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// random number generation (out of line) -*- C++ -*-
// Copyright (C) 2009-2025 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.tcc
* This is an internal header file, included by other library headers.
* Do not attempt to use it directly. @headername{random}
*/
#ifndef _RANDOM_TCC
#define _RANDOM_TCC 1
#include <numeric> // std::accumulate and std::partial_sum
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/// @cond undocumented
// (Further) implementation-space details.
namespace __detail
{
// General case for x = (ax + c) mod m -- use Schrage's algorithm
// to avoid integer overflow.
//
// Preconditions: a > 0, m > 0.
//
// Note: only works correctly for __m % __a < __m / __a.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
_Tp
_Mod<_Tp, __m, __a, __c, false, true>::
__calc(_Tp __x)
{
if (__a == 1)
__x %= __m;
else
{
static const _Tp __q = __m / __a;
static const _Tp __r = __m % __a;
_Tp __t1 = __a * (__x % __q);
_Tp __t2 = __r * (__x / __q);
if (__t1 >= __t2)
__x = __t1 - __t2;
else
__x = __m - __t2 + __t1;
}
if (__c != 0)
{
const _Tp __d = __m - __x;
if (__d > __c)
__x += __c;
else
__x = __c - __d;
}
return __x;
}
template<typename _InputIterator, typename _OutputIterator,
typename _Tp>
_OutputIterator
__normalize(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, const _Tp& __factor)
{
for (; __first != __last; ++__first, (void) ++__result)
*__result = *__first / __factor;
return __result;
}
} // namespace __detail
/// @endcond
#if ! __cpp_inline_variables
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
constexpr _UIntType
linear_congruential_engine<_UIntType, __a, __c, __m>::multiplier;
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
constexpr _UIntType
linear_congruential_engine<_UIntType, __a, __c, __m>::increment;
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
constexpr _UIntType
linear_congruential_engine<_UIntType, __a, __c, __m>::modulus;
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
constexpr _UIntType
linear_congruential_engine<_UIntType, __a, __c, __m>::default_seed;
#endif
/**
* Seeds the LCR with integral value @p __s, adjusted so that the
* ring identity is never a member of the convergence set.
*/
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
void
linear_congruential_engine<_UIntType, __a, __c, __m>::
seed(result_type __s)
{
if ((__detail::__mod<_UIntType, __m>(__c) == 0)
&& (__detail::__mod<_UIntType, __m>(__s) == 0))
_M_x = 1;
else
_M_x = __detail::__mod<_UIntType, __m>(__s);
}
/**
* Seeds the LCR engine with a value generated by @p __q.
*/
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
template<typename _Sseq>
auto
linear_congruential_engine<_UIntType, __a, __c, __m>::
seed(_Sseq& __q)
-> _If_seed_seq<_Sseq>
{
const _UIntType __k0 = __m == 0 ? std::numeric_limits<_UIntType>::digits
: std::__lg(__m);
const _UIntType __k = (__k0 + 31) / 32;
uint_least32_t __arr[__k + 3];
__q.generate(__arr + 0, __arr + __k + 3);
_UIntType __factor = 1u;
_UIntType __sum = 0u;
for (size_t __j = 0; __j < __k; ++__j)
{
__sum += __arr[__j + 3] * __factor;
__factor *= __detail::_Shift<_UIntType, 32>::__value;
}
seed(__sum);
}
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const linear_congruential_engine<_UIntType,
__a, __c, __m>& __lcr)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
__os.fill(__os.widen(' '));
__os << __lcr._M_x;
__os.flags(__flags);
__os.fill(__fill);
return __os;
}
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec);
__is >> __lcr._M_x;
__is.flags(__flags);
return __is;
}
#if ! __cpp_inline_variables
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::word_size;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::state_size;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::shift_size;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::mask_bits;
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>
constexpr _UIntType
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::xor_mask;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_u;
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>
constexpr _UIntType
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_d;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_s;
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>
constexpr _UIntType
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_b;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_t;
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>
constexpr _UIntType
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_c;
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>
constexpr size_t
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::tempering_l;
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>
constexpr _UIntType
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::
initialization_multiplier;
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>
constexpr _UIntType
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::default_seed;
#endif
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>
void
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::
seed(result_type __sd)
{
_M_x[0] = __detail::__mod<_UIntType,
__detail::_Shift<_UIntType, __w>::__value>(__sd);
for (size_t __i = 1; __i < state_size; ++__i)
{
_UIntType __x = _M_x[__i - 1];
__x ^= __x >> (__w - 2);
__x *= __f;
__x += __detail::__mod<_UIntType, __n>(__i);
_M_x[__i] = __detail::__mod<_UIntType,
__detail::_Shift<_UIntType, __w>::__value>(__x);
}
_M_p = state_size;
}
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>
template<typename _Sseq>
auto
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::
seed(_Sseq& __q)
-> _If_seed_seq<_Sseq>
{
const _UIntType __upper_mask = (~_UIntType()) << __r;
const size_t __k = (__w + 31) / 32;
uint_least32_t __arr[__n * __k];
__q.generate(__arr + 0, __arr + __n * __k);
bool __zero = true;
for (size_t __i = 0; __i < state_size; ++__i)
{
_UIntType __factor = 1u;
_UIntType __sum = 0u;
for (size_t __j = 0; __j < __k; ++__j)
{
__sum += __arr[__k * __i + __j] * __factor;
__factor *= __detail::_Shift<_UIntType, 32>::__value;
}
_M_x[__i] = __detail::__mod<_UIntType,
__detail::_Shift<_UIntType, __w>::__value>(__sum);
if (__zero)
{
if (__i == 0)
{
if ((_M_x[0] & __upper_mask) != 0u)
__zero = false;
}
else if (_M_x[__i] != 0u)
__zero = false;
}
}
if (__zero)
_M_x[0] = __detail::_Shift<_UIntType, __w - 1>::__value;
_M_p = state_size;
}
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>
void
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::
_M_gen_rand(void)
{
const _UIntType __upper_mask = (~_UIntType()) << __r;
const _UIntType __lower_mask = ~__upper_mask;
for (size_t __k = 0; __k < (__n - __m); ++__k)
{
_UIntType __y = ((_M_x[__k] & __upper_mask)
| (_M_x[__k + 1] & __lower_mask));
_M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
^ ((__y & 0x01) ? __a : 0));
}
for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
{
_UIntType __y = ((_M_x[__k] & __upper_mask)
| (_M_x[__k + 1] & __lower_mask));
_M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
^ ((__y & 0x01) ? __a : 0));
}
_UIntType __y = ((_M_x[__n - 1] & __upper_mask)
| (_M_x[0] & __lower_mask));
_M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
^ ((__y & 0x01) ? __a : 0));
_M_p = 0;
}
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>
void
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::
discard(unsigned long long __z)
{
while (__z > state_size - _M_p)
{
__z -= state_size - _M_p;
_M_gen_rand();
}
_M_p += __z;
}
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>
typename
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::result_type
mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
__s, __b, __t, __c, __l, __f>::
operator()()
{
// Reload the vector - cost is O(n) amortized over n calls.
if (_M_p >= state_size)
_M_gen_rand();
// Calculate o(x(i)).
