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// random number generation -*- C++ -*-
// Copyright (C) 2009-2026 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
// <http://www.gnu.org/licenses/>.
/**
* @file bits/random.h
* This is an internal header file, included by other library headers.
* Do not attempt to use it directly. @headername{random}
*/
#ifndef _RANDOM_H
#define _RANDOM_H 1
#include <vector>
#include <bits/ios_base.h>
#include <bits/uniform_int_dist.h>
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
// [26.4] Random number generation
/**
* @defgroup random Random Number Generation
* @ingroup numerics
*
* A facility for generating random numbers on selected distributions.
* @{
*/
// std::uniform_random_bit_generator is defined in <bits/uniform_int_dist.h>
#ifndef _GLIBCXX_USE_OLD_GENERATE_CANONICAL
_GLIBCXX_BEGIN_INLINE_ABI_NAMESPACE(_V2)
#endif
/**
* @brief A function template for converting the output of a (integral)
* uniform random number generator to a floatng point result in the range
* [0-1).
*/
template<typename _RealType, size_t __bits,
typename _UniformRandomNumberGenerator>
_RealType
generate_canonical(_UniformRandomNumberGenerator& __g);
#ifndef _GLIBCXX_USE_OLD_GENERATE_CANONICAL
_GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)
#endif
/// @cond undocumented
// Implementation-space details.
namespace __detail
{
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wc++17-extensions"
#ifndef __SIZEOF_INT128__
// Emulate 128-bit integer type, for the arithmetic ops used in <random>.
// The __detail::__mod function needs: (type(a) * x + c) % m.
// std::philox_engine needs multiplication and bitwise ops.
struct __rand_uint128
{
using type = __rand_uint128;
__rand_uint128() = default;
explicit constexpr
__rand_uint128(uint64_t __lo) noexcept : _M_lo(__lo) { }
__rand_uint128(const __rand_uint128&) = default;
__rand_uint128& operator=(const __rand_uint128&) = default;
constexpr explicit
operator bool() const noexcept
{ return _M_lo || _M_hi; }
_GLIBCXX14_CONSTEXPR type&
operator=(uint64_t __x) noexcept
{ return *this = type(__x); }
_GLIBCXX14_CONSTEXPR type&
operator++() noexcept
{ return *this = *this + 1; }
_GLIBCXX14_CONSTEXPR type&
operator--() noexcept
{ return *this = *this - 1; }
_GLIBCXX14_CONSTEXPR type
operator++(int) noexcept
{
auto __tmp = *this;
++*this;
return __tmp;
}
_GLIBCXX14_CONSTEXPR type
operator--(int) noexcept
{
auto __tmp = *this;
--*this;
return __tmp;
}
_GLIBCXX14_CONSTEXPR type&
operator+=(const type& __r) noexcept
{
_M_hi += __r._M_hi + __builtin_add_overflow(_M_lo, __r._M_lo, &_M_lo);
return *this;
}
friend _GLIBCXX14_CONSTEXPR type
operator+(type __l, const type& __r) noexcept
{ return __l += __r; }
// Addition with 64-bit operand
friend _GLIBCXX14_CONSTEXPR type
operator+(type __l, uint64_t __r) noexcept
{ return __l += type(__r); }
_GLIBCXX14_CONSTEXPR type&
operator-=(const type& __r) noexcept
{
_M_hi -= __r._M_hi + __builtin_sub_overflow(_M_lo, __r._M_lo, &_M_lo);
return *this;
}
// Subtraction with 64-bit operand
_GLIBCXX14_CONSTEXPR type&
operator-=(uint64_t __r) noexcept
{
_M_hi -= __builtin_sub_overflow(_M_lo, __r, &_M_lo);
return *this;
}
friend _GLIBCXX14_CONSTEXPR type
operator-(type __l, const type& __r) noexcept
{ return __l -= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator-(type __l, uint64_t __r) noexcept
{ return __l -= __r; }
_GLIBCXX14_CONSTEXPR type&
operator*=(const type& __x) noexcept
{
uint64_t __a[12] = {
uint32_t(_M_lo), _M_lo >> 32,
uint32_t(_M_hi), _M_hi >> 32,
uint32_t(__x._M_lo), __x._M_lo >> 32,
uint32_t(__x._M_hi), __x._M_hi >> 32,
0, 0,
0, 0 };
for (int __i = 0; __i < 4; ++__i)
{
uint64_t __c = 0;
for (int __j = __i; __j < 4; ++__j)
{
__c += __a[__i] * __a[4 + __j - __i] + __a[8 + __j];
__a[8 + __j] = uint32_t(__c);
__c >>= 32;
}
}
_M_lo = __a[8] + (__a[9] << 32);
_M_hi = __a[10] + (__a[11] << 32);
return *this;
}
// Multiplication with a 64-bit operand is simpler.
