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Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
// 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/beta_distribution.h"
#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <iterator>
#include <random>
#include <sstream>
#include <string>
#include <unordered_map>
#include <vector>
#include "gmock/gmock.h"
#include "gtest/gtest.h"
#include "absl/base/internal/raw_logging.h"
#include "absl/random/internal/chi_square.h"
#include "absl/random/internal/distribution_test_util.h"
#include "absl/random/internal/pcg_engine.h"
#include "absl/random/internal/sequence_urbg.h"
#include "absl/random/random.h"
#include "absl/strings/str_cat.h"
#include "absl/strings/str_format.h"
#include "absl/strings/str_replace.h"
#include "absl/strings/strip.h"
namespace {
template <typename IntType>
class BetaDistributionInterfaceTest : public ::testing::Test {};
using RealTypes = ::testing::Types<float, double, long double>;
TYPED_TEST_CASE(BetaDistributionInterfaceTest, RealTypes);
TYPED_TEST(BetaDistributionInterfaceTest, SerializeTest) {
// The threshold for whether std::exp(1/a) is finite.
const TypeParam kSmallA =
1.0f / std::log((std::numeric_limits<TypeParam>::max)());
// The threshold for whether a * std::log(a) is finite.
const TypeParam kLargeA =
std::exp(std::log((std::numeric_limits<TypeParam>::max)()) -
std::log(std::log((std::numeric_limits<TypeParam>::max)())));
const TypeParam kLargeAPPC = std::exp(
std::log((std::numeric_limits<TypeParam>::max)()) -
std::log(std::log((std::numeric_limits<TypeParam>::max)())) - 10.0f);
using param_type = typename absl::beta_distribution<TypeParam>::param_type;
constexpr int kCount = 1000;
absl::InsecureBitGen gen;
const TypeParam kValues[] = {
TypeParam(1e-20), TypeParam(1e-12), TypeParam(1e-8), TypeParam(1e-4),
TypeParam(1e-3), TypeParam(0.1), TypeParam(0.25),
std::nextafter(TypeParam(0.5), TypeParam(0)), // 0.5 - epsilon
std::nextafter(TypeParam(0.5), TypeParam(1)), // 0.5 + epsilon
TypeParam(0.5), TypeParam(1.0), //
std::nextafter(TypeParam(1), TypeParam(0)), // 1 - epsilon
std::nextafter(TypeParam(1), TypeParam(2)), // 1 + epsilon
TypeParam(12.5), TypeParam(1e2), TypeParam(1e8), TypeParam(1e12),
TypeParam(1e20), //
kSmallA, //
std::nextafter(kSmallA, TypeParam(0)), //
std::nextafter(kSmallA, TypeParam(1)), //
kLargeA, //
std::nextafter(kLargeA, TypeParam(0)), //
std::nextafter(kLargeA, std::numeric_limits<TypeParam>::max()),
kLargeAPPC, //
std::nextafter(kLargeAPPC, TypeParam(0)),
std::nextafter(kLargeAPPC, std::numeric_limits<TypeParam>::max()),
// Boundary cases.
std::numeric_limits<TypeParam>::max(),
std::numeric_limits<TypeParam>::epsilon(),
std::nextafter(std::numeric_limits<TypeParam>::min(),
TypeParam(1)), // min + epsilon
std::numeric_limits<TypeParam>::min(), // smallest normal
std::numeric_limits<TypeParam>::denorm_min(), // smallest denorm
std::numeric_limits<TypeParam>::min() / 2, // denorm
std::nextafter(std::numeric_limits<TypeParam>::min(),
TypeParam(0)), // denorm_max
};
for (TypeParam alpha : kValues) {
for (TypeParam beta : kValues) {
ABSL_INTERNAL_LOG(
INFO, absl::StrFormat("Smoke test for Beta(%a, %a)", alpha, beta));
param_type param(alpha, beta);
absl::beta_distribution<TypeParam> before(alpha, beta);
EXPECT_EQ(before.alpha(), param.alpha());
EXPECT_EQ(before.beta(), param.beta());
{
absl::beta_distribution<TypeParam> via_param(param);
EXPECT_EQ(via_param, before);
EXPECT_EQ(via_param.param(), before.param());
}
// Smoke test.
