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Diffstat (limited to 'third_party/abseil_cpp/absl/random/poisson_distribution_test.cc')
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1 files changed, 0 insertions, 573 deletions
diff --git a/third_party/abseil_cpp/absl/random/poisson_distribution_test.cc b/third_party/abseil_cpp/absl/random/poisson_distribution_test.cc deleted file mode 100644 index 8baabd111892..000000000000 --- a/third_party/abseil_cpp/absl/random/poisson_distribution_test.cc +++ /dev/null @@ -1,573 +0,0 @@ -// 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/poisson_distribution.h" - -#include <algorithm> -#include <cstddef> -#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/base/macros.h" -#include "absl/container/flat_hash_map.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" -#include "absl/strings/str_format.h" -#include "absl/strings/str_replace.h" -#include "absl/strings/strip.h" - -// Notes about generating poisson variates: -// -// It is unlikely that any implementation of std::poisson_distribution -// will be stable over time and across library implementations. For instance -// the three different poisson variate generators listed below all differ: -// -// https://github.com/ampl/gsl/tree/master/randist/poisson.c -// * GSL uses a gamma + binomial + knuth method to compute poisson variates. -// -// https://github.com/gcc-mirror/gcc/blob/master/libstdc%2B%2B-v3/include/bits/random.tcc -// * GCC uses the Devroye rejection algorithm, based on -// Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, -// New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!), ~p.511 -// http://www.nrbook.com/devroye/ -// -// https://github.com/llvm-mirror/libcxx/blob/master/include/random -// * CLANG uses a different rejection method, which appears to include a -// normal-distribution approximation and an exponential distribution to -// compute the threshold, including a similar factorial approximation to this -// one, but it is unclear where the algorithm comes from, exactly. -// - -namespace { - -using absl::random_internal::kChiSquared; - -// The PoissonDistributionInterfaceTest provides a basic test that -// absl::poisson_distribution conforms to the interface and serialization -// requirements imposed by [rand.req.dist] for the common integer types. - -template <typename IntType> -class PoissonDistributionInterfaceTest : public ::testing::Test {}; - -using IntTypes = ::testing::Types<int, int8_t, int16_t, int32_t, int64_t, - uint8_t, uint16_t, uint32_t, uint64_t>; -TYPED_TEST_CASE(PoissonDistributionInterfaceTest, IntTypes); - -TYPED_TEST(PoissonDistributionInterfaceTest, SerializeTest) { - using param_type = typename absl::poisson_distribution<TypeParam>::param_type; - const double kMax = - std::min(1e10 /* assertion limit */, - static_cast<double>(std::numeric_limits<TypeParam>::max())); - - const double kParams[] = { - // Cases around 1. - 1, // - std::nextafter(1.0, 0.0), // 1 - epsilon - std::nextafter(1.0, 2.0), // 1 + epsilon - // Arbitrary values. - 1e-8, 1e-4, - 0.0000005, // ~7.2e-7 - 0.2, // ~0.2x - 0.5, // 0.72 - 2, // ~2.8 - 20, // 3x ~9.6 - 100, 1e4, 1e8, 1.5e9, 1e20, - // Boundary cases. - std::numeric_limits<double>::max(), - std::numeric_limits<double>::epsilon(), - std::nextafter(std::numeric_limits<double>::min(), - 1.0), // min + epsilon - std::numeric_limits<double>::min(), // smallest normal - std::numeric_limits<double>::denorm_min(), // smallest denorm - std::numeric_limits<double>::min() / 