// 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/macros.h"
#include "absl/log/log.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) {
LOG(INFO) << "Range {" << lambda << "}: " << sample_min << ", "
<< sample_max << ", lambda=" << 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) {
// clang-format off
LOG(INFO)
<< "p=" << p << " max_err=" << max_err << "\n"
" lambda=" << lambda() << "\n"
" mean=" << m.mean << " vs. " << mean() << "\n"
" stddev=" << std::sqrt(m.variance) << " vs. " << stddev() << "\n"
" skewness=" << m.skewness << " vs. " << skew() << "\n"
" kurtosis=" << m.kurtosis << " vs. " << kurtosis() << "\n"
" z=" << z << " vs. 0";
// clang-format on
}
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 (size_t i = 0; i < cutoffs.size(); i++) {
LOG(INFO) << i << " : (" << cutoffs[i] << ") = " << counts[i];
}
// clang-format off
LOG(INFO) << "lambda " << lambda() << "\n"
" expected " << expected << "\n"
<< kChiSquared << " " << chi_square << " (" << p << ")\n"
<< kChiSquared << " @ 0.98 = " << threshold;
// clang-format on
}
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
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