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// random number generation -*- C++ -*- // Copyright (C) 2009, 2010 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free // software; you can redistribute it and/or modify it under the // terms of the GNU General Public License as published by the // Free Software Foundation; either version 3, or (at your option) // any later version. // This library is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // Under Section 7 of GPL version 3, you are granted additional // permissions described in the GCC Runtime Library Exception, version // 3.1, as published by the Free Software Foundation. // You should have received a copy of the GNU General Public License and // a copy of the GCC Runtime Library Exception along with this program; // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see // <http://www.gnu.org/licenses/>. /** * @file bits/random.h * This is an internal header file, included by other library headers. * You should not attempt to use it directly. */ #include <vector> namespace std { // [26.4] Random number generation /** * @defgroup random Random Number Generation * @ingroup numerics * * A facility for generating random numbers on selected distributions. * @{ */ /** * @brief A function template for converting the output of a (integral) * uniform random number generator to a floatng point result in the range * [0-1). */ template<typename _RealType, size_t __bits, typename _UniformRandomNumberGenerator> _RealType generate_canonical(_UniformRandomNumberGenerator& __g); /* * Implementation-space details. */ namespace __detail { template<typename _UIntType, size_t __w, bool = __w < static_cast<size_t> (std::numeric_limits<_UIntType>::digits)> struct _Shift { static const _UIntType __value = 0; }; template<typename _UIntType, size_t __w> struct _Shift<_UIntType, __w, true> { static const _UIntType __value = _UIntType(1) << __w; }; template<typename _Tp, _Tp __m, _Tp __a, _Tp __c, bool> struct _Mod; // Dispatch based on modulus value to prevent divide-by-zero compile-time // errors when m == 0. template<typename _Tp, _Tp __m, _Tp __a = 1, _Tp __c = 0> inline _Tp __mod(_Tp __x) { return _Mod<_Tp, __m, __a, __c, __m == 0>::__calc(__x); } /* * An adaptor class for converting the output of any Generator into * the input for a specific Distribution. */ template<typename _Engine, typename _DInputType> struct _Adaptor { public: _Adaptor(_Engine& __g) : _M_g(__g) { } _DInputType min() const { return _DInputType(0); } _DInputType max() const { return _DInputType(1); } /* * Converts a value generated by the adapted random number generator * into a value in the input domain for the dependent random number * distribution. */ _DInputType operator()() { return std::generate_canonical<_DInputType, std::numeric_limits<_DInputType>::digits, _Engine>(_M_g); } private: _Engine& _M_g; }; } // namespace __detail /** * @addtogroup random_generators Random Number Generators * @ingroup random * * These classes define objects which provide random or pseudorandom * numbers, either from a discrete or a continuous interval. The * random number generator supplied as a part of this library are * all uniform random number generators which provide a sequence of * random number uniformly distributed over their range. * * A number generator is a function object with an operator() that * takes zero arguments and returns a number. * * A compliant random number generator must satisfy the following * requirements. <table border=1 cellpadding=10 cellspacing=0> * <caption align=top>Random Number Generator Requirements</caption> * <tr><td>To be documented.</td></tr> </table> * * @{ */ /** * @brief A model of a linear congruential random number generator. * * A random number generator that produces pseudorandom numbers via * linear function: * @f[ * x_{i+1}\leftarrow(ax_{i} + c) \bmod m * @f] * * The template parameter @p _UIntType must be an unsigned integral type * large enough to store values up to (__m-1). If the template parameter * @p __m is 0, the modulus @p __m used is * std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template * parameters @p __a and @p __c must be less than @p __m. * * The size of the state is @f$1@f$. */ template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> class linear_congruential_engine { static_assert(std::is_unsigned<_UIntType>::value, "template argument " "substituting _UIntType not an unsigned integral type"); static_assert(__m == 0u || (__a < __m && __c < __m), "template argument substituting __m out of bounds"); public: /** The type of the generated random value. */ typedef _UIntType result_type; /** The multiplier. */ static const result_type multiplier = __a; /** An increment. */ static const result_type increment = __c; /** The modulus. */ static const result_type modulus = __m; static const result_type default_seed = 1u; /** * @brief Constructs a %linear_congruential_engine random number * generator engine with seed @p __s. The default seed value * is 1. * * @param __s The initial seed value. */ explicit linear_congruential_engine(result_type __s = default_seed) { seed(__s); } /** * @brief Constructs a %linear_congruential_engine random number * generator engine seeded from the seed sequence @p __q. * * @param __q the seed sequence. */ template<typename _Sseq, typename = typename std::enable_if<!std::is_same<_Sseq, linear_congruential_engine>::value> ::type> explicit linear_congruential_engine(_Sseq& __q) { seed(__q); } /** * @brief Reseeds the %linear_congruential_engine random number generator * engine sequence to the seed @p __s. * * @param __s The new seed. */ void seed(result_type __s = default_seed); /** * @brief Reseeds the %linear_congruential_engine random number generator * engine * sequence using values from the seed sequence @p __q. * * @param __q the seed sequence. */ template<typename _Sseq> typename std::enable_if<std::is_class<_Sseq>::value>::type seed(_Sseq& __q); /** * @brief Gets the smallest possible value in the output range. * * The minimum depends on the @p __c parameter: if it is zero, the * minimum generated must be > 0, otherwise 0 is allowed. * * @todo This should be constexpr. */ result_type min() const { return __c == 0u ? 1u : 0u; } /** * @brief Gets the largest possible value in the output range. * * @todo This should be constexpr. */ result_type max() const { return __m - 1u; } /** * @brief Discard a sequence of random numbers. * * @todo Look for a faster way to do discard. */ void discard(unsigned long long __z) { for (; __z != 0ULL; --__z) (*this)(); } /** * @brief Gets the next random number in the sequence. */ result_type operator()() { _M_x = __detail::__mod<_UIntType, __m, __a, __c>(_M_x); return _M_x; } /** * @brief Compares two linear congruential random number generator * objects of the same type for equality. * * @param __lhs A linear congruential random number generator object. * @param __rhs Another linear congruential random number generator * object. * * @returns true if the infinite sequences of generated values * would be equal, false otherwise. */ friend bool operator==(const linear_congruential_engine& __lhs, const linear_congruential_engine& __rhs) { return __lhs._M_x == __rhs._M_x; } /** * @brief Writes the textual representation of the state x(i) of x to * @p __os. * * @param __os The output stream. * @param __lcr A % linear_congruential_engine random number generator. * @returns __os. */ template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1, _UIntType1 __m1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::linear_congruential_engine<_UIntType1, __a1, __c1, __m1>&); /** * @brief Sets the state of the engine by reading its textual * representation from @p __is. * * The textual representation must have been previously written using * an output stream whose imbued locale and whose type's template * specialization arguments _CharT and _Traits were the same as those * of @p __is. * * @param __is The input stream. * @param __lcr A % linear_congruential_engine random number generator. * @returns __is. */ template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1, _UIntType1 __m1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::linear_congruential_engine<_UIntType1, __a1, __c1, __m1>&); private: _UIntType _M_x; }; /** * @brief Compares two linear congruential random number generator * objects of the same type for inequality. * * @param __lhs A linear congruential random number generator object. * @param __rhs Another linear congruential random number generator * object. * * @returns true if the infinite sequences of generated values * would be different, false otherwise. */ template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> inline bool operator!=(const std::linear_congruential_engine<_UIntType, __a, __c, __m>& __lhs, const std::linear_congruential_engine<_UIntType, __a, __c, __m>& __rhs) { return !(__lhs == __rhs); } /** * A generalized feedback shift register discrete random number generator. * * This algorithm avoids multiplication and division and is designed to be * friendly to a pipelined architecture. If the parameters are chosen * correctly, this generator will produce numbers with a very long period and * fairly good apparent entropy, although still not cryptographically strong. * * The best way to use this generator is with the predefined mt19937 class. * * This algorithm was originally invented by Makoto Matsumoto and * Takuji Nishimura. * * @var word_size The number of bits in each element of the state vector. * @var state_size The degree of recursion. * @var shift_size The period parameter. * @var mask_bits The separation point bit index. * @var parameter_a The last row of the twist matrix. * @var output_u The first right-shift tempering matrix parameter. * @var output_s The first left-shift tempering matrix parameter. * @var output_b The first left-shift tempering matrix mask. * @var output_t The second left-shift tempering matrix parameter. * @var output_c The second left-shift tempering matrix mask. * @var output_l The second right-shift tempering matrix parameter. */ template<typename _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 { static_assert(std::is_unsigned<_UIntType>::value, "template argument " "substituting _UIntType not an unsigned integral type"); static_assert(1u <= __m && __m <= __n, "template argument substituting __m out of bounds"); static_assert(__r <= __w, "template argument substituting " "__r out of bound"); static_assert(__u <= __w, "template argument substituting " "__u out of bound"); static_assert(__s <= __w, "template argument substituting " "__s out of bound"); static_assert(__t <= __w, "template argument substituting " "__t out of bound"); static_assert(__l <= __w, "template argument substituting " "__l out of bound"); static_assert(__w <= std::numeric_limits<_UIntType>::digits, "template argument substituting __w out of bound"); static_assert(__a <= (__detail::_Shift<_UIntType, __w>::__value - 1), "template argument substituting __a out of bound"); static_assert(__b <= (__detail::_Shift<_UIntType, __w>::__value - 1), "template argument substituting __b out of bound"); static_assert(__c <= (__detail::_Shift<_UIntType, __w>::__value - 1), "template argument substituting __c out of bound"); static_assert(__d <= (__detail::_Shift<_UIntType, __w>::__value - 1), "template argument substituting __d out of bound"); static_assert(__f <= (__detail::_Shift<_UIntType, __w>::__value - 1), "template argument substituting __f out of bound"); public: /** The type of the generated random value. */ typedef _UIntType result_type; // parameter values static const size_t word_size = __w; static const size_t state_size = __n; static const size_t shift_size = __m; static const size_t mask_bits = __r; static const result_type xor_mask = __a; static const size_t tempering_u = __u; static const result_type tempering_d = __d; static const size_t tempering_s = __s; static const result_type tempering_b = __b; static const size_t tempering_t = __t; static const result_type tempering_c = __c; static const size_t tempering_l = __l; static const result_type initialization_multiplier = __f; static const result_type default_seed = 5489u; // constructors and member function explicit mersenne_twister_engine(result_type __sd = default_seed) { seed(__sd); } /** * @brief Constructs a %mersenne_twister_engine random number generator * engine seeded from the seed sequence @p __q. * * @param __q the seed sequence. */ template<typename _Sseq, typename = typename std::enable_if<!std::is_same<_Sseq, mersenne_twister_engine>::value> ::type> explicit mersenne_twister_engine(_Sseq& __q) { seed(__q); } void seed(result_type __sd = default_seed); template<typename _Sseq> typename std::enable_if<std::is_class<_Sseq>::value>::type seed(_Sseq& __q); /** * @brief Gets the smallest possible value in the output range. * * @todo This should be constexpr. */ result_type min() const { return 0; }; /** * @brief Gets the largest possible value in the output range. * * @todo This should be constexpr. */ result_type max() const { return __detail::_Shift<_UIntType, __w>::__value - 1; } /** * @brief Discard a sequence of random numbers. * * @todo Look for a faster way to do discard. */ void discard(unsigned long long __z) { for (; __z != 0ULL; --__z) (*this)(); } result_type operator()(); /** * @brief Compares two % mersenne_twister_engine random number generator * objects of the same type for equality. * * @param __lhs A % mersenne_twister_engine random number generator * object. * @param __rhs Another % mersenne_twister_engine random number * generator object. * * @returns true if the infinite sequences of generated values * would be equal, false otherwise. */ friend bool operator==(const mersenne_twister_engine& __lhs, const mersenne_twister_engine& __rhs) { return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); } /** * @brief Inserts the current state of a % mersenne_twister_engine * random number generator engine @p __x into the output stream * @p __os. * * @param __os An output stream. * @param __x A % mersenne_twister_engine random number generator * engine. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _UIntType1, size_t __w1, size_t __n1, size_t __m1, size_t __r1, _UIntType1 __a1, size_t __u1, _UIntType1 __d1, size_t __s1, _UIntType1 __b1, size_t __t1, _UIntType1 __c1, size_t __l1, _UIntType1 __f1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::mersenne_twister_engine<_UIntType1, __w1, __n1, __m1, __r1, __a1, __u1, __d1, __s1, __b1, __t1, __c1, __l1, __f1>&); /** * @brief Extracts the current state of a % mersenne_twister_engine * random number generator engine @p __x from the input stream * @p __is. * * @param __is An input stream. * @param __x A % mersenne_twister_engine random number generator * engine. * * @returns The input stream with the state of @p __x extracted or in * an error state. */ template<typename _UIntType1, size_t __w1, size_t __n1, size_t __m1, size_t __r1, _UIntType1 __a1, size_t __u1, _UIntType1 __d1, size_t __s1, _UIntType1 __b1, size_t __t1, _UIntType1 __c1, size_t __l1, _UIntType1 __f1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::mersenne_twister_engine<_UIntType1, __w1, __n1, __m1, __r1, __a1, __u1, __d1, __s1, __b1, __t1, __c1, __l1, __f1>&); private: _UIntType _M_x[state_size]; size_t _M_p; }; /** * @brief Compares two % mersenne_twister_engine random number generator * objects of the same type for inequality. * * @param __lhs A % mersenne_twister_engine random number generator * object. * @param __rhs Another % mersenne_twister_engine random number * generator object. * * @returns true if the infinite sequences of generated values * would be different, false otherwise. */ template<typename _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> inline bool operator!=(const std::mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __lhs, const std::mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __rhs) { return !(__lhs == __rhs); } /** * @brief The Marsaglia-Zaman generator. * * This is a model of a Generalized Fibonacci discrete random number * generator, sometimes referred to as the SWC generator. * * A discrete random number generator that produces pseudorandom * numbers using: * @f[ * x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m * @f] * * The size of the state is @f$r@f$ * and the maximum period of the generator is @f$(m^r - m^s - 1)@f$. * * @var _M_x The state of the generator. This is a ring buffer. * @var _M_carry The carry. * @var _M_p Current index of x(i - r). */ template<typename _UIntType, size_t __w, size_t __s, size_t __r> class subtract_with_carry_engine { static_assert(std::is_unsigned<_UIntType>::value, "template argument " "substituting _UIntType not an unsigned integral type"); static_assert(0u < __s && __s < __r, "template argument substituting __s out of bounds"); static_assert(0u < __w && __w <= std::numeric_limits<_UIntType>::digits, "template argument substituting __w out of bounds"); public: /** The type of the generated random value. */ typedef _UIntType result_type; // parameter values static const size_t word_size = __w; static const size_t short_lag = __s; static const size_t long_lag = __r; static const result_type default_seed = 19780503u; /** * @brief Constructs an explicitly seeded % subtract_with_carry_engine * random number generator. */ explicit subtract_with_carry_engine(result_type __sd = default_seed) { seed(__sd); } /** * @brief Constructs a %subtract_with_carry_engine random number engine * seeded from the seed sequence @p __q. * * @param __q the seed sequence. */ template<typename _Sseq, typename = typename std::enable_if<!std::is_same<_Sseq, subtract_with_carry_engine>::value> ::type> explicit subtract_with_carry_engine(_Sseq& __q) { seed(__q); } /** * @brief Seeds the initial state @f$x_0@f$ of the random number * generator. * * N1688[4.19] modifies this as follows. If @p __value == 0, * sets value to 19780503. In any case, with a linear * congruential generator lcg(i) having parameters @f$ m_{lcg} = * 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value * @f$, sets @f$ x_{-r} \dots x_{-1} @f$ to @f$ lcg(1) \bmod m * \dots lcg(r) \bmod m @f$ respectively. If @f$ x_{-1} = 0 @f$ * set carry to 1, otherwise sets carry to 0. */ void seed(result_type __sd = default_seed); /** * @brief Seeds the initial state @f$x_0@f$ of the * % subtract_with_carry_engine random number generator. */ template<typename _Sseq> typename std::enable_if<std::is_class<_Sseq>::value>::type seed(_Sseq& __q); /** * @brief Gets the inclusive minimum value of the range of random * integers returned by this generator. * * @todo This should be constexpr. */ result_type min() const { return 0; } /** * @brief Gets the inclusive maximum value of the range of random * integers returned by this generator. * * @todo This should be constexpr. */ result_type max() const { return __detail::_Shift<_UIntType, __w>::__value - 1; } /** * @brief Discard a sequence of random numbers. * * @todo Look for a faster way to do discard. */ void discard(unsigned long long __z) { for (; __z != 0ULL; --__z) (*this)(); } /** * @brief Gets the next random number in the sequence. */ result_type operator()(); /** * @brief Compares two % subtract_with_carry_engine random number * generator objects of the same type for equality. * * @param __lhs A % subtract_with_carry_engine random number generator * object. * @param __rhs Another % subtract_with_carry_engine random number * generator object. * * @returns true if the infinite sequences of generated values * would be equal, false otherwise. */ friend bool operator==(const subtract_with_carry_engine& __lhs, const subtract_with_carry_engine& __rhs) { return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); } /** * @brief Inserts the current state of a % subtract_with_carry_engine * random number generator engine @p __x into the output stream * @p __os. * * @param __os An output stream. * @param __x A % subtract_with_carry_engine random number generator * engine. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _UIntType1, size_t __w1, size_t __s1, size_t __r1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::subtract_with_carry_engine<_UIntType1, __w1, __s1, __r1>&); /** * @brief Extracts the current state of a % subtract_with_carry_engine * random number generator engine @p __x from the input stream * @p __is. * * @param __is An input stream. * @param __x A % subtract_with_carry_engine random number generator * engine. * * @returns The input stream with the state of @p __x extracted or in * an error state. */ template<typename _UIntType1, size_t __w1, size_t __s1, size_t __r1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::subtract_with_carry_engine<_UIntType1, __w1, __s1, __r1>&); private: _UIntType _M_x[long_lag]; _UIntType _M_carry; size_t _M_p; }; /** * @brief Compares two % subtract_with_carry_engine random number * generator objects of the same type for inequality. * * @param __lhs A % subtract_with_carry_engine random number generator * object. * @param __rhs Another % subtract_with_carry_engine random number * generator object. * * @returns true if the infinite sequences of generated values * would be different, false otherwise. */ template<typename _UIntType, size_t __w, size_t __s, size_t __r> inline bool operator!=(const std::subtract_with_carry_engine<_UIntType, __w, __s, __r>& __lhs, const std::subtract_with_carry_engine<_UIntType, __w, __s, __r>& __rhs) { return !(__lhs == __rhs); } /** * Produces random numbers from some base engine by discarding blocks of * data. * * 0 <= @p __r <= @p __p */ template<typename _RandomNumberEngine, size_t __p, size_t __r> class discard_block_engine { static_assert(1 <= __r && __r <= __p, "template argument substituting __r out of bounds"); public: /** The type of the generated random value. */ typedef typename _RandomNumberEngine::result_type result_type; // parameter values static const size_t block_size = __p; static const size_t used_block = __r; /** * @brief Constructs a default %discard_block_engine engine. * * The underlying engine is default constructed as well. */ discard_block_engine() : _M_b(), _M_n(0) { } /** * @brief Copy constructs a %discard_block_engine engine. * * Copies an existing base class random number generator. * @param rng An existing (base class) engine object. */ explicit discard_block_engine(const _RandomNumberEngine& __rne) : _M_b(__rne), _M_n(0) { } /** * @brief Move constructs a %discard_block_engine engine. * * Copies an existing base class random number generator. * @param rng An existing (base class) engine object. */ explicit discard_block_engine(_RandomNumberEngine&& __rne) : _M_b(std::move(__rne)), _M_n(0) { } /** * @brief Seed constructs a %discard_block_engine engine. * * Constructs the underlying generator engine seeded with @p __s. * @param __s A seed value for the base class engine. */ explicit discard_block_engine(result_type __s) : _M_b(__s), _M_n(0) { } /** * @brief Generator construct a %discard_block_engine engine. * * @param __q A seed sequence. */ template<typename _Sseq, typename = typename std::enable_if<!std::is_same<_Sseq, discard_block_engine>::value && !std::is_same<_Sseq, _RandomNumberEngine>::value> ::type> explicit discard_block_engine(_Sseq& __q) : _M_b(__q), _M_n(0) { } /** * @brief Reseeds the %discard_block_engine object with the default * seed for the underlying base class generator engine. */ void seed() { _M_b.seed(); _M_n = 0; } /** * @brief Reseeds the %discard_block_engine object with the default * seed for the underlying base class generator engine. */ void seed(result_type __s) { _M_b.seed(__s); _M_n = 0; } /** * @brief Reseeds the %discard_block_engine object with the given seed * sequence. * @param __q A seed generator function. */ template<typename _Sseq> void seed(_Sseq& __q) { _M_b.seed(__q); _M_n = 0; } /** * @brief Gets a const reference to the underlying generator engine * object. */ const _RandomNumberEngine& base() const { return _M_b; } /** * @brief Gets the minimum value in the generated random number range. * * @todo This should be constexpr. */ result_type min() const { return _M_b.min(); } /** * @brief Gets the maximum value in the generated random number range. * * @todo This should be constexpr. */ result_type max() const { return _M_b.max(); } /** * @brief Discard a sequence of random numbers. * * @todo Look for a faster way to do discard. */ void discard(unsigned long long __z) { for (; __z != 0ULL; --__z) (*this)(); } /** * @brief Gets the next value in the generated random number sequence. */ result_type operator()(); /** * @brief Compares two %discard_block_engine random number generator * objects of the same type for equality. * * @param __lhs A %discard_block_engine random number generator object. * @param __rhs Another %discard_block_engine random number generator * object. * * @returns true if the infinite sequences of generated values * would be equal, false otherwise. */ friend bool operator==(const discard_block_engine& __lhs, const discard_block_engine& __rhs) { return __lhs._M_b == __rhs._M_b && __lhs._M_n == __rhs._M_n; } /** * @brief Inserts the current state of a %discard_block_engine random * number generator engine @p __x into the output stream * @p __os. * * @param __os An output stream. * @param __x A %discard_block_engine random number generator engine. