428 lines
14 KiB
C++
428 lines
14 KiB
C++
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// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "absl/random/zipf_distribution.h"
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#include <algorithm>
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#include <cstddef>
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#include <cstdint>
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#include <iterator>
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#include <random>
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#include <string>
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#include <utility>
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#include <vector>
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#include "gmock/gmock.h"
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#include "gtest/gtest.h"
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#include "absl/base/internal/raw_logging.h"
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#include "absl/random/internal/chi_square.h"
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#include "absl/random/internal/pcg_engine.h"
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#include "absl/random/internal/sequence_urbg.h"
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#include "absl/random/random.h"
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#include "absl/strings/str_cat.h"
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#include "absl/strings/str_replace.h"
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#include "absl/strings/strip.h"
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namespace {
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using ::absl::random_internal::kChiSquared;
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using ::testing::ElementsAre;
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template <typename IntType>
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class ZipfDistributionTypedTest : public ::testing::Test {};
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using IntTypes = ::testing::Types<int, int8_t, int16_t, int32_t, int64_t,
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uint8_t, uint16_t, uint32_t, uint64_t>;
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TYPED_TEST_CASE(ZipfDistributionTypedTest, IntTypes);
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TYPED_TEST(ZipfDistributionTypedTest, SerializeTest) {
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using param_type = typename absl::zipf_distribution<TypeParam>::param_type;
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constexpr int kCount = 1000;
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absl::InsecureBitGen gen;
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for (const auto& param : {
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param_type(),
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param_type(32),
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param_type(100, 3, 2),
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param_type(std::numeric_limits<TypeParam>::max(), 4, 3),
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param_type(std::numeric_limits<TypeParam>::max() / 2),
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}) {
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// Validate parameters.
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const auto k = param.k();
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const auto q = param.q();
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const auto v = param.v();
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absl::zipf_distribution<TypeParam> before(k, q, v);
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EXPECT_EQ(before.k(), param.k());
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EXPECT_EQ(before.q(), param.q());
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EXPECT_EQ(before.v(), param.v());
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{
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absl::zipf_distribution<TypeParam> via_param(param);
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EXPECT_EQ(via_param, before);
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}
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// Validate stream serialization.
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std::stringstream ss;
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ss << before;
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absl::zipf_distribution<TypeParam> after(4, 5.5, 4.4);
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EXPECT_NE(before.k(), after.k());
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EXPECT_NE(before.q(), after.q());
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EXPECT_NE(before.v(), after.v());
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EXPECT_NE(before.param(), after.param());
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EXPECT_NE(before, after);
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ss >> after;
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EXPECT_EQ(before.k(), after.k());
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EXPECT_EQ(before.q(), after.q());
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EXPECT_EQ(before.v(), after.v());
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EXPECT_EQ(before.param(), after.param());
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EXPECT_EQ(before, after);
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// Smoke test.
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auto sample_min = after.max();
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auto sample_max = after.min();
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for (int i = 0; i < kCount; i++) {
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auto sample = after(gen);
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EXPECT_GE(sample, after.min());
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EXPECT_LE(sample, after.max());
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if (sample > sample_max) sample_max = sample;
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if (sample < sample_min) sample_min = sample;
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}
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ABSL_INTERNAL_LOG(INFO,
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absl::StrCat("Range: ", +sample_min, ", ", +sample_max));
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}
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}
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class ZipfModel {
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public:
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ZipfModel(size_t k, double q, double v) : k_(k), q_(q), v_(v) {}
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double mean() const { return mean_; }
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// For the other moments of the Zipf distribution, see, for example,
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// http://mathworld.wolfram.com/ZipfDistribution.html
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// PMF(k) = (1 / k^s) / H(N,s)
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// Returns the probability that any single invocation returns k.
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double PMF(size_t i) { return i >= hnq_.size() ? 0.0 : hnq_[i] / sum_hnq_; }
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// CDF = H(k, s) / H(N,s)
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double CDF(size_t i) {
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if (i >= hnq_.size()) {
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return 1.0;
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}
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auto it = std::begin(hnq_);
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double h = 0.0;
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for (const auto end = it; it != end; it++) {
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h += *it;
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}
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return h / sum_hnq_;
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}
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// The InverseCDF returns the k values which bound p on the upper and lower
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// bound. Since there is no closed-form solution, this is implemented as a
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// bisction of the cdf.