result_type __z = _M_x[_M_p++];
__z ^= (__z >> __u) & __d;
__z ^= (__z << __s) & __b;
__z ^= (__z << __t) & __c;
__z ^= (__z >> __l);
return __z;
}
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, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const mersenne_twister_engine<_UIntType, __w, __n, __m,
__r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
__os.fill(__space);
for (size_t __i = 0; __i < __n; ++__i)
__os << __x._M_x[__i] << __space;
__os << __x._M_p;
__os.flags(__flags);
__os.fill(__fill);
return __os;
}
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, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
mersenne_twister_engine<_UIntType, __w, __n, __m,
__r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
for (size_t __i = 0; __i < __n; ++__i)
__is >> __x._M_x[__i];
__is >> __x._M_p;
__is.flags(__flags);
return __is;
}
#if ! __cpp_inline_variables
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
constexpr size_t
subtract_with_carry_engine<_UIntType, __w, __s, __r>::word_size;
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
constexpr size_t
subtract_with_carry_engine<_UIntType, __w, __s, __r>::short_lag;
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
constexpr size_t
subtract_with_carry_engine<_UIntType, __w, __s, __r>::long_lag;
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
constexpr uint_least32_t
subtract_with_carry_engine<_UIntType, __w, __s, __r>::default_seed;
#endif
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
void
subtract_with_carry_engine<_UIntType, __w, __s, __r>::
seed(result_type __value)
{
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// 3809. Is std::subtract_with_carry_engine<uint16_t> supposed to work?
// 4014. LWG 3809 changes behavior of some existing code
std::linear_congruential_engine<uint_least32_t, 40014u, 0u, 2147483563u>
__lcg(__value == 0u ? default_seed : __value % 2147483563u);
const size_t __n = (__w + 31) / 32;
for (size_t __i = 0; __i < long_lag; ++__i)
{
_UIntType __sum = 0u;
_UIntType __factor = 1u;
for (size_t __j = 0; __j < __n; ++__j)
{
__sum += __detail::__mod<uint_least32_t,
__detail::_Shift<uint_least32_t, 32>::__value>
(__lcg()) * __factor;
__factor *= __detail::_Shift<_UIntType, 32>::__value;
}
_M_x[__i] = __detail::__mod<_UIntType,
__detail::_Shift<_UIntType, __w>::__value>(__sum);
}
_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
_M_p = 0;
}
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
template<typename _Sseq>
auto
subtract_with_carry_engine<_UIntType, __w, __s, __r>::
seed(_Sseq& __q)
-> _If_seed_seq<_Sseq>
{
const size_t __k = (__w + 31) / 32;
uint_least32_t __arr[__r * __k];
__q.generate(__arr + 0, __arr + __r * __k);
for (size_t __i = 0; __i < long_lag; ++__i)
{
_UIntType __sum = 0u;
_UIntType __factor = 1u;
for (size_t __j = 0; __j < __k; ++__j)
{
__sum += __arr[__k * __i + __j] * __factor;
__factor *= __detail::_Shift<_UIntType, 32>::__value;
}
_M_x[__i] = __detail::__mod<_UIntType,
__detail::_Shift<_UIntType, __w>::__value>(__sum);
}
_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
_M_p = 0;
}
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
typename subtract_with_carry_engine<_UIntType, __w, __s, __r>::
result_type
subtract_with_carry_engine<_UIntType, __w, __s, __r>::
operator()()
{
// Derive short lag index from current index.
long __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 _UIntType, _M_x[_M_p] + _M_carry
// cannot overflow.
_UIntType __xi;
if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
{
__xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
_M_carry = 0;
}
else
{
__xi = (__detail::_Shift<_UIntType, __w>::__value
- _M_x[_M_p] - _M_carry + _M_x[__ps]);
_M_carry = 1;
}
_M_x[_M_p] = __xi;
// Adjust current index to loop around in ring buffer.
if (++_M_p >= long_lag)
_M_p = 0;
return __xi;
}
template<typename _UIntType, size_t __w, size_t __s, size_t __r,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const subtract_with_carry_engine<_UIntType,
__w, __s, __r>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
__os.fill(__space);
for (size_t __i = 0; __i < __r; ++__i)
__os << __x._M_x[__i] << __space;
__os << __x._M_carry << __space << __x._M_p;
__os.flags(__flags);
__os.fill(__fill);
return __os;
}
template<typename _UIntType, size_t __w, size_t __s, size_t __r,
typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
subtract_with_carry_engine<_UIntType, __w, __s, __r>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
for (size_t __i = 0; __i < __r; ++__i)
__is >> __x._M_x[__i];
__is >> __x._M_carry;
__is >> __x._M_p;
__is.flags(__flags);
return __is;
}
#if ! __cpp_inline_variables
template<typename _RandomNumberEngine, size_t __p, size_t __r>
constexpr size_t
discard_block_engine<_RandomNumberEngine, __p, __r>::block_size;
template<typename _RandomNumberEngine, size_t __p, size_t __r>
constexpr size_t
discard_block_engine<_RandomNumberEngine, __p, __r>::used_block;
#endif
template<typename _RandomNumberEngine, size_t __p, size_t __r>
typename discard_block_engine<_RandomNumberEngine,
__p, __r>::result_type
discard_block_engine<_RandomNumberEngine, __p, __r>::
operator()()
{
if (_M_n >= used_block)
{
_M_b.discard(block_size - _M_n);
_M_n = 0;
}
++_M_n;
return _M_b();
}
template<typename _RandomNumberEngine, size_t __p, size_t __r,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const discard_block_engine<_RandomNumberEngine,
__p, __r>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
__os.fill(__space);
__os << __x.base() << __space << __x._M_n;
__os.flags(__flags);
__os.fill(__fill);
return __os;
}
template<typename _RandomNumberEngine, size_t __p, size_t __r,
typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
discard_block_engine<_RandomNumberEngine, __p, __r>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
__is >> __x._M_b >> __x._M_n;
__is.flags(__flags);
return __is;
}
template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
result_type
independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
operator()()
{
typedef typename _RandomNumberEngine::result_type _Eresult_type;
const _Eresult_type __r
= (_M_b.max() - _M_b.min() < std::numeric_limits<_Eresult_type>::max()
? _M_b.max() - _M_b.min() + 1 : 0);
const unsigned __edig = std::numeric_limits<_Eresult_type>::digits;
const unsigned __m = __r ? std::__lg(__r) : __edig;
typedef typename std::common_type<_Eresult_type, result_type>::type
__ctype;
const unsigned __cdig = std::numeric_limits<__ctype>::digits;
unsigned __n, __n0;
__ctype __s0, __s1, __y0, __y1;
for (size_t __i = 0; __i < 2; ++__i)
{
__n = (__w + __m - 1) / __m + __i;
__n0 = __n - __w % __n;
const unsigned __w0 = __w / __n; // __w0 <= __m
__s0 = 0;
__s1 = 0;
if (__w0 < __cdig)
{
__s0 = __ctype(1) << __w0;
__s1 = __s0 << 1;
}
__y0 = 0;
__y1 = 0;
if (__r)
{
__y0 = __s0 * (__r / __s0);
if (__s1)
__y1 = __s1 * (__r / __s1);
if (__r - __y0 <= __y0 / __n)
break;
}
else
break;
}
result_type __sum = 0;
for (size_t __k = 0; __k < __n0; ++__k)
{
__ctype __u;
do
__u = _M_b() - _M_b.min();
while (__y0 && __u >= __y0);
__sum = __s0 * __sum + (__s0 ? __u % __s0 : __u);
}
for (size_t __k = __n0; __k < __n; ++__k)
{
__ctype __u;
do
__u = _M_b() - _M_b.min();
while (__y1 && __u >= __y1);
__sum = __s1 * __sum + (__s1 ? __u % __s1 : __u);
}
return __sum;
}
#if ! __cpp_inline_variables
template<typename _RandomNumberEngine, size_t __k>
constexpr size_t
shuffle_order_engine<_RandomNumberEngine, __k>::table_size;
#endif
namespace __detail
{
// Determine whether an integer is representable as double.
