fc8dc48020
git-subtree-dir: third_party/abseil_cpp git-subtree-mainline:ffb2ae54begit-subtree-split:768eb2ca28
579 lines
20 KiB
C++
579 lines
20 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/gaussian_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 <ios>
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#include <iterator>
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#include <random>
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#include <string>
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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/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 GaussianDistributionInterfaceTest : public ::testing::Test {};
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using RealTypes = ::testing::Types<float, double, long double>;
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TYPED_TEST_CASE(GaussianDistributionInterfaceTest, RealTypes);
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TYPED_TEST(GaussianDistributionInterfaceTest, SerializeTest) {
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using param_type =
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typename absl::gaussian_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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// Arbitrary values.
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TypeParam(1e-8), TypeParam(1e-4), TypeParam(2), TypeParam(1e4),
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TypeParam(1e8), TypeParam(1e20), TypeParam(2.5),
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// Boundary cases.
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std::numeric_limits<TypeParam>::infinity(),
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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,
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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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// Use a loop to generate the combinations of {+/-x, +/-y}, and assign x, y to
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// all values in kParams,
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for (const auto mod : {0, 1, 2, 3}) {
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for (const auto x : kParams) {
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if (!std::isfinite(x)) continue;
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for (const auto y : kParams) {
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const TypeParam mean = (mod & 0x1) ? -x : x;
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const TypeParam stddev = (mod & 0x2) ? -y : y;
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const param_type param(mean, stddev);
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absl::gaussian_distribution<TypeParam> before(mean, stddev);
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EXPECT_EQ(before.mean(), param.mean());
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EXPECT_EQ(before.stddev(), param.stddev());
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{
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absl::gaussian_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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if (sample > sample_max) sample_max = sample;
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if (sample < sample_min) sample_min = sample;
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EXPECT_GE(sample, before.min()) << before;
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EXPECT_LE(sample, before.max()) << before;
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}
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if (!std::is_same<TypeParam, long double>::value) {
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ABSL_INTERNAL_LOG(
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INFO, absl::StrFormat("Range{%f, %f}: %f, %f", mean, stddev,
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sample_min, sample_max));
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}
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std::stringstream ss;
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ss << before;
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if (!std::isfinite(mean) || !std::isfinite(stddev)) {
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// Streams do not parse inf/nan.
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continue;
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}
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// Validate stream serialization.
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absl::gaussian_distribution<TypeParam> after(-0.53f, 2.3456f);
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EXPECT_NE(before.mean(), after.mean());
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EXPECT_NE(before.stddev(), after.stddev());
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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__) || defined(__EMSCRIPTEN__)
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if (std::is_same<TypeParam, long double>::value) {
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// Roundtripping floating point values requires sufficient precision
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// to reconstruct the exact value. It turns out that long double
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// has some errors doing this on ppc, particularly for values
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// near {1.0 +/- epsilon}.
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//
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// Emscripten is even worse, implementing long double as a 128-bit
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// type, but shipping with a strtold() that doesn't support that.
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if (mean <= std::numeric_limits<double>::max() &&
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mean >= std::numeric_limits<double>::lowest()) {
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EXPECT_EQ(static_cast<double>(before.mean()),
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static_cast<double>(after.mean()))
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<< ss.str();
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}
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if (stddev <= std::numeric_limits<double>::max() &&
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stddev >= std::numeric_limits<double>::lowest()) {
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EXPECT_EQ(static_cast<double>(before.stddev()),
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static_cast<double>(after.stddev()))
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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.mean(), after.mean());
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EXPECT_EQ(before.stddev(), after.stddev()) //
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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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}
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}
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
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class GaussianModel {
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public:
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GaussianModel(double mean, double stddev) : mean_(mean), stddev_(stddev) {}
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double mean() const { return mean_; }
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double variance() const { return stddev() * stddev(); }
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double stddev() const { return stddev_; }
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double skew() const { return 0; }
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double kurtosis() const { return 3.0; }
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// The inverse CDF, or PercentPoint function.