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std::pair<size_t, size_t> InverseCDF(double p) {
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size_t min = 0;
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size_t max = hnq_.size();
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while (max > min + 1) {
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size_t target = (max + min) >> 1;
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double x = CDF(target);
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if (x > p) {
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max = target;
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} else {
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min = target;
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}
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}
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return {min, max};
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}
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// Compute the probability totals, which are based on the generalized harmonic
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// number, H(N,s).
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// H(N,s) == SUM(k=1..N, 1 / k^s)
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//
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// In the limit, H(N,s) == zetac(s) + 1.
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//
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// NOTE: The mean of a zipf distribution could be computed here as well.
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// Mean := H(N, s-1) / H(N,s).
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// Given the parameter v = 1, this gives the following function:
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// (Hn(100, 1) - Hn(1,1)) / (Hn(100,2) - Hn(1,2)) = 6.5944
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//
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void Init() {
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if (!hnq_.empty()) {
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return;
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}
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hnq_.clear();
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hnq_.reserve(std::min(k_, size_t{1000}));
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sum_hnq_ = 0;
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double qm1 = q_ - 1.0;
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double sum_hnq_m1 = 0;
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for (size_t i = 0; i < k_; i++) {
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// Partial n-th generalized harmonic number
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const double x = v_ + i;
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// H(n, q-1)
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const double hnqm1 =
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(q_ == 2.0) ? (1.0 / x)
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: (q_ == 3.0) ? (1.0 / (x * x)) : std::pow(x, -qm1);
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sum_hnq_m1 += hnqm1;
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// H(n, q)
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const double hnq =
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(q_ == 2.0) ? (1.0 / (x * x))
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: (q_ == 3.0) ? (1.0 / (x * x * x)) : std::pow(x, -q_);
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sum_hnq_ += hnq;
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hnq_.push_back(hnq);
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if (i > 1000 && hnq <= 1e-10) {
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// The harmonic number is too small.
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break;
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}
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}
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assert(sum_hnq_ > 0);
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mean_ = sum_hnq_m1 / sum_hnq_;
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}
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private:
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const size_t k_;
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const double q_;
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const double v_;
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double mean_;
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std::vector<double> hnq_;
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double sum_hnq_;
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};
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using zipf_u64 = absl::zipf_distribution<uint64_t>;
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class ZipfTest : public testing::TestWithParam<zipf_u64::param_type>,
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public ZipfModel {
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public:
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ZipfTest() : ZipfModel(GetParam().k(), GetParam().q(), GetParam().v()) {}
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// We use a fixed bit generator for distribution accuracy tests. This allows
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// these tests to be deterministic, while still testing the qualify of the
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// implementation.
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absl::random_internal::pcg64_2018_engine rng_{0x2B7E151628AED2A6};
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};
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TEST_P(ZipfTest, ChiSquaredTest) {
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const auto& param = GetParam();
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Init();
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size_t trials = 10000;
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// Find the split-points for the buckets.
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std::vector<size_t> points;
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std::vector<double> expected;
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{
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double last_cdf = 0.0;
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double min_p = 1.0;
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for (double p = 0.01; p < 1.0; p += 0.01) {
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auto x = InverseCDF(p);
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if (points.empty() || points.back() < x.second) {
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const double p = CDF(x.second);
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points.push_back(x.second);
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double q = p - last_cdf;
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expected.push_back(q);
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last_cdf = p;
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if (q < min_p) {
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min_p = q;
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}
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}
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}
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if (last_cdf < 0.999) {
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points.push_back(std::numeric_limits<size_t>::max());
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double q = 1.0 - last_cdf;
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expected.push_back(q);
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if (q < min_p) {
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min_p = q;
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}
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} else {
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points.back() = std::numeric_limits<size_t>::max();
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expected.back() += (1.0 - last_cdf);
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}
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// The Chi-Squared score is not completely scale-invariant; it works best
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// when the small values are in the small digits.
