardGaussian(0.5), 0, 1E-15);
 }

 struct InputOutput {
   double input;
   double expected_output;
 };

 using InverseCdfStandardGaussianIoTest = ::testing::TestWithParam<InputOutput>;

 TEST_P(InverseCdfStandardGaussianIoTest, RelativeAccuracy) {
   const InputOutput& test_case = GetParam();

   double output = InverseCdfStandardGaussian(test_case.input);
   double relative_accuracy = std::abs((output - test_case.expected_output) /
                                       test_case.expected_output);

   EXPECT_NEAR(0.0, relative_accuracy, 1e-15);
 }

 // Listing a number of correct input/output pairs.
 // The values were generated by the following python code:
 //
 // from scipy.stats import norm
 // from numpy.random import uniform
 //
 // numbers_per_order = 2
 //
 // # p close to 1, st. 1-p is of order 10**(-i)
 // # Due to rounding errors, this has limitations
 // for i in range(1,14):
 //   for j in range(numbers_per_order):
 //     rand = uniform(1-10**(-i), 1)
 //     print("{%.18e, %.18f}," % (rand, norm.ppf(rand)))
 //
 // # p close to 0, st. p is of order 10**(-i)
 // for i in [0, 1, 2, 4, 8, 15, 16, 17, 32, 64, 128, 256, 300]:
 //   for j in range(numbers_per_order):
 //     rand = uniform(0.1, 1) * 10**(-i)
 //     print("{%.18e, %.18f}," % (rand, norm.ppf(rand)))
 INSTANTIATE_TEST_SUITE_P(
     RelativeAccuracyTest, InverseCdfStandardGaussianIoTest,
     testing::ValuesIn<InputOutput>({
         {9.590875421333870943e-01, 1.740194245526870631},
         {9.204728130878864212e-01, 1.408259059429154192},
         {9.987822916403579221e-01, 3.031252275870897073},
         {9.925605599510384236e-01, 2.435313800480054969},
         {9.990447702229799942e-01, 3.103810031034545780},
         {9.996763629885648816e-01, 3.410990265746212557},
         {9.999886033679458164e-01, 4.235609454156513465},
         {9.999760495761819135e-01, 4.065639908388418711},
         {9.999918285209185020e-01, 4.309763019113548310},
         {9.999949297010878313e-01, 4.414153527077065320},
         {9.999995741498048929e-01, 4.923131819830989464},
         {9.999997043019083209e-01, 4.994005806628707411},
         {9.999999930150607064e-01, 5.673757581075118850},
         {9.999999627780953304e-01, 5.380101608071190533},
         {9.999999977551378150e-01, 5.865059216395640540},
         {9.999999987822485448e-01, 5.965724924667977547},
         {9.999999996778887734e-01, 6.179212230118906746},
         {9.999999995927016938e-01, 6.142056907043477842},
         {9.999999999050942501e-01, 6.369365733005997399},
         {9.999999999612441126e-01, 6.505351784059330456},
         {9.999999999965828446e-01, 6.861077421111833274},
         {9.999999999911421966e-01, 6.723709001398219698},
         {9.999999999990811794e-01, 7.046280136673924055},
         {9.999999999995440314e-01, 7.143183551114592689},
         {9.999999999999484857e-01, 7.436960043545139065},
         {9.999999999999442668e-01, 7.426550452501929911},
         {7.078202134622706421e-01, 0.547027887498922949},
         {3.389657500740557161e-01, -0.415287432523317290},
         {5.957715702260371615e-02, -1.558333067730558463},
         {7.814884269185563836e-02, -1.417633872953655949},
         {7.031239497917323583e-03, -2.455663440450241986},
         {1.539105641403513232e-03, -2.959817704299271046},
         {4.308036802518321198e-05, -3.926584208482659655},
         {4.792417534760087735e-05, -3.900868137755500342},
         {4.463560376039031862e-09, -5.749947420065786297},
         {4.134037552039715277e-09, -5.762900076062255295},
         {4.483536530421512750e-16, -8.040229004994209561},
         {3.339983254697393151e-16, -8.076230307018560595},
         {6.215336569124182823e-17, -8.278911061075142186},
         {9.601065568608536918e-17, -8.226962019547366722},
         {6.991559520245878977e-18, -8.535267778973684827},
         {7.798272601053520958e-18, -8.522633695927112285},
         {9.753826112572825312e-33, -11.858220714899207593},
         {7.239945717749332110e-33, -11.883153923605899394},
         {3.081878658827924595e-65, -17.016810944246216764},
         {5.854299805089005594e-65, -16.979192464465175050},
         {8.217571054262086351e-129, -24.117363860470103276},
         {5.940660698416777152e-129, -24.130790266655189669},
         {7.104594771285924014e-257, -34.215527373144254852},
         {5.222691495369919695e-257, -34.224512368673167373},
         {9.255861729918001973e-301, -37.049182013454569073},
         {5.918562407887116857e-301, -37.061240736056291212},
     }));

