2777 lines
85 KiB
C++
2777 lines
85 KiB
C++
// random number generation (out of line) -*- C++ -*-
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// Copyright (C) 2009 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 2, or (at your option)
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// any later version.
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License along
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// with this library; see the file COPYING. If not, write to the Free
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// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
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// USA.
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// As a special exception, you may use this file as part of a free software
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// library without restriction. Specifically, if other files instantiate
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// templates or use macros or inline functions from this file, or you compile
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// this file and link it with other files to produce an executable, this
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// file does not by itself cause the resulting executable to be covered by
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// the GNU General Public License. This exception does not however
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// invalidate any other reasons why the executable file might be covered by
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// the GNU General Public License.
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/** @file bits/random.tcc
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* This is an internal header file, included by other library headers.
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* You should not attempt to use it directly.
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*/
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#include <numeric>
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#include <algorithm>
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namespace std
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{
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/*
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* (Further) implementation-space details.
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*/
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namespace __detail
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{
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// General case for x = (ax + c) mod m -- use Schrage's algorithm to
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// avoid integer overflow.
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//
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// Because a and c are compile-time integral constants the compiler
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// kindly elides any unreachable paths.
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//
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// Preconditions: a > 0, m > 0.
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//
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template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool>
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struct _Mod
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{
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static _Tp
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__calc(_Tp __x)
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{
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if (__a == 1)
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__x %= __m;
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else
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{
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static const _Tp __q = __m / __a;
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static const _Tp __r = __m % __a;
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_Tp __t1 = __a * (__x % __q);
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_Tp __t2 = __r * (__x / __q);
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if (__t1 >= __t2)
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__x = __t1 - __t2;
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else
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__x = __m - __t2 + __t1;
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}
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if (__c != 0)
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{
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const _Tp __d = __m - __x;
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if (__d > __c)
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__x += __c;
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else
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__x = __c - __d;
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}
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return __x;
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}
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};
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// Special case for m == 0 -- use unsigned integer overflow as modulo
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// operator.
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template<typename _Tp, _Tp __a, _Tp __c, _Tp __m>
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struct _Mod<_Tp, __a, __c, __m, true>
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{
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static _Tp
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__calc(_Tp __x)
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{ return __a * __x + __c; }
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};
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} // namespace __detail
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/**
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* Seeds the LCR with integral value @p __x0, adjusted so that the
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* ring identity is never a member of the convergence set.
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*/
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template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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void
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linear_congruential_engine<_UIntType, __a, __c, __m>::
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seed(_UIntType __x0)
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{
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if ((__detail::__mod<_UIntType, 1U, 0U, __m>(__c) == 0U)
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&& (__detail::__mod<_UIntType, 1U, 0U, __m>(__x0) == 0U))
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_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(1U);
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else
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_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(__x0);
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}
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/**
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* Seeds the LCR engine with a value generated by @p __g.
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*/
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template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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void
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linear_congruential_engine<_UIntType, __a, __c, __m>::
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seed(seed_seq& __q)
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{
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const _UIntType __k = (std::log2(__m) + 31) / 32;
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_UIntType __arr[__k + 3];
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__q.generate(__arr + 0, __arr + 3);
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_UIntType __factor = 1U;
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_UIntType __sum = 0U;
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for (size_t __i = 0; __i < __k; ++__i)
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{
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__sum += __arr[__i + 3] * __factor;
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__factor *= __detail::_Shift<_UIntType, 32>::__value;
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}
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if ((__detail::__mod<_UIntType, 1U, 0U, __m>(__c) == 0U)
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&& (__detail::__mod<_UIntType, 1U, 0U, __m>(__sum) == 0U))
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_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(1U);
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else
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_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(__sum);
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}
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/**
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* Seeds the LCR engine with a value generated by @p __g.
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*/
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template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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template<typename _Gen>
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void
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linear_congruential_engine<_UIntType, __a, __c, __m>::
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seed(_Gen& __g, false_type)
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{
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_UIntType __x0 = __g();
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if ((__detail::__mod<_UIntType, 1U, 0U, __m>(__c) == 0U)
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&& (__detail::__mod<_UIntType, 1U, 0U, __m>(__x0) == 0U))
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_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(1U);
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else
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_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(__x0);
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}
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/**
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* Gets the next generated value in sequence.
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*/
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template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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typename linear_congruential_engine<_UIntType, __a, __c, __m>::
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result_type
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linear_congruential_engine<_UIntType, __a, __c, __m>::
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operator()()
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{
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_M_x = __detail::__mod<_UIntType, __a, __c, __m>(_M_x);
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return _M_x;
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}
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template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
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typename _CharT, typename _Traits>
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std::basic_ostream<_CharT, _Traits>&
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operator<<(std::basic_ostream<_CharT, _Traits>& __os,
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const linear_congruential_engine<_UIntType,
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__a, __c, __m>& __lcr)
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{
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typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
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typedef typename __ostream_type::ios_base __ios_base;
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const typename __ios_base::fmtflags __flags = __os.flags();
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const _CharT __fill = __os.fill();
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__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
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__os.fill(__os.widen(' '));
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__os << __lcr._M_x;
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__os.flags(__flags);
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__os.fill(__fill);
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return __os;
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}
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template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
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typename _CharT, typename _Traits>
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std::basic_istream<_CharT, _Traits>&
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operator>>(std::basic_istream<_CharT, _Traits>& __is,
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linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
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{
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typedef std::basic_istream<_CharT, _Traits> __istream_type;
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typedef typename __istream_type::ios_base __ios_base;
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const typename __ios_base::fmtflags __flags = __is.flags();
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__is.flags(__ios_base::dec);
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__is >> __lcr._M_x;
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__is.flags(__flags);
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return __is;
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}
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template<typename _UIntType,
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size_t __w, size_t __n, size_t __m, size_t __r,
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_UIntType __a, size_t __u, _UIntType __d, size_t __s,
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_UIntType __b, size_t __t, _UIntType __c, size_t __l,
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_UIntType __f>
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void
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mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
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__s, __b, __t, __c, __l, __f>::
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seed(result_type __sd)
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{
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_M_x[0] = __detail::__mod<_UIntType, 1, 0,
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__detail::_Shift<_UIntType, __w>::__value>(__sd);
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for (size_t __i = 1; __i < state_size; ++__i)
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{
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_UIntType __x = _M_x[__i - 1];
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__x ^= __x >> (__w - 2);
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__x *= __f;
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__x += __i;
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_M_x[__i] = __detail::__mod<_UIntType, 1, 0,
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__detail::_Shift<_UIntType, __w>::__value>(__x);
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}
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_M_p = state_size;
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}
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template<typename _UIntType,
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size_t __w, size_t __n, size_t __m, size_t __r,
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_UIntType __a, size_t __u, _UIntType __d, size_t __s,
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_UIntType __b, size_t __t, _UIntType __c, size_t __l,
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_UIntType __f>
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void
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mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
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__s, __b, __t, __c, __l, __f>::
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seed(seed_seq& __q)
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{
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const _UIntType __upper_mask = (~_UIntType()) << __r;
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const size_t __k = (__w + 31) / 32;
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_UIntType __arr[__k * __n];
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__q.generate(__arr + 0, __arr + __k * __n);
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bool __zero = true;
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for (size_t __i = 0; __i < state_size; ++__i)
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{
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_UIntType __factor = 1U;
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_UIntType __sum = 0U;
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for (size_t __j = 0; __j < __k; ++__j)
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{
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__sum += __arr[__i * __k + __j] * __factor;
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__factor *= __detail::_Shift<_UIntType, 32>::__value;
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}
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_M_x[__i] = __detail::__mod<_UIntType, 1U, 0U,
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__detail::_Shift<_UIntType, __w>::__value>(__sum);
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if (__zero)
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{
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if (__i == 0)
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{
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if ((_M_x[0] & __upper_mask) != 0U)
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__zero = false;
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}
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else if (_M_x[__i] != 0U)
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__zero = false;
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}
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}
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if (__zero)
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_M_x[0] = __detail::_Shift<_UIntType, __w - 1U>::__value;
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}
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template<typename _UIntType, size_t __w,
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size_t __n, size_t __m, size_t __r,
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_UIntType __a, size_t __u, _UIntType __d, size_t __s,
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_UIntType __b, size_t __t, _UIntType __c, size_t __l,
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_UIntType __f>
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typename
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mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
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__s, __b, __t, __c, __l, __f>::result_type
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mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
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__s, __b, __t, __c, __l, __f>::
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operator()()
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{
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// Reload the vector - cost is O(n) amortized over n calls.
