// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_RANDOM
#define _LIBCPP_RANDOM

/*
    random synopsis

#include <initializer_list>

namespace std
{
// [rand.req.urng], uniform random bit generator requirements
template<class G>
concept uniform_random_bit_generator = see below; // C++20

// Engines

template <class UIntType, UIntType a, UIntType c, UIntType m>
class linear_congruential_engine
{
public:
    // types
    typedef UIntType result_type;

    // engine characteristics
    static constexpr result_type multiplier = a;
    static constexpr result_type increment = c;
    static constexpr result_type modulus = m;
    static constexpr result_type min() { return c == 0u ? 1u: 0u;}
    static constexpr result_type max() { return m - 1u;}
    static constexpr result_type default_seed = 1u;

    // constructors and seeding functions
    explicit linear_congruential_engine(result_type s = default_seed);         // before C++20
    linear_congruential_engine() : linear_congruential_engine(default_seed) {} // C++20
    explicit linear_congruential_engine(result_type s);                        // C++20
    template<class Sseq> explicit linear_congruential_engine(Sseq& q);
    void seed(result_type s = default_seed);
    template<class Sseq> void seed(Sseq& q);

    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
};

template <class UIntType, UIntType a, UIntType c, UIntType m>
bool
operator==(const linear_congruential_engine<UIntType, a, c, m>& x,
           const linear_congruential_engine<UIntType, a, c, m>& y);

template <class UIntType, UIntType a, UIntType c, UIntType m>
bool
operator!=(const linear_congruential_engine<UIntType, a, c, m>& x,
           const linear_congruential_engine<UIntType, a, c, m>& y);

template <class charT, class traits,
          class UIntType, UIntType a, UIntType c, UIntType m>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& os,
           const linear_congruential_engine<UIntType, a, c, m>& x);

template <class charT, class traits,
          class UIntType, UIntType a, UIntType c, UIntType m>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is,
           linear_congruential_engine<UIntType, a, c, m>& x);

template <class UIntType, size_t w, size_t n, size_t m, size_t r,
          UIntType a, size_t u, UIntType d, size_t s,
          UIntType b, size_t t, UIntType c, size_t l, UIntType f>
class mersenne_twister_engine
{
public:
    // types
    typedef UIntType result_type;

    // engine characteristics
    static constexpr size_t word_size = w;
    static constexpr size_t state_size = n;
    static constexpr size_t shift_size = m;
    static constexpr size_t mask_bits = r;
    static constexpr result_type xor_mask = a;
    static constexpr size_t tempering_u = u;
    static constexpr result_type tempering_d = d;
    static constexpr size_t tempering_s = s;
    static constexpr result_type tempering_b = b;
    static constexpr size_t tempering_t = t;
    static constexpr result_type tempering_c = c;
    static constexpr size_t tempering_l = l;
    static constexpr result_type initialization_multiplier = f;
    static constexpr result_type min () { return 0; }
    static constexpr result_type max() { return 2^w - 1; }
    static constexpr result_type default_seed = 5489u;

    // constructors and seeding functions
    explicit mersenne_twister_engine(result_type s = default_seed);      // before C++20
    mersenne_twister_engine() : mersenne_twister_engine(default_seed) {} // C++20
    explicit mersenne_twister_engine(result_type s);                     // C++20
    template<class Sseq> explicit mersenne_twister_engine(Sseq& q);
    void seed(result_type value = default_seed);
    template<class Sseq> void seed(Sseq& q);

    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
};

template <class UIntType, size_t w, size_t n, size_t m, size_t r,
          UIntType a, size_t u, UIntType d, size_t s,
          UIntType b, size_t t, UIntType c, size_t l, UIntType f>
bool
operator==(
    const mersenne_twister_engine<UIntType, w, n, m, r, a, u, d, s, b, t, c, l, f>& x,
    const mersenne_twister_engine<UIntType, w, n, m, r, a, u, d, s, b, t, c, l, f>& y);

