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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/zipf_distribution.h"
+
+#include <algorithm>
+#include <cstddef>
+#include <cstdint>
+#include <iterator>
+#include <random>
+#include <string>
+#include <utility>
+#include <vector>
+
+#include "gmock/gmock.h"
+#include "gtest/gtest.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/random/internal/chi_square.h"
+#include "absl/random/internal/sequence_urbg.h"
+#include "absl/random/random.h"
+#include "absl/strings/str_cat.h"
+#include "absl/strings/str_replace.h"
+#include "absl/strings/strip.h"
+
+namespace {
+
+using ::absl::random_internal::kChiSquared;
+using ::testing::ElementsAre;
+
+template <typename IntType>
+class ZipfDistributionTypedTest : 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(ZipfDistributionTypedTest, IntTypes);
+
+TYPED_TEST(ZipfDistributionTypedTest, SerializeTest) {
+ using param_type = typename absl::zipf_distribution<TypeParam>::param_type;
+
+ constexpr int kCount = 1000;
+ absl::InsecureBitGen gen;
+ for (const auto& param : {
+ param_type(),
+ param_type(32),
+ param_type(100, 3, 2),
+ param_type(std::numeric_limits<TypeParam>::max(), 4, 3),
+ param_type(std::numeric_limits<TypeParam>::max() / 2),
+ }) {
+ // Validate parameters.
+ const auto k = param.k();
+ const auto q = param.q();
+ const auto v = param.v();
+
+ absl::zipf_distribution<TypeParam> before(k, q, v);
+ EXPECT_EQ(before.k(), param.k());
+ EXPECT_EQ(before.q(), param.q());
+ EXPECT_EQ(before.v(), param.v());
+
+ {
+ absl::zipf_distribution<TypeParam> via_param(param);
+ EXPECT_EQ(via_param, before);
+ }
+
+ // Validate stream serialization.
+ std::stringstream ss;
+ ss << before;
+ absl::zipf_distribution<TypeParam> after(4, 5.5, 4.4);
+
+ EXPECT_NE(before.k(), after.k());
+ EXPECT_NE(before.q(), after.q());
+ EXPECT_NE(before.v(), after.v());
+ EXPECT_NE(before.param(), after.param());
+ EXPECT_NE(before, after);
+
+ ss >> after;
+
+ EXPECT_EQ(before.k(), after.k());
+ EXPECT_EQ(before.q(), after.q());
+ EXPECT_EQ(before.v(), after.v());
+ EXPECT_EQ(before.param(), after.param());
+ EXPECT_EQ(before, after);
+
+ // Smoke test.
+ auto sample_min = after.max();
+ auto sample_max = after.min();
+ for (int i = 0; i < kCount; i++) {
+ auto sample = after(gen);
+ EXPECT_GE(sample, after.min());
+ EXPECT_LE(sample, after.max());
+ if (sample > sample_max) sample_max = sample;
+ if (sample < sample_min) sample_min = sample;
+ }
+ ABSL_INTERNAL_LOG(INFO,
+ absl::StrCat("Range: ", +sample_min, ", ", +sample_max));
+ }
+}
+
+class ZipfModel {
+ public:
+ ZipfModel(size_t k, double q, double v) : k_(k), q_(q), v_(v) {}
+
+ double mean() const { return mean_; }
+
+ // For the other moments of the Zipf distribution, see, for example,
+ // http://mathworld.wolfram.com/ZipfDistribution.html
+
+ // PMF(k) = (1 / k^s) / H(N,s)
+ // Returns the probability that any single invocation returns k.
+ double PMF(size_t i) { return i >= hnq_.size() ? 0.0 : hnq_[i] / sum_hnq_; }
+
+ // CDF = H(k, s) / H(N,s)
+ double CDF(size_t i) {
+ if (i >= hnq_.size()) {
+ return 1.0;
+ }
+ auto it = std::begin(hnq_);
+ double h = 0.0;
+ for (const auto end = it; it != end; it++) {
+ h += *it;
+ }
+ return h / sum_hnq_;
+ }
+
+ // The InverseCDF returns the k values which bound p on the upper and lower
+ // bound. Since there is no closed-form solution, this is implemented as a
+ // bisction of the cdf.
