Standard library header <random> (C++11)

 

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General utilities <any> (C++17) <bitset> <bit> (C++20) <charconv> (C++17) <expected> (C++23) <format> (C++20) <functional> <optional> (C++17) <tuple> (C++11) <typeindex> (C++11) <utility> <variant> (C++17) Containers <array> (C++11) <deque> <flat_map> (C++23) <flat_set> (C++23) <forward_list> (C++11) <inplace_vector> (C++26)    <list> <map> <mdspan> (C++23) <queue> <set> <span> (C++20) <stack> <unordered_map> (C++11) <unordered_set> (C++11) <vector> Iterators <iterator> Ranges <generator> (C++23) <ranges> (C++20)

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Input/output <cinttypes> (C++11) <cstdio> <filesystem> (C++17) <fstream> <iomanip> <iosfwd> <iostream> <ios> <istream> <ostream> <print> (C++23) <spanstream> (C++23) <sstream> <streambuf> <strstream> (C++98/26*) <syncstream> (C++20) Concurrency support <atomic> (C++11) <barrier> (C++20) <condition_variable> (C++11) <future> (C++11) <hazard_pointer> (C++26) <latch> (C++20) <mutex> (C++11) <rcu> (C++26) <semaphore> (C++20) <shared_mutex> (C++14) <stdatomic.h> (C++23) <stop_token> (C++20) <thread> (C++11) Execution support <execution> (C++17)

 

This header is part of the pseudo-random number generation library.

