fc8dc48020
git-subtree-dir: third_party/abseil_cpp git-subtree-mainline:ffb2ae54begit-subtree-split:768eb2ca28
430 lines
14 KiB
C++
430 lines
14 KiB
C++
// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "absl/random/exponential_distribution.h"
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#include <algorithm>
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#include <cmath>
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#include <cstddef>
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#include <cstdint>
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#include <iterator>
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#include <limits>
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#include <random>
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#include <sstream>
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#include <string>
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#include <type_traits>
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#include <vector>
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#include "gmock/gmock.h"
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#include "gtest/gtest.h"
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#include "absl/base/internal/raw_logging.h"
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#include "absl/base/macros.h"
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#include "absl/random/internal/chi_square.h"
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#include "absl/random/internal/distribution_test_util.h"
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#include "absl/random/internal/pcg_engine.h"
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#include "absl/random/internal/sequence_urbg.h"
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#include "absl/random/random.h"
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#include "absl/strings/str_cat.h"
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#include "absl/strings/str_format.h"
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#include "absl/strings/str_replace.h"
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#include "absl/strings/strip.h"
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namespace {
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using absl::random_internal::kChiSquared;
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template <typename RealType>
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class ExponentialDistributionTypedTest : public ::testing::Test {};
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#if defined(__EMSCRIPTEN__)
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using RealTypes = ::testing::Types<float, double>;
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#else
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using RealTypes = ::testing::Types<float, double, long double>;
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#endif // defined(__EMSCRIPTEN__)
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TYPED_TEST_CASE(ExponentialDistributionTypedTest, RealTypes);
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TYPED_TEST(ExponentialDistributionTypedTest, SerializeTest) {
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using param_type =
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typename absl::exponential_distribution<TypeParam>::param_type;
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const TypeParam kParams[] = {
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// Cases around 1.
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1, //
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std::nextafter(TypeParam(1), TypeParam(0)), // 1 - epsilon
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std::nextafter(TypeParam(1), TypeParam(2)), // 1 + epsilon
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// Typical cases.
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TypeParam(1e-8), TypeParam(1e-4), TypeParam(1), TypeParam(2),
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TypeParam(1e4), TypeParam(1e8), TypeParam(1e20), TypeParam(2.5),
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// Boundary cases.
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std::numeric_limits<TypeParam>::max(),
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std::numeric_limits<TypeParam>::epsilon(),
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std::nextafter(std::numeric_limits<TypeParam>::min(),
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TypeParam(1)), // min + epsilon
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std::numeric_limits<TypeParam>::min(), // smallest normal
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// There are some errors dealing with denorms on apple platforms.
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std::numeric_limits<TypeParam>::denorm_min(), // smallest denorm
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std::numeric_limits<TypeParam>::min() / 2, // denorm
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std::nextafter(std::numeric_limits<TypeParam>::min(),
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TypeParam(0)), // denorm_max
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};
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constexpr int kCount = 1000;
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absl::InsecureBitGen gen;
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for (const TypeParam lambda : kParams) {
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// Some values may be invalid; skip those.
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if (!std::isfinite(lambda)) continue;
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ABSL_ASSERT(lambda > 0);
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const param_type param(lambda);
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absl::exponential_distribution<TypeParam> before(lambda);
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EXPECT_EQ(before.lambda(), param.lambda());
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{
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absl::exponential_distribution<TypeParam> via_param(param);
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EXPECT_EQ(via_param, before);
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EXPECT_EQ(via_param.param(), before.param());
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}
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// Smoke test.
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auto sample_min = before.max();
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auto sample_max = before.min();
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for (int i = 0; i < kCount; i++) {
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auto sample = before(gen);
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EXPECT_GE(sample, before.min()) << before;
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EXPECT_LE(sample, before.max()) << before;
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if (sample > sample_max) sample_max = sample;
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if (sample < sample_min) sample_min = sample;
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}
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if (!std::is_same<TypeParam, long double>::value) {
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ABSL_INTERNAL_LOG(INFO,
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absl::StrFormat("Range {%f}: %f, %f, lambda=%f", lambda,
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sample_min, sample_max, lambda));
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}
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std::stringstream ss;
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ss << before;
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if (!std::isfinite(lambda)) {
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// Streams do not deserialize inf/nan correctly.
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continue;
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}
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// Validate stream serialization.
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absl::exponential_distribution<TypeParam> after(34.56f);
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EXPECT_NE(before.lambda(), after.lambda());
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EXPECT_NE(before.param(), after.param());
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EXPECT_NE(before, after);
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ss >> after;
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#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \
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defined(__ppc__) || defined(__PPC__)
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if (std::is_same<TypeParam, long double>::value) {
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// Roundtripping floating point values requires sufficient precision to
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// reconstruct the exact value. It turns out that long double has some
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// errors doing this on ppc, particularly for values
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// near {1.0 +/- epsilon}.
