Creation of LTS branch "lts_2019_08_08"20190808

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GitOrigin-RevId: 9ee91d3e430fb33a4590486573792eb0fa146c2d
Change-Id: Ia06e548bc106cc9d136f6c65714be6645317aced

1 files changed, 565 insertions, 0 deletions

diff --git a/absl/random/poisson_distribution_test.cc b/absl/random/poisson_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/poisson_distribution.h"
+
+#include <algorithm>
+#include <cstddef>
+#include <cstdint>
+#include <iterator>
+#include <random>
+#include <sstream>
+#include <string>
+#include <vector>
+
+#include "gmock/gmock.h"
+#include "gtest/gtest.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/base/macros.h"
+#include "absl/container/flat_hash_map.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"
+
+// Notes about generating poisson variates:
+//
+// It is unlikely that any implementation of std::poisson_distribution
+// will be stable over time and across library implementations. For instance
+// the three different poisson variate generators listed below all differ:
+//
+// https://github.com/ampl/gsl/tree/master/randist/poisson.c
+// * GSL uses a gamma + binomial + knuth method to compute poisson variates.
+//
+// https://github.com/gcc-mirror/gcc/blob/master/libstdc%2B%2B-v3/include/bits/random.tcc
+// * GCC uses the Devroye rejection algorithm, based on
+// Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
+// New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!), ~p.511
+//   http://www.nrbook.com/devroye/
+//
+// https://github.com/llvm-mirror/libcxx/blob/master/include/random
+// * CLANG uses a different rejection method, which appears to include a
+// normal-distribution approximation and an exponential distribution to
+// compute the threshold, including a similar factorial approximation to this
+// one, but it is unclear where the algorithm comes from, exactly.
+//
+
+namespace {
+
+using absl::random_internal::kChiSquared;
+
+// The PoissonDistributionInterfaceTest provides a basic test that
+// absl::poisson_distribution conforms to the interface and serialization
+// requirements imposed by [rand.req.dist] for the common integer types.
+
+template <typename IntType>
+class PoissonDistributionInterfaceTest : public ::testing::Test {};
+
+using IntTypes = ::testing::Types<int, int8_t, int16_t, int32_t, int64_t,
+                                  uint8_t, uint16_t, uint32_t, uint64_t>;
+TYPED_TEST_CASE(PoissonDistributionInterfaceTest, IntTypes);
+
+TYPED_TEST(PoissonDistributionInterfaceTest, SerializeTest) {
+  using param_type = typename absl::poisson_distribution<TypeParam>::param_type;
+  const double kMax =
+      std::min(1e10 /* assertion limit */,
+               static_cast<double>(std::numeric_limits<TypeParam>::max()));
+
+  const double kParams[] = {
+      // Cases around 1.
+      1,                         //
+      std::nextafter(1.0, 0.0),  // 1 - epsilon
+      std::nextafter(1.0, 2.0),  // 1 + epsilon
+      // Arbitrary values.
+      1e-8, 1e-4,
+      0.0000005,  // ~7.2e-7
+      0.2,        // ~0.2x
+      0.5,        // 0.72
+      2,          // ~2.8
+      20,         // 3x ~9.6
+      100, 1e4, 1e8, 1.5e9, 1e20,
+      // Boundary cases.
+      std::numeric_limits<double>::max(),
+      std::numeric_limits<double>::epsilon(),
+      std::nextafter(std::numeric_limits<double>::min(),
+                     1.0),                        // min + epsilon
+      std::numeric_limits<double>::min(),         // smallest normal
+      std::numeric_limits<double>::denorm_min(),  // smallest denorm
+      std::numeric_limits<double>::min() / 2,     // denorm
+      std::nextafter(std::numeric_limits<double>::min(),
+                     0.0),  // denorm_max
+  };
+
+
+  constexpr int kCount = 1000;
+  absl::InsecureBitGen gen;
+  for (const double m : kParams) {
+    const double mean = std::min(kMax, m);
+    const param_type param(mean);
+
+    // Validate parameters.
+    absl::poisson_distribution<TypeParam> before(mean);
+    EXPECT_EQ(before.mean(), param.mean());
+
+    {
+      absl::poisson_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());
+      EXPECT_LE(sample, before.max());
+      if (sample > sample_max) sample_max = sample;
+      if (sample < sample_min) sample_min = sample;
+    }
+
+    ABSL_INTERNAL_LOG(INFO, absl::StrCat("Range {", param.mean(), "}: ",
+                                         +sample_min, ", ", +sample_max));
+
+    // Validate stream serialization.
