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// 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
//
//
// 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/uniform_real_distribution.h"
#include <cfloat>
#include <cmath>
#include <cstdint>
#include <iterator>
#include <random>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>
#include "gmock/gmock.h"
#include "gtest/gtest.h"
#include "absl/log/log.h"
#include "absl/numeric/internal/representation.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"
// NOTES:
// * Some documentation on generating random real values suggests that
// it is possible to use std::nextafter(b, DBL_MAX) to generate a value on
// the closed range [a, b]. Unfortunately, that technique is not universally
// reliable due to floating point quantization.
//
// * absl::uniform_real_distribution<float> generates between 2^28 and 2^29
// distinct floating point values in the range [0, 1).
//
// * absl::uniform_real_distribution<float> generates at least 2^23 distinct
// floating point values in the range [1, 2). This should be the same as
// any other range covered by a single exponent in IEEE 754.
//
// * absl::uniform_real_distribution<double> generates more than 2^52 distinct
// values in the range [0, 1), and should generate at least 2^52 distinct
// values in the range of [1, 2).
//
namespace {
template <typename RealType>
class UniformRealDistributionTest : public ::testing::Test {};
// double-double arithmetic is not supported well by either GCC or Clang; see
// with double doubles until compiler support is better.
using RealTypes =
std::conditional<absl::numeric_internal::IsDoubleDouble(),
::testing::Types<float, double>,
::testing::Types<float, double, long double>>::type;
TYPED_TEST_SUITE(UniformRealDistributionTest, RealTypes);
TYPED_TEST(UniformRealDistributionTest, ParamSerializeTest) {
#if (defined(__i386__) || defined(_M_IX86)) && FLT_EVAL_METHOD != 0
// We're using an x87-compatible FPU, and intermediate operations are
// performed with 80-bit floats. This produces slightly different results from
// what we expect below.
GTEST_SKIP()
<< "Skipping the test because we detected x87 floating-point semantics";
#endif
using DistributionType = absl::uniform_real_distribution<TypeParam>;
using real_type = TypeParam;
using param_type = typename DistributionType::param_type;
constexpr const real_type kMax = std::numeric_limits<real_type>::max();
constexpr const real_type kMin = std::numeric_limits<real_type>::min();
constexpr const real_type kEpsilon =
std::numeric_limits<real_type>::epsilon();
constexpr const real_type kLowest =
std::numeric_limits<real_type>::lowest(); // -max
const real_type kDenormMax = std::nextafter(kMin, real_type{0});
const real_type kOneMinusE =
std::nextafter(real_type{1}, real_type{0}); // 1 - epsilon
constexpr const real_type kTwo60{1152921504606846976}; // 2^60
constexpr int kCount = 1000;
absl::InsecureBitGen gen;
for (const auto& param : {
param_type(),
param_type(real_type{0}, real_type{1}),
param_type(real_type(-0.1), real_type(0.1)),
param_type(real_type(0.05), real_type(0.12)),
param_type(real_type(-0.05), real_type(0.13)),
param_type(real_type(-0.05), real_type(-0.02)),
// range = 0
param_type(real_type(2.0), real_type(2.0)), // Same
// double range = 0
// 2^60 , 2^60 + 2^6
param_type(kTwo60, real_type(1152921504606847040)),
// 2^60 , 2^60 + 2^7
param_type(kTwo60, real_type(1152921504606847104)),
// double range = 2^8
// 2^60 , 2^60 + 2^8
param_type(kTwo60, real_type(1152921504606847232)),
// float range = 0
// 2^60 , 2^60 + 2^36
param_type(kTwo60, real_type(1152921573326323712)),
// 2^60 , 2^60 + 2^37
param_type(kTwo60, real_type(1152921642045800448)),
// float range = 2^38
// 2^60 , 2^60 + 2^38
param_type(kTwo60, real_type(1152921779484753920)),
// Limits
param_type(0, kMax),
param_type(kLowest, 0),
param_type(0, kMin),
param_type(0, kEpsilon),
param_type(-kEpsilon, kEpsilon),
param_type(0, kOneMinusE),
param_type(0, kDenormMax),
}) {
// Validate parameters.
