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| 1 /* |
| 2 * Copyright (c) 2015 The WebRTC project authors. All Rights Reserved. |
| 3 * |
| 4 * Use of this source code is governed by a BSD-style license |
| 5 * that can be found in the LICENSE file in the root of the source |
| 6 * tree. An additional intellectual property rights grant can be found |
| 7 * in the file PATENTS. All contributing project authors may |
| 8 * be found in the AUTHORS file in the root of the source tree. |
| 9 */ |
| 10 |
| 11 #include <math.h> |
| 12 |
| 13 #include <limits> |
| 14 #include <vector> |
| 15 |
| 16 #include "testing/gtest/include/gtest/gtest.h" |
| 17 #include "webrtc/base/random.h" |
| 18 |
| 19 namespace webrtc { |
| 20 |
| 21 namespace { |
| 22 // Computes the positive remainder of x/n. |
| 23 template <typename T> |
| 24 T fdiv_remainder(T x, T n) { |
| 25 RTC_CHECK_GE(n, static_cast<T>(0)); |
| 26 T remainder = x % n; |
| 27 if (remainder < 0) |
| 28 remainder += n; |
| 29 return remainder; |
| 30 } |
| 31 } // namespace |
| 32 |
| 33 // Sample a number of random integers of type T. Divide them into buckets |
| 34 // based on the remainder when dividing by bucket_count and check that each |
| 35 // bucket gets roughly the expected number of elements. |
| 36 template <typename T> |
| 37 void UniformBucketTest(T bucket_count, int samples, Random* prng) { |
| 38 std::vector<int> buckets(bucket_count, 0); |
| 39 |
| 40 uint64_t total_values = 1ull << (std::numeric_limits<T>::digits + |
| 41 std::numeric_limits<T>::is_signed); |
| 42 T upper_limit = |
| 43 std::numeric_limits<T>::max() - |
| 44 static_cast<T>(total_values % static_cast<uint64_t>(bucket_count)); |
| 45 ASSERT_GT(upper_limit, std::numeric_limits<T>::max() / 2); |
| 46 |
| 47 for (int i = 0; i < samples; i++) { |
| 48 T sample; |
| 49 do { |
| 50 // We exclude a few numbers from the range so that it is divisible by |
| 51 // the number of buckets. If we are unlucky and hit one of the excluded |
| 52 // numbers we just resample. Note that if the number of buckets is a |
| 53 // power of 2, then we don't have to exclude anything. |
| 54 sample = prng->Rand<T>(); |
| 55 } while (sample > upper_limit); |
| 56 buckets[fdiv_remainder(sample, bucket_count)]++; |
| 57 } |
| 58 |
| 59 for (T i = 0; i < bucket_count; i++) { |
| 60 // Expect the result to be within 3 standard deviations of the mean. |
| 61 EXPECT_NEAR(buckets[i], samples / bucket_count, |
| 62 3 * sqrt(samples / bucket_count)); |
| 63 } |
| 64 } |
| 65 |
| 66 TEST(RandomNumberGeneratorTest, BucketTestSignedChar) { |
| 67 Random prng(7297352569824ull); |
| 68 UniformBucketTest<signed char>(64, 640000, &prng); |
| 69 UniformBucketTest<signed char>(11, 440000, &prng); |
| 70 UniformBucketTest<signed char>(3, 270000, &prng); |
| 71 } |
| 72 |
| 73 TEST(RandomNumberGeneratorTest, BucketTestUnsignedChar) { |
| 74 Random prng(7297352569824ull); |
| 75 UniformBucketTest<unsigned char>(64, 640000, &prng); |
| 76 UniformBucketTest<unsigned char>(11, 440000, &prng); |
| 77 UniformBucketTest<unsigned char>(3, 270000, &prng); |
| 78 } |
| 79 |
| 80 TEST(RandomNumberGeneratorTest, BucketTestSignedShort) { |
| 81 Random prng(7297352569824ull); |
| 82 UniformBucketTest<int16_t>(64, 640000, &prng); |