_GLIBCXX14_CONSTEXPR type&
operator*=(uint64_t __x) noexcept
{
// Split 64-bit values _M_lo and __x into high and low 32-bit
// limbs and multiply those individually.
// l * x = (l0 + l1) * (x0 + x1) = l0x0 + l0x1 + l1x0 + l1x1
constexpr uint64_t __mask = 0xffffffff;
uint64_t __ll[2] = { _M_lo >> 32, _M_lo & __mask };
uint64_t __xx[2] = { __x >> 32, __x & __mask };
uint64_t __l0x0 = __ll[0] * __xx[0];
uint64_t __l0x1 = __ll[0] * __xx[1];
uint64_t __l1x0 = __ll[1] * __xx[0];
uint64_t __l1x1 = __ll[1] * __xx[1];
// These bits are the low half of _M_hi and the high half of _M_lo.
uint64_t __mid
= (__l0x1 & __mask) + (__l1x0 & __mask) + (__l1x1 >> 32);
_M_hi *= __x;
_M_hi += __l0x0 + (__l0x1 >> 32) + (__l1x0 >> 32) + (__mid >> 32);
_M_lo = (__mid << 32) + (__l1x1 & __mask);
return *this;
}
_GLIBCXX14_CONSTEXPR type&
operator/=(const type& __r) noexcept
{
if (!_M_hi)
{
if (!__r._M_hi)
_M_lo = _M_lo / __r._M_lo;
else
_M_lo = 0;
}
else
{
uint64_t __a[13] = {
uint32_t(_M_lo), _M_lo >> 32,
uint32_t(_M_hi), _M_hi >> 32,
0,
uint32_t(__r._M_lo), __r._M_lo >> 32,
uint32_t(__r._M_hi), __r._M_hi >> 32,
0, 0,
0, 0
};
uint64_t __c = 0, __w = 0;
if (!__r._M_hi && __r._M_lo <= ~uint32_t(0))
for (int __i = 3; ; --__i)
{
__w = __a[__i] + (__c << 32);
__a[9 + __i] = __w / __r._M_lo;
if (__i == 0)
break;
__c = __w % __r._M_lo;
}
else
{
// See Donald E. Knuth's "Seminumerical Algorithms".