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RandomNumberEngine1, size_t __p1, size_t __r1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::discard_block_engine<_RandomNumberEngine1, __p1, __r1>&); /** * @brief Extracts the current state of a % subtract_with_carry_engine * random number generator engine @p __x from the input stream * @p __is. * * @param __is An input stream. * @param __x A %discard_block_engine random number generator engine. * * @returns The input stream with the state of @p __x extracted or in * an error state. */ template<typename _RandomNumberEngine1, size_t __p1, size_t __r1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::discard_block_engine<_RandomNumberEngine1, __p1, __r1>&); private: _RandomNumberEngine _M_b; size_t _M_n; }; /** * @brief Compares two %discard_block_engine random number generator * objects of the same type for inequality. * * @param __lhs A %discard_block_engine random number generator object. * @param __rhs Another %discard_block_engine random number generator * object. * * @returns true if the infinite sequences of generated values * would be different, false otherwise. */ template<typename _RandomNumberEngine, size_t __p, size_t __r> inline bool operator!=(const std::discard_block_engine<_RandomNumberEngine, __p, __r>& __lhs, const std::discard_block_engine<_RandomNumberEngine, __p, __r>& __rhs) { return !(__lhs == __rhs); } /** * Produces random numbers by combining random numbers from some base * engine to produce random numbers with a specifies number of bits @p __w. */ template<typename _RandomNumberEngine, size_t __w, typename _UIntType> class independent_bits_engine { static_assert(std::is_unsigned<_UIntType>::value, "template argument " "substituting _UIntType not an unsigned integral type"); static_assert(0u < __w && __w <= std::numeric_limits<_UIntType>::digits, "template argument substituting __w out of bounds"); public: /** The type of the generated random value. */ typedef _UIntType result_type; /** * @brief Constructs a default %independent_bits_engine engine. * * The underlying engine is default constructed as well. */ independent_bits_engine() : _M_b() { } /** * @brief Copy constructs a %independent_bits_engine engine. * * Copies an existing base class random number generator. * @param rng An existing (base class) engine object. */ explicit independent_bits_engine(const _RandomNumberEngine& __rne) : _M_b(__rne) { } /** * @brief Move constructs a %independent_bits_engine engine. * * Copies an existing base class random number generator. * @param rng An existing (base class) engine object. */ explicit independent_bits_engine(_RandomNumberEngine&& __rne) : _M_b(std::move(__rne)) { } /** * @brief Seed constructs a %independent_bits_engine engine. * * Constructs the underlying generator engine seeded with @p __s. * @param __s A seed value for the base class engine. */ explicit independent_bits_engine(result_type __s) : _M_b(__s) { } /** * @brief Generator construct a %independent_bits_engine engine. * * @param __q A seed sequence. */ template<typename _Sseq, typename = typename std::enable_if<!std::is_same<_Sseq, independent_bits_engine>::value && !std::is_same<_Sseq, _RandomNumberEngine>::value> ::type> explicit independent_bits_engine(_Sseq& __q) : _M_b(__q) { } /** * @brief Reseeds the %independent_bits_engine object with the default * seed for the underlying base class generator engine. */ void seed() { _M_b.seed(); } /** * @brief Reseeds the %independent_bits_engine object with the default * seed for the underlying base class generator engine. */ void seed(result_type __s) { _M_b.seed(__s); } /** * @brief Reseeds the %independent_bits_engine object with the given * seed sequence. * @param __q A seed generator function. */ template<typename _Sseq> void seed(_Sseq& __q) { _M_b.seed(__q); } /** * @brief Gets a const reference to the underlying generator engine * object. */ const _RandomNumberEngine& base() const { return _M_b; } /** * @brief Gets the minimum value in the generated random number range. * * @todo This should be constexpr. */ result_type min() const { return 0U; } /** * @brief Gets the maximum value in the generated random number range. * * @todo This should be constexpr. */ result_type max() const { return __detail::_Shift<_UIntType, __w>::__value - 1; } /** * @brief Discard a sequence of random numbers. * * @todo Look for a faster way to do discard. */ void discard(unsigned long long __z) { for (; __z != 0ULL; --__z) (*this)(); } /** * @brief Gets the next value in the generated random number sequence. */ result_type operator()(); /** * @brief Compares two %independent_bits_engine random number generator * objects of the same type for equality. * * @param __lhs A %independent_bits_engine random number generator * object. * @param __rhs Another %independent_bits_engine random number generator * object. * * @returns true if the infinite sequences of generated values * would be equal, false otherwise. */ friend bool operator==(const independent_bits_engine& __lhs, const independent_bits_engine& __rhs) { return __lhs._M_b == __rhs._M_b; } /** * @brief Extracts the current state of a % subtract_with_carry_engine * random number generator engine @p __x from the input stream * @p __is. * * @param __is An input stream. * @param __x A %independent_bits_engine random number generator * engine. * * @returns The input stream with the state of @p __x extracted or in * an error state. */ template<typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, std::independent_bits_engine<_RandomNumberEngine, __w, _UIntType>& __x) { __is >> __x._M_b; return __is; } private: _RandomNumberEngine _M_b; }; /** * @brief Compares two %independent_bits_engine random number generator * objects of the same type for inequality. * * @param __lhs A %independent_bits_engine random number generator * object. * @param __rhs Another %independent_bits_engine random number generator * object. * * @returns true if the infinite sequences of generated values * would be different, false otherwise. */ template<typename _RandomNumberEngine, size_t __w, typename _UIntType> inline bool operator!=(const std::independent_bits_engine<_RandomNumberEngine, __w, _UIntType>& __lhs, const std::independent_bits_engine<_RandomNumberEngine, __w, _UIntType>& __rhs) { return !(__lhs == __rhs); } /** * @brief Inserts the current state of a %independent_bits_engine random * number generator engine @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %independent_bits_engine random number generator engine. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RandomNumberEngine, size_t __w, typename _UIntType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const std::independent_bits_engine<_RandomNumberEngine, __w, _UIntType>& __x) { __os << __x.base(); return __os; } /** * @brief Produces random numbers by combining random numbers from some * base engine to produce random numbers with a specifies number of bits * @p __w. */ template<typename _RandomNumberEngine, size_t __k> class shuffle_order_engine { static_assert(1u <= __k, "template argument substituting " "__k out of bound"); public: /** The type of the generated random value. */ typedef typename _RandomNumberEngine::result_type result_type; static const size_t table_size = __k; /** * @brief Constructs a default %shuffle_order_engine engine. * * The underlying engine is default constructed as well. */ shuffle_order_engine() : _M_b() { _M_initialize(); } /** * @brief Copy constructs a %shuffle_order_engine engine. * * Copies an existing base class random number generator. * @param rng An existing (base class) engine object. */ explicit shuffle_order_engine(const _RandomNumberEngine& __rne) : _M_b(__rne) { _M_initialize(); } /** * @brief Move constructs a %shuffle_order_engine engine. * * Copies an existing base class random number generator. * @param rng An existing (base class) engine object. */ explicit shuffle_order_engine(_RandomNumberEngine&& __rne) : _M_b(std::move(__rne)) { _M_initialize(); } /** * @brief Seed constructs a %shuffle_order_engine engine. * * Constructs the underlying generator engine seeded with @p __s. * @param __s A seed value for the base class engine. */ explicit shuffle_order_engine(result_type __s) : _M_b(__s) { _M_initialize(); } /** * @brief Generator construct a %shuffle_order_engine engine. * * @param __q A seed sequence. */ template<typename _Sseq, typename = typename std::enable_if<!std::is_same<_Sseq, shuffle_order_engine>::value && !std::is_same<_Sseq, _RandomNumberEngine>::value> ::type> explicit shuffle_order_engine(_Sseq& __q) : _M_b(__q) { _M_initialize(); } /** * @brief Reseeds the %shuffle_order_engine object with the default seed for the underlying base class generator engine. */ void seed() { _M_b.seed(); _M_initialize(); } /** * @brief Reseeds the %shuffle_order_engine object with the default seed * for the underlying base class generator engine. */ void seed(result_type __s) { _M_b.seed(__s); _M_initialize(); } /** * @brief Reseeds the %shuffle_order_engine object with the given seed * sequence. * @param __q A seed generator function. */ template<typename _Sseq> void seed(_Sseq& __q) { _M_b.seed(__q); _M_initialize(); } /** * Gets a const reference to the underlying generator engine object. */ const _RandomNumberEngine& base() const { return _M_b; } /** * Gets the minimum value in the generated random number range. * * @todo This should be constexpr. */ result_type min() const { return _M_b.min(); } /** * Gets the maximum value in the generated random number range. * * @todo This should be constexpr. */ result_type max() const { return _M_b.max(); } /** * Discard a sequence of random numbers. * * @todo Look for a faster way to do discard. */ void discard(unsigned long long __z) { for (; __z != 0ULL; --__z) (*this)(); } /** * Gets the next value in the generated random number sequence. */ result_type operator()(); /** * Compares two %shuffle_order_engine random number generator objects * of the same type for equality. * * @param __lhs A %shuffle_order_engine random number generator object. * @param __rhs Another %shuffle_order_engine random number generator * object. * * @returns true if the infinite sequences of generated values * would be equal, false otherwise. */ friend bool operator==(const shuffle_order_engine& __lhs, const shuffle_order_engine& __rhs) { return __lhs._M_b == __rhs._M_b; } /** * @brief Inserts the current state of a %shuffle_order_engine random * number generator engine @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %shuffle_order_engine random number generator engine. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RandomNumberEngine1, size_t __k1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::shuffle_order_engine<_RandomNumberEngine1, __k1>&); /** * @brief Extracts the current state of a % subtract_with_carry_engine * random number generator engine @p __x from the input stream * @p __is. * * @param __is An input stream. * @param __x A %shuffle_order_engine random number generator engine. * * @returns The input stream with the state of @p __x extracted or in * an error state. */ template<typename _RandomNumberEngine1, size_t __k1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::shuffle_order_engine<_RandomNumberEngine1, __k1>&); private: void _M_initialize() { for (size_t __i = 0; __i < __k; ++__i) _M_v[__i] = _M_b(); _M_y = _M_b(); } _RandomNumberEngine _M_b; result_type _M_v[__k]; result_type _M_y; }; /** * Compares two %shuffle_order_engine random number generator objects * of the same type for inequality. * * @param __lhs A %shuffle_order_engine random number generator object. * @param __rhs Another %shuffle_order_engine random number generator * object. * * @returns true if the infinite sequences of generated values * would be different, false otherwise. */ template<typename _RandomNumberEngine, size_t __k> inline bool operator!=(const std::shuffle_order_engine<_RandomNumberEngine, __k>& __lhs, const std::shuffle_order_engine<_RandomNumberEngine, __k>& __rhs) { return !(__lhs == __rhs); } /** * The classic Minimum Standard rand0 of Lewis, Goodman, and Miller. */ typedef linear_congruential_engine<uint_fast32_t, 16807UL, 0UL, 2147483647UL> minstd_rand0; /** * An alternative LCR (Lehmer Generator function). */ typedef linear_congruential_engine<uint_fast32_t, 48271UL, 0UL, 2147483647UL> minstd_rand; /** * The classic Mersenne Twister. * * Reference: * M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-Dimensionally * Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions * on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30. */ typedef mersenne_twister_engine< uint_fast32_t, 32, 624, 397, 31, 0x9908b0dfUL, 11, 0xffffffffUL, 7, 0x9d2c5680UL, 15, 0xefc60000UL, 18, 1812433253UL> mt19937; /** * An alternative Mersenne Twister. */ typedef mersenne_twister_engine< uint_fast64_t, 64, 312, 156, 31, 0xb5026f5aa96619e9ULL, 29, 0x5555555555555555ULL, 17, 0x71d67fffeda60000ULL, 37, 0xfff7eee000000000ULL, 43, 6364136223846793005ULL> 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_rand0 default_random_engine; /** * A standard interface to a platform-specific non-deterministic * random number generator (if any are available). */ class random_device { public: /** The type of the generated random value. */ typedef unsigned int result_type; // constructors, destructors and member functions #ifdef _GLIBCXX_USE_RANDOM_TR1 explicit random_device(const std::string& __token = "/dev/urandom") { if ((__token != "/dev/urandom" && __token != "/dev/random") || !(_M_file = std::fopen(__token.c_str(), "rb"))) std::__throw_runtime_error(__N("random_device::" "random_device(const std::string&)")); } ~random_device() { std::fclose(_M_file); } #else explicit random_device(const std::string& __token = "mt19937") : _M_mt(_M_strtoul(__token)) { } private: static unsigned long _M_strtoul(const std::string& __str) { unsigned long __ret = 5489UL; if (__str != "mt19937") { const char* __nptr = __str.c_str(); char* __endptr; __ret = std::strtoul(__nptr, &__endptr, 0); if (*__nptr == '\0' || *__endptr != '\0') std::__throw_runtime_error(__N("random_device::_M_strtoul" "(const std::string&)")); } return __ret; } public: #endif result_type min() const { return std::numeric_limits<result_type>::min(); } result_type max() const { return std::numeric_limits<result_type>::max(); } double entropy() const { return 0.0; } result_type operator()() { #ifdef _GLIBCXX_USE_RANDOM_TR1 result_type __ret; std::fread(reinterpret_cast<void*>(&__ret), sizeof(result_type), 1, _M_file); return __ret; #else return _M_mt(); #endif } // No copy functions. random_device(const random_device&) = delete; void operator=(const random_device&) = delete; private: #ifdef _GLIBCXX_USE_RANDOM_TR1 FILE* _M_file; #else mt19937 _M_mt; #endif }; /* @} */ // group random_generators /** * @addtogroup random_distributions Random Number Distributions * @ingroup random * @{ */ /** * @addtogroup random_distributions_uniform Uniform Distributions * @ingroup random_distributions * @{ */ /** * @brief Uniform discrete distribution for random numbers. * A discrete random distribution on the range @f$[min, max]@f$ with equal * probability throughout the range. */ template<typename _IntType = int> class uniform_int_distribution { static_assert(std::is_integral<_IntType>::value, "template argument not an integral type"); public: /** The type of the range of the distribution. */ typedef _IntType result_type; /** Parameter type. */ struct param_type { typedef uniform_int_distribution<_IntType> distribution_type; explicit param_type(_IntType __a = 0, _IntType __b = std::numeric_limits<_IntType>::max()) : _M_a(__a), _M_b(__b) { _GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b); } result_type a() const { return _M_a; } result_type b() const { return _M_b; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; } private: _IntType _M_a; _IntType _M_b; }; public: /** * @brief Constructs a uniform distribution object. */ explicit uniform_int_distribution(_IntType __a = 0, _IntType __b = std::numeric_limits<_IntType>::max()) : _M_param(__a, __b) { } explicit uniform_int_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. * * Does nothing for the uniform integer distribution. */ void reset() { } result_type a() const { return _M_param.a(); } result_type b() const { return _M_param.b(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the inclusive lower bound of the distribution range. */ result_type min() const { return this->a(); } /** * @brief Returns the inclusive upper bound of the distribution range. */ result_type max() const { return this->b(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); param_type _M_param; }; /** * @brief Return true if two uniform integer distributions have * the same parameters. */ template<typename _IntType> inline bool operator==(const std::uniform_int_distribution<_IntType>& __d1, const std::uniform_int_distribution<_IntType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two uniform integer distributions have * different parameters. */ template<typename _IntType> inline bool operator!=(const std::uniform_int_distribution<_IntType>& __d1, const std::uniform_int_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %uniform_int_distribution random number * distribution @p __x into the output stream @p os. * * @param __os An output stream. * @param __x A %uniform_int_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _IntType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::uniform_int_distribution<_IntType>&); /** * @brief Extracts a %uniform_int_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %uniform_int_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _IntType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::uniform_int_distribution<_IntType>&); /** * @brief Uniform continuous distribution for random numbers. * * A continuous random distribution on the range [min, max) with equal * probability throughout the range. The URNG should be real-valued and * deliver number in the range [0, 1). */ template<typename _RealType = double> class uniform_real_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef uniform_real_distribution<_RealType> distribution_type; explicit param_type(_RealType __a = _RealType(0), _RealType __b = _RealType(1)) : _M_a(__a), _M_b(__b) { _GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b); } result_type a() const { return _M_a; } result_type b() const { return _M_b; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; } private: _RealType _M_a; _RealType _M_b; }; public: /** * @brief Constructs a uniform_real_distribution object. * * @param __min [IN] The lower bound of the distribution. * @param __max [IN] The upper bound of the distribution. */ explicit uniform_real_distribution(_RealType __a = _RealType(0), _RealType __b = _RealType(1)) : _M_param(__a, __b) { } explicit uniform_real_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. * * Does nothing for the uniform real distribution. */ void reset() { } result_type a() const { return _M_param.a(); } result_type b() const { return _M_param.b(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the inclusive lower bound of the distribution range. */ result_type min() const { return this->a(); } /** * @brief Returns the inclusive upper bound of the distribution range. */ result_type max() const { return this->b(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { __detail::_Adaptor<_UniformRandomNumberGenerator, result_type> __aurng(__urng); return (__aurng() * (__p.b() - __p.a())) + __p.a(); } private: param_type _M_param; }; /** * @brief Return true if two uniform real distributions have * the same parameters. */ template<typename _IntType> inline bool operator==(const std::uniform_real_distribution<_IntType>& __d1, const std::uniform_real_distribution<_IntType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two uniform real distributions have * different parameters. */ template<typename _IntType> inline bool operator!=(const std::uniform_real_distribution<_IntType>& __d1, const std::uniform_real_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %uniform_real_distribution random number * distribution @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %uniform_real_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::uniform_real_distribution<_RealType>&); /** * @brief Extracts a %uniform_real_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %uniform_real_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::uniform_real_distribution<_RealType>&); /* @} */ // group random_distributions_uniform /** * @addtogroup random_distributions_normal Normal Distributions * @ingroup random_distributions * @{ */ /** * @brief A normal continuous distribution for random numbers. * * The formula for the normal probability density function is * @f[ * p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}} * e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} } * @f] */ template<typename _RealType = double> class normal_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef normal_distribution<_RealType> distribution_type; explicit param_type(_RealType __mean = _RealType(0), _RealType __stddev = _RealType(1)) : _M_mean(__mean), _M_stddev(__stddev) { _GLIBCXX_DEBUG_ASSERT(_M_stddev > _RealType(0)); } _RealType mean() const { return _M_mean; } _RealType stddev() const { return _M_stddev; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return (__p1._M_mean == __p2._M_mean && __p1._M_stddev == __p2._M_stddev); } private: _RealType _M_mean; _RealType _M_stddev; }; public: /** * Constructs a normal distribution with parameters @f$mean@f$ and * standard deviation. */ explicit normal_distribution(result_type __mean = result_type(0), result_type __stddev = result_type(1)) : _M_param(__mean, __stddev), _M_saved_available(false) { } explicit normal_distribution(const param_type& __p) : _M_param(__p), _M_saved_available(false) { } /** * @brief Resets the distribution state. */ void reset() { _M_saved_available = false; } /** * @brief Returns the mean of the distribution. */ _RealType mean() const { return _M_param.mean(); } /** * @brief Returns the standard deviation of the distribution. */ _RealType stddev() const { return _M_param.stddev(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return std::numeric_limits<result_type>::min(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Return true if two normal distributions have * the same parameters and the sequences that would * be generated are equal. */ template<typename _RealType1> friend bool operator==(const std::normal_distribution<_RealType1>& __d1, const std::normal_distribution<_RealType1>& __d2); /** * @brief Inserts a %normal_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %normal_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::normal_distribution<_RealType1>&); /** * @brief Extracts a %normal_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %normal_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error * state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::normal_distribution<_RealType1>&); private: param_type _M_param; result_type _M_saved; bool _M_saved_available; }; /** * @brief Return true if two normal distributions are different. */ template<typename _RealType> inline bool operator!