+    std::stringstream ss;
+    ss << before;
+
+    absl::poisson_distribution<TypeParam> after(3.8);
+
+    EXPECT_NE(before.mean(), after.mean());
+    EXPECT_NE(before.param(), after.param());
+    EXPECT_NE(before, after);
+
+    ss >> after;
+
+    EXPECT_EQ(before.mean(), after.mean())  //
+        << ss.str() << " "                  //
+        << (ss.good() ? "good " : "")       //
+        << (ss.bad() ? "bad " : "")         //
+        << (ss.eof() ? "eof " : "")         //
+        << (ss.fail() ? "fail " : "");
+  }
+}
+
+// See http://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm
+
+class PoissonModel {
+ public:
+  explicit PoissonModel(double mean) : mean_(mean) {}
+
+  double mean() const { return mean_; }
+  double variance() const { return mean_; }
+  double stddev() const { return std::sqrt(variance()); }
+  double skew() const { return 1.0 / mean_; }
+  double kurtosis() const { return 3.0 + 1.0 / mean_; }
+
+  // InitCDF() initializes the CDF for the distribution parameters.
+  void InitCDF();
+
+  // The InverseCDF, or the Percent-point function returns x, P(x) < v.
+  struct CDF {
+    size_t index;
+    double pmf;
+    double cdf;
+  };
+  CDF InverseCDF(double p) {
+    CDF target{0, 0, p};
+    auto it = std::upper_bound(
+        std::begin(cdf_), std::end(cdf_), target,
+        [](const CDF& a, const CDF& b) { return a.cdf < b.cdf; });
+    return *it;
+  }
+
+  void LogCDF() {
+    ABSL_INTERNAL_LOG(INFO, absl::StrCat("CDF (mean = ", mean_, ")"));
+    for (const auto c : cdf_) {
+      ABSL_INTERNAL_LOG(INFO,
+                        absl::StrCat(c.index, ": pmf=", c.pmf, " cdf=", c.cdf));
+    }
+  }
+
+ private:
+  const double mean_;
+
+  std::vector<CDF> cdf_;
+};
+
+// The goal is to compute an InverseCDF function, or percent point function for
+// the poisson distribution, and use that to partition our output into equal
+// range buckets.  However there is no closed form solution for the inverse cdf
+// for poisson distributions (the closest is the incomplete gamma function).
+// Instead, `InitCDF` iteratively computes the PMF and the CDF. This enables
+// searching for the bucket points.
+void PoissonModel::InitCDF() {
+  if (!cdf_.empty()) {
+    // State already initialized.
+    return;
+  }
+  ABSL_ASSERT(mean_ < 201.0);
+
+  const size_t max_i = 50 * stddev() + mean();
+  const double e_neg_mean = std::exp(-mean());
+  ABSL_ASSERT(e_neg_mean > 0);
+
+  double d = 1;
+  double last_result = e_neg_mean;
+  double cumulative = e_neg_mean;
+  if (e_neg_mean > 1e-10) {
+    cdf_.push_back({0, e_neg_mean, cumulative});
+  }
+  for (size_t i = 1; i < max_i; i++) {
+    d *= (mean() / i);
+    double result = e_neg_mean * d;
+    cumulative += result;
+    if (result < 1e-10 && result < last_result && cumulative > 0.999999) {
+      break;
+    }
+    if (result > 1e-7) {
+      cdf_.push_back({i, result, cumulative});
+    }
+    last_result = result;
+  }
+  ABSL_ASSERT(!cdf_.empty());
+}
+
+// PoissonDistributionZTest implements a z-test for the poisson distribution.
+
+struct ZParam {
+  double mean;
+  double p_fail;   // Z-Test probability of failure.
+  int trials;      // Z-Test trials.
+  size_t samples;  // Z-Test samples.
