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Diffstat (limited to 'absl/random/exponential_distribution_test.cc')
| -rw-r--r-- | absl/random/exponential_distribution_test.cc | 422 |
1 files changed, 422 insertions, 0 deletions
diff --git a/absl/random/exponential_distribution_test.cc b/absl/random/exponential_distribution_test.cc new file mode 100644 index 00000000..6f8865c2 --- /dev/null +++ b/absl/random/exponential_distribution_test.cc @@ -0,0 +1,422 @@ +// 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/exponential_distribution.h" + +#include <algorithm> +#include <cmath> +#include <cstddef> +#include <cstdint> +#include <iterator> +#include <limits> +#include <random> +#include <sstream> +#include <string> +#include <type_traits> +#include <vector> + +#include "gmock/gmock.h" +#include "gtest/gtest.h" +#include "absl/base/internal/raw_logging.h" +#include "absl/base/macros.h" +#include "absl/random/internal/chi_square.h" +#include "absl/random/internal/distribution_test_util.h" +#include "absl/random/internal/sequence_urbg.h" +#include "absl/random/random.h" +#include "absl/strings/str_cat.h" +#include "absl/strings/str_format.h" +#include "absl/strings/str_replace.h" +#include "absl/strings/strip.h" + +namespace { + +using absl::random_internal::kChiSquared; + +template <typename RealType> +class ExponentialDistributionTypedTest : public ::testing::Test {}; + +using RealTypes = ::testing::Types<float, double, long double>; +TYPED_TEST_CASE(ExponentialDistributionTypedTest, RealTypes); + +TYPED_TEST(ExponentialDistributionTypedTest, SerializeTest) { + using param_type = + typename absl::exponential_distribution<TypeParam>::param_type; + + const TypeParam kParams[] = { + // Cases around 1. + 1, // + std::nextafter(TypeParam(1), TypeParam(0)), // 1 - epsilon + std::nextafter(TypeParam(1), TypeParam(2)), // 1 + epsilon + // Typical cases. + TypeParam(1e-8), TypeParam(1e-4), TypeParam(1), TypeParam(2), + TypeParam(1e4), TypeParam(1e8), TypeParam(1e20), TypeParam(2.5), + // Boundary cases. + std::numeric_limits<TypeParam>::max(), + std::numeric_limits<TypeParam>::epsilon(), + std::nextafter(std::numeric_limits<TypeParam>::min(), + TypeParam(1)), // min + epsilon + std::numeric_limits<TypeParam>::min(), // smallest normal + // There are some errors dealing with denorms on apple platforms. + std::numeric_limits<TypeParam>::denorm_min(), // smallest denorm + std::numeric_limits<TypeParam>::min() / 2, // denorm + std::nextafter(std::numeric_limits<TypeParam>::min(), + TypeParam(0)), // denorm_max + }; + + constexpr int kCount = 1000; + absl::InsecureBitGen gen; + + for (const TypeParam lambda : kParams) { + // Some values may be invalid; skip those. + if (!std::isfinite(lambda)) continue; + ABSL_ASSERT(lambda > 0); + + const param_type param(lambda); + + absl::exponential_distribution<TypeParam> before(lambda); + EXPECT_EQ(before.lambda(), param.lambda()); + + { + absl::exponential_distribution<TypeParam> via_param(param); + EXPECT_EQ(via_param, before); + EXPECT_EQ(via_param.param(), before.param()); + } + + // Smoke test. + auto sample_min = before.max(); + auto sample_max = before.min(); + for (int i = 0; i < kCount; i++) { + auto sample = before(gen); + EXPECT_GE(sample, before.min()) << before; + EXPECT_LE(sample, before.max()) << before; + if (sample > sample_max) sample_max = sample; + if (sample < sample_min) sample_min = sample; + } + if (!std::is_same<TypeParam, long double>::value) { + ABSL_INTERNAL_LOG(INFO, + absl::StrFormat("Range {%f}: %f, %f, lambda=%f", lambda, + sample_min, sample_max, lambda)); + } + + std::stringstream ss; + ss << before; + + if (!std::isfinite(lambda)) { + // Streams do not deserialize inf/nan correctly. + continue; + } + // Validate stream serialization. + absl::exponential_distribution<TypeParam> after(34.56f); + + EXPECT_NE(before.lambda(), after.lambda()); + EXPECT_NE(before.param(), after.param()); + EXPECT_NE(before, after); + + ss >> after; + +#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \ + defined(__ppc__) || defined(__PPC__) + if (std::is_same<TypeParam, long double>::value) { + // Roundtripping floating point values requires sufficient precision to + // reconstruct the