for (int i = 0; i < kCount; ++i) {
auto sample = before(gen);
EXPECT_TRUE(std::isfinite(sample));
EXPECT_GE(sample, before.min());
EXPECT_LE(sample, before.max());
}
// Validate stream serialization.
std::stringstream ss;
ss << before;
absl::beta_distribution<TypeParam> after(3.8f, 1.43f);
EXPECT_NE(before.alpha(), after.alpha());
EXPECT_NE(before.beta(), after.beta());
EXPECT_NE(before.param(), after.param());
EXPECT_NE(before, after);
ss >> after;
#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \
defined(__ppc__) || defined(__PPC__)
if (std::is_same<TypeParam, long double>::value) {
// Roundtripping floating point values requires sufficient precision
// to reconstruct the exact value. It turns out that long double
// has some errors doing this on ppc.
if (alpha <= std::numeric_limits<double>::max() &&
alpha >= std::numeric_limits<double>::lowest()) {
EXPECT_EQ(static_cast<double>(before.alpha()),
static_cast<double>(after.alpha()))
<< ss.str();
}
if (beta <= std::numeric_limits<double>::max() &&
beta >= std::numeric_limits<double>::lowest()) {
EXPECT_EQ(static_cast<double>(before.beta()),
static_cast<double>(after.beta()))
<< ss.str();
}
continue;
}
#endif
EXPECT_EQ(before.alpha(), after.alpha());
EXPECT_EQ(before.beta(), after.beta());
EXPECT_EQ(before, after) //
<< ss.str() << " " //
<< (ss.good() ? "good " : "") //
<< (ss.bad() ? "bad " : "") //
<< (ss.eof() ? "eof " : "") //
<< (ss.fail() ? "fail " : "");
}
}
}
TYPED_TEST(BetaDistributionInterfaceTest, DegenerateCases) {
// 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);
// Extreme cases when the params are abnormal.
constexpr int kCount = 1000;
const TypeParam kSmallValues[] = {
std::numeric_limits<TypeParam>::min(),
std::numeric_limits<TypeParam>::denorm_min(),
std::nextafter(std::numeric_limits<TypeParam>::min(),
TypeParam(0)), // denorm_max
std::numeric_limits<TypeParam>::epsilon(),
};
const TypeParam kLargeValues[] = {
std::numeric_limits<TypeParam>::max() * static_cast<TypeParam>(0.9999),
std::numeric_limits<TypeParam>::max() - 1,
std::numeric_limits<TypeParam>::max(),
};
{
// Small alpha and beta.
// Useful WolframAlpha plots:
// * plot InverseBetaRegularized[x, 0.0001, 0.0001] from 0.495 to 0.505
// * Beta[1.0, 0.0000001, 0.0000001]
// * Beta[0.9999, 0.0000001, 0.0000001]
for (TypeParam alpha : kSmallValues) {
for (TypeParam beta : kSmallValues) {
int zeros = 0;
int ones = 0;
absl::beta_distribution<TypeParam> d(alpha, beta);
for (int i = 0; i < kCount; ++i) {
TypeParam x = d(rng);
if (x == 0.0) {
zeros++;
} else if (x == 1.0) {
ones++;
}
}
EXPECT_EQ(ones + zeros, kCount);
if (alpha == beta) {
EXPECT_NE(ones, 0);
EXPECT_NE(zeros, 0);
}
}
}
}
{
// Small alpha, large beta.
// Useful WolframAlpha plots:
// * plot InverseBetaRegularized[x, 0.0001, 10000] from 0.995 to 1
// * Beta[0, 0.0000001, 1000000]
// * Beta[0.001, 0.0000001, 1000000]
// * Beta[1, 0.0000001, 1000000]
for (TypeParam alpha : kSmallValues) {
for (TypeParam beta : kLargeValues) {
absl::beta_distribution<TypeParam> d(alpha, beta);
for (int i = 0; i < kCount; ++i) {
EXPECT_EQ(d(rng), 0.0);
}
}
}
}
{
// Large alpha, small beta.
