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/distributions.h"
16
17 #include <cfloat>
18 #include <cmath>
19 #include <cstdint>
20 #include <random>
21 #include <vector>
22
23 #include "gtest/gtest.h"
24 #include "absl/random/internal/distribution_test_util.h"
25 #include "absl/random/random.h"
26
27 namespace {
28
29 constexpr int kSize = 400000;
30
31 class RandomDistributionsTest : public testing::Test {};
32
33
34 struct Invalid {};
35
36 template <typename A, typename B>
37 auto InferredUniformReturnT(int)
38 -> decltype(absl::Uniform(std::declval<absl::InsecureBitGen&>(),
39 std::declval<A>(), std::declval<B>()));
40
41 template <typename, typename>
42 Invalid InferredUniformReturnT(...);
43
44 template <typename TagType, typename A, typename B>
45 auto InferredTaggedUniformReturnT(int)
46 -> decltype(absl::Uniform(std::declval<TagType>(),
47 std::declval<absl::InsecureBitGen&>(),
48 std::declval<A>(), std::declval<B>()));
49
50 template <typename, typename, typename>
51 Invalid InferredTaggedUniformReturnT(...);
52
53 // Given types <A, B, Expect>, CheckArgsInferType() verifies that
54 //
55 // absl::Uniform(gen, A{}, B{})
56 //
57 // returns the type "Expect".
58 //
59 // This interface can also be used to assert that a given absl::Uniform()
60 // overload does not exist / will not compile. Given types <A, B>, the
61 // expression
62 //
63 // decltype(absl::Uniform(..., std::declval<A>(), std::declval<B>()))
64 //
65 // will not compile, leaving the definition of InferredUniformReturnT<A, B> to
66 // resolve (via SFINAE) to the overload which returns type "Invalid". This
67 // allows tests to assert that an invocation such as
68 //
69 // absl::Uniform(gen, 1.23f, std::numeric_limits<int>::max() - 1)
70 //
71 // should not compile, since neither type, float nor int, can precisely
72 // represent both endpoint-values. Writing:
73 //
74 // CheckArgsInferType<float, int, Invalid>()
75 //
76 // will assert that this overload does not exist.
77 template <typename A, typename B, typename Expect>
CheckArgsInferType()78 void CheckArgsInferType() {
79 static_assert(
80 absl::conjunction<
81 std::is_same<Expect, decltype(InferredUniformReturnT<A, B>(0))>,
82 std::is_same<Expect,
83 decltype(InferredUniformReturnT<B, A>(0))>>::value,
84 "");
85 static_assert(
86 absl::conjunction<
87 std::is_same<Expect, decltype(InferredTaggedUniformReturnT<
88 absl::IntervalOpenOpenTag, A, B>(0))>,
89 std::is_same<Expect,
90 decltype(InferredTaggedUniformReturnT<
91 absl::IntervalOpenOpenTag, B, A>(0))>>::value,
92 "");
93 }
94
95 template <typename A, typename B, typename ExplicitRet>
96 auto ExplicitUniformReturnT(int) -> decltype(
97 absl::Uniform<ExplicitRet>(*std::declval<absl::InsecureBitGen*>(),
98 std::declval<A>(), std::declval<B>()));
99
100 template <typename, typename, typename ExplicitRet>
101 Invalid ExplicitUniformReturnT(...);
102
103 template <typename TagType, typename A, typename B, typename ExplicitRet>
104 auto ExplicitTaggedUniformReturnT(int) -> decltype(absl::Uniform<ExplicitRet>(
105 std::declval<TagType>(), *std::declval<absl::InsecureBitGen*>(),
106 std::declval<A>(), std::declval<B>()));
107
108 template <typename, typename, typename, typename ExplicitRet>
109 Invalid ExplicitTaggedUniformReturnT(...);
110
111 // Given types <A, B, Expect>, CheckArgsReturnExpectedType() verifies that
112 //
113 // absl::Uniform<Expect>(gen, A{}, B{})
114 //
115 // returns the type "Expect", and that the function-overload has the signature
116 //
117 // Expect(URBG&, Expect, Expect)
118 template <typename A, typename B, typename Expect>
CheckArgsReturnExpectedType()119 void CheckArgsReturnExpectedType() {
120 static_assert(
121 absl::conjunction<
122 std::is_same<Expect,
123 decltype(ExplicitUniformReturnT<A, B, Expect>(0))>,
124 std::is_same<Expect, decltype(ExplicitUniformReturnT<B, A, Expect>(
125 0))>>::value,
126 "");
127 static_assert(
128 absl::conjunction<
129 std::is_same<Expect,
130 decltype(ExplicitTaggedUniformReturnT<
131 absl::IntervalOpenOpenTag, A, B, Expect>(0))>,
132 std::is_same<Expect, decltype(ExplicitTaggedUniformReturnT<
133 absl::IntervalOpenOpenTag, B, A,
134 Expect>(0))>>::value,
135 "");
136 }
137
TEST_F(RandomDistributionsTest,UniformTypeInference)138 TEST_F(RandomDistributionsTest, UniformTypeInference) {
139 // Infers common types.
