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Diffstat (limited to 'third_party/abseil_cpp/absl/random/gaussian_distribution_test.cc')
| -rw-r--r-- | third_party/abseil_cpp/absl/random/gaussian_distribution_test.cc | 579 |
1 files changed, 0 insertions, 579 deletions
diff --git a/third_party/abseil_cpp/absl/random/gaussian_distribution_test.cc b/third_party/abseil_cpp/absl/random/gaussian_distribution_test.cc deleted file mode 100644 index 02ac578a5c18..000000000000 --- a/third_party/abseil_cpp/absl/random/gaussian_distribution_test.cc +++ /dev/null @@ -1,579 +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/gaussian_distribution.h" - -#include <algorithm> -#include <cmath> -#include <cstddef> -#include <ios> -#include <iterator> -#include <random> -#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/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 GaussianDistributionInterfaceTest : public ::testing::Test {}; - -using RealTypes = ::testing::Types<float, double, long double>; -TYPED_TEST_CASE(GaussianDistributionInterfaceTest, RealTypes); - -TYPED_TEST(GaussianDistributionInterfaceTest, SerializeTest) { - using param_type = - typename absl::gaussian_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 - // Arbitrary values. - TypeParam(1e-8), TypeParam(1e-4), TypeParam(2), TypeParam(1e4), - TypeParam(1e8), TypeParam(1e20), TypeParam(2.5), - // Boundary cases. - std::numeric_limits<TypeParam>::infinity(), - 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, - std::nextafter(std::numeric_limits<TypeParam>::min(), - TypeParam(0)), // denorm_max - }; - - constexpr int kCount = 1000; - absl::InsecureBitGen gen; - - // Use a loop to generate the combinations of {+/-x, +/-y}, and assign x, y to - // all values in kParams, - for (const auto mod : {0, 1, 2, 3}) { - for (const auto x : kParams) { - if (!std::isfinite(x)) continue; - for (const auto y : kParams) { - const TypeParam mean = (mod & 0x1) ? -x : x; - const TypeParam stddev = (mod & 0x2) ? -y : y; - const param_type param(mean, stddev); - - absl::gaussian_distribution<TypeParam> before(mean, stddev); - EXPECT_EQ(before.mean(), param.mean()); - EXPECT_EQ(before.stddev(), param.stddev()); - - { - absl::gaussian_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); - if (sample > sample_max) sample_max = sample; - if (sample < sample_min) sample_min = sample; - EXPECT_GE(sample, before.min()) << before; - EXPECT_LE(sample, before.max()) << before; - } - if (!std::is_same<TypeParam, long double>::value) { - ABSL_INTERNAL_LOG( - INFO, absl::StrFormat("Range{%f, %f}: %f, %f", mean, stddev, - sample_min, sample_max)); - } - - std::stringstream ss; - ss << before; - - if (!std::isfinite(mean) || !std::isfinite(stddev)) { - // Streams do not parse inf/nan. - continue; - } - - // Validate stream serialization. - absl::gaussian_distribution<TypeParam> after(-0.53f, 2.3456f); - - EXPECT_NE(before.mean(), after.mean()); - EXPECT_NE(before.stddev(), after.stddev()); - EXPECT_NE(before.param(), after.param()); - EXPECT_NE(before, after); - - ss >> after; - -#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \ - defined(__ppc__) || defined(__PPC__) || defined(__EMSCRIPTEN__) - 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}. - // - // Emscripten is even worse, implementing long double as a 128-bit - // type, but shipping with a strtold() that doesn't support that. - if (mean <= std::numeric_limits<double>::max() && - mean >= std::numeric_limits<double>::lowest()) { - EXPECT_EQ(static_cast<double>(before.mean()), - static_cast<double>(after.mean())) - << ss.str(); - } - if (stddev <= std::numeric_limits<double>::max() && - stddev >= std::numeric_limits<double>::lowest()) { - EXPECT_EQ(static_cast<double>(before.stddev()), - static_cast<double>(after.stddev())) - << ss.str(); - } - continue; - } -#endif - - EXPECT_EQ(before.mean(), after.mean()); - EXPECT_EQ(before.stddev(), after.stddev()) // - << ss.str() << " " // - << (ss.good() ? "good " : "") // - << (ss.bad() ? "bad " : "") // - << (ss.eof() ? "eof " : "") // - << (ss.fail() ? "fail " : ""); - } - } - } -} - -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm - -class GaussianModel { - public: - GaussianModel(double mean, double stddev) : mean_(mean), stddev_(stddev) {} - - double mean() const { return mean_; } - double variance() const { return stddev() * stddev(); } - double stddev() const { return stddev_; } - double skew() const { return 0; } - double kurtosis() const { return 3.0; } - - // The inverse CDF, or PercentPoint function. - double InverseCDF(double p) { - ABSL_ASSERT(p >= 0.0); - ABSL_ASSERT(p < 1.0); - return mean() + stddev() * -absl::random_internal::InverseNormalSurvival(p); - } - - private: - const double mean_; - const double stddev_; -}; - -struct Param { - double mean; - double stddev; - double p_fail; // Z-Test probability of failure. - int trials; // Z-Test trials. -}; - -// GaussianDistributionTests implements a z-test for the gaussian -// distribution. -class GaussianDistributionTests : public testing::TestWithParam<Param>, - public GaussianModel { - public: - GaussianDistributionTests() - : GaussianModel(GetParam().mean, GetParam().stddev) {} - - // 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(); - - // 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 GaussianDistributionTests::SingleZTest(const double p, - const size_t samples) { - D dis(mean(), stddev()); - - 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 double max_err = absl::random_internal::MaxErrorTolerance(p); - const auto m = absl::random_internal::ComputeDistributionMoments(data); - const double z = absl::random_internal::ZScore(mean(), m); - const bool pass = absl::random_internal::Near("z", z, 0.0, max_err); - - // NOTE: Informational statistical test: - // - // Compute the Jarque-Bera test statistic given the excess skewness - // and kurtosis. The statistic is drawn from a chi-square(2) distribution. - // https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test - // - // The null-hypothesis (normal distribution) is rejected when - // (p = 0.05 => jb > 5.99) - // (p = 0.01 => jb > 9.21) - // NOTE: JB has a large type-I error rate, so it will reject the - // null-hypothesis even when it is true more often than the z-test. - // - const double jb = - static_cast<double>(m.n) / 6.0 * - (std::pow(m.skewness, 2.0) + std::pow(m.kurtosis - 3.0, 2.0) / 4.0); - - if (!pass || jb > 9.21) { - 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 vs. 0\n" - " jb=%f vs. 9.21", - p, max_err, m.mean, mean(), std::sqrt(m.variance), - stddev(), m.skewness, skew(), m.kurtosis, - kurtosis(), z, jb)); - } - return pass; -} - -template <typename D> -double GaussianDistributionTests::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(mean(), stddev()); - - 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 a gaussian distribution - // with the provided mean and stddev (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); - - // Log if the chi_square value is above the threshold. - 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("mean=", mean(), " stddev=", stddev(), "\n", // - " expected ", expected, "\n", // - kChiSquared, " ", chi_square, " (", p, ")\n", // - kChiSquared, " @ 0.98 = ", threshold)); - } - return p; -} - -TEST_P(GaussianDistributionTests, ZTest) { - // TODO(absl-team): Run these tests against std::normal_distribution<double> - // to validate outcomes are similar. - 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::gaussian_distribution<double>>(p, kSamples) ? 