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if (lambda <= std::numeric_limits<double>::max() &&
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lambda >= std::numeric_limits<double>::lowest()) {
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EXPECT_EQ(static_cast<double>(before.lambda()),
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static_cast<double>(after.lambda()))
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<< ss.str();
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}
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continue;
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}
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#endif
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EXPECT_EQ(before.lambda(), after.lambda()) //
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<< ss.str() << " " //
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<< (ss.good() ? "good " : "") //
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<< (ss.bad() ? "bad " : "") //
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<< (ss.eof() ? "eof " : "") //
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<< (ss.fail() ? "fail " : "");
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}
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}
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm
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class ExponentialModel {
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public:
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explicit ExponentialModel(double lambda)
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: lambda_(lambda), beta_(1.0 / lambda) {}
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double lambda() const { return lambda_; }
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double mean() const { return beta_; }
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double variance() const { return beta_ * beta_; }
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double stddev() const { return std::sqrt(variance()); }
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double skew() const { return 2; }
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double kurtosis() const { return 6.0; }
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double CDF(double x) { return 1.0 - std::exp(-lambda_ * x); }
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// The inverse CDF, or PercentPoint function of the distribution
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double InverseCDF(double p) {
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ABSL_ASSERT(p >= 0.0);
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ABSL_ASSERT(p < 1.0);
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return -beta_ * std::log(1.0 - p);
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}
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private:
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const double lambda_;
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const double beta_;
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};
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struct Param {
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double lambda;
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double p_fail;
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int trials;
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};
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class ExponentialDistributionTests : public testing::TestWithParam<Param>,
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public ExponentialModel {
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public:
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ExponentialDistributionTests() : ExponentialModel(GetParam().lambda) {}
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// SingleZTest provides a basic z-squared test of the mean vs. expected
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// mean for data generated by the poisson distribution.
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template <typename D>
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bool SingleZTest(const double p, const size_t samples);
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// SingleChiSquaredTest provides a basic chi-squared test of the normal
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// distribution.
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template <typename D>
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double SingleChiSquaredTest();
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// We use a fixed bit generator for distribution accuracy tests. This allows
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// these tests to be deterministic, while still testing the qualify of the
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// implementation.
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absl::random_internal::pcg64_2018_engine rng_{0x2B7E151628AED2A6};
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};
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template <typename D>
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bool ExponentialDistributionTests::SingleZTest(const double p,
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const size_t samples) {
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D dis(lambda());
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std::vector<double> data;
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data.reserve(samples);
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for (size_t i = 0; i < samples; i++) {
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const double x = dis(rng_);
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data.push_back(x);
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}
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const auto m = absl::random_internal::ComputeDistributionMoments(data);
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const double max_err = absl::random_internal::MaxErrorTolerance(p);
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const double z = absl::random_internal::ZScore(mean(), m);
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const bool pass = absl::random_internal::Near("z", z, 0.0, max_err);
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if (!pass) {
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ABSL_INTERNAL_LOG(
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INFO, absl::StrFormat("p=%f max_err=%f\n"
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" lambda=%f\n"
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" mean=%f vs. %f\n"
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" stddev=%f vs. %f\n"
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" skewness=%f vs. %f\n"
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" kurtosis=%f vs. %f\n"
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" z=%f vs. 0",
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p, max_err, lambda(), m.mean, mean(),
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std::sqrt(m.variance), stddev(), m.skewness,
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skew(), m.kurtosis, kurtosis(), z));
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}
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return pass;
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}
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template <typename D>
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double ExponentialDistributionTests::SingleChiSquaredTest() {
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const size_t kSamples = 10000;
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const int kBuckets = 50;
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// The InverseCDF is the percent point function of the distribution, and can
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// be used to assign buckets roughly uniformly.
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std::vector<double> cutoffs;
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const double kInc = 1.0 / static_cast<double>(kBuckets);
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for (double p = kInc; p < 1.0; p += kInc) {
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cutoffs.push_back(InverseCDF(p));
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}
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if (cutoffs.back() != std::numeric_limits<double>::infinity()) {
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cutoffs.push_back(std::numeric_limits<double>::infinity());
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}
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D dis(lambda());
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std::vector<int32_t> counts(cutoffs.size(), 0);
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for (int j = 0; j < kSamples; j++) {
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const double x = dis(rng_);
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auto it = std::upper_bound(cutoffs.begin(), cutoffs.end(), x);
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counts[std::distance(cutoffs.begin(), it)]++;
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}
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// Null-hypothesis is that the distribution is exponentially distributed
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// with the provided lambda (not estimated from the data).
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const int dof = static_cast<int>(counts.size()) - 1;
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// Our threshold for logging is 1-in-50.