int __n = 0, __d = 0;
uint64_t __q = 0, __s = 0;
for (__d = 3; __a[5 + __d] == 0; --__d)
;
__s = (uint64_t(1) << 32) / (__a[5 + __d] + 1);
if (__s > 1)
{
for (int __i = 0; __i <= 3; ++__i)
{
__w = __a[__i] * __s + __c;
__a[__i] = uint32_t(__w);
__c = __w >> 32;
}
__a[4] = __c;
__c = 0;
for (int __i = 0; __i <= 3; ++__i)
{
__w = __a[5 + __i] * __s + __c;
__a[5 + __i] = uint32_t(__w);
__c = __w >> 32;
if (__a[5 + __i])
__d = __i;
}
}
__n = 4;
for (int __i = __n - __d - 1; __i >= 0; --__i)
{
__n = __i + __d + 1;
__w = (__a[__n] << 32) + __a[__n - 1];
if (__a[__n] != __a[5 + __d])
__q = __w / __a[5 + __d];
else
__q = ~uint32_t(0);
uint64_t __t = __w - __q * __a[5 + __d];
if (__t <= ~uint32_t(0)
&& __a[4 + __d] * __q > (__t << 32) + __a[__n - 2])
--__q;
__c = 0;
for (int __j = 0; __j <= __d; ++__j)
{
__w = __q * __a[5 + __j] + __c;
__c = __w >> 32;
__w = __a[__i + __j] - uint32_t(__w);
__a[__i + __j] = uint32_t(__w);
__c += (__w >> 32) != 0;
}
if (int64_t(__a[__n]) < int64_t(__c))
{
--__q;
__c = 0;
for (int __j = 0; __j <= __d; ++__j)
{
__w = __a[__i + __j] + __a[5 + __j] + __c;
__c = __w >> 32;
__a[__i + __j] = uint32_t(__w);
}
__a[__n] += __c;
}
__a[9 + __i] = __q;
}
}
_M_lo = __a[9] + (__a[10] << 32);
_M_hi = __a[11] + (__a[12] << 32);
}
return *this;
}
_GLIBCXX14_CONSTEXPR type&
operator/=(uint64_t __r) noexcept
{ return *this /= type(__r); }
// Currently only supported for 64-bit operands.
_GLIBCXX14_CONSTEXPR type&
operator%=(uint64_t __m) noexcept
{
if (_M_hi == 0)
{
_M_lo %= __m;
return *this;
}
int __shift = __builtin_clzll(__m) + 64 - __builtin_clzll(_M_hi);
type __x(0);
if (__shift >= 64)
{
__x._M_hi = __m << (__shift - 64);
__x._M_lo = 0;
}
else
{
__x._M_hi = __m >> (64 - __shift);
__x._M_lo = __m << __shift;
}
while (_M_hi != 0 || _M_lo >= __m)
{
if (__x <= *this)
{
_M_hi -= __x._M_hi;
_M_hi -= __builtin_sub_overflow(_M_lo, __x._M_lo,
&_M_lo);
}
__x._M_lo = (__x._M_lo >> 1) | (__x._M_hi << 63);
__x._M_hi >>= 1;
}
return *this;
}
friend _GLIBCXX14_CONSTEXPR type
operator*(type __l, const type& __r) noexcept
{ return __l *= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator*(type __l, uint64_t __r) noexcept
{ return __l *= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator/(type __l, const type& __r) noexcept
{ return __l /= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator/(type __l, uint64_t __r) noexcept
{ return __l /= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator%(type __l, uint64_t __m) noexcept
{ return __l %= __m; }
friend _GLIBCXX14_CONSTEXPR type
operator~(type __v) noexcept
{
__v._M_hi = ~__v._M_hi;
__v._M_lo = ~__v._M_lo;
return __v;
}
_GLIBCXX14_CONSTEXPR type&
operator>>=(unsigned __c) noexcept
{
if (__c >= 64)
{
_M_lo = _M_hi >>= (__c - 64);
_M_hi = 0;
}
else if (__c != 0)
{
_M_lo = (_M_lo >> __c) | (_M_hi << (64 - __c));
_M_hi >>= __c;
}
return *this;
}
_GLIBCXX14_CONSTEXPR type&
operator<<=(unsigned __c) noexcept
{
if (__c >= 64)
{
_M_hi = _M_lo << (__c - 64);
_M_lo = 0;
}
else if (__c != 0)
{
_M_hi = (_M_hi << __c) | (_M_lo >> (64 - __c));
_M_lo <<= __c;
}
return *this;
}
friend _GLIBCXX14_CONSTEXPR type
operator>>(type __x, unsigned __c) noexcept
{ return __x >>= __c; }
friend _GLIBCXX14_CONSTEXPR type
operator<<(type __x, unsigned __c) noexcept
{ return __x <<= __c; }
_GLIBCXX14_CONSTEXPR type&
