1719 lines
53 KiB
C++
1719 lines
53 KiB
C++
// random number generation (out of line) -*- C++ -*-
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// Copyright (C) 2009-2020 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 3, 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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// Under Section 7 of GPL version 3, you are granted additional
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// permissions described in the GCC Runtime Library Exception, version
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// 3.1, as published by the Free Software Foundation.
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// You should have received a copy of the GNU General Public License and
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// a copy of the GCC Runtime Library Exception along with this program;
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// <http://www.gnu.org/licenses/>.
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/** @file tr1/random.tcc
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* This is an internal header file, included by other library headers.
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* Do not attempt to use it directly. @headername{tr1/random}
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*/
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#ifndef _GLIBCXX_TR1_RANDOM_TCC
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#define _GLIBCXX_TR1_RANDOM_TCC 1
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namespace std _GLIBCXX_VISIBILITY(default)
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{
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_GLIBCXX_BEGIN_NAMESPACE_VERSION
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namespace tr1
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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 avoid
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// integer overflow.
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//
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// Because a and c are compile-time integral constants the compiler kindly
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// 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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template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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const _UIntType
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linear_congruential<_UIntType, __a, __c, __m>::multiplier;
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template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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const _UIntType
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linear_congruential<_UIntType, __a, __c, __m>::increment;
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template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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const _UIntType
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linear_congruential<_UIntType, __a, __c, __m>::modulus;
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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<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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void
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linear_congruential<_UIntType, __a, __c, __m>::
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seed(unsigned long __x0)
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{
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if ((__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0)
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&& (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0))
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_M_x = __detail::__mod<_UIntType, 1, 0, __m>(1);
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else
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_M_x = __detail::__mod<_UIntType, 1, 0, __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<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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template<class _Gen>
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void
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linear_congruential<_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, 1, 0, __m>(__c) == 0)
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&& (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0))
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_M_x = __detail::__mod<_UIntType, 1, 0, __m>(1);
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else
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_M_x = __detail::__mod<_UIntType, 1, 0, __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<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
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typename linear_congruential<_UIntType, __a, __c, __m>::result_type
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linear_congruential<_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<class _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<_UIntType, __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<class _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<_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<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::word_size;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::state_size;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::shift_size;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::mask_bits;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const _UIntType
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::parameter_a;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::output_u;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::output_s;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const _UIntType
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::output_b;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::output_t;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const _UIntType
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::output_c;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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const int
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::output_l;
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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void
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::
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seed(unsigned long __value)
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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>(__value);
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for (int __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 *= 1812433253ul;
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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<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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template<class _Gen>
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void
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::
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seed(_Gen& __gen, false_type)
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{
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for (int __i = 0; __i < state_size; ++__i)
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_M_x[__i] = __detail::__mod<_UIntType, 1, 0,
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__detail::_Shift<_UIntType, __w>::__value>(__gen());
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_M_p = state_size;
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}
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template<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s,
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_UIntType __b, int __t, _UIntType __c, int __l>
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typename
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::result_type
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mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
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__b, __t, __c, __l>::
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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 (int __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 (int __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);
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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<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s, _UIntType __b, int __t,
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_UIntType __c, int __l,
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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 mersenne_twister<_UIntType, __w, __n, __m,
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__r, __a, __u, __s, __b, __t, __c, __l>& __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 (int __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<class _UIntType, int __w, int __n, int __m, int __r,
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_UIntType __a, int __u, int __s, _UIntType __b, int __t,
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_UIntType __c, int __l,
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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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mersenne_twister<_UIntType, __w, __n, __m,
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__r, __a, __u, __s, __b, __t, __c, __l>& __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 (int __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 _IntType, _IntType __m, int __s, int __r>
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const _IntType
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subtract_with_carry<_IntType, __m, __s, __r>::modulus;
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template<typename _IntType, _IntType __m, int __s, int __r>
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const int
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subtract_with_carry<_IntType, __m, __s, __r>::long_lag;
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template<typename _IntType, _IntType __m, int __s, int __r>
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const int
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subtract_with_carry<_IntType, __m, __s, __r>::short_lag;
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template<typename _IntType, _IntType __m, int __s, int __r>
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void
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subtract_with_carry<_IntType, __m, __s, __r>::
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seed(unsigned long __value)
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|
{
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if (__value == 0)
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__value = 19780503;
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|
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std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563>
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__lcg(__value);
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for (int __i = 0; __i < long_lag; ++__i)
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_M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__lcg());
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|
|
_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
|
|
_M_p = 0;
|
|
}
|
|
|
|
template<typename _IntType, _IntType __m, int __s, int __r>
|
|
template<class _Gen>
|
|
void
|
|
subtract_with_carry<_IntType, __m, __s, __r>::
|
|
seed(_Gen& __gen, false_type)
|
|
{
|
|
const int __n = (std::numeric_limits<_UIntType>::digits + 31) / 32;
|
|
|
|
for (int __i = 0; __i < long_lag; ++__i)
|
|
{
|
|
_UIntType __tmp = 0;
|
|
_UIntType __factor = 1;
|
|
for (int __j = 0; __j < __n; ++__j)
|
|
{
|
|
__tmp += __detail::__mod<__detail::_UInt32Type, 1, 0, 0>
|
|
(__gen()) * __factor;
|
|
__factor *= __detail::_Shift<_UIntType, 32>::__value;
|
|
}
|
|
_M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__tmp);
|
|
}
|
|
_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
|
|
_M_p = 0;
|
|
}
|
|
|
|
template<typename _IntType, _IntType __m, int __s, int __r>
|
|
typename subtract_with_carry<_IntType, __m, __s, __r>::result_type
|
|
subtract_with_carry<_IntType, __m, __s, __r>::
|
|
operator()()
|
|
{
|
|
// Derive short lag index from current index.
