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/*
* Copyright (c) 2015 The WebRTC project authors. All Rights Reserved.
*
* Use of this source code is governed by a BSD-style license
* that can be found in the LICENSE file in the root of the source
* tree. An additional intellectual property rights grant can be found
* in the file PATENTS. All contributing project authors may
* be found in the AUTHORS file in the root of the source tree.
*/
#include "rtc_base/random.h"
#include <math.h>
#include <limits>
#include <vector>
#include "rtc_base/numerics/math_utils.h" // unsigned difference
#include "test/gtest.h"
namespace webrtc {
namespace {
// Computes the positive remainder of x/n.
template <typename T>
T fdiv_remainder(T x, T n) {
RTC_CHECK_GE(n, 0);
T remainder = x % n;
if (remainder < 0)
remainder += n;
return remainder;
}
} // namespace
// Sample a number of random integers of type T. Divide them into buckets
// based on the remainder when dividing by bucket_count and check that each
// bucket gets roughly the expected number of elements.
template <typename T>
void UniformBucketTest(T bucket_count, int samples, Random* prng) {
std::vector<int> buckets(bucket_count, 0);
uint64_t total_values = 1ull << (std::numeric_limits<T>::digits +
std::numeric_limits<T>::is_signed);
T upper_limit =
std::numeric_limits<T>::max() -
static_cast<T>(total_values % static_cast<uint64_t>(bucket_count));
ASSERT_GT(upper_limit, std::numeric_limits<T>::max() / 2);
for (int i = 0; i < samples; i++) {
T sample;
do {
// We exclude a few numbers from the range so that it is divisible by
// the number of buckets. If we are unlucky and hit one of the excluded
// numbers we just resample. Note that if the number of buckets is a
// power of 2, then we don't have to exclude anything.
sample = prng->Rand<T>();
} while (sample > upper_limit);
buckets[fdiv_remainder(sample, bucket_count)]++;
}
for (T i = 0; i < bucket_count; i++) {
// Expect the result to be within 3 standard deviations of the mean.
EXPECT_NEAR(buckets[i], samples / bucket_count,
3 * sqrt(samples / bucket_count));
}
}
TEST(RandomNumberGeneratorTest, BucketTestSignedChar) {
Random prng(7297352569824ull);
UniformBucketTest<signed char>(64, 640000, &prng);
UniformBucketTest<signed char>(11, 440000, &prng);
UniformBucketTest<signed char>(3, 270000, &prng);
}
TEST(RandomNumberGeneratorTest, BucketTestUnsignedChar) {
Random prng(7297352569824ull);
UniformBucketTest<unsigned char>(64, 640000, &prng);
UniformBucketTest<unsigned char>(11, 440000, &prng);
UniformBucketTest<unsigned char>(3, 270000, &prng);
}
TEST(RandomNumberGeneratorTest, BucketTestSignedShort) {
Random prng(7297352569824ull);
UniformBucketTest<int16_t>(64, 640000, &prng);
UniformBucketTest<int16_t>(11, 440000, &prng);
UniformBucketTest<int16_t>(3, 270000, &prng);
}
TEST(RandomNumberGeneratorTest, BucketTestUnsignedShort) {
Random prng(7297352569824ull);
UniformBucketTest<uint16_t>(64, 640000, &prng);
UniformBucketTest<uint16_t>(11, 440000, &prng);
UniformBucketTest<uint16_t>(3, 270000, &prng);
}
TEST(RandomNumberGeneratorTest, BucketTestSignedInt) {
Random prng(7297352569824ull);
UniformBucketTest<signed int>(64, 640000, &prng);
UniformBucketTest<signed int>(11, 440000, &prng);
UniformBucketTest<signed int>(3, 270000, &prng);
}
TEST(RandomNumberGeneratorTest, BucketTestUnsignedInt) {
Random prng(7297352569824ull);
UniformBucketTest<unsigned int>(64, 640000, &prng);
UniformBucketTest<unsigned int>(11, 440000, &prng);
UniformBucketTest<unsigned int>(3, 270000, &prng);
}
// The range of the random numbers is divided into bucket_count intervals
// of consecutive numbers. Check that approximately equally many numbers
// from each inteval are generated.
