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/uniform_real_distribution.h"
16
17 #include <cmath>
18 #include <cstdint>
19 #include <iterator>
20 #include <random>
21 #include <sstream>
22 #include <string>
23 #include <vector>
24
25 #include "gmock/gmock.h"
26 #include "gtest/gtest.h"
27 #include "absl/base/internal/raw_logging.h"
28 #include "absl/random/internal/chi_square.h"
29 #include "absl/random/internal/distribution_test_util.h"
30 #include "absl/random/internal/sequence_urbg.h"
31 #include "absl/random/random.h"
32 #include "absl/strings/str_cat.h"
33
34 // NOTES:
35 // * Some documentation on generating random real values suggests that
36 // it is possible to use std::nextafter(b, DBL_MAX) to generate a value on
37 // the closed range [a, b]. Unfortunately, that technique is not universally
38 // reliable due to floating point quantization.
39 //
40 // * absl::uniform_real_distribution<float> generates between 2^28 and 2^29
41 // distinct floating point values in the range [0, 1).
42 //
43 // * absl::uniform_real_distribution<float> generates at least 2^23 distinct
44 // floating point values in the range [1, 2). This should be the same as
45 // any other range covered by a single exponent in IEEE 754.
46 //
47 // * absl::uniform_real_distribution<double> generates more than 2^52 distinct
48 // values in the range [0, 1), and should generate at least 2^52 distinct
49 // values in the range of [1, 2).
50 //
51
52 namespace {
53
54 template <typename RealType>
55 class UniformRealDistributionTest : public ::testing::Test {};
56
57 #if defined(__EMSCRIPTEN__)
58 using RealTypes = ::testing::Types<float, double>;
59 #else
60 using RealTypes = ::testing::Types<float, double, long double>;
61 #endif // defined(__EMSCRIPTEN__)
62
63 TYPED_TEST_SUITE(UniformRealDistributionTest, RealTypes);
64
TYPED_TEST(UniformRealDistributionTest,ParamSerializeTest)65 TYPED_TEST(UniformRealDistributionTest, ParamSerializeTest) {
66 using param_type =
67 typename absl::uniform_real_distribution<TypeParam>::param_type;
68
69 constexpr const TypeParam a{1152921504606846976};
70
71 constexpr int kCount = 1000;
72 absl::InsecureBitGen gen;
73 for (const auto& param : {
74 param_type(),
75 param_type(TypeParam(2.0), TypeParam(2.0)), // Same
76 param_type(TypeParam(-0.1), TypeParam(0.1)),
77 param_type(TypeParam(0.05), TypeParam(0.12)),
78 param_type(TypeParam(-0.05), TypeParam(0.13)),
79 param_type(TypeParam(-0.05), TypeParam(-0.02)),
80 // double range = 0
81 // 2^60 , 2^60 + 2^6
82 param_type(a, TypeParam(1152921504606847040)),
83 // 2^60 , 2^60 + 2^7
84 param_type(a, TypeParam(1152921504606847104)),
85 // double range = 2^8
86 // 2^60 , 2^60 + 2^8
87 param_type(a, TypeParam(1152921504606847232)),
88 // float range = 0
89 // 2^60 , 2^60 + 2^36
90 param_type(a, TypeParam(1152921573326323712)),
91 // 2^60 , 2^60 + 2^37
92 param_type(a, TypeParam(1152921642045800448)),
93 // float range = 2^38
94 // 2^60 , 2^60 + 2^38
95 param_type(a, TypeParam(1152921779484753920)),
96 // Limits
97 param_type(0, std::numeric_limits<TypeParam>::max()),
98 param_type(std::numeric_limits<TypeParam>::lowest(), 0),
99 param_type(0, std::numeric_limits<TypeParam>::epsilon()),
100 param_type(-std::numeric_limits<TypeParam>::epsilon(),
101 std::numeric_limits<TypeParam>::epsilon()),
102 param_type(std::numeric_limits<TypeParam>::epsilon(),
103 2 * std::numeric_limits<TypeParam>::epsilon()),
104 }) {
105 // Validate parameters.