template<typename _Tp>
constexpr bool
__representable_as_double(_Tp __x) noexcept
{
static_assert(numeric_limits<_Tp>::is_integer, "");
static_assert(!numeric_limits<_Tp>::is_signed, "");
// All integers <= 2^53 are representable.
return (__x <= (1ull << __DBL_MANT_DIG__))
// Between 2^53 and 2^54 only even numbers are representable.
|| (!(__x & 1) && __detail::__representable_as_double(__x >> 1));
}
// Determine whether x+1 is representable as double.
template<typename _Tp>
constexpr bool
__p1_representable_as_double(_Tp __x) noexcept
{
static_assert(numeric_limits<_Tp>::is_integer, "");
static_assert(!numeric_limits<_Tp>::is_signed, "");
return numeric_limits<_Tp>::digits < __DBL_MANT_DIG__
|| (bool(__x + 1u) // return false if x+1 wraps around to zero
&& __detail::__representable_as_double(__x + 1u));
}
}
template<typename _RandomNumberEngine, size_t __k>
typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
shuffle_order_engine<_RandomNumberEngine, __k>::
operator()()
{
constexpr result_type __range = max() - min();
size_t __j = __k;
const result_type __y = _M_y - min();
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wc++17-extensions" // if constexpr
// Avoid using slower long double arithmetic if possible.
if constexpr (__detail::__p1_representable_as_double(__range))
__j *= __y / (__range + 1.0);
else
__j *= __y / (__range + 1.0L);
#pragma GCC diagnostic pop
_M_y = _M_v[__j];
_M_v[__j] = _M_b();
return _M_y;
}
template<typename _RandomNumberEngine, size_t __k,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const shuffle_order_engine<_RandomNumberEngine, __k>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
__os.fill(__space);
__os << __x.base();
for (size_t __i = 0; __i < __k; ++__i)
__os << __space << __x._M_v[__i];
__os << __space << __x._M_y;
__os.flags(__flags);
__os.fill(__fill);
return __os;
}
template<typename _RandomNumberEngine, size_t __k,
typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
shuffle_order_engine<_RandomNumberEngine, __k>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
__is >> __x._M_b;
for (size_t __i = 0; __i < __k; ++__i)
__is >> __x._M_v[__i];
__is >> __x._M_y;
__is.flags(__flags);
return __is;
}
#if __glibcxx_philox_engine // >= C++26
template<typename _UIntType, size_t __w, size_t __n, size_t __r,
_UIntType... __consts>
_UIntType
philox_engine<_UIntType, __w, __n, __r, __consts...>::
_S_mulhi(_UIntType __a, _UIntType __b)
{
using __type = typename __detail::_Select_uint_least_t<__w * 2>::type;
const __type __num = static_cast<__type>(__a) * __b;
return static_cast<_UIntType>(__num >> __w) & max();
}
template<typename _UIntType, size_t __w, size_t __n, size_t __r,
_UIntType... __consts>
_UIntType
philox_engine<_UIntType, __w, __n, __r, __consts...>::
_S_mullo(_UIntType __a, _UIntType __b)
{
return static_cast<_UIntType>((__a * __b) & max());
}
template<typename _UIntType, size_t __w, size_t __n, size_t __r,
_UIntType... __consts>
void
philox_engine<_UIntType, __w, __n, __r, __consts...>::_M_transition()
{
++_M_i;
if (_M_i != __n)
return;
using __type = typename __detail::_Select_uint_least_t<__w * 2>::type;
_M_philox();
if constexpr (__n == 4)
{
__type __uh
= (static_cast<__type>(_M_x[1]) << __w)
| (static_cast<__type>(_M_x[0]) + 1);
__type __lh
= (static_cast<__type>(_M_x[3]) << __w)
| static_cast<__type>(_M_x[2]);
__type __bigMask
= ~__type(0) >> ((sizeof(__type) * __CHAR_BIT__) - (__w * 2));
if ((__uh & __bigMask) == 0)
{
++__lh;
__uh = 0;
}
_M_x[0] = static_cast<_UIntType>(__uh & max());
_M_x[1] = static_cast<_UIntType>((__uh >> (__w)) & max());
_M_x[2] = static_cast<_UIntType>(__lh & max());
_M_x[3] = static_cast<_UIntType>((__lh >> (__w)) & max());
}
else
{
__type __num =
(static_cast<__type>(_M_x[1]) << __w)
| (static_cast<__type>(_M_x[0]) + 1);
_M_x[0] = __num & max();
_M_x[1] = (__num >> __w) & max();
}
_M_i = 0;
}
template<typename _UIntType, size_t __w, size_t __n, size_t __r,
_UIntType... __consts>
void
philox_engine<_UIntType, __w, __n, __r, __consts...>::_M_philox()
{
array<_UIntType, __n> __outputSeq = _M_x;
for (size_t __j = 0; __j < __r; ++__j)
{
array<_UIntType, __n> __intermedSeq{};
if constexpr (__n == 4)
{
__intermedSeq[0] = __outputSeq[2];
__intermedSeq[1] = __outputSeq[1];
__intermedSeq[2] = __outputSeq[0];
__intermedSeq[3] = __outputSeq[3];
}
else
{
__intermedSeq[0] = __outputSeq[0];
__intermedSeq[1] = __outputSeq[1];
}
for (unsigned long __k = 0; __k < (__n/2); ++__k)
{
__outputSeq[2*__k]
= _S_mulhi(__intermedSeq[2*__k], multipliers[__k])
^ (((_M_k[__k] + (__j * round_consts[__k])) & max()))
^ __intermedSeq[2*__k+1];
__outputSeq[(2*__k)+1]
= _S_mullo(__intermedSeq[2*__k], multipliers[__k]);
}
}
_M_y = __outputSeq;
}
template<typename _UIntType, size_t __w, size_t __n, size_t __r,
_UIntType... __consts>
template<typename _Sseq>
void
philox_engine<_UIntType, __w, __n, __r, __consts...>::seed(_Sseq& __q)
requires __is_seed_seq<_Sseq>
{
seed(0);
const unsigned __p = 1 + ((__w - 1) / 32);
uint_least32_t __tmpArr[(__n/2) * __p];
__q.generate(__tmpArr + 0, __tmpArr + ((__n/2) * __p));
for (unsigned __k = 0; __k < (__n/2); ++__k)
{
unsigned long long __precalc = 0;
for (unsigned __j = 0; __j < __p; ++__j)
{
unsigned long long __multiplicand = (1ull << (32 * __j));
__precalc += (__tmpArr[__k * __p + __j] * __multiplicand) & max();
}
_M_k[__k] = __precalc;
}
}
#endif // philox_engine
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const uniform_int_distribution<_IntType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os << __x.a() << __space << __x.b();
__os.flags(__flags);
__os.fill(__fill);
return __os;
}
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
uniform_int_distribution<_IntType>& __x)
{
using param_type
= typename uniform_int_distribution<_IntType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_IntType __a, __b;
if (__is >> __a >> __b)
__x.param(param_type(__a, __b));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
uniform_real_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
auto __range = __p.b() - __p.a();
while (__f != __t)
*__f++ = __aurng() * __range + __p.a();
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const uniform_real_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.a() << __space << __x.b();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
uniform_real_distribution<_RealType>& __x)
{
using param_type
= typename uniform_real_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::skipws);
_RealType __a, __b;
if (__is >> __a >> __b)
__x.param(param_type(__a, __b));
__is.flags(__flags);
return __is;
}
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::bernoulli_distribution::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
auto __limit = __p.p() * (__aurng.max() - __aurng.min());
while (__f != __t)
*__f++ = (__aurng() - __aurng.min()) < __limit;
}
template<typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const bernoulli_distribution& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__os.widen(' '));
__os.precision(std::numeric_limits<double>::max_digits10);
__os << __x.p();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename geometric_distribution<_IntType>::result_type
geometric_distribution<_IntType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
// About the epsilon thing see this thread:
// http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
const double __naf =
(1 - std::numeric_limits<double>::epsilon()) / 2;
// The largest _RealType convertible to _IntType.