|
|
int __ps = _M_p - short_lag;
|
|
if (__ps < 0)
|
|
__ps += long_lag;
|
|
|
|
// Calculate new x(i) without overflow or division.
|
|
// NB: Thanks to the requirements for _IntType, _M_x[_M_p] + _M_carry
|
|
// cannot overflow.
|
|
_UIntType __xi;
|
|
if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
|
|
{
|
|
__xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
|
|
_M_carry = 0;
|
|
}
|
|
else
|
|
{
|
|
__xi = modulus - _M_x[_M_p] - _M_carry + _M_x[__ps];
|
|
_M_carry = 1;
|
|
}
|
|
_M_x[_M_p] = __xi;
|
|
|
|
// Adjust current index to loop around in ring buffer.
|
|
if (++_M_p >= long_lag)
|
|
_M_p = 0;
|
|
|
|
return __xi;
|
|
}
|
|
|
|
template<typename _IntType, _IntType __m, int __s, int __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const subtract_with_carry<_IntType, __m, __s, __r>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
|
|
__os.fill(__space);
|
|
|
|
for (int __i = 0; __i < __r; ++__i)
|
|
__os << __x._M_x[__i] << __space;
|
|
__os << __x._M_carry;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType, _IntType __m, int __s, int __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
subtract_with_carry<_IntType, __m, __s, __r>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::dec | __ios_base::skipws);
|
|
|
|
for (int __i = 0; __i < __r; ++__i)
|
|
__is >> __x._M_x[__i];
|
|
__is >> __x._M_carry;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
const int
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::word_size;
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
const int
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::long_lag;
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
const int
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::short_lag;
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
void
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::
|
|
_M_initialize_npows()
|
|
{
|
|
for (int __j = 0; __j < __n; ++__j)
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
_M_npows[__j] = std::tr1::ldexp(_RealType(1), -__w + __j * 32);
|
|
#else
|
|
_M_npows[__j] = std::pow(_RealType(2), -__w + __j * 32);
|
|
#endif
|
|
}
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
void
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::
|
|
seed(unsigned long __value)
|
|
{
|
|
if (__value == 0)
|
|
__value = 19780503;
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// 512. Seeding subtract_with_carry_01 from a single unsigned long.
|
|
std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563>
|
|
__lcg(__value);
|
|
|
|
this->seed(__lcg);
|
|
}
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
template<class _Gen>
|
|
void
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::
|
|
seed(_Gen& __gen, false_type)
|
|
{
|
|
for (int __i = 0; __i < long_lag; ++__i)
|
|
{
|
|
for (int __j = 0; __j < __n - 1; ++__j)
|
|
_M_x[__i][__j] = __detail::__mod<_UInt32Type, 1, 0, 0>(__gen());
|
|
_M_x[__i][__n - 1] = __detail::__mod<_UInt32Type, 1, 0,
|
|
__detail::_Shift<_UInt32Type, __w % 32>::__value>(__gen());
|
|
}
|
|
|
|
_M_carry = 1;
|
|
for (int __j = 0; __j < __n; ++__j)
|
|
if (_M_x[long_lag - 1][__j] != 0)
|
|
{
|
|
_M_carry = 0;
|
|
break;
|
|
}
|
|
|
|
_M_p = 0;
|
|
}
|
|
|
|
template<typename _RealType, int __w, int __s, int __r>
|
|
typename subtract_with_carry_01<_RealType, __w, __s, __r>::result_type
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>::
|
|
operator()()
|
|
{
|
|
// Derive short lag index from current index.