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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 mean() + stddev() * -absl::random_internal::InverseNormalSurvival(p);
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}
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private:
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const double mean_;
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const double stddev_;
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};
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struct Param {
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double mean;
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double stddev;
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double p_fail; // Z-Test probability of failure.
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int trials; // Z-Test trials.
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};
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// GaussianDistributionTests implements a z-test for the gaussian
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// distribution.
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class GaussianDistributionTests : public testing::TestWithParam<Param>,
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public GaussianModel {
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public:
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GaussianDistributionTests()
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: GaussianModel(GetParam().mean, GetParam().stddev) {}
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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 GaussianDistributionTests::SingleZTest(const double p,
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const size_t samples) {
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D dis(mean(), stddev());
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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 double max_err = absl::random_internal::MaxErrorTolerance(p);
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const auto m = absl::random_internal::ComputeDistributionMoments(data);
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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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// NOTE: Informational statistical test:
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//
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// Compute the Jarque-Bera test statistic given the excess skewness
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// and kurtosis. The statistic is drawn from a chi-square(2) distribution.
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// https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test
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//
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// The null-hypothesis (normal distribution) is rejected when
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// (p = 0.05 => jb > 5.99)
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// (p = 0.01 => jb > 9.21)
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// NOTE: JB has a large type-I error rate, so it will reject the
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// null-hypothesis even when it is true more often than the z-test.
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//
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const double jb =
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static_cast<double>(m.n) / 6.0 *
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(std::pow(m.skewness, 2.0) + std::pow(m.kurtosis - 3.0, 2.0) / 4.0);
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if (!pass || jb > 9.21) {
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ABSL_INTERNAL_LOG(
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INFO, absl::StrFormat("p=%f max_err=%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\n"
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" jb=%f vs. 9.21",
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p, max_err, m.mean, mean(), std::sqrt(m.variance),
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stddev(), m.skewness, skew(), m.kurtosis,
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kurtosis(), z, jb));
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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 GaussianDistributionTests::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
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// distribution, and can be used to assign buckets
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// 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(mean(), stddev());
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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 a gaussian distribution
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// with the provided mean and stddev (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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// Log if the chi_square value is above the threshold.
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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(
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INFO, absl::StrCat("mean=", mean(), " stddev=", stddev(), "\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(GaussianDistributionTests, ZTest) {
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// TODO(absl-team): Run these tests against std::normal_distribution<double>
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// to validate outcomes are similar.
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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 +=
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SingleZTest<absl::gaussian_distribution<double>>(p, kSamples) ? 0 : 1;
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}
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EXPECT_LE(failures, expected_failures);
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}
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TEST_P(GaussianDistributionTests, 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::gaussian_distribution<double>>();
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if (p_value < 0.0025) { // 1/400
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failures++;
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}
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}
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// There is a 0.05% chance of producing at least one failure, so raise the
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// failure threshold high enough to allow for a flake rate of less than one in
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// 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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// Mean around 0.
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Param{0.0, 1.0, 0.01, 100},
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Param{0.0, 1e2, 0.01, 100},
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Param{0.0, 1e4, 0.01, 100},
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Param{0.0, 1e8, 0.01, 100},
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Param{0.0, 1e16, 0.01, 100},
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Param{0.0, 1e-3, 0.01, 100},
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Param{0.0, 1e-5, 0.01, 100},
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Param{0.0, 1e-9, 0.01, 100},
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Param{0.0, 1e-17, 0.01, 100},
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// Mean around 1.