Includes
<initializer_list> (C++11)	std::initializer_list class template
Concepts
Uniform random bit generator requirements
uniform_random_bit_generator (C++20)	specifies that a type qualifies as a uniform random bit generator (concept)
Classes
Random number engines
linear_congruential_engine (C++11)	implements linear congruential algorithm (class template)
mersenne_twister_engine (C++11)	implements Mersenne twister algorithm (class template)
subtract_with_carry_engine (C++11)	implements a subtract-with-carry (lagged Fibonacci) algorithm (class template)
philox_engine (C++26)	a counter-based parallelizable generator (class template)
Random number engine adaptors
discard_block_engine (C++11)	discards some output of a random number engine (class template)
independent_bits_engine (C++11)	packs the output of a random number engine into blocks of a specified number of bits (class template)
shuffle_order_engine (C++11)	delivers the output of a random number engine in a different order (class template)
Predefined generators
minstd_rand0 (C++11)	std::linear_congruential_engine<std::uint_fast32_t,                                 16807, 0, 2147483647> Discovered in 1969 by Lewis, Goodman and Miller, adopted as "Minimal standard" in 1988 by Park and Miller
minstd_rand (C++11)	std::linear_congruential_engine<std::uint_fast32_t,                                 48271, 0, 2147483647> Newer "Minimum standard", recommended by Park, Miller, and Stockmeyer in 1993
mt19937 (C++11)	std::mersenne_twister_engine<std::uint_fast32_t,                              32, 624, 397, 31,                              0x9908b0df, 11,                              0xffffffff, 7,                              0x9d2c5680, 15,                              0xefc60000, 18, 1812433253> 32-bit Mersenne Twister by Matsumoto and Nishimura, 1998
mt19937_64 (C++11)	std::mersenne_twister_engine<std::uint_fast64_t,                              64, 312, 156, 31,                              0xb5026f5aa96619e9, 29,                              0x5555555555555555, 17,                              0x71d67fffeda60000, 37,                              0xfff7eee000000000, 43,                              6364136223846793005> 64-bit Mersenne Twister by Matsumoto and Nishimura, 2000
ranlux24_base (C++11)	std::subtract_with_carry_engine<std::uint_fast32_t, 24, 10, 24>
ranlux48_base (C++11)	std::subtract_with_carry_engine<std::uint_fast64_t, 48, 5, 12>
ranlux24 (C++11)	std::discard_block_engine<std::ranlux24_base, 223, 23> 24-bit RANLUX generator by Martin Lüscher and Fred James, 1994
ranlux48 (C++11)	std::discard_block_engine<std::ranlux48_base, 389, 11> 48-bit RANLUX generator by Martin Lüscher and Fred James, 1994
knuth_b (C++11)	std::shuffle_order_engine<std::minstd_rand0, 256>
philox4x32 (C++26)	std::philox_engine<std::uint_fast32_t, 32, 4, 10,                    0xD2511F53, 0x9E3779B9,                    0xCD9E8D57, 0xBB67AE85>
philox4x64 (C++26)	std::philox_engine<std::uint_fast64_t, 64, 4, 10,                    0xD2E7470EE14C6C93, 0x9E3779B97F4A7C15,                    0xCA5A826395121157, 0xBB67AE8584CAA73B>
default_random_engine(C++11)	implementation-defined
Non-deterministic random numbers
random_device (C++11)	non-deterministic random number generator using hardware entropy source (class)
Uniform distributions
uniform_int_distribution (C++11)	produces integer values evenly distributed across a range (class template)
uniform_real_distribution (C++11)	produces real values evenly distributed across a range (class template)
Bernoulli distributions
bernoulli_distribution (C++11)	produces bool values on a Bernoulli distribution (class)
binomial_distribution (C++11)	produces integer values on a binomial distribution (class template)
negative_binomial_distribution (C++11)	produces integer values on a negative binomial distribution (class template)
geometric_distribution (C++11)	produces integer values on a geometric distribution (class template)
Poisson distributions
poisson_distribution (C++11)	produces integer values on a Poisson distribution (class template)
exponential_distribution (C++11)	produces real values on an exponential distribution (class template)
gamma_distribution (C++11)	produces real values on a gamma distribution (class template)
weibull_distribution (C++11)	produces real values on a Weibull distribution (class template)
extreme_value_distribution (C++11)	produces real values on an extreme value distribution (class template)
Normal distributions
normal_distribution (C++11)	produces real values on a standard normal (Gaussian) distribution (class template)
lognormal_distribution (C++11)	produces real values on a lognormal distribution (class template)
chi_squared_distribution (C++11)	produces real values on a chi-squared distribution (class template)
cauchy_distribution (C++11)	produces real values on a Cauchy distribution (class template)
fisher_f_distribution (C++11)	produces real values on a Fisher's F-distribution (class template)
student_t_distribution (C++11)	produces real values on a Student's t-distribution (class template)
Sampling distributions
discrete_distribution (C++11)	produces random integers on a discrete distribution (class template)
piecewise_constant_distribution (C++11)	produces real values distributed on constant subintervals (class template)
piecewise_linear_distribution (C++11)	produces real values distributed on defined subintervals (class template)
Utilities
seed_seq (C++11)	general-purpose bias-eliminating scrambled seed sequence generator (class)
Functions
generate_canonical (C++11)	evenly distributes real values of given precision across [​0​, 1) (function template)
ranges::generate_random (C++26)	fills a range with random numbers from a uniform random bit generator (niebloid)

Synopsis

#include <initializer_list>
 
namespace std {
  // uniform random bit generator requirements
  template<class G>
  concept uniform_random_bit_generator = /* see description */;
 
  // class template linear_congruential_engine
  template<class UIntType, UIntType a, UIntType c, UIntType m>
  class linear_congruential_engine;
 
  // class template mersenne_twister_engine
  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;
 
  // class template subtract_with_carry_engine
  template<class UIntType, size_t w, size_t s, size_t r>
  class subtract_with_carry_engine;
 
  // class template discard_block_engine
  template<class Engine, size_t p, size_t r>
  class discard_block_engine;
 
  // class template independent_bits_engine
  template<class Engine, size_t w, class UIntType>
  class independent_bits_engine;
 
  // class template shuffle_order_engine
  template<class Engine, size_t k>
  class shuffle_order_engine;
 
  // class template philox_engine
  template<class UIntType, size_t w, size_t n, size_t r, UIntType... consts>
  class philox_engine;
 
  // engines and engine adaptors with predefined parameters
  using minstd_rand0          = /* see description */;
  using minstd_rand           = /* see description */;
  using mt19937               = /* see description */;
  using mt19937_64            = /* see description */;
  using ranlux24_base         = /* see description */;
  using ranlux48_base         = /* see description */;
  using ranlux24              = /* see description */;
  using ranlux48              = /* see description */;
  using knuth_b               = /* see description */;
  using philox4x32            = /* see description */;
  using philox4x64            = /* see description */;
 
  using default_random_engine = /* see description */;
 