|
|
int __ps = _M_p - short_lag;
|
|
if (__ps < 0)
|
|
__ps += long_lag;
|
|
|
|
_UInt32Type __new_carry;
|
|
for (int __j = 0; __j < __n - 1; ++__j)
|
|
{
|
|
if (_M_x[__ps][__j] > _M_x[_M_p][__j]
|
|
|| (_M_x[__ps][__j] == _M_x[_M_p][__j] && _M_carry == 0))
|
|
__new_carry = 0;
|
|
else
|
|
__new_carry = 1;
|
|
|
|
_M_x[_M_p][__j] = _M_x[__ps][__j] - _M_x[_M_p][__j] - _M_carry;
|
|
_M_carry = __new_carry;
|
|
}
|
|
|
|
if (_M_x[__ps][__n - 1] > _M_x[_M_p][__n - 1]
|
|
|| (_M_x[__ps][__n - 1] == _M_x[_M_p][__n - 1] && _M_carry == 0))
|
|
__new_carry = 0;
|
|
else
|
|
__new_carry = 1;
|
|
|
|
_M_x[_M_p][__n - 1] = __detail::__mod<_UInt32Type, 1, 0,
|
|
__detail::_Shift<_UInt32Type, __w % 32>::__value>
|
|
(_M_x[__ps][__n - 1] - _M_x[_M_p][__n - 1] - _M_carry);
|
|
_M_carry = __new_carry;
|
|
|
|
result_type __ret = 0.0;
|
|
for (int __j = 0; __j < __n; ++__j)
|
|
__ret += _M_x[_M_p][__j] * _M_npows[__j];
|
|
|
|
// Adjust current index to loop around in ring buffer.
|
|
if (++_M_p >= long_lag)
|
|
_M_p = 0;
|
|
|
|
return __ret;
|
|
}
|
|
|
|
template<typename _RealType, int __w, int __s, int __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const subtract_with_carry_01<_RealType, __w, __s, __r>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
|
|
__os.fill(__space);
|
|
|
|
for (int __i = 0; __i < __r; ++__i)
|
|
for (int __j = 0; __j < __x.__n; ++__j)
|
|
__os << __x._M_x[__i][__j] << __space;
|
|
__os << __x._M_carry;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _RealType, int __w, int __s, int __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
subtract_with_carry_01<_RealType, __w, __s, __r>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::dec | __ios_base::skipws);
|
|
|
|
for (int __i = 0; __i < __r; ++__i)
|
|
for (int __j = 0; __j < __x.__n; ++__j)
|
|
__is >> __x._M_x[__i][__j];
|
|
__is >> __x._M_carry;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
template<class _UniformRandomNumberGenerator, int __p, int __r>
|
|
const int
|
|
discard_block<_UniformRandomNumberGenerator, __p, __r>::block_size;
|
|
|
|
template<class _UniformRandomNumberGenerator, int __p, int __r>
|
|
const int
|
|
discard_block<_UniformRandomNumberGenerator, __p, __r>::used_block;
|
|
|
|
template<class _UniformRandomNumberGenerator, int __p, int __r>
|
|
typename discard_block<_UniformRandomNumberGenerator,
|
|
__p, __r>::result_type
|
|
discard_block<_UniformRandomNumberGenerator, __p, __r>::
|
|
operator()()
|
|
{
|
|
if (_M_n >= used_block)
|
|
{
|
|
while (_M_n < block_size)
|
|
{
|
|
_M_b();
|
|
++_M_n;
|
|
}
|
|
_M_n = 0;
|
|
}
|
|
++_M_n;
|
|
return _M_b();
|
|
}
|
|
|
|
template<class _UniformRandomNumberGenerator, int __p, int __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const discard_block<_UniformRandomNumberGenerator,
|
|
__p, __r>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::dec | __ios_base::fixed
|
|
| __ios_base::left);
|
|
__os.fill(__space);
|
|
|
|
__os << __x._M_b << __space << __x._M_n;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<class _UniformRandomNumberGenerator, int __p, int __r,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
discard_block<_UniformRandomNumberGenerator, __p, __r>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::dec | __ios_base::skipws);
|
|
|
|
__is >> __x._M_b >> __x._M_n;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<class _UniformRandomNumberGenerator1, int __s1,
|
|
class _UniformRandomNumberGenerator2, int __s2>
|
|
const int
|
|
xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>::shift1;
|
|
|
|
template<class _UniformRandomNumberGenerator1, int __s1,
|
|
class _UniformRandomNumberGenerator2, int __s2>
|
|
const int
|
|
xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>::shift2;
|
|
|
|
template<class _UniformRandomNumberGenerator1, int __s1,
|
|
class _UniformRandomNumberGenerator2, int __s2>
|
|
void
|
|
xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>::
|
|
_M_initialize_max()
|
|
{
|
|
const int __w = std::numeric_limits<result_type>::digits;
|
|
|
|
const result_type __m1 =
|
|
std::min(result_type(_M_b1.max() - _M_b1.min()),
|
|
__detail::_Shift<result_type, __w - __s1>::__value - 1);
|
|
|
|
const result_type __m2 =
|
|
std::min(result_type(_M_b2.max() - _M_b2.min()),
|
|
__detail::_Shift<result_type, __w - __s2>::__value - 1);
|
|
|
|
// NB: In TR1 s1 is not required to be >= s2.