template <class UIntType, size_t w, size_t n, size_t m, size_t r,
          UIntType a, size_t u, UIntType d, size_t s,
          UIntType b, size_t t, UIntType c, size_t l, UIntType f>
bool
operator!=(
    const mersenne_twister_engine<UIntType, w, n, m, r, a, u, d, s, b, t, c, l, f>& x,
    const mersenne_twister_engine<UIntType, w, n, m, r, a, u, d, s, b, t, c, l, f>& y);

template <class charT, class traits,
          class UIntType, size_t w, size_t n, size_t m, size_t r,
          UIntType a, size_t u, UIntType d, size_t s,
          UIntType b, size_t t, UIntType c, size_t l, UIntType f>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& os,
           const mersenne_twister_engine<UIntType, w, n, m, r, a, u, d, s, b, t, c, l, f>& x);

template <class charT, class traits,
          class UIntType, size_t w, size_t n, size_t m, size_t r,
          UIntType a, size_t u, UIntType d, size_t s,
          UIntType b, size_t t, UIntType c, size_t l, UIntType f>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is,
           mersenne_twister_engine<UIntType, w, n, m, r, a, u, d, s, b, t, c, l, f>& x);

template<class UIntType, size_t w, size_t s, size_t r>
class subtract_with_carry_engine
{
public:
    // types
    typedef UIntType result_type;

    // engine characteristics
    static constexpr size_t word_size = w;
    static constexpr size_t short_lag = s;
    static constexpr size_t long_lag = r;
    static constexpr result_type min() { return 0; }
    static constexpr result_type max() { return m-1; }
    static constexpr result_type default_seed = 19780503u;

    // constructors and seeding functions
    explicit subtract_with_carry_engine(result_type value = default_seed);     // before C++20
    subtract_with_carry_engine() : subtract_with_carry_engine(default_seed) {} // C++20
    explicit subtract_with_carry_engine(result_type value);                    // C++20
    template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);
    void seed(result_type value = default_seed);
    template<class Sseq> void seed(Sseq& q);

    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
};

template<class UIntType, size_t w, size_t s, size_t r>
bool
operator==(
    const subtract_with_carry_engine<UIntType, w, s, r>& x,
    const subtract_with_carry_engine<UIntType, w, s, r>& y);

template<class UIntType, size_t w, size_t s, size_t r>
bool
operator!=(
    const subtract_with_carry_engine<UIntType, w, s, r>& x,
    const subtract_with_carry_engine<UIntType, w, s, r>& y);

template <class charT, class traits,
          class UIntType, size_t w, size_t s, size_t r>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& os,
           const subtract_with_carry_engine<UIntType, w, s, r>& x);

template <class charT, class traits,
          class UIntType, size_t w, size_t s, size_t r>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is,
           subtract_with_carry_engine<UIntType, w, s, r>& x);

template<class Engine, size_t p, size_t r>
class discard_block_engine
{
public:
    // types
    typedef typename Engine::result_type result_type;

    // engine characteristics
    static constexpr size_t block_size = p;
    static constexpr size_t used_block = r;
    static constexpr result_type min() { return Engine::min(); }
    static constexpr result_type max() { return Engine::max(); }

    // constructors and seeding functions
    discard_block_engine();
    explicit discard_block_engine(const Engine& e);
    explicit discard_block_engine(Engine&& e);
    explicit discard_block_engine(result_type s);
    template<class Sseq> explicit discard_block_engine(Sseq& q);
    void seed();
    void seed(result_type s);
    template<class Sseq> void seed(Sseq& q);

    // generating functions
    result_type operator()();
    void discard(unsigned long long z);

    // property functions
    const Engine& base() const noexcept;
};

template<class Engine, size_t p, size_t r>
bool
operator==(
    const discard_block_engine<Engine, p, r>& x,
    const discard_block_engine<Engine, p, r>& y);

template<class Engine, size_t p, size_t r>
bool
operator!=(
    const discard_block_engine<Engine, p, r>& x,
    const discard_block_engine<Engine, p, r>& y);

template <class charT, class traits,
          class Engine, size_t p, size_t r>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& os,
           const discard_block_engine<Engine, p, r>& x);

template <class charT, class traits,
          class Engine, size_t p, size_t r>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is,
           discard_block_engine<Engine, p, r>& x);

template<class Engine, size_t w, class UIntType>
class independent_bits_engine
{
public:
    // types
    typedef UIntType result_type;