const auto a = param.a();
const auto b = param.b();
DistributionType before(a, b);
EXPECT_EQ(before.a(), param.a());
EXPECT_EQ(before.b(), param.b());
{
DistributionType via_param(param);
EXPECT_EQ(via_param, before);
}
std::stringstream ss;
ss << before;
DistributionType after(real_type(1.0), real_type(3.1));
EXPECT_NE(before.a(), after.a());
EXPECT_NE(before.b(), after.b());
EXPECT_NE(before.param(), after.param());
EXPECT_NE(before, after);
ss >> after;
EXPECT_EQ(before.a(), after.a());
EXPECT_EQ(before.b(), after.b());
EXPECT_EQ(before.param(), after.param());
EXPECT_EQ(before, after);
// Smoke test.
auto sample_min = after.max();
auto sample_max = after.min();
for (int i = 0; i < kCount; i++) {
auto sample = after(gen);
// Failure here indicates a bug in uniform_real_distribution::operator(),
// or bad parameters--range too large, etc.
if (after.min() == after.max()) {
EXPECT_EQ(sample, after.min());
} else {
EXPECT_GE(sample, after.min());
EXPECT_LT(sample, after.max());
}
if (sample > sample_max) {
sample_max = sample;
}
if (sample < sample_min) {
sample_min = sample;
}
}
if (!std::is_same<real_type, long double>::value) {
// static_cast<double>(long double) can overflow.
LOG(INFO) << "Range: " << static_cast<double>(sample_min) << ", "
<< static_cast<double>(sample_max);
}
}
}
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable:4756) // Constant arithmetic overflow.
#endif
TYPED_TEST(UniformRealDistributionTest, ViolatesPreconditionsDeathTest) {
using DistributionType = absl::uniform_real_distribution<TypeParam>;
using real_type = TypeParam;
#if GTEST_HAS_DEATH_TEST
// Hi < Lo
EXPECT_DEBUG_DEATH({ DistributionType dist(10.0, 1.0); }, "");
// Hi - Lo > numeric_limits<>::max()
EXPECT_DEBUG_DEATH(
{
DistributionType dist(std::numeric_limits<real_type>::lowest(),
std::numeric_limits<real_type>::max());
},
"");
// kEpsilon guarantees that max + kEpsilon = inf.
const auto kEpsilon = std::nexttoward(
(std::numeric_limits<real_type>::max() -
std::nexttoward(std::numeric_limits<real_type>::max(), 0.0)) /
2,
std::numeric_limits<real_type>::max());
EXPECT_DEBUG_DEATH(
{
DistributionType dist(-kEpsilon, std::numeric_limits<real_type>::max());
},
"");
EXPECT_DEBUG_DEATH(
{
DistributionType dist(std::numeric_limits<real_type>::lowest(),
kEpsilon);
},
"");
#endif // GTEST_HAS_DEATH_TEST
#if defined(NDEBUG)
// opt-mode, for invalid parameters, will generate a garbage value,
// but should not enter an infinite loop.
absl::InsecureBitGen gen;
{
DistributionType dist(10.0, 1.0);
auto x = dist(gen);
EXPECT_FALSE(std::isnan(x)) << x;
}
{
DistributionType dist(std::numeric_limits<real_type>::lowest(),
std::numeric_limits<real_type>::max());
auto x = dist(gen);
// Infinite result.