|
|
if (__s1 < __s2)
|
|
_M_max = _M_initialize_max_aux(__m2, __m1, __s2 - __s1) << __s1;
|
|
else
|
|
_M_max = _M_initialize_max_aux(__m1, __m2, __s1 - __s2) << __s2;
|
|
}
|
|
|
|
template<class _UniformRandomNumberGenerator1, int __s1,
|
|
class _UniformRandomNumberGenerator2, int __s2>
|
|
typename xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>::result_type
|
|
xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>::
|
|
_M_initialize_max_aux(result_type __a, result_type __b, int __d)
|
|
{
|
|
const result_type __two2d = result_type(1) << __d;
|
|
const result_type __c = __a * __two2d;
|
|
|
|
if (__a == 0 || __b < __two2d)
|
|
return __c + __b;
|
|
|
|
const result_type __t = std::max(__c, __b);
|
|
const result_type __u = std::min(__c, __b);
|
|
|
|
result_type __ub = __u;
|
|
result_type __p;
|
|
for (__p = 0; __ub != 1; __ub >>= 1)
|
|
++__p;
|
|
|
|
const result_type __two2p = result_type(1) << __p;
|
|
const result_type __k = __t / __two2p;
|
|
|
|
if (__k & 1)
|
|
return (__k + 1) * __two2p - 1;
|
|
|
|
if (__c >= __b)
|
|
return (__k + 1) * __two2p + _M_initialize_max_aux((__t % __two2p)
|
|
/ __two2d,
|
|
__u % __two2p, __d);
|
|
else
|
|
return (__k + 1) * __two2p + _M_initialize_max_aux((__u % __two2p)
|
|
/ __two2d,
|
|
__t % __two2p, __d);
|
|
}
|
|
|
|
template<class _UniformRandomNumberGenerator1, int __s1,
|
|
class _UniformRandomNumberGenerator2, int __s2,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
|
|
__os.fill(__space);
|
|
|
|
__os << __x.base1() << __space << __x.base2();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<class _UniformRandomNumberGenerator1, int __s1,
|
|
class _UniformRandomNumberGenerator2, int __s2,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
xor_combine<_UniformRandomNumberGenerator1, __s1,
|
|
_UniformRandomNumberGenerator2, __s2>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::skipws);
|
|
|
|
__is >> __x._M_b1 >> __x._M_b2;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType>
|
|
template<typename _UniformRandomNumberGenerator>
|
|
typename uniform_int<_IntType>::result_type
|
|
uniform_int<_IntType>::
|
|
_M_call(_UniformRandomNumberGenerator& __urng,
|
|
result_type __min, result_type __max, true_type)
|
|
{
|
|
// XXX Must be fixed to work well for *arbitrary* __urng.max(),
|
|
// __urng.min(), __max, __min. Currently works fine only in the
|
|
// most common case __urng.max() - __urng.min() >= __max - __min,
|
|
// with __urng.max() > __urng.min() >= 0.
|
|
typedef typename __gnu_cxx::__add_unsigned<typename
|
|
_UniformRandomNumberGenerator::result_type>::__type __urntype;
|
|
typedef typename __gnu_cxx::__add_unsigned<result_type>::__type
|
|
__utype;
|
|
typedef typename __gnu_cxx::__conditional_type<(sizeof(__urntype)
|
|
> sizeof(__utype)),
|
|
__urntype, __utype>::__type __uctype;
|
|
|
|
result_type __ret;
|
|
|
|
const __urntype __urnmin = __urng.min();
|
|
const __urntype __urnmax = __urng.max();
|
|
const __urntype __urnrange = __urnmax - __urnmin;
|
|
const __uctype __urange = __max - __min;
|
|
const __uctype __udenom = (__urnrange <= __urange
|
|
? 1 : __urnrange / (__urange + 1));
|
|
do
|
|
__ret = (__urntype(__urng()) - __urnmin) / __udenom;
|
|
while (__ret > __max - __min);
|
|
|
|
return __ret + __min;
|
|
}
|
|
|
|
template<typename _IntType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const uniform_int<_IntType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
|
|
__os << __x.min() << __space << __x.max();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType, typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
uniform_int<_IntType>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::dec | __ios_base::skipws);
|
|
|
|
__is >> __x._M_min >> __x._M_max;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const bernoulli_distribution& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__os.widen(' '));
|
|
__os.precision(__gnu_cxx::__numeric_traits<double>::__max_digits10);
|
|
|
|
__os << __x.p();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
|
|
template<typename _IntType, typename _RealType>
|
|
template<class _UniformRandomNumberGenerator>
|
|
typename geometric_distribution<_IntType, _RealType>::result_type
|
|
geometric_distribution<_IntType, _RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng)
|
|
{
|
|
// About the epsilon thing see this thread:
|
|
// http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
|
|
const _RealType __naf =
|
|
(1 - std::numeric_limits<_RealType>::epsilon()) / 2;
|
|
// The largest _RealType convertible to _IntType.
