// random number generation (out of line) -*- C++ -*- // Copyright (C) 2009-2020 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/random.tcc * This is an internal header file, included by other library headers. * Do not attempt to use it directly. @headername{tr1/random} */ #ifndef _GLIBCXX_TR1_RANDOM_TCC #define _GLIBCXX_TR1_RANDOM_TCC 1 namespace std _GLIBCXX_VISIBILITY(default) { _GLIBCXX_BEGIN_NAMESPACE_VERSION namespace tr1 { /* * (Further) implementation-space details. */ namespace __detail { // General case for x = (ax + c) mod m -- use Schrage's algorithm to avoid // integer overflow. // // Because a and c are compile-time integral constants the compiler kindly // elides any unreachable paths. // // Preconditions: a > 0, m > 0. // template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool> struct _Mod { static _Tp __calc(_Tp __x) { if (__a == 1) __x %= __m; else { static const _Tp __q = __m / __a; static const _Tp __r = __m % __a; _Tp __t1 = __a * (__x % __q); _Tp __t2 = __r * (__x / __q); if (__t1 >= __t2) __x = __t1 - __t2; else __x = __m - __t2 + __t1; } if (__c != 0) { const _Tp __d = __m - __x; if (__d > __c) __x += __c; else __x = __c - __d; } return __x; } }; // Special case for m == 0 -- use unsigned integer overflow as modulo // operator. template<typename _Tp, _Tp __a, _Tp __c, _Tp __m> struct _Mod<_Tp, __a, __c, __m, true> { static _Tp __calc(_Tp __x) { return __a * __x + __c; } }; } // namespace __detail template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> const _UIntType linear_congruential<_UIntType, __a, __c, __m>::multiplier; template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> const _UIntType linear_congruential<_UIntType, __a, __c, __m>::increment; template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> const _UIntType linear_congruential<_UIntType, __a, __c, __m>::modulus; /** * Seeds the LCR with integral value @p __x0, adjusted so that the * ring identity is never a member of the convergence set. */ template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> void linear_congruential<_UIntType, __a, __c, __m>:: seed(unsigned long __x0) { if ((__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0) && (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0)) _M_x = __detail::__mod<_UIntType, 1, 0, __m>(1); else _M_x = __detail::__mod<_UIntType, 1, 0, __m>(__x0); } /** * Seeds the LCR engine with a value generated by @p __g. */ template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> template<class _Gen> void linear_congruential<_UIntType, __a, __c, __m>:: seed(_Gen& __g, false_type) { _UIntType __x0 = __g(); if ((__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0) && (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0)) _M_x = __detail::__mod<_UIntType, 1, 0, __m>(1); else _M_x = __detail::__mod<_UIntType, 1, 0, __m>(__x0); } /** * Gets the next generated value in sequence. */ template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m> typename linear_congruential<_UIntType, __a, __c, __m>::result_type linear_congruential<_UIntType, __a, __c, __m>:: operator()() { _M_x = __detail::__mod<_UIntType, __a, __c, __m>(_M_x); return _M_x; } template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const linear_congruential<_UIntType, __a, __c, __m>& __lcr) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left); __os.fill(__os.widen(' ')); __os << __lcr._M_x; __os.flags(__flags); __os.fill(__fill); return __os; } template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, linear_congruential<_UIntType, __a, __c, __m>& __lcr) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec); __is >> __lcr._M_x; __is.flags(__flags); return __is; } 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::word_size; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::state_size; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::shift_size; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::mask_bits; 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> const _UIntType mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::parameter_a; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::output_u; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::output_s; 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> const _UIntType mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::output_b; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::output_t; 