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if (_M_p >= state_size)
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{
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const _UIntType __upper_mask = (~_UIntType()) << __r;
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const _UIntType __lower_mask = ~__upper_mask;
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for (size_t __k = 0; __k < (__n - __m); ++__k)
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{
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_UIntType __y = ((_M_x[__k] & __upper_mask)
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| (_M_x[__k + 1] & __lower_mask));
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_M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
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^ ((__y & 0x01) ? __a : 0));
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}
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for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
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{
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_UIntType __y = ((_M_x[__k] & __upper_mask)
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| (_M_x[__k + 1] & __lower_mask));
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_M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
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^ ((__y & 0x01) ? __a : 0));
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}
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_UIntType __y = ((_M_x[__n - 1] & __upper_mask)
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| (_M_x[0] & __lower_mask));
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_M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
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^ ((__y & 0x01) ? __a : 0));
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_M_p = 0;
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}
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// Calculate o(x(i)).
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result_type __z = _M_x[_M_p++];
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__z ^= (__z >> __u) & __d;
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__z ^= (__z << __s) & __b;
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__z ^= (__z << __t) & __c;
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__z ^= (__z >> __l);
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return __z;
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}
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template<typename _UIntType, size_t __w,
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size_t __n, size_t __m, size_t __r,
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_UIntType __a, size_t __u, _UIntType __d, size_t __s,
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_UIntType __b, size_t __t, _UIntType __c, size_t __l,
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_UIntType __f, typename _CharT, typename _Traits>
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std::basic_ostream<_CharT, _Traits>&
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operator<<(std::basic_ostream<_CharT, _Traits>& __os,
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const mersenne_twister_engine<_UIntType, __w, __n, __m,
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__r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
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{
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typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
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typedef typename __ostream_type::ios_base __ios_base;
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const typename __ios_base::fmtflags __flags = __os.flags();
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const _CharT __fill = __os.fill();
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const _CharT __space = __os.widen(' ');
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__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
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__os.fill(__space);
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for (size_t __i = 0; __i < __n - 1; ++__i)
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__os << __x._M_x[__i] << __space;
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__os << __x._M_x[__n - 1];
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__os.flags(__flags);
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__os.fill(__fill);
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return __os;
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}
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template<typename _UIntType, size_t __w,
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size_t __n, size_t __m, size_t __r,
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_UIntType __a, size_t __u, _UIntType __d, size_t __s,
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_UIntType __b, size_t __t, _UIntType __c, size_t __l,
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_UIntType __f, typename _CharT, typename _Traits>
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std::basic_istream<_CharT, _Traits>&
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operator>>(std::basic_istream<_CharT, _Traits>& __is,
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mersenne_twister_engine<_UIntType, __w, __n, __m,
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__r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
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{
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typedef std::basic_istream<_CharT, _Traits> __istream_type;
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typedef typename __istream_type::ios_base __ios_base;
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const typename __ios_base::fmtflags __flags = __is.flags();
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__is.flags(__ios_base::dec | __ios_base::skipws);
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for (size_t __i = 0; __i < __n; ++__i)
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__is >> __x._M_x[__i];
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__is.flags(__flags);
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return __is;
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}
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template<typename _UIntType, size_t __w, size_t __s, size_t __r>
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void
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subtract_with_carry_engine<_UIntType, __w, __s, __r>::
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seed(result_type __value)
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{
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if (__value == 0)
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__value = default_seed;
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std::linear_congruential_engine<result_type, 40014U, 0U, 2147483563U>
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__lcg(__value);
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// I hope this is right. The "10000" tests work for the ranluxen.
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const size_t __n = (word_size + 31) / 32;
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for (size_t __i = 0; __i < long_lag; ++__i)
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{
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_UIntType __sum = 0U;
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_UIntType __factor = 1U;
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for (size_t __j = 0; __j < __n; ++__j)
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{
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__sum += __detail::__mod<__detail::_UInt32Type, 1, 0, 0>
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(__lcg()) * __factor;
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__factor *= __detail::_Shift<_UIntType, 32>::__value;
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}
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_M_x[__i] = __detail::__mod<_UIntType, 1, 0, _S_modulus>(__sum);
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}
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_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
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_M_p = 0;
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}
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template<typename _UIntType, size_t __w, size_t __s, size_t __r>
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void
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subtract_with_carry_engine<_UIntType, __w, __s, __r>::
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seed(seed_seq& __q)
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{
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const size_t __n = (word_size + 31) / 32;
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unsigned int __arr[long_lag + __n];
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__q.generate(__arr + 0, __arr + long_lag + __n);
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for (size_t __i = 0; __i < long_lag; ++__i)
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{
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_UIntType __sum = 0U;
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_UIntType __factor = 1U;
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for (size_t __j = 0; __j < __n; ++__j)
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{
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__sum += __detail::__mod<__detail::_UInt32Type, 1, 0, 0>
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(__arr[__i * __n + __j]) * __factor;
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__factor *= __detail::_Shift<_UIntType, 32>::__value;
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}
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_M_x[__i] = __detail::__mod<_UIntType, 1, 0, _S_modulus>(__sum);
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}
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_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
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_M_p = 0;
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}
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template<typename _UIntType, size_t __w, size_t __s, size_t __r>
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typename subtract_with_carry_engine<_UIntType, __w, __s, __r>::
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result_type
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subtract_with_carry_engine<_UIntType, __w, __s, __r>::
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operator()()
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{
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// Derive short lag index from current index.