|
|
const _RealType __thr =
|
|
std::numeric_limits<_IntType>::max() + __naf;
|
|
|
|
_RealType __cand;
|
|
do
|
|
__cand = std::ceil(std::log(__urng()) / _M_log_p);
|
|
while (__cand >= __thr);
|
|
|
|
return result_type(__cand + __naf);
|
|
}
|
|
|
|
template<typename _IntType, typename _RealType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const geometric_distribution<_IntType, _RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__os.widen(' '));
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x.p();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
|
|
template<typename _IntType, typename _RealType>
|
|
void
|
|
poisson_distribution<_IntType, _RealType>::
|
|
_M_initialize()
|
|
{
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (_M_mean >= 12)
|
|
{
|
|
const _RealType __m = std::floor(_M_mean);
|
|
_M_lm_thr = std::log(_M_mean);
|
|
_M_lfm = std::tr1::lgamma(__m + 1);
|
|
_M_sm = std::sqrt(__m);
|
|
|
|
const _RealType __pi_4 = 0.7853981633974483096156608458198757L;
|
|
const _RealType __dx = std::sqrt(2 * __m * std::log(32 * __m
|
|
/ __pi_4));
|
|
_M_d = std::tr1::round(std::max(_RealType(6),
|
|
std::min(__m, __dx)));
|
|
const _RealType __cx = 2 * __m + _M_d;
|
|
_M_scx = std::sqrt(__cx / 2);
|
|
_M_1cx = 1 / __cx;
|
|
|
|
_M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
|
|
_M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2)) / _M_d;
|
|
}
|
|
else
|
|
#endif
|
|
_M_lm_thr = std::exp(-_M_mean);
|
|
}
|
|
|
|
/**
|
|
* A rejection algorithm when mean >= 12 and a simple method based
|
|
* upon the multiplication of uniform random variates otherwise.
|
|
* NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
|
|
* is defined.
|
|
*
|
|
* Reference:
|
|
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
|
|
* New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
|
|
*/
|
|
template<typename _IntType, typename _RealType>
|
|
template<class _UniformRandomNumberGenerator>
|
|
typename poisson_distribution<_IntType, _RealType>::result_type
|
|
poisson_distribution<_IntType, _RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng)
|
|
{
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (_M_mean >= 12)
|
|
{
|
|
_RealType __x;
|
|
|
|
// See comments above...
|
|
const _RealType __naf =
|
|
(1 - std::numeric_limits<_RealType>::epsilon()) / 2;
|
|
const _RealType __thr =
|
|
std::numeric_limits<_IntType>::max() + __naf;
|
|
|
|
const _RealType __m = std::floor(_M_mean);
|
|
// sqrt(pi / 2)
|
|
const _RealType __spi_2 = 1.2533141373155002512078826424055226L;
|
|
const _RealType __c1 = _M_sm * __spi_2;
|
|
const _RealType __c2 = _M_c2b + __c1;
|
|
const _RealType __c3 = __c2 + 1;
|
|
const _RealType __c4 = __c3 + 1;
|
|
// e^(1 / 78)
|
|
const _RealType __e178 = 1.0129030479320018583185514777512983L;
|
|
const _RealType __c5 = __c4 + __e178;
|
|
const _RealType __c = _M_cb + __c5;
|
|
const _RealType __2cx = 2 * (2 * __m + _M_d);
|
|
|
|
bool __reject = true;
|
|
do
|
|
{
|
|
const _RealType __u = __c * __urng();
|
|
const _RealType __e = -std::log(__urng());
|
|
|
|
_RealType __w = 0.0;
|
|
|
|
if (__u <= __c1)
|
|
{
|
|
const _RealType __n = _M_nd(__urng);
|
|
const _RealType __y = -std::abs(__n) * _M_sm - 1;
|
|
__x = std::floor(__y);
|
|
__w = -__n * __n / 2;
|
|
if (__x < -__m)
|
|
continue;
|
|
}
|
|
else if (__u <= __c2)
|
|
{
|
|
const _RealType __n = _M_nd(__urng);
|
|
const _RealType __y = 1 + std::abs(__n) * _M_scx;
|
|
__x = std::ceil(__y);
|
|
__w = __y * (2 - __y) * _M_1cx;
|
|
if (__x > _M_d)
|
|
continue;
|
|
}
|
|
else if (__u <= __c3)
|
|
// NB: This case not in the book, nor in the Errata,
|
|
// but should be ok...