+};
+
+class PoissonDistributionZTest : public testing::TestWithParam<ZParam>,
+                                 public PoissonModel {
+ public:
+  PoissonDistributionZTest() : PoissonModel(GetParam().mean) {}
+
+  // ZTestImpl 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);
+
+  absl::InsecureBitGen rng_;
+};
+
+template <typename D>
+bool PoissonDistributionZTest::SingleZTest(const double p,
+                                           const size_t samples) {
+  D dis(mean());
+
+  absl::flat_hash_map<int32_t, int> buckets;
+  std::vector<double> data;
+  data.reserve(samples);
+  for (int j = 0; j < samples; j++) {
+    const auto x = dis(rng_);
+    buckets[x]++;
+    data.push_back(x);
+  }
+
+  // The null-hypothesis is that the distribution is a poisson distribution with
+  // the provided mean (not estimated from the data).
+  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"
+                              " mean=%f vs. %f\n"
+                              " stddev=%f vs. %f\n"
+                              " skewness=%f vs. %f\n"
+                              " kurtosis=%f vs. %f\n"
+                              " z=%f",
+                              p, max_err, m.mean, mean(), std::sqrt(m.variance),
+                              stddev(), m.skewness, skew(), m.kurtosis,
+                              kurtosis(), z));
+  }
+  return pass;
+}
+
+TEST_P(PoissonDistributionZTest, AbslPoissonDistribution) {
+  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::poisson_distribution<int32_t>>(p, param.samples) ? 0
+                                                                           : 1;
+  }
+  EXPECT_LE(failures, expected_failures);
+}
+
+std::vector<ZParam> GetZParams() {
+  // These values have been adjusted from the "exact" computed values to reduce
+  // failure rates.
+  //
+  // It turns out that the actual values are not as close to the expected values
+  // as would be ideal.
+  return std::vector<ZParam>({
+      // Knuth method.
+      ZParam{0.5, 0.01, 100, 1000},
+      ZParam{1.0, 0.01, 100, 1000},
+      ZParam{10.0, 0.01, 100, 5000},
+      // Split-knuth method.
+      ZParam{20.0, 0.01, 100, 10000},
+      ZParam{50.0, 0.01, 100, 10000},
+      // Ratio of gaussians method.
+      ZParam{51.0, 0.01, 100, 10000},
+      ZParam{200.0, 0.05, 10, 100000},
+      ZParam{100000.0, 0.05, 10, 1000000},
+  });
+}
+
+std::string ZParamName(const ::testing::TestParamInfo<ZParam>& info) {
+  const auto& p = info.param;
+  std::string name = absl::StrCat("mean_", absl::SixDigits(p.mean));
+  return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
+}
+
+INSTANTIATE_TEST_SUITE_P(, PoissonDistributionZTest,
+                         ::testing::ValuesIn(GetZParams()), ZParamName);
+
+// The PoissonDistributionChiSquaredTest class provides a basic test framework
+// for variates generated by a conforming poisson_distribution.
+class PoissonDistributionChiSquaredTest : public testing::TestWithParam<double>,
+                                          public PoissonModel {
+ public:
+  PoissonDistributionChiSquaredTest() : PoissonModel(GetParam()) {}
+
+  // The ChiSquaredTestImpl provides a chi-squared goodness of fit test for data
+  // generated by the poisson distribution.
+  template <typename D>
+  double ChiSquaredTestImpl();
+
+ private:
+  void InitChiSquaredTest(const double buckets);
+
+  absl::InsecureBitGen rng_;
+  std::vector<size_t> cutoffs_;
+  std::vector<double> expected_;
+};
+
+void PoissonDistributionChiSquaredTest::InitChiSquaredTest(
+    const double buckets) {
+  if (!cutoffs_.empty() && !expected_.empty()) {
+    return;
+  }
+  InitCDF();
+
+  // The code below finds cuttoffs that yield approximately equally-sized
+  // buckets to the extent that it is possible. However for poisson
+  // distributions this is particularly challenging for small mean parameters.
+  // Track the expected proportion of items in each bucket.
+  double last_cdf = 0;
+  const double inc = 1.0 / buckets;
+  for (double p = inc; p <= 1.0; p += inc) {
+    auto result = InverseCDF(p);
+    if (!cutoffs_.empty() && cutoffs_.back() == result.index) {
+      continue;
+    }
+    double d = result.cdf - last_cdf;
+    cutoffs_.push_back(result.index);
+    expected_.push_back(d);
+    last_cdf = result.cdf;
+  }
+  cutoffs_.push_back(std::numeric_limits<size_t>::max());
+  expected_.push_back(std::max(0.0, 1.0 - last_cdf));
+}
+
+template <typename D>
+double PoissonDistributionChiSquaredTest::ChiSquaredTestImpl() {
+  const int kSamples = 2000;
+  const int kBuckets = 50;
+
+  // The poisson CDF fails for large mean values, since e^-mean exceeds the
+  // machine precision. For these cases, using a normal approximation would be
+  // appropriate.