| 83 UniformBucketTest<int16_t>(11, 440000, &prng); |
| 84 UniformBucketTest<int16_t>(3, 270000, &prng); |
| 85 } |
| 86 |
| 87 TEST(RandomNumberGeneratorTest, BucketTestUnsignedShort) { |
| 88 Random prng(7297352569824ull); |
| 89 UniformBucketTest<uint16_t>(64, 640000, &prng); |
| 90 UniformBucketTest<uint16_t>(11, 440000, &prng); |
| 91 UniformBucketTest<uint16_t>(3, 270000, &prng); |
| 92 } |
| 93 |
| 94 TEST(RandomNumberGeneratorTest, BucketTestSignedInt) { |
| 95 Random prng(7297352569824ull); |
| 96 UniformBucketTest<signed int>(64, 640000, &prng); |
| 97 UniformBucketTest<signed int>(11, 440000, &prng); |
| 98 UniformBucketTest<signed int>(3, 270000, &prng); |
| 99 } |
| 100 |
| 101 TEST(RandomNumberGeneratorTest, BucketTestUnsignedInt) { |
| 102 Random prng(7297352569824ull); |
| 103 UniformBucketTest<unsigned int>(64, 640000, &prng); |
| 104 UniformBucketTest<unsigned int>(11, 440000, &prng); |
| 105 UniformBucketTest<unsigned int>(3, 270000, &prng); |
| 106 } |
| 107 |
| 108 // The range of the random numbers is divided into bucket_count intervals |
| 109 // of consecutive numbers. Check that approximately equally many numbers |
| 110 // from each inteval are generated. |
| 111 void BucketTestSignedInterval(unsigned int bucket_count, |
| 112 unsigned int samples, |
| 113 int32_t low, |
| 114 int32_t high, |
| 115 int sigma_level, |
| 116 Random* prng) { |
| 117 std::vector<unsigned int> buckets(bucket_count, 0); |
| 118 |
| 119 ASSERT_GE(high, low); |
| 120 ASSERT_GE(bucket_count, 2u); |
| 121 uint32_t interval = static_cast<uint32_t>(high - low + 1); |
| 122 uint32_t numbers_per_bucket; |
| 123 if (interval == 0) { |
| 124 // The computation high - low + 1 should be 2^32 but overflowed |
| 125 // Hence, bucket_count must be a power of 2 |
| 126 ASSERT_EQ(bucket_count & (bucket_count - 1), 0u); |
| 127 numbers_per_bucket = (0x80000000u / bucket_count) * 2; |
| 128 } else { |
| 129 ASSERT_EQ(interval % bucket_count, 0u); |
| 130 numbers_per_bucket = interval / bucket_count; |
| 131 } |
| 132 |
| 133 for (unsigned int i = 0; i < samples; i++) { |
| 134 int32_t sample = prng->Rand(low, high); |
| 135 EXPECT_LE(low, sample); |
| 136 EXPECT_GE(high, sample); |
| 137 buckets[static_cast<uint32_t>(sample - low) / numbers_per_bucket]++; |
| 138 } |
| 139 |
| 140 for (unsigned int i = 0; i < bucket_count; i++) { |
| 141 // Expect the result to be within 3 standard deviations of the mean, |
| 142 // or more generally, within sigma_level standard deviations of the mean. |
| 143 double mean = static_cast<double>(samples) / bucket_count; |
| 144 EXPECT_NEAR(buckets[i], mean, sigma_level * sqrt(mean)); |
| 145 } |
| 146 } |
| 147 |
| 148 // The range of the random numbers is divided into bucket_count intervals |
| 149 // of consecutive numbers. Check that approximately equally many numbers |
| 150 // from each inteval are generated. |
| 151 void BucketTestUnsignedInterval(unsigned int bucket_count, |
| 152 unsigned int samples, |
| 153 uint32_t low, |
| 154 uint32_t high, |
| 155 int sigma_level, |
| 156 Random* prng) { |
| 157 std::vector<unsigned int> buckets(bucket_count, 0); |
| 158 |
| 159 ASSERT_GE(high, low); |
| 160 ASSERT_GE(bucket_count, 2u); |