 }  // namespace
 }  // namespace differential_privacy::third_party::cephes
	// Distributed under 3-clause BSD license with permission from the author,
	// see https://lists.debian.org/debian-legal/2004/12/msg00295.html
	//
	// Cephes Math Library Release 2.8: June, 2000
	//
	// Copyright 1984, 1995, 2000 by Stephen L. Moshier
	//
	// This software is derived from the Cephes Math Library and is
	// incorporated herein by permission of the author.
	//
	// All rights reserved.
	//
	// Redistribution and use in source and binary forms, with or without
	// modification, are permitted provided that the following conditions are met:
	//
	// * Redistributions of source code must retain the above copyright
	// notice, this list of conditions and the following disclaimer.
	// * Redistributions in binary form must reproduce the above copyright
	// notice, this list of conditions and the following disclaimer in the
	// documentation and/or other materials provided with the distribution.
	// * Neither the name of the <organization> nor the
	// names of its contributors may be used to endorse or promote products
	// derived from this software without specific prior written permission.
	//
	// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
	// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	// ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
	// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
	// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
	// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
	// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
	// DAMAGE.
	//
	// Note: The file inverse_gaussian_cdf.cc is a rewrite of the implementation
	// of the ndtri function in the cephes library. It is not a copy; modification
	// was permitted by the author under the above license. The original file can be
	// found here: https://netlib.org/cephes/doubldoc.html#ndtri
	#include "third_party/cephes/inverse_gaussian_cdf.h"

	#include <cstdlib>
	#include <limits>

	#include "gtest/gtest.h"

	namespace differential_privacy::third_party::cephes {
	namespace {

	TEST(InverseCdfStandardGaussianTest, InputZeroReturnsNagativeInfinity) {
	EXPECT_EQ(InverseCdfStandardGaussian(0.0),
	-std::numeric_limits<double>::infinity());
	}

	TEST(InverseCdfStandardGaussianTest, InputOneReturnsInfinity) {
	EXPECT_EQ(InverseCdfStandardGaussian(1.0),
	std::numeric_limits<double>::infinity());
	}

	TEST(InverseCdfStandardGaussianTest, VerifiesThatMedianOfGaussianIsZero) {
	EXPECT_NEAR(InverseCdfStandardGaussian(0.5), 0, 1E-15);
	}

	struct InputOutput {
	double input;
	double expected_output;
	};

	using InverseCdfStandardGaussianIoTest = ::testing::TestWithParam<InputOutput>;

	TEST_P(InverseCdfStandardGaussianIoTest, RelativeAccuracy) {
	const InputOutput& test_case = GetParam();

	double output = InverseCdfStandardGaussian(test_case.input);
	double relative_accuracy = std::abs((output - test_case.expected_output) /
	test_case.expected_output);