const double __thr =
std::numeric_limits<_IntType>::max() + __naf;
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
double __cand;
do
__cand = std::floor(std::log(1.0 - __aurng()) / __param._M_log_1_p);
while (__cand >= __thr);
return result_type(__cand + __naf);
}
template<typename _IntType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
geometric_distribution<_IntType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
// About the epsilon thing see this thread:
// http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
const double __naf =
(1 - std::numeric_limits<double>::epsilon()) / 2;
// The largest _RealType convertible to _IntType.
const double __thr =
std::numeric_limits<_IntType>::max() + __naf;
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
while (__f != __t)
{
double __cand;
do
__cand = std::floor(std::log(1.0 - __aurng())
/ __param._M_log_1_p);
while (__cand >= __thr);
*__f++ = __cand + __naf;
}
}
template<typename _IntType,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const geometric_distribution<_IntType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__os.widen(' '));
__os.precision(std::numeric_limits<double>::max_digits10);
__os << __x.p();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _IntType,
typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
geometric_distribution<_IntType>& __x)
{
using param_type = typename geometric_distribution<_IntType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::skipws);
double __p;
if (__is >> __p)
__x.param(param_type(__p));
__is.flags(__flags);
return __is;
}
// This is Leger's algorithm, also in Devroye, Ch. X, Example 1.5.
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename negative_binomial_distribution<_IntType>::result_type
negative_binomial_distribution<_IntType>::
operator()(_UniformRandomNumberGenerator& __urng)
{
const double __y = _M_gd(__urng);
// XXX Is the constructor too slow?
std::poisson_distribution<result_type> __poisson(__y);
return __poisson(__urng);
}
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename negative_binomial_distribution<_IntType>::result_type
negative_binomial_distribution<_IntType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
typedef typename std::gamma_distribution<double>::param_type
param_type;
const double __y =
_M_gd(__urng, param_type(__p.k(), (1.0 - __p.p()) / __p.p()));
std::poisson_distribution<result_type> __poisson(__y);
return __poisson(__urng);
}
template<typename _IntType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
negative_binomial_distribution<_IntType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
while (__f != __t)
{
const double __y = _M_gd(__urng);
// XXX Is the constructor too slow?
std::poisson_distribution<result_type> __poisson(__y);
*__f++ = __poisson(__urng);
}
}
template<typename _IntType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
negative_binomial_distribution<_IntType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
typename std::gamma_distribution<result_type>::param_type
__p2(__p.k(), (1.0 - __p.p()) / __p.p());
while (__f != __t)
{
const double __y = _M_gd(__urng, __p2);
std::poisson_distribution<result_type> __poisson(__y);
*__f++ = __poisson(__urng);
}
}
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const negative_binomial_distribution<_IntType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__os.widen(' '));
__os.precision(std::numeric_limits<double>::max_digits10);
__os << __x.k() << __space << __x.p()
<< __space << __x._M_gd;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
negative_binomial_distribution<_IntType>& __x)
{
using param_type
= typename negative_binomial_distribution<_IntType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::skipws);
_IntType __k;
double __p;
if (__is >> __k >> __p >> __x._M_gd)
__x.param(param_type(__k, __p));
__is.flags(__flags);
return __is;
}
template<typename _IntType>
void
poisson_distribution<_IntType>::param_type::
_M_initialize()
{
#if _GLIBCXX_USE_C99_MATH_FUNCS
if (_M_mean >= 12)
{
const double __m = std::floor(_M_mean);
_M_lm_thr = std::log(_M_mean);
_M_lfm = std::lgamma(__m + 1);
_M_sm = std::sqrt(__m);
const double __pi_4 = 0.7853981633974483096156608458198757L;
const double __dx = std::sqrt(2 * __m * std::log(32 * __m
/ __pi_4));
_M_d = std::round(std::max<double>(6.0, std::min(__m, __dx)));
const double __cx = 2 * __m + _M_d;
_M_scx = std::sqrt(__cx / 2);
_M_1cx = 1 / __cx;
_M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
_M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2))
/ _M_d;
}
else
#endif
_M_lm_thr = std::exp(-_M_mean);
}
/**
* A rejection algorithm when mean >= 12 and a simple method based
* upon the multiplication of uniform random variates otherwise.
* NB: The former is available only if _GLIBCXX_USE_C99_MATH_FUNCS
* is defined.
*
* Reference:
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
* New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
*/
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename poisson_distribution<_IntType>::result_type
poisson_distribution<_IntType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
#if _GLIBCXX_USE_C99_MATH_FUNCS
if (__param.mean() >= 12)
{
double __x;
// See comments above...
const double __naf =
(1 - std::numeric_limits<double>::epsilon()) / 2;
const double __thr =
std::numeric_limits<_IntType>::max() + __naf;
const double __m = std::floor(__param.mean());
// sqrt(pi / 2)
const double __spi_2 = 1.2533141373155002512078826424055226L;
const double __c1 = __param._M_sm * __spi_2;
const double __c2 = __param._M_c2b + __c1;
const double __c3 = __c2 + 1;
const double __c4 = __c3 + 1;
// 1 / 78
const double __178 = 0.0128205128205128205128205128205128L;
// e^(1 / 78)
const double __e178 = 1.0129030479320018583185514777512983L;
const double __c5 = __c4 + __e178;
const double __c = __param._M_cb + __c5;
const double __2cx = 2 * (2 * __m + __param._M_d);
bool __reject = true;
do
{
const double __u = __c * __aurng();
const double __e = -std::log(1.0 - __aurng());
double __w = 0.0;
if (__u <= __c1)
{
const double __n = _M_nd(__urng);
const double __y = -std::abs(__n) * __param._M_sm - 1;
__x = std::floor(__y);
__w = -__n * __n / 2;
if (__x < -__m)
continue;
}
else if (__u <= __c2)
{
const double __n = _M_nd(__urng);
const double __y = 1 + std::abs(__n) * __param._M_scx;
__x = std::ceil(__y);
__w = __y * (2 - __y) * __param._M_1cx;
if (__x > __param._M_d)
continue;
}
else if (__u <= __c3)
// NB: This case not in the book, nor in the Errata,
// but should be ok...