void BucketTestSignedInterval(unsigned int bucket_count,
unsigned int samples,
int32_t low,
int32_t high,
int sigma_level,
Random* prng) {
std::vector<unsigned int> buckets(bucket_count, 0);
ASSERT_GE(high, low);
ASSERT_GE(bucket_count, 2u);
uint32_t interval = webrtc_impl::unsigned_difference<int32_t>(high, low) + 1;
uint32_t numbers_per_bucket;
if (interval == 0) {
// The computation high - low + 1 should be 2^32 but overflowed
// Hence, bucket_count must be a power of 2
ASSERT_EQ(bucket_count & (bucket_count - 1), 0u);
numbers_per_bucket = (0x80000000u / bucket_count) * 2;
} else {
ASSERT_EQ(interval % bucket_count, 0u);
numbers_per_bucket = interval / bucket_count;
}
for (unsigned int i = 0; i < samples; i++) {
int32_t sample = prng->Rand(low, high);
EXPECT_LE(low, sample);
EXPECT_GE(high, sample);
buckets[webrtc_impl::unsigned_difference<int32_t>(sample, low) /
numbers_per_bucket]++;
}
for (unsigned int i = 0; i < bucket_count; i++) {
// Expect the result to be within 3 standard deviations of the mean,
// or more generally, within sigma_level standard deviations of the mean.
double mean = static_cast<double>(samples) / bucket_count;
EXPECT_NEAR(buckets[i], mean, sigma_level * sqrt(mean));
}
}
// The range of the random numbers is divided into bucket_count intervals
// of consecutive numbers. Check that approximately equally many numbers
// from each inteval are generated.
void BucketTestUnsignedInterval(unsigned int bucket_count,
unsigned int samples,
uint32_t low,
uint32_t high,
int sigma_level,
Random* prng) {
std::vector<unsigned int> buckets(bucket_count, 0);
ASSERT_GE(high, low);
ASSERT_GE(bucket_count, 2u);
uint32_t interval = high - low + 1;
uint32_t numbers_per_bucket;
if (interval == 0) {
// The computation high - low + 1 should be 2^32 but overflowed
// Hence, bucket_count must be a power of 2
ASSERT_EQ(bucket_count & (bucket_count - 1), 0u);
numbers_per_bucket = (0x80000000u / bucket_count) * 2;
} else {
ASSERT_EQ(interval % bucket_count, 0u);
numbers_per_bucket = interval / bucket_count;
}
for (unsigned int i = 0; i < samples; i++) {
uint32_t sample = prng->Rand(low, high);
EXPECT_LE(low, sample);
EXPECT_GE(high, sample);
buckets[(sample - low) / numbers_per_bucket]++;
}
for (unsigned int i = 0; i < bucket_count; i++) {
// Expect the result to be within 3 standard deviations of the mean,
// or more generally, within sigma_level standard deviations of the mean.
double mean = static_cast<double>(samples) / bucket_count;
EXPECT_NEAR(buckets[i], mean, sigma_level * sqrt(mean));
}
}
TEST(RandomNumberGeneratorTest, UniformUnsignedInterval) {
Random prng(299792458ull);
BucketTestUnsignedInterval(2, 100000, 0, 1, 3, &prng);
BucketTestUnsignedInterval(7, 100000, 1, 14, 3, &prng);
BucketTestUnsignedInterval(11, 100000, 1000, 1010, 3, &prng);
BucketTestUnsignedInterval(100, 100000, 0, 99, 3, &prng);
BucketTestUnsignedInterval(2, 100000, 0, 4294967295, 3, &prng);
BucketTestUnsignedInterval(17, 100000, 455, 2147484110, 3, &prng);
// 99.7% of all samples will be within 3 standard deviations of the mean,
// but since we test 1000 buckets we allow an interval of 4 sigma.
BucketTestUnsignedInterval(1000, 1000000, 0, 2147483999, 4, &prng);
}
TEST(RandomNumberGeneratorTest, UniformSignedInterval) {
Random prng(66260695729ull);
BucketTestSignedInterval(2, 100000, 0, 1, 3, &prng);
BucketTestSignedInterval(7, 100000, -2, 4, 3, &prng);
BucketTestSignedInterval(11, 100000, 1000, 1010, 3, &prng);
BucketTestSignedInterval(100, 100000, 0, 99, 3, &prng);
BucketTestSignedInterval(2, 100000, std::numeric_limits<int32_t>::min(),
std::numeric_limits<int32_t>::max(), 3, &prng);
BucketTestSignedInterval(17, 100000, -1073741826, 1073741829, 3, &prng);
// 99.7% of all samples will be within 3 standard deviations of the mean,
// but since we test 1000 buckets we allow an interval of 4 sigma.