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long __ps = _M_p - short_lag;
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if (__ps < 0)
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__ps += long_lag;
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|
|
// Calculate new x(i) without overflow or division.
|
|
// NB: Thanks to the requirements for _UIntType, _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 = _S_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 _UIntType, size_t __w, size_t __s, size_t __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const subtract_with_carry_engine<_UIntType,
|
|
__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 (size_t __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 _UIntType, size_t __w, size_t __s, size_t __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
subtract_with_carry_engine<_UIntType, __w, __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 (size_t __i = 0; __i < __r; ++__i)
|
|
__is >> __x._M_x[__i];
|
|
__is >> __x._M_carry;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RandomNumberEngine, size_t __p, size_t __r>
|
|
typename discard_block_engine<_RandomNumberEngine,
|
|
__p, __r>::result_type
|
|
discard_block_engine<_RandomNumberEngine, __p, __r>::
|
|
operator()()
|
|
{
|
|
if (_M_n >= used_block)
|
|
{
|
|
_M_b.discard(block_size - _M_n);
|
|
_M_n = 0;
|
|
}
|
|
++_M_n;
|
|
return _M_b();
|
|
}
|
|
|
|
template<typename _RandomNumberEngine, size_t __p, size_t __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const discard_block_engine<_RandomNumberEngine,
|
|
__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.base() << __space << __x._M_n;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _RandomNumberEngine, size_t __p, size_t __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
discard_block_engine<_RandomNumberEngine, __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<typename _RandomNumberEngine, size_t __w, typename _UIntType>
|
|
typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
|
|
result_type
|
|
independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
|
|
operator()()
|
|
{
|
|
const long double __r = static_cast<long double>(this->max())
|
|
- static_cast<long double>(this->min()) + 1.0L;
|
|
const result_type __m = std::log2l(__r);
|
|
result_type __n, __n0, __y0, __y1, __s0, __s1;
|
|
for (size_t __i = 0; __i < 2; ++__i)
|
|
{
|
|
__n = (__w + __m - 1) / __m + __i;
|
|
__n0 = __n - __w % __n;
|
|
const result_type __w0 = __w / __n;
|
|
const result_type __w1 = __w0 + 1;
|
|
__s0 = 1UL << __w0;
|
|
__s1 = 1UL << __w1;
|
|
__y0 = __s0 * (__r / __s0);
|
|
__y1 = __s1 * (__r / __s1);
|
|
if (__r - __y0 <= __y0 / __n)
|
|
break;
|
|
}
|
|
|
|
result_type __sum = 0;
|
|
for (size_t __k = 0; __k < __n0; ++__k)
|
|
{
|
|
result_type __u;
|
|
do
|
|
__u = _M_b() - this->min();
|
|
while (__u >= __y0);
|
|
__sum = __s0 * __sum
|
|
+ __u % __s0;
|
|
}
|
|
for (size_t __k = __n0; __k < __n; ++__k)
|
|
{
|
|
result_type __u;
|
|
do
|
|
__u = _M_b() - this->min();
|
|
while (__u >= __y1);
|
|
__sum = __s1 * __sum
|
|
+ __u % __s1;
|
|
}
|
|
return __sum;
|
|
}
|
|
|
|
|
|
template<typename _RandomNumberEngine, size_t __k>
|
|
typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
|
|
shuffle_order_engine<_RandomNumberEngine, __k>::
|
|
operator()()
|
|
{
|
|
size_t __j = (__k * (_M_y - _M_b.min()))
|
|
/ (_M_b.max() - _M_b.min() + 1);
|
|
_M_y = _M_v[__j];
|
|
_M_v[__j] = _M_b();
|
|
|
|
return _M_y;
|
|
}
|
|
|
|
template<typename _RandomNumberEngine, size_t __k,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const shuffle_order_engine<_RandomNumberEngine, __k>& __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.base();
|
|
for (size_t __i = 0; __i < __k; ++__i)
|
|
__os << __space << __x._M_v[__i];
|
|
__os << __space << __x._M_y;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _RandomNumberEngine, size_t __k,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
shuffle_order_engine<_RandomNumberEngine, __k>& __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;
|
|
for (size_t __i = 0; __i < __k; ++__i)
|
|
__is >> __x._M_v[__i];
|
|
__is >> __x._M_y;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename uniform_int_distribution<_IntType>::result_type
|
|
uniform_int_distribution<_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_distribution<_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.a() << __space << __x.b();
|
|
|
|
__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_distribution<_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);
|
|
|
|
_IntType __a, __b;
|
|
__is >> __a >> __b;
|
|
__x.param(typename uniform_int_distribution<_IntType>::
|
|
param_type(__a, __b));
|
|
|
|
__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_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.a() << __space << __x.b();
|
|
|
|
__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_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::skipws);
|
|
|
|
_RealType __a, __b;
|
|
__is >> __a >> __b;
|
|
__x.param(typename uniform_real_distribution<_RealType>::
|
|
param_type(__a, __b));
|
|
|
|
__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(std::numeric_limits<double>::digits10 + 1);
|
|
|
|
__os << __x.p();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename geometric_distribution<_IntType>::result_type
|
|
geometric_distribution<_IntType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
// About the epsilon thing see this thread:
|
|
// http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
|
|
const double __naf =
|
|
(1 - std::numeric_limits<double>::epsilon()) / 2;
|
|
// The largest _RealType convertible to _IntType.
|
|
const double __thr =
|
|
std::numeric_limits<_IntType>::max() + __naf;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
double __cand;
|
|
do
|
|
__cand = std::ceil(std::log(__aurng()) / __param._M_log_p);
|
|
while (__cand >= __thr);
|
|
|
|
return result_type(__cand + __naf);
|
|
}
|
|
|
|
template<typename _IntType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const geometric_distribution<_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 std::streamsize __precision = __os.precision();
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__os.widen(' '));
|
|
__os.precision(std::numeric_limits<double>::digits10 + 1);
|
|
|
|
__os << __x.p();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
geometric_distribution<_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::skipws);
|
|
|
|
double __p;
|
|
__is >> __p;
|
|
__x.param(typename geometric_distribution<_IntType>::param_type(__p));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
template<typename _IntType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename negative_binomial_distribution<_IntType>::result_type
|
|
negative_binomial_distribution<_IntType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __p)
|
|
{
|
|
typename gamma_distribution<>::param_type
|
|
__gamma_param(__p.k(), 1.0);
|
|
gamma_distribution<> __gamma(__gamma_param);
|
|
double __x = __gamma(__urng);
|
|
|
|
typename poisson_distribution<result_type>::param_type
|
|
__poisson_param(__x * __p.p() / (1.0 - __p.p()));
|
|
poisson_distribution<result_type> __poisson(__poisson_param);
|
|
result_type __m = __poisson(__urng);
|
|
|
|
return __m;
|
|
}
|
|
|
|
template<typename _IntType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const negative_binomial_distribution<_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 std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__os.widen(' '));
|
|
__os.precision(std::numeric_limits<double>::digits10 + 1);
|
|
|
|
__os << __x.k() << __space << __x.p();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType, typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
negative_binomial_distribution<_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::skipws);
|
|
|
|
_IntType __k;
|
|
double __p;
|
|
__is >> __k >> __p;
|
|
__x.param(typename negative_binomial_distribution<_IntType>::
|
|
param_type(__k, __p));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
void
|
|
poisson_distribution<_IntType>::param_type::
|
|
_M_initialize()
|
|
{
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (_M_mean >= 12)
|
|
{
|
|
const double __m = std::floor(_M_mean);
|
|
_M_lm_thr = std::log(_M_mean);
|
|
_M_lfm = std::lgamma(__m + 1);
|
|
_M_sm = std::sqrt(__m);
|
|
|
|
const double __pi_4 = 0.7853981633974483096156608458198757L;
|
|
const double __dx = std::sqrt(2 * __m * std::log(32 * __m
|
|
/ __pi_4));
|
|
_M_d = std::round(std::max(6.0, std::min(__m, __dx)));
|
|
const double __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>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename poisson_distribution<_IntType>::result_type
|
|
poisson_distribution<_IntType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
|
|
__aurng(__urng);
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (__param.mean() >= 12)
|
|
{
|
|
double __x;
|
|
|
|
// See comments above...