__x = -1;
else if (__u <= __c4)
__x = 0;
else if (__u <= __c5)
{
__x = 1;
// Only in the Errata, see libstdc++/83237.
__w = __178;
}
else
{
const double __v = -std::log(1.0 - __aurng());
const double __y = __param._M_d
+ __v * __2cx / __param._M_d;
__x = std::ceil(__y);
__w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
}
__reject = (__w - __e - __x * __param._M_lm_thr
> __param._M_lfm - std::lgamma(__x + __m + 1));
__reject |= __x + __m >= __thr;
} while (__reject);
return result_type(__x + __m + __naf);
}
else
#endif
{
_IntType __x = 0;
double __prod = 1.0;
do
{
__prod *= __aurng();
__x += 1;
}
while (__prod > __param._M_lm_thr);
return __x - 1;
}
}
template<typename _IntType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
poisson_distribution<_IntType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
// We could duplicate everything from operator()...
while (__f != __t)
*__f++ = this->operator()(__urng, __param);
}
template<typename _IntType,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const poisson_distribution<_IntType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<double>::max_digits10);
__os << __x.mean() << __space << __x._M_nd;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _IntType,
typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
poisson_distribution<_IntType>& __x)
{
using param_type = typename poisson_distribution<_IntType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::skipws);
double __mean;
if (__is >> __mean >> __x._M_nd)
__x.param(param_type(__mean));
__is.flags(__flags);
return __is;
}
template<typename _IntType>
void
binomial_distribution<_IntType>::param_type::
_M_initialize()
{
const double __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
_M_easy = true;
#if _GLIBCXX_USE_C99_MATH_FUNCS
if (_M_t * __p12 >= 8)
{
_M_easy = false;
const double __np = std::floor(_M_t * __p12);
const double __pa = __np / _M_t;
const double __1p = 1 - __pa;
const double __pi_4 = 0.7853981633974483096156608458198757L;
const double __d1x =
std::sqrt(__np * __1p * std::log(32 * __np
/ (81 * __pi_4 * __1p)));
_M_d1 = std::round(std::max<double>(1.0, __d1x));
const double __d2x =
std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
/ (__pi_4 * __pa)));
_M_d2 = std::round(std::max<double>(1.0, __d2x));
// sqrt(pi / 2)
const double __spi_2 = 1.2533141373155002512078826424055226L;
_M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
_M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * (_M_t * __1p)));
_M_c = 2 * _M_d1 / __np;
_M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
const double __a12 = _M_a1 + _M_s2 * __spi_2;
const double __s1s = _M_s1 * _M_s1;
_M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
* 2 * __s1s / _M_d1
* std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
const double __s2s = _M_s2 * _M_s2;
_M_s = (_M_a123 + 2 * __s2s / _M_d2
* std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
_M_lf = (std::lgamma(__np + 1)
+ std::lgamma(_M_t - __np + 1));
_M_lp1p = std::log(__pa / __1p);
_M_q = -std::log(1 - (__p12 - __pa) / __1p);
}
else
#endif
_M_q = -std::log(1 - __p12);
}
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename binomial_distribution<_IntType>::result_type
binomial_distribution<_IntType>::
_M_waiting(_UniformRandomNumberGenerator& __urng,
_IntType __t, double __q)
{
_IntType __x = 0;
double __sum = 0.0;
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
do
{
if (__t == __x)
return __x;
const double __e = -std::log(1.0 - __aurng());
__sum += __e / (__t - __x);
__x += 1;
}
while (__sum <= __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_FUNCS
* is defined.
*
* Reference:
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
* New York, 1986, Ch. X, Sect. 4 (+ Errata!).
*/
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename binomial_distribution<_IntType>::result_type
binomial_distribution<_IntType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
result_type __ret;
const _IntType __t = __param.t();
const double __p = __param.p();
const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
#if _GLIBCXX_USE_C99_MATH_FUNCS
if (!__param._M_easy)
{
double __x;
// See comments above...
const double __naf =
(1 - std::numeric_limits<double>::epsilon()) / 2;
const double __thr =
std::numeric_limits<_IntType>::max() + __naf;
const double __np = std::floor(__t * __p12);
// sqrt(pi / 2)
const double __spi_2 = 1.2533141373155002512078826424055226L;
const double __a1 = __param._M_a1;
const double __a12 = __a1 + __param._M_s2 * __spi_2;
const double __a123 = __param._M_a123;
const double __s1s = __param._M_s1 * __param._M_s1;
const double __s2s = __param._M_s2 * __param._M_s2;
bool __reject;
do
{
const double __u = __param._M_s * __aurng();
double __v;
if (__u <= __a1)
{
const double __n = _M_nd(__urng);
const double __y = __param._M_s1 * std::abs(__n);
__reject = __y >= __param._M_d1;
if (!__reject)
{
const double __e = -std::log(1.0 - __aurng());
__x = std::floor(__y);
__v = -__e - __n * __n / 2 + __param._M_c;
}
}
else if (__u <= __a12)
{
const double __n = _M_nd(__urng);
const double __y = __param._M_s2 * std::abs(__n);
__reject = __y >= __param._M_d2;
if (!__reject)
{
const double __e = -std::log(1.0 - __aurng());
__x = std::floor(-__y);
__v = -__e - __n * __n / 2;
}
}
else if (__u <= __a123)
{
const double __e1 = -std::log(1.0 - __aurng());
const double __e2 = -std::log(1.0 - __aurng());
const double __y = __param._M_d1
+ 2 * __s1s * __e1 / __param._M_d1;
__x = std::floor(__y);
__v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
-__y / (2 * __s1s)));
__reject = false;
}
else
{
const double __e1 = -std::log(1.0 - __aurng());
const double __e2 = -std::log(1.0 - __aurng());
const double __y = __param._M_d2
+ 2 * __s2s * __e1 / __param._M_d2;
__x = std::floor(-__y);
__v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
__reject = false;
}
__reject = __reject || __x < -__np || __x > __t - __np;
if (!__reject)
{
const double __lfx =
std::lgamma(__np + __x + 1)
+ std::lgamma(__t - (__np + __x) + 1);
__reject = __v > __param._M_lf - __lfx
+ __x * __param._M_lp1p;
}
__reject |= __x + __np >= __thr;
}
while (__reject);
__x += __np + __naf;
const _IntType __z = _M_waiting(__urng, __t - _IntType(__x),
__param._M_q);
__ret = _IntType(__x) + __z;
}
else
#endif
__ret = _M_waiting(__urng, __t, __param._M_q);
if (__p12 != __p)
__ret = __t - __ret;
return __ret;
}
template<typename _IntType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
binomial_distribution<_IntType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
// We could duplicate everything from operator()...
while (__f != __t)
*__f++ = this->operator()(__urng, __param);
}
template<typename _IntType,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const binomial_distribution<_IntType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<double>::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 _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
binomial_distribution<_IntType>& __x)
{
using param_type = typename binomial_distribution<_IntType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_IntType __t;
double __p;
if (__is >> __t >> __p >> __x._M_nd)
__x.param(param_type(__t, __p));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::exponential_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
while (__f != __t)
*__f++ = -std::log(result_type(1) - __aurng()) / __p.lambda();
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const exponential_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__os.widen(' '));
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.lambda();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
exponential_distribution<_RealType>& __x)
{
using param_type
= typename exponential_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __lambda;
if (__is >> __lambda)
__x.param(param_type(__lambda));
__is.flags(__flags);
return __is;
}
/**
* Polar method due to Marsaglia.