exact value. It turns out that long double has some + // errors doing this on ppc, particularly for values + // near {1.0 +/- epsilon}. + if (lambda <= std::numeric_limits<double>::max() && + lambda >= std::numeric_limits<double>::lowest()) { + EXPECT_EQ(static_cast<double>(before.lambda()), + static_cast<double>(after.lambda())) + << ss.str(); + } + continue; + } +#endif + + EXPECT_EQ(before.lambda(), after.lambda()) // + << ss.str() << " " // + << (ss.good() ? "good " : "") // + << (ss.bad() ? "bad " : "") // + << (ss.eof() ? "eof " : "") // + << (ss.fail() ? "fail " : ""); + } +} + +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm + +class ExponentialModel { + public: + explicit ExponentialModel(double lambda) + : lambda_(lambda), beta_(1.0 / lambda) {} + + double lambda() const { return lambda_; } + + double mean() const { return beta_; } + double variance() const { return beta_ * beta_; } + double stddev() const { return std::sqrt(variance()); } + double skew() const { return 2; } + double kurtosis() const { return 6.0; } + + double CDF(double x) { return 1.0 - std::exp(-lambda_ * x); } + + // The inverse CDF, or PercentPoint function of the distribution + double InverseCDF(double p) { + ABSL_ASSERT(p >= 0.0); + ABSL_ASSERT(p < 1.0); + return -beta_ * std::log(1.0 - p); + } + + private: + const double lambda_; + const double beta_; +}; + +struct Param { + double lambda; + double p_fail; + int trials; +}; + +class ExponentialDistributionTests : public testing::TestWithParam<Param>, + public ExponentialModel { + public: + ExponentialDistributionTests() : ExponentialModel(GetParam().lambda) {} + + // SingleZTest provides a basic z-squared test of the mean vs. expected + // mean for data generated by the poisson distribution. + template <typename D> + bool SingleZTest(const double p, const size_t samples); + + // SingleChiSquaredTest provides a basic chi-squared test of the normal + // distribution. + template <typename D> + double SingleChiSquaredTest(); + + absl::InsecureBitGen rng_; +}; + +template <typename D> +bool ExponentialDistributionTests::SingleZTest(const double p, + const size_t samples) { + D dis(lambda()); + + std::vector<double> data; + data.reserve(samples); + for (size_t i = 0; i < samples; i++) { + const double x = dis(rng_); + data.push_back(x); + } + + const auto m = absl::random_internal::ComputeDistributionMoments(data); + const double max_err = absl::random_internal::MaxErrorTolerance(p); + const double z = absl::random_internal::ZScore(mean(), m); + const bool pass = absl::random_internal::Near("z", z, 0.0, max_err); + + if (!pass) { + ABSL_INTERNAL_LOG( + INFO, absl::StrFormat("p=%f max_err=%f\n" + " lambda=%f\n" + " mean=%f vs. %f\n" + " stddev=%f vs. %f\n" + " skewness=%f vs. %f\n" + " kurtosis=%f vs. %f\n" + " z=%f vs. 0", + p, max_err, lambda(), m.mean, mean(), + std::sqrt(m.variance), stddev(), m.skewness, + skew(), m.kurtosis, kurtosis(), z)); + } + return pass; +} + +template <typename D> +double ExponentialDistributionTests::SingleChiSquaredTest() { + const size_t kSamples = 10000; + const int kBuckets = 50; + + // The InverseCDF is the percent point function of the distribution, and can + // be used to assign buckets roughly uniformly. + std::vector<double> cutoffs; + const double kInc = 1.0 / static_cast<double>(kBuckets); + for (double p = kInc; p < 1.0; p += kInc) { + cutoffs.push_back(InverseCDF(p)); + } + if (cutoffs.back() != std::numeric_limits<double>::infinity()) { + cutoffs.push_back(std::numeric_limits<double>::infinity()); + } + + D dis(lambda()); + + std::vector<int32_t> counts(cutoffs.size(), 0); + for (int j = 0; j < kSamples; j++) { + const double x = dis(rng_); + auto it = std::upper_bound(cutoffs.begin(), cutoffs.end(), x); + counts[std::distance(cutoffs.begin(), it)]++; + } + + // Null-hypothesis is that the distribution is exponentially distributed + // with the provided lambda (not estimated from the data). + const int dof = static_cast<int>(counts.size()) - 1; + + // Our threshold for logging is 1-in-50. + const double threshold = absl::random_internal::ChiSquareValue(dof, 0.98); + + const double expected = + static_cast<double>(kSamples) / static_cast<double>(counts.size()); + + double