// Copyright 2017 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "absl/random/bernoulli_distribution.h"
#include <cmath>
#include <cstddef>
#include <random>
#include <sstream>
#include <utility>
#include "gtest/gtest.h"
#include "absl/random/internal/pcg_engine.h"
#include "absl/random/internal/sequence_urbg.h"
#include "absl/random/random.h"
namespace {
class BernoulliTest : public testing::TestWithParam<std::pair<double, size_t>> {
};
TEST_P(BernoulliTest, Serialize) {
const double d = GetParam().first;
absl::bernoulli_distribution before(d);
{
absl::bernoulli_distribution via_param{
absl::bernoulli_distribution::param_type(d)};
EXPECT_EQ(via_param, before);
}
std::stringstream ss;
ss << before;
absl::bernoulli_distribution after(0.6789);
EXPECT_NE(before.p(), after.p());
EXPECT_NE(before.param(), after.param());
EXPECT_NE(before, after);
ss >> after;
EXPECT_EQ(before.p(), after.p());
EXPECT_EQ(before.param(), after.param());
EXPECT_EQ(before, after);
}
TEST_P(BernoulliTest, Accuracy) {
// Sadly, the claim to fame for this implementation is precise accuracy, which
// is very, very hard to measure, the improvements come as trials approach the
// limit of double accuracy; thus the outcome differs from the
// std::bernoulli_distribution with a probability of approximately 1 in 2^-53.
const std::pair<double, size_t> para = GetParam();
size_t trials = para.second;
double p = para.first;
// We use a fixed bit generator for distribution accuracy tests. This allows
// these tests to be deterministic, while still testing the qualify of the
// implementation.
absl::random_internal::pcg64_2018_engine rng(0x2B7E151628AED2A6);
size_t yes = 0;
absl::bernoulli_distribution dist(p);
for (size_t i = 0; i < trials; ++i) {
if (dist(rng)) yes++;
}
// Compute the distribution parameters for a binomial test, using a normal
// approximation for the confidence interval, as there are a sufficiently
// large number of trials that the central limit theorem applies.
const double stddev_p = std::sqrt((p * (1.0 - p)) / trials);
const double expected = trials * p;
const double stddev = trials * stddev_p;
// 5 sigma, approved by Richard Feynman
EXPECT_NEAR(yes, expected, 5 * stddev)
<< "@" << p << ", "
<< std::abs(static_cast<double>(yes) - expected) / stddev << " stddev";
}
// There must be many more trials to make the mean approximately normal for `p`
// closes to 0 or 1.
INSTANTIATE_TEST_SUITE_P(
All, BernoulliTest,
::testing::Values(
// Typical values.
std::make_pair(0, 30000), std::make_pair(1e-3, 30000000),
std::make_pair(0.1, 3000000), std::make_pair(0.5, 3000000),
std::make_pair(0.9, 30000000), std::make_pair(0.999, 30000000),
std::make_pair(1, 30000),
// Boundary cases.
std::make_pair(std::nextafter(1.0, 0.0), 1), // ~1 - epsilon
std::make_pair(std::numeric_limits<double>::epsilon(), 1),
std::make_pair(std::nextafter(std::numeric_limits<double>::min(),
1.0), // min + epsilon
1),
std::make_pair(std::numeric_limits<double>::min(), // smallest normal
1),
std::make_pair(
std::numeric_limits<double>::denorm_min(), // smallest denorm
1),
std::make_pair(std::numeric_limits<double>::min() / 2, 1), // denorm
std::make_pair(std::nextafter(std::numeric_limits<double>::min(),
0.0), // denorm_max
1)));
// NOTE: absl::bernoulli_distribution is not guaranteed to be stable.
TEST(BernoulliTest, StabilityTest) {
// absl::bernoulli_distribution stability relies on FastUniformBits and
// integer arithmetic.
absl::random_internal::sequence_urbg urbg({
0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull,
0x4864f22c059bf29eull, 0x247856d8b862665cull, 0xe46e86e9a1337e10ull,
0xd8c8541f3519b133ull, 0xe75b5162c567b9e4ull, 0xf732e5ded7009c5bull,
0xb170b98353121eacull, 0x1ec2e8986d2362caull, 0x814c8e35fe9a961aull,
0x0c3cd59c9b638a02ull, 0xcb3bb6478a07715cull, 0x1224e62c978bbc7full,
0x671ef2cb04e81f6eull, 0x3c1cbd811eaf1808ull, 0x1bbc23cfa8fac721ull,
0xa4c2cda65e596a51ull, 0xb77216fad37adf91ull, 0x836d794457c08849ull,
0xe083df03475f49d7ull, 0xbc9feb512e6b0d6cull, 0xb12d74fdd718c8c5ull,
0x12ff09653bfbe4caull, 0x8dd03a105bc4ee7eull, 0x5738341045ba0d85ull,
0xe3fd722dc65ad09eull, 0x5a14fd21ea2a5705ull, 0x14e6ea4d6edb0c73ull,
0x275b0dc7e0a18acfull, 0x36cebe0d2653682eull, 0x0361e9b23861596bull,
});
// Generate a string of '0' and '1' for the distribution output.
auto generate = [&urbg](absl::bernoulli_distribution& dist) {
std::string output;
output.reserve(36);
urbg.reset();
for (int i = 0; i < 35; i++) {
output.append(dist(urbg) ? "1" : "0");
}
return output;
};
const double kP = 0.0331289862362;
{
absl::bernoulli_distribution dist(kP);
auto v = generate(dist);
EXPECT_EQ(35, urbg.invocations());
EXPECT_EQ(v, "00000000000010000000000010000000000") << dist;
}
{
absl::bernoulli_distribution dist(kP * 10.0);
auto v = generate(dist);
EXPECT_EQ(35, urbg.invocations());
EXPECT_EQ(v, "00000100010010010010000011000011010") << dist;
}
{
absl::bernoulli_distribution dist(kP * 20.0);
auto v = generate(dist);
EXPECT_EQ(35, urbg.invocations());
EXPECT_EQ(v, "00011110010110110011011111110111011") << dist;
}
{
absl::bernoulli_distribution dist(1.0 - kP);
auto v = generate(dist);
EXPECT_EQ(35, urbg.invocations());
EXPECT_EQ(v, "11111111111111111111011111111111111") << dist;
}
}
TEST(BernoulliTest, StabilityTest2) {
absl::random_internal::sequence_urbg urbg(
{0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
// Generate a string of '0' and '1' for the distribution output.
auto generate = [&urbg](absl::bernoulli_distribution& dist) {
std::string output;
output.reserve(13);
urbg.reset();
for (int i = 0; i < 12; i++) {
output.append(dist(urbg) ? "1" : "0");
}
return output;
};
constexpr double b0 = 1.0 / 13.0 / 0.2;
constexpr double b1 = 2.0 / 13.0 / 0.2;
constexpr double b3 = (5.0 / 13.0 / 0.2) - ((1 - b0) + (1 - b1) + (1 - b1));
{
absl::bernoulli_distribution dist(b0);
auto v = generate(dist);
EXPECT_EQ(12, urbg.invocations());
EXPECT_EQ(v, "000011100101") << dist;
}
{
absl::bernoulli_distribution dist(b1);
auto v = generate(dist);
EXPECT_EQ(12, urbg.invocations());
EXPECT_EQ(v, "001111101101") << dist;
}
{
absl::bernoulli_distribution dist(b3);
auto v = generate(dist);
EXPECT_EQ(12, urbg.invocations());
EXPECT_EQ(v, "001111101111") << dist;
}
}
} // namespace