operator|=(const type& __r) noexcept
{
_M_hi |= __r._M_hi;
_M_lo |= __r._M_lo;
return *this;
}
_GLIBCXX14_CONSTEXPR type&
operator^=(const type& __r) noexcept
{
_M_hi ^= __r._M_hi;
_M_lo ^= __r._M_lo;
return *this;
}
_GLIBCXX14_CONSTEXPR type&
operator&=(const type& __r) noexcept
{
_M_hi &= __r._M_hi;
_M_lo &= __r._M_lo;
return *this;
}
friend _GLIBCXX14_CONSTEXPR type
operator|(type __l, const type& __r) noexcept
{ return __l |= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator^(type __l, const type& __r) noexcept
{ return __l ^= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator&(type __l, const type& __r) noexcept
{ return __l &= __r; }
friend _GLIBCXX14_CONSTEXPR type
operator&(type __l, uint64_t __r) noexcept
{
__l._M_hi = 0;
__l._M_lo &= __r;
return __l;
}
#if __cpp_impl_three_way_comparison >= 201907L
friend std::strong_ordering
operator<=>(const type&, const type&) = default;
friend bool
operator==(const type&, const type&) = default;
#else
friend constexpr bool
operator==(const type& __l, const type& __r) noexcept
{ return __l._M_hi == __r._M_hi && __l._M_lo == __r._M_lo; }
friend _GLIBCXX14_CONSTEXPR bool
operator<(const type& __l, const type& __r) noexcept
{
if (__l._M_hi < __r._M_hi)
return true;
else if (__l._M_hi == __r._M_hi)
return __l._M_lo < __r._M_lo;
else
return false;
}
friend _GLIBCXX14_CONSTEXPR bool
operator>(const type& __l, const type& __r) noexcept
{ return __r < __l; }
friend _GLIBCXX14_CONSTEXPR bool
operator<=(const type& __l, const type& __r) noexcept
{ return !(__r < __l); }
friend _GLIBCXX14_CONSTEXPR bool
operator>=(const type& __l, const type& __r) noexcept
{ return !(__l < __r); }
#endif
friend _GLIBCXX14_CONSTEXPR bool
operator==(const type& __l, uint64_t __r) noexcept
{ return __l == type(__r); }
template<typename _RealT>
constexpr explicit operator _RealT() const noexcept
{
static_assert(std::is_floating_point<_RealT>::value,
"template argument must be a floating point type");
return _M_hi == 0
? _RealT(_M_lo)
: _RealT(_M_hi) * _RealT(18446744073709551616.0)
+ _RealT(_M_lo);
}
// pre: _M_hi == 0
constexpr explicit operator uint64_t() const noexcept
{ return _M_lo; }
uint64_t _M_hi = 0;
uint64_t _M_lo = 0;
};
#endif // ! __SIZEOF_INT128__
template<typename _UIntType, size_t __w,
bool = __w < static_cast<size_t>
(std::numeric_limits<_UIntType>::digits)>
struct _Shift
{ static constexpr _UIntType __value = 0; };
template<typename _UIntType, size_t __w>
struct _Shift<_UIntType, __w, true>
{ static constexpr _UIntType __value = _UIntType(1) << __w; };
template<int __s,
int __which = ((__s <= __CHAR_BIT__ * sizeof (int))
+ (__s <= __CHAR_BIT__ * sizeof (long))
+ (__s <= __CHAR_BIT__ * sizeof (long long))
/* assume long long no bigger than __int128 */
+ (__s <= 128))>
struct _Select_uint_least_t
{
static_assert(__which < 0, /* needs to be dependent */
"sorry, would be too much trouble for a slow result");
};
template<int __s>
struct _Select_uint_least_t<__s, 4>
{ using type = unsigned int; };
template<int __s>
struct _Select_uint_least_t<__s, 3>
{ using type = unsigned long; };
template<int __s>
struct _Select_uint_least_t<__s, 2>
{ using type = unsigned long long; };
#if __SIZEOF_INT128__ > __SIZEOF_LONG_LONG__
template<int __s>
struct _Select_uint_least_t<__s, 1>
{ __extension__ using type = unsigned __int128; };
#elif __has_builtin(__builtin_add_overflow) \