| 161 uint32_t interval = static_cast<uint32_t>(high - low + 1); |
| 162 uint32_t numbers_per_bucket; |
| 163 if (interval == 0) { |
| 164 // The computation high - low + 1 should be 2^32 but overflowed |
| 165 // Hence, bucket_count must be a power of 2 |
| 166 ASSERT_EQ(bucket_count & (bucket_count - 1), 0u); |
| 167 numbers_per_bucket = (0x80000000u / bucket_count) * 2; |
| 168 } else { |
| 169 ASSERT_EQ(interval % bucket_count, 0u); |
| 170 numbers_per_bucket = interval / bucket_count; |
| 171 } |
| 172 |
| 173 for (unsigned int i = 0; i < samples; i++) { |
| 174 uint32_t sample = prng->Rand(low, high); |
| 175 EXPECT_LE(low, sample); |
| 176 EXPECT_GE(high, sample); |
| 177 buckets[static_cast<uint32_t>(sample - low) / numbers_per_bucket]++; |
| 178 } |
| 179 |
| 180 for (unsigned int i = 0; i < bucket_count; i++) { |
| 181 // Expect the result to be within 3 standard deviations of the mean, |
| 182 // or more generally, within sigma_level standard deviations of the mean. |
| 183 double mean = static_cast<double>(samples) / bucket_count; |
| 184 EXPECT_NEAR(buckets[i], mean, sigma_level * sqrt(mean)); |
| 185 } |
| 186 } |
| 187 |
| 188 TEST(RandomNumberGeneratorTest, UniformUnsignedInterval) { |
| 189 Random prng(299792458ull); |
| 190 BucketTestUnsignedInterval(2, 100000, 0, 1, 3, &prng); |
| 191 BucketTestUnsignedInterval(7, 100000, 1, 14, 3, &prng); |
| 192 BucketTestUnsignedInterval(11, 100000, 1000, 1010, 3, &prng); |
| 193 BucketTestUnsignedInterval(100, 100000, 0, 99, 3, &prng); |
| 194 BucketTestUnsignedInterval(2, 100000, 0, 4294967295, 3, &prng); |
| 195 BucketTestUnsignedInterval(17, 100000, 455, 2147484110, 3, &prng); |
| 196 // 99.7% of all samples will be within 3 standard deviations of the mean, |
| 197 // but since we test 1000 buckets we allow an interval of 4 sigma. |
| 198 BucketTestUnsignedInterval(1000, 1000000, 0, 2147483999, 4, &prng); |
| 199 } |
| 200 |
| 201 TEST(RandomNumberGeneratorTest, UniformSignedInterval) { |
| 202 Random prng(66260695729ull); |
| 203 BucketTestSignedInterval(2, 100000, 0, 1, 3, &prng); |
| 204 BucketTestSignedInterval(7, 100000, -2, 4, 3, &prng); |
| 205 BucketTestSignedInterval(11, 100000, 1000, 1010, 3, &prng); |
| 206 BucketTestSignedInterval(100, 100000, 0, 99, 3, &prng); |
| 207 BucketTestSignedInterval(2, 100000, std::numeric_limits<int32_t>::min(), |
| 208 std::numeric_limits<int32_t>::max(), 3, &prng); |
| 209 BucketTestSignedInterval(17, 100000, -1073741826, 1073741829, 3, &prng); |
| 210 // 99.7% of all samples will be within 3 standard deviations of the mean, |
| 211 // but since we test 1000 buckets we allow an interval of 4 sigma. |
| 212 BucketTestSignedInterval(1000, 1000000, -352, 2147483647, 4, &prng); |
| 213 } |
| 214 |
| 215 // The range of the random numbers is divided into bucket_count intervals |
| 216 // of consecutive numbers. Check that approximately equally many numbers |
| 217 // from each inteval are generated. |
| 218 void BucketTestFloat(unsigned int bucket_count, |
| 219 unsigned int samples, |
| 220 int sigma_level, |
| 221 Random* prng) { |
| 222 ASSERT_GE(bucket_count, 2u); |
| 223 std::vector<unsigned int> buckets(bucket_count, 0); |
| 224 |
| 225 for (unsigned int i = 0; i < samples; i++) { |
