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Diffstat (limited to 'gcc-4.4.3/libstdc++-v3/include/tr1_impl/random')
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diff --git a/gcc-4.4.3/libstdc++-v3/include/tr1_impl/random b/gcc-4.4.3/libstdc++-v3/include/tr1_impl/random new file mode 100644 index 000000000..0cf4dc4cd --- /dev/null +++ b/gcc-4.4.3/libstdc++-v3/include/tr1_impl/random @@ -0,0 +1,2407 @@ +// random number generation -*- C++ -*- + +// Copyright (C) 2007, 2008, 2009 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 tr1_impl/random + * This is an internal header file, included by other library headers. + * You should not attempt to use it directly. + */ + +namespace std +{ +_GLIBCXX_BEGIN_NAMESPACE_TR1 + + // [5.1] Random number generation + + /** + * @defgroup tr1_random Random Number Generation + * @ingroup numerics + * A facility for generating random numbers on selected distributions. + * @{ + */ + + /* + * Implementation-space details. + */ + namespace __detail + { + template<typename _UIntType, int __w, + bool = __w < std::numeric_limits<_UIntType>::digits> + struct _Shift + { static const _UIntType __value = 0; }; + + template<typename _UIntType, int __w> + struct _Shift<_UIntType, __w, true> + { static const _UIntType __value = _UIntType(1) << __w; }; + + template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool> + struct _Mod; + + // Dispatch based on modulus value to prevent divide-by-zero compile-time + // errors when m == 0. + template<typename _Tp, _Tp __a, _Tp __c, _Tp __m> + inline _Tp + __mod(_Tp __x) + { return _Mod<_Tp, __a, __c, __m, __m == 0>::__calc(__x); } + + typedef __gnu_cxx::__conditional_type<(sizeof(unsigned) == 4), + unsigned, unsigned long>::__type _UInt32Type; + + /* + * An adaptor class for converting the output of any Generator into + * the input for a specific Distribution. + */ + template<typename _Engine, typename _Distribution> + struct _Adaptor + { + typedef typename remove_reference<_Engine>::type _BEngine; + typedef typename _BEngine::result_type _Engine_result_type; + typedef typename _Distribution::input_type result_type; + + public: + _Adaptor(const _Engine& __g) + : _M_g(__g) { } + + result_type + min() const + { + result_type __return_value; + if (is_integral<_Engine_result_type>::value + && is_integral<result_type>::value) + __return_value = _M_g.min(); + else + __return_value = result_type(0); + return __return_value; + } + + result_type + max() const + { + result_type __return_value; + if (is_integral<_Engine_result_type>::value + && is_integral<result_type>::value) + __return_value = _M_g.max(); + else if (!is_integral<result_type>::value) + __return_value = result_type(1); + else + __return_value = std::numeric_limits<result_type>::max() - 1; + return __return_value; + } + + /* + * Converts a value generated by the adapted random number generator + * into a value in the input domain for the dependent random number + * distribution. + * + * Because the type traits are compile time constants only the + * appropriate clause of the if statements will actually be emitted + * by the compiler. + */ + result_type + operator()() + { + result_type __return_value; + if (is_integral<_Engine_result_type>::value + && is_integral<result_type>::value) + __return_value = _M_g(); + else if (!is_integral<_Engine_result_type>::value + && !is_integral<result_type>::value) + __return_value = result_type(_M_g() - _M_g.min()) + / result_type(_M_g.max() - _M_g.min()); + else if (is_integral<_Engine_result_type>::value + && !is_integral<result_type>::value) + __return_value = result_type(_M_g() - _M_g.min()) + / result_type(_M_g.max() - _M_g.min() + result_type(1)); + else + __return_value = (((_M_g() - _M_g.min()) + / (_M_g.max() - _M_g.min())) + * std::numeric_limits<result_type>::max()); + return __return_value; + } + + private: + _Engine _M_g; + }; + + // Specialization for _Engine*. + template<typename _Engine, typename _Distribution> + struct _Adaptor<_Engine*, _Distribution> + { + typedef typename _Engine::result_type _Engine_result_type; + typedef typename _Distribution::input_type result_type; + + public: + _Adaptor(_Engine* __g) + : _M_g(__g) { } + + result_type + min() const + { + result_type __return_value; + if (is_integral<_Engine_result_type>::value + && is_integral<result_type>::value) + __return_value = _M_g->min(); + else + __return_value = result_type(0); + return __return_value; + } + + result_type + max() const + { + result_type __return_value; + if (is_integral<_Engine_result_type>::value + && is_integral<result_type>::value) + __return_value = _M_g->max(); + else if (!is_integral<result_type>::value) + __return_value = result_type(1); + else + __return_value = std::numeric_limits<result_type>::max() - 1; + return __return_value; + } + + result_type + operator()() + { + result_type __return_value; + if (is_integral<_Engine_result_type>::value + && is_integral<result_type>::value) + __return_value = (*_M_g)(); + else if (!is_integral<_Engine_result_type>::value + && !is_integral<result_type>::value) + __return_value = result_type((*_M_g)() - _M_g->min()) + / result_type(_M_g->max() - _M_g->min()); + else if (is_integral<_Engine_result_type>::value + && !is_integral<result_type>::value) + __return_value = result_type((*_M_g)() - _M_g->min()) + / result_type(_M_g->max() - _M_g->min() + result_type(1)); + else + __return_value = ((((*_M_g)() - _M_g->min()) + / (_M_g->max() - _M_g->min())) + * std::numeric_limits<result_type>::max()); + return __return_value; + } + + private: + _Engine* _M_g; + }; + } // namespace __detail + + /** + * Produces random numbers on a given distribution function using a + * non-uniform random number generation engine. + * + * @todo the engine_value_type needs to be studied more carefully. + */ + template<typename _Engine, typename _Dist> + class variate_generator + { + // Concept requirements. + __glibcxx_class_requires(_Engine, _CopyConstructibleConcept) + // __glibcxx_class_requires(_Engine, _EngineConcept) + // __glibcxx_class_requires(_Dist, _EngineConcept) + + public: + typedef _Engine engine_type; + typedef __detail::_Adaptor<_Engine, _Dist> engine_value_type; + typedef _Dist distribution_type; + typedef typename _Dist::result_type result_type; + + // tr1:5.1.1 