  // class random_device
  class random_device;
 
  // class seed_seq
  class seed_seq;
 
  // function template generate_canonical
  template<class RealType, size_t digits, class URBG>
  RealType generate_canonical(URBG& g);
 
  namespace ranges {
    // generate_random
    template<class R, class G>
      requires output_range<R, invoke_result_t<G&>> &&
               uniform_random_bit_generator<remove_cvref_t<G>>
    constexpr borrowed_iterator_t<R> generate_random(R&& r, G&& g);
 
    template<class G, output_iterator<invoke_result_t<G&>> O, sentinel_for<O> S>
      requires uniform_random_bit_generator<remove_cvref_t<G>>
    constexpr O generate_random(O first, S last, G&& g);
 
    template<class R, class G, class D>
      requires output_range<R, invoke_result_t<D&, G&>> && invocable<D&, G&> &&
               uniform_random_bit_generator<remove_cvref_t<G>>
    constexpr borrowed_iterator_t<R> generate_random(R&& r, G&& g, D&& d);
 
    template<class G,
             class D,
             output_iterator<invoke_result_t<D&, G&>> O,
             sentinel_for<O> S>
      requires invocable<D&, G&> && uniform_random_bit_generator<remove_cvref_t<G>>
    constexpr O generate_random(O first, S last, G&& g, D&& d);
  }
 
  // class template uniform_int_distribution
  template<class IntType = int>
  class uniform_int_distribution;
 
  // class template uniform_real_distribution
  template<class RealType = double>
  class uniform_real_distribution;
 
  // class bernoulli_distribution
  class bernoulli_distribution;
 
  // class template binomial_distribution
  template<class IntType = int>
  class binomial_distribution;
 
  // class template geometric_distribution
  template<class IntType = int>
  class geometric_distribution;
 
  // class template negative_binomial_distribution
  template<class IntType = int>
  class negative_binomial_distribution;
 
  // class template poisson_distribution
  template<class IntType = int>
  class poisson_distribution;
 
  // class template exponential_distribution
  template<class RealType = double>
  class exponential_distribution;
 
  // class template gamma_distribution
  template<class RealType = double>
  class gamma_distribution;
 
  // class template weibull_distribution
  template<class RealType = double>
  class weibull_distribution;
 
  // class template extreme_value_distribution
  template<class RealType = double>
  class extreme_value_distribution;
 
  // class template normal_distribution
  template<class RealType = double>
  class normal_distribution;
 
  // class template lognormal_distribution
  template<class RealType = double>
  class lognormal_distribution;
 
  // class template chi_squared_distribution
  template<class RealType = double>
  class chi_squared_distribution;
 
  // class template cauchy_distribution
  template<class RealType = double>
  class cauchy_distribution;
 
  // class template fisher_f_distribution
  template<class RealType = double>
  class fisher_f_distribution;
 
  // class template student_t_distribution
  template<class RealType = double>
  class student_t_distribution;
 
  // class template discrete_distribution
  template<class IntType = int>
  class discrete_distribution;
 
  // class template piecewise_constant_distribution
  template<class RealType = double>
  class piecewise_constant_distribution;
 
  // class template piecewise_linear_distribution
  template<class RealType = double>
  class piecewise_linear_distribution;
}

Concept uniform_random_bit_generator

namespace std {
  template<class G>
  concept uniform_random_bit_generator =
    invocable<G&> && unsigned_integral<invoke_result_t<G&>> && requires {
      {
        G::min()
      } -> same_as<invoke_result_t<G&>>;
      {
        G::max()
      } -> same_as<invoke_result_t<G&>>;
      requires bool_constant<(G::min() < G::max())>::value;
    };
}

Class template std::linear_congruential_engine

namespace std {
  template<class UIntType, UIntType a, UIntType c, UIntType m>
  class linear_congruential_engine
  {
  public:
    // types
    using result_type = UIntType;
 