// Useful WolframAlpha plots:
// * plot InverseBetaRegularized[x, 10000, 0.0001] from 0 to 0.001
// * Beta[0.99, 1000000, 0.0000001]
// * Beta[1, 1000000, 0.0000001]
for (TypeParam alpha : kLargeValues) {
for (TypeParam beta : kSmallValues) {
absl::beta_distribution<TypeParam> d(alpha, beta);
for (int i = 0; i < kCount; ++i) {
EXPECT_EQ(d(rng), 1.0);
}
}
}
}
{
// Large alpha and beta.
absl::beta_distribution<TypeParam> d(std::numeric_limits<TypeParam>::max(),
std::numeric_limits<TypeParam>::max());
for (int i = 0; i < kCount; ++i) {
EXPECT_EQ(d(rng), 0.5);
}
}
{
// Large alpha and beta but unequal.
absl::beta_distribution<TypeParam> d(
std::numeric_limits<TypeParam>::max(),
std::numeric_limits<TypeParam>::max() * 0.9999);
for (int i = 0; i < kCount; ++i) {
TypeParam x = d(rng);
EXPECT_NE(x, 0.5f);
EXPECT_FLOAT_EQ(x, 0.500025f);
}
}
}
class BetaDistributionModel {
public:
explicit BetaDistributionModel(::testing::tuple<double, double> p)
: alpha_(::testing::get<0>(p)), beta_(::testing::get<1>(p)) {}
double Mean() const { return alpha_ / (alpha_ + beta_); }
double Variance() const {
return alpha_ * beta_ / (alpha_ + beta_ + 1) / (alpha_ + beta_) /
(alpha_ + beta_);
}
double Kurtosis() const {
return 3 + 6 *
((alpha_ - beta_) * (alpha_ - beta_) * (alpha_ + beta_ + 1) -
alpha_ * beta_ * (2 + alpha_ + beta_)) /
alpha_ / beta_ / (alpha_ + beta_ + 2) / (alpha_ + beta_ + 3);
}
protected:
const double alpha_;
const double beta_;
};
class BetaDistributionTest
: public ::testing::TestWithParam<::testing::tuple<double, double>>,
public BetaDistributionModel {
public:
BetaDistributionTest() : BetaDistributionModel(GetParam()) {}
protected:
template <class D>
bool SingleZTestOnMeanAndVariance(double p, size_t samples);
template <class D>
bool SingleChiSquaredTest(double p, size_t samples, size_t buckets);
absl::InsecureBitGen rng_;
};
template <class D>
bool BetaDistributionTest::SingleZTestOnMeanAndVariance(double p,
size_t samples) {
D dis(alpha_, beta_);
std::vector<double> data;
data.reserve(samples);
for (size_t i = 0; i < samples; i++) {
const double variate = dis(rng_);
EXPECT_FALSE(std::isnan(variate));
// Note that equality is allowed on both sides.
EXPECT_GE(variate, 0.0);
EXPECT_LE(variate, 1.0);
data.push_back(variate);
}
// We validate that the sample mean and sample variance are indeed from a
// Beta distribution with the given shape parameters.
const auto m = absl::random_internal::ComputeDistributionMoments(data);
// The variance of the sample mean is variance / n.
const double mean_stddev = std::sqrt(Variance() / static_cast<double>(m.n));
// The variance of the sample variance is (approximately):
// (kurtosis - 1) * variance^2 / n
const double variance_stddev = std::sqrt(
(Kurtosis() - 1) * Variance() * Variance() / static_cast<double>(m.n));
// z score for the sample variance.