2, // denorm - std::nextafter(std::numeric_limits<double>::min(), - 0.0), // denorm_max - }; - - - constexpr int kCount = 1000; - absl::InsecureBitGen gen; - for (const double m : kParams) { - const double mean = std::min(kMax, m); - const param_type param(mean); - - // Validate parameters. - absl::poisson_distribution<TypeParam> before(mean); - EXPECT_EQ(before.mean(), param.mean()); - - { - absl::poisson_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()); - EXPECT_LE(sample, before.max()); - if (sample > sample_max) sample_max = sample; - if (sample < sample_min) sample_min = sample; - } - - ABSL_INTERNAL_LOG(INFO, absl::StrCat("Range {", param.mean(), "}: ", - +sample_min, ", ", +sample_max)); - - // Validate stream serialization. - std::stringstream ss; - ss << before; - - absl::poisson_distribution<TypeParam> after(3.8); - - EXPECT_NE(before.mean(), after.mean()); - EXPECT_NE(before.param(), after.param()); - EXPECT_NE(before, after); - - ss >> after; - - EXPECT_EQ(before.mean(), after.mean()) // - << ss.str() << " " // - << (ss.good() ? "good " : "") // - << (ss.bad() ? "bad " : "") // - << (ss.eof() ? "eof " : "") // - << (ss.fail() ? "fail " : ""); - } -} - -// See http://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm - -class PoissonModel { - public: - explicit PoissonModel(double mean) : mean_(mean) {} - - double mean() const { return mean_; } - double variance() const { return mean_; } - double stddev() const { return std::sqrt(variance()); } - double skew() const { return 1.0 / mean_; } - double kurtosis() const { return 3.0 + 1.0 / mean_; } - - // InitCDF() initializes the CDF for the distribution parameters. - void InitCDF(); - - // The InverseCDF, or the Percent-point function returns x, P(x) < v. - struct CDF { - size_t index; - double pmf; - double cdf; - }; - CDF InverseCDF(double p) { - CDF target{0, 0, p}; - auto it = std::upper_bound( - std::begin(cdf_), std::end(cdf_), target, - [](const CDF& a, const CDF& b) { return a.cdf < b.cdf; }); - return *it; - } - - void LogCDF() { - ABSL_INTERNAL_LOG(INFO, absl::StrCat("CDF (mean = ", mean_, ")")); - for (const auto c : cdf_) { - ABSL_INTERNAL_LOG(INFO, - absl::StrCat(c.index, ": pmf=", c.pmf, " cdf=", c.cdf)); - } - } - - private: - const double mean_; - - std::vector<CDF> cdf_; -}; - -// The goal is to compute an InverseCDF function, or percent point function for -// the poisson distribution, and use that to partition our output into equal -// range buckets. However there is no closed form solution for the inverse cdf -// for poisson distributions (the closest is the incomplete gamma function). -// Instead, `InitCDF` iteratively computes the PMF and the CDF. This enables -// searching for the bucket points. -void PoissonModel::InitCDF() { - if (!cdf_.empty()) { - // State already initialized. - return; - } - ABSL_ASSERT(mean_ < 201.0); - - const size_t max_i = 50 * stddev() + mean(); - const double e_neg_mean = std::exp(-mean()); - ABSL_ASSERT(e_neg_mean > 0); - - double d = 1; - double last_result = e_neg_mean; - double cumulative = e_neg_mean; - if (e_neg_mean > 1e-10) { - cdf_.push_back({0, e_neg_mean, cumulative}); - } - for (size_t i = 1; i < max_i; i++) { - d *= (mean() / i); - double result = e_neg_mean * d; - cumulative += result; - if (result < 1e-10 && result < last_result && cumulative > 0.999999) { - break; - } - if (result > 1e-7) { - cdf_.push_back({i, result, cumulative}); - } - last_result = result; - } - ABSL_ASSERT(!cdf_.empty()); -} - -// PoissonDistributionZTest