|
|
const double __naf =
|
|
(1 - std::numeric_limits<double>::epsilon()) / 2;
|
|
const double __thr =
|
|
std::numeric_limits<_IntType>::max() + __naf;
|
|
|
|
const double __m = std::floor(__param.mean());
|
|
// sqrt(pi / 2)
|
|
const double __spi_2 = 1.2533141373155002512078826424055226L;
|
|
const double __c1 = __param._M_sm * __spi_2;
|
|
const double __c2 = __param._M_c2b + __c1;
|
|
const double __c3 = __c2 + 1;
|
|
const double __c4 = __c3 + 1;
|
|
// e^(1 / 78)
|
|
const double __e178 = 1.0129030479320018583185514777512983L;
|
|
const double __c5 = __c4 + __e178;
|
|
const double __c = __param._M_cb + __c5;
|
|
const double __2cx = 2 * (2 * __m + __param._M_d);
|
|
|
|
bool __reject = true;
|
|
do
|
|
{
|
|
const double __u = __c * __aurng();
|
|
const double __e = -std::log(__aurng());
|
|
|
|
double __w = 0.0;
|
|
|
|
if (__u <= __c1)
|
|
{
|
|
const double __n = _M_nd(__urng);
|
|
const double __y = -std::abs(__n) * __param._M_sm - 1;
|
|
__x = std::floor(__y);
|
|
__w = -__n * __n / 2;
|
|
if (__x < -__m)
|
|
continue;
|
|
}
|
|
else if (__u <= __c2)
|
|
{
|
|
const double __n = _M_nd(__urng);
|
|
const double __y = 1 + std::abs(__n) * __param._M_scx;
|
|
__x = std::ceil(__y);
|
|
__w = __y * (2 - __y) * __param._M_1cx;
|
|
if (__x > __param._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 double __v = -std::log(__aurng());
|
|
const double __y = __param._M_d
|
|
+ __v * __2cx / __param._M_d;
|
|
__x = std::ceil(__y);
|
|
__w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
|
|
}
|
|
|
|
__reject = (__w - __e - __x * __param._M_lm_thr
|
|
> __param._M_lfm - std::lgamma(__x + __m + 1));
|
|
|
|
__reject |= __x + __m >= __thr;
|
|
|
|
} while (__reject);
|
|
|
|
return result_type(__x + __m + __naf);
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
_IntType __x = 0;
|
|
double __prod = 1.0;
|
|
|
|
do
|
|
{
|
|
__prod *= __aurng();
|
|
__x += 1;
|
|
}
|
|
while (__prod > __param._M_lm_thr);
|
|
|
|
return __x - 1;
|
|
}
|
|
}
|
|
|
|
template<typename _IntType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const poisson_distribution<_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 std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(std::numeric_limits<double>::digits10 + 1);
|
|
|
|
__os << __x.mean() << __space << __x._M_nd;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
poisson_distribution<_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::skipws);
|
|
|
|
double __mean;
|
|
__is >> __mean >> __x._M_nd;
|
|
__x.param(typename poisson_distribution<_IntType>::param_type(__mean));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
void
|
|
binomial_distribution<_IntType>::param_type::
|
|
_M_initialize()
|
|
{
|
|
const double __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 double __np = std::floor(_M_t * __p12);
|
|
const double __pa = __np / _M_t;
|
|
const double __1p = 1 - __pa;
|
|
|
|
const double __pi_4 = 0.7853981633974483096156608458198757L;
|
|
const double __d1x =
|
|
std::sqrt(__np * __1p * std::log(32 * __np
|
|
/ (81 * __pi_4 * __1p)));
|
|
_M_d1 = std::round(std::max(1.0, __d1x));
|
|
const double __d2x =
|
|
std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
|
|
/ (__pi_4 * __pa)));
|
|
_M_d2 = std::round(std::max(1.0, __d2x));
|
|
|
|
// sqrt(pi / 2)
|
|
const double __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 double __a12 = _M_a1 + _M_s2 * __spi_2;
|
|
const double __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 double __s2s = _M_s2 * _M_s2;
|
|
_M_s = (_M_a123 + 2 * __s2s / _M_d2
|
|
* std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
|
|
_M_lf = (std::lgamma(__np + 1)
|
|
+ std::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>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename binomial_distribution<_IntType>::result_type
|
|
binomial_distribution<_IntType>::
|
|
_M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t)
|
|
{
|
|
_IntType __x = 0;
|
|
double __sum = 0.0;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
|
|
__aurng(__urng);
|
|
|
|
do
|
|
{
|
|
const double __e = -std::log(__aurng());
|
|
__sum += __e / (__t - __x);
|
|
__x += 1;
|
|
}
|
|
while (__sum <= _M_param._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>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename binomial_distribution<_IntType>::result_type
|
|
binomial_distribution<_IntType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
result_type __ret;
|
|
const _IntType __t = __param.t();
|
|
const _IntType __p = __param.p();
|
|
const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
|
|
__aurng(__urng);
|
|
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (!__param._M_easy)
|
|
{
|
|
double __x;
|
|
|
|
// See comments above...
|
|
const double __naf =
|
|
(1 - std::numeric_limits<double>::epsilon()) / 2;
|
|
const double __thr =
|
|
std::numeric_limits<_IntType>::max() + __naf;
|
|
|
|
const double __np = std::floor(__t * __p12);
|
|
|
|
// sqrt(pi / 2)
|
|
const double __spi_2 = 1.2533141373155002512078826424055226L;
|
|
const double __a1 = __param._M_a1;
|
|
const double __a12 = __a1 + __param._M_s2 * __spi_2;
|
|
const double __a123 = __param._M_a123;
|
|
const double __s1s = __param._M_s1 * __param._M_s1;
|
|
const double __s2s = __param._M_s2 * __param._M_s2;
|
|
|
|
bool __reject;
|
|
do
|
|
{
|
|
const double __u = __param._M_s * __aurng();
|
|
|
|
double __v;
|
|
|
|
if (__u <= __a1)
|
|
{
|
|
const double __n = _M_nd(__urng);
|
|
const double __y = __param._M_s1 * std::abs(__n);
|
|
__reject = __y >= __param._M_d1;
|
|
if (!__reject)
|
|
{
|
|
const double __e = -std::log(__aurng());
|
|
__x = std::floor(__y);
|
|
__v = -__e - __n * __n / 2 + __param._M_c;
|
|
}
|
|
}
|
|
else if (__u <= __a12)
|
|
{
|
|
const double __n = _M_nd(__urng);
|
|
const double __y = __param._M_s2 * std::abs(__n);
|
|
__reject = __y >= __param._M_d2;
|
|
if (!__reject)
|
|
{
|
|
const double __e = -std::log(__aurng());
|
|
__x = std::floor(-__y);
|
|
__v = -__e - __n * __n / 2;
|
|
}
|
|
}
|
|
else if (__u <= __a123)
|
|
{
|
|
const double __e1 = -std::log(__aurng());
|
|
const double __e2 = -std::log(__aurng());
|
|
|
|
const double __y = __param._M_d1
|
|
+ 2 * __s1s * __e1 / __param._M_d1;
|
|
__x = std::floor(__y);
|
|
__v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
|
|
-__y / (2 * __s1s)));
|
|
__reject = false;
|
|
}
|
|
else
|
|
{
|
|
const double __e1 = -std::log(__aurng());
|
|
const double __e2 = -std::log(__aurng());
|
|
|
|
const double __y = __param._M_d2
|
|
+ 2 * __s2s * __e1 / __param._M_d2;
|
|
__x = std::floor(-__y);
|
|
__v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
|
|
__reject = false;
|
|
}
|
|
|
|
__reject = __reject || __x < -__np || __x > __t - __np;
|
|
if (!__reject)
|
|
{
|
|
const double __lfx =
|
|
std::lgamma(__np + __x + 1)
|
|
+ std::lgamma(__t - (__np + __x) + 1);
|
|
__reject = __v > __param._M_lf - __lfx
|
|
+ __x * __param._M_lp1p;
|
|
}
|
|
|
|
__reject |= __x + __np >= __thr;
|
|
}
|
|
while (__reject);
|
|
|
|
__x += __np + __naf;
|
|
|
|
const _IntType __z = _M_waiting(__urng, __t - _IntType(__x));
