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/sequence_urbg.h"
33 #include "absl/random/random.h"
34 #include "absl/strings/str_cat.h"
35 #include "absl/strings/strip.h"
36 
37 namespace {
38 
39 template <typename IntType>
40 class DiscreteDistributionTypeTest : public ::testing::Test {};
41 
42 using IntTypes = ::testing::Types<int8_t, uint8_t, int16_t, uint16_t, int32_t,
43                                   uint32_t, int64_t, uint64_t>;
44 TYPED_TEST_SUITE(DiscreteDistributionTypeTest, IntTypes);
45 
TYPED_TEST(DiscreteDistributionTypeTest,ParamSerializeTest)46 TYPED_TEST(DiscreteDistributionTypeTest, ParamSerializeTest) {
47   using param_type =
48       typename absl::discrete_distribution<TypeParam>::param_type;
49 
50   absl::discrete_distribution<TypeParam> empty;
51   EXPECT_THAT(empty.probabilities(), testing::ElementsAre(1.0));
52 
53   absl::discrete_distribution<TypeParam> before({1.0, 2.0, 1.0});
54 
55   // Validate that the probabilities sum to 1.0. We picked values which
56   // can be represented exactly to avoid floating-point roundoff error.
57   double s = 0;
58   for (const auto& x : before.probabilities()) {
59     s += x;
60   }
61   EXPECT_EQ(s, 1.0);
62   EXPECT_THAT(before.probabilities(), testing::ElementsAre(0.25, 0.5, 0.25));
63 
64   // Validate the same data via an initializer list.
65   {
66     std::vector<double> data({1.0, 2.0, 1.0});
67 
68     absl::discrete_distribution<TypeParam> via_param{
69         param_type(std::begin(data), std::end(data))};
70 
71     EXPECT_EQ(via_param, before);
72   }
73 
74   std::stringstream ss;
75   ss << before;
76   absl::discrete_distribution<TypeParam> after;
77 
78   EXPECT_NE(before, after);
79 
80   ss >> after;
81 
82   EXPECT_EQ(before, after);
83 }
84 
TYPED_TEST(DiscreteDistributionTypeTest,Constructor)85 TYPED_TEST(DiscreteDistributionTypeTest, Constructor) {
86   auto fn = [](double x) { return x; };
87   {
88     absl::discrete_distribution<int> unary(0, 1.0, 9.0, fn);
89     EXPECT_THAT(unary.probabilities(), testing::ElementsAre(1.0));
90   }
91 
92   {
93     absl::discrete_distribution<int> unary(2, 1.0, 9.0, fn);
94     // => fn(1.0 + 0 * 4 + 2) => 3
95     // => fn(1.0 + 1 * 4 + 2) => 7
96     EXPECT_THAT(unary.probabilities(), testing::ElementsAre(0.3, 0.7));
97   }
98 }
99 
TEST(DiscreteDistributionTest,InitDiscreteDistribution)100 TEST(DiscreteDistributionTest, InitDiscreteDistribution) {
101   using testing::Pair;
102 
103   {
104     std::vector<double> p({1.0, 2.0, 3.0});
105     std::vector<std::pair<double, size_t>> q =
106         absl::random_internal::InitDiscreteDistribution(&p);
107 
108     EXPECT_THAT(p, testing::ElementsAre(1 / 6.0, 2 / 6.0, 3 / 6.0));
109 
110     // Each bucket is p=1/3, so bucket 0 will send half it's traffic
111     // to bucket 2, while the rest will retain all of their traffic.
112     EXPECT_THAT(q, testing::ElementsAre(Pair(0.5, 2),  //
113                                         Pair(1.0, 1),  //
114                                         Pair(1.0, 2)));
115   }
116 
117   {
118     std::vector<double> p({1.0, 2.0, 3.0, 5.0, 2.0});
119 
120     std::vector<std::pair<double, size_t>> q =
121         absl::random_internal::InitDiscreteDistribution(&p);
122 
123     EXPECT_THAT(p, testing::ElementsAre(1 / 13.0, 2 / 13.0, 3 / 13.0, 5 / 13.0,
124                                         2 / 13.0));
125 
126     // A more complex bucketing solution: Each bucket has p=0.2
127     // So buckets 0, 1, 4 will send their alternate traffic elsewhere, which
128     // happens to be bucket 3.
129     // However, summing up that alternate traffic gives bucket 3 too much
130     // traffic, so it will send some traffic to bucket 2.