implements a z-test for the poisson distribution. - -struct ZParam { - double mean; - double p_fail; // Z-Test probability of failure. - int trials; // Z-Test trials. - size_t samples; // Z-Test samples. -}; - -class PoissonDistributionZTest : public testing::TestWithParam<ZParam>, - public PoissonModel { - public: - PoissonDistributionZTest() : PoissonModel(GetParam().mean) {} - - // ZTestImpl 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); - - // 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}; -}; - -template <typename D> -bool PoissonDistributionZTest::SingleZTest(const double p, - const size_t samples) { - D dis(mean()); - - absl::flat_hash_map<int32_t, int> buckets; - std::vector<double> data; - data.reserve(samples); - for (int j = 0; j < samples; j++) { - const auto x = dis(rng_); - buckets[x]++; - data.push_back(x); - } - - // The null-hypothesis is that the distribution is a poisson distribution with - // the provided mean (not estimated from the data). - 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" - " mean=%f vs. %f\n" - " stddev=%f vs. %f\n" - " skewness=%f vs. %f\n" - " kurtosis=%f vs. %f\n" - " z=%f", - p, max_err, m.mean, mean(), std::sqrt(m.variance), - stddev(), m.skewness, skew(), m.kurtosis, - kurtosis(), z)); - } - return pass; -} - -TEST_P(PoissonDistributionZTest, AbslPoissonDistribution) { - 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::poisson_distribution<int32_t>>(p, param.samples) ? 0 - : 1; - } - EXPECT_LE(failures, expected_failures); -} - -std::vector<ZParam> GetZParams() { - // These values have been adjusted from the "exact" computed values to reduce - // failure rates. - // - // It turns out that the actual values are not as close to the expected values - // as would be ideal. - return std::vector<ZParam>({ - // Knuth method. - ZParam{0.5, 0.01, 100, 1000}, - ZParam{1.0, 0.01, 100, 1000}, - ZParam{10.0, 0.01, 100, 5000}, - // Split-knuth method. - ZParam{20.0, 0.01, 100, 10000}, - ZParam{50.0, 0.01, 100, 10000}, - // Ratio of gaussians method. - ZParam{51.0, 0.01, 100, 10000}, - ZParam{200.0, 0.05, 10, 100000}, - ZParam{100000.0, 0.05, 10, 1000000}, - }); -} - -std::string ZParamName(const ::testing::TestParamInfo<ZParam>& info) { - const auto& p = info.param; - std::string name = absl::StrCat("mean_", absl::SixDigits(p.mean)); - return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}}); -} - -INSTANTIATE_TEST_SUITE_P(All, PoissonDistributionZTest, - ::testing::ValuesIn(GetZParams()), ZParamName); - -// The PoissonDistributionChiSquaredTest class provides a basic test framework -// for variates generated by a conforming poisson_distribution. -class PoissonDistributionChiSquaredTest : public testing::TestWithParam<double>, - public PoissonModel { - public: - PoissonDistributionChiSquaredTest() : PoissonModel(GetParam()) {} - - // The ChiSquaredTestImpl provides a chi-squared goodness of fit test for data - // generated by the poisson distribution. - template <typename D> - double ChiSquaredTestImpl(); - - private: - void InitChiSquaredTest(const double buckets); - - std::vector<size_t> cutoffs_; - std::vector<double> expected_; - - // 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}; -}; - -void PoissonDistributionChiSquaredTest::InitChiSquaredTest( - const double buckets) { - if (!cutoffs_.empty() && !expected_.empty()) { - return; - } - InitCDF(); - - // The code below finds cuttoffs that yield approximately equally-sized - // buckets to