    // 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
    linear_congruential_engine()
      : linear_congruential_engine(default_seed)
    {
    }
    explicit linear_congruential_engine(result_type s);
    template<class Sseq>
    explicit linear_congruential_engine(Sseq& q);
    void seed(result_type s = default_seed);
    template<class Sseq>
    void seed(Sseq& q);
 
    // equality operators
    friend bool operator==(const linear_congruential_engine& x,
                           const linear_congruential_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const linear_congruential_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    linear_congruential_engine& x);
  };
}

Class template std::mersenne_twister_engine

namespace std {
  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
    using result_type = UIntType;
 
    // 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 UIntType xor_mask                  = a;
    static constexpr size_t tempering_u                 = u;
    static constexpr UIntType tempering_d               = d;
    static constexpr size_t tempering_s                 = s;
    static constexpr UIntType tempering_b               = b;
    static constexpr size_t tempering_t                 = t;
    static constexpr UIntType tempering_c               = c;
    static constexpr size_t tempering_l                 = l;
    static constexpr UIntType 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
    mersenne_twister_engine()
      : mersenne_twister_engine(default_seed)
    {
    }
    explicit mersenne_twister_engine(result_type value);
    template<class Sseq>
    explicit mersenne_twister_engine(Sseq& q);
    void seed(result_type value = default_seed);
    template<class Sseq>
    void seed(Sseq& q);
 
    // equality operators
    friend bool operator==(const mersenne_twister_engine& x,
                           const mersenne_twister_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const mersenne_twister_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    mersenne_twister_engine& x);
  };
}

Class template std::subtract_with_carry_engine

namespace std {
  template<class UIntType, size_t w, size_t s, size_t r>
  class subtract_with_carry_engine
  {
  public:
    // types
    using result_type = UIntType;
 
    // 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 uint_least32_t default_seed = 19780503u;
 
    // constructors and seeding functions
    subtract_with_carry_engine()
      : subtract_with_carry_engine(0u)
    {
    }
    explicit subtract_with_carry_engine(result_type value);
    template<class Sseq>
    explicit subtract_with_carry_engine(Sseq& q);
    void seed(result_type value = 0u);
    template<class Sseq>
    void seed(Sseq& q);
 
    // equality operators
    friend bool operator==(const subtract_with_carry_engine& x,
                           const subtract_with_carry_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const subtract_with_carry_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    subtract_with_carry_engine& x);
  };
}

Class template std::philox_engine

namespace std {
  template<class UIntType, size_t w, size_t n, size_t r, UIntType... consts>
  class philox_engine
  {
    static constexpr size_t /*array-size*/ = n / 2; // exposition only
  public:
    // types
    using result_type = UIntType;
 
    // engine characteristics
    static constexpr size_t word_size   = w;
    static constexpr size_t word_count  = n;
    static constexpr size_t round_count = r;
    static constexpr array<result_type, /*array-size*/> multipliers;
    static constexpr array < result_type, @exposition onlyid { array - size > }
    @round_consts;
    static constexpr result_type min() { return 0; }
    static constexpr result_type max() { return m - 1; }
    static constexpr result_type default_seed = 20111115u;
 
    // constructors and seeding functions
    philox_engine()
      : philox_engine(default_seed)
    {
    }
    explicit philox_engine(result_type value);
    template<class Sseq>
    explicit philox_engine(Sseq& q);
    void seed(result_type value = default_seed);
    template<class Sseq>
    void seed(Sseq& q);
 
    void set_counter(const array<result_type, n>& counter);
 
    // equality operators
    friend bool operator==(const philox_engine& x, const philox_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const philox_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    philox_engine& x);
  };
}

Class template std::discard_block_engine

namespace std {
  template<class Engine, size_t p, size_t r>
  class discard_block_engine
  {
  public:
    // types
    using result_type = typename Engine::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);
 
    // equality operators
    friend bool operator==(const discard_block_engine& x, const discard_block_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // property functions
    const Engine& base() const noexcept { return e; }
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const discard_block_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    discard_block_engine& x);
 
  private:
    Engine e; // exposition only
    size_t n; // exposition only
  };
}

Class template std::independent_bits_engine

namespace std {
  template<class Engine, size_t w, class UIntType>
  class independent_bits_engine
  {
  public:
    // types
    using result_type = UIntType;
 
