THUAI6/CAPI/cpp/grpc/include/absl/random/poisson_distribution.h

// 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.

#ifndef ABSL_RANDOM_POISSON_DISTRIBUTION_H_
#define ABSL_RANDOM_POISSON_DISTRIBUTION_H_

#include <cassert>
#include <cmath>
#include <istream>
#include <limits>
#include <ostream>
#include <type_traits>

#include "absl/random/internal/fast_uniform_bits.h"
#include "absl/random/internal/fastmath.h"
#include "absl/random/internal/generate_real.h"
#include "absl/random/internal/iostream_state_saver.h"
#include "absl/random/internal/traits.h"

namespace absl
{
    ABSL_NAMESPACE_BEGIN

    // absl::poisson_distribution:
    // Generates discrete variates conforming to a Poisson distribution.
    //   p(n) = (mean^n / n!) exp(-mean)
    //
    // Depending on the parameter, the distribution selects one of the following
    // algorithms:
    // * The standard algorithm, attributed to Knuth, extended using a split method
    // for larger values
    // * The "Ratio of Uniforms as a convenient method for sampling from classical
    // discrete distributions", Stadlober, 1989.
    // http://www.sciencedirect.com/science/article/pii/0377042790903495
    //
    // NOTE: param_type.mean() is a double, which permits values larger than
    // poisson_distribution<IntType>::max(), however this should be avoided and
    // the distribution results are limited to the max() value.
    //
    // The goals of this implementation are to provide good performance while still
    // beig thread-safe: This limits the implementation to not using lgamma provided
    // by <math.h>.
    //
    template<typename IntType = int>
    class poisson_distribution
    {
    public:
        using result_type = IntType;

        class param_type
        {
        public:
            using distribution_type = poisson_distribution;
            explicit param_type(double mean = 1.0);

            double mean() const
            {
                return mean_;
            }

            friend bool operator==(const param_type& a, const param_type& b)
            {
                return a.mean_ == b.mean_;
            }

            friend bool operator!=(const param_type& a, const param_type& b)
            {
                return !(a == b);
            }

        private:
            friend class poisson_distribution;

            double mean_;
            double emu_;  // e ^ -mean_
            double lmu_;  // ln(mean_)
            double s_;
            double log_k_;
            int split_;

            static_assert(random_internal::IsIntegral<IntType>::value, "Class-template absl::poisson_distribution<> must be "
                                                                       "parameterized using an integral type.");
        };

        poisson_distribution() :
            poisson_distribution(1.0)
        {
        }

        explicit poisson_distribution(double mean) :
            param_(mean)
        {
        }

        explicit poisson_distribution(const param_type& p) :
            param_(p)
        {
        }

        void reset()
        {
        }

        // generating functions
        template<typename URBG>
        result_type operator()(URBG& g)
        {  // NOLINT(runtime/references)
            return (*this)(g, param_);
        }

        template<typename URBG>
        result_type operator()(URBG& g,  // NOLINT(runtime/references)
                               const param_type& p);

        param_type param() const
        {
            return param_;
        }
        void param(const param_type& p)
        {
            param_ = p;
        }

        result_type(min)() const
        {
            return 0;
        }
        result_type(max)() const
        {
            return (std::numeric_limits<result_type>::max)();
        }

        double mean() const
        {
            return param_.mean();
        }

        friend bool operator==(const poisson_distribution& a, const poisson_distribution& b)
        {
            return a.param_ == b.param_;
        }
        friend bool operator!=(const poisson_distribution& a, const poisson_distribution& b)
        {
            return a.param_ != b.param_;
        }

    private:
        param_type param_;
        random_internal::FastUniformBits<uint64_t> fast_u64_;
    };

    // -----------------------------------------------------------------------------
    // Implementation details follow
    // -----------------------------------------------------------------------------

    template<typename IntType>
    poisson_distribution<IntType>::param_type::param_type(double mean) :
        mean_(mean),
        split_(0)
    {
        assert(mean >= 0);
        assert(mean <= static_cast<double>((std::numeric_limits<result_type>::max)()));
        // As a defensive measure, avoid large values of the mean.  The rejection
        // algorithm used does not support very large values well.  It my be worth
        // changing algorithms to better deal with these cases.
        assert(mean <= 1e10);
        if (mean_ < 10)
        {
            // For small lambda, use the knuth method.
            split_ = 1;
            emu_ = std::exp(-mean_);
        }
        else if (mean_ <= 50)
        {
            // Use split-knuth method.
            split_ = 1 + static_cast<int>(mean_ / 10.0);
            emu_ = std::exp(-mean_ / static_cast<double>(split_));
        }
        else
        {
            // Use ratio of uniforms method.
            constexpr double k2E = 0.7357588823428846;
            constexpr double kSA = 0.4494580810294493;