+ std::pair<size_t, size_t> InverseCDF(double p) {
+ size_t min = 0;
+ size_t max = hnq_.size();
+ while (max > min + 1) {
+ size_t target = (max + min) >> 1;
+ double x = CDF(target);
+ if (x > p) {
+ max = target;
+ } else {
+ min = target;
+ }
+ }
+ return {min, max};
+ }
+
+ // Compute the probability totals, which are based on the generalized harmonic
+ // number, H(N,s).
+ // H(N,s) == SUM(k=1..N, 1 / k^s)
+ //
+ // In the limit, H(N,s) == zetac(s) + 1.
+ //
+ // NOTE: The mean of a zipf distribution could be computed here as well.
+ // Mean := H(N, s-1) / H(N,s).
+ // Given the parameter v = 1, this gives the following function:
+ // (Hn(100, 1) - Hn(1,1)) / (Hn(100,2) - Hn(1,2)) = 6.5944
+ //
+ void Init() {
+ if (!hnq_.empty()) {
+ return;
+ }
+ hnq_.clear();
+ hnq_.reserve(std::min(k_, size_t{1000}));
+
+ sum_hnq_ = 0;
+ double qm1 = q_ - 1.0;
+ double sum_hnq_m1 = 0;
+ for (size_t i = 0; i < k_; i++) {
+ // Partial n-th generalized harmonic number
+ const double x = v_ + i;
+
+ // H(n, q-1)
+ const double hnqm1 =
+ (q_ == 2.0) ? (1.0 / x)
+ : (q_ == 3.0) ? (1.0 / (x * x)) : std::pow(x, -qm1);
+ sum_hnq_m1 += hnqm1;
+
+ // H(n, q)
+ const double hnq =
+ (q_ == 2.0) ? (1.0 / (x * x))
+ : (q_ == 3.0) ? (1.0 / (x * x * x)) : std::pow(x, -q_);
+ sum_hnq_ += hnq;
+ hnq_.push_back(hnq);
+ if (i > 1000 && hnq <= 1e-10) {
+ // The harmonic number is too small.
+ break;
+ }
+ }
+ assert(sum_hnq_ > 0);
+ mean_ = sum_hnq_m1 / sum_hnq_;
+ }
+
+ private:
+ const size_t k_;
+ const double q_;
+ const double v_;
+
+ double mean_;
+ std::vector<double> hnq_;
+ double sum_hnq_;
+};
+
+using zipf_u64 = absl::zipf_distribution<uint64_t>;
+
+class ZipfTest : public testing::TestWithParam<zipf_u64::param_type>,
+ public ZipfModel {
+ public:
+ ZipfTest() : ZipfModel(GetParam().k(), GetParam().q(), GetParam().v()) {}
+
+ absl::InsecureBitGen rng_;
+};
+
+TEST_P(ZipfTest, ChiSquaredTest) {
+ const auto& param = GetParam();
+ Init();
+
+ size_t trials = 10000;
+
+ // Find the split-points for the buckets.
+ std::vector<size_t> points;
+ std::vector<double> expected;
+ {
+ double last_cdf = 0.0;
+ double min_p = 1.0;
+ for (double p = 0.01; p < 1.0; p += 0.01) {
+ auto x = InverseCDF(p);
+ if (points.empty() || points.back() < x.second) {
+ const double p = CDF(x.second);
+ points.push_back(x.second);
+ double q = p - last_cdf;
+ expected.push_back(q);
+ last_cdf = p;
+ if (q < min_p) {
+ min_p = q;
+ }
+ }
+ }
+ if (last_cdf < 0.999) {
+ points.push_back(std::numeric_limits<size_t>::max());
+ double q = 1.0 - last_cdf;
+ expected.push_back(q);
+ if (q < min_p) {
+ min_p = q;
+ }
+ } else {
+ points.back() = std::numeric_limits<size_t>::max();
+ expected.back() += (1.0 - last_cdf);
+ }
+ // The Chi-Squared score is not completely scale-invariant; it works best
+ // when the small values are in the small digits.
+ trials = static_cast<size_t>(8.0 / min_p);
+ }
+ ASSERT_GT(points.size(), 0);
+
+ // Generate n variates and fill the counts vector with the count of their
+ // occurrences.