|
|
__ret = _IntType(__x) + __z;
|
|
}
|
|
else
|
|
#endif
|
|
__ret = _M_waiting(__urng, __t);
|
|
|
|
if (__p12 != __p)
|
|
__ret = __t - __ret;
|
|
return __ret;
|
|
}
|
|
|
|
template<typename _IntType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const binomial_distribution<_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 std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(std::numeric_limits<double>::digits10 + 1);
|
|
|
|
__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 _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
binomial_distribution<_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);
|
|
|
|
_IntType __t;
|
|
double __p;
|
|
__is >> __t >> __p >> __x._M_nd;
|
|
__x.param(typename binomial_distribution<_IntType>::
|
|
param_type(__t, __p));
|
|
|
|
__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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.lambda();
|
|
|
|
__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,
|
|
exponential_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);
|
|
|
|
_RealType __lambda;
|
|
__is >> __lambda;
|
|
__x.param(typename exponential_distribution<_RealType>::
|
|
param_type(__lambda));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
bool
|
|
operator==(const normal_distribution<_RealType>& __d1,
|
|
const normal_distribution<_RealType>& __d2)
|
|
{
|
|
if (__d1._M_param == __d2._M_param)
|
|
{
|
|
if (__d1._M_saved_available == __d2._M_saved_available)
|
|
{
|
|
if (__d1._M_saved_available
|
|
&& __d1._M_saved == __d2._M_saved)
|
|
return true;
|
|
else if(!__d1._M_saved_available)
|
|
return true;
|
|
else
|
|
return false;
|
|
}
|
|
else
|
|
return false;
|
|
}
|
|
else
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* 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<typename _UniformRandomNumberGenerator>
|
|
typename normal_distribution<_RealType>::result_type
|
|
normal_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
result_type __ret;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
if (_M_saved_available)
|
|
{
|
|
_M_saved_available = false;
|
|
__ret = _M_saved;
|
|
}
|
|
else
|
|
{
|
|
result_type __x, __y, __r2;
|
|
do
|
|
{
|
|
__x = result_type(2.0) * __aurng() - 1.0;
|
|
__y = result_type(2.0) * __aurng() - 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 * __param.stddev() + __param.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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.mean() << __space << __x.stddev()
|
|
<< __space << __x._M_saved_available;
|
|
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);
|
|
|
|
double __mean, __stddev;
|
|
__is >> __mean >> __stddev
|
|
>> __x._M_saved_available;
|
|
if (__x._M_saved_available)
|
|
__is >> __x._M_saved;
|
|
__x.param(typename normal_distribution<_RealType>::
|
|
param_type(__mean, __stddev));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename lognormal_distribution<_RealType>::result_type
|
|
lognormal_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __p)
|
|
{
|
|
_RealType __u, __v, __r2, __normal;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
do
|
|
{
|
|
// Choose x,y in uniform square (-1,-1) to (+1,+1).
|
|
__u = 2 * __aurng() - 1;
|
|
__v = 2 * __aurng() - 1;
|
|
|
|
// See if it is in the unit circle.
|
|
__r2 = __u * __u + __v * __v;
|
|
}
|
|
while (__r2 > 1 || __r2 == 0);
|
|
|
|
__normal = __u * std::sqrt(-2 * std::log(__r2) / __r2);
|
|
|
|
return std::exp(__p.s() * __normal + __p.m());
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const lognormal_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.m() << __space << __x.s();
|
|
|
|
__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,
|
|
lognormal_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);
|
|
|
|
_RealType __m, __s;
|
|
__is >> __m >> __s;
|
|
__x.param(typename lognormal_distribution<_RealType>::
|
|
param_type(__m, __s));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename chi_squared_distribution<_RealType>::result_type
|
|
chi_squared_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __p)
|
|
{
|
|
typename gamma_distribution<_RealType>::param_type
|
|
__gamma_param(__p.n() / 2, 1.0);
|
|
gamma_distribution<_RealType> __gamma(__gamma_param);
|
|
return 2 * __gamma(__urng);
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const chi_squared_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.n();
|
|
|
|
__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,
|
|
chi_squared_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);
|
|
|
|
_RealType __n;
|
|
__is >> __n;
|
|
__x.param(typename chi_squared_distribution<_RealType>::
|
|
param_type(__n));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename cauchy_distribution<_RealType>::result_type
|
|
cauchy_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __p)
|
|
{
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
_RealType __u;
|
|
do
|
|
{
|
|
__u = __aurng();
|
|
}
|
|
while (__u == 0.5);
|
|
|
|
return __p.a() + __p.b() * std::tan(M_PI * __u);
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const cauchy_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.a() << __space << __x.b();
|
|
|
|
__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,
|
|
cauchy_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);
|
|
|
|
_RealType __a, __b;
|
|
__is >> __a >> __b;
|
|
__x.param(typename cauchy_distribution<_RealType>::
|
|
param_type(__a, __b));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename fisher_f_distribution<_RealType>::result_type
|
|
fisher_f_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __p)
|
|
{
|
|
gamma_distribution<_RealType> __gamma;
|
|
_RealType __ym = __gamma(__urng,
|
|
typename gamma_distribution<_RealType>::param_type(__p.m() / 2, 2));
|
|
|
|
_RealType __yn = __gamma(__urng,
|
|
typename gamma_distribution<_RealType>::param_type(__p.n() / 2, 2));
|
|
|
|
return (__ym * __p.n()) / (__yn * __p.m());
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const fisher_f_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.m() << __space << __x.n();
|
|
|
|
__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,
|
|
fisher_f_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);
|
|
|
|
_RealType __m, __n;
|
|
__is >> __m >> __n;
|
|
__x.param(typename fisher_f_distribution<_RealType>::
|
|
param_type(__m, __n));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
//
|
|
// This could be operator() for a Gaussian distribution.
|
|
//
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename student_t_distribution<_RealType>::result_type
|
|
student_t_distribution<_RealType>::
|
|
_M_gaussian(_UniformRandomNumberGenerator& __urng,
|
|
const result_type __sigma)
|
|
{
|
|
_RealType __x, __y, __r2;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
do
|
|
{
|
|
// Choose x,y in uniform square (-1,-1) to (+1,+1).
|
|
__x = 2 * __aurng() - 1;
|
|
__y = 2 * __aurng() - 1;
|
|
|
|
// See if it is in the unit circle.
|
|
__r2 = __x * __x + __y * __y;
|
|
}
|
|
while (__r2 > 1 || __r2 == 0);
|
|
|
|
// Box-Muller transform.
