absl/random/discrete_distribution_test.cc - third_party/abseil-cpp - Git at Google

 // 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/discrete_distribution.h"

 #include <cmath>
 #include <cstddef>
 #include <cstdint>
 #include <iterator>
 #include <numeric>
 #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/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/strip.h"

 namespace {

 template <typename IntType>
 class DiscreteDistributionTypeTest : public ::testing::Test {};

 using IntTypes = ::testing::Types<int8_t, uint8_t, int16_t, uint16_t, int32_t,
                                   uint32_t, int64_t, uint64_t>;
 TYPED_TEST_SUITE(DiscreteDistributionTypeTest, IntTypes);

 TYPED_TEST(DiscreteDistributionTypeTest, ParamSerializeTest) {
   using param_type =
       typename absl::discrete_distribution<TypeParam>::param_type;

   absl::discrete_distribution<TypeParam> empty;
   EXPECT_THAT(empty.probabilities(), testing::ElementsAre(1.0));

   absl::discrete_distribution<TypeParam> before({1.0, 2.0, 1.0});

   // Validate that the probabilities sum to 1.0. We picked values which
   // can be represented exactly to avoid floating-point roundoff error.
   double s = 0;
   for (const auto& x : before.probabilities()) {
     s += x;
   }
   EXPECT_EQ(s, 1.0);
   EXPECT_THAT(before.probabilities(), testing::ElementsAre(0.25, 0.5, 0.25));

   // Validate the same data via an initializer list.
   {
     std::vector<double> data({1.0, 2.0, 1.0});

     absl::discrete_distribution<TypeParam> via_param{
         param_type(std::begin(data), std::end(data))};

     EXPECT_EQ(via_param, before);
   }

   std::stringstream ss;
   ss << before;
   absl::discrete_distribution<TypeParam> after;

   EXPECT_NE(before, after);

   ss >> after;

   EXPECT_EQ(before, after);
 }

 TYPED_TEST(DiscreteDistributionTypeTest, Constructor) {
   auto fn = [](double x) { return x; };
   {
     absl::discrete_distribution<int> unary(0, 1.0, 9.0, fn);
     EXPECT_THAT(unary.probabilities(), testing::ElementsAre(1.0));
   }

   {
     absl::discrete_distribution<int> unary(2, 1.0, 9.0, fn);
     // => fn(1.0 + 0 * 4 + 2) => 3
     // => fn(1.0 + 1 * 4 + 2) => 7
     EXPECT_THAT(unary.probabilities(), testing::ElementsAre(0.3, 0.7));
   }
 }

 TEST(DiscreteDistributionTest, InitDiscreteDistribution) {
   using testing::Pair;

   {
     std::vector<double> p({1.0, 2.0, 3.0});
     std::vector<std::pair<double, size_t>> q =
         absl::random_internal::InitDiscreteDistribution(&p);

     EXPECT_THAT(p, testing::ElementsAre(1 / 6.0, 2 / 6.0, 3 / 6.0));

     // Each bucket is p=1/3, so bucket 0 will send half it's traffic
     // to bucket 2, while the rest will retain all of their traffic.
     EXPECT_THAT(q, testing::ElementsAre(Pair(0.5, 2),  //
                                         Pair(1.0, 1),  //
                                         Pair(1.0, 2)));
   }

   {
     std::vector<double> p({1.0, 2.0, 3.0, 5.0, 2.0});

     std::vector<std::pair<double, size_t>> q =
         absl::random_internal::InitDiscreteDistribution(&p);

     EXPECT_THAT(p, testing::ElementsAre(1 / 13.0, 2 / 13.0, 3 / 13.0, 5 / 13.0,
                                         2 / 13.0));