*
* Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
* New York, 1986, Ch. V, Sect. 4.4.
*/
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename normal_distribution<_RealType>::result_type
normal_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
result_type __ret;
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
if (_M_saved_available)
{
_M_saved_available = false;
__ret = _M_saved;
}
else
{
result_type __x, __y, __r2;
do
{
__x = result_type(2.0) * __aurng() - 1.0;
__y = result_type(2.0) * __aurng() - 1.0;
__r2 = __x * __x + __y * __y;
}
while (__r2 > 1.0 || __r2 == 0.0);
const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
_M_saved = __x * __mult;
_M_saved_available = true;
__ret = __y * __mult;
}
__ret = __ret * __param.stddev() + __param.mean();
return __ret;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
normal_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
if (__f == __t)
return;
if (_M_saved_available)
{
_M_saved_available = false;
*__f++ = _M_saved * __param.stddev() + __param.mean();
if (__f == __t)
return;
}
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
while (__f + 1 < __t)
{
result_type __x, __y, __r2;
do
{
__x = result_type(2.0) * __aurng() - 1.0;
__y = result_type(2.0) * __aurng() - 1.0;
__r2 = __x * __x + __y * __y;
}
while (__r2 > 1.0 || __r2 == 0.0);
const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
*__f++ = __y * __mult * __param.stddev() + __param.mean();
*__f++ = __x * __mult * __param.stddev() + __param.mean();
}
if (__f != __t)
{
result_type __x, __y, __r2;
do
{
__x = result_type(2.0) * __aurng() - 1.0;
__y = result_type(2.0) * __aurng() - 1.0;
__r2 = __x * __x + __y * __y;
}
while (__r2 > 1.0 || __r2 == 0.0);
const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
_M_saved = __x * __mult;
_M_saved_available = true;
*__f = __y * __mult * __param.stddev() + __param.mean();
}
}
template<typename _RealType>
bool
operator==(const std::normal_distribution<_RealType>& __d1,
const std::normal_distribution<_RealType>& __d2)
{
if (__d1._M_param == __d2._M_param
&& __d1._M_saved_available == __d2._M_saved_available)
return __d1._M_saved_available ? __d1._M_saved == __d2._M_saved : true;
else
return false;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const normal_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.mean() << __space << __x.stddev()
<< __space << __x._M_saved_available;
if (__x._M_saved_available)
__os << __space << __x._M_saved;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
normal_distribution<_RealType>& __x)
{
using param_type = typename normal_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
double __mean, __stddev;
bool __saved_avail;
if (__is >> __mean >> __stddev >> __saved_avail)
{
if (!__saved_avail || (__is >> __x._M_saved))
{
__x._M_saved_available = __saved_avail;
__x.param(param_type(__mean, __stddev));
}
}
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
lognormal_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
while (__f != __t)
*__f++ = std::exp(__p.s() * _M_nd(__urng) + __p.m());
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const lognormal_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.m() << __space << __x.s()
<< __space << __x._M_nd;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
lognormal_distribution<_RealType>& __x)
{
using param_type
= typename lognormal_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __m, __s;
if (__is >> __m >> __s >> __x._M_nd)
__x.param(param_type(__m, __s));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::chi_squared_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
while (__f != __t)
*__f++ = 2 * _M_gd(__urng);
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::chi_squared_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const typename
std::gamma_distribution<result_type>::param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
while (__f != __t)
*__f++ = 2 * _M_gd(__urng, __p);
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const chi_squared_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.n() << __space << __x._M_gd;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
chi_squared_distribution<_RealType>& __x)
{
using param_type
= typename chi_squared_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __n;
if (__is >> __n >> __x._M_gd)
__x.param(param_type(__n));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename cauchy_distribution<_RealType>::result_type
cauchy_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
_RealType __u;
do
__u = __aurng();
while (__u == 0.5);
const _RealType __pi = 3.1415926535897932384626433832795029L;
return __p.a() + __p.b() * std::tan(__pi * __u);
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
cauchy_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
const _RealType __pi = 3.1415926535897932384626433832795029L;
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
while (__f != __t)
{
_RealType __u;
do
__u = __aurng();
while (__u == 0.5);
*__f++ = __p.a() + __p.b() * std::tan(__pi * __u);
}
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const cauchy_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.a() << __space << __x.b();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
cauchy_distribution<_RealType>& __x)
{
using param_type = typename cauchy_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __a, __b;
if (__is >> __a >> __b)
__x.param(param_type(__a, __b));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::fisher_f_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
while (__f != __t)
*__f++ = ((_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()));
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::fisher_f_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
typedef typename std::gamma_distribution<result_type>::param_type
param_type;
param_type __p1(__p.m() / 2);
param_type __p2(__p.n() / 2);
while (__f != __t)
*__f++ = ((_M_gd_x(__urng, __p1) * n())
/ (_M_gd_y(__urng, __p2) * m()));
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const fisher_f_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.m() << __space << __x.n()
<< __space << __x._M_gd_x << __space << __x._M_gd_y;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
fisher_f_distribution<_RealType>& __x)
{
using param_type
= typename fisher_f_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __m, __n;
if (__is >> __m >> __n >> __x._M_gd_x >> __x._M_gd_y)
__x.param(param_type(__m, __n));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::student_t_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
while (__f != __t)
*__f++ = _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng));
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
std::student_t_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
typename std::gamma_distribution<result_type>::param_type
__p2(__p.n() / 2, 2);
while (__f != __t)
*__f++ = _M_nd(__urng) * std::sqrt(__p.n() / _M_gd(__urng, __p2));
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const student_t_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.n() << __space << __x._M_nd << __space << __x._M_gd;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
student_t_distribution<_RealType>& __x)
{
using param_type
= typename student_t_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __n;
if (__is >> __n >> __x._M_nd >> __x._M_gd)
__x.param(param_type(__n));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
void
gamma_distribution<_RealType>::param_type::
_M_initialize()
{
_M_malpha = _M_alpha < 1.0 ? _M_alpha + _RealType(1.0) : _M_alpha;
const _RealType __a1 = _M_malpha - _RealType(1.0) / _RealType(3.0);
_M_a2 = _RealType(1.0) / std::sqrt(_RealType(9.0) * __a1);
}
/**
* Marsaglia, G. and Tsang, W. W.
* "A Simple Method for Generating Gamma Variables"
* ACM Transactions on Mathematical Software, 26, 3, 363-372, 2000.