|
|
return __sigma * __y * std::sqrt(-2 * std::log(__r2) / __r2);
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename student_t_distribution<_RealType>::result_type
|
|
student_t_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
if (__param.n() <= 2.0)
|
|
{
|
|
_RealType __y1 = _M_gaussian(__urng, 1.0);
|
|
typename chi_squared_distribution<_RealType>::param_type
|
|
__chisq_param(__param.n());
|
|
chi_squared_distribution<_RealType> __chisq(__chisq_param);
|
|
_RealType __y2 = __chisq(__urng);
|
|
|
|
return __y1 / std::sqrt(__y2 / __param.n());
|
|
}
|
|
else
|
|
{
|
|
_RealType __y1, __y2, __z;
|
|
do
|
|
{
|
|
__y1 = _M_gaussian(__urng, 1.0);
|
|
typename exponential_distribution<_RealType>::param_type
|
|
__exp_param(1.0 / (__param.n() / 2.0 - 1.0));
|
|
exponential_distribution<_RealType>
|
|
__exponential(__exp_param);
|
|
__y2 = __exponential(__urng);
|
|
|
|
__z = __y1 * __y1 / (__param.n() - 2.0);
|
|
}
|
|
while (1.0 - __z < 0.0 || std::exp(-__y2 - __z) > (1.0 - __z));
|
|
|
|
// Note that there is a typo in Knuth's formula, the line below
|
|
// is taken from the original paper of Marsaglia, Mathematics of
|
|
// Computation, 34 (1980), p 234-256
|
|
return __y1 / std::sqrt((1.0 - 2.0 / __param.n()) * (1.0 - __z));
|
|
}
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const student_t_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.n();
|
|
|
|
__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,
|
|
student_t_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);
|
|
|
|
_RealType __n;
|
|
__is >> __n;
|
|
__x.param(typename student_t_distribution<_RealType>::param_type(__n));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
void
|
|
gamma_distribution<_RealType>::param_type::
|
|
_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<typename _UniformRandomNumberGenerator>
|
|
typename gamma_distribution<_RealType>::result_type
|
|
gamma_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
result_type __x;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
bool __reject;
|
|
const _RealType __alpha = __param.alpha();
|
|
const _RealType __beta = __param.beta();
|
|
if (__alpha >= 1)
|
|
{
|
|
// alpha - log(4)
|
|
const result_type __b = __alpha
|
|
- result_type(1.3862943611198906188344642429163531L);
|
|
const result_type __c = __alpha + __param._M_l_d;
|
|
const result_type __1l = 1 / __param._M_l_d;
|
|
|
|
// 1 + log(9 / 2)
|
|
const result_type __k = 2.5040773967762740733732583523868748L;
|
|
|
|
do
|
|
{
|
|
const result_type __u = __aurng() / __beta;
|
|
const result_type __v = __aurng() / __beta;
|
|
|
|
const result_type __y = __1l * std::log(__v / (1 - __v));
|
|
__x = __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 / __alpha;
|
|
|
|
do
|
|
{
|
|
const result_type __z = -std::log(__aurng() / __beta);
|
|
const result_type __e = -std::log(__aurng() / __beta);
|
|
|
|
__x = std::pow(__z, __c);
|
|
|
|
__reject = __z + __e < __param._M_l_d + __x;
|
|
}
|
|
while (__reject);
|
|
}
|
|
|
|
return __beta * __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();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.alpha() << __space << __x.beta();
|
|
|
|
__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,
|
|
gamma_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);
|
|
|
|
_RealType __alpha, __beta;
|
|
__is >> __alpha >> __beta;
|
|
__x.param(typename gamma_distribution<_RealType>::
|
|
param_type(__alpha, __beta));
|
|
|
|
__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 weibull_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.a() << __space << __x.b();
|
|
|
|
__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,
|
|
weibull_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);
|
|
|
|
_RealType __a, __b;
|
|
__is >> __a >> __b;
|
|
__x.param(typename weibull_distribution<_RealType>::
|
|
param_type(__a, __b));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename extreme_value_distribution<_RealType>::result_type
|
|
extreme_value_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __p)
|
|
{
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
return __p.a() - __p.b() * std::log(-std::log(__aurng()));
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const extreme_value_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
__os << __x.a() << __space << __x.b();
|
|
|
|
__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,
|
|
extreme_value_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);
|
|
|
|
_RealType __a, __b;
|
|
__is >> __a >> __b;
|
|
__x.param(typename extreme_value_distribution<_RealType>::
|
|
param_type(__a, __b));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
void
|
|
discrete_distribution<_IntType>::param_type::
|
|
_M_initialize()
|
|
{
|
|
if (_M_prob.size() < 2)
|
|
{
|
|
_M_prob.clear();
|
|
_M_prob.push_back(1.0);
|
|
return;
|
|
}
|
|
|
|
double __sum = std::accumulate(_M_prob.begin(), _M_prob.end(), 0.0);
|
|
// Now normalize the densities.
|
|
std::transform(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
|
|
std::bind2nd(std::divides<double>(), __sum));
|
|
// Accumulate partial sums.
|
|
std::partial_sum(_M_prob.begin(), _M_prob.end(),
|
|
std::back_inserter(_M_cp));
|
|
// Make sure the last cumulative probablility is one.
|
|
_M_cp[_M_cp.size() - 1] = 1.0;
|
|
}
|
|
|
|
template<typename _IntType>
|
|
template<typename _Func>
|
|
discrete_distribution<_IntType>::param_type::
|
|
param_type(size_t __nw, double __xmin, double __xmax,
|
|
_Func __fw)
|
|
: _M_prob(), _M_cp()
|
|
{
|
|
for (size_t __i = 0; __i < __nw; ++__i)
|
|
{
|
|
const double __x = ((__nw - __i - 0.5) * __xmin
|
|
+ (__i + 0.5) * __xmax) / __nw;
|
|
_M_prob.push_back(__fw(__x));
|
|
}
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _IntType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename discrete_distribution<_IntType>::result_type
|
|
discrete_distribution<_IntType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
const double __p = __aurng();
|
|
auto __pos = std::lower_bound(__param._M_cp.begin(),
|
|
__param._M_cp.end(), __p);
|
|
if (__pos == __param._M_cp.end())
|
|
return 0;
|
|
const size_t __i = __pos - __param._M_cp.begin();
|
|
|
|
return __i;
|
|
}
|
|
|
|
template<typename _IntType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const discrete_distribution<_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 std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(std::numeric_limits<double>::digits10 + 1);
|
|
|
|
std::vector<double> __prob = __x.probabilities();
|
|
__os << __prob.size();
|
|
for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
|
|
__os << __space << *__dit;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType, typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
discrete_distribution<_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);
|
|
|
|
size_t __n;
|
|
__is >> __n;
|
|
|
|
std::vector<double> __prob_vec;
|
|
for (; __n != 0; --__n)
|
|
{
|
|
double __prob;
|
|
__is >> __prob;
|
|
__prob_vec.push_back(__prob);
|
|
}
|
|
|
|
__x.param(typename discrete_distribution<_IntType>::
|
|
param_type(__prob_vec.begin(), __prob_vec.end()));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
void
|
|
piecewise_constant_distribution<_RealType>::param_type::
|
|
_M_initialize()
|
|
{
|
|
if (_M_int.size() < 2)
|
|
{
|
|
_M_int.clear();
|
|
_M_int.push_back(_RealType(0));
|
|
_M_int.push_back(_RealType(1));
|
|
|
|
_M_den.clear();
|
|
_M_den.push_back(1.0);
|
|
|
|
return;
|
|
}
|
|
|
|
double __sum = 0.0;
|
|
for (size_t __i = 0; __i < _M_den.size(); ++__i)
|
|
{
|
|
__sum += _M_den[__i] * (_M_int[__i + 1] - _M_int[__i]);
|
|
_M_cp.push_back(__sum);
|
|
}
|
|
|
|
// Now normalize the densities...