const double z_variance = (m.variance - Variance()) / variance_stddev;
const double max_err = absl::random_internal::MaxErrorTolerance(p);
const double z_mean = absl::random_internal::ZScore(Mean(), m);
const bool pass =
absl::random_internal::Near("z", z_mean, 0.0, max_err) &&
absl::random_internal::Near("z_variance", z_variance, 0.0, max_err);
if (!pass) {
ABSL_INTERNAL_LOG(
INFO,
absl::StrFormat(
"Beta(%f, %f), "
"mean: sample %f, expect %f, which is %f stddevs away, "
"variance: sample %f, expect %f, which is %f stddevs away.",
alpha_, beta_, m.mean, Mean(),
std::abs(m.mean - Mean()) / mean_stddev, m.variance, Variance(),
std::abs(m.variance - Variance()) / variance_stddev));
}
return pass;
}
template <class D>
bool BetaDistributionTest::SingleChiSquaredTest(double p, size_t samples,
size_t buckets) {
constexpr double kErr = 1e-7;
std::vector<double> cutoffs, expected;
const double bucket_width = 1.0 / static_cast<double>(buckets);
int i = 1;
int unmerged_buckets = 0;
for (; i < buckets; ++i) {
const double p = bucket_width * static_cast<double>(i);
const double boundary =
absl::random_internal::BetaIncompleteInv(alpha_, beta_, p);
// The intention is to add `boundary` to the list of `cutoffs`. It becomes
// problematic, however, when the boundary values are not monotone, due to
// numerical issues when computing the inverse regularized incomplete
// Beta function. In these cases, we merge that bucket with its previous
// neighbor and merge their expected counts.
if ((cutoffs.empty() && boundary < kErr) ||
(!cutoffs.empty() && boundary <= cutoffs.back())) {
unmerged_buckets++;
continue;
}
if (boundary >= 1.0 - 1e-10) {
break;
}
cutoffs.push_back(boundary);
expected.push_back(static_cast<double>(1 + unmerged_buckets) *
bucket_width * static_cast<double>(samples));
unmerged_buckets = 0;
}
cutoffs.push_back(std::numeric_limits<double>::infinity());
// Merge all remaining buckets.
expected.push_back(static_cast<double>(buckets - i + 1) * bucket_width *
static_cast<double>(samples));
// Make sure that we don't merge all the buckets, making this test
// meaningless.
EXPECT_GE(cutoffs.size(), 3) << alpha_ << ", " << beta_;
D dis(alpha_, beta_);
std::vector<int32_t> counts(cutoffs.size(), 0);
for (int i = 0; i < samples; i++) {
const double x = dis(rng_);
auto it = std::upper_bound(cutoffs.begin(), cutoffs.end(), x);
counts[std::distance(cutoffs.begin(), it)]++;
}
// Null-hypothesis is that the distribution is beta distributed with the
// provided alpha, beta params (not estimated from the data).
const int dof = cutoffs.size() - 1;
const double chi_square = absl::random_internal::ChiSquare(
counts.begin(), counts.end(), expected.begin(), expected.end());
const bool pass =
(absl::random_internal::ChiSquarePValue(chi_square, dof) >= p);
if (!pass) {
for (int i = 0; i < cutoffs.size(); i++) {
ABSL_INTERNAL_LOG(
INFO, absl::StrFormat("cutoff[%d] = %f, actual count %d, expected %d",
i, cutoffs[i], counts[i],
static_cast<int>(expected[i])));
}
ABSL_INTERNAL_LOG(
INFO, absl::StrFormat(
"Beta(%f, %f) %s %f, p = %f", alpha_, beta_,
absl::random_internal::kChiSquared, chi_square,
absl::random_internal::ChiSquarePValue(chi_square, dof)));
}
return pass;
}
TEST_P(BetaDistributionTest, TestSampleStatistics) {
static constexpr int kRuns = 20;
static constexpr double kPFail = 0.02;
const double p =
absl::random_internal::RequiredSuccessProbability(kPFail, kRuns);
static constexpr int kSampleCount = 10000;
static constexpr int kBucketCount = 100;
int failed = 0;
for (int i = 0; i < kRuns; ++i) {
if (!SingleZTestOnMeanAndVariance<absl::beta_distribution<double>>(
p, kSampleCount)) {
failed++;
}
if (!SingleChiSquaredTest<absl::beta_distribution<double>>(
0.005, kSampleCount, kBucketCount)) {
failed++;
}
}
// Set so that the test is not flaky at --runs_per_test=10000
EXPECT_LE(failed, 5);
}
std::string ParamName(
const ::testing::TestParamInfo<::testing::tuple<double, double>>& info) {
std::string name = absl::StrCat("alpha_", ::testing::get<0>(info.param),
"__beta_", ::testing::get<1>(info.param));
return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
}
INSTANTIATE_TEST_CASE_P(
TestSampleStatisticsCombinations, BetaDistributionTest,
::testing::Combine(::testing::Values(0.1, 0.2, 0.9, 1.1, 2.5, 10.0, 123.4),
::testing::Values(0.1, 0.2, 0.9, 1.1, 2.5, 10.0, 123.4)),
ParamName);
INSTANTIATE_TEST_CASE_P(
TestSampleStatistics_SelectedPairs, BetaDistributionTest,
::testing::Values(std::make_pair(0.5, 1000), std::make_pair(1000, 0.5),
std::make_pair(900, 1000), std::make_pair(10000, 20000),
std::make_pair(4e5, 2e7), std::make_pair(1e7, 1e5)),
ParamName);
// NOTE: absl::beta_distribution is not guaranteed to be stable.