    // 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);
 
    // equality operators
    friend bool operator==(const independent_bits_engine& x,
                           const independent_bits_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // property functions
    const Engine& base() const noexcept { return e; }
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const independent_bits_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    independent_bits_engine& x);
 
  private:
    Engine e; // exposition only
  };
}

Class template std::shuffle_order_engine

namespace std {
  template<class Engine, size_t k>
  class shuffle_order_engine
  {
  public:
    // types
    using result_type = typename Engine::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);
 
    // equality operators
    friend bool operator==(const shuffle_order_engine& x, const shuffle_order_engine& y);
 
    // generating functions
    result_type operator()();
    void discard(unsigned long long z);
 
    // property functions
    const Engine& base() const noexcept { return e; }
 
    // inserters and extractors
    template<class CharT, class Traits>
    friend basic_ostream<CharT, Traits>& operator<<(basic_ostream<CharT, Traits>& os,
                                                    const shuffle_order_engine& x);
    template<class CharT, class Traits>
    friend basic_istream<CharT, Traits>& operator>>(basic_istream<CharT, Traits>& is,
                                                    shuffle_order_engine& x);
 
  private:
    Engine e;         // exposition only
    result_type V[k]; // exposition only
    result_type Y;    // exposition only
  };
}

Engines and engine adaptors with predefined parameters

namespace std {
using minstd_rand0 = linear_congruential_engine<uint_fast32_t, 16'807, 0, 2'147'483'647>;
using minstd_rand = linear_congruential_engine<uint_fast32_t, 48'271, 0, 2'147'483'647>;
using mt19937 = mersenne_twister_engine<uint_fast32_t,
                                        32,
                                        624,
                                        397,
                                        31,
                                        0x9908'b0df,
                                        11,
                                        0xffff'ffff,
                                        7,
                                        0x9d2c'5680,
                                        15,
                                        0xefc6'0000,
                                        18,
                                        1'812'433'253>; //'
using mt19937_64 = mersenne_twister_engine<uint_fast64_t,
                                           64,
                                           312,
                                           156,
                                           31,
                                           0xb502'6f5a'a966'19e9,
                                           29,
                                           0x5555'5555'5555'5555,
                                           17,
                                           0x71d6'7fff'eda6'0000,
                                           37,
                                           0xfff7'eee0'0000'0000,
                                           43,
                                           6'364'136'223'846'793'005>;
using ranlux24_base = subtract_with_carry_engine<uint_fast32_t, 24, 10, 24>;
using ranlux48_base = subtract_with_carry_engine<uint_fast64_t, 48, 5, 12>;
using ranlux24 = discard_block_engine<ranlux24_base, 223, 23>;
using ranlux48 = discard_block_engine<ranlux48_base, 389, 11>;
using knuth_b = shuffle_order_engine<minstd_rand0, 256>;
using default_random_engine = /* implementation-defined */;
using philox4x32 = philox_engine<uint_fast32_t,
                                 32,
                                 4,
                                 10,
                                 0xD2511F53,
                                 0x9E3779B9,
                                 0xCD9E8D57,
                                 0xBB67AE85>;
using philox4x64 = philox_engine<uint_fast64_t,
                                 64,
                                 4,
                                 10,
                                 0xD2E7470EE14C6C93,
                                 0x9E3779B97F4A7C15,
                                 0xCA5A826395121157,
                                 0xBB67AE8584CAA73B>;
}

Class std::random_device

namespace std {
  class random_device
  {
  public:
    // types
    using result_type = unsigned int;
 
    // 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
    random_device()
      : random_device(/* implementation-defined */)
    {
    }
    explicit random_device(const string& token);
 
    // 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;
  };
}

Class std::seed_seq

namespace std {
  class seed_seq
  {
  public:
    // types
    using result_type = uint_least32_t;
 
    // constructors
    seed_seq() noexcept;
    template<class T>
    seed_seq(initializer_list<T> il);
    template<class InputIter>
    seed_seq(InputIter begin, InputIter end);
 
    // generating functions
    template<class RandomAccessIter>
    void generate(RandomAccessIter begin, RandomAccessIter end);
 