     // A more complex bucketing solution: Each bucket has p=0.2
     // So buckets 0, 1, 4 will send their alternate traffic elsewhere, which
     // happens to be bucket 3.
     // However, summing up that alternate traffic gives bucket 3 too much
     // traffic, so it will send some traffic to bucket 2.
     constexpr double b0 = 1.0 / 13.0 / 0.2;
     constexpr double b1 = 2.0 / 13.0 / 0.2;
     constexpr double b3 = (5.0 / 13.0 / 0.2) - ((1 - b0) + (1 - b1) + (1 - b1));

     EXPECT_THAT(q, testing::ElementsAre(Pair(b0, 3),   //
                                         Pair(b1, 3),   //
                                         Pair(1.0, 2),  //
                                         Pair(b3, 2),   //
                                         Pair(b1, 3)));
   }
 }

 TEST(DiscreteDistributionTest, ChiSquaredTest50) {
   using absl::random_internal::kChiSquared;

   constexpr size_t kTrials = 10000;
   constexpr int kBuckets = 50;  // inclusive, so actally +1

   // 1-in-100000 threshold, but remember, there are about 8 tests
   // in this file. And the test could fail for other reasons.
   // Empirically validated with --runs_per_test=10000.
   const int kThreshold =
       absl::random_internal::ChiSquareValue(kBuckets, 0.99999);

   std::vector<double> weights(kBuckets, 0);
   std::iota(std::begin(weights), std::end(weights), 1);
   absl::discrete_distribution<int> dist(std::begin(weights), std::end(weights));

   absl::InsecureBitGen rng;

   std::vector<int32_t> counts(kBuckets, 0);
   for (size_t i = 0; i < kTrials; i++) {
     auto x = dist(rng);
     counts[x]++;
   }

   // Scale weights.
   double sum = 0;
   for (double x : weights) {
     sum += x;
   }
   for (double& x : weights) {
     x = kTrials * (x / sum);
   }

   double chi_square =
       absl::random_internal::ChiSquare(std::begin(counts), std::end(counts),
                                        std::begin(weights), std::end(weights));

   if (chi_square > kThreshold) {
     double p_value =
         absl::random_internal::ChiSquarePValue(chi_square, kBuckets);

     // Chi-squared test failed. Output does not appear to be uniform.
     std::string msg;
     for (size_t i = 0; i < counts.size(); i++) {
       absl::StrAppend(&msg, i, ": ", counts[i], " vs ", weights[i], "\n");
     }
     absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n");
     absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ",
                     kThreshold);
     ABSL_RAW_LOG(INFO, "%s", msg.c_str());
     FAIL() << msg;
   }
 }

 TEST(DiscreteDistributionTest, StabilityTest) {
   // absl::discrete_distribution stabilitiy relies on
   // absl::uniform_int_distribution and absl::bernoulli_distribution.
   absl::random_internal::sequence_urbg urbg(
       {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
        0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
        0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
        0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});

   std::vector<int> output(6);

   {
     absl::discrete_distribution<int32_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
     EXPECT_EQ(0, dist.min());
     EXPECT_EQ(4, dist.max());
     for (auto& v : output) {
       v = dist(urbg);
     }
     EXPECT_EQ(12, urbg.invocations());
   }

   // With 12 calls to urbg, each call into discrete_distribution consumes
   // precisely 2 values: one for the uniform call, and a second for the
   // bernoulli.
   //
   // Given the alt mapping: 0=>3, 1=>3, 2=>2, 3=>2, 4=>3, we can
   //
   // uniform:      443210143131
   // bernoulli: b0 000011100101
   // bernoulli: b1 001111101101
   // bernoulli: b2 111111111111
   // bernoulli: b3 001111101111
   // bernoulli: b4 001111101101
   // ...
   EXPECT_THAT(output, testing::ElementsAre(3, 3, 1, 3, 3, 3));

   {
     urbg.reset();
     absl::discrete_distribution<int64_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
     EXPECT_EQ(0, dist.min());
     EXPECT_EQ(4, dist.max());
     for (auto& v : output) {
       v = dist(urbg);
     }
     EXPECT_EQ(12, urbg.invocations());
   }
   EXPECT_THAT(output, testing::ElementsAre(3, 3, 0, 3, 0, 4));
 }