TEST(BetaDistributionTest, StabilityTest) {
// absl::beta_distribution stability relies on the stability of
// absl::random_interna::RandU64ToDouble, std::exp, std::log, std::pow,
// and std::sqrt.
//
// This test also depends on the stability of std::frexp.
using testing::ElementsAre;
absl::random_internal::sequence_urbg urbg({
0xffff00000000e6c8ull, 0xffff0000000006c8ull, 0x800003766295CFA9ull,
0x11C819684E734A41ull, 0x832603766295CFA9ull, 0x7fbe76c8b4395800ull,
0xB3472DCA7B14A94Aull, 0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull,
0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull, 0x00035C904C70A239ull,
0x00009E0BCBAADE14ull, 0x0000000000622CA7ull, 0x4864f22c059bf29eull,
0x247856d8b862665cull, 0xe46e86e9a1337e10ull, 0xd8c8541f3519b133ull,
0xffe75b52c567b9e4ull, 0xfffff732e5709c5bull, 0xff1f7f0b983532acull,
0x1ec2e8986d2362caull, 0xC332DDEFBE6C5AA5ull, 0x6558218568AB9702ull,
0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull, 0xECDD4775619F1510ull,
0x814c8e35fe9a961aull, 0x0c3cd59c9b638a02ull, 0xcb3bb6478a07715cull,
0x1224e62c978bbc7full, 0x671ef2cb04e81f6eull, 0x3c1cbd811eaf1808ull,
0x1bbc23cfa8fac721ull, 0xa4c2cda65e596a51ull, 0xb77216fad37adf91ull,
0x836d794457c08849ull, 0xe083df03475f49d7ull, 0xbc9feb512e6b0d6cull,
0xb12d74fdd718c8c5ull, 0x12ff09653bfbe4caull, 0x8dd03a105bc4ee7eull,
0x5738341045ba0d85ull, 0xf3fd722dc65ad09eull, 0xfa14fd21ea2a5705ull,
0xffe6ea4d6edb0c73ull, 0xD07E9EFE2BF11FB4ull, 0x95DBDA4DAE909198ull,
0xEAAD8E716B93D5A0ull, 0xD08ED1D0AFC725E0ull, 0x8E3C5B2F8E7594B7ull,
0x8FF6E2FBF2122B64ull, 0x8888B812900DF01Cull, 0x4FAD5EA0688FC31Cull,
0xD1CFF191B3A8C1ADull, 0x2F2F2218BE0E1777ull, 0xEA752DFE8B021FA1ull,
});
// Convert the real-valued result into a unit64 where we compare
// 5 (float) or 10 (double) decimal digits plus the base-2 exponent.
