429 lines
14 KiB
C++
429 lines
14 KiB
C++
// 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/exponential_distribution.h"
|
|
|
|
#include <algorithm>
|
|
#include <cfloat>
|
|
#include <cmath>
|
|
#include <cstddef>
|
|
#include <cstdint>
|
|
#include <iterator>
|
|
#include <limits>
|
|
#include <random>
|
|
#include <sstream>
|
|
#include <string>
|
|
#include <type_traits>
|
|
#include <vector>
|
|
|
|
#include "gmock/gmock.h"
|
|
#include "gtest/gtest.h"
|
|
#include "absl/base/internal/raw_logging.h"
|
|
#include "absl/base/macros.h"
|
|
#include "absl/numeric/internal/representation.h"
|
|
#include "absl/random/internal/chi_square.h"
|
|
#include "absl/random/internal/distribution_test_util.h"
|
|
#include "absl/random/internal/pcg_engine.h"
|
|
#include "absl/random/internal/sequence_urbg.h"
|
|
#include "absl/random/random.h"
|
|
#include "absl/strings/str_cat.h"
|
|
#include "absl/strings/str_format.h"
|
|
#include "absl/strings/str_replace.h"
|
|
#include "absl/strings/strip.h"
|
|
|
|
namespace {
|
|
|
|
using absl::random_internal::kChiSquared;
|
|
|
|
template <typename RealType>
|
|
class ExponentialDistributionTypedTest : public ::testing::Test {};
|
|
|
|
// double-double arithmetic is not supported well by either GCC or Clang; see
|
|
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=99048,
|
|
// https://bugs.llvm.org/show_bug.cgi?id=49131, and
|
|
// https://bugs.llvm.org/show_bug.cgi?id=49132. Don't bother running these tests
|
|
// with double doubles until compiler support is better.
|
|
using RealTypes =
|
|
std::conditional<absl::numeric_internal::IsDoubleDouble(),
|
|
::testing::Types<float, double>,
|
|
::testing::Types<float, double, long double>>::type;
|
|
TYPED_TEST_SUITE(ExponentialDistributionTypedTest, RealTypes);
|
|
|
|
TYPED_TEST(ExponentialDistributionTypedTest, SerializeTest) {
|
|
using param_type =
|
|
typename absl::exponential_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
|
|
// Typical cases.
|
|
TypeParam(1e-8), TypeParam(1e-4), TypeParam(1), TypeParam(2),
|
|
TypeParam(1e4), TypeParam(1e8), TypeParam(1e20), TypeParam(2.5),
|
|
// Boundary cases.
|
|
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, // denorm
|
|
std::nextafter(std::numeric_limits<TypeParam>::min(),
|
|
TypeParam(0)), // denorm_max
|
|
};
|
|
|
|
constexpr int kCount = 1000;
|
|
absl::InsecureBitGen gen;
|
|
|
|
for (const TypeParam lambda : kParams) {
|
|
// Some values may be invalid; skip those.
|
|
if (!std::isfinite(lambda)) continue;
|
|
ABSL_ASSERT(lambda > 0);
|
|
|
|
const param_type param(lambda);
|
|
|
|
absl::exponential_distribution<TypeParam> before(lambda);
|
|
EXPECT_EQ(before.lambda(), param.lambda());
|
|
|
|
{
|
|
absl::exponential_distribution<TypeParam> via_param(param);
|
|
EXPECT_EQ(via_param, before);
|
|
EXPECT_EQ(via_param.param(), before.param());
|
|
}
|
|
|
|
// Smoke test.
|
|
auto sample_min = before.max();
|
|
auto sample_max = before.min();
|
|
for (int i = 0; i < kCount; i++) {
|
|
auto sample = before(gen);
|
|
EXPECT_GE(sample, before.min()) << before;
|
|
EXPECT_LE(sample, before.max()) << before;
|
|
if (sample > sample_max) sample_max = sample;
|
|
if (sample < sample_min) sample_min = sample;
|
|
}
|
|
if (!std::is_same<TypeParam, long double>::value) {
|
|
ABSL_INTERNAL_LOG(INFO,
|
|
absl::StrFormat("Range {%f}: %f, %f, lambda=%f", lambda,
|
|
sample_min, sample_max, lambda));
|
|
}
|
|
|
|
std::stringstream ss;
|
|
ss << before;
|
|
|
|
if (!std::isfinite(lambda)) {
|
|
// Streams do not deserialize inf/nan correctly.
|
|
continue;
|
|
}
|
|
// Validate stream serialization.