=(const std::normal_distribution<_RealType>& __d1, const std::normal_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief A lognormal_distribution random number distribution. * * The formula for the normal probability mass function is * @f[ * p(x|m,s) = \frac{1}{sx\sqrt{2\pi}} * \exp{-\frac{(\ln{x} - m)^2}{2s^2}} * @f] */ template<typename _RealType = double> class lognormal_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef lognormal_distribution<_RealType> distribution_type; explicit param_type(_RealType __m = _RealType(0), _RealType __s = _RealType(1)) : _M_m(__m), _M_s(__s) { } _RealType m() const { return _M_m; } _RealType s() const { return _M_s; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_m == __p2._M_m && __p1._M_s == __p2._M_s; } private: _RealType _M_m; _RealType _M_s; }; explicit lognormal_distribution(_RealType __m = _RealType(0), _RealType __s = _RealType(1)) : _M_param(__m, __s), _M_nd() { } explicit lognormal_distribution(const param_type& __p) : _M_param(__p), _M_nd() { } /** * Resets the distribution state. */ void reset() { _M_nd.reset(); } /** * */ _RealType m() const { return _M_param.m(); } _RealType s() const { return _M_param.s(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { return std::exp(__p.s() * _M_nd(__urng) + __p.m()); } /** * @brief Return true if two lognormal distributions have * the same parameters and the sequences that would * be generated are equal. */ template<typename _RealType1> friend bool operator==(const std::lognormal_distribution<_RealType1>& __d1, const std::lognormal_distribution<_RealType1>& __d2) { return (__d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd); } /** * @brief Inserts a %lognormal_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %lognormal_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::lognormal_distribution<_RealType1>&); /** * @brief Extracts a %lognormal_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %lognormal_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::lognormal_distribution<_RealType1>&); private: param_type _M_param; std::normal_distribution<result_type> _M_nd; }; /** * @brief Return true if two lognormal distributions are different. */ template<typename _RealType> inline bool operator!=(const std::lognormal_distribution<_RealType>& __d1, const std::lognormal_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief A gamma continuous distribution for random numbers. * * The formula for the gamma probability density function is: * @f[ * p(x|\alpha,\beta) = \frac{1}{\beta\Gamma(\alpha)} * (x/\beta)^{\alpha - 1} e^{-x/\beta} * @f] */ template<typename _RealType = double> class gamma_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef gamma_distribution<_RealType> distribution_type; friend class gamma_distribution<_RealType>; explicit param_type(_RealType __alpha_val = _RealType(1), _RealType __beta_val = _RealType(1)) : _M_alpha(__alpha_val), _M_beta(__beta_val) { _GLIBCXX_DEBUG_ASSERT(_M_alpha > _RealType(0)); _M_initialize(); } _RealType alpha() const { return _M_alpha; } _RealType beta() const { return _M_beta; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return (__p1._M_alpha == __p2._M_alpha && __p1._M_beta == __p2._M_beta); } private: void _M_initialize(); _RealType _M_alpha; _RealType _M_beta; _RealType _M_malpha, _M_a2; }; public: /** * @brief Constructs a gamma distribution with parameters * @f$\alpha@f$ and @f$\beta@f$. */ explicit gamma_distribution(_RealType __alpha_val = _RealType(1), _RealType __beta_val = _RealType(1)) : _M_param(__alpha_val, __beta_val), _M_nd() { } explicit gamma_distribution(const param_type& __p) : _M_param(__p), _M_nd() { } /** * @brief Resets the distribution state. */ void reset() { _M_nd.reset(); } /** * @brief Returns the @f$\alpha@f$ of the distribution. */ _RealType alpha() const { return _M_param.alpha(); } /** * @brief Returns the @f$\beta@f$ of the distribution. */ _RealType beta() const { return _M_param.beta(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Return true if two gamma distributions have the same * parameters and the sequences that would be generated * are equal. */ template<typename _RealType1> friend bool operator==(const std::gamma_distribution<_RealType1>& __d1, const std::gamma_distribution<_RealType1>& __d2) { return (__d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd); } /** * @brief Inserts a %gamma_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %gamma_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::gamma_distribution<_RealType1>&); /** * @brief Extracts a %gamma_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %gamma_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::gamma_distribution<_RealType1>&); private: param_type _M_param; std::normal_distribution<result_type> _M_nd; }; /** * @brief Return true if two gamma distributions are different. */ template<typename _RealType> inline bool operator!=(const std::gamma_distribution<_RealType>& __d1, const std::gamma_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief A chi_squared_distribution random number distribution. * * The formula for the normal probability mass function is * @f$p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}@f$ */ template<typename _RealType = double> class chi_squared_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef chi_squared_distribution<_RealType> distribution_type; explicit param_type(_RealType __n = _RealType(1)) : _M_n(__n) { } _RealType n() const { return _M_n; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_n == __p2._M_n; } private: _RealType _M_n; }; explicit chi_squared_distribution(_RealType __n = _RealType(1)) : _M_param(__n), _M_gd(__n / 2) { } explicit chi_squared_distribution(const param_type& __p) : _M_param(__p), _M_gd(__p.n() / 2) { } /** * @brief Resets the distribution state. */ void reset() { _M_gd.reset(); } /** * */ _RealType n() const { return _M_param.n(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return 2 * _M_gd(__urng); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { typedef typename std::gamma_distribution<result_type>::param_type param_type; return 2 * _M_gd(__urng, param_type(__p.n() / 2)); } /** * @brief Return true if two Chi-squared distributions have * the same parameters and the sequences that would be * generated are equal. */ template<typename _RealType1> friend bool operator==(const std::chi_squared_distribution<_RealType1>& __d1, const std::chi_squared_distribution<_RealType1>& __d2) { return __d1.param() == __d2.param() && __d1._M_gd == __d2._M_gd; } /** * @brief Inserts a %chi_squared_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %chi_squared_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::chi_squared_distribution<_RealType1>&); /** * @brief Extracts a %chi_squared_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %chi_squared_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::chi_squared_distribution<_RealType1>&); private: param_type _M_param; std::gamma_distribution<result_type> _M_gd; }; /** * @brief Return true if two Chi-squared distributions are different. */ template<typename _RealType> inline bool operator!=(const std::chi_squared_distribution<_RealType>& __d1, const std::chi_squared_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief A cauchy_distribution random number distribution. * * The formula for the normal probability mass function is * @f$p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}@f$ */ template<typename _RealType = double> class cauchy_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef cauchy_distribution<_RealType> distribution_type; explicit param_type(_RealType __a = _RealType(0), _RealType __b = _RealType(1)) : _M_a(__a), _M_b(__b) { } _RealType a() const { return _M_a; } _RealType b() const { return _M_b; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; } private: _RealType _M_a; _RealType _M_b; }; explicit cauchy_distribution(_RealType __a = _RealType(0), _RealType __b = _RealType(1)) : _M_param(__a, __b) { } explicit cauchy_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. */ void reset() { } /** * */ _RealType a() const { return _M_param.a(); } _RealType b() const { return _M_param.b(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return std::numeric_limits<result_type>::min(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); private: param_type _M_param; }; /** * @brief Return true if two Cauchy distributions have * the same parameters. */ template<typename _RealType> inline bool operator==(const std::cauchy_distribution<_RealType>& __d1, const std::cauchy_distribution<_RealType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two Cauchy distributions have * different parameters. */ template<typename _RealType> inline bool operator!=(const std::cauchy_distribution<_RealType>& __d1, const std::cauchy_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %cauchy_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %cauchy_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::cauchy_distribution<_RealType>&); /** * @brief Extracts a %cauchy_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %cauchy_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::cauchy_distribution<_RealType>&); /** * @brief A fisher_f_distribution random number distribution. * * The formula for the normal probability mass function is * @f[ * p(x|m,n) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)} * (\frac{m}{n})^{m/2} x^{(m/2)-1} * (1 + \frac{mx}{n})^{-(m+n)/2} * @f] */ template<typename _RealType = double> class fisher_f_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef fisher_f_distribution<_RealType> distribution_type; explicit param_type(_RealType __m = _RealType(1), _RealType __n = _RealType(1)) : _M_m(__m), _M_n(__n) { } _RealType m() const { return _M_m; } _RealType n() const { return _M_n; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_m == __p2._M_m && __p1._M_n == __p2._M_n; } private: _RealType _M_m; _RealType _M_n; }; explicit fisher_f_distribution(_RealType __m = _RealType(1), _RealType __n = _RealType(1)) : _M_param(__m, __n), _M_gd_x(__m / 2), _M_gd_y(__n / 2) { } explicit fisher_f_distribution(const param_type& __p) : _M_param(__p), _M_gd_x(__p.m() / 2), _M_gd_y(__p.n() / 2) { } /** * @brief Resets the distribution state. */ void reset() { _M_gd_x.reset(); _M_gd_y.reset(); } /** * */ _RealType m() const { return _M_param.m(); } _RealType n() const { return _M_param.n(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return (_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { typedef typename std::gamma_distribution<result_type>::param_type param_type; return ((_M_gd_x(__urng, param_type(__p.m() / 2)) * n()) / (_M_gd_y(__urng, param_type(__p.n() / 2)) * m())); } /** * @brief Return true if two Fisher f distributions have * the same parameters and the sequences that would * be generated are equal. */ template<typename _RealType1> friend bool operator==(const std::fisher_f_distribution<_RealType1>& __d1, const std::fisher_f_distribution<_RealType1>& __d2) { return (__d1.param() == __d2.param() && __d1._M_gd_x == __d2._M_gd_x && __d1._M_gd_y == __d2._M_gd_y); } /** * @brief Inserts a %fisher_f_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %fisher_f_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::fisher_f_distribution<_RealType1>&); /** * @brief Extracts a %fisher_f_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %fisher_f_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::fisher_f_distribution<_RealType1>&); private: param_type _M_param; std::gamma_distribution<result_type> _M_gd_x, _M_gd_y; }; /** * @brief Return true if two Fisher f distributions are diferent. */ template<typename _RealType> inline bool operator!