the extent that it is possible. However for poisson - // distributions this is particularly challenging for small mean parameters. - // Track the expected proportion of items in each bucket. - double last_cdf = 0; - const double inc = 1.0 / buckets; - for (double p = inc; p <= 1.0; p += inc) { - auto result = InverseCDF(p); - if (!cutoffs_.empty() && cutoffs_.back() == result.index) { - continue; - } - double d = result.cdf - last_cdf; - cutoffs_.push_back(result.index); - expected_.push_back(d); - last_cdf = result.cdf; - } - cutoffs_.push_back(std::numeric_limits<size_t>::max()); - expected_.push_back(std::max(0.0, 1.0 - last_cdf)); -} - -template <typename D> -double PoissonDistributionChiSquaredTest::ChiSquaredTestImpl() { - const int kSamples = 2000; - const int kBuckets = 50; - - // The poisson CDF fails for large mean values, since e^-mean exceeds the - // machine precision. For these cases, using a normal approximation would be - // appropriate. - ABSL_ASSERT(mean() <= 200); - InitChiSquaredTest(kBuckets); - - D dis(mean()); - - std::vector<int32_t> counts(cutoffs_.size(), 0); - for (int j = 0; j < kSamples; j++) { - const size_t x = dis(rng_); - auto it = std::lower_bound(std::begin(cutoffs_), std::end(cutoffs_), x); - counts[std::distance(cutoffs_.begin(), it)]++; - } - - // Normalize the counts. - std::vector<int32_t> e(expected_.size(), 0); - for (int i = 0; i < e.size(); i++) { - e[i] = kSamples * expected_[i]; - } - - // The null-hypothesis is that the distribution is a poisson distribution with - // the provided mean (not estimated from the data). - const int dof = static_cast<int>(counts.size()) - 1; - - // The threshold for logging is 1-in-50. - const double threshold = absl::random_internal::ChiSquareValue(dof, 0.98); - - const double chi_square = absl::random_internal::ChiSquare( - std::begin(counts), std::end(counts), std::begin(e), std::end(e)); - - const double p = absl::random_internal::ChiSquarePValue(chi_square, dof); - - // Log if the chi_squared value is above the threshold. - if (chi_square > threshold) { - LogCDF(); - - ABSL_INTERNAL_LOG(INFO, absl::StrCat("VALUES buckets=", counts.size(), - " samples=", kSamples)); - for (size_t i = 0; i < counts.size(); i++) { - ABSL_INTERNAL_LOG( - INFO, absl::StrCat(cutoffs_[i], ": ", counts[i], " vs. E=", e[i])); - } - - ABSL_INTERNAL_LOG( - INFO, - absl::StrCat(kChiSquared, "(data, dof=", dof, ") = ", chi_square, " (", - p, ")\n", " vs.\n", kChiSquared, " @ 0.98 = ", threshold)); - } - return p; -} - -TEST_P(PoissonDistributionChiSquaredTest, AbslPoissonDistribution) { - const int kTrials = 20; - - // Large values are not yet supported -- this requires estimating the cdf - // using the normal distribution instead of the poisson in this case. - ASSERT_LE(mean(), 200.0); - if (mean() > 200.0) { - return; - } - - int failures = 0; - for (int i = 0; i < kTrials; i++) { - double p_value = ChiSquaredTestImpl<absl::poisson_distribution<int32_t>>(); - if (p_value < 0.005) { - 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); -} - -INSTANTIATE_TEST_SUITE_P(All, PoissonDistributionChiSquaredTest, - ::testing::Values(0.5, 1.0, 2.0, 10.0, 50.0, 51.0, - 200.0)); - -// NOTE: absl::poisson_distribution is not guaranteed to be stable. -TEST(PoissonDistributionTest, StabilityTest) { - using testing::ElementsAre; - // absl::poisson_distribution stability relies on stability of - // std::exp, std::log, std::sqrt, std::ceil, std::floor, and - // absl::FastUniformBits, absl::StirlingLogFactorial, absl::RandU64ToDouble. - absl::random_internal::sequence_urbg urbg({ - 0x035b0dc7e0a18acfull, 0x06cebe0d2653682eull, 0x0061e9b23861596bull, - 0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull, - 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull, - 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull, - 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull, - 0x4864f22c059bf29eull, 0x247856d8b862665cull, 0xe46e86e9a1337e10ull, - 0xd8c8541f3519b133ull, 0xe75b5162c567b9e4ull, 0xf732e5ded7009c5bull, - 0xb170b98353121eacull, 0x1ec2e8986d2362caull, 0x814c8e35fe9a961aull, - 0x0c3cd59c9b638a02ull, 0xcb3bb6478a07715cull, 0x1224e62c978bbc7full, - 0x671ef2cb04e81f6eull, 0x3c1cbd811eaf1808ull, 0x1bbc23cfa8fac721ull, - 0xa4c2cda65e596a51ull, 0xb77216fad37adf91ull, 0x836d794457c08849ull, - 0xe083df03475f49d7ull, 0xbc9feb512e6b0d6cull, 0xb12d74fdd718c8c5ull, - 0x12ff09653bfbe4caull, 0x8dd03a105bc4ee7eull, 0x5738341045ba0d85ull, - 0xf3fd722dc65ad09eull, 0xfa14fd21ea2a5705ull, 0xffe6ea4d6edb0c73ull, - 0xD07E9EFE2BF11FB4ull, 0x95DBDA4DAE909198ull, 0xEAAD8E716B93D5A0ull, - 0xD08ED1D0AFC725E0ull, 0x8E3C5B2F8E7594B7ull, 0x8FF6E2FBF2122B64ull, - 0x8888B812900DF01Cull, 0x4FAD5EA0688FC31Cull, 0xD1CFF191B3A8C1ADull, - 0x2F2F2218BE0E1777ull, 0xEA752DFE8B021FA1ull, 0xE5A0CC0FB56F74E8ull, - 0x18ACF3D6CE89E299ull, 0xB4A84FE0FD13E0B7ull, 0x7CC43B81D2ADA8D9ull, - 0x165FA26680957705ull, 0x93CC7314211A1477ull, 0xE6AD206577B5FA86ull, - 0xC75442F5FB9D35CFull, 0xEBCDAF0C7B3E89A0ull, 0xD6411BD3AE1E7E49ull, - 0x00250E2D2071B35Eull, 0x226800BB57B8E0AFull, 0x2464369BF009B91Eull, - 0x5563911D59DFA6AAull, 0x78C14389D95A537Full, 0x207D5BA202E5B9C5ull, - 0x832603766295CFA9ull, 0x11C819684E734A41ull, 0xB3472DCA7B14A94Aull, - }); - - std::vector<int> output(10); - - // Method 1. - { - absl::poisson_distribution<int> dist(5); - std::generate(std::begin(output), std::end(output), - [&] { return dist(urbg); }); - } - EXPECT_THAT(output, // mean = 4.2 - ElementsAre(1, 0, 0, 4, 2, 10, 3, 3, 7, 12)); - - // Method 2. - { - urbg.reset(); - absl::poisson_distribution<int> dist(25); - std::generate(std::begin(output), std::end(output), - [&] { return dist(urbg); }); - } - EXPECT_THAT(output, // mean = 19.8 - ElementsAre(9, 35, 18, 10, 35, 18, 10, 35, 18, 10)); - - // Method 3. - { - urbg.reset(); - absl::poisson_distribution<int> dist(121); - std::generate(std::begin(output), std::end(output), - [&] { return dist(urbg); }); - } - EXPECT_THAT(output, // mean = 124.1 - ElementsAre(161, 122, 129, 124, 112, 112, 117, 120, 130, 114)); -} - -TEST(PoissonDistributionTest, AlgorithmExpectedValue_1) { - // This tests small values of the Knuth method. - // The underlying uniform distribution will generate exactly 0.5. - absl::random_internal::sequence_urbg urbg({0x8000000000000001ull}); - absl::poisson_distribution<int> dist(5); - EXPECT_EQ(7, dist(urbg)); -} - -TEST(PoissonDistributionTest, AlgorithmExpectedValue_2) { - // This tests larger values of the Knuth method. - // The underlying uniform distribution will generate exactly 0.5. - absl::random_internal::sequence_urbg urbg({0x8000000000000001ull}); - absl::poisson_distribution<int> dist(25); - EXPECT_EQ(36, dist(urbg)); -} - -TEST(PoissonDistributionTest, AlgorithmExpectedValue_3) { - // This variant uses the ratio of uniforms method. - absl::random_internal::sequence_urbg urbg( - {0x7fffffffffffffffull, 0x8000000000000000ull}); - - absl::poisson_distribution<int> dist(121); - EXPECT_EQ(121, dist(urbg)); -} - -} // namespace |