EXPECT_FALSE(std::isfinite(x)) << x;
}
#endif // NDEBUG
}
#ifdef _MSC_VER
#pragma warning(pop) // warning(disable:4756)
#endif
TYPED_TEST(UniformRealDistributionTest, TestMoments) {
using DistributionType = absl::uniform_real_distribution<TypeParam>;
constexpr int kSize = 1000000;
std::vector<double> values(kSize);
// 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};
DistributionType dist;
for (int i = 0; i < kSize; i++) {
values[i] = dist(rng);
}
const auto moments =
absl::random_internal::ComputeDistributionMoments(values);
EXPECT_NEAR(0.5, moments.mean, 0.01);
EXPECT_NEAR(1 / 12.0, moments.variance, 0.015);
EXPECT_NEAR(0.0, moments.skewness, 0.02);
EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.015);
}
TYPED_TEST(UniformRealDistributionTest, ChiSquaredTest50) {
using DistributionType = absl::uniform_real_distribution<TypeParam>;
using param_type = typename DistributionType::param_type;
using absl::random_internal::kChiSquared;
constexpr size_t kTrials = 100000;
constexpr int kBuckets = 50;
constexpr double kExpected =
static_cast<double>(kTrials) / static_cast<double>(kBuckets);
// 1-in-100000 threshold, but remember, there are about 8 tests
// in this file. And the test could fail for other reasons.
// Empirically validated with --runs_per_test=10000.
const int kThreshold =
absl::random_internal::ChiSquareValue(kBuckets - 1, 0.999999);
// 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};
for (const auto& param : {param_type(0, 1), param_type(5, 12),
param_type(-5, 13), param_type(-5, -2)}) {
const double min_val = param.a();
const double max_val = param.b();
const double factor = kBuckets / (max_val - min_val);
std::vector<int32_t> counts(kBuckets, 0);
DistributionType dist(param);
for (size_t i = 0; i < kTrials; i++) {
auto x = dist(rng);
auto bucket = static_cast<size_t>((x - min_val) * factor);
counts[bucket]++;
}
double chi_square = absl::random_internal::ChiSquareWithExpected(
std::begin(counts), std::end(counts), kExpected);
if (chi_square > kThreshold) {
double p_value =
absl::random_internal::ChiSquarePValue(chi_square, kBuckets);
// Chi-squared test failed. Output does not appear to be uniform.
std::string msg;
for (const auto& a : counts) {
absl::StrAppend(&msg, a, "\n");
}
absl::StrAppend(&msg, kChiSquared, " p-value ", p_value, "\n");
absl::StrAppend(&msg, "High ", kChiSquared, " value: ", chi_square, " > ",
kThreshold);
LOG(INFO) << msg;
FAIL() << msg;
}
}
}
TYPED_TEST(UniformRealDistributionTest, StabilityTest) {
using DistributionType = absl::uniform_real_distribution<TypeParam>;
using real_type = TypeParam;
// absl::uniform_real_distribution stability relies only on
// random_internal::GenerateRealFromBits.
absl::random_internal::sequence_urbg urbg(
{0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
std::vector<int> output(12);
DistributionType dist;
std::generate(std::begin(output), std::end(output), [&] {
return static_cast<int>(real_type(1000000) * dist(urbg));
});
EXPECT_THAT(
output, //
testing::ElementsAre(59, 999246, 762494, 395876, 167716, 82545, 925251,
77341, 12527, 708791, 834451, 932808));
}
TEST(UniformRealDistributionTest, AlgorithmBounds) {
absl::uniform_real_distribution<double> dist;
{
// This returns the smallest value >0 from absl::uniform_real_distribution.
absl::random_internal::sequence_urbg urbg({0x0000000000000001ull});
double a = dist(urbg);
EXPECT_EQ(a, 5.42101086242752217004e-20);
}
{
// This returns a value very near 0.5 from absl::uniform_real_distribution.
absl::random_internal::sequence_urbg urbg({0x7fffffffffffffefull});
double a = dist(urbg);
EXPECT_EQ(a, 0.499999999999999944489);
}
{
// This returns a value very near 0.5 from absl::uniform_real_distribution.
absl::random_internal::sequence_urbg urbg({0x8000000000000000ull});
double a = dist(urbg);
EXPECT_EQ(a, 0.5);
}
{
// This returns the largest value <1 from absl::uniform_real_distribution.
absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFEFull});
double a = dist(urbg);
EXPECT_EQ(a, 0.999999999999999888978);
}
{
// This *ALSO* returns the largest value <1.
absl::random_internal::sequence_urbg urbg({0xFFFFFFFFFFFFFFFFull});
double a = dist(urbg);
EXPECT_EQ(a, 0.999999999999999888978);
}
}
} // namespace