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GitOrigin-RevId: 9ee91d3e430fb33a4590486573792eb0fa146c2d
Change-Id: Ia06e548bc106cc9d136f6c65714be6645317aced

1 files changed, 422 insertions, 0 deletions

diff --git a/absl/random/exponential_distribution_test.cc b/absl/random/exponential_distribution_test.cc
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+++ b/absl/random/exponential_distribution_test.cc
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+// 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 <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/random/internal/chi_square.h"
+#include "absl/random/internal/distribution_test_util.h"
+#include "absl/random/internal/sequence_urbg.h"
+#include "absl/random/random.h"
+#include "absl/strings/str_cat.h"
+#include "absl/strings/str_format.h"
+#include "absl/strings/str_replace.h"
+#include "absl/strings/strip.h"
+
+namespace {
+
+using absl::random_internal::kChiSquared;
+
+template <typename RealType>
+class ExponentialDistributionTypedTest : public ::testing::Test {};
+
+using RealTypes = ::testing::Types<float, double, long double>;
+TYPED_TEST_CASE(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;
+
+#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \
+    defined(__ppc__) || defined(__PPC__)
+    if (std::is_same<TypeParam, long double>::value) {
+      // Roundtripping floating point values requires sufficient precision to
+      // reconstruct the exact value. It turns out that long double has some
+      // errors doing this on ppc, particularly for values
+      // near {1.0 +/- epsilon}.
+      if (lambda <= std::numeric_limits<double>::max() &&
+          lambda >= std::numeric_limits<double>::lowest()) {
+        EXPECT_EQ(static_cast<double>(before.lambda()),
+                  static_cast<double>(after.lambda()))
+            << ss.str();
+      }
+      continue;
+    }
+#endif
+
+    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();
+
+  absl::InsecureBitGen rng_;
+};
+
+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_CASE_P(, 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.
+  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