    // engine characteristics
    static constexpr result_type min() { return 0; }
    static constexpr result_type max() { return 2^w - 1; }

    // constructors and seeding functions
    independent_bits_engine();
    explicit independent_bits_engine(const Engine& e);
    explicit independent_bits_engine(Engine&& e);
    explicit independent_bits_engine(result_type s);
    template<class Sseq> explicit independent_bits_engine(Sseq& q);
    void seed();
    void seed(result_type s);
    template<class Sseq> void seed(Sseq& q);

    // generating functions
    result_type operator()(); void discard(unsigned long long z);

    // property functions
    const Engine& base() const noexcept;
};

template<class Engine, size_t w, class UIntType>
bool
operator==(
    const independent_bits_engine<Engine, w, UIntType>& x,
    const independent_bits_engine<Engine, w, UIntType>& y);

template<class Engine, size_t w, class UIntType>
bool
operator!=(
    const independent_bits_engine<Engine, w, UIntType>& x,
    const independent_bits_engine<Engine, w, UIntType>& y);

template <class charT, class traits,
          class Engine, size_t w, class UIntType>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& os,
           const independent_bits_engine<Engine, w, UIntType>& x);

template <class charT, class traits,
          class Engine, size_t w, class UIntType>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is,
           independent_bits_engine<Engine, w, UIntType>& x);

template<class Engine, size_t k>
class shuffle_order_engine
{
public:
    // types
    typedef typename Engine::result_type result_type;

    // engine characteristics
    static constexpr size_t table_size = k;
    static constexpr result_type min() { return Engine::min; }
    static constexpr result_type max() { return Engine::max; }

    // constructors and seeding functions
    shuffle_order_engine();
    explicit shuffle_order_engine(const Engine& e);
    explicit shuffle_order_engine(Engine&& e);
    explicit shuffle_order_engine(result_type s);
    template<class Sseq> explicit shuffle_order_engine(Sseq& q);
    void seed();
    void seed(result_type s);
    template<class Sseq> void seed(Sseq& q);

    // generating functions
    result_type operator()();
    void discard(unsigned long long z);

    // property functions
    const Engine& base() const noexcept;
};

template<class Engine, size_t k>
bool
operator==(
    const shuffle_order_engine<Engine, k>& x,
    const shuffle_order_engine<Engine, k>& y);

template<class Engine, size_t k>
bool
operator!=(
    const shuffle_order_engine<Engine, k>& x,
    const shuffle_order_engine<Engine, k>& y);

template <class charT, class traits,
          class Engine, size_t k>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& os,
           const shuffle_order_engine<Engine, k>& x);

template <class charT, class traits,
          class Engine, size_t k>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is,
           shuffle_order_engine<Engine, k>& x);

typedef linear_congruential_engine<uint_fast32_t, 16807, 0, 2147483647>
                                                                   minstd_rand0;
typedef linear_congruential_engine<uint_fast32_t, 48271, 0, 2147483647>
                                                                    minstd_rand;
typedef mersenne_twister_engine<uint_fast32_t, 32, 624, 397, 31,
                                0x9908b0df,
                                11, 0xffffffff,
                                7,  0x9d2c5680,
                                15, 0xefc60000,
                                18, 1812433253>                         mt19937;
typedef mersenne_twister_engine<uint_fast64_t, 64, 312, 156, 31,
                                0xb5026f5aa96619e9,
                                29, 0x5555555555555555,
                                17, 0x71d67fffeda60000,
                                37, 0xfff7eee000000000,
                                43, 6364136223846793005>             mt19937_64;
typedef subtract_with_carry_engine<uint_fast32_t, 24, 10, 24>     ranlux24_base;
typedef subtract_with_carry_engine<uint_fast64_t, 48,  5, 12>     ranlux48_base;
typedef discard_block_engine<ranlux24_base, 223, 23>                   ranlux24;
typedef discard_block_engine<ranlux48_base, 389, 11>                   ranlux48;
typedef shuffle_order_engine<minstd_rand0, 256>                         knuth_b;
typedef minstd_rand                                       default_random_engine;