    // property functions
    size_t size() const noexcept;
    template<class OutputIter>
    void param(OutputIter dest) const;
 
    // no copy functions
    seed_seq(const seed_seq&)       = delete;
    void operator=(const seed_seq&) = delete;
 
  private:
    vector<result_type> v; // exposition only
  };
}

Class template std::uniform_int_distribution

namespace std {
  template<class IntType = int>
  class uniform_int_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    uniform_int_distribution()
      : uniform_int_distribution(0)
    {
    }
    explicit uniform_int_distribution(IntType a,
                                      IntType b = numeric_limits<IntType>::max());
    explicit uniform_int_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const uniform_int_distribution& x,
                           const uniform_int_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::uniform_real_distribution

namespace std {
  template<class RealType = double>
  class uniform_real_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    uniform_real_distribution()
      : uniform_real_distribution(0.0)
    {
    }
    explicit uniform_real_distribution(RealType a, RealType b = 1.0);
    explicit uniform_real_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const uniform_real_distribution& x,
                           const uniform_real_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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 std::bernoulli_distribution

namespace std {
  class bernoulli_distribution
  {
  public:
    // types
    using result_type = bool;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    bernoulli_distribution()
      : bernoulli_distribution(0.5)
    {
    }
    explicit bernoulli_distribution(double p);
    explicit bernoulli_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const bernoulli_distribution& x,
                           const bernoulli_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::binomial_distribution

namespace std {
  template<class IntType = int>
  class binomial_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    binomial_distribution()
      : binomial_distribution(1)
    {
    }
    explicit binomial_distribution(IntType t, double p = 0.5);
    explicit binomial_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const binomial_distribution& x,
                           const binomial_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::geometric_distribution

namespace std {
  template<class IntType = int>
  class geometric_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    geometric_distribution()
      : geometric_distribution(0.5)
    {
    }
    explicit geometric_distribution(double p);
    explicit geometric_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const geometric_distribution& x,
                           const geometric_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::negative_binomial_distribution

namespace std {
  template<class IntType = int>
  class negative_binomial_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    negative_binomial_distribution()
      : negative_binomial_distribution(1)
    {
    }
    explicit negative_binomial_distribution(IntType k, double p = 0.5);
    explicit negative_binomial_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const negative_binomial_distribution& x,
                           const negative_binomial_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    IntType k() const;
    double p() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::poisson_distribution

namespace std {
  template<class IntType = int>
  class poisson_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    poisson_distribution()
      : poisson_distribution(1.0)
    {
    }
    explicit poisson_distribution(double mean);
    explicit poisson_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const poisson_distribution& x, const poisson_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::exponential_distribution

namespace std {
  template<class RealType = double>
  class exponential_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    exponential_distribution()
      : exponential_distribution(1.0)
    {
    }
    explicit exponential_distribution(RealType lambda);
    explicit exponential_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const exponential_distribution& x,
                           const exponential_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType lambda() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::gamma_distribution

namespace std {
  template<class RealType = double>
  class gamma_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    gamma_distribution()
      : gamma_distribution(1.0)
    {
    }
    explicit gamma_distribution(RealType alpha, RealType beta = 1.0);
    explicit gamma_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const gamma_distribution& x, const gamma_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType alpha() const;
    RealType beta() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::weibull_distribution

namespace std {
  template<class RealType = double>
  class weibull_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    weibull_distribution()
      : weibull_distribution(1.0)
    {
    }
    explicit weibull_distribution(RealType a, RealType b = 1.0);
    explicit weibull_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const weibull_distribution& x, const weibull_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType a() const;
    RealType b() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::extreme_value_distribution

namespace std {
  template<class RealType = double>
  class extreme_value_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    extreme_value_distribution()
      : extreme_value_distribution(0.0)
    {
    }
    explicit extreme_value_distribution(RealType a, RealType b = 1.0);
    explicit extreme_value_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const extreme_value_distribution& x,
                           const extreme_value_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType a() const;
    RealType b() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::normal_distribution

