466 lines
16 KiB
C++
466 lines
16 KiB
C++
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// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "absl/random/distributions.h"
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#include <cfloat>
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#include <cmath>
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#include <cstdint>
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#include <random>
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#include <vector>
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#include "gtest/gtest.h"
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#include "absl/random/internal/distribution_test_util.h"
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#include "absl/random/random.h"
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namespace {
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constexpr int kSize = 400000;
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class RandomDistributionsTest : public testing::Test {};
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struct Invalid {};
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template <typename A, typename B>
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auto InferredUniformReturnT(int)
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-> decltype(absl::Uniform(std::declval<absl::InsecureBitGen&>(),
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std::declval<A>(), std::declval<B>()));
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template <typename, typename>
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Invalid InferredUniformReturnT(...);
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template <typename TagType, typename A, typename B>
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auto InferredTaggedUniformReturnT(int)
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-> decltype(absl::Uniform(std::declval<TagType>(),
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std::declval<absl::InsecureBitGen&>(),
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std::declval<A>(), std::declval<B>()));
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template <typename, typename, typename>
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Invalid InferredTaggedUniformReturnT(...);
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// Given types <A, B, Expect>, CheckArgsInferType() verifies that
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//
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// absl::Uniform(gen, A{}, B{})
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//
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// returns the type "Expect".
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//
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// This interface can also be used to assert that a given absl::Uniform()
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// overload does not exist / will not compile. Given types <A, B>, the
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// expression
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//
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// decltype(absl::Uniform(..., std::declval<A>(), std::declval<B>()))
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//
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// will not compile, leaving the definition of InferredUniformReturnT<A, B> to
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// resolve (via SFINAE) to the overload which returns type "Invalid". This
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// allows tests to assert that an invocation such as
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//
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// absl::Uniform(gen, 1.23f, std::numeric_limits<int>::max() - 1)
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//
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// should not compile, since neither type, float nor int, can precisely
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// represent both endpoint-values. Writing:
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//
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// CheckArgsInferType<float, int, Invalid>()
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//
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// will assert that this overload does not exist.
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template <typename A, typename B, typename Expect>
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void CheckArgsInferType() {
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static_assert(
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absl::conjunction<
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std::is_same<Expect, decltype(InferredUniformReturnT<A, B>(0))>,
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std::is_same<Expect,
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decltype(InferredUniformReturnT<B, A>(0))>>::value,
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"");
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static_assert(
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absl::conjunction<
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std::is_same<Expect, decltype(InferredTaggedUniformReturnT<
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absl::IntervalOpenOpenTag, A, B>(0))>,
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std::is_same<Expect,
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decltype(InferredTaggedUniformReturnT<
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absl::IntervalOpenOpenTag, B, A>(0))>>::value,
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"");
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}
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template <typename A, typename B, typename ExplicitRet>
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auto ExplicitUniformReturnT(int) -> decltype(
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absl::Uniform<ExplicitRet>(*std::declval<absl::InsecureBitGen*>(),
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std::declval<A>(), std::declval<B>()));
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template <typename, typename, typename ExplicitRet>
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Invalid ExplicitUniformReturnT(...);
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template <typename TagType, typename A, typename B, typename ExplicitRet>
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auto ExplicitTaggedUniformReturnT(int) -> decltype(absl::Uniform<ExplicitRet>(
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std::declval<TagType>(), *std::declval<absl::InsecureBitGen*>(),
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std::declval<A>(), std::declval<B>()));
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template <typename, typename, typename, typename ExplicitRet>
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Invalid ExplicitTaggedUniformReturnT(...);
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// Given types <A, B, Expect>, CheckArgsReturnExpectedType() verifies that
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//
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// absl::Uniform<Expect>(gen, A{}, B{})
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//
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// returns the type "Expect", and that the function-overload has the signature
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//
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// Expect(URBG&, Expect, Expect)
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template <typename A, typename B, typename Expect>
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void CheckArgsReturnExpectedType() {
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static_assert(
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absl::conjunction<
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std::is_same<Expect,
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decltype(ExplicitUniformReturnT<A, B, Expect>(0))>,
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std::is_same<Expect, decltype(ExplicitUniformReturnT<B, A, Expect>(
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0))>>::value,
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"");
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static_assert(
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absl::conjunction<
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std::is_same<Expect,
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decltype(ExplicitTaggedUniformReturnT<
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absl::IntervalOpenOpenTag, A, B, Expect>(0))>,
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std::is_same<Expect, decltype(ExplicitTaggedUniformReturnT<
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absl::IntervalOpenOpenTag, B, A,
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Expect>(0))>>::value,
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"");
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}
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TEST_F(RandomDistributionsTest, UniformTypeInference) {
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// Infers common types.