table 5.1 requirement + typedef typename __gnu_cxx::__enable_if< + is_arithmetic<result_type>::value, result_type>::__type _IsValidType; + + /** + * Constructs a variate generator with the uniform random number + * generator @p __eng for the random distribution @p __dist. + * + * @throws Any exceptions which may thrown by the copy constructors of + * the @p _Engine or @p _Dist objects. + */ + variate_generator(engine_type __eng, distribution_type __dist) + : _M_engine(__eng), _M_dist(__dist) { } + + /** + * Gets the next generated value on the distribution. + */ + result_type + operator()() + { return _M_dist(_M_engine); } + + /** + * WTF? + */ + template<typename _Tp> + result_type + operator()(_Tp __value) + { return _M_dist(_M_engine, __value); } + + /** + * Gets a reference to the underlying uniform random number generator + * object. + */ + engine_value_type& + engine() + { return _M_engine; } + + /** + * Gets a const reference to the underlying uniform random number + * generator object. + */ + const engine_value_type& + engine() const + { return _M_engine; } + + /** + * Gets a reference to the underlying random distribution. + */ + distribution_type& + distribution() + { return _M_dist; } + + /** + * Gets a const reference to the underlying random distribution. + */ + const distribution_type& + distribution() const + { return _M_dist; } + + /** + * Gets the closed lower bound of the distribution interval. + */ + result_type + min() const + { return this->distribution().min(); } + + /** + * Gets the closed upper bound of the distribution interval. + */ + result_type + max() const + { return this->distribution().max(); } + + private: + engine_value_type _M_engine; + distribution_type _M_dist; + }; + + + /** + * @defgroup tr1_random_generators Random Number Generators + * @ingroup tr1_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 using the + * 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<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> + class linear_congruential + { + __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept) + // __glibcpp_class_requires(__a < __m && __c < __m) + + public: + /** The type of the generated random value. */ + typedef _UIntType result_type; + + /** The multiplier. */ + static const _UIntType multiplier = __a; + /** An increment. */ + static const _UIntType increment = __c; + /** The modulus. */ + static const _UIntType modulus = __m; + + /** + * Constructs a %linear_congruential random number generator engine with + * seed @p __s. The default seed value is 1. + * + * @param __s The initial seed value. + */ + explicit + linear_congruential(unsigned long __x0 = 1) + { this->seed(__x0); } + + /** + * Constructs a %linear_congruential random number generator engine + * seeded from the generator function @p __g. + * + * @param __g The seed generator function. + */ + template<class _Gen> + linear_congruential(_Gen& __g) + { this->seed(__g); } + + /** + * Reseeds the %linear_congruential random number generator engine + * sequence to the seed @g __s. + * + * @param __s The new seed. + */ + void + seed(unsigned long __s = 1); + + /** + * Reseeds the %linear_congruential random number generator engine + * sequence using values from the generator function @p __g. + * + * @param __g the seed generator function. + */ + template<class _Gen> + void + seed(_Gen& __g) + { seed(__g, typename is_fundamental<_Gen>::type()); } + + /** + * 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. + */ + result_type + min() const + { return (__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0) ? 1 : 0; } + + /** + * Gets the largest possible value in the output range. + */ + result_type + max() const + { return __m - 1; } + + /** + * Gets the next random number in the sequence. + */ + result_type + operator()(); + + /** + * 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 obj. + * + * @returns true if the two objects are equal, false otherwise. + */ + friend bool + operator==(const linear_congruential& __lhs, + const linear_congruential& __rhs) + { return __lhs._M_x == __rhs._M_x; } + + /** + * 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 obj. + * + * @returns true if the two objects are not equal, false otherwise. + */ + friend bool + operator!=(const linear_congruential& __lhs, + const linear_congruential& __rhs) + { return !(__lhs == __rhs); } + + /** + * Writes the textual representation of the state x(i) of x to @p __os. + * + * @param __os The output stream. + * @param __lcr A % linear_congruential random number generator. + * @returns __os. + */ + template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1, + _UIntType1 __m1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const linear_congruential<_UIntType1, __a1, __c1, + __m1>& __lcr); + + /** + * 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 random number generator. + * @returns __is. + */ + template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1, + _UIntType1 __m1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + linear_congruential<_UIntType1, __a1, __c1, __m1>& __lcr); + + private: + template<class _Gen> + void + seed(_Gen& __g, true_type) + { return seed(static_cast<unsigned long>(__g)); } + + template<class _Gen> + void + seed(_Gen& __g, false_type); + + _UIntType _M_x; + }; + + /** + * The classic Minimum Standard rand0 of Lewis, Goodman, and Miller. + */ + typedef linear_congruential<unsigned long, 16807, 0, 2147483647> minstd_rand0; + + /** + * An alternative LCR (Lehmer Generator function) . + */ + typedef linear_congruential<unsigned long, 48271, 0, 2147483647> minstd_rand; + + + /** + * 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<class _UIntType, int __w, int __n, int __m, int __r, + _UIntType __a, int __u, int __s, _UIntType __b, int __t, + _UIntType __c, int __l> + class mersenne_twister + { + __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept) + + public: + // types + typedef _UIntType result_type; + + // parameter values + static const int word_size = __w; + static const int state_size = __n; + static const int shift_size = __m; + static const int mask_bits = __r; + static const _UIntType parameter_a = __a; + static const int output_u = __u; + static const int output_s = __s; + static const _UIntType