            lmu_ = std::log(mean_);
            double a = mean_ + 0.5;
            s_ = kSA + std::sqrt(k2E * a);
            const double mode = std::ceil(mean_) - 1;
            log_k_ = lmu_ * mode - absl::random_internal::StirlingLogFactorial(mode);
        }
    }

    template<typename IntType>
    template<typename URBG>
    typename poisson_distribution<IntType>::result_type
        poisson_distribution<IntType>::operator()(
            URBG& g,  // NOLINT(runtime/references)
            const param_type& p
        )
    {
        using random_internal::GeneratePositiveTag;
        using random_internal::GenerateRealFromBits;
        using random_internal::GenerateSignedTag;

        if (p.split_ != 0)
        {
            // Use Knuth's algorithm with range splitting to avoid floating-point
            // errors. Knuth's algorithm is: Ui is a sequence of uniform variates on
            // (0,1); return the number of variates required for product(Ui) <
            // exp(-lambda).
            //
            // The expected number of variates required for Knuth's method can be
            // computed as follows:
            // The expected value of U is 0.5, so solving for 0.5^n < exp(-lambda) gives
            // the expected number of uniform variates
            // required for a given lambda, which is:
            //  lambda = [2, 5,  9, 10, 11, 12, 13, 14, 15, 16, 17]
            //  n      = [3, 8, 13, 15, 16, 18, 19, 21, 22, 24, 25]
            //
            result_type n = 0;
            for (int split = p.split_; split > 0; --split)
            {
                double r = 1.0;
                do
                {
                    r *= GenerateRealFromBits<double, GeneratePositiveTag, true>(
                        fast_u64_(g)
                    );  // U(-1, 0)
                    ++n;
                } while (r > p.emu_);
                --n;
            }
            return n;
        }

        // Use ratio of uniforms method.
        //
        // Let u ~ Uniform(0, 1), v ~ Uniform(-1, 1),
        //     a = lambda + 1/2,
        //     s = 1.5 - sqrt(3/e) + sqrt(2(lambda + 1/2)/e),
        //     x = s * v/u + a.
        // P(floor(x) = k | u^2 < f(floor(x))/k), where
        // f(m) = lambda^m exp(-lambda)/ m!, for 0 <= m, and f(m) = 0 otherwise,
        // and k = max(f).
        const double a = p.mean_ + 0.5;
        for (;;)
        {
            const double u = GenerateRealFromBits<double, GeneratePositiveTag, false>(
                fast_u64_(g)
            );  // U(0, 1)
            const double v = GenerateRealFromBits<double, GenerateSignedTag, false>(
                fast_u64_(g)
            );  // U(-1, 1)

            const double x = std::floor(p.s_ * v / u + a);
            if (x < 0)
                continue;  // f(negative) = 0
            const double rhs = x * p.lmu_;
            // clang-format off
    double s = (x <= 1.0) ? 0.0
             : (x == 2.0) ? 0.693147180559945
             : absl::random_internal::StirlingLogFactorial(x);
            // clang-format on
            const double lhs = 2.0 * std::log(u) + p.log_k_ + s;
            if (lhs < rhs)
            {
                return x > static_cast<double>((max)()) ? (max)() : static_cast<result_type>(x);  // f(x)/k >= u^2
            }
        }
    }

    template<typename CharT, typename Traits, typename IntType>
    std::basic_ostream<CharT, Traits>& operator<<(
        std::basic_ostream<CharT, Traits>& os,  // NOLINT(runtime/references)
        const poisson_distribution<IntType>& x
    )
    {
        auto saver = random_internal::make_ostream_state_saver(os);
        os.precision(random_internal::stream_precision_helper<double>::kPrecision);
        os << x.mean();
        return os;
    }

    template<typename CharT, typename Traits, typename IntType>
    std::basic_istream<CharT, Traits>& operator>>(
        std::basic_istream<CharT, Traits>& is,  // NOLINT(runtime/references)
        poisson_distribution<IntType>& x
    )
    {  // NOLINT(runtime/references)
        using param_type = typename poisson_distribution<IntType>::param_type;

        auto saver = random_internal::make_istream_state_saver(is);
        double mean = random_internal::read_floating_point<double>(is);
        if (!is.fail())
        {
            x.param(param_type(mean));
        }
        return is;
    }

    ABSL_NAMESPACE_END
}  // namespace absl

#endif  // ABSL_RANDOM_POISSON_DISTRIBUTION_H_