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CheckArgsInferType<uint16_t, uint16_t, uint16_t>();
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CheckArgsInferType<uint32_t, uint32_t, uint32_t>();
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CheckArgsInferType<uint64_t, uint64_t, uint64_t>();
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CheckArgsInferType<int16_t, int16_t, int16_t>();
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CheckArgsInferType<int32_t, int32_t, int32_t>();
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CheckArgsInferType<int64_t, int64_t, int64_t>();
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CheckArgsInferType<float, float, float>();
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CheckArgsInferType<double, double, double>();
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// Explicitly-specified return-values override inferences.
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CheckArgsReturnExpectedType<int16_t, int16_t, int32_t>();
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CheckArgsReturnExpectedType<uint16_t, uint16_t, int32_t>();
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CheckArgsReturnExpectedType<int16_t, int16_t, int64_t>();
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CheckArgsReturnExpectedType<int16_t, int32_t, int64_t>();
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CheckArgsReturnExpectedType<int16_t, int32_t, double>();
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CheckArgsReturnExpectedType<float, float, double>();
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CheckArgsReturnExpectedType<int, int, int16_t>();
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// Properly promotes uint16_t.
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CheckArgsInferType<uint16_t, uint32_t, uint32_t>();
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CheckArgsInferType<uint16_t, uint64_t, uint64_t>();
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CheckArgsInferType<uint16_t, int32_t, int32_t>();
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CheckArgsInferType<uint16_t, int64_t, int64_t>();
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CheckArgsInferType<uint16_t, float, float>();
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CheckArgsInferType<uint16_t, double, double>();
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// Properly promotes int16_t.
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CheckArgsInferType<int16_t, int32_t, int32_t>();
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CheckArgsInferType<int16_t, int64_t, int64_t>();
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CheckArgsInferType<int16_t, float, float>();
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CheckArgsInferType<int16_t, double, double>();
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// Invalid (u)int16_t-pairings do not compile.
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// See "CheckArgsInferType" comments above, for how this is achieved.
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CheckArgsInferType<uint16_t, int16_t, Invalid>();
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CheckArgsInferType<int16_t, uint32_t, Invalid>();
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CheckArgsInferType<int16_t, uint64_t, Invalid>();
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// Properly promotes uint32_t.
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CheckArgsInferType<uint32_t, uint64_t, uint64_t>();
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CheckArgsInferType<uint32_t, int64_t, int64_t>();
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CheckArgsInferType<uint32_t, double, double>();
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// Properly promotes int32_t.
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CheckArgsInferType<int32_t, int64_t, int64_t>();
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CheckArgsInferType<int32_t, double, double>();
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// Invalid (u)int32_t-pairings do not compile.
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CheckArgsInferType<uint32_t, int32_t, Invalid>();
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CheckArgsInferType<int32_t, uint64_t, Invalid>();
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CheckArgsInferType<int32_t, float, Invalid>();
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CheckArgsInferType<uint32_t, float, Invalid>();
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// Invalid (u)int64_t-pairings do not compile.
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CheckArgsInferType<uint64_t, int64_t, Invalid>();
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CheckArgsInferType<int64_t, float, Invalid>();
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CheckArgsInferType<int64_t, double, Invalid>();
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// Properly promotes float.
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CheckArgsInferType<float, double, double>();
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}
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TEST_F(RandomDistributionsTest, UniformExamples) {
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// Examples.