output_b = __b; + static const int output_t = __t; + static const _UIntType output_c = __c; + static const int output_l = __l; + + // constructors and member function + mersenne_twister() + { seed(); } + + explicit + mersenne_twister(unsigned long __value) + { seed(__value); } + + template<class _Gen> + mersenne_twister(_Gen& __g) + { seed(__g); } + + void + seed() + { seed(5489UL); } + + void + seed(unsigned long __value); + + template<class _Gen> + void + seed(_Gen& __g) + { seed(__g, typename is_fundamental<_Gen>::type()); } + + result_type + min() const + { return 0; }; + + result_type + max() const + { return __detail::_Shift<_UIntType, __w>::__value - 1; } + + result_type + operator()(); + + /** + * Compares two % mersenne_twister random number generator objects of + * the same type for equality. + * + * @param __lhs A % mersenne_twister random number generator object. + * @param __rhs Another % mersenne_twister random number generator + * object. + * + * @returns true if the two objects are equal, false otherwise. + */ + friend bool + operator==(const mersenne_twister& __lhs, + const mersenne_twister& __rhs) + { return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); } + + /** + * Compares two % mersenne_twister random number generator objects of + * the same type for inequality. + * + * @param __lhs A % mersenne_twister random number generator object. + * @param __rhs Another % mersenne_twister random number generator + * object. + * + * @returns true if the two objects are not equal, false otherwise. + */ + friend bool + operator!=(const mersenne_twister& __lhs, + const mersenne_twister& __rhs) + { return !(__lhs == __rhs); } + + /** + * Inserts the current state of a % mersenne_twister random number + * generator engine @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A % mersenne_twister random number generator engine. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<class _UIntType1, int __w1, int __n1, int __m1, int __r1, + _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1, + _UIntType1 __c1, int __l1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1, + __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x); + + /** + * Extracts the current state of a % mersenne_twister random number + * generator engine @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A % mersenne_twister random number generator engine. + * + * @returns The input stream with the state of @p __x extracted or in + * an error state. + */ + template<class _UIntType1, int __w1, int __n1, int __m1, int __r1, + _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1, + _UIntType1 __c1, int __l1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1, + __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x); + + private: + template<class _Gen> + void + seed(_Gen& __g, true_type) + { return seed(static_cast<unsigned long>(__g)); } + + template<class _Gen> + void + seed(_Gen& __g, false_type); + + _UIntType _M_x[state_size]; + int _M_p; + }; + + /** + * 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< + unsigned long, 32, 624, 397, 31, + 0x9908b0dful, 11, 7, + 0x9d2c5680ul, 15, + 0xefc60000ul, 18 + > mt19937; + + + /** + * @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$. + * + * N1688[4.13] says "the template parameter _IntType shall denote an integral + * type large enough to store values up to m." + * + * @var _M_x The state of the generator. This is a ring buffer. + * @var _M_carry The carry. + * @var _M_p Current index of x(i - r). + */ + template<typename _IntType, _IntType __m, int __s, int __r> + class subtract_with_carry + { + __glibcxx_class_requires(_IntType, _IntegerConcept) + + public: + /** The type of the generated random value. */ + typedef _IntType result_type; + + // parameter values + static const _IntType modulus = __m; + static const int long_lag = __r; + static const int short_lag = __s; + + /** + * Constructs a default-initialized % subtract_with_carry random number + * generator. + */ + subtract_with_carry() + { this->seed(); } + + /** + * Constructs an explicitly seeded % subtract_with_carry random number + * generator. + */ + explicit + subtract_with_carry(unsigned long __value) + { this->seed(__value); } + + /** + * Constructs a %subtract_with_carry random number generator engine + * seeded from the generator function @p __g. + * + * @param __g The seed generator function. + */ + template<class _Gen> + subtract_with_carry(_Gen& __g) + { this->seed(__g); } + + /** + * Seeds the initial state @f$ 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(unsigned long __value = 19780503); + + /** + * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry + * random number generator. + */ + template<class _Gen> + void + seed(_Gen& __g) + { seed(__g, typename is_fundamental<_Gen>::type()); } + + /** + * Gets the inclusive minimum value of the range of random integers + * returned by this generator. + */ + result_type + min() const + { return 0; } + + /** + * Gets the inclusive maximum value of the range of random integers + * returned by this generator. + */ + result_type + max() const + { return this->modulus - 1; } + + /** + * Gets the next random number in the sequence. + */ + result_type + operator()(); + + /** + * Compares two % subtract_with_carry random number generator objects of + * the same type for equality. + * + * @param __lhs A % subtract_with_carry random number generator object. + * @param __rhs Another % subtract_with_carry random number generator + * object. + * + * @returns true if the two objects are equal, false otherwise. + */ + friend bool + operator==(const subtract_with_carry& __lhs, + const subtract_with_carry& __rhs) + { return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); } + + /** + * Compares two % subtract_with_carry random number generator objects of + * the same type for inequality. + * + * @param __lhs A % subtract_with_carry random number generator object. + * @param __rhs Another % subtract_with_carry random number generator + * object. + * + * @returns true if the two objects are not equal, false otherwise. + */ + friend bool + operator!=(const subtract_with_carry& __lhs, + const subtract_with_carry& __rhs) + { return !