0 : 1; - } - EXPECT_LE(failures, expected_failures); -} - -TEST_P(GaussianDistributionTests, ChiSquaredTest) { - const int kTrials = 20; - int failures = 0; - - for (int i = 0; i < kTrials; i++) { - double p_value = - SingleChiSquaredTest<absl::gaussian_distribution<double>>(); - if (p_value < 0.0025) { // 1/400 - failures++; - } - } - // There is a 0.05% chance of producing at least one failure, so raise the - // failure threshold high enough to allow for a flake rate of less than one in - // 10,000. - EXPECT_LE(failures, 4); -} - -std::vector<Param> GenParams() { - return { - // Mean around 0. - Param{0.0, 1.0, 0.01, 100}, - Param{0.0, 1e2, 0.01, 100}, - Param{0.0, 1e4, 0.01, 100}, - Param{0.0, 1e8, 0.01, 100}, - Param{0.0, 1e16, 0.01, 100}, - Param{0.0, 1e-3, 0.01, 100}, - Param{0.0, 1e-5, 0.01, 100}, - Param{0.0, 1e-9, 0.01, 100}, - Param{0.0, 1e-17, 0.01, 100}, - - // Mean around 1. - Param{1.0, 1.0, 0.01, 100}, - Param{1.0, 1e2, 0.01, 100}, - Param{1.0, 1e-2, 0.01, 100}, - - // Mean around 100 / -100 - Param{1e2, 1.0, 0.01, 100}, - Param{-1e2, 1.0, 0.01, 100}, - Param{1e2, 1e6, 0.01, 100}, - Param{-1e2, 1e6, 0.01, 100}, - - // More extreme - Param{1e4, 1e4, 0.01, 100}, - Param{1e8, 1e4, 0.01, 100}, - Param{1e12, 1e4, 0.01, 100}, - }; -} - -std::string ParamName(const ::testing::TestParamInfo<Param>& info) { - const auto& p = info.param; - std::string name = absl::StrCat("mean_", absl::SixDigits(p.mean), "__stddev_", - absl::SixDigits(p.stddev)); - return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}}); -} - -INSTANTIATE_TEST_SUITE_P(All, GaussianDistributionTests, - ::testing::ValuesIn(GenParams()), ParamName); - -// NOTE: absl::gaussian_distribution is not guaranteed to be stable. -TEST(GaussianDistributionTest, StabilityTest) { - // absl::gaussian_distribution stability relies on the underlying zignor - // data, absl::random_interna::RandU64ToDouble, std::exp, std::log, and - // std::abs. - absl::random_internal::sequence_urbg urbg( - {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull, - 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull, - 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull, - 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull}); - - std::vector<int> output(11); - - { - absl::gaussian_distribution<double> dist; - std::generate(std::begin(output), std::end(output), - [&] { return static_cast<int>(10000000.0 * dist(urbg)); }); - - EXPECT_EQ(13, urbg.invocations()); - EXPECT_THAT(output, // - testing::ElementsAre(1494, 25518841, 9991550, 1351856, - -20373238, 3456682, 333530, -6804981, - -15279580, -16459654, 1494)); - } - - urbg.reset(); - { - absl::gaussian_distribution<float> dist; - std::generate(std::begin(output), std::end(output), - [&] { return static_cast<int>(1000000.0f * dist(urbg)); }); - - EXPECT_EQ(13, urbg.invocations()); - EXPECT_THAT( - output, // - testing::ElementsAre(149, 2551884, 999155, 135185, -2037323, 345668, - 33353, -680498, -1527958, -1645965, 149)); - } -} - -// This is an implementation-specific test. If any part of the implementation -// changes, then it is likely that this test will change as well. -// Also, if dependencies of the distribution change, such as RandU64ToDouble, -// then this is also likely to change. -TEST(GaussianDistributionTest, AlgorithmBounds) { - absl::gaussian_distribution<double> dist; - - // In ~95% of cases, a single value is used to generate the output. - // for all inputs where |x| < 0.750461021389 this should be the case. - // - // The exact constraints are based on the ziggurat tables, and any - // changes to the ziggurat tables may require adjusting these bounds. - // - // for i in range(0, len(X)-1): - // print i, X[i+1]/X[i], (X[i+1]/X[i] > 0.984375) - // - // 0.125 <= |values| <= 0.75 - const uint64_t kValues[] = { - 0x1000000000000100ull, 0x2000000000000100ull, 0x3000000000000100ull, - 0x4000000000000100ull, 