	EXPECT_NEAR(0.0, relative_accuracy, 1e-15);
	}

	// Listing a number of correct input/output pairs.
	// The values were generated by the following python code:
	//
	// from scipy.stats import norm
	// from numpy.random import uniform
	//
	// numbers_per_order = 2
	//
	// # p close to 1, st. 1-p is of order 10**(-i)
	// # Due to rounding errors, this has limitations
	// for i in range(1,14):
	// for j in range(numbers_per_order):
	// rand = uniform(1-10**(-i), 1)
	// print("{%.18e, %.18f}," % (rand, norm.ppf(rand)))
	//
	// # p close to 0, st. p is of order 10**(-i)
	// for i in [0, 1, 2, 4, 8, 15, 16, 17, 32, 64, 128, 256, 300]:
	// for j in range(numbers_per_order):
	// rand = uniform(0.1, 1) * 10**(-i)
	// print("{%.18e, %.18f}," % (rand, norm.ppf(rand)))
	INSTANTIATE_TEST_SUITE_P(
	RelativeAccuracyTest, InverseCdfStandardGaussianIoTest,
	testing::ValuesIn<InputOutput>({
	{9.590875421333870943e-01, 1.740194245526870631},
	{9.204728130878864212e-01, 1.408259059429154192},
	{9.987822916403579221e-01, 3.031252275870897073},
	{9.925605599510384236e-01, 2.435313800480054969},
	{9.990447702229799942e-01, 3.103810031034545780},
	{9.996763629885648816e-01, 3.410990265746212557},
	{9.999886033679458164e-01, 4.235609454156513465},
	{9.999760495761819135e-01, 4.065639908388418711},
	{9.999918285209185020e-01, 4.309763019113548310},
	{9.999949297010878313e-01, 4.414153527077065320},
	{9.999995741498048929e-01, 4.923131819830989464},
	{9.999997043019083209e-01, 4.994005806628707411},
	{9.999999930150607064e-01, 5.673757581075118850},
	{9.999999627780953304e-01, 5.380101608071190533},
	{9.999999977551378150e-01, 5.865059216395640540},
	{9.999999987822485448e-01, 5.965724924667977547},
	{9.999999996778887734e-01, 6.179212230118906746},
	{9.999999995927016938e-01, 6.142056907043477842},
	{9.999999999050942501e-01, 6.369365733005997399},
	{9.999999999612441126e-01, 6.505351784059330456},
	{9.999999999965828446e-01, 6.861077421111833274},
	{9.999999999911421966e-01, 6.723709001398219698},
	{9.999999999990811794e-01, 7.046280136673924055},
	{9.999999999995440314e-01, 7.143183551114592689},
	{9.999999999999484857e-01, 7.436960043545139065},
	{9.999999999999442668e-01, 7.426550452501929911},
	{7.078202134622706421e-01, 0.547027887498922949},
	{3.389657500740557161e-01, -0.415287432523317290},
	{5.957715702260371615e-02, -1.558333067730558463},
	{7.814884269185563836e-02, -1.417633872953655949},
	{7.031239497917323583e-03, -2.455663440450241986},
	{1.539105641403513232e-03, -2.959817704299271046},
	{4.308036802518321198e-05, -3.926584208482659655},
	{4.792417534760087735e-05, -3.900868137755500342},
	{4.463560376039031862e-09, -5.749947420065786297},
	{4.134037552039715277e-09, -5.762900076062255295},
	{4.483536530421512750e-16, -8.040229004994209561},
	{3.339983254697393151e-16, -8.076230307018560595},
	{6.215336569124182823e-17, -8.278911061075142186},
	{9.601065568608536918e-17, -8.226962019547366722},
	{6.991559520245878977e-18, -8.535267778973684827},
	{7.798272601053520958e-18, -8.522633695927112285},
	{9.753826112572825312e-33, -11.858220714899207593},
	{7.239945717749332110e-33, -11.883153923605899394},
	{3.081878658827924595e-65, -17.016810944246216764},
	{5.854299805089005594e-65, -16.979192464465175050},
	{8.217571054262086351e-129, -24.117363860470103276},
	{5.940660698416777152e-129, -24.130790266655189669},
	{7.104594771285924014e-257, -34.215527373144254852},
	{5.222691495369919695e-257, -34.224512368673167373},
	{9.255861729918001973e-301, -37.049182013454569073},
	{5.918562407887116857e-301, -37.061240736056291212},
	}));

	} // namespace
	} // namespace differential_privacy::third_party::cephes