=(const std::fisher_f_distribution<_RealType>& __d1, const std::fisher_f_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief A student_t_distribution random number distribution. * * The formula for the normal probability mass function is: * @f[ * p(x|n) = \frac{1}{\sqrt(n\pi)} \frac{\Gamma((n+1)/2)}{\Gamma(n/2)} * (1 + \frac{x^2}{n}) ^{-(n+1)/2} * @f] */ template<typename _RealType = double> class student_t_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef student_t_distribution<_RealType> distribution_type; explicit param_type(_RealType __n = _RealType(1)) : _M_n(__n) { } _RealType n() const { return _M_n; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_n == __p2._M_n; } private: _RealType _M_n; }; explicit student_t_distribution(_RealType __n = _RealType(1)) : _M_param(__n), _M_nd(), _M_gd(__n / 2, 2) { } explicit student_t_distribution(const param_type& __p) : _M_param(__p), _M_nd(), _M_gd(__p.n() / 2, 2) { } /** * @brief Resets the distribution state. */ void reset() { _M_nd.reset(); _M_gd.reset(); } /** * */ _RealType n() const { return _M_param.n(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return std::numeric_limits<result_type>::min(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng)); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { typedef typename std::gamma_distribution<result_type>::param_type param_type; const result_type __g = _M_gd(__urng, param_type(__p.n() / 2, 2)); return _M_nd(__urng) * std::sqrt(__p.n() / __g); } /** * @brief Return true if two Student t distributions have * the same parameters and the sequences that would * be generated are equal. */ template<typename _RealType1> friend bool operator==(const std::student_t_distribution<_RealType1>& __d1, const std::student_t_distribution<_RealType1>& __d2) { return (__d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd && __d1._M_gd == __d2._M_gd); } /** * @brief Inserts a %student_t_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %student_t_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::student_t_distribution<_RealType1>&); /** * @brief Extracts a %student_t_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %student_t_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::student_t_distribution<_RealType1>&); private: param_type _M_param; std::normal_distribution<result_type> _M_nd; std::gamma_distribution<result_type> _M_gd; }; /** * @brief Return true if two Student t distributions are different. */ template<typename _RealType> inline bool operator!=(const std::student_t_distribution<_RealType>& __d1, const std::student_t_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /* @} */ // group random_distributions_normal /** * @addtogroup random_distributions_bernoulli Bernoulli Distributions * @ingroup random_distributions * @{ */ /** * @brief A Bernoulli random number distribution. * * Generates a sequence of true and false values with likelihood @f$p@f$ * that true will come up and @f$(1 - p)@f$ that false will appear. */ class bernoulli_distribution { public: /** The type of the range of the distribution. */ typedef bool result_type; /** Parameter type. */ struct param_type { typedef bernoulli_distribution distribution_type; explicit param_type(double __p = 0.5) : _M_p(__p) { _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0)); } double p() const { return _M_p; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_p == __p2._M_p; } private: double _M_p; }; public: /** * @brief Constructs a Bernoulli distribution with likelihood @p p. * * @param __p [IN] The likelihood of a true result being returned. * Must be in the interval @f$[0, 1]@f$. */ explicit bernoulli_distribution(double __p = 0.5) : _M_param(__p) { } explicit bernoulli_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. * * Does nothing for a Bernoulli distribution. */ void reset() { } /** * @brief Returns the @p p parameter of the distribution. */ double p() const { return _M_param.p(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return std::numeric_limits<result_type>::min(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { __detail::_Adaptor<_UniformRandomNumberGenerator, double> __aurng(__urng); if ((__aurng() - __aurng.min()) < __p.p() * (__aurng.max() - __aurng.min())) return true; return false; } private: param_type _M_param; }; /** * @brief Return true if two Bernoulli distributions have * the same parameters. */ inline bool operator==(const std::bernoulli_distribution& __d1, const std::bernoulli_distribution& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two Bernoulli distributions have * different parameters. */ inline bool operator!=(const std::bernoulli_distribution& __d1, const std::bernoulli_distribution& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %bernoulli_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %bernoulli_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::bernoulli_distribution&); /** * @brief Extracts a %bernoulli_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %bernoulli_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, std::bernoulli_distribution& __x) { double __p; __is >> __p; __x.param(bernoulli_distribution::param_type(__p)); return __is; } /** * @brief A discrete binomial random number distribution. * * The formula for the binomial probability density function is * @f$p(i|t,p) = \binom{n}{i} p^i (1 - p)^{t - i}@f$ where @f$t@f$ * and @f$p@f$ are the parameters of the distribution. */ template<typename _IntType = int> class binomial_distribution { static_assert(std::is_integral<_IntType>::value, "template argument not an integral type"); public: /** The type of the range of the distribution. */ typedef _IntType result_type; /** Parameter type. */ struct param_type { typedef binomial_distribution<_IntType> distribution_type; friend class binomial_distribution<_IntType>; explicit param_type(_IntType __t = _IntType(1), double __p = 0.5) : _M_t(__t), _M_p(__p) { _GLIBCXX_DEBUG_ASSERT((_M_t >= _IntType(0)) && (_M_p >= 0.0) && (_M_p <= 1.0)); _M_initialize(); } _IntType t() const { return _M_t; } double p() const { return _M_p; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_t == __p2._M_t && __p1._M_p == __p2._M_p; } private: void _M_initialize(); _IntType _M_t; double _M_p; double _M_q; #if _GLIBCXX_USE_C99_MATH_TR1 double _M_d1, _M_d2, _M_s1, _M_s2, _M_c, _M_a1, _M_a123, _M_s, _M_lf, _M_lp1p; #endif bool _M_easy; }; // constructors and member function explicit binomial_distribution(_IntType __t = _IntType(1), double __p = 0.5) : _M_param(__t, __p), _M_nd() { } explicit binomial_distribution(const param_type& __p) : _M_param(__p), _M_nd() { } /** * @brief Resets the distribution state. */ void reset() { _M_nd.reset(); } /** * @brief Returns the distribution @p t parameter. */ _IntType t() const { return _M_param.t(); } /** * @brief Returns the distribution @p p parameter. */ double p() const { return _M_param.p(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return 0; } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return _M_param.t(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Return true if two binomial distributions have * the same parameters and the sequences that would * be generated are equal. */ template<typename _IntType1> friend bool operator==(const std::binomial_distribution<_IntType1>& __d1, const std::binomial_distribution<_IntType1>& __d2) #ifdef _GLIBCXX_USE_C99_MATH_TR1 { return __d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd; } #else { return __d1.param() == __d2.param(); } #endif /** * @brief Inserts a %binomial_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %binomial_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::binomial_distribution<_IntType1>&); /** * @brief Extracts a %binomial_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %binomial_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error * state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::binomial_distribution<_IntType1>&); private: template<typename _UniformRandomNumberGenerator> result_type _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t); param_type _M_param; // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined. std::normal_distribution<double> _M_nd; }; /** * @brief Return true if two binomial distributions are different. */ template<typename _IntType> inline bool operator!=(const std::binomial_distribution<_IntType>& __d1, const std::binomial_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /** * @brief A discrete geometric random number distribution. * * The formula for the geometric probability density function is * @f$p(i|p) = (1 - p)p^{i-1}@f$ where @f$p@f$ is the parameter of the * distribution. */ template<typename _IntType = int> class geometric_distribution { static_assert(std::is_integral<_IntType>::value, "template argument not an integral type"); public: /** The type of the range of the distribution. */ typedef _IntType result_type; /** Parameter type. */ struct param_type { typedef geometric_distribution<_IntType> distribution_type; friend class geometric_distribution<_IntType>; explicit param_type(double __p = 0.5) : _M_p(__p) { _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0)); _M_initialize(); } double p() const { return _M_p; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_p == __p2._M_p; } private: void _M_initialize() { _M_log_p = std::log(_M_p); } double _M_p; double _M_log_p; }; // constructors and member function explicit geometric_distribution(double __p = 0.5) : _M_param(__p) { } explicit geometric_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. * * Does nothing for the geometric distribution. */ void reset() { } /** * @brief Returns the distribution parameter @p p. */ double p() const { return _M_param.p(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return 0; } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); private: param_type _M_param; }; /** * @brief Return true if two geometric distributions have * the same parameters. */ template<typename _IntType> inline bool operator==(const std::geometric_distribution<_IntType>& __d1, const std::geometric_distribution<_IntType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two geometric distributions have * different parameters. */ template<typename _IntType> inline bool operator!=(const std::geometric_distribution<_IntType>& __d1, const std::geometric_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %geometric_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %geometric_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _IntType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::geometric_distribution<_IntType>&); /** * @brief Extracts a %geometric_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %geometric_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _IntType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::geometric_distribution<_IntType>&); /** * @brief A negative_binomial_distribution random number distribution. * * The formula for the negative binomial probability mass function is * @f$p(i) = \binom{n}{i} p^i (1 - p)^{t - i}@f$ where @f$t@f$ * and @f$p@f$ are the parameters of the distribution. */ template<typename _IntType = int> class negative_binomial_distribution { static_assert(std::is_integral<_IntType>::value, "template argument not an integral type"); public: /** The type of the range of the distribution. */ typedef _IntType result_type; /** Parameter type. */ struct param_type { typedef negative_binomial_distribution<_IntType> distribution_type; explicit param_type(_IntType __k = 1, double __p = 0.5) : _M_k(__k), _M_p(__p) { } _IntType k() const { return _M_k; } double p() const { return _M_p; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_k == __p2._M_k && __p1._M_p == __p2._M_p; } private: _IntType _M_k; double _M_p; }; explicit negative_binomial_distribution(_IntType __k = 1, double __p = 0.5) : _M_param(__k, __p), _M_gd(__k, __p / (1.0 - __p)) { } explicit negative_binomial_distribution(const param_type& __p) : _M_param(__p), _M_gd(__p.k(), __p.p() / (1.0 - __p.p())) { } /** * @brief Resets the distribution state. */ void reset() { _M_gd.reset(); } /** * @brief Return the @f$k@f$ parameter of the distribution. */ _IntType k() const { return _M_param.k(); } /** * @brief Return the @f$p@f$ parameter of the distribution. */ double p() const { return _M_param.p(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng); template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Return true if two negative binomial distributions have * the same parameters and the sequences that would be * generated are equal. */ template<typename _IntType1> friend bool operator==(const std::negative_binomial_distribution<_IntType1>& __d1, const std::negative_binomial_distribution<_IntType1>& __d2) { return __d1.param() == __d2.param() && __d1._M_gd == __d2._M_gd; } /** * @brief Inserts a %negative_binomial_distribution random * number distribution @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %negative_binomial_distribution random number * distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::negative_binomial_distribution<_IntType1>&); /** * @brief Extracts a %negative_binomial_distribution random number * distribution @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %negative_binomial_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::negative_binomial_distribution<_IntType1>&); private: param_type _M_param; std::gamma_distribution<double> _M_gd; }; /** * @brief Return true if two negative binomial distributions are different. */ template<typename _IntType> inline bool operator!