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absl::InsecureBitGen gen;
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EXPECT_NE(1, absl::Uniform(gen, static_cast<uint16_t>(0), 1.0f));
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EXPECT_NE(1, absl::Uniform(gen, 0, 1.0));
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EXPECT_NE(1, absl::Uniform(absl::IntervalOpenOpen, gen,
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static_cast<uint16_t>(0), 1.0f));
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EXPECT_NE(1, absl::Uniform(absl::IntervalOpenOpen, gen, 0, 1.0));
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EXPECT_NE(1, absl::Uniform(absl::IntervalOpenOpen, gen, -1, 1.0));
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EXPECT_NE(1, absl::Uniform<double>(absl::IntervalOpenOpen, gen, -1, 1));
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EXPECT_NE(1, absl::Uniform<float>(absl::IntervalOpenOpen, gen, 0, 1));
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EXPECT_NE(1, absl::Uniform<float>(gen, 0, 1));
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}
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TEST_F(RandomDistributionsTest, UniformNoBounds) {
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absl::InsecureBitGen gen;
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absl::Uniform<uint8_t>(gen);
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absl::Uniform<uint16_t>(gen);
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absl::Uniform<uint32_t>(gen);
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absl::Uniform<uint64_t>(gen);
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}
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TEST_F(RandomDistributionsTest, UniformNonsenseRanges) {
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// The ranges used in this test are undefined behavior.
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// The results are arbitrary and subject to future changes.
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#if (defined(__i386__) || defined(_M_IX86)) && FLT_EVAL_METHOD != 0
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// We're using an x87-compatible FPU, and intermediate operations can be
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// performed with 80-bit floats. This produces slightly different results from
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// what we expect below.
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GTEST_SKIP()
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<< "Skipping the test because we detected x87 floating-point semantics";
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#endif
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absl::InsecureBitGen gen;
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// <uint>
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EXPECT_EQ(0, absl::Uniform<uint64_t>(gen, 0, 0));
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EXPECT_EQ(1, absl::Uniform<uint64_t>(gen, 1, 0));
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EXPECT_EQ(0, absl::Uniform<uint64_t>(absl::IntervalOpenOpen, gen, 0, 0));
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EXPECT_EQ(1, absl::Uniform<uint64_t>(absl::IntervalOpenOpen, gen, 1, 0));
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constexpr auto m = (std::numeric_limits<uint64_t>::max)();
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EXPECT_EQ(m, absl::Uniform(gen, m, m));
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EXPECT_EQ(m, absl::Uniform(gen, m, m - 1));
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EXPECT_EQ(m - 1, absl::Uniform(gen, m - 1, m));
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EXPECT_EQ(m, absl::Uniform(absl::IntervalOpenOpen, gen, m, m));
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EXPECT_EQ(m, absl::Uniform(absl::IntervalOpenOpen, gen, m, m - 1));
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EXPECT_EQ(m - 1, absl::Uniform(absl::IntervalOpenOpen, gen, m - 1, m));
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// <int>
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EXPECT_EQ(0, absl::Uniform<int64_t>(gen, 0, 0));
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EXPECT_EQ(1, absl::Uniform<int64_t>(gen, 1, 0));
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EXPECT_EQ(0, absl::Uniform<int64_t>(absl::IntervalOpenOpen, gen, 0, 0));
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EXPECT_EQ(1, absl::Uniform<int64_t>(absl::IntervalOpenOpen, gen, 1, 0));
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constexpr auto l = (std::numeric_limits<int64_t>::min)();
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constexpr auto r = (std::numeric_limits<int64_t>::max)();
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EXPECT_EQ(l, absl::Uniform(gen, l, l));
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EXPECT_EQ(r, absl::Uniform(gen, r, r));
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EXPECT_EQ(r, absl::Uniform(gen, r, r - 1));
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EXPECT_EQ(r - 1, absl::Uniform(gen, r - 1, r));
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EXPECT_EQ(l, absl::Uniform(absl::IntervalOpenOpen, gen, l, l));
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EXPECT_EQ(r, absl::Uniform(absl::IntervalOpenOpen, gen, r, r));
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EXPECT_EQ(r, absl::Uniform(absl::IntervalOpenOpen, gen, r, r - 1));
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EXPECT_EQ(r - 1, absl::Uniform(absl::IntervalOpenOpen, gen, r - 1, r));
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// <double>
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const double e = std::nextafter(1.0, 2.0); // 1 + epsilon
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const double f = std::nextafter(1.0, 0.0); // 1 - epsilon
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const double g = std::numeric_limits<double>::denorm_min();
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EXPECT_EQ(1.0, absl::Uniform(gen, 1.0, e));
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EXPECT_EQ(1.0, absl::Uniform(gen, 1.0, f));
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EXPECT_EQ(0.0, absl::Uniform(gen, 0.0, g));
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EXPECT_EQ(e, absl::Uniform(absl::IntervalOpenOpen, gen, 1.0, e));
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EXPECT_EQ(f, absl::Uniform(absl::IntervalOpenOpen, gen, 1.0, f));
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EXPECT_EQ(g, absl::Uniform(absl::IntervalOpenOpen, gen, 0.0, g));
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}
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// TODO(lar): Validate properties of non-default interval-semantics.