106 const auto a = param.a();
107 const auto b = param.b();
108 absl::uniform_real_distribution<TypeParam> before(a, b);
109 EXPECT_EQ(before.a(), param.a());
110 EXPECT_EQ(before.b(), param.b());
111
112 {
113 absl::uniform_real_distribution<TypeParam> via_param(param);
114 EXPECT_EQ(via_param, before);
115 }
116
117 std::stringstream ss;
118 ss << before;
119 absl::uniform_real_distribution<TypeParam> after(TypeParam(1.0),
120 TypeParam(3.1));
121
122 EXPECT_NE(before.a(), after.a());
123 EXPECT_NE(before.b(), after.b());
124 EXPECT_NE(before.param(), after.param());
125 EXPECT_NE(before, after);
126
127 ss >> after;
128
129 EXPECT_EQ(before.a(), after.a());
130 EXPECT_EQ(before.b(), after.b());
131 EXPECT_EQ(before.param(), after.param());
132 EXPECT_EQ(before, after);
133
134 // Smoke test.
135 auto sample_min = after.max();
136 auto sample_max = after.min();
137 for (int i = 0; i < kCount; i++) {
138 auto sample = after(gen);
139 // Failure here indicates a bug in uniform_real_distribution::operator(),
140 // or bad parameters--range too large, etc.
141 if (after.min() == after.max()) {
142 EXPECT_EQ(sample, after.min());
143 } else {
144 EXPECT_GE(sample, after.min());
145 EXPECT_LT(sample, after.max());
146 }
147 if (sample > sample_max) {
148 sample_max = sample;
149 }
150 if (sample < sample_min) {
151 sample_min = sample;
152 }
153 }
154
155 if (!std::is_same<TypeParam, long double>::value) {
156 // static_cast<double>(long double) can overflow.
157 std::string msg = absl::StrCat("Range: ", static_cast<double>(sample_min),
158 ", ", static_cast<double>(sample_max));
159 ABSL_RAW_LOG(INFO, "%s", msg.c_str());
160 }
161 }
162 }
163
164 #ifdef _MSC_VER
165 #pragma warning(push)
166 #pragma warning(disable:4756) // Constant arithmetic overflow.
167 #endif
TYPED_TEST(UniformRealDistributionTest,ViolatesPreconditionsDeathTest)168 TYPED_TEST(UniformRealDistributionTest, ViolatesPreconditionsDeathTest) {
169 #if GTEST_HAS_DEATH_TEST
170 // Hi < Lo
171 EXPECT_DEBUG_DEATH(
172 { absl::uniform_real_distribution<TypeParam> dist(10.0, 1.0); }, "");
173
174 // Hi - Lo > numeric_limits<>::max()
175 EXPECT_DEBUG_DEATH(
176 {
177 absl::uniform_real_distribution<TypeParam> dist(
178 std::numeric_limits<TypeParam>::lowest(),
179 std::numeric_limits<TypeParam>::max());
180 },
181 "");
182 #endif // GTEST_HAS_DEATH_TEST
183 #if defined(NDEBUG)
184 // opt-mode, for invalid parameters, will generate a garbage value,
185 // but should not enter an infinite loop.
186 absl::InsecureBitGen gen;
187 {
188 absl::uniform_real_distribution<TypeParam> dist(10.0, 1.0);
189 auto x = dist(gen);
190 EXPECT_FALSE(std::isnan(x)) << x;
191 }
192 {
193 absl::uniform_real_distribution<TypeParam> dist(
194 std::numeric_limits<TypeParam>::lowest(),
195 std::numeric_limits<TypeParam>::max());
196 auto x = dist(gen);
197 // Infinite result.
198 EXPECT_FALSE(std::isfinite(x)) << x;
199 }
200 #endif // NDEBUG
201 }
202 #ifdef _MSC_VER
203 #pragma warning(pop) // warning(disable:4756)
204 #endif
205
TYPED_TEST(UniformRealDistributionTest,TestMoments)206 TYPED_TEST(UniformRealDistributionTest, TestMoments) {
207 constexpr int kSize = 1000000;
208 std::vector<double> values(kSize);
209
210 absl::InsecureBitGen rng;
211 absl::uniform_real_distribution<TypeParam> dist;
212 for (int i = 0; i < kSize; i++) {
213 values[i] = dist(rng);
214 }
215
216 const auto moments =
217 absl::random_internal::ComputeDistributionMoments(values);
218 EXPECT_NEAR(0.5, moments.mean, 0.01);
219 EXPECT_NEAR(1 / 12.0, moments.variance, 0.015);
220 EXPECT_NEAR(0.0, moments.skewness, 0.02);
221 EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.015);
222 }
223
TYPED_TEST(UniformRealDistributionTest,ChiSquaredTest50)224 TYPED_TEST(UniformRealDistributionTest, ChiSquaredTest50) {
225 using absl::random_internal::kChiSquared;
226 using param_type =
227 typename absl::uniform_real_distribution<TypeParam>::param_type;
228
229 constexpr size_t kTrials = 100000;
230 constexpr int kBuckets = 50;
231 constexpr double kExpected =
232 static_cast<double>(kTrials) / static_cast<double>(kBuckets);
233
234 // 1-in-100000 threshold, but remember, there are about 8 tests
235 // in this file. And the test could fail for other reasons.