*/
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename gamma_distribution<_RealType>::result_type
gamma_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
result_type __u, __v, __n;
const result_type __a1 = (__param._M_malpha
- _RealType(1.0) / _RealType(3.0));
do
{
do
{
__n = _M_nd(__urng);
__v = result_type(1.0) + __param._M_a2 * __n;
}
while (__v <= 0.0);
__v = __v * __v * __v;
__u = __aurng();
}
while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
&& (std::log(__u) > (0.5 * __n * __n + __a1
* (1.0 - __v + std::log(__v)))));
if (__param.alpha() == __param._M_malpha)
return __a1 * __v * __param.beta();
else
{
do
__u = __aurng();
while (__u == 0.0);
return (std::pow(__u, result_type(1.0) / __param.alpha())
* __a1 * __v * __param.beta());
}
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
gamma_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
result_type __u, __v, __n;
const result_type __a1 = (__param._M_malpha
- _RealType(1.0) / _RealType(3.0));
if (__param.alpha() == __param._M_malpha)
while (__f != __t)
{
do
{
do
{
__n = _M_nd(__urng);
__v = result_type(1.0) + __param._M_a2 * __n;
}
while (__v <= 0.0);
__v = __v * __v * __v;
__u = __aurng();
}
while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
&& (std::log(__u) > (0.5 * __n * __n + __a1
* (1.0 - __v + std::log(__v)))));
*__f++ = __a1 * __v * __param.beta();
}
else
while (__f != __t)
{
do
{
do
{
__n = _M_nd(__urng);
__v = result_type(1.0) + __param._M_a2 * __n;
}
while (__v <= 0.0);
__v = __v * __v * __v;
__u = __aurng();
}
while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
&& (std::log(__u) > (0.5 * __n * __n + __a1
* (1.0 - __v + std::log(__v)))));
do
__u = __aurng();
while (__u == 0.0);
*__f++ = (std::pow(__u, result_type(1.0) / __param.alpha())
* __a1 * __v * __param.beta());
}
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const gamma_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.alpha() << __space << __x.beta()
<< __space << __x._M_nd;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
gamma_distribution<_RealType>& __x)
{
using param_type = typename gamma_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __alpha_val, __beta_val;
if (__is >> __alpha_val >> __beta_val >> __x._M_nd)
__x.param(param_type(__alpha_val, __beta_val));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename weibull_distribution<_RealType>::result_type
weibull_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
return __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
result_type(1) / __p.a());
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
weibull_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
auto __inv_a = result_type(1) / __p.a();
while (__f != __t)
*__f++ = __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
__inv_a);
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const weibull_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.a() << __space << __x.b();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
weibull_distribution<_RealType>& __x)
{
using param_type = typename weibull_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __a, __b;
if (__is >> __a >> __b)
__x.param(param_type(__a, __b));
__is.flags(__flags);
return __is;
}
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename extreme_value_distribution<_RealType>::result_type
extreme_value_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
return __p.a() - __p.b() * std::log(-std::log(result_type(1)
- __aurng()));
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
extreme_value_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
while (__f != __t)
*__f++ = __p.a() - __p.b() * std::log(-std::log(result_type(1)
- __aurng()));
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const extreme_value_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
__os << __x.a() << __space << __x.b();
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
extreme_value_distribution<_RealType>& __x)
{
using param_type
= typename extreme_value_distribution<_RealType>::param_type;
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
_RealType __a, __b;
if (__is >> __a >> __b)
__x.param(param_type(__a, __b));
__is.flags(__flags);
return __is;
}
template<typename _IntType>
void
discrete_distribution<_IntType>::param_type::
_M_initialize()
{
if (_M_prob.size() < 2)
{
_M_prob.clear();
return;
}
const double __sum = std::accumulate(_M_prob.begin(),
_M_prob.end(), 0.0);
__glibcxx_assert(__sum > 0);
// Now normalize the probabilites.
__detail::__normalize(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
__sum);
// Accumulate partial sums.
_M_cp.reserve(_M_prob.size());
std::partial_sum(_M_prob.begin(), _M_prob.end(),
std::back_inserter(_M_cp));
// Make sure the last cumulative probability is one.
_M_cp[_M_cp.size() - 1] = 1.0;
}
template<typename _IntType>
template<typename _Func>
discrete_distribution<_IntType>::param_type::
param_type(size_t __nw, double __xmin, double __xmax, _Func __fw)
: _M_prob(), _M_cp()
{
const size_t __n = __nw == 0 ? 1 : __nw;
const double __delta = (__xmax - __xmin) / __n;
_M_prob.reserve(__n);
for (size_t __k = 0; __k < __nw; ++__k)
_M_prob.push_back(__fw(__xmin + __k * __delta + 0.5 * __delta));
_M_initialize();
}
template<typename _IntType>
template<typename _UniformRandomNumberGenerator>
typename discrete_distribution<_IntType>::result_type
discrete_distribution<_IntType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
if (__param._M_cp.empty())
return result_type(0);
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
const double __p = __aurng();
auto __pos = std::lower_bound(__param._M_cp.begin(),
__param._M_cp.end(), __p);
return __pos - __param._M_cp.begin();
}
template<typename _IntType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
discrete_distribution<_IntType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
if (__param._M_cp.empty())
{
while (__f != __t)
*__f++ = result_type(0);
return;
}
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
while (__f != __t)
{
const double __p = __aurng();
auto __pos = std::lower_bound(__param._M_cp.begin(),
__param._M_cp.end(), __p);
*__f++ = __pos - __param._M_cp.begin();
}
}
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const discrete_distribution<_IntType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<double>::max_digits10);
std::vector<double> __prob = __x.probabilities();
__os << __prob.size();
for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
__os << __space << *__dit;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
namespace __detail
{
template<typename _ValT, typename _CharT, typename _Traits>
basic_istream<_CharT, _Traits>&
__extract_params(basic_istream<_CharT, _Traits>& __is,
vector<_ValT>& __vals, size_t __n)
{
__vals.reserve(__n);
while (__n--)
{
_ValT __val;
if (__is >> __val)
__vals.push_back(__val);
else
break;
}
return __is;
}
} // namespace __detail
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
discrete_distribution<_IntType>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
size_t __n;
if (__is >> __n)
{
std::vector<double> __prob_vec;
if (__detail::__extract_params(__is, __prob_vec, __n))
__x.param({__prob_vec.begin(), __prob_vec.end()});
}
__is.flags(__flags);
return __is;
}
template<typename _RealType>
void
piecewise_constant_distribution<_RealType>::param_type::
_M_initialize()
{
if (_M_int.size() < 2
|| (_M_int.size() == 2
&& _M_int[0] == _RealType(0)
&& _M_int[1] == _RealType(1)))
{
_M_int.clear();
_M_den.clear();
return;
}
const double __sum = std::accumulate(_M_den.begin(),
_M_den.end(), 0.0);
__glibcxx_assert(__sum > 0);
__detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
__sum);
_M_cp.reserve(_M_den.size());
std::partial_sum(_M_den.begin(), _M_den.end(),
std::back_inserter(_M_cp));
// Make sure the last cumulative probability is one.
