// 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/log/log.h"
#include "absl/random/internal/chi_square.h"
#include "absl/random/internal/distribution_test_util.h"
#include "absl/random/internal/pcg_engine.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::_;
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, _), //
Pair(1.0, _)));
}
{
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, _), //
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 actually +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));
// We use a fixed bit generator for distribution accuracy tests. This allows
// these tests to be deterministic, while still testing the qualify of the
// implementation.
absl::random_internal::pcg64_2018_engine rng(0x2B7E151628AED2A6);
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);
LOG(INFO) << msg;
FAIL() << msg;
}
}
TEST(DiscreteDistributionTest, StabilityTest) {
// absl::discrete_distribution stability 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
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