namespace std {
  template<class RealType = double>
  class normal_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructors and reset functions
    normal_distribution()
      : normal_distribution(0.0)
    {
    }
    explicit normal_distribution(RealType mean, RealType stddev = 1.0);
    explicit normal_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const normal_distribution& x, const normal_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType mean() const;
    RealType stddev() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::lognormal_distribution

namespace std {
  template<class RealType = double>
  class lognormal_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    lognormal_distribution()
      : lognormal_distribution(0.0)
    {
    }
    explicit lognormal_distribution(RealType m, RealType s = 1.0);
    explicit lognormal_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const lognormal_distribution& x,
                           const lognormal_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType m() const;
    RealType s() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::chi_squared_distribution

namespace std {
  template<class RealType = double>
  class chi_squared_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    chi_squared_distribution()
      : chi_squared_distribution(1.0)
    {
    }
    explicit chi_squared_distribution(RealType n);
    explicit chi_squared_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const chi_squared_distribution& x,
                           const chi_squared_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType n() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::cauchy_distribution

namespace std {
  template<class RealType = double>
  class cauchy_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    cauchy_distribution()
      : cauchy_distribution(0.0)
    {
    }
    explicit cauchy_distribution(RealType a, RealType b = 1.0);
    explicit cauchy_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const cauchy_distribution& x, const cauchy_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType a() const;
    RealType b() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::fisher_f_distribution

namespace std {
  template<class RealType = double>
  class fisher_f_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    fisher_f_distribution()
      : fisher_f_distribution(1.0)
    {
    }
    explicit fisher_f_distribution(RealType m, RealType n = 1.0);
    explicit fisher_f_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const fisher_f_distribution& x,
                           const fisher_f_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType m() const;
    RealType n() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::student_t_distribution

namespace std {
  template<class RealType = double>
  class student_t_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    student_t_distribution()
      : student_t_distribution(1.0)
    {
    }
    explicit student_t_distribution(RealType n);
    explicit student_t_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const student_t_distribution& x,
                           const student_t_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);
 
    // property functions
    RealType n() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
 
    // inserters and extractors
    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);
  };
}

Class template std::discrete_distribution

namespace std {
  template<class IntType = int>
  class discrete_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    discrete_distribution();
    template<class InputIter>
    discrete_distribution(InputIter firstW, InputIter 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();
 
    // equality operators
    friend bool operator==(const discrete_distribution& x,
                           const discrete_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::piecewise_constant_distribution

namespace std {
  template<class RealType = double>
  class piecewise_constant_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    piecewise_constant_distribution();
    template<class InputIterB, class InputIterW>
    piecewise_constant_distribution(InputIterB firstB,
                                    InputIterB lastB,
                                    InputIterW firstW);
    template<class UnaryOperation>
    piecewise_constant_distribution(initializer_list<RealType> bl, UnaryOperation fw);
    template<class UnaryOperation>
    piecewise_constant_distribution(size_t nw,
                                    RealType xmin,
                                    RealType xmax,
                                    UnaryOperation fw);
    explicit piecewise_constant_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const piecewise_constant_distribution& x,
                           const piecewise_constant_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}

Class template std::piecewise_linear_distribution

namespace std {
  template<class RealType = double>
  class piecewise_linear_distribution
  {
  public:
    // types
    using result_type = RealType;
    using param_type  = /* unspecified */;
 
    // constructor and reset functions
    piecewise_linear_distribution();
    template<class InputIterB, class InputIterW>
    piecewise_linear_distribution(InputIterB firstB, InputIterB lastB, InputIterW firstW);
    template<class UnaryOperation>
    piecewise_linear_distribution(initializer_list<RealType> bl, UnaryOperation fw);
    template<class UnaryOperation>
    piecewise_linear_distribution(size_t nw,
                                  RealType xmin,
                                  RealType xmax,
                                  UnaryOperation fw);
    explicit piecewise_linear_distribution(const param_type& parm);
    void reset();
 
    // equality operators
    friend bool operator==(const piecewise_linear_distribution& x,
                           const piecewise_linear_distribution& y);
 
    // generating functions
    template<class URBG>
    result_type operator()(URBG& g);
    template<class URBG>
    result_type operator()(URBG& 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;
 
    // inserters and extractors
    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);
  };
}