| // 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 <cfloat> |
| #include <cmath> |
| #include <cstdint> |
| #include <iterator> |
| #include <random> |
| #include <sstream> |
| #include <string> |
| #include <type_traits> |
| #include <vector> |
| |
| #include "gmock/gmock.h" |
| #include "gtest/gtest.h" |
| #include "absl/log/log.h" |
| #include "absl/numeric/internal/representation.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 {}; |
| |
| // double-double arithmetic is not supported well by either GCC or Clang; see |
| // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=99048, |
| // https://bugs.llvm.org/show_bug.cgi?id=49131, and |
| // https://bugs.llvm.org/show_bug.cgi?id=49132. Don't bother running these tests |
| // with double doubles until compiler support is better. |
| using RealTypes = |
| std::conditional<absl::numeric_internal::IsDoubleDouble(), |
| ::testing::Types<float, double>, |
| ::testing::Types<float, double, long double>>::type; |
| |
| TYPED_TEST_SUITE(UniformRealDistributionTest, RealTypes); |
| |
| TYPED_TEST(UniformRealDistributionTest, ParamSerializeTest) { |
| #if (defined(__i386__) || defined(_M_IX86)) && FLT_EVAL_METHOD != 0 |
| // We're using an x87-compatible FPU, and intermediate operations are |
| // performed with 80-bit floats. This produces slightly different results from |
| // what we expect below. |
| GTEST_SKIP() |
| << "Skipping the test because we detected x87 floating-point semantics"; |
| #endif |
| using DistributionType = absl::uniform_real_distribution<TypeParam>; |
| using real_type = TypeParam; |
| using param_type = typename DistributionType::param_type; |
| |
| constexpr const real_type kMax = std::numeric_limits<real_type>::max(); |
| constexpr const real_type kMin = std::numeric_limits<real_type>::min(); |
| constexpr const real_type kEpsilon = |
| std::numeric_limits<real_type>::epsilon(); |
| constexpr const real_type kLowest = |
| std::numeric_limits<real_type>::lowest(); // -max |
| |
| const real_type kDenormMax = std::nextafter(kMin, real_type{0}); |
| const real_type kOneMinusE = |
| std::nextafter(real_type{1}, real_type{0}); // 1 - epsilon |
| |
| constexpr const real_type kTwo60{1152921504606846976}; // 2^60 |
| |
| constexpr int kCount = 1000; |
| absl::InsecureBitGen gen; |
| for (const auto& param : { |
| param_type(), |
| param_type(real_type{0}, real_type{1}), |
| param_type(real_type(-0.1), real_type(0.1)), |
| param_type(real_type(0.05), real_type(0.12)), |
| param_type(real_type(-0.05), real_type(0.13)), |
| param_type(real_type(-0.05), real_type(-0.02)), |
| // range = 0 |
| param_type(real_type(2.0), real_type(2.0)), // Same |
| // double range = 0 |
| // 2^60 , 2^60 + 2^6 |
| param_type(kTwo60, real_type(1152921504606847040)), |
| // 2^60 , 2^60 + 2^7 |
| param_type(kTwo60, real_type(1152921504606847104)), |
| // double range = 2^8 |
| // 2^60 , 2^60 + 2^8 |
| param_type(kTwo60, real_type(1152921504606847232)), |
| // float range = 0 |
| // 2^60 , 2^60 + 2^36 |
| param_type(kTwo60, real_type(1152921573326323712)), |
| // 2^60 , 2^60 + 2^37 |
| param_type(kTwo60, real_type(1152921642045800448)), |
| // float range = 2^38 |
| // 2^60 , 2^60 + 2^38 |
| param_type(kTwo60, real_type(1152921779484753920)), |
| // Limits |
| param_type(0, kMax), |
| param_type(kLowest, 0), |
| param_type(0, kMin), |
| param_type(0, kEpsilon), |
| param_type(-kEpsilon, kEpsilon), |
| param_type(0, kOneMinusE), |
| param_type(0, kDenormMax), |
| }) { |
| // Validate parameters. |
| const auto a = param.a(); |
| const auto b = param.b(); |
| DistributionType before(a, b); |
| EXPECT_EQ(before.a(), param.a()); |
| EXPECT_EQ(before.b(), param.b()); |
| |
| { |
| DistributionType via_param(param); |
| EXPECT_EQ(via_param, before); |
| } |
| |
| std::stringstream ss; |
| ss << before; |
| DistributionType after(real_type(1.0), real_type(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<real_type, long double>::value) { |
| // static_cast<double>(long double) can overflow. |
| LOG(INFO) << "Range: " << static_cast<double>(sample_min) << ", " |
| << static_cast<double>(sample_max); |
| } |
| } |
| } |
| |
| #ifdef _MSC_VER |
| #pragma warning(push) |
| #pragma warning(disable:4756) // Constant arithmetic overflow. |
| #endif |
| TYPED_TEST(UniformRealDistributionTest, ViolatesPreconditionsDeathTest) { |
| using DistributionType = absl::uniform_real_distribution<TypeParam>; |
| using real_type = TypeParam; |
| |
| #if GTEST_HAS_DEATH_TEST |
| // Hi < Lo |
| EXPECT_DEBUG_DEATH({ DistributionType dist(10.0, 1.0); }, ""); |
| |
| // Hi - Lo > numeric_limits<>::max() |
| EXPECT_DEBUG_DEATH( |
| { |
| DistributionType dist(std::numeric_limits<real_type>::lowest(), |
| std::numeric_limits<real_type>::max()); |
| }, |
| ""); |
| |
| // kEpsilon guarantees that max + kEpsilon = inf. |
| const auto kEpsilon = std::nexttoward( |
| (std::numeric_limits<real_type>::max() - |
| std::nexttoward(std::numeric_limits<real_type>::max(), 0.0)) / |
| 2, |
| std::numeric_limits<real_type>::max()); |
| EXPECT_DEBUG_DEATH( |
| { |
| DistributionType dist(-kEpsilon, std::numeric_limits<real_type>::max()); |
| }, |
| ""); |
| EXPECT_DEBUG_DEATH( |
| { |
| DistributionType dist(std::numeric_limits<real_type>::lowest(), |
| kEpsilon); |
| }, |
| ""); |
| |
| #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; |
| { |
| DistributionType dist(10.0, 1.0); |
| auto x = dist(gen); |
| EXPECT_FALSE(std::isnan(x)) << x; |
| } |
| { |
| DistributionType dist(std::numeric_limits<real_type>::lowest(), |
| std::numeric_limits<real_type>::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) { |
| using DistributionType = absl::uniform_real_distribution<TypeParam>; |
| |
| 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}; |
| |
| DistributionType 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 DistributionType = absl::uniform_real_distribution<TypeParam>; |
| using param_type = typename DistributionType::param_type; |
| |
| using absl::random_internal::kChiSquared; |
| |
| 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); |
| DistributionType 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); |
| LOG(INFO) << msg; |
| FAIL() << msg; |
| } |
| } |
| } |
| |
| TYPED_TEST(UniformRealDistributionTest, StabilityTest) { |
| using DistributionType = absl::uniform_real_distribution<TypeParam>; |
| using real_type = TypeParam; |
| |
| // absl::uniform_real_distribution stability relies only on |
| // random_internal::GenerateRealFromBits. |
| absl::random_internal::sequence_urbg urbg( |
| {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull, |
| 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull, |
| 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull, |
| 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull}); |
| |
| std::vector<int> output(12); |
| |
| DistributionType dist; |
| std::generate(std::begin(output), std::end(output), [&] { |
| return static_cast<int>(real_type(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 |