&& __has_builtin(__builtin_sub_overflow) \
&& defined __UINT64_TYPE__
template<int __s>
struct _Select_uint_least_t<__s, 1>
{ using type = __rand_uint128; };
#endif
// Assume a != 0, a < m, c < m, x < m.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c,
bool __big_enough = (!(__m & (__m - 1))
|| (_Tp(-1) - __c) / __a >= __m - 1),
bool __schrage_ok = __m % __a < __m / __a>
struct _Mod
{
static _Tp
__calc(_Tp __x)
{
using _Tp2
= typename _Select_uint_least_t<std::__lg(__a)
+ std::__lg(__m) + 2>::type;
return static_cast<_Tp>((_Tp2(__a) * __x + __c) % __m);
}
};
// Schrage.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
struct _Mod<_Tp, __m, __a, __c, false, true>
{
static _Tp
__calc(_Tp __x);
};
// Special cases:
// - for m == 2^n or m == 0, unsigned integer overflow is safe.
// - a * (m - 1) + c fits in _Tp, there is no overflow.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c, bool __s>
struct _Mod<_Tp, __m, __a, __c, true, __s>
{
static _Tp
__calc(_Tp __x)
{
_Tp __res = __a * __x + __c;
if (__m)
__res %= __m;
return __res;
}
};
template<typename _Tp, _Tp __m, _Tp __a = 1, _Tp __c = 0>
inline _Tp
__mod(_Tp __x)
{
if constexpr (__a == 0)
return __c;
else // N.B. _Mod must not be instantiated with a == 0
return _Mod<_Tp, __m, __a, __c>::__calc(__x);
}
/*
* An adaptor class for converting the output of any Generator into
* the input for a specific Distribution.
*/
template<typename _Engine, typename _DInputType>
struct _Adaptor
{
static_assert(std::is_floating_point<_DInputType>::value,
"template argument must be a floating point type");
public:
_Adaptor(_Engine& __g)
: _M_g(__g) { }
_DInputType
min() const
{ return _DInputType(0); }
_DInputType
max() const
{ return _DInputType(1); }
/*
* Converts a value generated by the adapted random number generator
* into a value in the input domain for the dependent random number
* distribution.
*/
_DInputType
operator()()
{
return std::generate_canonical<_DInputType,
std::numeric_limits<_DInputType>::digits,
_Engine>(_M_g);
}
private:
_Engine& _M_g;
};
// Detect whether a template argument _Sseq is a valid seed sequence for
// a random number engine _Engine with result type _Res.
// Used to constrain _Engine::_Engine(_Sseq&) and _Engine::seed(_Sseq&)
// as required by [rand.eng.general].
template<typename _Sseq>
using __seed_seq_generate_t = decltype(
std::declval<_Sseq&>().generate(std::declval<uint_least32_t*>(),
std::declval<uint_least32_t*>()));
template<typename _Sseq, typename _Engine, typename _Res,
typename _GenerateCheck = __seed_seq_generate_t<_Sseq>>
using _If_seed_seq_for = _Require<
__not_<is_same<__remove_cvref_t<_Sseq>, _Engine>>,
is_unsigned<typename _Sseq::result_type>,
__not_<is_convertible<_Sseq, _Res>>
>;
#pragma GCC diagnostic pop
} // namespace __detail
/// @endcond
/**
* @addtogroup random_generators Random Number Generators
* @ingroup random
*
* These classes define objects which provide random or pseudorandom
* numbers, either from a discrete or a continuous interval. The
* random number generator supplied as a part of this library are
* all uniform random number generators which provide a sequence of
* random number uniformly distributed over their range.
*
* A number generator is a function object with an operator() that
* takes zero arguments and returns a number.