140 CheckArgsInferType<uint16_t, uint16_t, uint16_t>();
141 CheckArgsInferType<uint32_t, uint32_t, uint32_t>();
142 CheckArgsInferType<uint64_t, uint64_t, uint64_t>();
143 CheckArgsInferType<int16_t, int16_t, int16_t>();
144 CheckArgsInferType<int32_t, int32_t, int32_t>();
145 CheckArgsInferType<int64_t, int64_t, int64_t>();
146 CheckArgsInferType<float, float, float>();
147 CheckArgsInferType<double, double, double>();
148
149 // Explicitly-specified return-values override inferences.
150 CheckArgsReturnExpectedType<int16_t, int16_t, int32_t>();
151 CheckArgsReturnExpectedType<uint16_t, uint16_t, int32_t>();
152 CheckArgsReturnExpectedType<int16_t, int16_t, int64_t>();
153 CheckArgsReturnExpectedType<int16_t, int32_t, int64_t>();
154 CheckArgsReturnExpectedType<int16_t, int32_t, double>();
155 CheckArgsReturnExpectedType<float, float, double>();
156 CheckArgsReturnExpectedType<int, int, int16_t>();
157
158 // Properly promotes uint16_t.
159 CheckArgsInferType<uint16_t, uint32_t, uint32_t>();
160 CheckArgsInferType<uint16_t, uint64_t, uint64_t>();
161 CheckArgsInferType<uint16_t, int32_t, int32_t>();
162 CheckArgsInferType<uint16_t, int64_t, int64_t>();
163 CheckArgsInferType<uint16_t, float, float>();
164 CheckArgsInferType<uint16_t, double, double>();
165
166 // Properly promotes int16_t.
167 CheckArgsInferType<int16_t, int32_t, int32_t>();
168 CheckArgsInferType<int16_t, int64_t, int64_t>();
169 CheckArgsInferType<int16_t, float, float>();
170 CheckArgsInferType<int16_t, double, double>();
171
172 // Invalid (u)int16_t-pairings do not compile.
173 // See "CheckArgsInferType" comments above, for how this is achieved.
174 CheckArgsInferType<uint16_t, int16_t, Invalid>();
175 CheckArgsInferType<int16_t, uint32_t, Invalid>();
176 CheckArgsInferType<int16_t, uint64_t, Invalid>();
177
178 // Properly promotes uint32_t.
179 CheckArgsInferType<uint32_t, uint64_t, uint64_t>();
180 CheckArgsInferType<uint32_t, int64_t, int64_t>();
181 CheckArgsInferType<uint32_t, double, double>();
182
183 // Properly promotes int32_t.
184 CheckArgsInferType<int32_t, int64_t, int64_t>();
185 CheckArgsInferType<int32_t, double, double>();
186
187 // Invalid (u)int32_t-pairings do not compile.
188 CheckArgsInferType<uint32_t, int32_t, Invalid>();
189 CheckArgsInferType<int32_t, uint64_t, Invalid>();
190 CheckArgsInferType<int32_t, float, Invalid>();
191 CheckArgsInferType<uint32_t, float, Invalid>();
192
193 // Invalid (u)int64_t-pairings do not compile.
194 CheckArgsInferType<uint64_t, int64_t, Invalid>();
195 CheckArgsInferType<int64_t, float, Invalid>();
196 CheckArgsInferType<int64_t, double, Invalid>();
197
198 // Properly promotes float.
199 CheckArgsInferType<float, double, double>();
200 }
201
TEST_F(RandomDistributionsTest,UniformExamples)202 TEST_F(RandomDistributionsTest, UniformExamples) {
203 // Examples.