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> const _UIntType mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::output_c; 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> const int mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::output_l; 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> void mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>:: seed(unsigned long __value) { _M_x[0] = __detail::__mod<_UIntType, 1, 0, __detail::_Shift<_UIntType, __w>::__value>(__value); for (int __i = 1; __i < state_size; ++__i) { _UIntType __x = _M_x[__i - 1]; __x ^= __x >> (__w - 2); __x *= 1812433253ul; __x += __i; _M_x[__i] = __detail::__mod<_UIntType, 1, 0, __detail::_Shift<_UIntType, __w>::__value>(__x); } _M_p = state_size; } 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> template<class _Gen> void mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>:: seed(_Gen& __gen, false_type) { for (int __i = 0; __i < state_size; ++__i) _M_x[__i] = __detail::__mod<_UIntType, 1, 0, __detail::_Shift<_UIntType, __w>::__value>(__gen()); _M_p = state_size; } 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> typename mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>::result_type mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>:: operator()() { // Reload the vector - cost is O(n) amortized over n calls. if (_M_p >= state_size) { const _UIntType __upper_mask = (~_UIntType()) << __r; const _UIntType __lower_mask = ~__upper_mask; for (int __k = 0; __k < (__n - __m); ++__k) { _UIntType __y = ((_M_x[__k] & __upper_mask) | (_M_x[__k + 1] & __lower_mask)); _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1) ^ ((__y & 0x01) ? __a : 0)); } for (int __k = (__n - __m); __k < (__n - 1); ++__k) { _UIntType __y = ((_M_x[__k] & __upper_mask) | (_M_x[__k + 1] & __lower_mask)); _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1) ^ ((__y & 0x01) ? __a : 0)); } _UIntType __y = ((_M_x[__n - 1] & __upper_mask) | (_M_x[0] & __lower_mask)); _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1) ^ ((__y & 0x01) ? __a : 0)); _M_p = 0; } // Calculate o(x(i)). result_type __z = _M_x[_M_p++]; __z ^= (__z >> __u); __z ^= (__z << __s) & __b; __z ^= (__z << __t) & __c; __z ^= (__z >> __l); return __z; } 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, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left); __os.fill(__space); for (int __i = 0; __i < __n - 1; ++__i) __os << __x._M_x[__i] << __space; __os << __x._M_x[__n - 1]; __os.flags(__flags); __os.fill(__fill); return __os; } 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, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s, __b, __t, __c, __l>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); for (int __i = 0; __i < __n; ++__i) __is >> __x._M_x[__i]; __is.flags(__flags); return __is; } template<typename _IntType, _IntType __m, int __s, int __r> const _IntType subtract_with_carry<_IntType, __m, __s, __r>::modulus; template<typename _IntType, _IntType __m, int __s, int __r> const int subtract_with_carry<_IntType, __m, __s, __r>::long_lag; template<typename _IntType, _IntType __m, int __s, int __r> const int subtract_with_carry<_IntType, __m, __s, __r>::short_lag; template<typename _IntType, _IntType __m, int __s, int __r> void subtract_with_carry<_IntType, __m, __s, __r>:: seed(unsigned long __value) { if (__value == 0) __value = 19780503; std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563> __lcg(__value); for (int __i = 0; __i < long_lag; ++__i) _M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__lcg()); _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0; _M_p = 0; } template<typename _IntType, _IntType __m, int __s, int __r> template<class _Gen> void subtract_with_carry<_IntType, __m, __s, __r>:: seed(_Gen& __gen, false_type) { const int __n = (std::numeric_limits<_UIntType>::digits + 31) / 32; for (int __i = 0; __i < long_lag; ++__i) { _UIntType __tmp = 0; _UIntType __factor = 1; for (int __j = 0; __j < __n; ++__j) { __tmp += __detail::__mod<__detail::_UInt32Type, 1, 0, 0> (__gen()) * __factor; __factor *= __detail::_Shift<_UIntType, 32>::__value; } _M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__tmp); } _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0; _M_p = 0; } template<typename _IntType, _IntType __m, int __s, int __r> typename subtract_with_carry<_IntType, __m, __s, __r>::result_type