|
|
absl::exponential_distribution<TypeParam> after(34.56f);
|
|
|
|
EXPECT_NE(before.lambda(), after.lambda());
|
|
EXPECT_NE(before.param(), after.param());
|
|
EXPECT_NE(before, after);
|
|
|
|
ss >> after;
|
|
|
|
EXPECT_EQ(before.lambda(), after.lambda()) //
|
|
<< ss.str() << " " //
|
|
<< (ss.good() ? "good " : "") //
|
|
<< (ss.bad() ? "bad " : "") //
|
|
<< (ss.eof() ? "eof " : "") //
|
|
<< (ss.fail() ? "fail " : "");
|
|
}
|
|
}
|
|
|
|
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm
|
|
|
|
class ExponentialModel {
|
|
public:
|
|
explicit ExponentialModel(double lambda)
|
|
: lambda_(lambda), beta_(1.0 / lambda) {}
|
|
|
|
double lambda() const { return lambda_; }
|
|
|
|
double mean() const { return beta_; }
|
|
double variance() const { return beta_ * beta_; }
|
|
double stddev() const { return std::sqrt(variance()); }
|
|
double skew() const { return 2; }
|
|
double kurtosis() const { return 6.0; }
|
|
|
|
double CDF(double x) { return 1.0 - std::exp(-lambda_ * x); }
|
|
|
|
// The inverse CDF, or PercentPoint function of the distribution
|
|
double InverseCDF(double p) {
|
|
ABSL_ASSERT(p >= 0.0);
|
|
ABSL_ASSERT(p < 1.0);
|
|
return -beta_ * std::log(1.0 - p);
|
|
}
|
|
|
|
private:
|
|
const double lambda_;
|
|
const double beta_;
|
|
};
|
|
|
|
struct Param {
|
|
double lambda;
|
|
double p_fail;
|
|
int trials;
|
|
};
|
|
|
|
class ExponentialDistributionTests : public testing::TestWithParam<Param>,
|
|
public ExponentialModel {
|
|
public:
|
|
ExponentialDistributionTests() : ExponentialModel(GetParam().lambda) {}
|
|
|
|
// SingleZTest provides a basic z-squared test of the mean vs. expected
|
|
// mean for data generated by the poisson distribution.
|
|
template <typename D>
|
|
bool SingleZTest(const double p, const size_t samples);
|
|
|
|
// SingleChiSquaredTest provides a basic chi-squared test of the normal
|
|
// distribution.
|
|
template <typename D>
|
|
double SingleChiSquaredTest();
|
|
|
|
// We use a fixed bit generator for distribution accuracy tests. This allows
|
|
// these tests to be deterministic, while still testing the qualify of the
|
|
// implementation.
|
|
absl::random_internal::pcg64_2018_engine rng_{0x2B7E151628AED2A6};
|
|
};
|
|
|
|
template <typename D>
|
|
bool ExponentialDistributionTests::SingleZTest(const double p,
|
|
const size_t samples) {
|
|
D dis(lambda());
|
|
|
|
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 auto m = absl::random_internal::ComputeDistributionMoments(data);
|
|
const double max_err = absl::random_internal::MaxErrorTolerance(p);
|
|
const double z = absl::random_internal::ZScore(mean(), m);
|
|
const bool pass = absl::random_internal::Near("z", z, 0.0, max_err);
|
|
|
|
if (!pass) {
|
|
ABSL_INTERNAL_LOG(
|
|
INFO, absl::StrFormat("p=%f max_err=%f\n"
|
|
" lambda=%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",
|
|
p, max_err, lambda(), m.mean, mean(),
|
|
std::sqrt(m.variance), stddev(), m.skewness,
|
|
skew(), m.kurtosis, kurtosis(), z));
|
|
}
|
|
return pass;
|
|
}
|
|
|
|
template <typename D>
|
|
double ExponentialDistributionTests::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(lambda());
|
|
|
|
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 exponentially distributed
|
|
// with the provided lambda (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);
|
|
|
|
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("lambda ", lambda(), "\n", //
|
|
" expected ", expected, "\n", //
|
|
kChiSquared, " ", chi_square, " (", p, ")\n",
|
|
kChiSquared, " @ 0.98 = ", threshold));
|
|
}
|
|
return p;
|
|
}
|
|
|
|
TEST_P(ExponentialDistributionTests, ZTest) {
|
|
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::exponential_distribution<double>>(p, kSamples)
|
|
? 0
|
|
: 1;
|
|
}
|
|
EXPECT_LE(failures, expected_failures);
|
|
}
|
|
|
|
TEST_P(ExponentialDistributionTests, ChiSquaredTest) {
|
|
const int kTrials = 20;
|
|
int failures = 0;
|
|
|
|
for (int i = 0; i < kTrials; i++) {
|
|
double p_value =
|
|
SingleChiSquaredTest<absl::exponential_distribution<double>>();
|
|
if (p_value < 0.005) { // 1/200
|
|
failures++;
|
|
}
|
|
}
|
|
|
|
// There is a 0.10% chance of producing at least one failure, so raise the
|
|
// failure threshold high enough to allow for a flake rate < 10,000.