// Generators

class random_device
{
public:
    // types
    typedef unsigned int result_type;

    // generator characteristics
    static constexpr result_type min() { return numeric_limits<result_type>::min(); }
    static constexpr result_type max() { return numeric_limits<result_type>::max(); }

    // constructors
    explicit random_device(const string& token = implementation-defined); // before C++20
    random_device() : random_device(implementation-defined) {}            // C++20
    explicit random_device(const string& token);                          // C++20

    // generating functions
    result_type operator()();

    // property functions
    double entropy() const noexcept;

    // no copy functions
    random_device(const random_device& ) = delete;
    void operator=(const random_device& ) = delete;
};

// Utilities

class seed_seq
{
public:
    // types
    typedef uint_least32_t result_type;

    // constructors
    seed_seq();
    template<class T>
        seed_seq(initializer_list<T> il);
    template<class InputIterator>
        seed_seq(InputIterator begin, InputIterator end);

    // generating functions
    template<class RandomAccessIterator>
        void generate(RandomAccessIterator begin, RandomAccessIterator end);

    // property functions
    size_t size() const;
    template<class OutputIterator>
        void param(OutputIterator dest) const;

    // no copy functions
    seed_seq(const seed_seq&) = delete;
    void operator=(const seed_seq& ) = delete;
};

template<class RealType, size_t bits, class URNG>
    RealType generate_canonical(URNG& g);

// Distributions

template<class IntType = int>
class uniform_int_distribution
{
public:
    // types
    typedef IntType result_type;

    class param_type
    {
    public:
        typedef uniform_int_distribution distribution_type;

        explicit param_type(IntType a = 0,
                                    IntType b = numeric_limits<IntType>::max());

        result_type a() const;
        result_type b() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit uniform_int_distribution(IntType a = 0,
                                      IntType b = numeric_limits<IntType>::max()); // before C++20
    uniform_int_distribution() : uniform_int_distribution(0) {}                    // C++20
    explicit uniform_int_distribution(IntType a,
                                      IntType b = numeric_limits<IntType>::max()); // C++20
    explicit uniform_int_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type a() const;
    result_type b() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const uniform_int_distribution& x,
                           const uniform_int_distribution& y);
    friend bool operator!=(const uniform_int_distribution& x,
                           const uniform_int_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const uniform_int_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               uniform_int_distribution& x);
};

template<class RealType = double>
class uniform_real_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef uniform_real_distribution distribution_type;

        explicit param_type(RealType a = 0,
                            RealType b = 1);

        result_type a() const;
        result_type b() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit uniform_real_distribution(RealType a = 0.0, RealType b = 1.0); // before C++20
    uniform_real_distribution() : uniform_real_distribution(0.0) {}         // C++20
    explicit uniform_real_distribution(RealType a, RealType b = 1.0);       // C++20
    explicit uniform_real_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type a() const;
    result_type b() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const uniform_real_distribution& x,
                           const uniform_real_distribution& y);
    friend bool operator!=(const uniform_real_distribution& x,
                           const uniform_real_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const uniform_real_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               uniform_real_distribution& x);
};

class bernoulli_distribution
{
public:
    // types
    typedef bool result_type;

    class param_type
    {
    public:
        typedef bernoulli_distribution distribution_type;

        explicit param_type(double p = 0.5);

        double p() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit bernoulli_distribution(double p = 0.5);          // before C++20
    bernoulli_distribution() : bernoulli_distribution(0.5) {} // C++20
    explicit bernoulli_distribution(double p);                // C++20
    explicit bernoulli_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    double p() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const bernoulli_distribution& x,
                           const bernoulli_distribution& y);
    friend bool operator!=(const bernoulli_distribution& x,
                           const bernoulli_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const bernoulli_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               bernoulli_distribution& x);
};

template<class IntType = int>
class binomial_distribution
{
public:
    // types
    typedef IntType result_type;

    class param_type
    {
    public:
        typedef binomial_distribution distribution_type;

        explicit param_type(IntType t = 1, double p = 0.5);