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TEST_F(RandomDistributionsTest, UniformReal) {
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std::vector<double> values(kSize);
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absl::InsecureBitGen gen;
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for (int i = 0; i < kSize; i++) {
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values[i] = absl::Uniform(gen, 0, 1.0);
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}
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const auto moments =
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absl::random_internal::ComputeDistributionMoments(values);
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EXPECT_NEAR(0.5, moments.mean, 0.02);
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EXPECT_NEAR(1 / 12.0, moments.variance, 0.02);
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EXPECT_NEAR(0.0, moments.skewness, 0.02);
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EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.02);
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}
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TEST_F(RandomDistributionsTest, UniformInt) {
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std::vector<double> values(kSize);
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absl::InsecureBitGen gen;
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for (int i = 0; i < kSize; i++) {
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const int64_t kMax = 1000000000000ll;
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int64_t j = absl::Uniform(absl::IntervalClosedClosed, gen, 0, kMax);
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// convert to double.
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values[i] = static_cast<double>(j) / static_cast<double>(kMax);
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}
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const auto moments =
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absl::random_internal::ComputeDistributionMoments(values);
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EXPECT_NEAR(0.5, moments.mean, 0.02);
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EXPECT_NEAR(1 / 12.0, moments.variance, 0.02);
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EXPECT_NEAR(0.0, moments.skewness, 0.02);
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EXPECT_NEAR(9 / 5.0, moments.kurtosis, 0.02);
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/*
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// NOTE: These are not supported by absl::Uniform, which is specialized
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// on integer and real valued types.
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enum E { E0, E1 }; // enum
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enum S : int { S0, S1 }; // signed enum
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enum U : unsigned int { U0, U1 }; // unsigned enum
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absl::Uniform(gen, E0, E1);
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absl::Uniform(gen, S0, S1);
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absl::Uniform(gen, U0, U1);
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*/
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}
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TEST_F(RandomDistributionsTest, Exponential) {
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std::vector<double> values(kSize);
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absl::InsecureBitGen gen;
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for (int i = 0; i < kSize; i++) {
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values[i] = absl::Exponential<double>(gen);
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}
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const auto moments =
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absl::random_internal::ComputeDistributionMoments(values);
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EXPECT_NEAR(1.0, moments.mean, 0.02);
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EXPECT_NEAR(1.0, moments.variance, 0.025);
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EXPECT_NEAR(2.0, moments.skewness, 0.1);
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EXPECT_LT(5.0, moments.kurtosis);