*
* A compliant random number generator must satisfy the following
* requirements. <table border=1 cellpadding=10 cellspacing=0>
* <caption align=top>Random Number Generator Requirements</caption>
* <tr><td>To be documented.</td></tr> </table>
*
* @{
*/
/**
* @brief A model of a linear congruential random number generator.
*
* A random number generator that produces pseudorandom numbers via
* linear function:
* @f[
* x_{i+1}\leftarrow(ax_{i} + c) \bmod m
* @f]
*
* The template parameter @p _UIntType must be an unsigned integral type
* large enough to store values up to (__m-1). If the template parameter
* @p __m is 0, the modulus @p __m used is
* std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template
* parameters @p __a and @p __c must be less than @p __m.
*
* The size of the state is @f$1@f$.
*
* @headerfile random
* @since C++11
*/
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
class linear_congruential_engine
{
static_assert(std::is_unsigned<_UIntType>::value,
"result_type must be an unsigned integral type");
static_assert(__m == 0u || (__a < __m && __c < __m),
"template argument substituting __m out of bounds");
template<typename _Sseq>
using _If_seed_seq
= __detail::_If_seed_seq_for<_Sseq, linear_congruential_engine,
_UIntType>;
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
/** The multiplier. */
static constexpr result_type multiplier = __a;
/** An increment. */
static constexpr result_type increment = __c;
/** The modulus. */
static constexpr result_type modulus = __m;
static constexpr result_type default_seed = 1u;
/**
* @brief Constructs a %linear_congruential_engine random number
* generator engine with seed 1.
*/
linear_congruential_engine() : linear_congruential_engine(default_seed)
{ }
/**
* @brief Constructs a %linear_congruential_engine random number
* generator engine with seed @p __s. The default seed value
* is 1.
*
* @param __s The initial seed value.
*/
explicit
linear_congruential_engine(result_type __s)
{ seed(__s); }
/**
* @brief Constructs a %linear_congruential_engine random number
* generator engine seeded from the seed sequence @p __q.
*
* @param __q the seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
linear_congruential_engine(_Sseq& __q)
{ seed(__q); }
/**
* @brief Reseeds the %linear_congruential_engine random number generator
* engine sequence to the seed @p __s.
*
* @param __s The new seed.
*/
void
seed(result_type __s = default_seed);
/**
* @brief Reseeds the %linear_congruential_engine random number generator
* engine
* sequence using values from the seed sequence @p __q.
*
* @param __q the seed sequence.
*/
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q);
/**
* @brief Gets the smallest possible value in the output range.
*
* The minimum depends on the @p __c parameter: if it is zero, the
* minimum generated must be > 0, otherwise 0 is allowed.
*/
static constexpr result_type
min()
{ return __c == 0u ? 1u : 0u; }
/**
* @brief Gets the largest possible value in the output range.
*/
static constexpr result_type
max()
{ return __m - 1u; }
/**
* @brief Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z)
{
for (; __z != 0ULL; --__z)
(*this)();
}
/**
* @brief Gets the next random number in the sequence.
*/
result_type
operator()()
{
_M_x = __detail::__mod<_UIntType, __m, __a, __c>(_M_x);
return _M_x;
}
/**
* @brief Compares two linear congruential random number generator
* objects of the same type for equality.
*
* @param __lhs A linear congruential random number generator object.
* @param __rhs Another linear congruential random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const linear_congruential_engine& __lhs,
const linear_congruential_engine& __rhs)
{ return __lhs._M_x == __rhs._M_x; }
/**
* @brief Writes the textual representation of the state x(i) of x to
* @p __os.
*
* @param __os The output stream.
* @param __lcr A % linear_congruential_engine random number generator.
* @returns __os.
*/
template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
_UIntType1 __m1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::linear_congruential_engine<_UIntType1,
__a1, __c1, __m1>& __lcr);
/**
* @brief Sets the state of the engine by reading its textual
* representation from @p __is.
*
* The textual representation must have been previously written using
* an output stream whose imbued locale and whose type's template
* specialization arguments _CharT and _Traits were the same as those
* of @p __is.