|
|
std::transform(_M_den.begin(), _M_den.end(), _M_den.begin(),
|
|
std::bind2nd(std::divides<double>(), __sum));
|
|
// ... and partial sums.
|
|
std::transform(_M_cp.begin(), _M_cp.end(), _M_cp.begin(),
|
|
std::bind2nd(std::divides<double>(), __sum));
|
|
// Make sure the last cumulative probablility is one.
|
|
_M_cp[_M_cp.size() - 1] = 1.0;
|
|
}
|
|
|
|
template<typename _RealType>
|
|
piecewise_constant_distribution<_RealType>::param_type::
|
|
param_type()
|
|
: _M_int(), _M_den(), _M_cp()
|
|
{ _M_initialize(); }
|
|
|
|
template<typename _RealType>
|
|
template<typename _InputIteratorB, typename _InputIteratorW>
|
|
piecewise_constant_distribution<_RealType>::param_type::
|
|
param_type(_InputIteratorB __bbegin,
|
|
_InputIteratorB __bend,
|
|
_InputIteratorW __wbegin)
|
|
: _M_int(), _M_den(), _M_cp()
|
|
{
|
|
do
|
|
{
|
|
_M_int.push_back(*__bbegin);
|
|
++__bbegin;
|
|
if (__bbegin != __bend)
|
|
{
|
|
_M_den.push_back(*__wbegin);
|
|
++__wbegin;
|
|
}
|
|
}
|
|
while (__bbegin != __bend);
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _Func>
|
|
piecewise_constant_distribution<_RealType>::param_type::
|
|
param_type(initializer_list<_RealType> __bil, _Func __fw)
|
|
: _M_int(), _M_den(), _M_cp()
|
|
{
|
|
for (auto __biter = __bil.begin(); __biter != __bil.end(); ++__biter)
|
|
_M_int.push_back(*__biter);
|
|
|
|
for (size_t __i = 0; __i < _M_int.size() - 1; ++__i)
|
|
{
|
|
_RealType __x = 0.5 * (_M_int[__i] + _M_int[__i + 1]);
|
|
_M_den.push_back(__fw(__x));
|
|
}
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _Func>
|
|
piecewise_constant_distribution<_RealType>::param_type::
|
|
param_type(size_t __nw, _RealType __xmin, _RealType __xmax,
|
|
_Func __fw)
|
|
: _M_int(), _M_den(), _M_cp()
|
|
{
|
|
for (size_t __i = 0; __i <= __nw; ++__i)
|
|
{
|
|
const _RealType __x = ((__nw - __i) * __xmin
|
|
+ __i * __xmax) / __nw;
|
|
_M_int.push_back(__x);
|
|
}
|
|
for (size_t __i = 0; __i < __nw; ++__i)
|
|
{
|
|
const _RealType __x = ((__nw - __i - 0.5) * __xmin
|
|
+ (__i + 0.5) * __xmax) / __nw;
|
|
_M_den.push_back(__fw(__x));
|
|
}
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename piecewise_constant_distribution<_RealType>::result_type
|
|
piecewise_constant_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
const double __p = __aurng();
|
|
auto __pos = std::lower_bound(__param._M_cp.begin(),
|
|
__param._M_cp.end(), __p);
|
|
const size_t __i = __pos - __param._M_cp.begin();
|
|
|
|
return __param._M_int[__i]
|
|
+ (__p - __param._M_cp[__i]) / __param._M_den[__i];
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const piecewise_constant_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
std::vector<_RealType> __int = __x.intervals();
|
|
__os << __int.size() - 1;
|
|
|
|
for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
|
|
__os << __space << *__xit;
|
|
|
|
std::vector<double> __den = __x.densities();
|
|
for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
|
|
__os << __space << *__dit;
|
|
|
|
__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,
|
|
piecewise_constant_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);
|
|
|
|
size_t __n;
|
|
__is >> __n;
|
|
|
|
std::vector<_RealType> __int_vec;
|
|
for (size_t __i = 0; __i <= __n; ++__i)
|
|
{
|
|
_RealType __int;
|
|
__is >> __int;
|
|
__int_vec.push_back(__int);
|
|
}
|
|
|
|
std::vector<double> __den_vec;
|
|
for (size_t __i = 0; __i < __n; ++__i)
|
|
{
|
|
double __den;
|
|
__is >> __den;
|
|
__den_vec.push_back(__den);
|
|
}
|
|
|
|
__x.param(typename piecewise_constant_distribution<_RealType>::
|
|
param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
void
|
|
piecewise_linear_distribution<_RealType>::param_type::
|
|
_M_initialize()
|
|
{
|
|
if (_M_int.size() < 2)
|
|
{
|
|
_M_int.clear();
|
|
_M_int.push_back(_RealType(0));
|
|
_M_int.push_back(_RealType(1));
|
|
|
|
_M_den.clear();
|
|
_M_den.push_back(1.0);
|
|
_M_den.push_back(1.0);
|
|
|
|
return;
|
|
}
|
|
|
|
double __sum = 0.0;
|
|
for (size_t __i = 0; __i < _M_int.size() - 1; ++__i)
|
|
{
|
|
const _RealType __delta = _M_int[__i + 1] - _M_int[__i];
|
|
__sum += 0.5 * (_M_den[__i + 1] + _M_den[__i]) * __delta;
|
|
_M_cp.push_back(__sum);
|
|
_M_m.push_back((_M_den[__i + 1] - _M_den[__i]) / __delta);
|
|
}
|
|
|
|
// Now normalize the densities...
|
|
std::transform(_M_den.begin(), _M_den.end(), _M_den.begin(),
|
|
std::bind2nd(std::divides<double>(),__sum));
|
|
// ... and partial sums...
|
|
std::transform(_M_cp.begin(), _M_cp.end(), _M_cp.begin(),
|
|
std::bind2nd(std::divides<double>(), __sum));
|
|
// ... and slopes.
|
|
std::transform(_M_m.begin(), _M_m.end(), _M_m.begin(),
|
|
std::bind2nd(std::divides<double>(), __sum));
|
|
// Make sure the last cumulative probablility is one.