+  ABSL_ASSERT(mean() <= 200);
+  InitChiSquaredTest(kBuckets);
+
+  D dis(mean());
+
+  std::vector<int32_t> counts(cutoffs_.size(), 0);
+  for (int j = 0; j < kSamples; j++) {
+    const size_t x = dis(rng_);
+    auto it = std::lower_bound(std::begin(cutoffs_), std::end(cutoffs_), x);
+    counts[std::distance(cutoffs_.begin(), it)]++;
+  }
+
+  // Normalize the counts.
+  std::vector<int32_t> e(expected_.size(), 0);
+  for (int i = 0; i < e.size(); i++) {
+    e[i] = kSamples * expected_[i];
+  }
+
+  // The null-hypothesis is that the distribution is a poisson distribution with
+  // the provided mean (not estimated from the data).
+  const int dof = static_cast<int>(counts.size()) - 1;
+
+  // The threshold for logging is 1-in-50.
+  const double threshold = absl::random_internal::ChiSquareValue(dof, 0.98);
+
+  const double chi_square = absl::random_internal::ChiSquare(
+      std::begin(counts), std::end(counts), std::begin(e), std::end(e));
+
+  const double p = absl::random_internal::ChiSquarePValue(chi_square, dof);
+
+  // Log if the chi_squared value is above the threshold.
+  if (chi_square > threshold) {
+    LogCDF();
+
+    ABSL_INTERNAL_LOG(INFO, absl::StrCat("VALUES  buckets=", counts.size(),
+                                         "  samples=", kSamples));
+    for (size_t i = 0; i < counts.size(); i++) {
+      ABSL_INTERNAL_LOG(
+          INFO, absl::StrCat(cutoffs_[i], ": ", counts[i], " vs. E=", e[i]));
+    }
+
+    ABSL_INTERNAL_LOG(
+        INFO,
+        absl::StrCat(kChiSquared, "(data, dof=", dof, ") = ", chi_square, " (",
+                     p, ")\n", " vs.\n", kChiSquared, " @ 0.98 = ", threshold));
+  }
+  return p;
+}
+
+TEST_P(PoissonDistributionChiSquaredTest, AbslPoissonDistribution) {
+  const int kTrials = 20;
+
+  // Large values are not yet supported -- this requires estimating the cdf
+  // using the normal distribution instead of the poisson in this case.
+  ASSERT_LE(mean(), 200.0);
+  if (mean() > 200.0) {
+    return;
+  }
+
+  int failures = 0;
+  for (int i = 0; i < kTrials; i++) {
+    double p_value = ChiSquaredTestImpl<absl::poisson_distribution<int32_t>>();
+    if (p_value < 0.005) {
+      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);
+}
+
+INSTANTIATE_TEST_SUITE_P(, PoissonDistributionChiSquaredTest,
+                         ::testing::Values(0.5, 1.0, 2.0, 10.0, 50.0, 51.0,
+                                           200.0));
+
+// NOTE: absl::poisson_distribution is not guaranteed to be stable.
+TEST(PoissonDistributionTest, StabilityTest) {
+  using testing::ElementsAre;
+  // absl::poisson_distribution stability relies on stability of
+  // std::exp, std::log, std::sqrt, std::ceil, std::floor, and
+  // absl::FastUniformBits, absl::StirlingLogFactorial, absl::RandU64ToDouble.
