// Copyright 2017 The Abseil Authors. // // Licensed 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 // // https://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. #include "absl/random/uniform_real_distribution.h" #include <cmath> #include <cstdint> #include <iterator> #include <random> #include <sstream> #include <string> #include <vector> #include "gmock/gmock.h" #include "gtest/gtest.h" #include "absl/base/internal/raw_logging.h" #include "absl/random/internal/chi_square.h" #include "absl/random/internal/distribution_test_util.h" #include "absl/random/internal/pcg_engine.h" #include "absl/random/internal/sequence_urbg.h" #include "absl/random/random.h" #include "absl/strings/str_cat.h" // NOTES: // * Some documentation on generating random real values suggests that // it is possible to use std::nextafter(b, DBL_MAX) to generate a value on // the closed range [a, b]. Unfortunately, that technique is not universally // reliable due to floating point quantization. // // * absl::uniform_real_distribution<float> generates between 2^28 and 2^29 // distinct floating point values in the range [0, 1). // // * absl::uniform_real_distribution<float> generates at least 2^23 distinct // floating point values in the range [1, 2). This should be the same as // any other range covered by a single exponent in IEEE 754. // // * absl::uniform_real_distribution<double> generates more than 2^52 distinct // values in the range [0, 1), and should generate at least 2^52 distinct // values in the range of [1, 2). // namespace { template <typename RealType> class UniformRealDistributionTest : public ::testing::Test {}; #if defined(__EMSCRIPTEN__) using RealTypes = ::testing::Types<float, double>; #else using RealTypes = ::testing::Types<float, double, long double>; #endif // defined(__EMSCRIPTEN__) TYPED_TEST_SUITE(UniformRealDistributionTest, RealTypes); TYPED_TEST(UniformRealDistributionTest, ParamSerializeTest) { using param_type = typename absl::uniform_real_distribution<TypeParam>::param_type; constexpr const TypeParam a{1152921504606846976}; constexpr int kCount = 1000; absl::InsecureBitGen gen; for (const auto& param : { param_type(), param_type(TypeParam(2.0), TypeParam(2.0)), // Same param_type(TypeParam(-0.1), TypeParam(0.1)), param_type(TypeParam(0.05), TypeParam(0.12)), param_type(TypeParam(-0.05), TypeParam(0.13)), param_type(TypeParam(-0.05), TypeParam(-0.02)), // double range = 0 // 2^60 , 2^60 + 2^6 param_type(a, TypeParam(1152921504606847040)), // 2^60 , 2^60 + 2^7 param_type(a, TypeParam(1152921504606847104)), // double range = 2^8 // 2^60 , 2^60 + 2^8 param_type(a, TypeParam(1152921504606847232)), // float range = 0 // 2^60 , 2^60 + 2^36 param_type(a, TypeParam(1152921573326323712)), // 2^60 , 2^60 + 2^37 param_type(a, TypeParam(1152921642045800448)), // float range = 2^38 // 2^60 , 2^60 + 2^38 param_type(a, TypeParam(1152921779484753920)), // Limits param_type(0, std::numeric_limits<TypeParam>::max()), param_type(std::numeric_limits<TypeParam>::lowest(), 0), param_type(0, std::numeric_limits<TypeParam>::epsilon()), param_type(-std::numeric_limits<TypeParam>::epsilon(), std::numeric_limits<TypeParam>::epsilon()), param_type(std::numeric_limits<TypeParam>::epsilon(), 2 * std::numeric_limits<TypeParam>::epsilon()), }) { // Validate parameters. const auto a = param.a(); const auto b = param.b(); absl::uniform_real_distribution<TypeParam> before(a, b); EXPECT_EQ(before.a(), param.a()); EXPECT_EQ(before.b(), param.b()); { absl::uniform_real_distribution<TypeParam> via_param(param); EXPECT_EQ(via_param, before); } std::stringstream ss; ss << before; absl::uniform_real_distribution<TypeParam> after(TypeParam(1.0), TypeParam(3.1)); EXPECT_NE(before.a(), after.a()); EXPECT_NE(before.b(), after.b()); EXPECT_NE(before.param(), after.param()); EXPECT_NE(before, after); ss >> after; EXPECT_EQ(before.a(), after.a()); EXPECT_EQ(before.b(), after.b()); EXPECT_EQ(before.param(), after.param()); EXPECT_EQ(before, after); // Smoke test. auto sample_min = after.max(); auto sample_max = after.min(); for (int i = 0; i < kCount; i++) { auto sample = after(gen); // Failure here indicates a bug in uniform_real_distribution::operator(), // or bad parameters--range too large, etc. if (after.min() == after.max()) { EXPECT_EQ(sample, after.min()); } else { EXPECT_GE(sample, after.min()); EXPECT_LT(sample, after.max()); } if (sample > sample_max) { sample_max = sample; } if (sample < sample_min) { sample_min = sample; } } if (!std::is_same<TypeParam, long double>::value) { // static_cast<double>(long double) can overflow. std::string msg = absl::StrCat("Range: ", static_cast<double>(sample_min), ", ", static_cast<double>(sample_max)); ABSL_RAW_LOG(INFO, "%s", msg.c_str()); } } } #ifdef _MSC_VER #pragma warning(push) #pragma warning(disable:4756) // Constant arithmetic overflow. #endif TYPED_TEST(UniformRealDistributionTest, ViolatesPreconditionsDeathTest) { #if GTEST_HAS_DEATH_TEST // Hi < Lo EXPECT_DEBUG_DEATH( { absl::uniform_real_distribution<TypeParam> dist(10.0, 1.0); }, ""); // Hi - Lo > numeric_limits<>::max() EXPECT_DEBUG_DEATH( { absl::uniform_real_distribution<TypeParam> dist( std::numeric_limits<TypeParam>::lowest(), std::numeric_limits<TypeParam>::max()); }, ""); #endif // GTEST_HAS_DEATH_TEST #if defined(NDEBUG) // opt-mode, for invalid parameters, will generate a garbage value, // but should not enter an infinite loop. absl::InsecureBitGen gen; { absl::uniform_real_distribution<TypeParam> dist(10.0, 1.0); auto x = dist(gen); EXPECT_FALSE(std::isnan(x)) << x; } { absl::uniform_real_distribution<TypeParam> dist( std::numeric_limits<TypeParam>::lowest(), std::numeric_limits<TypeParam>::max()); auto x = dist(gen); // Infinite result. EXPECT_FALSE(std::isfinite(x)) << x; } #endif // NDEBUG } #ifdef _MSC_VER #pragma warning(pop) // warning(disable:4756) #endif TYPED_TEST(UniformRealDistributionTest, TestMoments) { constexpr int kSize = 1000000; std::vector<double> values(kSize); // We use a fixed bit generator for distribution accuracy tests. This allows // these tests to be deterministic, while still testing the qualify of the // implementation. absl::random_internal::pcg64_2018_engine rng{0x2B7E151628AED2A6}; absl::uniform_real_distribution<TypeParam> dist; for (int i = 0; i < kSize; i++) { values[i] = dist(rng); } const auto moments = absl::random_internal::ComputeDistributionMoments(values); EXPECT_NEAR(0.5, moments.mean, 0.01); EXPECT_NEAR(1 / 12.0, moments.variance, 0.015); EXPECT_NEAR(0.0, moments.skewness, 0.02); EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.015); } TYPED_TEST(UniformRealDistributionTest, ChiSquaredTest50) { using absl::random_internal::kChiSquared; using param_type = typename absl::uniform_real_distribution<TypeParam>::param_type; constexpr size_t kTrials = 100000; constexpr int kBuckets = 50; constexpr double kExpected = static_cast<double>(kTrials) / static_cast<double>(kBuckets); // 1-in-100000 threshold, but remember, there are about 8 tests // in this file. And the test could fail for other reasons. // Empirically validated with --runs_per_test=10000. const int kThreshold = absl::random_internal::ChiSquareValue(kBuckets - 1, 0.999999); // We use a fixed bit generator for distribution accuracy tests. This allows // these tests to be deterministic, while still testing the qualify of the // implementation. absl::random_internal::pcg64_2018_engine rng{0x2B7E151628AED2A6}; for (const auto& param : {param_type(0, 1), param_type(5, 12), param_type(-5, 13), param_type(-5, -2)}) { const double min_val = param.a(); const double max_val = param.b(); const double factor = kBuckets / (max_val - min_val); std::vector<int32_t> counts(kBuckets, 0); absl::uniform_real_distribution<TypeParam> dist(param); for (size_t i = 0; i < kTrials; i++) { auto x = dist(rng); auto bucket = static_cast<size_t>((x - min_val) * factor); counts[bucket]++; } double chi_square = absl::random_internal::ChiSquareWithExpected( std::begin(counts), std::end(counts), kExpected); if (chi_square > kThreshold) { double p_value = absl::random_internal::ChiSquarePValue(chi_square, kBuckets); // Chi-squared test failed. Output does not appear to be uniform. std::string msg; for (const auto& a : counts) { absl::StrAppend(&msg, a, "\n"); } absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n"); absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ", kThreshold); ABSL_RAW_LOG(INFO, "%s", msg.c_str()); FAIL() << msg; } } } TYPED_TEST(UniformRealDistributionTest, StabilityTest) { // absl::uniform_real_distribution stability relies only on // random_internal::RandU64ToDouble and random_internal::RandU64ToFloat. absl::random_internal::sequence_urbg urbg( {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull, 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull, 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull, 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull}); std::vector<int> output(12); absl::uniform_real_distribution<TypeParam> dist; std::generate(std::begin(output), std::end(output), [&] { return static_cast<int>(TypeParam(1000000) * dist(urbg)); }); EXPECT_THAT( output, // testing::ElementsAre(59, 999246, 762494, 395876, 167716, 82545, 925251, 77341, 12527, 708791, 834451, 932808)); } TEST(UniformRealDistributionTest, AlgorithmBounds) { absl::uniform_real_distribution<double> dist; { // This returns the smallest value >0 from absl::uniform_real_distribution. absl::random_internal::sequence_urbg urbg({0x0000000000000001ull}); double a = dist(urbg); EXPECT_EQ(a, 5.42101086242752217004e-20); } { // This returns a value very near 0.5 from absl::uniform_real_distribution. absl::random_internal::sequence_urbg urbg({0x7fffffffffffffefull}); double a = dist(urbg); EXPECT_EQ(a, 0.499999999999999944489); } { // This returns a value very near 0.5 from absl::uniform_real_distribution. absl::random_internal::sequence_urbg urbg({0x8000000000000000ull}); double a = dist(urbg); EXPECT_EQ(a, 0.5); } { // This returns the largest value <1 from absl::uniform_real_distribution. absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFEFull}); double a = dist(urbg); EXPECT_EQ(a, 0.999999999999999888978); } { // This *ALSO* returns the largest value <1. absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFFFull}); double a = dist(urbg); EXPECT_EQ(a, 0.999999999999999888978); } } } // namespace