|
|
__x = -1;
|
|
else if (__u <= __c4)
|
|
__x = 0;
|
|
else if (__u <= __c5)
|
|
__x = 1;
|
|
else
|
|
{
|
|
const _RealType __v = -std::log(__urng());
|
|
const _RealType __y = _M_d + __v * __2cx / _M_d;
|
|
__x = std::ceil(__y);
|
|
__w = -_M_d * _M_1cx * (1 + __y / 2);
|
|
}
|
|
|
|
__reject = (__w - __e - __x * _M_lm_thr
|
|
> _M_lfm - std::tr1::lgamma(__x + __m + 1));
|
|
|
|
__reject |= __x + __m >= __thr;
|
|
|
|
} while (__reject);
|
|
|
|
return result_type(__x + __m + __naf);
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
_IntType __x = 0;
|
|
_RealType __prod = 1.0;
|
|
|
|
do
|
|
{
|
|
__prod *= __urng();
|
|
__x += 1;
|
|
}
|
|
while (__prod > _M_lm_thr);
|
|
|
|
return __x - 1;
|
|
}
|
|
}
|
|
|
|
template<typename _IntType, typename _RealType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const poisson_distribution<_IntType, _RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x.mean() << __space << __x._M_nd;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType, typename _RealType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
poisson_distribution<_IntType, _RealType>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::skipws);
|
|
|
|
__is >> __x._M_mean >> __x._M_nd;
|
|
__x._M_initialize();
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _IntType, typename _RealType>
|
|
void
|
|
binomial_distribution<_IntType, _RealType>::
|
|
_M_initialize()
|
|
{
|
|
const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
|
|
|
|
_M_easy = true;
|
|
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (_M_t * __p12 >= 8)
|
|
{
|
|
_M_easy = false;
|
|
const _RealType __np = std::floor(_M_t * __p12);
|
|
const _RealType __pa = __np / _M_t;
|
|
const _RealType __1p = 1 - __pa;
|
|
|
|
const _RealType __pi_4 = 0.7853981633974483096156608458198757L;
|
|
const _RealType __d1x =
|
|
std::sqrt(__np * __1p * std::log(32 * __np
|
|
/ (81 * __pi_4 * __1p)));
|
|
_M_d1 = std::tr1::round(std::max(_RealType(1), __d1x));
|
|
const _RealType __d2x =
|
|
std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
|
|
/ (__pi_4 * __pa)));
|
|
_M_d2 = std::tr1::round(std::max(_RealType(1), __d2x));
|
|
|
|
// sqrt(pi / 2)
|
|
const _RealType __spi_2 = 1.2533141373155002512078826424055226L;
|
|
_M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
|
|
_M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p));
|
|
_M_c = 2 * _M_d1 / __np;
|
|
_M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
|
|
const _RealType __a12 = _M_a1 + _M_s2 * __spi_2;
|
|
const _RealType __s1s = _M_s1 * _M_s1;
|
|
_M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
|
|
* 2 * __s1s / _M_d1
|
|
* std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
|
|
const _RealType __s2s = _M_s2 * _M_s2;
|
|
_M_s = (_M_a123 + 2 * __s2s / _M_d2
|
|
* std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
|
|
_M_lf = (std::tr1::lgamma(__np + 1)
|
|
+ std::tr1::lgamma(_M_t - __np + 1));
|
|
_M_lp1p = std::log(__pa / __1p);
|
|
|
|
_M_q = -std::log(1 - (__p12 - __pa) / __1p);
|
|
}
|
|
else
|
|
#endif
|
|
_M_q = -std::log(1 - __p12);
|
|
}
|
|
|
|
template<typename _IntType, typename _RealType>
|
|
template<class _UniformRandomNumberGenerator>
|
|
typename binomial_distribution<_IntType, _RealType>::result_type
|
|
binomial_distribution<_IntType, _RealType>::
|
|
_M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t)
|
|
{
|
|
_IntType __x = 0;
|
|
_RealType __sum = 0;
|
|
|
|
do
|
|
{
|
|
const _RealType __e = -std::log(__urng());
|
|
__sum += __e / (__t - __x);
|
|
__x += 1;
|
|
}
|
|
while (__sum <= _M_q);
|
|
|
|
return __x - 1;
|
|
}
|
|
|
|
/**
|
|
* A rejection algorithm when t * p >= 8 and a simple waiting time
|
|
* method - the second in the referenced book - otherwise.
|
|
* NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
|
|
* is defined.
|
|
*
|
|
* Reference:
|
|
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
|
|
* New York, 1986, Ch. X, Sect. 4 (+ Errata!).
|
|
*/
|
|
template<typename _IntType, typename _RealType>
|
|
template<class _UniformRandomNumberGenerator>
|
|
typename binomial_distribution<_IntType, _RealType>::result_type
|
|
binomial_distribution<_IntType, _RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng)
|
|
{
|
|
result_type __ret;
|
|
const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
|
|
|
|
#if _GLIBCXX_USE_C99_MATH_TR1
|
|
if (!_M_easy)
|
|
{
|
|
_RealType __x;
|
|
|
|
// See comments above...