        IntType t() const;
        double p() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit binomial_distribution(IntType t = 1, double p = 0.5); // before C++20
    binomial_distribution() : binomial_distribution(1) {}          // C++20
    explicit binomial_distribution(IntType t, double p = 0.5);     // C++20
    explicit binomial_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    IntType t() const;
    double p() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const binomial_distribution& x,
                           const binomial_distribution& y);
    friend bool operator!=(const binomial_distribution& x,
                           const binomial_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const binomial_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               binomial_distribution& x);
};

template<class IntType = int>
class geometric_distribution
{
public:
    // types
    typedef IntType result_type;

    class param_type
    {
    public:
        typedef geometric_distribution distribution_type;

        explicit param_type(double p = 0.5);

        double p() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit geometric_distribution(double p = 0.5);          // before C++20
    geometric_distribution() : geometric_distribution(0.5) {} // C++20
    explicit geometric_distribution(double p);                // C++20
    explicit geometric_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    double p() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const geometric_distribution& x,
                           const geometric_distribution& y);
    friend bool operator!=(const geometric_distribution& x,
                           const geometric_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const geometric_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               geometric_distribution& x);
};

template<class IntType = int>
class negative_binomial_distribution
{
public:
    // types
    typedef IntType result_type;

    class param_type
    {
    public:
        typedef negative_binomial_distribution distribution_type;

        explicit param_type(result_type k = 1, double p = 0.5);

        result_type k() const;
        double p() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit negative_binomial_distribution(IntType k = 1, double p = 0.5); // before C++20
    negative_binomial_distribution() : negative_binomial_distribution(1) {} // C++20
    explicit negative_binomial_distribution(IntType k, double p = 0.5);     // C++20
    explicit negative_binomial_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type k() const;
    double p() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const negative_binomial_distribution& x,
                           const negative_binomial_distribution& y);
    friend bool operator!=(const negative_binomial_distribution& x,
                           const negative_binomial_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const negative_binomial_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               negative_binomial_distribution& x);
};

template<class IntType = int>
class poisson_distribution
{
public:
    // types
    typedef IntType result_type;

    class param_type
    {
    public:
        typedef poisson_distribution distribution_type;

        explicit param_type(double mean = 1.0);

        double mean() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit poisson_distribution(double mean = 1.0);     // before C++20
    poisson_distribution() : poisson_distribution(1.0) {} // C++20
    explicit poisson_distribution(double mean);           // C++20
    explicit poisson_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    double mean() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const poisson_distribution& x,
                           const poisson_distribution& y);
    friend bool operator!=(const poisson_distribution& x,
                           const poisson_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const poisson_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               poisson_distribution& x);
};

template<class RealType = double>
class exponential_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef exponential_distribution distribution_type;

        explicit param_type(result_type lambda = 1.0);

        result_type lambda() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit exponential_distribution(RealType lambda = 1.0);     // before C++20
    exponential_distribution() : exponential_distribution(1.0) {} // C++20
    explicit exponential_distribution(RealType lambda);           // C++20
    explicit exponential_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type lambda() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const exponential_distribution& x,
                           const exponential_distribution& y);
    friend bool operator!=(const exponential_distribution& x,
                           const exponential_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const exponential_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               exponential_distribution& x);
};

template<class RealType = double>
class gamma_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef gamma_distribution distribution_type;

        explicit param_type(result_type alpha = 1, result_type beta = 1);

        result_type alpha() const;
        result_type beta() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit gamma_distribution(RealType alpha = 0.0, RealType beta = 1.0); // before C++20
    gamma_distribution() : gamma_distribution(0.0) {}                       // C++20
    explicit gamma_distribution(RealType alpha, RealType beta = 1.0);       // C++20
    explicit gamma_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type alpha() const;
    result_type beta() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const gamma_distribution& x,
                           const gamma_distribution& y);
    friend bool operator!=(const gamma_distribution& x,
                           const gamma_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const gamma_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               gamma_distribution& x);
};

template<class RealType = double>
class weibull_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef weibull_distribution distribution_type;