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const double threshold = absl::random_internal::ChiSquareValue(dof, 0.98);
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const double expected =
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static_cast<double>(kSamples) / static_cast<double>(counts.size());
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double chi_square = absl::random_internal::ChiSquareWithExpected(
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std::begin(counts), std::end(counts), expected);
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double p = absl::random_internal::ChiSquarePValue(chi_square, dof);
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if (chi_square > threshold) {
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for (int i = 0; i < cutoffs.size(); i++) {
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ABSL_INTERNAL_LOG(
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INFO, absl::StrFormat("%d : (%f) = %d", i, cutoffs[i], counts[i]));
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}
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ABSL_INTERNAL_LOG(INFO,
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absl::StrCat("lambda ", lambda(), "\n", //
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" expected ", expected, "\n", //
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kChiSquared, " ", chi_square, " (", p, ")\n",
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kChiSquared, " @ 0.98 = ", threshold));
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}
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return p;
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}
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TEST_P(ExponentialDistributionTests, ZTest) {
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const size_t kSamples = 10000;
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const auto& param = GetParam();
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const int expected_failures =
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std::max(1, static_cast<int>(std::ceil(param.trials * param.p_fail)));
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const double p = absl::random_internal::RequiredSuccessProbability(
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param.p_fail, param.trials);
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int failures = 0;
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for (int i = 0; i < param.trials; i++) {
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failures += SingleZTest<absl::exponential_distribution<double>>(p, kSamples)
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? 0
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: 1;
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}
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EXPECT_LE(failures, expected_failures);
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}
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TEST_P(ExponentialDistributionTests, ChiSquaredTest) {
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const int kTrials = 20;
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int failures = 0;
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for (int i = 0; i < kTrials; i++) {
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double p_value =
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SingleChiSquaredTest<absl::exponential_distribution<double>>();
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if (p_value < 0.005) { // 1/200
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failures++;
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}
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}
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// There is a 0.10% chance of producing at least one failure, so raise the
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// failure threshold high enough to allow for a flake rate < 10,000.
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EXPECT_LE(failures, 4);
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}
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std::vector<Param> GenParams() {
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return {
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Param{1.0, 0.02, 100},
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Param{2.5, 0.02, 100},
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Param{10, 0.02, 100},
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// large
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Param{1e4, 0.02, 100},
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Param{1e9, 0.02, 100},
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// small
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Param{0.1, 0.02, 100},
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Param{1e-3, 0.02, 100},
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Param{1e-5, 0.02, 100},
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};
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}
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std::string ParamName(const ::testing::TestParamInfo<Param>& info) {
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const auto& p = info.param;
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std::string name = absl::StrCat("lambda_", absl::SixDigits(p.lambda));
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return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
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}
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INSTANTIATE_TEST_CASE_P(All, ExponentialDistributionTests,
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::testing::ValuesIn(GenParams()), ParamName);
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// NOTE: absl::exponential_distribution is not guaranteed to be stable.
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TEST(ExponentialDistributionTest, StabilityTest) {
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// absl::exponential_distribution stability relies on std::log1p and
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// absl::uniform_real_distribution.
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absl::random_internal::sequence_urbg urbg(
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{0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
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0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
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0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
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0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
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std::vector<int> output(14);
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{
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absl::exponential_distribution<double> dist;
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std::generate(std::begin(output), std::end(output),
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[&] { return static_cast<int>(10000.0 * dist(urbg)); });
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EXPECT_EQ(14, urbg.invocations());
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EXPECT_THAT(output,
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testing::ElementsAre(0, 71913, 14375, 5039, 1835, 861, 25936,
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804, 126, 12337, 17984, 27002, 0, 71913));
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}
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urbg.reset();
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{
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absl::exponential_distribution<float> dist;
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std::generate(std::begin(output), std::end(output),
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[&] { return static_cast<int>(10000.0f * dist(urbg)); });
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EXPECT_EQ(14, urbg.invocations());
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EXPECT_THAT(output,
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testing::ElementsAre(0, 71913, 14375, 5039, 1835, 861, 25936,
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804, 126, 12337, 17984, 27002, 0, 71913));
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}
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}
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TEST(ExponentialDistributionTest, AlgorithmBounds) {
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// Relies on absl::uniform_real_distribution, so some of these comments
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// reference that.
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absl::exponential_distribution<double> dist;
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{
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// This returns the smallest value >0 from absl::uniform_real_distribution.
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absl::random_internal::sequence_urbg urbg({0x0000000000000001ull});
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double a = dist(urbg);
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EXPECT_EQ(a, 5.42101086242752217004e-20);
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}
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{
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// This returns a value very near 0.5 from absl::uniform_real_distribution.
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absl::random_internal::sequence_urbg urbg({0x7fffffffffffffefull});
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double a = dist(urbg);
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EXPECT_EQ(a, 0.693147180559945175204);
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}
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{
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// This returns the largest value <1 from absl::uniform_real_distribution.
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// WolframAlpha: ~39.1439465808987766283058547296341915292187253
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absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFeFull});
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double a = dist(urbg);
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EXPECT_EQ(a, 36.7368005696771007251);
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}
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{
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// This *ALSO* returns the largest value <1.
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absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFFFull});
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double a = dist(urbg);
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EXPECT_EQ(a, 36.7368005696771007251);
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}
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}
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} // namespace
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