|
|
_M_cp[_M_cp.size() - 1] = 1.0;
|
|
}
|
|
|
|
template<typename _RealType>
|
|
piecewise_linear_distribution<_RealType>::param_type::
|
|
param_type()
|
|
: _M_int(), _M_den(), _M_cp(), _M_m()
|
|
{ _M_initialize(); }
|
|
|
|
template<typename _RealType>
|
|
template<typename _InputIteratorB, typename _InputIteratorW>
|
|
piecewise_linear_distribution<_RealType>::param_type::
|
|
param_type(_InputIteratorB __bbegin,
|
|
_InputIteratorB __bend,
|
|
_InputIteratorW __wbegin)
|
|
: _M_int(), _M_den(), _M_cp(), _M_m()
|
|
{
|
|
for (; __bbegin != __bend; ++__bbegin, ++__wbegin)
|
|
{
|
|
_M_int.push_back(*__bbegin);
|
|
_M_den.push_back(*__wbegin);
|
|
}
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _Func>
|
|
piecewise_linear_distribution<_RealType>::param_type::
|
|
param_type(initializer_list<_RealType> __bil, _Func __fw)
|
|
: _M_int(), _M_den(), _M_cp(), _M_m()
|
|
{
|
|
for (auto __biter = __bil.begin(); __biter != __bil.end(); ++__biter)
|
|
{
|
|
_M_int.push_back(*__biter);
|
|
_M_den.push_back(__fw(*__biter));
|
|
}
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _Func>
|
|
piecewise_linear_distribution<_RealType>::param_type::
|
|
param_type(size_t __nw, _RealType __xmin, _RealType __xmax,
|
|
_Func __fw)
|
|
: _M_int(), _M_den(), _M_cp(), _M_m()
|
|
{
|
|
for (size_t __i = 0; __i <= __nw; ++__i)
|
|
{
|
|
const _RealType __x = ((__nw - __i) * __xmin
|
|
+ __i * __xmax) / __nw;
|
|
_M_int.push_back(__x);
|
|
_M_den.push_back(__fw(__x));
|
|
}
|
|
|
|
_M_initialize();
|
|
}
|
|
|
|
template<typename _RealType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename piecewise_linear_distribution<_RealType>::result_type
|
|
piecewise_linear_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng,
|
|
const param_type& __param)
|
|
{
|
|
result_type __x;
|
|
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
|
|
__aurng(__urng);
|
|
|
|
const double __p = __aurng();
|
|
auto __pos = std::lower_bound(__param._M_cp.begin(),
|
|
__param._M_cp.end(), __p);
|
|
const size_t __i = __pos - __param._M_cp.begin();
|
|
const double __a = 0.5 * __param._M_m[__i];
|
|
const double __b = __param._M_den[__i];
|
|
const double __c = __param._M_cp[__i];
|
|
const double __q = -0.5 * (__b
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
+ std::copysign(std::sqrt(__b * __b
|
|
- 4.0 * __a * __c), __b));
|
|
#else
|
|
+ (__b < 0.0 ? -1.0 : 1.0)
|
|
* std::sqrt(__b * __b - 4.0 * __a * __c)));
|
|
#endif
|
|
const double __x0 = __param._M_int[__i];
|
|
const double __x1 = __q / __a;
|
|
const double __x2 = __c / __q;
|
|
__x = std::max(__x0 + __x1, __x0 + __x2);
|
|
|
|
return __x;
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const piecewise_linear_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(std::numeric_limits<_RealType>::digits10 + 1);
|
|
|
|
std::vector<_RealType> __int = __x.intervals();
|
|
__os << __int.size() - 1;
|
|
|
|
for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
|
|
__os << __space << *__xit;
|
|
|
|
std::vector<double> __den = __x.densities();
|
|
for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
|
|
__os << __space << *__dit;
|
|
|
|
__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,
|
|
piecewise_linear_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);
|
|
|
|
size_t __n;
|
|
__is >> __n;
|
|
|
|
std::vector<_RealType> __int_vec;
|
|
for (size_t __i = 0; __i <= __n; ++__i)
|
|
{
|
|
_RealType __int;
|
|
__is >> __int;
|
|
__int_vec.push_back(__int);
|
|
}
|
|
|
|
std::vector<double> __den_vec;
|
|
for (size_t __i = 0; __i <= __n; ++__i)
|
|
{
|
|
double __den;
|
|
__is >> __den;
|
|
__den_vec.push_back(__den);
|
|
}
|
|
|
|
__x.param(typename piecewise_linear_distribution<_RealType>::
|
|
param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
seed_seq::seed_seq(std::initializer_list<_IntType> __il)
|
|
{
|
|
for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
|
|
_M_v.push_back(__detail::__mod<result_type, 1, 0,
|
|
__detail::_Shift<result_type, 32>::__value>(*__iter));
|
|
}
|
|
|
|
template<typename _InputIterator>
|
|
seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
|
|
{
|
|
for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
|
|
_M_v.push_back(__detail::__mod<result_type, 1, 0,
|
|
__detail::_Shift<result_type, 32>::__value>(*__iter));
|
|
}
|
|
|
|
template<typename _RandomAccessIterator>
|
|
void
|
|
seed_seq::generate(_RandomAccessIterator __begin,
|
|
_RandomAccessIterator __end)
|
|
{
|
|
typedef typename iterator_traits<_RandomAccessIterator>::value_type
|
|
__Type;
|
|
|
|
if (__begin == __end)
|
|
return;
|
|
|
|
std::fill(__begin, __end, __Type(0x8b8b8b8bU));
|
|
|
|
const size_t __n = __end - __begin;
|
|
const size_t __s = _M_v.size();
|
|
const size_t __t = (__n >= 623) ? 11
|
|
: (__n >= 68) ? 7
|
|
: (__n >= 39) ? 5
|
|
: (__n >= 7) ? 3
|
|
: (__n - 1) / 2;
|
|
const size_t __p = (__n - __t) / 2;
|
|
const size_t __q = __p + __t;
|
|
const size_t __m = std::max(__s + 1, __n);
|
|
|
|
for (size_t __k = 0; __k < __m; ++__k)
|
|
{
|
|
__Type __arg = __begin[__k % __n]
|
|
^ __begin[(__k + __p) % __n]
|
|
^ __begin[(__k - 1) % __n];
|
|
__Type __r1 = __arg ^ (__arg << 27);
|
|
__r1 = __detail::__mod<__Type, 1664525U, 0U,
|
|
__detail::_Shift<__Type, 32>::__value>(__r1);
|
|
__Type __r2 = __r1;
|
|
if (__k == 0)
|
|
__r2 += __s;
|
|
else if (__k <= __s)
|
|
__r2 += __k % __n + _M_v[__k - 1];
|
|
else
|
|
__r2 += __k % __n;
|
|
__r2 = __detail::__mod<__Type, 1U, 0U,
|
|
__detail::_Shift<__Type, 32>::__value>(__r2);
|
|
__begin[(__k + __p) % __n] += __r1;
|
|
__begin[(__k + __q) % __n] += __r2;
|
|
__begin[__k % __n] = __r2;
|
|
}
|
|
|
|
for (size_t __k = __m; __k < __m + __n; ++__k)
|
|
{
|
|
__Type __arg = __begin[__k % __n]
|
|
+ __begin[(__k + __p) % __n]
|
|
+ __begin[(__k - 1) % __n];
|
|
__Type __r3 = __arg ^ (__arg << 27);
|
|
__r3 = __detail::__mod<__Type, 1566083941U, 0U,
|
|
__detail::_Shift<__Type, 32>::__value>(__r3);
|
|
__Type __r4 = __r3 - __k % __n;
|
|
__r4 = __detail::__mod<__Type, 1U, 0U,
|
|
__detail::_Shift<__Type, 32>::__value>(__r4);
|
|
__begin[(__k + __p) % __n] ^= __r4;
|
|
__begin[(__k + __q) % __n] ^= __r3;
|
|
__begin[__k % __n] = __r4;
|
|
}
|
|
}
|
|
|
|
template<typename _RealType, size_t __bits,
|
|
typename _UniformRandomNumberGenerator>
|
|
_RealType
|
|
generate_canonical(_UniformRandomNumberGenerator& __urng)
|
|
{
|
|
const size_t __b
|
|
= std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
|
|
__bits);
|
|
const long double __r = static_cast<long double>(__urng.max())
|
|
- static_cast<long double>(__urng.min()) + 1.0L;
|
|
const size_t __log2r = std::log2l(__r);
|
|
size_t __k = std::max<size_t>(1UL, (__b + __log2r - 1UL) / __log2r);
|
|
_RealType __sum = _RealType(0);
|
|
_RealType __tmp = _RealType(1);
|
|
for (; __k != 0; --__k)
|
|
{
|
|
__sum += _RealType(__urng() - __urng.min()) * __tmp;
|
|
__tmp *= __r;
|
|
}
|
|
return __sum / __tmp;
|
|
}
|
|
}
|