|
|
const _RealType __naf =
|
|
(1 - std::numeric_limits<_RealType>::epsilon()) / 2;
|
|
const _RealType __thr =
|
|
std::numeric_limits<_IntType>::max() + __naf;
|
|
|
|
const _RealType __np = std::floor(_M_t * __p12);
|
|
const _RealType __pa = __np / _M_t;
|
|
|
|
// sqrt(pi / 2)
|
|
const _RealType __spi_2 = 1.2533141373155002512078826424055226L;
|
|
const _RealType __a1 = _M_a1;
|
|
const _RealType __a12 = __a1 + _M_s2 * __spi_2;
|
|
const _RealType __a123 = _M_a123;
|
|
const _RealType __s1s = _M_s1 * _M_s1;
|
|
const _RealType __s2s = _M_s2 * _M_s2;
|
|
|
|
bool __reject;
|
|
do
|
|
{
|
|
const _RealType __u = _M_s * __urng();
|
|
|
|
_RealType __v;
|
|
|
|
if (__u <= __a1)
|
|
{
|
|
const _RealType __n = _M_nd(__urng);
|
|
const _RealType __y = _M_s1 * std::abs(__n);
|
|
__reject = __y >= _M_d1;
|
|
if (!__reject)
|
|
{
|
|
const _RealType __e = -std::log(__urng());
|
|
__x = std::floor(__y);
|
|
__v = -__e - __n * __n / 2 + _M_c;
|
|
}
|
|
}
|
|
else if (__u <= __a12)
|
|
{
|
|
const _RealType __n = _M_nd(__urng);
|
|
const _RealType __y = _M_s2 * std::abs(__n);
|
|
__reject = __y >= _M_d2;
|
|
if (!__reject)
|
|
{
|
|
const _RealType __e = -std::log(__urng());
|
|
__x = std::floor(-__y);
|
|
__v = -__e - __n * __n / 2;
|
|
}
|
|
}
|
|
else if (__u <= __a123)
|
|
{
|
|
const _RealType __e1 = -std::log(__urng());
|
|
const _RealType __e2 = -std::log(__urng());
|
|
|
|
const _RealType __y = _M_d1 + 2 * __s1s * __e1 / _M_d1;
|
|
__x = std::floor(__y);
|
|
__v = (-__e2 + _M_d1 * (1 / (_M_t - __np)
|
|
-__y / (2 * __s1s)));
|
|
__reject = false;
|
|
}
|
|
else
|
|
{
|
|
const _RealType __e1 = -std::log(__urng());
|
|
const _RealType __e2 = -std::log(__urng());
|
|
|
|
const _RealType __y = _M_d2 + 2 * __s2s * __e1 / _M_d2;
|
|
__x = std::floor(-__y);
|
|
__v = -__e2 - _M_d2 * __y / (2 * __s2s);
|
|
__reject = false;
|
|
}
|
|
|
|
__reject = __reject || __x < -__np || __x > _M_t - __np;
|
|
if (!__reject)
|
|
{
|
|
const _RealType __lfx =
|
|
std::tr1::lgamma(__np + __x + 1)
|
|
+ std::tr1::lgamma(_M_t - (__np + __x) + 1);
|
|
__reject = __v > _M_lf - __lfx + __x * _M_lp1p;
|
|
}
|
|
|
|
__reject |= __x + __np >= __thr;
|
|
}
|
|
while (__reject);
|
|
|
|
__x += __np + __naf;
|
|
|
|
const _IntType __z = _M_waiting(__urng, _M_t - _IntType(__x));
|
|
__ret = _IntType(__x) + __z;
|
|
}
|
|
else
|
|
#endif
|
|
__ret = _M_waiting(__urng, _M_t);
|
|
|
|
if (__p12 != _M_p)
|
|
__ret = _M_t - __ret;
|
|
return __ret;
|
|
}
|
|
|
|
template<typename _IntType, typename _RealType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const binomial_distribution<_IntType, _RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x.t() << __space << __x.p()
|
|
<< __space << __x._M_nd;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _IntType, typename _RealType,
|
|
typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
binomial_distribution<_IntType, _RealType>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::dec | __ios_base::skipws);
|
|
|
|
__is >> __x._M_t >> __x._M_p >> __x._M_nd;
|
|
__x._M_initialize();
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const uniform_real<_RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x.min() << __space << __x.max();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
uniform_real<_RealType>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::skipws);
|
|
|
|
__is >> __x._M_min >> __x._M_max;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const exponential_distribution<_RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__os.widen(' '));
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x.lambda();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
|
|
/**
|
|
* Polar method due to Marsaglia.
|
|
*
|
|
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
|
|
* New York, 1986, Ch. V, Sect. 4.4.
