1 // Copyright 2017 The Abseil Authors.
2 //
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
6 //
7 //      https://www.apache.org/licenses/LICENSE-2.0
8 //
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
14 
15 #include "absl/random/discrete_distribution.h"
16 
17 #include <cmath>
18 #include <cstddef>
19 #include <cstdint>
20 #include <iterator>
21 #include <numeric>
22 #include <random>
23 #include <sstream>
24 #include <string>
25 #include <vector>
26 
27 #include "gmock/gmock.h"
28 #include "gtest/gtest.h"
29 #include "absl/base/internal/raw_logging.h"
30 #include "absl/random/internal/chi_square.h"
31 #include "absl/random/internal/distribution_test_util.h"
32 #include "absl/random/internal/pcg_engine.h"
33 #include "absl/random/internal/sequence_urbg.h"
34 #include "absl/random/random.h"
35 #include "absl/strings/str_cat.h"
36 #include "absl/strings/strip.h"
37 
38 namespace {
39 
40 template <typename IntType>
41 class DiscreteDistributionTypeTest : public ::testing::Test {};
42 
43 using IntTypes = ::testing::Types<int8_t, uint8_t, int16_t, uint16_t, int32_t,
44                                   uint32_t, int64_t, uint64_t>;
45 TYPED_TEST_SUITE(DiscreteDistributionTypeTest, IntTypes);
46 
TYPED_TEST(DiscreteDistributionTypeTest,ParamSerializeTest)47 TYPED_TEST(DiscreteDistributionTypeTest, ParamSerializeTest) {
48   using param_type =
49       typename absl::discrete_distribution<TypeParam>::param_type;
50 
51   absl::discrete_distribution<TypeParam> empty;
52   EXPECT_THAT(empty.probabilities(), testing::ElementsAre(1.0));
53 
54   absl::discrete_distribution<TypeParam> before({1.0, 2.0, 1.0});
55 
56   // Validate that the probabilities sum to 1.0. We picked values which
57   // can be represented exactly to avoid floating-point roundoff error.
58   double s = 0;
59   for (const auto& x : before.probabilities()) {
60     s += x;
61   }
62   EXPECT_EQ(s, 1.0);
63   EXPECT_THAT(before.probabilities(), testing::ElementsAre(0.25, 0.5, 0.25));
64 
65   // Validate the same data via an initializer list.
66   {
67     std::vector<double> data({1.0, 2.0, 1.0});
68 
69     absl::discrete_distribution<TypeParam> via_param{
70         param_type(std::begin(data), std::end(data))};
71 
72     EXPECT_EQ(via_param, before);
73   }
74 
75   std::stringstream ss;
76   ss << before;
77   absl::discrete_distribution<TypeParam> after;
78 
79   EXPECT_NE(before, after);
80 
81   ss >> after;
82 
83   EXPECT_EQ(before, after);
84 }
85 
TYPED_TEST(DiscreteDistributionTypeTest,Constructor)86 TYPED_TEST(DiscreteDistributionTypeTest, Constructor) {
87   auto fn = [](double x) { return x; };
88   {
89     absl::discrete_distribution<int> unary(0, 1.0, 9.0, fn);
90     EXPECT_THAT(unary.probabilities(), testing::ElementsAre(1.0));
91   }
92 
93   {
94     absl::discrete_distribution<int> unary(2, 1.0, 9.0, fn);
95     // => fn(1.0 + 0 * 4 + 2) => 3
96     // => fn(1.0 + 1 * 4 + 2) => 7
97     EXPECT_THAT(unary.probabilities(), testing::ElementsAre(0.3, 0.7));
98   }
99 }
100 
TEST(DiscreteDistributionTest,InitDiscreteDistribution)101 TEST(DiscreteDistributionTest, InitDiscreteDistribution) {
102   using testing::Pair;
103 
104   {
105     std::vector<double> p({1.0, 2.0, 3.0});
106     std::vector<std::pair<double, size_t>> q =
107         absl::random_internal::InitDiscreteDistribution(&p);
108 
109     EXPECT_THAT(p, testing::ElementsAre(1 / 6.0, 2 / 6.0, 3 / 6.0));
110 
111     // Each bucket is p=1/3, so bucket 0 will send half it's traffic
112     // to bucket 2, while the rest will retain all of their traffic.
113     EXPECT_THAT(q, testing::ElementsAre(Pair(0.5, 2),  //
114                                         Pair(1.0, 1),  //
115                                         Pair(1.0, 2)));
116   }
117 
118   {
119     std::vector<double> p({1.0, 2.0, 3.0, 5.0, 2.0});
120 
121     std::vector<std::pair<double, size_t>> q =
122         absl::random_internal::InitDiscreteDistribution(&p);
123 
124     EXPECT_THAT(p, testing::ElementsAre(1 / 13.0, 2 / 13.0, 3 / 13.0, 5 / 13.0,
125                                         2 / 13.0));
126 
127     // A more complex bucketing solution: Each bucket has p=0.2
128     // So buckets 0, 1, 4 will send their alternate traffic elsewhere, which
129     // happens to be bucket 3.