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trials = static_cast<size_t>(8.0 / min_p);
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}
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ASSERT_GT(points.size(), 0);
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// Generate n variates and fill the counts vector with the count of their
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// occurrences.
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std::vector<int64_t> buckets(points.size(), 0);
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double avg = 0;
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{
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zipf_u64 dis(param);
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for (size_t i = 0; i < trials; i++) {
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uint64_t x = dis(rng_);
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ASSERT_LE(x, dis.max());
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ASSERT_GE(x, dis.min());
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avg += static_cast<double>(x);
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auto it = std::upper_bound(std::begin(points), std::end(points),
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static_cast<size_t>(x));
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buckets[std::distance(std::begin(points), it)]++;
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}
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avg = avg / static_cast<double>(trials);
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}
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// Validate the output using the Chi-Squared test.
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for (auto& e : expected) {
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e *= trials;
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}
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// The null-hypothesis is that the distribution is a poisson distribution with
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// the provided mean (not estimated from the data).
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const int dof = static_cast<int>(expected.size()) - 1;
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// NOTE: This test runs about 15x per invocation, so a value of 0.9995 is
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// approximately correct for a test suite failure rate of 1 in 100. In
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// practice we see failures slightly higher than that.
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const double threshold = absl::random_internal::ChiSquareValue(dof, 0.9999);
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const double chi_square = absl::random_internal::ChiSquare(
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std::begin(buckets), std::end(buckets), std::begin(expected),
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std::end(expected));
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const double p_actual =
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absl::random_internal::ChiSquarePValue(chi_square, dof);
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// Log if the chi_squared value is above the threshold.
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if (chi_square > threshold) {
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ABSL_INTERNAL_LOG(INFO, "values");
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for (size_t i = 0; i < expected.size(); i++) {
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ABSL_INTERNAL_LOG(INFO, absl::StrCat(points[i], ": ", buckets[i],
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" vs. E=", expected[i]));
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}
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ABSL_INTERNAL_LOG(INFO, absl::StrCat("trials ", trials));
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ABSL_INTERNAL_LOG(INFO,
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absl::StrCat("mean ", avg, " vs. expected ", mean()));
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ABSL_INTERNAL_LOG(INFO, absl::StrCat(kChiSquared, "(data, ", dof, ") = ",
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chi_square, " (", p_actual, ")"));
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ABSL_INTERNAL_LOG(INFO,
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absl::StrCat(kChiSquared, " @ 0.9995 = ", threshold));
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FAIL() << kChiSquared << " value of " << chi_square
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<< " is above the threshold.";
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}
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}
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std::vector<zipf_u64::param_type> GenParams() {
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using param = zipf_u64::param_type;
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const auto k = param().k();
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const auto q = param().q();
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const auto v = param().v();
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const uint64_t k2 = 1 << 10;
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return std::vector<zipf_u64::param_type>{
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// Default
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param(k, q, v),
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// vary K
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param(4, q, v), param(1 << 4, q, v), param(k2, q, v),
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// vary V
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param(k2, q, 0.5), param(k2, q, 1.5), param(k2, q, 2.5), param(k2, q, 10),
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// vary Q
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param(k2, 1.5, v), param(k2, 3, v), param(k2, 5, v), param(k2, 10, v),
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// Vary V & Q
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param(k2, 1.5, 0.5), param(k2, 3, 1.5), param(k, 10, 10)};
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}
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std::string ParamName(
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const ::testing::TestParamInfo<zipf_u64::param_type>& info) {
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const auto& p = info.param;
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std::string name = absl::StrCat("k_", p.k(), "__q_", absl::SixDigits(p.q()),
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"__v_", absl::SixDigits(p.v()));
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return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
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}
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INSTANTIATE_TEST_SUITE_P(All, ZipfTest, ::testing::ValuesIn(GenParams()),
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||
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|
ParamName);
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|
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||
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// NOTE: absl::zipf_distribution is not guaranteed to be stable.
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|
|
TEST(ZipfDistributionTest, StabilityTest) {
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// absl::zipf_distribution stability relies on
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||
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// 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
|