|
|
EXPECT_LE(failures, 4);
|
|
}
|
|
|
|
std::vector<Param> GenParams() {
|
|
return {
|
|
Param{1.0, 0.02, 100},
|
|
Param{2.5, 0.02, 100},
|
|
Param{10, 0.02, 100},
|
|
// large
|
|
Param{1e4, 0.02, 100},
|
|
Param{1e9, 0.02, 100},
|
|
// small
|
|
Param{0.1, 0.02, 100},
|
|
Param{1e-3, 0.02, 100},
|
|
Param{1e-5, 0.02, 100},
|
|
};
|
|
}
|
|
|
|
std::string ParamName(const ::testing::TestParamInfo<Param>& info) {
|
|
const auto& p = info.param;
|
|
std::string name = absl::StrCat("lambda_", absl::SixDigits(p.lambda));
|
|
return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
|
|
}
|
|
|
|
INSTANTIATE_TEST_SUITE_P(All, ExponentialDistributionTests,
|
|
::testing::ValuesIn(GenParams()), ParamName);
|
|
|
|
// NOTE: absl::exponential_distribution is not guaranteed to be stable.
|
|
TEST(ExponentialDistributionTest, StabilityTest) {
|
|
// absl::exponential_distribution stability relies on std::log1p and
|
|
// absl::uniform_real_distribution.
|
|
absl::random_internal::sequence_urbg urbg(
|
|
{0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
|
|
0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
|
|
0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
|
|
0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
|
|
|
|
std::vector<int> output(14);
|
|
|
|
{
|
|
absl::exponential_distribution<double> dist;
|
|
std::generate(std::begin(output), std::end(output),
|
|
[&] { return static_cast<int>(10000.0 * dist(urbg)); });
|
|
|
|
EXPECT_EQ(14, urbg.invocations());
|
|
EXPECT_THAT(output,
|
|
testing::ElementsAre(0, 71913, 14375, 5039, 1835, 861, 25936,
|
|
804, 126, 12337, 17984, 27002, 0, 71913));
|
|
}
|
|
|
|
urbg.reset();
|
|
{
|
|
absl::exponential_distribution<float> dist;
|
|
std::generate(std::begin(output), std::end(output),
|
|
[&] { return static_cast<int>(10000.0f * dist(urbg)); });
|
|
|
|
EXPECT_EQ(14, urbg.invocations());
|
|
EXPECT_THAT(output,
|
|
testing::ElementsAre(0, 71913, 14375, 5039, 1835, 861, 25936,
|
|
804, 126, 12337, 17984, 27002, 0, 71913));
|
|
}
|
|
}
|
|
|
|
TEST(ExponentialDistributionTest, AlgorithmBounds) {
|
|
// Relies on absl::uniform_real_distribution, so some of these comments
|
|
// reference that.
|
|
|
|
#if (defined(__i386__) || defined(_M_IX86)) && FLT_EVAL_METHOD != 0
|
|
// We're using an x87-compatible FPU, and intermediate operations can be
|
|
// performed with 80-bit floats. This produces slightly different results from
|
|
// what we expect below.
|
|
GTEST_SKIP()
|
|
<< "Skipping the test because we detected x87 floating-point semantics";
|
|
#endif
|
|
|
|
absl::exponential_distribution<double> dist;
|
|
|
|
{
|
|
// This returns the smallest value >0 from absl::uniform_real_distribution.
|
|
absl::random_internal::sequence_urbg urbg({0x0000000000000001ull});
|
|
double a = dist(urbg);
|
|
EXPECT_EQ(a, 5.42101086242752217004e-20);
|
|
}
|
|
|
|
{
|
|
// This returns a value very near 0.5 from absl::uniform_real_distribution.
|
|
absl::random_internal::sequence_urbg urbg({0x7fffffffffffffefull});
|
|
double a = dist(urbg);
|
|
EXPECT_EQ(a, 0.693147180559945175204);
|
|
}
|
|
|
|
{
|
|
// This returns the largest value <1 from absl::uniform_real_distribution.
|
|
// WolframAlpha: ~39.1439465808987766283058547296341915292187253
|
|
absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFeFull});
|
|
double a = dist(urbg);
|
|
EXPECT_EQ(a, 36.7368005696771007251);
|
|
}
|
|
{
|
|
// This *ALSO* returns the largest value <1.
|
|
absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFFFull});
|
|
double a = dist(urbg);
|
|
EXPECT_EQ(a, 36.7368005696771007251);
|
|
}
|
|
}
|
|
|
|
} // namespace
|