130     // However, summing up that alternate traffic gives bucket 3 too much
131     // traffic, so it will send some traffic to bucket 2.
132     constexpr double b0 = 1.0 / 13.0 / 0.2;
133     constexpr double b1 = 2.0 / 13.0 / 0.2;
134     constexpr double b3 = (5.0 / 13.0 / 0.2) - ((1 - b0) + (1 - b1) + (1 - b1));
135 
136     EXPECT_THAT(q, testing::ElementsAre(Pair(b0, 3),   //
137                                         Pair(b1, 3),   //
138                                         Pair(1.0, 2),  //
139                                         Pair(b3, 2),   //
140                                         Pair(b1, 3)));
141   }
142 }
143 
TEST(DiscreteDistributionTest,ChiSquaredTest50)144 TEST(DiscreteDistributionTest, ChiSquaredTest50) {
145   using absl::random_internal::kChiSquared;
146 
147   constexpr size_t kTrials = 10000;
148   constexpr int kBuckets = 50;  // inclusive, so actally +1
149 
150   // 1-in-100000 threshold, but remember, there are about 8 tests
151   // in this file. And the test could fail for other reasons.
152   // Empirically validated with --runs_per_test=10000.
153   const int kThreshold =
154       absl::random_internal::ChiSquareValue(kBuckets, 0.99999);
155 
156   std::vector<double> weights(kBuckets, 0);
157   std::iota(std::begin(weights), std::end(weights), 1);
158   absl::discrete_distribution<int> dist(std::begin(weights), std::end(weights));
159 
160   // We use a fixed bit generator for distribution accuracy tests.  This allows
161   // these tests to be deterministic, while still testing the qualify of the
162   // implementation.
163   absl::random_internal::pcg64_2018_engine rng(0x2B7E151628AED2A6);
164 
165   std::vector<int32_t> counts(kBuckets, 0);
166   for (size_t i = 0; i < kTrials; i++) {
167     auto x = dist(rng);
168     counts[x]++;
169   }
170 
171   // Scale weights.
172   double sum = 0;
173   for (double x : weights) {
174     sum += x;
175   }
176   for (double& x : weights) {
177     x = kTrials * (x / sum);
178   }
179 
180   double chi_square =
181       absl::random_internal::ChiSquare(std::begin(counts), std::end(counts),
182                                        std::begin(weights), std::end(weights));
183 
184   if (chi_square > kThreshold) {
185     double p_value =
186         absl::random_internal::ChiSquarePValue(chi_square, kBuckets);
187 
188     // Chi-squared test failed. Output does not appear to be uniform.
189     std::string msg;
190     for (size_t i = 0; i < counts.size(); i++) {
191       absl::StrAppend(&msg, i, ": ", counts[i], " vs ", weights[i], "\n");
192     }
193     absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n");
194     absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ",
195                     kThreshold);
196     ABSL_RAW_LOG(INFO, "%s", msg.c_str());
197     FAIL() << msg;
198   }
199 }
200 
TEST(DiscreteDistributionTest,StabilityTest)201 TEST(DiscreteDistributionTest, StabilityTest) {
202   // absl::discrete_distribution stabilitiy relies on
203   // absl::uniform_int_distribution and absl::bernoulli_distribution.
204   absl::random_internal::sequence_urbg urbg(
205       {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
206        0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
207        0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
208        0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
209 
210   std::vector<int> output(6);
211 
212   {
213     absl::discrete_distribution<int32_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
214     EXPECT_EQ(0, dist.min());
215     EXPECT_EQ(4, dist.max());
216     for (auto& v : output) {
217       v = dist(urbg);
218     }
219     EXPECT_EQ(12, urbg.invocations());
220   }
221 
222   // With 12 calls to urbg, each call into discrete_distribution consumes
223   // precisely 2 values: one for the uniform call, and a second for the
224   // bernoulli.
225   //
226   // Given the alt mapping: 0=>3, 1=>3, 2=>2, 3=>2, 4=>3, we can
227   //
228   // uniform:      443210143131
229   // bernoulli: b0 000011100101
230   // bernoulli: b1 001111101101
231   // bernoulli: b2 111111111111
232   // bernoulli: b3 001111101111
233   // bernoulli: b4 001111101101
234   // ...
235   EXPECT_THAT(output, testing::ElementsAre(3, 3, 1, 3, 3, 3));
236 
237   {
238     urbg.reset();
239     absl::discrete_distribution<int64_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
240     EXPECT_EQ(0, dist.min());
241     EXPECT_EQ(4, dist.max());
242     for (auto& v : output) {
243       v = dist(urbg);
244     }
245     EXPECT_EQ(12, urbg.invocations());
246   }
247   EXPECT_THAT(output, testing::ElementsAre(3, 3, 0, 3, 0, 4));
248 }
249 
250 }  // namespace
251