subtract_with_carry<_IntType, __m, __s, __r>:: operator()() { // Derive short lag index from current index. int __ps = _M_p - short_lag; if (__ps < 0) __ps += long_lag; // Calculate new x(i) without overflow or division. // NB: Thanks to the requirements for _IntType, _M_x[_M_p] + _M_carry // cannot overflow. _UIntType __xi; if (_M_x[__ps] >= _M_x[_M_p] + _M_carry) { __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry; _M_carry = 0; } else { __xi = modulus - _M_x[_M_p] - _M_carry + _M_x[__ps]; _M_carry = 1; } _M_x[_M_p] = __xi; // Adjust current index to loop around in ring buffer. if (++_M_p >= long_lag) _M_p = 0; return __xi; } template<typename _IntType, _IntType __m, int __s, int __r, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const subtract_with_carry<_IntType, __m, __s, __r>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left); __os.fill(__space); for (int __i = 0; __i < __r; ++__i) __os << __x._M_x[__i] << __space; __os << __x._M_carry; __os.flags(__flags); __os.fill(__fill); return __os; } template<typename _IntType, _IntType __m, int __s, int __r, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, subtract_with_carry<_IntType, __m, __s, __r>& __x) { typedef std::basic_ostream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); for (int __i = 0; __i < __r; ++__i) __is >> __x._M_x[__i]; __is >> __x._M_carry; __is.flags(__flags); return __is; } template<typename _RealType, int __w, int __s, int __r> const int subtract_with_carry_01<_RealType, __w, __s, __r>::word_size; template<typename _RealType, int __w, int __s, int __r> const int subtract_with_carry_01<_RealType, __w, __s, __r>::long_lag; template<typename _RealType, int __w, int __s, int __r> const int subtract_with_carry_01<_RealType, __w, __s, __r>::short_lag; template<typename _RealType, int __w, int __s, int __r> void subtract_with_carry_01<_RealType, __w, __s, __r>:: _M_initialize_npows() { for (int __j = 0; __j < __n; ++__j) #if _GLIBCXX_USE_C99_MATH_TR1 _M_npows[__j] = std::tr1::ldexp(_RealType(1), -__w + __j * 32); #else _M_npows[__j] = std::pow(_RealType(2), -__w + __j * 32); #endif } template<typename _RealType, int __w, int __s, int __r> void subtract_with_carry_01<_RealType, __w, __s, __r>:: seed(unsigned long __value) { if (__value == 0) __value = 19780503; // _GLIBCXX_RESOLVE_LIB_DEFECTS // 512. Seeding subtract_with_carry_01 from a single unsigned long. std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563> __lcg(__value); this->seed(__lcg); } template<typename _RealType, int __w, int __s, int __r> template<class _Gen> void subtract_with_carry_01<_RealType, __w, __s, __r>:: seed(_Gen& __gen, false_type) { for (int __i = 0; __i < long_lag; ++__i) { for (int __j = 0; __j < __n - 1; ++__j) _M_x[__i][__j] = __detail::__mod<_UInt32Type, 1, 0, 0>(__gen()); _M_x[__i][__n - 1] = __detail::__mod<_UInt32Type, 1, 0, __detail::_Shift<_UInt32Type, __w % 32>::__value>(__gen()); } _M_carry = 1; for (int __j = 0; __j < __n; ++__j) if (_M_x[long_lag - 1][__j] != 0) { _M_carry = 0; break; } _M_p = 0; } template<typename _RealType, int __w, int __s, int __r> typename subtract_with_carry_01<_RealType, __w, __s, __r>::result_type subtract_with_carry_01<_RealType, __w, __s, __r>:: operator()() { // Derive short lag index from current index. int __ps = _M_p - short_lag; if (__ps < 0) __ps += long_lag; _UInt32Type __new_carry; for (int __j = 0; __j < __n - 1; ++__j) { if (_M_x[__ps][__j] > _M_x[_M_p][__j] || (_M_x[__ps][__j] == _M_x[_M_p][__j] && _M_carry == 0)) __new_carry = 0; else __new_carry = 1; _M_x[_M_p][__j] = _M_x[__ps][__j] - _M_x[_M_p][__j] - _M_carry; _M_carry = __new_carry; } if (_M_x[__ps][__n - 1] > _M_x[_M_p][__n - 1] || (_M_x[__ps][__n - 1] == _M_x[_M_p][__n - 1] && _M_carry == 0)) __new_carry = 0; else __new_carry = 1; _M_x[_M_p][__n - 1] = __detail::__mod<_UInt32Type, 1, 0, __detail::_Shift<_UInt32Type, __w % 32>::__value> (_M_x[__ps][__n - 1] - _M_x[_M_p][__n - 1] - _M_carry); _M_carry = __new_carry; result_type __ret = 0.0; for (int __j = 0; __j < __n; ++__j) __ret += _M_x[_M_p][__j] * _M_npows[__j]; // Adjust current index to loop around in ring buffer. if (++_M_p >= long_lag) _M_p = 0; return __ret; } template<typename _RealType, int __w, int __s, int __r, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const subtract_with_carry_01<_RealType, __w, __s, __r>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left); __os.fill(__space); for (int __i = 0; __i < __r; ++__i) for (int __j = 0; __j < __x.