|
|
*/
|
|
template<typename _RealType>
|
|
template<class _UniformRandomNumberGenerator>
|
|
typename normal_distribution<_RealType>::result_type
|
|
normal_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng)
|
|
{
|
|
result_type __ret;
|
|
|
|
if (_M_saved_available)
|
|
{
|
|
_M_saved_available = false;
|
|
__ret = _M_saved;
|
|
}
|
|
else
|
|
{
|
|
result_type __x, __y, __r2;
|
|
do
|
|
{
|
|
__x = result_type(2.0) * __urng() - 1.0;
|
|
__y = result_type(2.0) * __urng() - 1.0;
|
|
__r2 = __x * __x + __y * __y;
|
|
}
|
|
while (__r2 > 1.0 || __r2 == 0.0);
|
|
|
|
const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
|
|
_M_saved = __x * __mult;
|
|
_M_saved_available = true;
|
|
__ret = __y * __mult;
|
|
}
|
|
|
|
__ret = __ret * _M_sigma + _M_mean;
|
|
return __ret;
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const normal_distribution<_RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
const _CharT __space = __os.widen(' ');
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__space);
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x._M_saved_available << __space
|
|
<< __x.mean() << __space
|
|
<< __x.sigma();
|
|
if (__x._M_saved_available)
|
|
__os << __space << __x._M_saved;
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_istream<_CharT, _Traits>&
|
|
operator>>(std::basic_istream<_CharT, _Traits>& __is,
|
|
normal_distribution<_RealType>& __x)
|
|
{
|
|
typedef std::basic_istream<_CharT, _Traits> __istream_type;
|
|
typedef typename __istream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __is.flags();
|
|
__is.flags(__ios_base::dec | __ios_base::skipws);
|
|
|
|
__is >> __x._M_saved_available >> __x._M_mean
|
|
>> __x._M_sigma;
|
|
if (__x._M_saved_available)
|
|
__is >> __x._M_saved;
|
|
|
|
__is.flags(__flags);
|
|
return __is;
|
|
}
|
|
|
|
|
|
template<typename _RealType>
|
|
void
|
|
gamma_distribution<_RealType>::
|
|
_M_initialize()
|
|
{
|
|
if (_M_alpha >= 1)
|
|
_M_l_d = std::sqrt(2 * _M_alpha - 1);
|
|
else
|
|
_M_l_d = (std::pow(_M_alpha, _M_alpha / (1 - _M_alpha))
|
|
* (1 - _M_alpha));
|
|
}
|
|
|
|
/**
|
|
* Cheng's rejection algorithm GB for alpha >= 1 and a modification
|
|
* of Vaduva's rejection from Weibull algorithm due to Devroye for
|
|
* alpha < 1.
|
|
*
|
|
* References:
|
|
* Cheng, R. C. The Generation of Gamma Random Variables with Non-integral
|
|
* Shape Parameter. Applied Statistics, 26, 71-75, 1977.
|
|
*
|
|
* Vaduva, I. Computer Generation of Gamma Gandom Variables by Rejection
|
|
* and Composition Procedures. Math. Operationsforschung and Statistik,
|
|
* Series in Statistics, 8, 545-576, 1977.
|
|
*
|
|
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
|
|
* New York, 1986, Ch. IX, Sect. 3.4 (+ Errata!).
|
|
*/
|
|
template<typename _RealType>
|
|
template<class _UniformRandomNumberGenerator>
|
|
typename gamma_distribution<_RealType>::result_type
|
|
gamma_distribution<_RealType>::
|
|
operator()(_UniformRandomNumberGenerator& __urng)
|
|
{
|
|
result_type __x;
|
|
|
|
bool __reject;
|
|
if (_M_alpha >= 1)
|
|
{
|
|
// alpha - log(4)
|
|
const result_type __b = _M_alpha
|
|
- result_type(1.3862943611198906188344642429163531L);
|
|
const result_type __c = _M_alpha + _M_l_d;
|
|
const result_type __1l = 1 / _M_l_d;
|
|
|
|
// 1 + log(9 / 2)
|
|
const result_type __k = 2.5040773967762740733732583523868748L;
|
|
|
|
do
|
|
{
|
|
const result_type __u = __urng();
|
|
const result_type __v = __urng();
|
|
|
|
const result_type __y = __1l * std::log(__v / (1 - __v));
|
|
__x = _M_alpha * std::exp(__y);
|
|
|
|
const result_type __z = __u * __v * __v;
|
|
const result_type __r = __b + __c * __y - __x;
|
|
|
|
__reject = __r < result_type(4.5) * __z - __k;
|
|
if (__reject)
|
|
__reject = __r < std::log(__z);
|
|
}
|
|
while (__reject);
|
|
}
|
|
else
|
|
{
|
|
const result_type __c = 1 / _M_alpha;
|
|
|
|
do
|
|
{
|
|
const result_type __z = -std::log(__urng());
|
|
const result_type __e = -std::log(__urng());
|
|
|
|
__x = std::pow(__z, __c);
|
|
|
|
__reject = __z + __e < _M_l_d + __x;
|
|
}
|
|
while (__reject);
|
|
}
|
|
|
|
return __x;
|
|
}
|
|
|
|
template<typename _RealType, typename _CharT, typename _Traits>
|
|
std::basic_ostream<_CharT, _Traits>&
|
|
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
|
|
const gamma_distribution<_RealType>& __x)
|
|
{
|
|
typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
|
|
typedef typename __ostream_type::ios_base __ios_base;
|
|
|
|
const typename __ios_base::fmtflags __flags = __os.flags();
|
|
const _CharT __fill = __os.fill();
|
|
const std::streamsize __precision = __os.precision();
|
|
__os.flags(__ios_base::scientific | __ios_base::left);
|
|
__os.fill(__os.widen(' '));
|
|
__os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
|
|
|
|
__os << __x.alpha();
|
|
|
|
__os.flags(__flags);
|
|
__os.fill(__fill);
|
|
__os.precision(__precision);
|
|
return __os;
|
|
}
|
|
}
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
}
|
|
|
|
#endif
|