chi_square = absl::random_internal::ChiSquareWithExpected( + std::begin(counts), std::end(counts), expected); + double p = absl::random_internal::ChiSquarePValue(chi_square, dof); + + if (chi_square > threshold) { + for (int i = 0; i < cutoffs.size(); i++) { + ABSL_INTERNAL_LOG( + INFO, absl::StrFormat("%d : (%f) = %d", i, cutoffs[i], counts[i])); + } + + ABSL_INTERNAL_LOG(INFO, + absl::StrCat("lambda ", lambda(), "\n", // + " expected ", expected, "\n", // + kChiSquared, " ", chi_square, " (", p, ")\n", + kChiSquared, " @ 0.98 = ", threshold)); + } + return p; +} + +TEST_P(ExponentialDistributionTests, ZTest) { + const size_t kSamples = 10000; + const auto& param = GetParam(); + const int expected_failures = + std::max(1, static_cast<int>(std::ceil(param.trials * param.p_fail))); + const double p = absl::random_internal::RequiredSuccessProbability( + param.p_fail, param.trials); + + int failures = 0; + for (int i = 0; i < param.trials; i++) { + failures += SingleZTest<absl::exponential_distribution<double>>(p, kSamples) + ? 0 + : 1; + } + EXPECT_LE(failures, expected_failures); +} + +TEST_P(ExponentialDistributionTests, ChiSquaredTest) { + const int kTrials = 20; + int failures = 0; + + for (int i = 0; i < kTrials; i++) { + double p_value = + SingleChiSquaredTest<absl::exponential_distribution<double>>(); + if (p_value < 0.005) { // 1/200 + failures++; + } + } + + // There is a 0.10% chance of producing at least one failure, so raise the + // failure threshold high enough to allow for a flake rate < 10,000. + EXPECT_LE(failures, 4); +} + +std::vector<Param> GenParams() { + return { + Param{1.0, 0.02, 100}, + Param{2.5, 0.02, 100}, + Param{10, 0.02, 100}, + // large + Param{1e4, 0.02, 100}, + Param{1e9, 0.02, 100}, + // small + Param{0.1, 0.02, 100}, + Param{1e-3, 0.02, 100}, + Param{1e-5, 0.02, 100}, + }; +} + +std::string ParamName(const ::testing::TestParamInfo<Param>& info) { + const auto& p = info.param; + std::string name = absl::StrCat("lambda_", absl::SixDigits(p.lambda)); + return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}}); +} + +INSTANTIATE_TEST_CASE_P(, ExponentialDistributionTests, + ::testing::ValuesIn(GenParams()), ParamName); + +// NOTE: absl::exponential_distribution is not guaranteed to be stable. +TEST(ExponentialDistributionTest, StabilityTest) { + // absl::exponential_distribution stability relies on std::log1p and + // absl::uniform_real_distribution. + absl::random_internal::sequence_urbg urbg( + {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull, + 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull, + 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull, + 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull}); + + std::vector<int> output(14); + + { + absl::exponential_distribution<double> dist; + std::generate(std::begin(output), std::end(output), + [&] { return static_cast<int>(10000.0 * dist(urbg)); }); + + EXPECT_EQ(14, urbg.invocations()); + EXPECT_THAT(output, + testing::ElementsAre(0, 71913, 14375, 5039, 1835, 861, 25936, + 804, 126, 12337, 17984, 27002, 0, 71913)); + } + + urbg.reset(); + { + absl::exponential_distribution<float> dist; + std::generate(std::begin(output), std::end(output), + [&] { return static_cast<int>(10000.0f * dist(urbg)); }); + + EXPECT_EQ(14, urbg.invocations()); + EXPECT_THAT(output, + testing::ElementsAre(0, 71913, 14375, 5039, 1835, 861, 25936, + 804, 126, 12337, 17984, 27002, 0, 71913)); + } +} + +TEST(ExponentialDistributionTest, AlgorithmBounds) { + // Relies on absl::uniform_real_distribution, so some of these comments + // reference that. + absl::exponential_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, 0.693147180559945175204); + } + + { + // This returns the largest value <1 from absl::uniform_real_distribution. + // WolframAlpha: ~39.1439465808987766283058547296341915292187253 + absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFeFull}); + double a = dist(urbg); + EXPECT_EQ(a, 36.7368005696771007251); + } + { + // This *ALSO* returns the largest value <1. + absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFFFull}); + double a = dist(urbg); + EXPECT_EQ(a, 36.7368005696771007251); + } +} + +} // namespace |