(__lhs == __rhs); } + + /** + * Inserts the current state of a % subtract_with_carry random number + * generator engine @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A % subtract_with_carry random number generator engine. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<typename _IntType1, _IntType1 __m1, int __s1, int __r1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const subtract_with_carry<_IntType1, __m1, __s1, + __r1>& __x); + + /** + * Extracts the current state of a % subtract_with_carry random number + * generator engine @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A % subtract_with_carry random number generator engine. + * + * @returns The input stream with the state of @p __x extracted or in + * an error state. + */ + template<typename _IntType1, _IntType1 __m1, int __s1, int __r1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + subtract_with_carry<_IntType1, __m1, __s1, __r1>& __x); + + private: + template<class _Gen> + void + seed(_Gen& __g, true_type) + { return seed(static_cast<unsigned long>(__g)); } + + template<class _Gen> + void + seed(_Gen& __g, false_type); + + typedef typename __gnu_cxx::__add_unsigned<_IntType>::__type _UIntType; + + _UIntType _M_x[long_lag]; + _UIntType _M_carry; + int _M_p; + }; + + + /** + * @brief The Marsaglia-Zaman generator (floats version). + * + * @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). + * @var _M_npows Precomputed negative powers of 2. + */ + template<typename _RealType, int __w, int __s, int __r> + class subtract_with_carry_01 + { + public: + /** The type of the generated random value. */ + typedef _RealType result_type; + + // parameter values + static const int word_size = __w; + static const int long_lag = __r; + static const int short_lag = __s; + + /** + * Constructs a default-initialized % subtract_with_carry_01 random + * number generator. + */ + subtract_with_carry_01() + { + this->seed(); + _M_initialize_npows(); + } + + /** + * Constructs an explicitly seeded % subtract_with_carry_01 random number + * generator. + */ + explicit + subtract_with_carry_01(unsigned long __value) + { + this->seed(__value); + _M_initialize_npows(); + } + + /** + * Constructs a % subtract_with_carry_01 random number generator engine + * seeded from the generator function @p __g. + * + * @param __g The seed generator function. + */ + template<class _Gen> + subtract_with_carry_01(_Gen& __g) + { + this->seed(__g); + _M_initialize_npows(); + } + + /** + * Seeds the initial state @f$ x_0 @f$ of the random number generator. + */ + void + seed(unsigned long __value = 19780503); + + /** + * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry_01 + * random number generator. + */ + template<class _Gen> + void + seed(_Gen& __g) + { seed(__g, typename is_fundamental<_Gen>::type()); } + + /** + * Gets the minimum value of the range of random floats + * returned by this generator. + */ + result_type + min() const + { return 0.0; } + + /** + * Gets the maximum value of the range of random floats + * returned by this generator. + */ + result_type + max() const + { return 1.0; } + + /** + * Gets the next random number in the sequence. + */ + result_type + operator()(); + + /** + * Compares two % subtract_with_carry_01 random number generator objects + * of the same type for equality. + * + * @param __lhs A % subtract_with_carry_01 random number + * generator object. + * @param __rhs Another % subtract_with_carry_01 random number generator + * object. + * + * @returns true if the two objects are equal, false otherwise. + */ + friend bool + operator==(const subtract_with_carry_01& __lhs, + const subtract_with_carry_01& __rhs) + { + for (int __i = 0; __i < long_lag; ++__i) + if (!std::equal(__lhs._M_x[__i], __lhs._M_x[__i] + __n, + __rhs._M_x[__i])) + return false; + return true; + } + + /** + * Compares two % subtract_with_carry_01 random number generator objects + * of the same type for inequality. + * + * @param __lhs A % subtract_with_carry_01 random number + * generator object. + * + * @param __rhs Another % subtract_with_carry_01 random number generator + * object. + * + * @returns true if the two objects are not equal, false otherwise. + */ + friend bool + operator!=(const subtract_with_carry_01& __lhs, + const subtract_with_carry_01& __rhs) + { return !(__lhs == __rhs); } + + /** + * Inserts the current state of a % subtract_with_carry_01 random number + * generator engine @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A % subtract_with_carry_01 random number generator engine. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<typename _RealType1, int __w1, int __s1, int __r1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const subtract_with_carry_01<_RealType1, __w1, __s1, + __r1>& __x); + + /** + * Extracts the current state of a % subtract_with_carry_01 random number + * generator engine @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A % subtract_with_carry_01 random number generator engine. + * + * @returns The input stream with the state of @p __x extracted or in + * an error state. + */ + template<typename _RealType1, int __w1, int __s1, int __r1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + subtract_with_carry_01<_RealType1, __w1, __s1, __r1>& __x); + + private: + template<class _Gen> + void + seed(_Gen& __g, true_type) + { return seed(static_cast<unsigned long>(__g)); } + + template<class _Gen> + void + seed(_Gen& __g, false_type); + + void + _M_initialize_npows(); + + static const int __n = (__w + 31) / 32; + + typedef __detail::_UInt32Type _UInt32Type; + _UInt32Type _M_x[long_lag][__n]; + _RealType _M_npows[__n]; + _UInt32Type _M_carry; + int _M_p; + }; + + typedef subtract_with_carry_01<float, 24, 10, 24> ranlux_base_01; + + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // 508. Bad parameters for ranlux64_base_01. + typedef subtract_with_carry_01<double, 48, 5, 12> ranlux64_base_01; + + + /** + * Produces random numbers from some base engine by discarding blocks of + * data. + * + * 0 <= @p __r <= @p __p + */ + template<class _UniformRandomNumberGenerator, int __p, int __r> + class discard_block + { + // __glibcxx_class_requires(typename base_type::result_type, + // ArithmeticTypeConcept) + + public: + /** The type of the underlying generator engine. */ + typedef _UniformRandomNumberGenerator base_type; + /** The type of the