0x5000000000000100ull, 0x6000000000000100ull, - // negative values - 0x9000000000000100ull, 0xa000000000000100ull, 0xb000000000000100ull, - 0xc000000000000100ull, 0xd000000000000100ull, 0xe000000000000100ull}; - - // 0.875 <= |values| <= 0.984375 - const uint64_t kExtraValues[] = { - 0x7000000000000100ull, 0x7800000000000100ull, // - 0x7c00000000000100ull, 0x7e00000000000100ull, // - // negative values - 0xf000000000000100ull, 0xf800000000000100ull, // - 0xfc00000000000100ull, 0xfe00000000000100ull}; - - auto make_box = [](uint64_t v, uint64_t box) { - return (v & 0xffffffffffffff80ull) | box; - }; - - // The box is the lower 7 bits of the value. When the box == 0, then - // the algorithm uses an escape hatch to select the result for large - // outputs. - for (uint64_t box = 0; box < 0x7f; box++) { - for (const uint64_t v : kValues) { - // Extra values are added to the sequence to attempt to avoid - // infinite loops from rejection sampling on bugs/errors. - absl::random_internal::sequence_urbg urbg( - {make_box(v, box), 0x0003eb76f6f7f755ull, 0x5FCEA50FDB2F953Bull}); - - auto a = dist(urbg); - EXPECT_EQ(1, urbg.invocations()) << box << " " << std::hex << v; - if (v & 0x8000000000000000ull) { - EXPECT_LT(a, 0.0) << box << " " << std::hex << v; - } else { - EXPECT_GT(a, 0.0) << box << " " << std::hex << v; - } - } - if (box > 10 && box < 100) { - // The center boxes use the fast algorithm for more - // than 98.4375% of values. - for (const uint64_t v : kExtraValues) { - absl::random_internal::sequence_urbg urbg( - {make_box(v, box), 0x0003eb76f6f7f755ull, 0x5FCEA50FDB2F953Bull}); - - auto a = dist(urbg); - EXPECT_EQ(1, urbg.invocations()) << box << " " << std::hex << v; - if (v & 0x8000000000000000ull) { - EXPECT_LT(a, 0.0) << box << " " << std::hex << v; - } else { - EXPECT_GT(a, 0.0) << box << " " << std::hex << v; - } - } - } - } - - // When the box == 0, the fallback algorithm uses a ratio of uniforms, - // which consumes 2 additional values from the urbg. - // Fallback also requires that the initial value be > 0.9271586026096681. - auto make_fallback = [](uint64_t v) { return (v & 0xffffffffffffff80ull); }; - - double tail[2]; - { - // 0.9375 - absl::random_internal::sequence_urbg urbg( - {make_fallback(0x7800000000000000ull), 0x13CCA830EB61BD96ull, - 0x00000076f6f7f755ull}); - tail[0] = dist(urbg); - EXPECT_EQ(3, urbg.invocations()); - EXPECT_GT(tail[0], 0); - } - { - // -0.9375 - absl::random_internal::sequence_urbg urbg( - {make_fallback(0xf800000000000000ull), 0x13CCA830EB61BD96ull, - 0x00000076f6f7f755ull}); - tail[1] = dist(urbg); - EXPECT_EQ(3, urbg.invocations()); - EXPECT_LT(tail[1], 0); - } - EXPECT_EQ(tail[0], -tail[1]); - EXPECT_EQ(418610, static_cast<int64_t>(tail[0] * 100000.0)); - - // When the box != 0, the fallback algorithm computes a wedge function. - // Depending on the box, the threshold for varies as high as - // 0.991522480228. - { - // 0.9921875, 0.875 - absl::random_internal::sequence_urbg urbg( - {make_box(0x7f00000000000000ull, 120), 0xe000000000000001ull, - 0x13CCA830EB61BD96ull}); - tail[0] = dist(urbg); - EXPECT_EQ(2, urbg.invocations()); - EXPECT_GT(tail[0], 0); - } - { - // -0.9921875, 0.875 - absl::random_internal::sequence_urbg urbg( - {make_box(0xff00000000000000ull, 120), 0xe000000000000001ull, - 0x13CCA830EB61BD96ull}); - tail[1] = dist(urbg); - EXPECT_EQ(2, urbg.invocations()); - EXPECT_LT(tail[1], 0); - } - EXPECT_EQ(tail[0], -tail[1]); - EXPECT_EQ(61948, static_cast<int64_t>(tail[0] * 100000.0)); - - // Fallback rejected, try again. - { - // -0.9921875, 0.0625 - absl::random_internal::sequence_urbg urbg( - {make_box(0xff00000000000000ull, 120), 0x1000000000000001, - make_box(0x1000000000000100ull, 50), 0x13CCA830EB61BD96ull}); - dist(urbg); - EXPECT_EQ(3, urbg.invocations()); - } -} - -} // namespace |