204 absl::InsecureBitGen gen;
205 EXPECT_NE(1, absl::Uniform(gen, static_cast<uint16_t>(0), 1.0f));
206 EXPECT_NE(1, absl::Uniform(gen, 0, 1.0));
207 EXPECT_NE(1, absl::Uniform(absl::IntervalOpenOpen, gen,
208 static_cast<uint16_t>(0), 1.0f));
209 EXPECT_NE(1, absl::Uniform(absl::IntervalOpenOpen, gen, 0, 1.0));
210 EXPECT_NE(1, absl::Uniform(absl::IntervalOpenOpen, gen, -1, 1.0));
211 EXPECT_NE(1, absl::Uniform<double>(absl::IntervalOpenOpen, gen, -1, 1));
212 EXPECT_NE(1, absl::Uniform<float>(absl::IntervalOpenOpen, gen, 0, 1));
213 EXPECT_NE(1, absl::Uniform<float>(gen, 0, 1));
214 }
215
TEST_F(RandomDistributionsTest,UniformNoBounds)216 TEST_F(RandomDistributionsTest, UniformNoBounds) {
217 absl::InsecureBitGen gen;
218
219 absl::Uniform<uint8_t>(gen);
220 absl::Uniform<uint16_t>(gen);
221 absl::Uniform<uint32_t>(gen);
222 absl::Uniform<uint64_t>(gen);
223 }
224
TEST_F(RandomDistributionsTest,UniformNonsenseRanges)225 TEST_F(RandomDistributionsTest, UniformNonsenseRanges) {
226 // The ranges used in this test are undefined behavior.
227 // The results are arbitrary and subject to future changes.
228
229 #if (defined(__i386__) || defined(_M_IX86)) && FLT_EVAL_METHOD != 0
230 // We're using an x87-compatible FPU, and intermediate operations can be
231 // performed with 80-bit floats. This produces slightly different results from
232 // what we expect below.
233 GTEST_SKIP()
234 << "Skipping the test because we detected x87 floating-point semantics";
235 #endif
236
237 absl::InsecureBitGen gen;
238
239 // <uint>
240 EXPECT_EQ(0, absl::Uniform<uint64_t>(gen, 0, 0));
241 EXPECT_EQ(1, absl::Uniform<uint64_t>(gen, 1, 0));
242 EXPECT_EQ(0, absl::Uniform<uint64_t>(absl::IntervalOpenOpen, gen, 0, 0));
243 EXPECT_EQ(1, absl::Uniform<uint64_t>(absl::IntervalOpenOpen, gen, 1, 0));
244
245 constexpr auto m = (std::numeric_limits<uint64_t>::max)();
246
247 EXPECT_EQ(m, absl::Uniform(gen, m, m));
248 EXPECT_EQ(m, absl::Uniform(gen, m, m - 1));
249 EXPECT_EQ(m - 1, absl::Uniform(gen, m - 1, m));
250 EXPECT_EQ(m, absl::Uniform(absl::IntervalOpenOpen, gen, m, m));
251 EXPECT_EQ(m, absl::Uniform(absl::IntervalOpenOpen, gen, m, m - 1));
252 EXPECT_EQ(m - 1, absl::Uniform(absl::IntervalOpenOpen, gen, m - 1, m));
253
254 // <int>
255 EXPECT_EQ(0, absl::Uniform<int64_t>(gen, 0, 0));
256 EXPECT_EQ(1, absl::Uniform<int64_t>(gen, 1, 0));
257 EXPECT_EQ(0, absl::Uniform<int64_t>(absl::IntervalOpenOpen, gen, 0, 0));
258 EXPECT_EQ(1, absl::Uniform<int64_t>(absl::IntervalOpenOpen, gen, 1, 0));
259
260 constexpr auto l = (std::numeric_limits<int64_t>::min)();
261 constexpr auto r = (std::numeric_limits<int64_t>::max)();
262
263 EXPECT_EQ(l, absl::Uniform(gen, l, l));
264 EXPECT_EQ(r, absl::Uniform(gen, r, r));
265 EXPECT_EQ(r, absl::Uniform(gen, r, r - 1));
266 EXPECT_EQ(r - 1, absl::Uniform(gen, r - 1, r));
267 EXPECT_EQ(l, absl::Uniform(absl::IntervalOpenOpen, gen, l, l));
268 EXPECT_EQ(r, absl::Uniform(absl::IntervalOpenOpen, gen, r, r));
269 EXPECT_EQ(r, absl::Uniform(absl::IntervalOpenOpen, gen, r, r - 1));
270 EXPECT_EQ(r - 1, absl::Uniform(absl::IntervalOpenOpen, gen, r - 1, r));
271
272 // <double>
273 const double e = std::nextafter(1.0, 2.0); // 1 + epsilon
274 const double f = std::nextafter(1.0, 0.0); // 1 - epsilon
275 const double g = std::numeric_limits<double>::denorm_min();
276
277 EXPECT_EQ(1.0, absl::Uniform(gen, 1.0, e));
278 EXPECT_EQ(1.0, absl::Uniform(gen, 1.0, f));
279 EXPECT_EQ(0.0, absl::Uniform(gen, 0.0, g));
280
281 EXPECT_EQ(e, absl::Uniform(absl::IntervalOpenOpen, gen, 1.0, e));
282 EXPECT_EQ(f, absl::Uniform(absl::IntervalOpenOpen, gen, 1.0, f));
283 EXPECT_EQ(g, absl::Uniform(absl::IntervalOpenOpen, gen, 0.0, g));
284 }
285
286 // TODO(lar): Validate properties of non-default interval-semantics.