auto float_to_u64 = [](float d) {
int exp = 0;
auto f = std::frexp(d, &exp);
return (static_cast<uint64_t>(1e5 * f) * 10000) + std::abs(exp);
};
auto double_to_u64 = [](double d) {
int exp = 0;
auto f = std::frexp(d, &exp);
return (static_cast<uint64_t>(1e10 * f) * 10000) + std::abs(exp);
};
std::vector<uint64_t> output(20);
{
// Algorithm Joehnk (float)
absl::beta_distribution<float> dist(0.1f, 0.2f);
std::generate(std::begin(output), std::end(output),
[&] { return float_to_u64(dist(urbg)); });
EXPECT_EQ(44, urbg.invocations());
EXPECT_THAT(output, //
testing::ElementsAre(
998340000, 619030004, 500000001, 999990000, 996280000,
500000001, 844740004, 847210001, 999970000, 872320000,
585480007, 933280000, 869080042, 647670031, 528240004,
969980004, 626050008, 915930002, 833440033, 878040015));
}
urbg.reset();
{
// Algorithm Joehnk (double)
absl::beta_distribution<double> dist(0.1, 0.2);
std::generate(std::begin(output), std::end(output),
[&] { return double_to_u64(dist(urbg)); });
EXPECT_EQ(44, urbg.invocations());
EXPECT_THAT(
output, //
testing::ElementsAre(
99834713000000, 61903356870004, 50000000000001, 99999721170000,
99628374770000, 99999999990000, 84474397860004, 84721276240001,
99997407490000, 87232528120000, 58548364780007, 93328932910000,
86908237770042, 64767917930031, 52824581970004, 96998544140004,
62605946270008, 91593604380002, 83345031740033, 87804397230015));
}
urbg.reset();
{
// Algorithm Cheng 1
absl::beta_distribution<double> dist(0.9, 2.0);
std::generate(std::begin(output), std::end(output),
[&] { return double_to_u64(dist(urbg)); });
EXPECT_EQ(62, urbg.invocations());
EXPECT_THAT(
output, //
testing::ElementsAre(
62069004780001, 64433204450001, 53607416560000, 89644295430008,
61434586310019, 55172615890002, 62187161490000, 56433684810003,
80454622050005, 86418558710003, 92920514700001, 64645184680001,
58549183380000, 84881283650005, 71078728590002, 69949694970000,
73157461710001, 68592191300001, 70747623900000, 78584696930005));
}
urbg.reset();
{
// Algorithm Cheng 2
absl::beta_distribution<double> dist(1.5, 2.5);
std::generate(std::begin(output), std::end(output),
[&] { return double_to_u64(dist(urbg)); });
EXPECT_EQ(54, urbg.invocations());
EXPECT_THAT(
output, //
testing::ElementsAre(
75000029250001, 76751482860001, 53264575220000, 69193133650005,
78028324470013, 91573587560002, 59167523770000, 60658618560002,
80075870540000, 94141320460004, 63196592770003, 78883906300002,
96797992590001, 76907587800001, 56645167560000, 65408302280003,
53401156320001, 64731238570000, 83065573750001, 79788333820001));
}
}
// This is an implementation-specific test. If any part of the implementation
// changes, then it is likely that this test will change as well. Also, if
// dependencies of the distribution change, such as RandU64ToDouble, then this
// is also likely to change.
TEST(BetaDistributionTest, AlgorithmBounds) {
{
absl::random_internal::sequence_urbg urbg(
{0x7fbe76c8b4395800ull, 0x8000000000000000ull});
// u=0.499, v=0.5
absl::beta_distribution<double> dist(1e-4, 1e-4);
double a = dist(urbg);
EXPECT_EQ(a, 2.0202860861567108529e-09);
EXPECT_EQ(2, urbg.invocations());
}
// Test that both the float & double algorithms appropriately reject the
// initial draw.
{
// 1/alpha = 1/beta = 2.
absl::beta_distribution<float> dist(0.5, 0.5);
// first two outputs are close to 1.0 - epsilon,
// thus: (u ^ 2 + v ^ 2) > 1.0
absl::random_internal::sequence_urbg urbg(
{0xffff00000006e6c8ull, 0xffff00000007c7c8ull, 0x800003766295CFA9ull,
0x11C819684E734A41ull});
{
double y = absl::beta_distribution<double>(0.5, 0.5)(urbg);
EXPECT_EQ(4, urbg.invocations());
EXPECT_EQ(y, 0.9810668952633862) << y;
}
// ...and: log(u) * a ~= log(v) * b ~= -0.02
// thus z ~= -0.02 + log(1 + e(~0))
// ~= -0.02 + 0.69
// thus z > 0
urbg.reset();
{
float x = absl::beta_distribution<float>(0.5, 0.5)(urbg);
EXPECT_EQ(4, urbg.invocations());
EXPECT_NEAR(0.98106688261032104, x, 0.0000005) << x << "f";
}
}
}
} // namespace