+ std::vector<int64_t> buckets(points.size(), 0);
+ double avg = 0;
+ {
+ zipf_u64 dis(param);
+ for (size_t i = 0; i < trials; i++) {
+ uint64_t x = dis(rng_);
+ ASSERT_LE(x, dis.max());
+ ASSERT_GE(x, dis.min());
+ avg += static_cast<double>(x);
+ auto it = std::upper_bound(std::begin(points), std::end(points),
+ static_cast<size_t>(x));
+ buckets[std::distance(std::begin(points), it)]++;
+ }
+ avg = avg / static_cast<double>(trials);
+ }
+
+ // Validate the output using the Chi-Squared test.
+ for (auto& e : expected) {
+ e *= trials;
+ }
+
+ // 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>(expected.size()) - 1;
+
+ // NOTE: This test runs about 15x per invocation, so a value of 0.9995 is
+ // approximately correct for a test suite failure rate of 1 in 100. In
+ // practice we see failures slightly higher than that.
+ const double threshold = absl::random_internal::ChiSquareValue(dof, 0.9999);
+
+ const double chi_square = absl::random_internal::ChiSquare(
+ std::begin(buckets), std::end(buckets), std::begin(expected),
+ std::end(expected));
+
+ const double p_actual =
+ absl::random_internal::ChiSquarePValue(chi_square, dof);
+
+ // Log if the chi_squared value is above the threshold.
+ if (chi_square > threshold) {
+ ABSL_INTERNAL_LOG(INFO, "values");
+ for (size_t i = 0; i < expected.size(); i++) {
+ ABSL_INTERNAL_LOG(INFO, absl::StrCat(points[i], ": ", buckets[i],
+ " vs. E=", expected[i]));
+ }
+ ABSL_INTERNAL_LOG(INFO, absl::StrCat("trials ", trials));
+ ABSL_INTERNAL_LOG(INFO,
+ absl::StrCat("mean ", avg, " vs. expected ", mean()));
+ ABSL_INTERNAL_LOG(INFO, absl::StrCat(kChiSquared, "(data, ", dof, ") = ",
+ chi_square, " (", p_actual, ")"));
+ ABSL_INTERNAL_LOG(INFO,
+ absl::StrCat(kChiSquared, " @ 0.9995 = ", threshold));
+ FAIL() << kChiSquared << " value of " << chi_square
+ << " is above the threshold.";
+ }
+}
+
+std::vector<zipf_u64::param_type> GenParams() {
+ using param = zipf_u64::param_type;
+ const auto k = param().k();
+ const auto q = param().q();
+ const auto v = param().v();
+ const uint64_t k2 = 1 << 10;
+ return std::vector<zipf_u64::param_type>{
+ // Default
+ param(k, q, v),
+ // vary K
+ param(4, q, v), param(1 << 4, q, v), param(k2, q, v),
+ // vary V
+ param(k2, q, 0.5), param(k2, q, 1.5), param(k2, q, 2.5), param(k2, q, 10),
+ // vary Q
+ param(k2, 1.5, v), param(k2, 3, v), param(k2, 5, v), param(k2, 10, v),
+ // Vary V & Q
+ param(k2, 1.5, 0.5), param(k2, 3, 1.5), param(k, 10, 10)};
+}
+
+std::string ParamName(
+ const ::testing::TestParamInfo<zipf_u64::param_type>& info) {
+ const auto& p = info.param;
+ std::string name = absl::StrCat("k_", p.k(), "__q_", absl::SixDigits(p.q()),
+ "__v_", absl::SixDigits(p.v()));
+ return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
+}
+
+INSTANTIATE_TEST_SUITE_P(All, ZipfTest, ::testing::ValuesIn(GenParams()),
+ ParamName);
+
+// NOTE: absl::zipf_distribution is not guaranteed to be stable.