+  absl::random_internal::sequence_urbg urbg({
+      0x035b0dc7e0a18acfull, 0x06cebe0d2653682eull, 0x0061e9b23861596bull,
+      0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
+      0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
+      0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
+      0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull,
+      0x4864f22c059bf29eull, 0x247856d8b862665cull, 0xe46e86e9a1337e10ull,
+      0xd8c8541f3519b133ull, 0xe75b5162c567b9e4ull, 0xf732e5ded7009c5bull,
+      0xb170b98353121eacull, 0x1ec2e8986d2362caull, 0x814c8e35fe9a961aull,
+      0x0c3cd59c9b638a02ull, 0xcb3bb6478a07715cull, 0x1224e62c978bbc7full,
+      0x671ef2cb04e81f6eull, 0x3c1cbd811eaf1808ull, 0x1bbc23cfa8fac721ull,
+      0xa4c2cda65e596a51ull, 0xb77216fad37adf91ull, 0x836d794457c08849ull,
+      0xe083df03475f49d7ull, 0xbc9feb512e6b0d6cull, 0xb12d74fdd718c8c5ull,
+      0x12ff09653bfbe4caull, 0x8dd03a105bc4ee7eull, 0x5738341045ba0d85ull,
+      0xf3fd722dc65ad09eull, 0xfa14fd21ea2a5705ull, 0xffe6ea4d6edb0c73ull,
+      0xD07E9EFE2BF11FB4ull, 0x95DBDA4DAE909198ull, 0xEAAD8E716B93D5A0ull,
+      0xD08ED1D0AFC725E0ull, 0x8E3C5B2F8E7594B7ull, 0x8FF6E2FBF2122B64ull,
+      0x8888B812900DF01Cull, 0x4FAD5EA0688FC31Cull, 0xD1CFF191B3A8C1ADull,
+      0x2F2F2218BE0E1777ull, 0xEA752DFE8B021FA1ull, 0xE5A0CC0FB56F74E8ull,
+      0x18ACF3D6CE89E299ull, 0xB4A84FE0FD13E0B7ull, 0x7CC43B81D2ADA8D9ull,
+      0x165FA26680957705ull, 0x93CC7314211A1477ull, 0xE6AD206577B5FA86ull,
+      0xC75442F5FB9D35CFull, 0xEBCDAF0C7B3E89A0ull, 0xD6411BD3AE1E7E49ull,
+      0x00250E2D2071B35Eull, 0x226800BB57B8E0AFull, 0x2464369BF009B91Eull,
+      0x5563911D59DFA6AAull, 0x78C14389D95A537Full, 0x207D5BA202E5B9C5ull,
+      0x832603766295CFA9ull, 0x11C819684E734A41ull, 0xB3472DCA7B14A94Aull,
+  });
+
+  std::vector<int> output(10);
+
+  // Method 1.
+  {
+    absl::poisson_distribution<int> dist(5);
+    std::generate(std::begin(output), std::end(output),
+                  [&] { return dist(urbg); });
+  }
+  EXPECT_THAT(output,  // mean = 4.2
+              ElementsAre(1, 0, 0, 4, 2, 10, 3, 3, 7, 12));
+
+  // Method 2.
+  {
+    urbg.reset();
+    absl::poisson_distribution<int> dist(25);
+    std::generate(std::begin(output), std::end(output),
+                  [&] { return dist(urbg); });
+  }
+  EXPECT_THAT(output,  // mean = 19.8
+              ElementsAre(9, 35, 18, 10, 35, 18, 10, 35, 18, 10));
+
+  // Method 3.
+  {
+    urbg.reset();
+    absl::poisson_distribution<int> dist(121);
+    std::generate(std::begin(output), std::end(output),
+                  [&] { return dist(urbg); });
+  }
+  EXPECT_THAT(output,  // mean = 124.1
+              ElementsAre(161, 122, 129, 124, 112, 112, 117, 120, 130, 114));
+}
+
+TEST(PoissonDistributionTest, AlgorithmExpectedValue_1) {
+  // This tests small values of the Knuth method.
+  // The underlying uniform distribution will generate exactly 0.5.
+  absl::random_internal::sequence_urbg urbg({0x8000000000000001ull});
+  absl::poisson_distribution<int> dist(5);
+  EXPECT_EQ(7, dist(urbg));
+}
+
+TEST(PoissonDistributionTest, AlgorithmExpectedValue_2) {
+  // This tests larger values of the Knuth method.
+  // The underlying uniform distribution will generate exactly 0.5.
+  absl::random_internal::sequence_urbg urbg({0x8000000000000001ull});
+  absl::poisson_distribution<int> dist(25);
+  EXPECT_EQ(36, dist(urbg));
+}
+
+TEST(PoissonDistributionTest, AlgorithmExpectedValue_3) {
+  // This variant uses the ratio of uniforms method.
+  absl::random_internal::sequence_urbg urbg(
+      {0x7fffffffffffffffull, 0x8000000000000000ull});
+
+  absl::poisson_distribution<int> dist(121);
+  EXPECT_EQ(121, dist(urbg));
+}
+
+}  // namespace