        explicit param_type(result_type alpha = 1, result_type beta = 1);

        result_type a() const;
        result_type b() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit weibull_distribution(RealType a = 1.0, RealType b = 1.0); // before C++20
    weibull_distribution() : weibull_distribution(1.0) {}              // C++20
    explicit weibull_distribution(RealType a, RealType b = 1.0);       // C++20
    explicit weibull_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type a() const;
    result_type b() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const weibull_distribution& x,
                           const weibull_distribution& y);
    friend bool operator!=(const weibull_distribution& x,
                           const weibull_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const weibull_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               weibull_distribution& x);
};

template<class RealType = double>
class extreme_value_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef extreme_value_distribution distribution_type;

        explicit param_type(result_type a = 0, result_type b = 1);

        result_type a() const;
        result_type b() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit extreme_value_distribution(RealType a = 0.0, RealType b = 1.0); // before C++20
    extreme_value_distribution() : extreme_value_distribution(0.0) {}        // C++20
    explicit extreme_value_distribution(RealType a, RealType b = 1.0);       // C++20
    explicit extreme_value_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type a() const;
    result_type b() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const extreme_value_distribution& x,
                           const extreme_value_distribution& y);
    friend bool operator!=(const extreme_value_distribution& x,
                           const extreme_value_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const extreme_value_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               extreme_value_distribution& x);
};

template<class RealType = double>
class normal_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef normal_distribution distribution_type;

        explicit param_type(result_type mean = 0, result_type stddev = 1);

        result_type mean() const;
        result_type stddev() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructors and reset functions
    explicit normal_distribution(RealType mean = 0.0, RealType stddev = 1.0); // before C++20
    normal_distribution() : normal_distribution(0.0) {}                       // C++20
    explicit normal_distribution(RealType mean, RealType stddev = 1.0);       // C++20
    explicit normal_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type mean() const;
    result_type stddev() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const normal_distribution& x,
                           const normal_distribution& y);
    friend bool operator!=(const normal_distribution& x,
                           const normal_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const normal_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               normal_distribution& x);
};

template<class RealType = double>
class lognormal_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef lognormal_distribution distribution_type;

        explicit param_type(result_type m = 0, result_type s = 1);

        result_type m() const;
        result_type s() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit lognormal_distribution(RealType mean = 0.0, RealType stddev = 1.0); // before C++20
    lognormal_distribution() : lognormal_distribution(0.0) {}                    // C++20
    explicit lognormal_distribution(RealType mean, RealType stddev = 1.0);       // C++20
    explicit lognormal_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type m() const;
    result_type s() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const lognormal_distribution& x,
                           const lognormal_distribution& y);
    friend bool operator!=(const lognormal_distribution& x,
                           const lognormal_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const lognormal_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               lognormal_distribution& x);
};

template<class RealType = double>
class chi_squared_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef chi_squared_distribution distribution_type;

        explicit param_type(result_type n = 1);

        result_type n() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit chi_squared_distribution(RealType n = 1.0);          // before C++20
    chi_squared_distribution() : chi_squared_distribution(1.0) {} // C++20
    explicit chi_squared_distribution(RealType n);                // C++20
    explicit chi_squared_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type n() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const chi_squared_distribution& x,
                           const chi_squared_distribution& y);
    friend bool operator!=(const chi_squared_distribution& x,
                           const chi_squared_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const chi_squared_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               chi_squared_distribution& x);
};

template<class RealType = double>
class cauchy_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef cauchy_distribution distribution_type;

        explicit param_type(result_type a = 0, result_type b = 1);

        result_type a() const;
        result_type b() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit cauchy_distribution(RealType a = 0.0, RealType b = 1.0); // before C++20
    cauchy_distribution() : cauchy_distribution(0.0) {}               // C++20
    explicit cauchy_distribution(RealType a, RealType b = 1.0);       // C++20
    explicit cauchy_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type a() const;
    result_type b() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const cauchy_distribution& x,
                           const cauchy_distribution& y);
    friend bool operator!=(const cauchy_distribution& x,
                           const cauchy_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const cauchy_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               cauchy_distribution& x);
};