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Param{1.0, 1.0, 0.01, 100},
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Param{1.0, 1e2, 0.01, 100},
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Param{1.0, 1e-2, 0.01, 100},
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// Mean around 100 / -100
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Param{1e2, 1.0, 0.01, 100},
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Param{-1e2, 1.0, 0.01, 100},
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Param{1e2, 1e6, 0.01, 100},
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Param{-1e2, 1e6, 0.01, 100},
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// More extreme
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Param{1e4, 1e4, 0.01, 100},
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Param{1e8, 1e4, 0.01, 100},
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Param{1e12, 1e4, 0.01, 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("mean_", absl::SixDigits(p.mean), "__stddev_",
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absl::SixDigits(p.stddev));
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return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
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}
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INSTANTIATE_TEST_SUITE_P(All, GaussianDistributionTests,
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::testing::ValuesIn(GenParams()), ParamName);
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// NOTE: absl::gaussian_distribution is not guaranteed to be stable.
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TEST(GaussianDistributionTest, StabilityTest) {
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// absl::gaussian_distribution stability relies on the underlying zignor
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// data, absl::random_interna::RandU64ToDouble, std::exp, std::log, and
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// std::abs.
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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(11);
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{
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absl::gaussian_distribution<double> dist;
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std::generate(std::begin(output), std::end(output),
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[&] { return static_cast<int>(10000000.0 * dist(urbg)); });
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EXPECT_EQ(13, urbg.invocations());
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EXPECT_THAT(output, //
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testing::ElementsAre(1494, 25518841, 9991550, 1351856,
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-20373238, 3456682, 333530, -6804981,
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-15279580, -16459654, 1494));
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}
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urbg.reset();
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{
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absl::gaussian_distribution<float> dist;
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std::generate(std::begin(output), std::end(output),
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[&] { return static_cast<int>(1000000.0f * dist(urbg)); });
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EXPECT_EQ(13, urbg.invocations());
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EXPECT_THAT(
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output, //
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testing::ElementsAre(149, 2551884, 999155, 135185, -2037323, 345668,
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33353, -680498, -1527958, -1645965, 149));
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}
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}
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// This is an implementation-specific test. If any part of the implementation
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// changes, then it is likely that this test will change as well.
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// Also, if dependencies of the distribution change, such as RandU64ToDouble,
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// then this is also likely to change.
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TEST(GaussianDistributionTest, AlgorithmBounds) {
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absl::gaussian_distribution<double> dist;
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// In ~95% of cases, a single value is used to generate the output.
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// for all inputs where |x| < 0.750461021389 this should be the case.
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//
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// The exact constraints are based on the ziggurat tables, and any
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// changes to the ziggurat tables may require adjusting these bounds.
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//
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// for i in range(0, len(X)-1):
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// print i, X[i+1]/X[i], (X[i+1]/X[i] > 0.984375)
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//
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// 0.125 <= |values| <= 0.75
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const uint64_t kValues[] = {
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0x1000000000000100ull, 0x2000000000000100ull, 0x3000000000000100ull,
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0x4000000000000100ull, 0x5000000000000100ull, 0x6000000000000100ull,
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// negative values
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0x9000000000000100ull, 0xa000000000000100ull, 0xb000000000000100ull,
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0xc000000000000100ull, 0xd000000000000100ull, 0xe000000000000100ull};
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|
|
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// 0.875 <= |values| <= 0.984375
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const uint64_t kExtraValues[] = {
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0x7000000000000100ull, 0x7800000000000100ull, //
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|
0x7c00000000000100ull, 0x7e00000000000100ull, //
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// negative values
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0xf000000000000100ull, 0xf800000000000100ull, //
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0xfc00000000000100ull, 0xfe00000000000100ull};
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|
|
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auto make_box = [](uint64_t v, uint64_t box) {
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return (v & 0xffffffffffffff80ull) | box;
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};
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|
|
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// 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.
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|
for (uint64_t box = 0; box < 0x7f; box++) {
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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.
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|
absl::random_internal::sequence_urbg urbg(
|
|
{make_box(v, box), 0x0003eb76f6f7f755ull, 0x5FCEA50FDB2F953Bull});
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|
|
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auto a = dist(urbg);
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EXPECT_EQ(1, urbg.invocations()) << box << " " << std::hex << v;
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|
if (v & 0x8000000000000000ull) {
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|
EXPECT_LT(a, 0.0) << box << " " << std::hex << v;
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|
} 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
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