+TEST(ZipfDistributionTest, StabilityTest) {
+ // absl::zipf_distribution stability relies on
+ // absl::uniform_real_distribution, std::log, std::exp, std::log1p
+ absl::random_internal::sequence_urbg urbg(
+ {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
+ 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
+ 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
+ 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
+
+ std::vector<int> output(10);
+
+ {
+ absl::zipf_distribution<int32_t> dist;
+ std::generate(std::begin(output), std::end(output),
+ [&] { return dist(urbg); });
+ EXPECT_THAT(output, ElementsAre(10031, 0, 0, 3, 6, 0, 7, 47, 0, 0));
+ }
+ urbg.reset();
+ {
+ absl::zipf_distribution<int32_t> dist(std::numeric_limits<int32_t>::max(),
+ 3.3);
+ std::generate(std::begin(output), std::end(output),
+ [&] { return dist(urbg); });
+ EXPECT_THAT(output, ElementsAre(44, 0, 0, 0, 0, 1, 0, 1, 3, 0));
+ }
+}
+
+TEST(ZipfDistributionTest, AlgorithmBounds) {
+ absl::zipf_distribution<int32_t> dist;
+
+ // Small values from absl::uniform_real_distribution map to larger Zipf
+ // distribution values.
+ const std::pair<uint64_t, int32_t> kInputs[] = {
+ {0xffffffffffffffff, 0x0}, {0x7fffffffffffffff, 0x0},
+ {0x3ffffffffffffffb, 0x1}, {0x1ffffffffffffffd, 0x4},
+ {0xffffffffffffffe, 0x9}, {0x7ffffffffffffff, 0x12},
+ {0x3ffffffffffffff, 0x25}, {0x1ffffffffffffff, 0x4c},
+ {0xffffffffffffff, 0x99}, {0x7fffffffffffff, 0x132},
+ {0x3fffffffffffff, 0x265}, {0x1fffffffffffff, 0x4cc},
+ {0xfffffffffffff, 0x999}, {0x7ffffffffffff, 0x1332},
+ {0x3ffffffffffff, 0x2665}, {0x1ffffffffffff, 0x4ccc},
+ {0xffffffffffff, 0x9998}, {0x7fffffffffff, 0x1332f},
+ {0x3fffffffffff, 0x2665a}, {0x1fffffffffff, 0x4cc9e},
+ {0xfffffffffff, 0x998e0}, {0x7ffffffffff, 0x133051},
+ {0x3ffffffffff, 0x265ae4}, {0x1ffffffffff, 0x4c9ed3},
+ {0xffffffffff, 0x98e223}, {0x7fffffffff, 0x13058c4},
+ {0x3fffffffff, 0x25b178e}, {0x1fffffffff, 0x4a062b2},
+ {0xfffffffff, 0x8ee23b8}, {0x7ffffffff, 0x10b21642},
+ {0x3ffffffff, 0x1d89d89d}, {0x1ffffffff, 0x2fffffff},
+ {0xffffffff, 0x45d1745d}, {0x7fffffff, 0x5a5a5a5a},
+ {0x3fffffff, 0x69ee5846}, {0x1fffffff, 0x73ecade3},
+ {0xfffffff, 0x79a9d260}, {0x7ffffff, 0x7cc0532b},
+ {0x3ffffff, 0x7e5ad146}, {0x1ffffff, 0x7f2c0bec},
+ {0xffffff, 0x7f95adef}, {0x7fffff, 0x7fcac0da},
+ {0x3fffff, 0x7fe55ae2}, {0x1fffff, 0x7ff2ac0e},
+ {0xfffff, 0x7ff955ae}, {0x7ffff, 0x7ffcaac1},
+ {0x3ffff, 0x7ffe555b}, {0x1ffff, 0x7fff2aac},
+ {0xffff, 0x7fff9556}, {0x7fff, 0x7fffcaab},
+ {0x3fff, 0x7fffe555}, {0x1fff, 0x7ffff2ab},
+ {0xfff, 0x7ffff955}, {0x7ff, 0x7ffffcab},
+ {0x3ff, 0x7ffffe55}, {0x1ff, 0x7fffff2b},
+ {0xff, 0x7fffff95}, {0x7f, 0x7fffffcb},
+ {0x3f, 0x7fffffe5}, {0x1f, 0x7ffffff3},
+ {0xf, 0x7ffffff9}, {0x7, 0x7ffffffd},
+ {0x3, 0x7ffffffe}, {0x1, 0x7fffffff},
+ };
+
+ for (const auto& instance : kInputs) {
+ absl::random_internal::sequence_urbg urbg({instance.first});
+ EXPECT_EQ(instance.second, dist(urbg));
+ }
+}
+
+} // namespace
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