| 226 uint32_t sample = bucket_count * prng->Rand<float>(); |
| 227 EXPECT_LE(0u, sample); |
| 228 EXPECT_GE(bucket_count - 1, sample); |
| 229 buckets[sample]++; |
| 230 } |
| 231 |
| 232 for (unsigned int i = 0; i < bucket_count; i++) { |
| 233 // Expect the result to be within 3 standard deviations of the mean, |
| 234 // or more generally, within sigma_level standard deviations of the mean. |
| 235 double mean = static_cast<double>(samples) / bucket_count; |
| 236 EXPECT_NEAR(buckets[i], mean, sigma_level * sqrt(mean)); |
| 237 } |
| 238 } |
| 239 |
| 240 TEST(RandomNumberGeneratorTest, UniformFloatInterval) { |
| 241 Random prng(1380648813ull); |
| 242 BucketTestFloat(100, 100000, 3, &prng); |
| 243 // 99.7% of all samples will be within 3 standard deviations of the mean, |
| 244 // but since we test 1000 buckets we allow an interval of 4 sigma. |
| 245 // BucketTestSignedInterval(1000, 1000000, -352, 2147483647, 4, &prng); |
| 246 } |
| 247 |
| 248 TEST(RandomNumberGeneratorTest, SignedHasSameBitPattern) { |
| 249 Random prng_signed(66738480ull), prng_unsigned(66738480ull); |
| 250 |
| 251 for (int i = 0; i < 1000; i++) { |
| 252 signed int s = prng_signed.Rand<signed int>(); |
| 253 unsigned int u = prng_unsigned.Rand<unsigned int>(); |
| 254 EXPECT_EQ(u, static_cast<unsigned int>(s)); |
| 255 } |
| 256 |
| 257 for (int i = 0; i < 1000; i++) { |
| 258 int16_t s = prng_signed.Rand<int16_t>(); |
| 259 uint16_t u = prng_unsigned.Rand<uint16_t>(); |
| 260 EXPECT_EQ(u, static_cast<uint16_t>(s)); |
| 261 } |
| 262 |
| 263 for (int i = 0; i < 1000; i++) { |
| 264 signed char s = prng_signed.Rand<signed char>(); |
| 265 unsigned char u = prng_unsigned.Rand<unsigned char>(); |
| 266 EXPECT_EQ(u, static_cast<unsigned char>(s)); |
| 267 } |
| 268 } |
| 269 |
| 270 TEST(RandomNumberGeneratorTest, Gaussian) { |
| 271 const int kN = 100000; |
| 272 const int kBuckets = 100; |
| 273 const double kMean = 49; |
| 274 const double kStddev = 10; |
| 275 |
| 276 Random prng(1256637061); |
| 277 |
| 278 std::vector<unsigned int> buckets(kBuckets, 0); |
| 279 for (int i = 0; i < kN; i++) { |
| 280 int index = prng.Gaussian(kMean, kStddev) + 0.5; |
| 281 if (index >= 0 && index < kBuckets) { |
| 282 buckets[index]++; |
| 283 } |
| 284 } |
| 285 |
| 286 const double kPi = 3.14159265358979323846; |
| 287 const double kScale = 1 / (kStddev * sqrt(2.0 * kPi)); |
| 288 const double kDiv = -2.0 * kStddev * kStddev; |
| 289 for (int n = 0; n < kBuckets; ++n) { |
| 290 // Use Simpsons rule to estimate the probability that a random gaussian |
| 291 // sample is in the interval [n-0.5, n+0.5]. |
| 292 double f_left = kScale * exp((n - kMean - 0.5) * (n - kMean - 0.5) / kDiv); |
| 293 double f_mid = kScale * exp((n - kMean) * (n - kMean) / kDiv); |
| 294 double f_right = kScale * exp((n - kMean + 0.5) * (n - kMean + 0.5) / kDiv); |
| 295 double normal_dist = (f_left + 4 * f_mid + f_right) / 6; |
| 296 // Expect the number of samples to be within 3 standard deviations |
| 297 // (rounded up) of the expected number of samples in the bucket. |
| 298 EXPECT_NEAR(buckets[n], kN * normal_dist, 3 * sqrt(kN * normal_dist) + 1); |
| 299 } |
| 300 } |
| 301 |
| 302 } // namespace webrtc |
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