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Diffstat (limited to 'absl/random/gaussian_distribution_test.cc')
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diff --git a/absl/random/gaussian_distribution_test.cc b/absl/random/gaussian_distribution_test.cc new file mode 100644 index 000000000000..47c2989d340b --- /dev/null +++ b/absl/random/gaussian_distribution_test.cc @@ -0,0 +1,573 @@ +// 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__) + 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 (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(); + + absl::InsecureBitGen rng_; +}; + +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(, 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 |