*
* @param __is The input stream.
* @param __lcr A % linear_congruential_engine random number generator.
* @returns __is.
*/
template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
_UIntType1 __m1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::linear_congruential_engine<_UIntType1, __a1,
__c1, __m1>& __lcr);
private:
_UIntType _M_x;
};
#if __cpp_impl_three_way_comparison < 201907L
/**
* @brief Compares two linear congruential random number generator
* objects of the same type for inequality.
*
* @param __lhs A linear congruential random number generator object.
* @param __rhs Another linear congruential random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
inline bool
operator!=(const std::linear_congruential_engine<_UIntType, __a,
__c, __m>& __lhs,
const std::linear_congruential_engine<_UIntType, __a,
__c, __m>& __rhs)
{ return !(__lhs == __rhs); }
#endif
/**
* A generalized feedback shift register discrete random number generator.
*
* This algorithm avoids multiplication and division and is designed to be
* friendly to a pipelined architecture. If the parameters are chosen
* correctly, this generator will produce numbers with a very long period and
* fairly good apparent entropy, although still not cryptographically strong.
*
* The best way to use this generator is with the predefined mt19937 class.
*
* This algorithm was originally invented by Makoto Matsumoto and
* Takuji Nishimura.
*
* @tparam __w Word size, the number of bits in each element of
* the state vector.
* @tparam __n The degree of recursion.
* @tparam __m The period parameter.
* @tparam __r The separation point bit index.
* @tparam __a The last row of the twist matrix.
* @tparam __u The first right-shift tempering matrix parameter.
* @tparam __d The first right-shift tempering matrix mask.
* @tparam __s The first left-shift tempering matrix parameter.
* @tparam __b The first left-shift tempering matrix mask.
* @tparam __t The second left-shift tempering matrix parameter.
* @tparam __c The second left-shift tempering matrix mask.
* @tparam __l The second right-shift tempering matrix parameter.
* @tparam __f Initialization multiplier.
*
* @headerfile random
* @since C++11
*/
template<typename _UIntType, size_t __w,
size_t __n, size_t __m, size_t __r,
_UIntType __a, size_t __u, _UIntType __d, size_t __s,
_UIntType __b, size_t __t,
_UIntType __c, size_t __l, _UIntType __f>
class mersenne_twister_engine
{
static_assert(std::is_unsigned<_UIntType>::value,
"result_type must be an unsigned integral type");
static_assert(1u <= __m && __m <= __n,
"template argument substituting __m out of bounds");
static_assert(__r <= __w, "template argument substituting "
"__r out of bound");
static_assert(__u <= __w, "template argument substituting "
"__u out of bound");
static_assert(__s <= __w, "template argument substituting "
"__s out of bound");
static_assert(__t <= __w, "template argument substituting "
"__t out of bound");
static_assert(__l <= __w, "template argument substituting "
"__l out of bound");
static_assert(__w <= std::numeric_limits<_UIntType>::digits,
"template argument substituting __w out of bound");
static_assert(__a <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __a out of bound");
static_assert(__b <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __b out of bound");
static_assert(__c <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __c out of bound");
static_assert(__d <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __d out of bound");
static_assert(__f <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __f out of bound");
template<typename _Sseq>
using _If_seed_seq
= __detail::_If_seed_seq_for<_Sseq, mersenne_twister_engine,
_UIntType>;
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
// parameter values
static constexpr size_t word_size = __w;
static constexpr size_t state_size = __n;
static constexpr size_t shift_size = __m;
static constexpr size_t mask_bits = __r;
static constexpr result_type xor_mask = __a;
static constexpr size_t tempering_u = __u;
static constexpr result_type tempering_d = __d;
static constexpr size_t tempering_s = __s;
static constexpr result_type tempering_b = __b;
static constexpr size_t tempering_t = __t;
static constexpr result_type tempering_c = __c;
static constexpr size_t tempering_l = __l;
static constexpr result_type initialization_multiplier = __f;