236 // Empirically validated with --runs_per_test=10000.
237 const int kThreshold =
238 absl::random_internal::ChiSquareValue(kBuckets - 1, 0.999999);
239
240 absl::InsecureBitGen rng;
241 for (const auto& param : {param_type(0, 1), param_type(5, 12),
242 param_type(-5, 13), param_type(-5, -2)}) {
243 const double min_val = param.a();
244 const double max_val = param.b();
245 const double factor = kBuckets / (max_val - min_val);
246
247 std::vector<int32_t> counts(kBuckets, 0);
248 absl::uniform_real_distribution<TypeParam> dist(param);
249 for (size_t i = 0; i < kTrials; i++) {
250 auto x = dist(rng);
251 auto bucket = static_cast<size_t>((x - min_val) * factor);
252 counts[bucket]++;
253 }
254
255 double chi_square = absl::random_internal::ChiSquareWithExpected(
256 std::begin(counts), std::end(counts), kExpected);
257 if (chi_square > kThreshold) {
258 double p_value =
259 absl::random_internal::ChiSquarePValue(chi_square, kBuckets);
260
261 // Chi-squared test failed. Output does not appear to be uniform.
262 std::string msg;
263 for (const auto& a : counts) {
264 absl::StrAppend(&msg, a, "\n");
265 }
266 absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n");
267 absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ",
268 kThreshold);
269 ABSL_RAW_LOG(INFO, "%s", msg.c_str());
270 FAIL() << msg;
271 }
272 }
273 }
274
TYPED_TEST(UniformRealDistributionTest,StabilityTest)275 TYPED_TEST(UniformRealDistributionTest, StabilityTest) {
276 // absl::uniform_real_distribution stability relies only on
277 // random_internal::RandU64ToDouble and random_internal::RandU64ToFloat.
278 absl::random_internal::sequence_urbg urbg(
279 {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
280 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
281 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
282 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
283
284 std::vector<int> output(12);
285
286 absl::uniform_real_distribution<TypeParam> dist;
287 std::generate(std::begin(output), std::end(output), [&] {
288 return static_cast<int>(TypeParam(1000000) * dist(urbg));
289 });
290
291 EXPECT_THAT(
292 output, //
293 testing::ElementsAre(59, 999246, 762494, 395876, 167716, 82545, 925251,
294 77341, 12527, 708791, 834451, 932808));
295 }
296
TEST(UniformRealDistributionTest,AlgorithmBounds)297 TEST(UniformRealDistributionTest, AlgorithmBounds) {
298 absl::uniform_real_distribution<double> dist;
299
300 {
301 // This returns the smallest value >0 from absl::uniform_real_distribution.
302 absl::random_internal::sequence_urbg urbg({0x0000000000000001ull});
303 double a = dist(urbg);
304 EXPECT_EQ(a, 5.42101086242752217004e-20);
305 }
306
307 {
308 // This returns a value very near 0.5 from absl::uniform_real_distribution.
309 absl::random_internal::sequence_urbg urbg({0x7fffffffffffffefull});
310 double a = dist(urbg);
311 EXPECT_EQ(a, 0.499999999999999944489);
312 }
313 {
314 // This returns a value very near 0.5 from absl::uniform_real_distribution.
315 absl::random_internal::sequence_urbg urbg({0x8000000000000000ull});
316 double a = dist(urbg);
317 EXPECT_EQ(a, 0.5);
318 }
319
320 {
321 // This returns the largest value <1 from absl::uniform_real_distribution.
322 absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFEFull});
323 double a = dist(urbg);
324 EXPECT_EQ(a, 0.999999999999999888978);
325 }
326 {
327 // This *ALSO* returns the largest value <1.
328 absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFFFull});
329 double a = dist(urbg);
330 EXPECT_EQ(a, 0.999999999999999888978);
331 }
332 }
333
334 } // namespace
335