template<class RealType = double>
class fisher_f_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef fisher_f_distribution distribution_type;

        explicit param_type(result_type m = 1, result_type n = 1);

        result_type m() const;
        result_type n() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit fisher_f_distribution(RealType m = 1.0, RealType n = 1.0); // before C++20
    fisher_f_distribution() : fisher_f_distribution(1.0) {}             // C++20
    explicit fisher_f_distribution(RealType m, RealType n = 1.0);       // C++20
    explicit fisher_f_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type m() const;
    result_type n() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const fisher_f_distribution& x,
                           const fisher_f_distribution& y);
    friend bool operator!=(const fisher_f_distribution& x,
                           const fisher_f_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const fisher_f_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               fisher_f_distribution& x);
};

template<class RealType = double>
class student_t_distribution
{
public:
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef student_t_distribution distribution_type;

        explicit param_type(result_type n = 1);

        result_type n() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    explicit student_t_distribution(RealType n = 1.0);        // before C++20
    student_t_distribution() : student_t_distribution(1.0) {} // C++20
    explicit student_t_distribution(RealType n);              // C++20
    explicit student_t_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    result_type n() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const student_t_distribution& x,
                           const student_t_distribution& y);
    friend bool operator!=(const student_t_distribution& x,
                           const student_t_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const student_t_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               student_t_distribution& x);
};

template<class IntType = int>
class discrete_distribution
{
public:
    // types
    typedef IntType result_type;

    class param_type
    {
    public:
        typedef discrete_distribution distribution_type;

        param_type();
        template<class InputIterator>
            param_type(InputIterator firstW, InputIterator lastW);
        param_type(initializer_list<double> wl);
        template<class UnaryOperation>
            param_type(size_t nw, double xmin, double xmax, UnaryOperation fw);

        vector<double> probabilities() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    discrete_distribution();
    template<class InputIterator>
        discrete_distribution(InputIterator firstW, InputIterator lastW);
    discrete_distribution(initializer_list<double> wl);
    template<class UnaryOperation>
        discrete_distribution(size_t nw, double xmin, double xmax,
                              UnaryOperation fw);
    explicit discrete_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    vector<double> probabilities() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const discrete_distribution& x,
                           const discrete_distribution& y);
    friend bool operator!=(const discrete_distribution& x,
                           const discrete_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const discrete_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               discrete_distribution& x);
};

template<class RealType = double>
class piecewise_constant_distribution
{
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef piecewise_constant_distribution distribution_type;

        param_type();
        template<class InputIteratorB, class InputIteratorW>
            param_type(InputIteratorB firstB, InputIteratorB lastB,
                       InputIteratorW firstW);
        template<class UnaryOperation>
            param_type(initializer_list<result_type> bl, UnaryOperation fw);
        template<class UnaryOperation>
            param_type(size_t nw, result_type xmin, result_type xmax,
                       UnaryOperation fw);

        vector<result_type> intervals() const;
        vector<result_type> densities() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    piecewise_constant_distribution();
    template<class InputIteratorB, class InputIteratorW>
        piecewise_constant_distribution(InputIteratorB firstB,
                                        InputIteratorB lastB,
                                        InputIteratorW firstW);
    template<class UnaryOperation>
        piecewise_constant_distribution(initializer_list<result_type> bl,
                                        UnaryOperation fw);
    template<class UnaryOperation>
        piecewise_constant_distribution(size_t nw, result_type xmin,
                                        result_type xmax, UnaryOperation fw);
    explicit piecewise_constant_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    vector<result_type> intervals() const;
    vector<result_type> densities() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const piecewise_constant_distribution& x,
                           const piecewise_constant_distribution& y);
    friend bool operator!=(const piecewise_constant_distribution& x,
                           const piecewise_constant_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const piecewise_constant_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               piecewise_constant_distribution& x);
};

template<class RealType = double>
class piecewise_linear_distribution
{
    // types
    typedef RealType result_type;

    class param_type
    {
    public:
        typedef piecewise_linear_distribution distribution_type;

        param_type();
        template<class InputIteratorB, class InputIteratorW>
            param_type(InputIteratorB firstB, InputIteratorB lastB,
                       InputIteratorW firstW);
        template<class UnaryOperation>
            param_type(initializer_list<result_type> bl, UnaryOperation fw);
        template<class UnaryOperation>
            param_type(size_t nw, result_type xmin, result_type xmax,
                       UnaryOperation fw);

        vector<result_type> intervals() const;
        vector<result_type> densities() const;

        friend bool operator==(const param_type& x, const param_type& y);
        friend bool operator!=(const param_type& x, const param_type& y);
    };