131     constexpr double b0 = 1.0 / 13.0 / 0.2;
132     constexpr double b1 = 2.0 / 13.0 / 0.2;
133     constexpr double b3 = (5.0 / 13.0 / 0.2) - ((1 - b0) + (1 - b1) + (1 - b1));
134 
135     EXPECT_THAT(q, testing::ElementsAre(Pair(b0, 3),   //
136                                         Pair(b1, 3),   //
137                                         Pair(1.0, 2),  //
138                                         Pair(b3, 2),   //
139                                         Pair(b1, 3)));
140   }
141 }
142 
TEST(DiscreteDistributionTest,ChiSquaredTest50)143 TEST(DiscreteDistributionTest, ChiSquaredTest50) {
144   using absl::random_internal::kChiSquared;
145 
146   constexpr size_t kTrials = 10000;
147   constexpr int kBuckets = 50;  // inclusive, so actally +1
148 
149   // 1-in-100000 threshold, but remember, there are about 8 tests
150   // in this file. And the test could fail for other reasons.
151   // Empirically validated with --runs_per_test=10000.
152   const int kThreshold =
153       absl::random_internal::ChiSquareValue(kBuckets, 0.99999);
154 
155   std::vector<double> weights(kBuckets, 0);
156   std::iota(std::begin(weights), std::end(weights), 1);
157   absl::discrete_distribution<int> dist(std::begin(weights), std::end(weights));
158 
159   absl::InsecureBitGen rng;
160 
161   std::vector<int32_t> counts(kBuckets, 0);
162   for (size_t i = 0; i < kTrials; i++) {
163     auto x = dist(rng);
164     counts[x]++;
165   }
166 
167   // Scale weights.
168   double sum = 0;
169   for (double x : weights) {
170     sum += x;
171   }
172   for (double& x : weights) {
173     x = kTrials * (x / sum);
174   }
175 
176   double chi_square =
177       absl::random_internal::ChiSquare(std::begin(counts), std::end(counts),
178                                        std::begin(weights), std::end(weights));
179 
180   if (chi_square > kThreshold) {
181     double p_value =
182         absl::random_internal::ChiSquarePValue(chi_square, kBuckets);
183 
184     // Chi-squared test failed. Output does not appear to be uniform.
185     std::string msg;
186     for (size_t i = 0; i < counts.size(); i++) {
187       absl::StrAppend(&msg, i, ": ", counts[i], " vs ", weights[i], "\n");
188     }
189     absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n");
190     absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ",
191                     kThreshold);
192     ABSL_RAW_LOG(INFO, "%s", msg.c_str());
193     FAIL() << msg;
194   }
195 }
196 
TEST(DiscreteDistributionTest,StabilityTest)197 TEST(DiscreteDistributionTest, StabilityTest) {
198   // absl::discrete_distribution stabilitiy relies on
199   // absl::uniform_int_distribution and absl::bernoulli_distribution.
200   absl::random_internal::sequence_urbg urbg(
201       {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
202        0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
203        0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
204        0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
205 
206   std::vector<int> output(6);
207 
208   {
209     absl::discrete_distribution<int32_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
210     EXPECT_EQ(0, dist.min());
211     EXPECT_EQ(4, dist.max());
212     for (auto& v : output) {
213       v = dist(urbg);
214     }
215     EXPECT_EQ(12, urbg.invocations());
216   }
217 
218   // With 12 calls to urbg, each call into discrete_distribution consumes
219   // precisely 2 values: one for the uniform call, and a second for the
220   // bernoulli.
221   //
222   // Given the alt mapping: 0=>3, 1=>3, 2=>2, 3=>2, 4=>3, we can
223   //
224   // uniform:      443210143131
225   // bernoulli: b0 000011100101
226   // bernoulli: b1 001111101101
227   // bernoulli: b2 111111111111
228   // bernoulli: b3 001111101111
229   // bernoulli: b4 001111101101
230   // ...
231   EXPECT_THAT(output, testing::ElementsAre(3, 3, 1, 3, 3, 3));
232 
233   {
234     urbg.reset();
235     absl::discrete_distribution<int64_t> dist({1.0, 2.0, 3.0, 5.0, 2.0});
236     EXPECT_EQ(0, dist.min());
237     EXPECT_EQ(4, dist.max());
238     for (auto& v : output) {
239       v = dist(urbg);
240     }
241     EXPECT_EQ(12, urbg.invocations());
242   }
243   EXPECT_THAT(output, testing::ElementsAre(3, 3, 0, 3, 0, 4));
244 }
245 
246 }  // namespace
247