TEST_F(RandomDistributionsTest,UniformReal)287 TEST_F(RandomDistributionsTest, UniformReal) {
288 std::vector<double> values(kSize);
289
290 absl::InsecureBitGen gen;
291 for (int i = 0; i < kSize; i++) {
292 values[i] = absl::Uniform(gen, 0, 1.0);
293 }
294
295 const auto moments =
296 absl::random_internal::ComputeDistributionMoments(values);
297 EXPECT_NEAR(0.5, moments.mean, 0.02);
298 EXPECT_NEAR(1 / 12.0, moments.variance, 0.02);
299 EXPECT_NEAR(0.0, moments.skewness, 0.02);
300 EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.02);
301 }
302
TEST_F(RandomDistributionsTest,UniformInt)303 TEST_F(RandomDistributionsTest, UniformInt) {
304 std::vector<double> values(kSize);
305
306 absl::InsecureBitGen gen;
307 for (int i = 0; i < kSize; i++) {
308 const int64_t kMax = 1000000000000ll;
309 int64_t j = absl::Uniform(absl::IntervalClosedClosed, gen, 0, kMax);
310 // convert to double.
311 values[i] = static_cast<double>(j) / static_cast<double>(kMax);
312 }
313
314 const auto moments =
315 absl::random_internal::ComputeDistributionMoments(values);
316 EXPECT_NEAR(0.5, moments.mean, 0.02);
317 EXPECT_NEAR(1 / 12.0, moments.variance, 0.02);
318 EXPECT_NEAR(0.0, moments.skewness, 0.02);
319 EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.02);
320
321 /*
322 // NOTE: These are not supported by absl::Uniform, which is specialized
323 // on integer and real valued types.
324
325 enum E { E0, E1 }; // enum
326 enum S : int { S0, S1 }; // signed enum
327 enum U : unsigned int { U0, U1 }; // unsigned enum
328
329 absl::Uniform(gen, E0, E1);
330 absl::Uniform(gen, S0, S1);
331 absl::Uniform(gen, U0, U1);
332 */
333 }
334
TEST_F(RandomDistributionsTest,Exponential)335 TEST_F(RandomDistributionsTest, Exponential) {
336 std::vector<double> values(kSize);
337
338 absl::InsecureBitGen gen;
339 for (int i = 0; i < kSize; i++) {
340 values[i] = absl::Exponential<double>(gen);
341 }
342
343 const auto moments =
344 absl::random_internal::ComputeDistributionMoments(values);
345 EXPECT_NEAR(1.0, moments.mean, 0.02);
346 EXPECT_NEAR(1.0, moments.variance, 0.025);
347 EXPECT_NEAR(2.0, moments.skewness, 0.1);
348 EXPECT_LT(5.0, moments.kurtosis);
349 }
350
TEST_F(RandomDistributionsTest,PoissonDefault)351 TEST_F(RandomDistributionsTest, PoissonDefault) {
352 std::vector<double> values(kSize);
353
354 absl::InsecureBitGen gen;
355 for (int i = 0; i < kSize; i++) {
356 values[i] = absl::Poisson<int64_t>(gen);
357 }
358
359 const auto moments =
360 absl::random_internal::ComputeDistributionMoments(values);
361 EXPECT_NEAR(1.0, moments.mean, 0.02);
362 EXPECT_NEAR(1.0, moments.variance, 0.02);
363 EXPECT_NEAR(1.0, moments.skewness, 0.025);
364 EXPECT_LT(2.0, moments.kurtosis);
365 }
366
TEST_F(RandomDistributionsTest,PoissonLarge)367 TEST_F(RandomDistributionsTest, PoissonLarge) {
368 constexpr double kMean = 100000000.0;
369 std::vector<double> values(kSize);
370
371 absl::InsecureBitGen gen;
372 for (int i = 0; i < kSize; i++) {
373 values[i] = absl::Poisson<int64_t>(gen, kMean);
374 }
375
376 const auto moments =