=(const std::negative_binomial_distribution<_IntType>& __d1, const std::negative_binomial_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /* @} */ // group random_distributions_bernoulli /** * @addtogroup random_distributions_poisson Poisson Distributions * @ingroup random_distributions * @{ */ /** * @brief A discrete Poisson random number distribution. * * The formula for the Poisson probability density function is * @f$p(i|\mu) = \frac{\mu^i}{i!} e^{-\mu}@f$ where @f$\mu@f$ is the * parameter of the distribution. */ template<typename _IntType = int> class poisson_distribution { static_assert(std::is_integral<_IntType>::value, "template argument not an integral type"); public: /** The type of the range of the distribution. */ typedef _IntType result_type; /** Parameter type. */ struct param_type { typedef poisson_distribution<_IntType> distribution_type; friend class poisson_distribution<_IntType>; explicit param_type(double __mean = 1.0) : _M_mean(__mean) { _GLIBCXX_DEBUG_ASSERT(_M_mean > 0.0); _M_initialize(); } double mean() const { return _M_mean; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_mean == __p2._M_mean; } private: // Hosts either log(mean) or the threshold of the simple method. void _M_initialize(); double _M_mean; double _M_lm_thr; #if _GLIBCXX_USE_C99_MATH_TR1 double _M_lfm, _M_sm, _M_d, _M_scx, _M_1cx, _M_c2b, _M_cb; #endif }; // constructors and member function explicit poisson_distribution(double __mean = 1.0) : _M_param(__mean), _M_nd() { } explicit poisson_distribution(const param_type& __p) : _M_param(__p), _M_nd() { } /** * @brief Resets the distribution state. */ void reset() { _M_nd.reset(); } /** * @brief Returns the distribution parameter @p mean. */ double mean() const { return _M_param.mean(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return 0; } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Return true if two Poisson distributions have the same * parameters and the sequences that would be generated * are equal. */ template<typename _IntType1> friend bool operator==(const std::poisson_distribution<_IntType1>& __d1, const std::poisson_distribution<_IntType1>& __d2) #ifdef _GLIBCXX_USE_C99_MATH_TR1 { return __d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd; } #else { return __d1.param() == __d2.param(); } #endif /** * @brief Inserts a %poisson_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %poisson_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::poisson_distribution<_IntType1>&); /** * @brief Extracts a %poisson_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %poisson_distribution random number generator engine. * * @returns The input stream with @p __x extracted or in an error * state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::poisson_distribution<_IntType1>&); private: param_type _M_param; // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined. std::normal_distribution<double> _M_nd; }; /** * @brief Return true if two Poisson distributions are different. */ template<typename _IntType> inline bool operator!=(const std::poisson_distribution<_IntType>& __d1, const std::poisson_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /** * @brief An exponential continuous distribution for random numbers. * * The formula for the exponential probability density function is * @f$p(x|\lambda) = \lambda e^{-\lambda x}@f$. * * <table border=1 cellpadding=10 cellspacing=0> * <caption align=top>Distribution Statistics</caption> * <tr><td>Mean</td><td>@f$\frac{1}{\lambda}@f$</td></tr> * <tr><td>Median</td><td>@f$\frac{\ln 2}{\lambda}@f$</td></tr> * <tr><td>Mode</td><td>@f$zero@f$</td></tr> * <tr><td>Range</td><td>@f$[0, \infty]@f$</td></tr> * <tr><td>Standard Deviation</td><td>@f$\frac{1}{\lambda}@f$</td></tr> * </table> */ template<typename _RealType = double> class exponential_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef exponential_distribution<_RealType> distribution_type; explicit param_type(_RealType __lambda = _RealType(1)) : _M_lambda(__lambda) { _GLIBCXX_DEBUG_ASSERT(_M_lambda > _RealType(0)); } _RealType lambda() const { return _M_lambda; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_lambda == __p2._M_lambda; } private: _RealType _M_lambda; }; public: /** * @brief Constructs an exponential distribution with inverse scale * parameter @f$\lambda@f$. */ explicit exponential_distribution(const result_type& __lambda = result_type(1)) : _M_param(__lambda) { } explicit exponential_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. * * Has no effect on exponential distributions. */ void reset() { } /** * @brief Returns the inverse scale parameter of the distribution. */ _RealType lambda() const { return _M_param.lambda(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p) { __detail::_Adaptor<_UniformRandomNumberGenerator, result_type> __aurng(__urng); return -std::log(__aurng()) / __p.lambda(); } private: param_type _M_param; }; /** * @brief Return true if two exponential distributions have the same * parameters. */ template<typename _RealType> inline bool operator==(const std::exponential_distribution<_RealType>& __d1, const std::exponential_distribution<_RealType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two exponential distributions have different * parameters. */ template<typename _RealType> inline bool operator!=(const std::exponential_distribution<_RealType>& __d1, const std::exponential_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %exponential_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %exponential_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::exponential_distribution<_RealType>&); /** * @brief Extracts a %exponential_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %exponential_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::exponential_distribution<_RealType>&); /** * @brief A weibull_distribution random number distribution. * * The formula for the normal probability density function is: * @f[ * p(x|\alpha,\beta) = \frac{\alpha}{\beta} (\frac{x}{\beta})^{\alpha-1} * \exp{(-(\frac{x}{\beta})^\alpha)} * @f] */ template<typename _RealType = double> class weibull_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef weibull_distribution<_RealType> distribution_type; explicit param_type(_RealType __a = _RealType(1), _RealType __b = _RealType(1)) : _M_a(__a), _M_b(__b) { } _RealType a() const { return _M_a; } _RealType b() const { return _M_b; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; } private: _RealType _M_a; _RealType _M_b; }; explicit weibull_distribution(_RealType __a = _RealType(1), _RealType __b = _RealType(1)) : _M_param(__a, __b) { } explicit weibull_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. */ void reset() { } /** * @brief Return the @f$a@f$ parameter of the distribution. */ _RealType a() const { return _M_param.a(); } /** * @brief Return the @f$b@f$ parameter of the distribution. */ _RealType b() const { return _M_param.b(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); private: param_type _M_param; }; /** * @brief Return true if two Weibull distributions have the same * parameters. */ template<typename _RealType> inline bool operator==(const std::weibull_distribution<_RealType>& __d1, const std::weibull_distribution<_RealType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two Weibull distributions have different * parameters. */ template<typename _RealType> inline bool operator!=(const std::weibull_distribution<_RealType>& __d1, const std::weibull_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %weibull_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %weibull_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::weibull_distribution<_RealType>&); /** * @brief Extracts a %weibull_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %weibull_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::weibull_distribution<_RealType>&); /** * @brief A extreme_value_distribution random number distribution. * * The formula for the normal probability mass function is * @f[ * p(x|a,b) = \frac{1}{b} * \exp( \frac{a-x}{b} - \exp(\frac{a-x}{b})) * @f] */ template<typename _RealType = double> class extreme_value_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef extreme_value_distribution<_RealType> distribution_type; explicit param_type(_RealType __a = _RealType(0), _RealType __b = _RealType(1)) : _M_a(__a), _M_b(__b) { } _RealType a() const { return _M_a; } _RealType b() const { return _M_b; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; } private: _RealType _M_a; _RealType _M_b; }; explicit extreme_value_distribution(_RealType __a = _RealType(0), _RealType __b = _RealType(1)) : _M_param(__a, __b) { } explicit extreme_value_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. */ void reset() { } /** * @brief Return the @f$a@f$ parameter of the distribution. */ _RealType a() const { return _M_param.a(); } /** * @brief Return the @f$b@f$ parameter of the distribution. */ _RealType b() const { return _M_param.b(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return std::numeric_limits<result_type>::min(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return std::numeric_limits<result_type>::max(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); private: param_type _M_param; }; /** * @brief Return true if two extreme value distributions have the same * parameters. */ template<typename _RealType> inline bool operator==(const std::extreme_value_distribution<_RealType>& __d1, const std::extreme_value_distribution<_RealType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two extreme value distributions have different * parameters. */ template<typename _RealType> inline bool operator!