    // constructor and reset functions
    piecewise_linear_distribution();
    template<class InputIteratorB, class InputIteratorW>
        piecewise_linear_distribution(InputIteratorB firstB,
                                      InputIteratorB lastB,
                                      InputIteratorW firstW);

    template<class UnaryOperation>
        piecewise_linear_distribution(initializer_list<result_type> bl,
                                      UnaryOperation fw);

    template<class UnaryOperation>
        piecewise_linear_distribution(size_t nw, result_type xmin,
                                      result_type xmax, UnaryOperation fw);

    explicit piecewise_linear_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URNG> result_type operator()(URNG& g);
    template<class URNG> result_type operator()(URNG& g, const param_type& parm);

    // property functions
    vector<result_type> intervals() const;
    vector<result_type> densities() const;

    param_type param() const;
    void param(const param_type& parm);

    result_type min() const;
    result_type max() const;

    friend bool operator==(const piecewise_linear_distribution& x,
                           const piecewise_linear_distribution& y);
    friend bool operator!=(const piecewise_linear_distribution& x,
                           const piecewise_linear_distribution& y);

    template <class charT, class traits>
    friend
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os,
               const piecewise_linear_distribution& x);

    template <class charT, class traits>
    friend
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is,
               piecewise_linear_distribution& x);
};

} // std
*/

#include <__assert> // all public C++ headers provide the assertion handler
#include <__config>
#include <__random/bernoulli_distribution.h>
#include <__random/binomial_distribution.h>
#include <__random/cauchy_distribution.h>
#include <__random/chi_squared_distribution.h>
#include <__random/clamp_to_integral.h>
#include <__random/default_random_engine.h>
#include <__random/discard_block_engine.h>
#include <__random/discrete_distribution.h>
#include <__random/exponential_distribution.h>
#include <__random/extreme_value_distribution.h>
#include <__random/fisher_f_distribution.h>
#include <__random/gamma_distribution.h>
#include <__random/generate_canonical.h>
#include <__random/geometric_distribution.h>
#include <__random/independent_bits_engine.h>
#include <__random/is_seed_sequence.h>
#include <__random/is_valid.h>
#include <__random/knuth_b.h>
#include <__random/linear_congruential_engine.h>
#include <__random/log2.h>
#include <__random/lognormal_distribution.h>
#include <__random/mersenne_twister_engine.h>
#include <__random/negative_binomial_distribution.h>
#include <__random/normal_distribution.h>
#include <__random/piecewise_constant_distribution.h>
#include <__random/piecewise_linear_distribution.h>
#include <__random/poisson_distribution.h>
#include <__random/random_device.h>
#include <__random/ranlux.h>
#include <__random/seed_seq.h>
#include <__random/shuffle_order_engine.h>
#include <__random/student_t_distribution.h>
#include <__random/subtract_with_carry_engine.h>
#include <__random/uniform_int_distribution.h>
#include <__random/uniform_random_bit_generator.h>
#include <__random/uniform_real_distribution.h>
#include <__random/weibull_distribution.h>
#include <version>

// standard-mandated includes

// [rand.synopsis]
#include <initializer_list>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#  pragma GCC system_header
#endif

#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
#  include <algorithm>
#  include <climits>
#  include <cmath>
#  include <concepts>
#  include <cstddef>
#  include <cstdint>
#  include <iosfwd>
#  include <limits>
#  include <numeric>
#  include <string>
#  include <type_traits>
#  include <vector>
#endif

#endif // _LIBCPP_RANDOM