377 absl::random_internal::ComputeDistributionMoments(values);
378 EXPECT_NEAR(kMean, moments.mean, kMean * 0.015);
379 EXPECT_NEAR(kMean, moments.variance, kMean * 0.015);
380 EXPECT_NEAR(std::sqrt(kMean), moments.skewness, kMean * 0.02);
381 EXPECT_LT(2.0, moments.kurtosis);
382 }
383
TEST_F(RandomDistributionsTest,Bernoulli)384 TEST_F(RandomDistributionsTest, Bernoulli) {
385 constexpr double kP = 0.5151515151;
386 std::vector<double> values(kSize);
387
388 absl::InsecureBitGen gen;
389 for (int i = 0; i < kSize; i++) {
390 values[i] = absl::Bernoulli(gen, kP);
391 }
392
393 const auto moments =
394 absl::random_internal::ComputeDistributionMoments(values);
395 EXPECT_NEAR(kP, moments.mean, 0.01);
396 }
397
TEST_F(RandomDistributionsTest,Beta)398 TEST_F(RandomDistributionsTest, Beta) {
399 constexpr double kAlpha = 2.0;
400 constexpr double kBeta = 3.0;
401 std::vector<double> values(kSize);
402
403 absl::InsecureBitGen gen;
404 for (int i = 0; i < kSize; i++) {
405 values[i] = absl::Beta(gen, kAlpha, kBeta);
406 }
407
408 const auto moments =
409 absl::random_internal::ComputeDistributionMoments(values);
410 EXPECT_NEAR(0.4, moments.mean, 0.01);
411 }
412
TEST_F(RandomDistributionsTest,Zipf)413 TEST_F(RandomDistributionsTest, Zipf) {
414 std::vector<double> values(kSize);
415
416 absl::InsecureBitGen gen;
417 for (int i = 0; i < kSize; i++) {
418 values[i] = absl::Zipf<int64_t>(gen, 100);
419 }
420
421 // The mean of a zipf distribution is: H(N, s-1) / H(N,s).
422 // Given the parameter v = 1, this gives the following function:
423 // (Hn(100, 1) - Hn(1,1)) / (Hn(100,2) - Hn(1,2)) = 6.5944
424 const auto moments =
425 absl::random_internal::ComputeDistributionMoments(values);
426 EXPECT_NEAR(6.5944, moments.mean, 2000) << moments;
427 }
428
TEST_F(RandomDistributionsTest,Gaussian)429 TEST_F(RandomDistributionsTest, Gaussian) {
430 std::vector<double> values(kSize);
431
432 absl::InsecureBitGen gen;
433 for (int i = 0; i < kSize; i++) {
434 values[i] = absl::Gaussian<double>(gen);
435 }
436
437 const auto moments =
438 absl::random_internal::ComputeDistributionMoments(values);
439 EXPECT_NEAR(0.0, moments.mean, 0.02);
440 EXPECT_NEAR(1.0, moments.variance, 0.04);
441 EXPECT_NEAR(0, moments.skewness, 0.2);
442 EXPECT_NEAR(3.0, moments.kurtosis, 0.5);
443 }
444
TEST_F(RandomDistributionsTest,LogUniform)445 TEST_F(RandomDistributionsTest, LogUniform) {
446 std::vector<double> values(kSize);
447
448 absl::InsecureBitGen gen;
449 for (int i = 0; i < kSize; i++) {
450 values[i] = absl::LogUniform<int64_t>(gen, 0, (1 << 10) - 1);
451 }
452
453 // The mean is the sum of the fractional means of the uniform distributions:
454 // [0..0][1..1][2..3][4..7][8..15][16..31][32..63]
455 // [64..127][128..255][256..511][512..1023]
456 const double mean = (0 + 1 + 1 + 2 + 3 + 4 + 7 + 8 + 15 + 16 + 31 + 32 + 63 +
457 64 + 127 + 128 + 255 + 256 + 511 + 512 + 1023) /
458 (2.0 * 11.0);
459
460 const auto moments =
461 absl::random_internal::ComputeDistributionMoments(values);
462 EXPECT_NEAR(mean, moments.mean, 2) << moments;
463 }
464
465 } // namespace
466