BucketTestSignedInterval(1000, 1000000, -352, 2147483647, 4, &prng);
}
// The range of the random numbers is divided into bucket_count intervals
// of consecutive numbers. Check that approximately equally many numbers
// from each inteval are generated.
void BucketTestFloat(unsigned int bucket_count,
unsigned int samples,
int sigma_level,
Random* prng) {
ASSERT_GE(bucket_count, 2u);
std::vector<unsigned int> buckets(bucket_count, 0);
for (unsigned int i = 0; i < samples; i++) {
uint32_t sample = bucket_count * prng->Rand<float>();
EXPECT_LE(0u, sample);
EXPECT_GE(bucket_count - 1, sample);
buckets[sample]++;
}
for (unsigned int i = 0; i < bucket_count; i++) {
// Expect the result to be within 3 standard deviations of the mean,
// or more generally, within sigma_level standard deviations of the mean.
double mean = static_cast<double>(samples) / bucket_count;
EXPECT_NEAR(buckets[i], mean, sigma_level * sqrt(mean));
}
}
TEST(RandomNumberGeneratorTest, UniformFloatInterval) {
Random prng(1380648813ull);
BucketTestFloat(100, 100000, 3, &prng);
// 99.7% of all samples will be within 3 standard deviations of the mean,
// but since we test 1000 buckets we allow an interval of 4 sigma.
// BucketTestSignedInterval(1000, 1000000, -352, 2147483647, 4, &prng);
}
TEST(RandomNumberGeneratorTest, SignedHasSameBitPattern) {
Random prng_signed(66738480ull), prng_unsigned(66738480ull);
for (int i = 0; i < 1000; i++) {
signed int s = prng_signed.Rand<signed int>();
unsigned int u = prng_unsigned.Rand<unsigned int>();
EXPECT_EQ(u, static_cast<unsigned int>(s));
}
for (int i = 0; i < 1000; i++) {
int16_t s = prng_signed.Rand<int16_t>();
uint16_t u = prng_unsigned.Rand<uint16_t>();
EXPECT_EQ(u, static_cast<uint16_t>(s));
}
for (int i = 0; i < 1000; i++) {
signed char s = prng_signed.Rand<signed char>();
unsigned char u = prng_unsigned.Rand<unsigned char>();
EXPECT_EQ(u, static_cast<unsigned char>(s));
}
}
TEST(RandomNumberGeneratorTest, Gaussian) {
const int kN = 100000;
const int kBuckets = 100;
const double kMean = 49;
const double kStddev = 10;
Random prng(1256637061);
std::vector<unsigned int> buckets(kBuckets, 0);
for (int i = 0; i < kN; i++) {
int index = prng.Gaussian(kMean, kStddev) + 0.5;
if (index >= 0 && index < kBuckets) {
buckets[index]++;
}
}
const double kPi = 3.14159265358979323846;
const double kScale = 1 / (kStddev * sqrt(2.0 * kPi));
const double kDiv = -2.0 * kStddev * kStddev;
for (int n = 0; n < kBuckets; ++n) {
// Use Simpsons rule to estimate the probability that a random gaussian
// sample is in the interval [n-0.5, n+0.5].
double f_left = kScale * exp((n - kMean - 0.5) * (n - kMean - 0.5) / kDiv);
double f_mid = kScale * exp((n - kMean) * (n - kMean) / kDiv);
double f_right = kScale * exp((n - kMean + 0.5) * (n - kMean + 0.5) / kDiv);
double normal_dist = (f_left + 4 * f_mid + f_right) / 6;
// Expect the number of samples to be within 3 standard deviations
// (rounded up) of the expected number of samples in the bucket.
EXPECT_NEAR(buckets[n], kN * normal_dist, 3 * sqrt(kN * normal_dist) + 1);
}
}
} // namespace webrtc