 }  // namespace
	// 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/discrete_distribution.h"

	#include <cmath>
	#include <cstddef>
	#include <cstdint>
	#include <iterator>
	#include <numeric>
	#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/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/strip.h"

	namespace {

	template <typename IntType>
	class DiscreteDistributionTypeTest : public ::testing::Test {};

	using IntTypes = ::testing::Types<int8_t, uint8_t, int16_t, uint16_t, int32_t,
	uint32_t, int64_t, uint64_t>;
	TYPED_TEST_SUITE(DiscreteDistributionTypeTest, IntTypes);

	TYPED_TEST(DiscreteDistributionTypeTest, ParamSerializeTest) {
	using param_type =
	typename absl::discrete_distribution<TypeParam>::param_type;

	absl::discrete_distribution<TypeParam> empty;
	EXPECT_THAT(empty.probabilities(), testing::ElementsAre(1.0));

	absl::discrete_distribution<TypeParam> before({1.0, 2.0, 1.0});

	// Validate that the probabilities sum to 1.0. We picked values which
	// can be represented exactly to avoid floating-point roundoff error.
	double s = 0;
	for (const auto& x : before.probabilities()) {
	s += x;
	}
	EXPECT_EQ(s, 1.0);
	EXPECT_THAT(before.probabilities(), testing::ElementsAre(0.25, 0.5, 0.25));

	// Validate the same data via an initializer list.
	{
	std::vector<double> data({1.0, 2.0, 1.0});

	absl::discrete_distribution<TypeParam> via_param{
	param_type(std::begin(data), std::end(data))};

	EXPECT_EQ(via_param, before);
	}

	std::stringstream ss;
	ss << before;
	absl::discrete_distribution<TypeParam> after;

	EXPECT_NE(before, after);

	ss >> after;

	EXPECT_EQ(before, after);
	}

	TYPED_TEST(DiscreteDistributionTypeTest, Constructor) {
	auto fn = [](double x) { return x; };
	{
	absl::discrete_distribution<int> unary(0, 1.0, 9.0, fn);
	EXPECT_THAT(unary.probabilities(), testing::ElementsAre(1.0));
	}

	{
	absl::discrete_distribution<int> unary(2, 1.0, 9.0, fn);
	// => fn(1.0 + 0 * 4 + 2) => 3
	// => fn(1.0 + 1 * 4 + 2) => 7
	EXPECT_THAT(unary.probabilities(), testing::ElementsAre(0.3, 0.7));
	}
	}

	TEST(DiscreteDistributionTest, InitDiscreteDistribution) {
	using testing::Pair;

	{
	std::vector<double> p({1.0, 2.0, 3.0});
	std::vector<std::pair<double, size_t>> q =
	absl::random_internal::InitDiscreteDistribution(&p);

	EXPECT_THAT(p, testing::ElementsAre(1 / 6.0, 2 / 6.0, 3 / 6.0));

	// Each bucket is p=1/3, so bucket 0 will send half it's traffic
	// to bucket 2, while the rest will retain all of their traffic.
	EXPECT_THAT(q, testing::ElementsAre(Pair(0.5, 2), //
	Pair(1.0, 1), //
	Pair(1.0, 2)));
	}

	{
	std::vector<double> p({1.0, 2.0, 3.0, 5.0, 2.0});

	std::vector<std::pair<double, size_t>> q =
	absl::random_internal::InitDiscreteDistribution(&p);

	EXPECT_THAT(p, testing::ElementsAre(1 / 13.0, 2 / 13.0, 3 / 13.0, 5 / 13.0,
	2 / 13.0));

	// A more complex bucketing solution: Each bucket has p=0.2
	// So buckets 0, 1, 4 will send their alternate traffic elsewhere, which
	// happens to be bucket 3.
	// However, summing up that alternate traffic gives bucket 3 too much
	// traffic, so it will send some traffic to bucket 2.
	constexpr double b0 = 1.0 / 13.0 / 0.2;
	constexpr double b1 = 2.0 / 13.0 / 0.2;
	constexpr double b3 = (5.0 / 13.0 / 0.2) - ((1 - b0) + (1 - b1) + (1 - b1));