=(const std::extreme_value_distribution<_RealType>& __d1, const std::extreme_value_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief Inserts a %extreme_value_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %extreme_value_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::extreme_value_distribution<_RealType>&); /** * @brief Extracts a %extreme_value_distribution random number * distribution @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %extreme_value_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error state. */ template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::extreme_value_distribution<_RealType>&); /** * @brief A discrete_distribution random number distribution. * * The formula for the discrete probability mass function is * */ template<typename _IntType = int> class discrete_distribution { static_assert(std::is_integral<_IntType>::value, "template argument not an integral type"); public: /** The type of the range of the distribution. */ typedef _IntType result_type; /** Parameter type. */ struct param_type { typedef discrete_distribution<_IntType> distribution_type; friend class discrete_distribution<_IntType>; param_type() : _M_prob(), _M_cp() { _M_initialize(); } template<typename _InputIterator> param_type(_InputIterator __wbegin, _InputIterator __wend) : _M_prob(__wbegin, __wend), _M_cp() { _M_initialize(); } param_type(initializer_list<double> __wil) : _M_prob(__wil.begin(), __wil.end()), _M_cp() { _M_initialize(); } template<typename _Func> param_type(size_t __nw, double __xmin, double __xmax, _Func __fw); std::vector<double> probabilities() const { return _M_prob; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_prob == __p2._M_prob; } private: void _M_initialize(); std::vector<double> _M_prob; std::vector<double> _M_cp; }; discrete_distribution() : _M_param() { } template<typename _InputIterator> discrete_distribution(_InputIterator __wbegin, _InputIterator __wend) : _M_param(__wbegin, __wend) { } discrete_distribution(initializer_list<double> __wl) : _M_param(__wl) { } template<typename _Func> discrete_distribution(size_t __nw, double __xmin, double __xmax, _Func __fw) : _M_param(__nw, __xmin, __xmax, __fw) { } explicit discrete_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. */ void reset() { } /** * @brief Returns the probabilities of the distribution. */ std::vector<double> probabilities() const { return _M_param.probabilities(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return result_type(0); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return this->_M_param._M_prob.size() - 1; } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Inserts a %discrete_distribution random number distribution * @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %discrete_distribution random number distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::discrete_distribution<_IntType1>&); /** * @brief Extracts a %discrete_distribution random number distribution * @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %discrete_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error * state. */ template<typename _IntType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::discrete_distribution<_IntType1>&); private: param_type _M_param; }; /** * @brief Return true if two discrete distributions have the same * parameters. */ template<typename _IntType> inline bool operator==(const std::discrete_distribution<_IntType>& __d1, const std::discrete_distribution<_IntType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two discrete distributions have different * parameters. */ template<typename _IntType> inline bool operator!=(const std::discrete_distribution<_IntType>& __d1, const std::discrete_distribution<_IntType>& __d2) { return !(__d1 == __d2); } /** * @brief A piecewise_constant_distribution random number distribution. * * The formula for the piecewise constant probability mass function is * */ template<typename _RealType = double> class piecewise_constant_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef piecewise_constant_distribution<_RealType> distribution_type; friend class piecewise_constant_distribution<_RealType>; param_type() : _M_int(), _M_den(), _M_cp() { _M_initialize(); } template<typename _InputIteratorB, typename _InputIteratorW> param_type(_InputIteratorB __bfirst, _InputIteratorB __bend, _InputIteratorW __wbegin); template<typename _Func> param_type(initializer_list<_RealType> __bi, _Func __fw); template<typename _Func> param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw); std::vector<_RealType> intervals() const { return _M_int; } std::vector<double> densities() const { return _M_den; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return __p1._M_int == __p2._M_int && __p1._M_den == __p2._M_den; } private: void _M_initialize(); std::vector<_RealType> _M_int; std::vector<double> _M_den; std::vector<double> _M_cp; }; explicit piecewise_constant_distribution() : _M_param() { } template<typename _InputIteratorB, typename _InputIteratorW> piecewise_constant_distribution(_InputIteratorB __bfirst, _InputIteratorB __bend, _InputIteratorW __wbegin) : _M_param(__bfirst, __bend, __wbegin) { } template<typename _Func> piecewise_constant_distribution(initializer_list<_RealType> __bl, _Func __fw) : _M_param(__bl, __fw) { } template<typename _Func> piecewise_constant_distribution(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw) : _M_param(__nw, __xmin, __xmax, __fw) { } explicit piecewise_constant_distribution(const param_type& __p) : _M_param(__p) { } /** * @brief Resets the distribution state. */ void reset() { } /** * @brief Returns a vector of the intervals. */ std::vector<_RealType> intervals() const { return _M_param.intervals(); } /** * @brief Returns a vector of the probability densities. */ std::vector<double> densities() const { return _M_param.densities(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return this->_M_param._M_int.front(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return this->_M_param._M_int.back(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Inserts a %piecewise_constan_distribution random * number distribution @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %piecewise_constan_distribution random number * distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::piecewise_constant_distribution<_RealType1>&); /** * @brief Extracts a %piecewise_constan_distribution random * number distribution @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %piecewise_constan_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error * state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::piecewise_constant_distribution<_RealType1>&); private: param_type _M_param; }; /** * @brief Return true if two piecewise constant distributions have the * same parameters. */ template<typename _RealType> inline bool operator==(const std::piecewise_constant_distribution<_RealType>& __d1, const std::piecewise_constant_distribution<_RealType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two piecewise constant distributions have * different parameters. */ template<typename _RealType> inline bool operator!=(const std::piecewise_constant_distribution<_RealType>& __d1, const std::piecewise_constant_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /** * @brief A piecewise_linear_distribution random number distribution. * * The formula for the piecewise linear probability mass function is * */ template<typename _RealType = double> class piecewise_linear_distribution { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); public: /** The type of the range of the distribution. */ typedef _RealType result_type; /** Parameter type. */ struct param_type { typedef piecewise_linear_distribution<_RealType> distribution_type; friend class piecewise_linear_distribution<_RealType>; param_type() : _M_int(), _M_den(), _M_cp(), _M_m() { _M_initialize(); } template<typename _InputIteratorB, typename _InputIteratorW> param_type(_InputIteratorB __bfirst, _InputIteratorB __bend, _InputIteratorW __wbegin); template<typename _Func> param_type(initializer_list<_RealType> __bl, _Func __fw); template<typename _Func> param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw); std::vector<_RealType> intervals() const { return _M_int; } std::vector<double> densities() const { return _M_den; } friend bool operator==(const param_type& __p1, const param_type& __p2) { return (__p1._M_int == __p2._M_int && __p1._M_den == __p2._M_den); } private: void _M_initialize(); std::vector<_RealType> _M_int; std::vector<double> _M_den; std::vector<double> _M_cp; std::vector<double> _M_m; }; explicit piecewise_linear_distribution() : _M_param() { } template<typename _InputIteratorB, typename _InputIteratorW> piecewise_linear_distribution(_InputIteratorB __bfirst, _InputIteratorB __bend, _InputIteratorW __wbegin) : _M_param(__bfirst, __bend, __wbegin) { } template<typename _Func> piecewise_linear_distribution(initializer_list<_RealType> __bl, _Func __fw) : _M_param(__bl, __fw) { } template<typename _Func> piecewise_linear_distribution(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw) : _M_param(__nw, __xmin, __xmax, __fw) { } explicit piecewise_linear_distribution(const param_type& __p) : _M_param(__p) { } /** * Resets the distribution state. */ void reset() { } /** * @brief Return the intervals of the distribution. */ std::vector<_RealType> intervals() const { return _M_param.intervals(); } /** * @brief Return a vector of the probability densities of the * distribution. */ std::vector<double> densities() const { return _M_param.densities(); } /** * @brief Returns the parameter set of the distribution. */ param_type param() const { return _M_param; } /** * @brief Sets the parameter set of the distribution. * @param __param The new parameter set of the distribution. */ void param(const param_type& __param) { _M_param = __param; } /** * @brief Returns the greatest lower bound value of the distribution. */ result_type min() const { return this->_M_param._M_int.front(); } /** * @brief Returns the least upper bound value of the distribution. */ result_type max() const { return this->_M_param._M_int.back(); } /** * @brief Generating functions. */ template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng) { return this->operator()(__urng, this->param()); } template<typename _UniformRandomNumberGenerator> result_type operator()(_UniformRandomNumberGenerator& __urng, const param_type& __p); /** * @brief Inserts a %piecewise_linear_distribution random number * distribution @p __x into the output stream @p __os. * * @param __os An output stream. * @param __x A %piecewise_linear_distribution random number * distribution. * * @returns The output stream with the state of @p __x inserted or in * an error state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>&, const std::piecewise_linear_distribution<_RealType1>&); /** * @brief Extracts a %piecewise_linear_distribution random number * distribution @p __x from the input stream @p __is. * * @param __is An input stream. * @param __x A %piecewise_linear_distribution random number * generator engine. * * @returns The input stream with @p __x extracted or in an error * state. */ template<typename _RealType1, typename _CharT, typename _Traits> friend std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>&, std::piecewise_linear_distribution<_RealType1>&); private: param_type _M_param; }; /** * @brief Return true if two piecewise linear distributions have the * same parameters. */ template<typename _RealType> inline bool operator==(const std::piecewise_linear_distribution<_RealType>& __d1, const std::piecewise_linear_distribution<_RealType>& __d2) { return __d1.param() == __d2.param(); } /** * @brief Return true if two piecewise linear distributions have * different parameters. */ template<typename _RealType> inline bool operator!=(const std::piecewise_linear_distribution<_RealType>& __d1, const std::piecewise_linear_distribution<_RealType>& __d2) { return !(__d1 == __d2); } /* @} */ // group random_distributions_poisson /* @} */ // group random_distributions /** * @addtogroup random_utilities Random Number Utilities * @ingroup random * @{ */ /** * @brief The seed_seq class generates sequences of seeds for random * number generators. */ class seed_seq { public: /** The type of the seed vales. */ typedef uint_least32_t result_type; /** Default constructor. */ seed_seq() : _M_v() { } template<typename _IntType> seed_seq(std::initializer_list<_IntType> il); template<typename _InputIterator> seed_seq(_InputIterator __begin, _InputIterator __end); // generating functions template<typename _RandomAccessIterator> void generate(_RandomAccessIterator __begin, _RandomAccessIterator __end); // property functions size_t size() const { return _M_v.size(); } template<typename OutputIterator> void param(OutputIterator __dest) const { std::copy(_M_v.begin(), _M_v.end(), __dest); } private: /// std::vector<result_type> _M_v; }; /* @} */ // group random_utilities /* @} */ // group random }
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