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||
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|
}
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||
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||
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TEST_F(RandomDistributionsTest, PoissonDefault) {
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std::vector<double> values(kSize);
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|
|
||
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absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
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||
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values[i] = absl::Poisson<int64_t>(gen);
|
||
|
|
}
|
||
|
|
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(1.0, moments.mean, 0.02);
|
||
|
|
EXPECT_NEAR(1.0, moments.variance, 0.02);
|
||
|
|
EXPECT_NEAR(1.0, moments.skewness, 0.025);
|
||
|
|
EXPECT_LT(2.0, moments.kurtosis);
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST_F(RandomDistributionsTest, PoissonLarge) {
|
||
|
|
constexpr double kMean = 100000000.0;
|
||
|
|
std::vector<double> values(kSize);
|
||
|
|
|
||
|
|
absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
|
||
|
|
values[i] = absl::Poisson<int64_t>(gen, kMean);
|
||
|
|
}
|
||
|
|
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(kMean, moments.mean, kMean * 0.015);
|
||
|
|
EXPECT_NEAR(kMean, moments.variance, kMean * 0.015);
|
||
|
|
EXPECT_NEAR(std::sqrt(kMean), moments.skewness, kMean * 0.02);
|
||
|
|
EXPECT_LT(2.0, moments.kurtosis);
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST_F(RandomDistributionsTest, Bernoulli) {
|
||
|
|
constexpr double kP = 0.5151515151;
|
||
|
|
std::vector<double> values(kSize);
|
||
|
|
|
||
|
|
absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
|
||
|
|
values[i] = absl::Bernoulli(gen, kP);
|
||
|
|
}
|
||
|
|
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(kP, moments.mean, 0.01);
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST_F(RandomDistributionsTest, Beta) {
|
||
|
|
constexpr double kAlpha = 2.0;
|
||
|
|
constexpr double kBeta = 3.0;
|
||
|
|
std::vector<double> values(kSize);
|
||
|
|
|
||
|
|
absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
|
||
|
|
values[i] = absl::Beta(gen, kAlpha, kBeta);
|
||
|
|
}
|
||
|
|
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(0.4, moments.mean, 0.01);
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST_F(RandomDistributionsTest, Zipf) {
|
||
|
|
std::vector<double> values(kSize);
|
||
|
|
|
||
|
|
absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
|
||
|
|
values[i] = absl::Zipf<int64_t>(gen, 100);
|
||
|
|
}
|
||
|
|
|
||
|
|
// The mean of a zipf distribution is: H(N, s-1) / H(N,s).
|
||
|
|
// Given the parameter v = 1, this gives the following function:
|
||
|
|
// (Hn(100, 1) - Hn(1,1)) / (Hn(100,2) - Hn(1,2)) = 6.5944
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(6.5944, moments.mean, 2000) << moments;
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST_F(RandomDistributionsTest, Gaussian) {
|
||
|
|
std::vector<double> values(kSize);
|
||
|
|
|
||
|
|
absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
|
||
|
|
values[i] = absl::Gaussian<double>(gen);
|
||
|
|
}
|
||
|
|
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(0.0, moments.mean, 0.02);
|
||
|
|
EXPECT_NEAR(1.0, moments.variance, 0.04);
|
||
|
|
EXPECT_NEAR(0, moments.skewness, 0.2);
|
||
|
|
EXPECT_NEAR(3.0, moments.kurtosis, 0.5);
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST_F(RandomDistributionsTest, LogUniform) {
|
||
|
|
std::vector<double> values(kSize);
|
||
|
|
|
||
|
|
absl::InsecureBitGen gen;
|
||
|
|
for (int i = 0; i < kSize; i++) {
|
||
|
|
values[i] = absl::LogUniform<int64_t>(gen, 0, (1 << 10) - 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
// The mean is the sum of the fractional means of the uniform distributions:
|
||
|
|
// [0..0][1..1][2..3][4..7][8..15][16..31][32..63]
|
||
|
|
// [64..127][128..255][256..511][512..1023]
|
||
|
|
const double mean = (0 + 1 + 1 + 2 + 3 + 4 + 7 + 8 + 15 + 16 + 31 + 32 + 63 +
|
||
|
|
64 + 127 + 128 + 255 + 256 + 511 + 512 + 1023) /
|
||
|
|
(2.0 * 11.0);
|
||
|
|
|
||
|
|
const auto moments =
|
||
|
|
absl::random_internal::ComputeDistributionMoments(values);
|
||
|
|
EXPECT_NEAR(mean, moments.mean, 2) << moments;
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace
|