	EXPECT_THAT(q, testing::ElementsAre(Pair(b0, 3), //
	Pair(b1, 3), //
	Pair(1.0, 2), //
	Pair(b3, 2), //
	Pair(b1, 3)));
	}
	}

	TEST(DiscreteDistributionTest, ChiSquaredTest50) {
	using absl::random_internal::kChiSquared;

	constexpr size_t kTrials = 10000;
	constexpr int kBuckets = 50; // inclusive, so actally +1

	// 1-in-100000 threshold, but remember, there are about 8 tests
	// in this file. And the test could fail for other reasons.
	// Empirically validated with --runs_per_test=10000.
	const int kThreshold =
	absl::random_internal::ChiSquareValue(kBuckets, 0.99999);

	std::vector<double> weights(kBuckets, 0);
	std::iota(std::begin(weights), std::end(weights), 1);
	absl::discrete_distribution<int> dist(std::begin(weights), std::end(weights));

	absl::InsecureBitGen rng;

	std::vector<int32_t> counts(kBuckets, 0);
	for (size_t i = 0; i < kTrials; i++) {
	auto x = dist(rng);
	counts[x]++;
	}

	// Scale weights.
	double sum = 0;
	for (double x : weights) {
	sum += x;
	}
	for (double& x : weights) {
	x = kTrials * (x / sum);
	}

	double chi_square =
	absl::random_internal::ChiSquare(std::begin(counts), std::end(counts),
	std::begin(weights), std::end(weights));

	if (chi_square > kThreshold) {
	double p_value =
	absl::random_internal::ChiSquarePValue(chi_square, kBuckets);

	// Chi-squared test failed. Output does not appear to be uniform.
	std::string msg;
	for (size_t i = 0; i < counts.size(); i++) {
	absl::StrAppend(&msg, i, ": ", counts[i], " vs ", weights[i], "\n");
	}
	absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n");
	absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ",
	kThreshold);
	ABSL_RAW_LOG(INFO, "%s", msg.c_str());
	FAIL() << msg;
	}
	}

	TEST(DiscreteDistributionTest, StabilityTest) {
	// absl::discrete_distribution stabilitiy relies on
	// absl::uniform_int_distribution and absl::bernoulli_distribution.
	absl::random_internal::sequence_urbg urbg(
	{0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
	0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
	0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
	0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});

	std::vector<int> output(6);

	{
	absl::discrete_distribution<int32_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
	EXPECT_EQ(0, dist.min());
	EXPECT_EQ(4, dist.max());
	for (auto& v : output) {
	v = dist(urbg);
	}
	EXPECT_EQ(12, urbg.invocations());
	}

	// With 12 calls to urbg, each call into discrete_distribution consumes
	// precisely 2 values: one for the uniform call, and a second for the
	// bernoulli.
	//
	// Given the alt mapping: 0=>3, 1=>3, 2=>2, 3=>2, 4=>3, we can
	//
	// uniform: 443210143131
	// bernoulli: b0 000011100101
	// bernoulli: b1 001111101101
	// bernoulli: b2 111111111111
	// bernoulli: b3 001111101111
	// bernoulli: b4 001111101101
	// ...
	EXPECT_THAT(output, testing::ElementsAre(3, 3, 1, 3, 3, 3));

	{
	urbg.reset();
	absl::discrete_distribution<int64_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
	EXPECT_EQ(0, dist.min());
	EXPECT_EQ(4, dist.max());
	for (auto& v : output) {
	v = dist(urbg);
	}
	EXPECT_EQ(12, urbg.invocations());
	}
	EXPECT_THAT(output, testing::ElementsAre(3, 3, 0, 3, 0, 4));
	}

	} // namespace