__n; ++__j) __os << __x._M_x[__i][__j] << __space; __os << __x._M_carry; __os.flags(__flags); __os.fill(__fill); return __os; } template<typename _RealType, int __w, int __s, int __r, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, subtract_with_carry_01<_RealType, __w, __s, __r>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); for (int __i = 0; __i < __r; ++__i) for (int __j = 0; __j < __x.__n; ++__j) __is >> __x._M_x[__i][__j]; __is >> __x._M_carry; __is.flags(__flags); return __is; } template<class _UniformRandomNumberGenerator, int __p, int __r> const int discard_block<_UniformRandomNumberGenerator, __p, __r>::block_size; template<class _UniformRandomNumberGenerator, int __p, int __r> const int discard_block<_UniformRandomNumberGenerator, __p, __r>::used_block; template<class _UniformRandomNumberGenerator, int __p, int __r> typename discard_block<_UniformRandomNumberGenerator, __p, __r>::result_type discard_block<_UniformRandomNumberGenerator, __p, __r>:: operator()() { if (_M_n >= used_block) { while (_M_n < block_size) { _M_b(); ++_M_n; } _M_n = 0; } ++_M_n; return _M_b(); } template<class _UniformRandomNumberGenerator, int __p, int __r, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const discard_block<_UniformRandomNumberGenerator, __p, __r>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left); __os.fill(__space); __os << __x._M_b << __space << __x._M_n; __os.flags(__flags); __os.fill(__fill); return __os; } template<class _UniformRandomNumberGenerator, int __p, int __r, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, discard_block<_UniformRandomNumberGenerator, __p, __r>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); __is >> __x._M_b >> __x._M_n; __is.flags(__flags); return __is; } template<class _UniformRandomNumberGenerator1, int __s1, class _UniformRandomNumberGenerator2, int __s2> const int xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>::shift1; template<class _UniformRandomNumberGenerator1, int __s1, class _UniformRandomNumberGenerator2, int __s2> const int xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>::shift2; template<class _UniformRandomNumberGenerator1, int __s1, class _UniformRandomNumberGenerator2, int __s2> void xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>:: _M_initialize_max() { const int __w = std::numeric_limits<result_type>::digits; const result_type __m1 = std::min(result_type(_M_b1.max() - _M_b1.min()), __detail::_Shift<result_type, __w - __s1>::__value - 1); const result_type __m2 = std::min(result_type(_M_b2.max() - _M_b2.min()), __detail::_Shift<result_type, __w - __s2>::__value - 1); // NB: In TR1 s1 is not required to be >= s2. if (__s1 < __s2) _M_max = _M_initialize_max_aux(__m2, __m1, __s2 - __s1) << __s1; else _M_max = _M_initialize_max_aux(__m1, __m2, __s1 - __s2) << __s2; } template<class _UniformRandomNumberGenerator1, int __s1, class _UniformRandomNumberGenerator2, int __s2> typename xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>::result_type xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>:: _M_initialize_max_aux(result_type __a, result_type __b, int __d) { const result_type __two2d = result_type(1) << __d; const result_type __c = __a * __two2d; if (__a == 0 || __b < __two2d) return __c + __b; const result_type __t = std::max(__c, __b); const result_type __u = std::min(__c, __b); result_type __ub = __u; result_type __p; for (__p = 0; __ub != 1; __ub >>= 1) ++__p; const result_type __two2p = result_type(1) << __p; const result_type __k = __t / __two2p; if (__k & 1) return (__k + 1) * __two2p - 1; if (__c >= __b) return (__k + 1) * __two2p + _M_initialize_max_aux((__t % __two2p) / __two2d, __u % __two2p, __d); else return (__k + 1) * __two2p + _M_initialize_max_aux((__u % __two2p) / __two2d, __t % __two2p, __d); } template<class _UniformRandomNumberGenerator1, int __s1, class _UniformRandomNumberGenerator2, int __s2, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left); __os.fill(__space); __os << __x.base1() << __space << __x.base2(); __os.flags(__flags); __os.fill(__fill); return __os; } template<class _UniformRandomNumberGenerator1, int __s1, class _UniformRandomNumberGenerator2, int __s2, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, xor_combine<_UniformRandomNumberGenerator1, __s1, _UniformRandomNumberGenerator2, __s2>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::skipws); __is >> __x._M_b1 >> __x._M_b2; __is.flags(__flags); return __is; } template<typename _IntType> template<typename _UniformRandomNumberGenerator> typename uniform_int<_IntType>::result_type uniform_int<_IntType>:: _M_call(_UniformRandomNumberGenerator& __urng, result_type __min, result_type __max, true_type) { // XXX Must be fixed to work well for *arbitrary* __urng.max(), // __urng.min(), __max, __min. Currently works fine only in the // most common case __urng.max() - __urng.min() >= __max - __min, // with __urng.max() > __urng.min() >= 0. typedef typename __gnu_cxx::__add_unsigned<typename _UniformRandomNumberGenerator::result_type>::__type __urntype; typedef typename __gnu_cxx::__add_unsigned<result_type>::__type __utype; typedef typename __gnu_cxx::__conditional_type<(sizeof(__urntype) > sizeof(__utype)), __urntype, __utype>::__type __uctype; result_type __ret; const __urntype __urnmin = __urng.min(); const __urntype __urnmax = __urng.max(); const __urntype __urnrange = __urnmax - __urnmin; const __uctype __urange = __max - __min; const __uctype __udenom = (__urnrange <= __urange ? 1 : __urnrange / (__urange + 1)); do __ret = (__urntype(__urng()) - __urnmin) / __udenom; while (__ret > __max - __min); return __ret + __min; } template<typename _IntType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const uniform_int<_IntType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__space); __os << __x.min() << __space << __x.max(); __os.flags(__flags); __os.fill(__fill); return __os; } template<typename _IntType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, uniform_int<_IntType>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); __is >> __x._M_min >> __x._M_max; __is.flags(__flags); return __is; } template<typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const bernoulli_distribution& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__os.widen(' ')); __os.precision(__gnu_cxx::__numeric_traits<double>::__max_digits10); __os << __x.p(); __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } template<typename _IntType, typename _RealType> template<class _UniformRandomNumberGenerator> typename geometric_distribution<_IntType, _RealType>::result_type geometric_distribution<_IntType, _RealType>:: operator()(_UniformRandomNumberGenerator& __urng) { // About the epsilon thing see this thread: // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html const _RealType __naf = (1 - std::numeric_limits<_RealType>::epsilon()) / 2; // The largest _RealType convertible to _IntType. const _RealType __thr = std::numeric_limits<_IntType>::max() + __naf; _RealType __cand; do __cand = std::ceil(std::log(__urng()) / _M_log_p); while (__cand >= __thr); return result_type(__cand + __naf); } template<typename _IntType, typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const geometric_distribution<_IntType, _RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__os.widen(' ')); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x.p(); __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } template<typename _IntType, typename _RealType> void poisson_distribution<_IntType, _RealType>:: _M_initialize() { #if _GLIBCXX_USE_C99_MATH_TR1 if (_M_mean >= 12) { const _RealType __m = std::floor(_M_mean); _M_lm_thr = std::log(_M_mean); _M_lfm = std::tr1::lgamma(__m + 1); _M_sm = std::sqrt(__m); const _RealType __pi_4 = 0.7853981633974483096156608458198757L; const _RealType __dx = std::sqrt(2 * __m * std::log(32 * __m / __pi_4)); _M_d = std::tr1::round(std::max(_RealType(6), std::min(__m, __dx))); const _RealType __cx = 2 * __m + _M_d; _M_scx = std::sqrt(__cx / 2); _M_1cx = 1 / __cx; _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx); _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2)) / _M_d; } else #endif _M_lm_thr = std::exp(-_M_mean); } /** * A rejection algorithm when mean >= 12 and a simple method based * upon the multiplication of uniform random variates otherwise. * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1 * is defined. * * Reference: * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!). */ template<typename _IntType, typename _RealType> template<class _UniformRandomNumberGenerator> typename poisson_distribution<_IntType, _RealType>::result_type poisson_distribution<_IntType, _RealType>:: operator()(_UniformRandomNumberGenerator& __urng) { #if _GLIBCXX_USE_C99_MATH_TR1 if (_M_mean >= 12) { _RealType __x; // See comments above... const _RealType __naf = (1 - std::numeric_limits<_RealType>::epsilon()) / 2; const _RealType __thr = std::numeric_limits<_IntType>::max() + __naf; const _RealType __m = std::floor(_M_mean); // sqrt(pi / 2) const _RealType __spi_2 = 1.2533141373155002512078826424055226L; const _RealType __c1 = _M_sm * __spi_2; const _RealType __c2 = _M_c2b + __c1; const _RealType __c3 = __c2 + 1; const _RealType __c4 = __c3 + 1; // e^(1 / 78) const _RealType __e178 = 1.0129030479320018583185514777512983L; const _RealType __c5 = __c4 + __e178; const _RealType __c = _M_cb + __c5; const _RealType __2cx = 2 * (2 * __m + _M_d); bool __reject = true; do { const _RealType __u = __c * __urng(); const _RealType __e = -std::log(__urng()); _RealType __w = 0.0; if (__u <= __c1) { const _RealType __n = _M_nd(__urng); const _RealType __y = -std::abs(__n) * _M_sm - 1; __x = std::floor(__y); __w = -__n * __n / 2; if (__x < -__m) continue; } else if (__u <= __c2) { const _RealType __n = _M_nd(__urng); const _RealType __y = 1 + std::abs(__n) * _M_scx; __x = std::ceil(__y); __w = __y * (2 - __y) * _M_1cx; if (__x > _M_d) continue; } else if (__u <= __c3) // NB: This case not in the book, nor in the Errata, // but should be ok... __x = -1; else if (__u <= __c4) __x = 0; else if (__u <= __c5) __x = 1; else { const _RealType __v = -std::log(__urng()); const _RealType __y = _M_d + __v * __2cx / _M_d; __x = std::ceil(__y); __w = -_M_d * _M_1cx * (1 + __y / 2); } __reject = (__w - __e - __x * _M_lm_thr > _M_lfm - std::tr1::lgamma(__x + __m + 1)); __reject |= __x + __m >= __thr; } while (__reject); return result_type(__x + __m + __naf); } else #endif { _IntType __x = 0; _RealType __prod = 1.0; do { __prod *= __urng(); __x += 1; } while (__prod > _M_lm_thr); return __x - 1; } } template<typename _IntType, typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const poisson_distribution<_IntType, _RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__space); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x.mean() << __space << __x._M_nd; __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } template<typename _IntType, typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, poisson_distribution<_IntType, _RealType>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::skipws); __is >> __x._M_mean >> __x._M_nd; __x._M_initialize(); __is.flags(__flags); return __is; } template<typename _IntType, typename _RealType> void binomial_distribution<_IntType, _RealType>:: _M_initialize() { const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p; _M_easy = true; #if _GLIBCXX_USE_C99_MATH_TR1 if (_M_t * __p12 >= 8) { _M_easy = false; const _RealType __np = std::floor(_M_t * __p12); const _RealType __pa = __np / _M_t; const _RealType __1p = 1 - __pa; const _RealType __pi_4 = 0.7853981633974483096156608458198757L; const _RealType __d1x = std::sqrt(__np * __1p * std::log(32 * __np / (81 * __pi_4 * __1p))); _M_d1 = std::tr1::round(std::max(_RealType(1), __d1x)); const _RealType __d2x = std::sqrt(__np * __1p * std::log(32 * _M_t * __1p / (__pi_4 * __pa))); _M_d2 = std::tr1::round(std::max(_RealType(1), __d2x)); // sqrt(pi / 2) const _RealType __spi_2 = 1.2533141373155002512078826424055226L; _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np)); _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p)); _M_c = 2 * _M_d1 / __np; _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2; const _RealType __a12 = _M_a1 + _M_s2 * __spi_2; const _RealType __s1s = _M_s1 * _M_s1; _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p)) * 2 * __s1s / _M_d1 * std::exp(-_M_d1 * _M_d1 / (2 * __s1s))); const _RealType __s2s = _M_s2 * _M_s2; _M_s = (_M_a123 + 2 * __s2s / _M_d2 * std::exp(-_M_d2 * _M_d2 / (2 * __s2s))); _M_lf = (std::tr1::lgamma(__np + 1) + std::tr1::lgamma(_M_t - __np + 1)); _M_lp1p = std::log(__pa / __1p); _M_q = -std::log(1 - (__p12 - __pa) / __1p); } else #endif _M_q = -std::log(1 - __p12); } template<typename _IntType, typename _RealType> template<class _UniformRandomNumberGenerator> typename binomial_distribution<_IntType, _RealType>::result_type binomial_distribution<_IntType, _RealType>:: _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t) { _IntType __x = 0; _RealType __sum = 0; do { const _RealType __e = -std::log(__urng()); __sum += __e / (__t - __x); __x += 1; } while (__sum <= _M_q); return __x - 1; } /** * A rejection algorithm when t * p >= 8 and a simple waiting time * method - the second in the referenced book - otherwise. * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1 * is defined. * * Reference: * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, * New York, 1986, Ch. X, Sect. 4 (+ Errata!). */ template<typename _IntType, typename _RealType> template<class _UniformRandomNumberGenerator> typename binomial_distribution<_IntType, _RealType>::result_type binomial_distribution<_IntType, _RealType>:: operator()(_UniformRandomNumberGenerator& __urng) { result_type __ret; const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p; #if _GLIBCXX_USE_C99_MATH_TR1 if (!_M_easy) { _RealType __x; // See comments above... const _RealType __naf = (1 - std::numeric_limits<_RealType>::epsilon()) / 2; const _RealType __thr = std::numeric_limits<_IntType>::max() + __naf; const _RealType __np = std::floor(_M_t * __p12); const _RealType __pa = __np / _M_t; // sqrt(pi / 2) const _RealType __spi_2 = 1.2533141373155002512078826424055226L; const _RealType __a1 = _M_a1; const _RealType __a12 = __a1 + _M_s2 * __spi_2; const _RealType __a123 = _M_a123; const _RealType __s1s = _M_s1 * _M_s1; const _RealType __s2s = _M_s2 * _M_s2; bool __reject; do { const _RealType __u = _M_s * __urng(); _RealType __v; if (__u <= __a1) { const _RealType __n = _M_nd(__urng); const _RealType __y = _M_s1 * std::abs(__n); __reject = __y >= _M_d1; if (!__reject) { const _RealType __e = -std::log(__urng()); __x = std::floor(__y); __v = -__e - __n * __n / 2 + _M_c; } } else if (__u <= __a12) { const _RealType __n = _M_nd(__urng); const _RealType __y = _M_s2 * std::abs(__n); __reject = __y >= _M_d2; if (!__reject) { const _RealType __e = -std::log(__urng()); __x = std::floor(-__y); __v = -__e - __n * __n / 2; } } else if (__u <= __a123) { const _RealType __e1 = -std::log(__urng()); const _RealType __e2 = -std::log(__urng()); const _RealType __y = _M_d1 + 2 * __s1s * __e1 / _M_d1; __x = std::floor(__y); __v = (-__e2 + _M_d1 * (1 / (_M_t - __np) -__y / (2 * __s1s))); __reject = false; } else { const _RealType __e1 = -std::log(__urng()); const _RealType __e2 = -std::log(__urng()); const _RealType __y = _M_d2 + 2 * __s2s * __e1 / _M_d2; __x = std::floor(-__y); __v = -__e2 - _M_d2 * __y / (2 * __s2s); __reject = false; } __reject = __reject || __x < -__np || __x > _M_t - __np; if (!__reject) { const _RealType __lfx = std::tr1::lgamma(__np + __x + 1) + std::tr1::lgamma(_M_t - (__np + __x) + 1); __reject = __v > _M_lf - __lfx + __x * _M_lp1p; } __reject |= __x + __np >= __thr; } while (__reject); __x += __np + __naf; const _IntType __z = _M_waiting(__urng, _M_t - _IntType(__x)); __ret = _IntType(__x) + __z; } else #endif __ret = _M_waiting(__urng, _M_t); if (__p12 != _M_p) __ret = _M_t - __ret; return __ret; } template<typename _IntType, typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const binomial_distribution<_IntType, _RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__space); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x.t() << __space << __x.p() << __space << __x._M_nd; __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } template<typename _IntType, typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, binomial_distribution<_IntType, _RealType>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); __is >> __x._M_t >> __x._M_p >> __x._M_nd; __x._M_initialize(); __is.flags(__flags); return __is; } template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const uniform_real<_RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__space); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x.min() << __space << __x.max(); __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, uniform_real<_RealType>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::skipws); __is >> __x._M_min >> __x._M_max; __is.flags(__flags); return __is; } template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const exponential_distribution<_RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__os.widen(' ')); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x.lambda(); __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } /** * Polar method due to Marsaglia. * * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, * New York, 1986, Ch. V, Sect. 4.4. */ template<typename _RealType> template<class _UniformRandomNumberGenerator> typename normal_distribution<_RealType>::result_type normal_distribution<_RealType>:: operator()(_UniformRandomNumberGenerator& __urng) { result_type __ret; if (_M_saved_available) { _M_saved_available = false; __ret = _M_saved; } else { result_type __x, __y, __r2; do { __x = result_type(2.0) * __urng() - 1.0; __y = result_type(2.0) * __urng() - 1.0; __r2 = __x * __x + __y * __y; } while (__r2 > 1.0 || __r2 == 0.0); const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2); _M_saved = __x * __mult; _M_saved_available = true; __ret = __y * __mult; } __ret = __ret * _M_sigma + _M_mean; return __ret; } template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const normal_distribution<_RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); const _CharT __space = __os.widen(' '); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__space); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x._M_saved_available << __space << __x.mean() << __space << __x.sigma(); if (__x._M_saved_available) __os << __space << __x._M_saved; __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } template<typename _RealType, typename _CharT, typename _Traits> std::basic_istream<_CharT, _Traits>& operator>>(std::basic_istream<_CharT, _Traits>& __is, normal_distribution<_RealType>& __x) { typedef std::basic_istream<_CharT, _Traits> __istream_type; typedef typename __istream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __is.flags(); __is.flags(__ios_base::dec | __ios_base::skipws); __is >> __x._M_saved_available >> __x._M_mean >> __x._M_sigma; if (__x._M_saved_available) __is >> __x._M_saved; __is.flags(__flags); return __is; } template<typename _RealType> void gamma_distribution<_RealType>:: _M_initialize() { if (_M_alpha >= 1) _M_l_d = std::sqrt(2 * _M_alpha - 1); else _M_l_d = (std::pow(_M_alpha, _M_alpha / (1 - _M_alpha)) * (1 - _M_alpha)); } /** * Cheng's rejection algorithm GB for alpha >= 1 and a modification * of Vaduva's rejection from Weibull algorithm due to Devroye for * alpha < 1. * * References: * Cheng, R. C. The Generation of Gamma Random Variables with Non-integral * Shape Parameter. Applied Statistics, 26, 71-75, 1977. * * Vaduva, I. Computer Generation of Gamma Gandom Variables by Rejection * and Composition Procedures. Math. Operationsforschung and Statistik, * Series in Statistics, 8, 545-576, 1977. * * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, * New York, 1986, Ch. IX, Sect. 3.4 (+ Errata!). */ template<typename _RealType> template<class _UniformRandomNumberGenerator> typename gamma_distribution<_RealType>::result_type gamma_distribution<_RealType>:: operator()(_UniformRandomNumberGenerator& __urng) { result_type __x; bool __reject; if (_M_alpha >= 1) { // alpha - log(4) const result_type __b = _M_alpha - result_type(1.3862943611198906188344642429163531L); const result_type __c = _M_alpha + _M_l_d; const result_type __1l = 1 / _M_l_d; // 1 + log(9 / 2) const result_type __k = 2.5040773967762740733732583523868748L; do { const result_type __u = __urng(); const result_type __v = __urng(); const result_type __y = __1l * std::log(__v / (1 - __v)); __x = _M_alpha * std::exp(__y); const result_type __z = __u * __v * __v; const result_type __r = __b + __c * __y - __x; __reject = __r < result_type(4.5) * __z - __k; if (__reject) __reject = __r < std::log(__z); } while (__reject); } else { const result_type __c = 1 / _M_alpha; do { const result_type __z = -std::log(__urng()); const result_type __e = -std::log(__urng()); __x = std::pow(__z, __c); __reject = __z + __e < _M_l_d + __x; } while (__reject); } return __x; } template<typename _RealType, typename _CharT, typename _Traits> std::basic_ostream<_CharT, _Traits>& operator<<(std::basic_ostream<_CharT, _Traits>& __os, const gamma_distribution<_RealType>& __x) { typedef std::basic_ostream<_CharT, _Traits> __ostream_type; typedef typename __ostream_type::ios_base __ios_base; const typename __ios_base::fmtflags __flags = __os.flags(); const _CharT __fill = __os.fill(); const std::streamsize __precision = __os.precision(); __os.flags(__ios_base::scientific | __ios_base::left); __os.fill(__os.widen(' ')); __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10); __os << __x.alpha(); __os.flags(__flags); __os.fill(__fill); __os.precision(__precision); return __os; } } _GLIBCXX_END_NAMESPACE_VERSION } #endif