generated random value. */ + typedef typename base_type::result_type result_type; + + // parameter values + static const int block_size = __p; + static const int used_block = __r; + + /** + * Constructs a default %discard_block engine. + * + * The underlying engine is default constructed as well. + */ + discard_block() + : _M_n(0) { } + + /** + * Copy constructs a %discard_block engine. + * + * Copies an existing base class random number generator. + * @param rng An existing (base class) engine object. + */ + explicit + discard_block(const base_type& __rng) + : _M_b(__rng), _M_n(0) { } + + /** + * Seed constructs a %discard_block engine. + * + * Constructs the underlying generator engine seeded with @p __s. + * @param __s A seed value for the base class engine. + */ + explicit + discard_block(unsigned long __s) + : _M_b(__s), _M_n(0) { } + + /** + * Generator construct a %discard_block engine. + * + * @param __g A seed generator function. + */ + template<class _Gen> + discard_block(_Gen& __g) + : _M_b(__g), _M_n(0) { } + + /** + * Reseeds the %discard_block object with the default seed for the + * underlying base class generator engine. + */ + void seed() + { + _M_b.seed(); + _M_n = 0; + } + + /** + * Reseeds the %discard_block object with the given seed generator + * function. + * @param __g A seed generator function. + */ + template<class _Gen> + void seed(_Gen& __g) + { + _M_b.seed(__g); + _M_n = 0; + } + + /** + * Gets a const reference to the underlying generator engine object. + */ + const base_type& + base() const + { return _M_b; } + + /** + * Gets the minimum value in the generated random number range. + */ + result_type + min() const + { return _M_b.min(); } + + /** + * Gets the maximum value in the generated random number range. + */ + result_type + max() const + { return _M_b.max(); } + + /** + * Gets the next value in the generated random number sequence. + */ + result_type + operator()(); + + /** + * Compares two %discard_block random number generator objects of + * the same type for equality. + * + * @param __lhs A %discard_block random number generator object. + * @param __rhs Another %discard_block random number generator + * object. + * + * @returns true if the two objects are equal, false otherwise. + */ + friend bool + operator==(const discard_block& __lhs, const discard_block& __rhs) + { return (__lhs._M_b == __rhs._M_b) && (__lhs._M_n == __rhs._M_n); } + + /** + * Compares two %discard_block random number generator objects of + * the same type for inequality. + * + * @param __lhs A %discard_block random number generator object. + * @param __rhs Another %discard_block random number generator + * object. + * + * @returns true if the two objects are not equal, false otherwise. + */ + friend bool + operator!=(const discard_block& __lhs, const discard_block& __rhs) + { return !(__lhs == __rhs); } + + /** + * Inserts the current state of a %discard_block random number + * generator engine @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A %discard_block random number generator engine. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<class _UniformRandomNumberGenerator1, int __p1, int __r1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const discard_block<_UniformRandomNumberGenerator1, + __p1, __r1>& __x); + + /** + * Extracts the current state of a % subtract_with_carry random number + * generator engine @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A %discard_block random number generator engine. + * + * @returns The input stream with the state of @p __x extracted or in + * an error state. + */ + template<class _UniformRandomNumberGenerator1, int __p1, int __r1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + discard_block<_UniformRandomNumberGenerator1, + __p1, __r1>& __x); + + private: + base_type _M_b; + int _M_n; + }; + + + /** + * James's luxury-level-3 integer adaptation of Luescher's generator. + */ + typedef discard_block< + subtract_with_carry<unsigned long, (1UL << 24), 10, 24>, + 223, + 24 + > ranlux3; + + /** + * James's luxury-level-4 integer adaptation of Luescher's generator. + */ + typedef discard_block< + subtract_with_carry<unsigned long, (1UL << 24), 10, 24>, + 389, + 24 + > ranlux4; + + typedef discard_block< + subtract_with_carry_01<float, 24, 10, 24>, + 223, + 24 + > ranlux3_01; + + typedef discard_block< + subtract_with_carry_01<float, 24, 10, 24>, + 389, + 24 + > ranlux4_01; + + + /** + * A random number generator adaptor class that combines two random number + * generator engines into a single output sequence. + */ + template<class _UniformRandomNumberGenerator1, int __s1, + class _UniformRandomNumberGenerator2, int __s2> + class xor_combine + { + // __glibcxx_class_requires(typename _UniformRandomNumberGenerator1:: + // result_type, ArithmeticTypeConcept) + // __glibcxx_class_requires(typename _UniformRandomNumberGenerator2:: + // result_type, ArithmeticTypeConcept) + + public: + /** The type of the first underlying generator engine. */ + typedef _UniformRandomNumberGenerator1 base1_type; + /** The type of the second underlying generator engine. */ + typedef _UniformRandomNumberGenerator2 base2_type; + + private: + typedef typename base1_type::result_type _Result_type1; + typedef typename base2_type::result_type _Result_type2; + + public: + /** The type of the generated random value. */ + typedef typename __gnu_cxx::__conditional_type<(sizeof(_Result_type1) + > sizeof(_Result_type2)), + _Result_type1, _Result_type2>::__type result_type; + + // parameter values + static const int shift1 = __s1; + static const int shift2 = __s2; + + // constructors and member function + xor_combine() + : _M_b1(), _M_b2() + { _M_initialize_max(); } + + xor_combine(const base1_type& __rng1, const base2_type& __rng2) + : _M_b1(__rng1), _M_b2(__rng2) + { _M_initialize_max(); } + + xor_combine(unsigned long __s) + : _M_b1(__s), _M_b2(__s + 1) + { _M_initialize_max(); } + + template<class _Gen> + xor_combine(_Gen& __g) + : _M_b1(__g), _M_b2(__g) + { _M_initialize_max(); } + + void + seed() + { + _M_b1.seed(); + _M_b2.seed(); + } + + template<class _Gen> + void + seed(_Gen& __g) + { + _M_b1.seed(__g); + _M_b2.seed(__g); + } + + const base1_type& + base1() const + { return _M_b1; } + + const base2_type& + base2() const + { return _M_b2; } + + result_type + min() const + { return 0; } + + result_type + max() const + { return _M_max; } + + /** + * Gets the next random number in the sequence. + */ + // NB: Not exactly the TR1 formula, per N2079 instead. + result_type + operator()() + { + return ((result_type(_M_b1() - _M_b1.min()) << shift1) + ^ (result_type(_M_b2() - _M_b2.min()) << shift2)); + } + + /** + * Compares two %xor_combine random number generator objects of + * the same type for equality. + * + * @param __lhs A %xor_combine random number generator object. + * @param __rhs Another %xor_combine random number generator + * object. + * + * @returns true if the two objects are equal, false otherwise. + */ + friend bool + operator==(const xor_combine& __lhs, const xor_combine& __rhs) + { + return (__lhs.base1() == __rhs.base1()) + && (__lhs.base2() == __rhs.base2()); + } + + /** + * Compares two %xor_combine random number generator objects of + * the same type for inequality. + * + * @param __lhs A %xor_combine random number generator object. + * @param __rhs Another %xor_combine random number generator + * object. + * + * @returns true if the two objects are not equal, false otherwise. + */ + friend bool + operator!=(const xor_combine& __lhs, const xor_combine& __rhs) + { return !(__lhs == __rhs); } + + /** + * Inserts the current state of a %xor_combine random number + * generator engine @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A %xor_combine random number generator engine. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<class _UniformRandomNumberGenerator11, int __s11, + class _UniformRandomNumberGenerator21, int __s21, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const xor_combine<_UniformRandomNumberGenerator11, __s11, + _UniformRandomNumberGenerator21, __s21>& __x); + + /** + * Extracts the current state of a %xor_combine random number + * generator engine @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A %xor_combine random number generator engine. + * + * @returns The input stream with the state of @p __x extracted or in + * an error state. + */ + template<class _UniformRandomNumberGenerator11, int __s11, + class _UniformRandomNumberGenerator21, int __s21, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + xor_combine<_UniformRandomNumberGenerator11, __s11, + _UniformRandomNumberGenerator21, __s21>& __x); + + private: + void + _M_initialize_max(); + + result_type + _M_initialize_max_aux(result_type, result_type, int); + + base1_type _M_b1; + base2_type _M_b2; + result_type _M_max; + }; + + + /** + * A standard interface to a platform-specific non-deterministic + * random number generator (if any are available). + */ + class random_device + { + public: + // types + 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 + } + + private: + random_device(const random_device&); + void operator=(const random_device&); + +#ifdef _GLIBCXX_USE_RANDOM_TR1 + FILE* _M_file; +#else + mt19937 _M_mt; +#endif + }; + + /* @} */ // group tr1_random_generators + + /** + * @defgroup tr1_random_distributions Random Number Distributions + * @ingroup tr1_random + * @{ + */ + + /** + * @defgroup tr1_random_distributions_discrete Discrete Distributions + * @ingroup tr1_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 + { + __glibcxx_class_requires(_IntType, _IntegerConcept) + + public: + /** The type of the parameters of the distribution. */ + typedef _IntType input_type; + /** The type of the range of the distribution. */ + typedef _IntType result_type; + + public: + /** + * Constructs a uniform distribution object. + */ + explicit + uniform_int(_IntType __min = 0, _IntType __max = 9) + : _M_min(__min), _M_max(__max) + { + _GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max); + } + + /** + * Gets the inclusive lower bound of the distribution range. + */ + result_type + min() const + { return _M_min; } + + /** + * Gets the inclusive upper bound of the distribution range. + */ + result_type + max() const + { return _M_max; } + + /** + * Resets the distribution state. + * + * Does nothing for the uniform integer distribution. + */ + void + reset() { } + + /** + * Gets a uniformly distributed random number in the range + * @f$(min, max)@f$. + */ + template<typename _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng) + { + typedef typename _UniformRandomNumberGenerator::result_type + _UResult_type; + return _M_call(__urng, _M_min, _M_max, + typename is_integral<_UResult_type>::type()); + } + + /** + * Gets a uniform random number in the range @f$[0, n)@f$. + * + * This function is aimed at use with std::random_shuffle. + */ + template<typename _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng, result_type __n) + { + typedef typename _UniformRandomNumberGenerator::result_type + _UResult_type; + return _M_call(__urng, 0, __n - 1, + typename is_integral<_UResult_type>::type()); + } + + /** + * Inserts a %uniform_int random number distribution @p __x into the + * output stream @p os. + * + * @param __os An output stream. + * @param __x A %uniform_int 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>& __os, + const uniform_int<_IntType1>& __x); + + /** + * Extracts a %uniform_int random number distribution + * @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A %uniform_int 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>& __is, + uniform_int<_IntType1>& __x); + + private: + template<typename _UniformRandomNumberGenerator> + result_type + _M_call(_UniformRandomNumberGenerator& __urng, + result_type __min, result_type __max, true_type); + + template<typename _UniformRandomNumberGenerator> + result_type + _M_call(_UniformRandomNumberGenerator& __urng, + result_type __min, result_type __max, false_type) + { + return result_type((__urng() - __urng.min()) + / (__urng.max() - __urng.min()) + * (__max - __min + 1)) + __min; + } + + _IntType _M_min; + _IntType _M_max; + }; + + + /** + * @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: + typedef int input_type; + typedef bool result_type; + + public: + /** + * 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$. + */ + explicit + bernoulli_distribution(double __p = 0.5) + : _M_p(__p) + { + _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0)); + } + + /** + * Gets the @p p parameter of the distribution. + */ + double + p() const + { return _M_p; } + + /** + * Resets the distribution state. + * + * Does nothing for a Bernoulli distribution. + */ + void + reset() { } + + /** + * Gets the next value in the Bernoullian sequence. + */ + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng) + { + if ((__urng() - __urng.min()) < _M_p * (__urng.max() - __urng.min())) + return true; + return false; + } + + /** + * Inserts a %bernoulli_distribution random number distribution + * @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A %bernoulli_distribution random number distribution. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const bernoulli_distribution& __x); + + /** + * Extracts a %bernoulli_distribution random number distribution + * @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A %bernoulli_distribution random number generator engine. + * + * @returns The input stream with @p __x extracted or in an error state. + */ + template<typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + bernoulli_distribution& __x) + { return __is >> __x._M_p; } + + private: + double _M_p; + }; + + + /** + * @brief A discrete geometric random number distribution. + * + * The formula for the geometric probability mass function is + * @f$ p(i) = (1 - p)p^{i-1} @f$ where @f$ p @f$ is the parameter of the + * distribution. + */ + template<typename _IntType = int, typename _RealType = double> + class geometric_distribution + { + public: + // types + typedef _RealType input_type; + typedef _IntType result_type; + + // constructors and member function + explicit + geometric_distribution(const _RealType& __p = _RealType(0.5)) + : _M_p(__p) + { + _GLIBCXX_DEBUG_ASSERT((_M_p > 0.0) && (_M_p < 1.0)); + _M_initialize(); + } + + /** + * Gets the distribution parameter @p p. + */ + _RealType + p() const + { return _M_p; } + + void + reset() { } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng); + + /** + * 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 _IntType1, typename _RealType1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const geometric_distribution<_IntType1, _RealType1>& __x); + + /** + * 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 _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + geometric_distribution& __x) + { + __is >> __x._M_p; + __x._M_initialize(); + return __is; + } + + private: + void + _M_initialize() + { _M_log_p = std::log(_M_p); } + + _RealType _M_p; + _RealType _M_log_p; + }; + + + template<typename _RealType> + class normal_distribution; + + /** + * @brief A discrete Poisson random number distribution. + * + * The formula for the Poisson probability mass function is + * @f$ p(i) = \frac{mean^i}{i!} e^{-mean} @f$ where @f$ mean @f$ is the + * parameter of the distribution. + */ + template<typename _IntType = int, typename _RealType = double> + class poisson_distribution + { + public: + // types + typedef _RealType input_type; + typedef _IntType result_type; + + // constructors and member function + explicit + poisson_distribution(const _RealType& __mean = _RealType(1)) + : _M_mean(__mean), _M_nd() + { + _GLIBCXX_DEBUG_ASSERT(_M_mean > 0.0); + _M_initialize(); + } + + /** + * Gets the distribution parameter @p mean. + */ + _RealType + mean() const + { return _M_mean; } + + void + reset() + { _M_nd.reset(); } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng); + + /** + * 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 _RealType1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const poisson_distribution<_IntType1, _RealType1>& __x); + + /** + * 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 _RealType1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + poisson_distribution<_IntType1, _RealType1>& __x); + + private: + void + _M_initialize(); + + // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined. + normal_distribution<_RealType> _M_nd; + + _RealType _M_mean; + + // Hosts either log(mean) or the threshold of the simple method. + _RealType _M_lm_thr; +#if _GLIBCXX_USE_C99_MATH_TR1 + _RealType _M_lfm, _M_sm, _M_d, _M_scx, _M_1cx, _M_c2b, _M_cb; +#endif + }; + + + /** + * @brief A discrete binomial random number distribution. + * + * The formula for the 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, typename _RealType = double> + class binomial_distribution + { + public: + // types + typedef _RealType input_type; + typedef _IntType result_type; + + // constructors and member function + explicit + binomial_distribution(_IntType __t = 1, + const _RealType& __p = _RealType(0.5)) + : _M_t(__t), _M_p(__p), _M_nd() + { + _GLIBCXX_DEBUG_ASSERT((_M_t >= 0) && (_M_p >= 0.0) && (_M_p <= 1.0)); + _M_initialize(); + } + + /** + * Gets the distribution @p t parameter. + */ + _IntType + t() const + { return _M_t; } + + /** + * Gets the distribution @p p parameter. + */ + _RealType + p() const + { return _M_p; } + + void + reset() + { _M_nd.reset(); } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng); + + /** + * 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 _RealType1, + typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const binomial_distribution<_IntType1, _RealType1>& __x); + + /** + * 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 _RealType1, + typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + binomial_distribution<_IntType1, _RealType1>& __x); + + private: + void + _M_initialize(); + + template<class _UniformRandomNumberGenerator> + result_type + _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t); + + // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined. + normal_distribution<_RealType> _M_nd; + + _RealType _M_q; +#if _GLIBCXX_USE_C99_MATH_TR1 + _RealType _M_d1, _M_d2, _M_s1, _M_s2, _M_c, + _M_a1, _M_a123, _M_s, _M_lf, _M_lp1p; +#endif + _RealType _M_p; + _IntType _M_t; + + bool _M_easy; + }; + + /* @} */ // group tr1_random_distributions_discrete + + /** + * @defgroup tr1_random_distributions_continuous Continuous Distributions + * @ingroup tr1_random_distributions + * @{ + */ + + /** + * @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 + { + public: + // types + typedef _RealType input_type; + typedef _RealType result_type; + + public: + /** + * Constructs a uniform_real object. + * + * @param __min [IN] The lower bound of the distribution. + * @param __max [IN] The upper bound of the distribution. + */ + explicit + uniform_real(_RealType __min = _RealType(0), + _RealType __max = _RealType(1)) + : _M_min(__min), _M_max(__max) + { + _GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max); + } + + result_type + min() const + { return _M_min; } + + result_type + max() const + { return _M_max; } + + void + reset() { } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng) + { return (__urng() * (_M_max - _M_min)) + _M_min; } + + /** + * Inserts a %uniform_real random number distribution @p __x into the + * output stream @p __os. + * + * @param __os An output stream. + * @param __x A %uniform_real 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>& __os, + const uniform_real<_RealType1>& __x); + + /** + * Extracts a %uniform_real random number distribution + * @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A %uniform_real 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>& __is, + uniform_real<_RealType1>& __x); + + private: + _RealType _M_min; + _RealType _M_max; + }; + + + /** + * @brief An exponential continuous distribution for random numbers. + * + * The formula for the exponential probability mass function is + * @f$ p(x) = \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$</td></tr> + * </table> + */ + template<typename _RealType = double> + class exponential_distribution + { + public: + // types + typedef _RealType input_type; + typedef _RealType result_type; + + public: + /** + * Constructs an exponential distribution with inverse scale parameter + * @f$ \lambda @f$. + */ + explicit + exponential_distribution(const result_type& __lambda = result_type(1)) + : _M_lambda(__lambda) + { + _GLIBCXX_DEBUG_ASSERT(_M_lambda > 0); + } + + /** + * Gets the inverse scale parameter of the distribution. + */ + _RealType + lambda() const + { return _M_lambda; } + + /** + * Resets the distribution. + * + * Has no effect on exponential distributions. + */ + void + reset() { } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng) + { return -std::log(__urng()) / _M_lambda; } + + /** + * Inserts a %exponential_distribution random number distribution + * @p __x into the output stream @p __os. + * + * @param __os An output stream. + * @param __x A %exponential_distribution random number distribution. + * + * @returns The output stream with the state of @p __x inserted or in + * an error state. + */ + template<typename _RealType1, typename _CharT, typename _Traits> + friend std::basic_ostream<_CharT, _Traits>& + operator<<(std::basic_ostream<_CharT, _Traits>& __os, + const exponential_distribution<_RealType1>& __x); + + /** + * Extracts a %exponential_distribution random number distribution + * @p __x from the input stream @p __is. + * + * @param __is An input stream. + * @param __x A %exponential_distribution random number + * generator engine. + * + * @returns The input stream with @p __x extracted or in an error state. + */ + template<typename _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + exponential_distribution& __x) + { return __is >> __x._M_lambda; } + + private: + result_type _M_lambda; + }; + + + /** + * @brief A normal continuous distribution for random numbers. + * + * The formula for the normal probability mass function is + * @f$ p(x) = \frac{1}{\sigma \sqrt{2 \pi}} + * e^{- \frac{{x - mean}^ {2}}{2 \sigma ^ {2}} } @f$. + */ + template<typename _RealType = double> + class normal_distribution + { + public: + // types + typedef _RealType input_type; + typedef _RealType result_type; + + public: + /** + * Constructs a normal distribution with parameters @f$ mean @f$ and + * @f$ \sigma @f$. + */ + explicit + normal_distribution(const result_type& __mean = result_type(0), + const result_type& __sigma = result_type(1)) + : _M_mean(__mean), _M_sigma(__sigma), _M_saved_available(false) + { + _GLIBCXX_DEBUG_ASSERT(_M_sigma > 0); + } + + /** + * Gets the mean of the distribution. + */ + _RealType + mean() const + { return _M_mean; } + + /** + * Gets the @f$ \sigma @f$ of the distribution. + */ + _RealType + sigma() const + { return _M_sigma; } + + /** + * Resets the distribution. + */ + void + reset() + { _M_saved_available = false; } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng); + + /** + * 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>& __os, + const normal_distribution<_RealType1>& __x); + + /** + * 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>& __is, + normal_distribution<_RealType1>& __x); + + private: + result_type _M_mean; + result_type _M_sigma; + result_type _M_saved; + bool _M_saved_available; + }; + + + /** + * @brief A gamma continuous distribution for random numbers. + * + * The formula for the gamma probability mass function is + * @f$ p(x) = \frac{1}{\Gamma(\alpha)} x^{\alpha - 1} e^{-x} @f$. + */ + template<typename _RealType = double> + class gamma_distribution + { + public: + // types + typedef _RealType input_type; + typedef _RealType result_type; + + public: + /** + * Constructs a gamma distribution with parameters @f$ \alpha @f$. + */ + explicit + gamma_distribution(const result_type& __alpha_val = result_type(1)) + : _M_alpha(__alpha_val) + { + _GLIBCXX_DEBUG_ASSERT(_M_alpha > 0); + _M_initialize(); + } + + /** + * Gets the @f$ \alpha @f$ of the distribution. + */ + _RealType + alpha() const + { return _M_alpha; } + + /** + * Resets the distribution. + */ + void + reset() { } + + template<class _UniformRandomNumberGenerator> + result_type + operator()(_UniformRandomNumberGenerator& __urng); + + /** + * 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>& __os, + const gamma_distribution<_RealType1>& __x); + + /** + * 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 _CharT, typename _Traits> + friend std::basic_istream<_CharT, _Traits>& + operator>>(std::basic_istream<_CharT, _Traits>& __is, + gamma_distribution& __x) + { + __is >> __x._M_alpha; + __x._M_initialize(); + return __is; + } + + private: + void + _M_initialize(); + + result_type _M_alpha; + + // Hosts either lambda of GB or d of modified Vaduva's. + result_type _M_l_d; + }; + + /* @} */ // group tr1_random_distributions_continuous + /* @} */ // group tr1_random_distributions + /* @} */ // group tr1_random + +_GLIBCXX_END_NAMESPACE_TR1 +} + +#include <tr1_impl/random.tcc> |