_M_cp[_M_cp.size() - 1] = 1.0;
for (size_t __k = 0; __k < _M_den.size(); ++__k)
_M_den[__k] /= _M_int[__k + 1] - _M_int[__k];
}
template<typename _RealType>
template<typename _InputIteratorB, typename _InputIteratorW>
piecewise_constant_distribution<_RealType>::param_type::
param_type(_InputIteratorB __bbegin,
_InputIteratorB __bend,
_InputIteratorW __wbegin)
: _M_int(), _M_den(), _M_cp()
{
if (__bbegin != __bend)
{
for (;;)
{
_M_int.push_back(*__bbegin);
++__bbegin;
if (__bbegin == __bend)
break;
_M_den.push_back(*__wbegin);
++__wbegin;
}
}
_M_initialize();
}
template<typename _RealType>
template<typename _Func>
piecewise_constant_distribution<_RealType>::param_type::
param_type(initializer_list<_RealType> __bl, _Func __fw)
: _M_int(), _M_den(), _M_cp()
{
_M_int.reserve(__bl.size());
for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
_M_int.push_back(*__biter);
_M_den.reserve(_M_int.size() - 1);
for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
_M_den.push_back(__fw(0.5 * (_M_int[__k + 1] + _M_int[__k])));
_M_initialize();
}
template<typename _RealType>
template<typename _Func>
piecewise_constant_distribution<_RealType>::param_type::
param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
: _M_int(), _M_den(), _M_cp()
{
const size_t __n = __nw == 0 ? 1 : __nw;
const _RealType __delta = (__xmax - __xmin) / __n;
_M_int.reserve(__n + 1);
for (size_t __k = 0; __k <= __nw; ++__k)
_M_int.push_back(__xmin + __k * __delta);
_M_den.reserve(__n);
for (size_t __k = 0; __k < __nw; ++__k)
_M_den.push_back(__fw(_M_int[__k] + 0.5 * __delta));
_M_initialize();
}
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename piecewise_constant_distribution<_RealType>::result_type
piecewise_constant_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
const double __p = __aurng();
if (__param._M_cp.empty())
return __p;
auto __pos = std::lower_bound(__param._M_cp.begin(),
__param._M_cp.end(), __p);
const size_t __i = __pos - __param._M_cp.begin();
const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
return __param._M_int[__i] + (__p - __pref) / __param._M_den[__i];
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
piecewise_constant_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
if (__param._M_cp.empty())
{
while (__f != __t)
*__f++ = __aurng();
return;
}
while (__f != __t)
{
const double __p = __aurng();
auto __pos = std::lower_bound(__param._M_cp.begin(),
__param._M_cp.end(), __p);
const size_t __i = __pos - __param._M_cp.begin();
const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
*__f++ = (__param._M_int[__i]
+ (__p - __pref) / __param._M_den[__i]);
}
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const piecewise_constant_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
std::vector<_RealType> __int = __x.intervals();
__os << __int.size() - 1;
for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
__os << __space << *__xit;
std::vector<double> __den = __x.densities();
for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
__os << __space << *__dit;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
piecewise_constant_distribution<_RealType>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
size_t __n;
if (__is >> __n)
{
std::vector<_RealType> __int_vec;
if (__detail::__extract_params(__is, __int_vec, __n + 1))
{
std::vector<double> __den_vec;
if (__detail::__extract_params(__is, __den_vec, __n))
{
__x.param({ __int_vec.begin(), __int_vec.end(),
__den_vec.begin() });
}
}
}
__is.flags(__flags);
return __is;
}
template<typename _RealType>
void
piecewise_linear_distribution<_RealType>::param_type::
_M_initialize()
{
if (_M_int.size() < 2
|| (_M_int.size() == 2
&& _M_int[0] == _RealType(0)
&& _M_int[1] == _RealType(1)
&& _M_den[0] == _M_den[1]))
{
_M_int.clear();
_M_den.clear();
return;
}
double __sum = 0.0;
_M_cp.reserve(_M_int.size() - 1);
_M_m.reserve(_M_int.size() - 1);
for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
{
const _RealType __delta = _M_int[__k + 1] - _M_int[__k];
__sum += 0.5 * (_M_den[__k + 1] + _M_den[__k]) * __delta;
_M_cp.push_back(__sum);
_M_m.push_back((_M_den[__k + 1] - _M_den[__k]) / __delta);
}
__glibcxx_assert(__sum > 0);
// Now normalize the densities...
__detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
__sum);
// ... and partial sums...
__detail::__normalize(_M_cp.begin(), _M_cp.end(), _M_cp.begin(), __sum);
// ... and slopes.
__detail::__normalize(_M_m.begin(), _M_m.end(), _M_m.begin(), __sum);
// Make sure the last cumulative probablility is one.
_M_cp[_M_cp.size() - 1] = 1.0;
}
template<typename _RealType>
template<typename _InputIteratorB, typename _InputIteratorW>
piecewise_linear_distribution<_RealType>::param_type::
param_type(_InputIteratorB __bbegin,
_InputIteratorB __bend,
_InputIteratorW __wbegin)
: _M_int(), _M_den(), _M_cp(), _M_m()
{
for (; __bbegin != __bend; ++__bbegin, (void) ++__wbegin)
{
_M_int.push_back(*__bbegin);
_M_den.push_back(*__wbegin);
}
_M_initialize();
}
template<typename _RealType>
template<typename _Func>
piecewise_linear_distribution<_RealType>::param_type::
param_type(initializer_list<_RealType> __bl, _Func __fw)
: _M_int(), _M_den(), _M_cp(), _M_m()
{
_M_int.reserve(__bl.size());
_M_den.reserve(__bl.size());
for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
{
_M_int.push_back(*__biter);
_M_den.push_back(__fw(*__biter));
}
_M_initialize();
}
template<typename _RealType>
template<typename _Func>
piecewise_linear_distribution<_RealType>::param_type::
param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
: _M_int(), _M_den(), _M_cp(), _M_m()
{
const size_t __n = __nw == 0 ? 1 : __nw;
const _RealType __delta = (__xmax - __xmin) / __n;
_M_int.reserve(__n + 1);
_M_den.reserve(__n + 1);
for (size_t __k = 0; __k <= __nw; ++__k)
{
_M_int.push_back(__xmin + __k * __delta);
_M_den.push_back(__fw(_M_int[__k] + __delta));
}
_M_initialize();
}
template<typename _RealType>
template<typename _UniformRandomNumberGenerator>
typename piecewise_linear_distribution<_RealType>::result_type
piecewise_linear_distribution<_RealType>::
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, double>
__aurng(__urng);
const double __p = __aurng();
if (__param._M_cp.empty())
return __p;
auto __pos = std::lower_bound(__param._M_cp.begin(),
__param._M_cp.end(), __p);
const size_t __i = __pos - __param._M_cp.begin();
const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
const double __a = 0.5 * __param._M_m[__i];
const double __b = __param._M_den[__i];
const double __cm = __p - __pref;
_RealType __x = __param._M_int[__i];
if (__a == 0)
__x += __cm / __b;
else
{
const double __d = __b * __b + 4.0 * __a * __cm;
__x += 0.5 * (std::sqrt(__d) - __b) / __a;
}
return __x;
}
template<typename _RealType>
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
piecewise_linear_distribution<_RealType>::
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __param)
{
__glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
// We could duplicate everything from operator()...
while (__f != __t)
*__f++ = this->operator()(__urng, __param);
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const piecewise_linear_distribution<_RealType>& __x)
{
using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __os.flags();
const _CharT __fill = __os.fill();
const std::streamsize __precision = __os.precision();
const _CharT __space = __os.widen(' ');
__os.flags(__ios_base::scientific | __ios_base::left);
__os.fill(__space);
__os.precision(std::numeric_limits<_RealType>::max_digits10);
std::vector<_RealType> __int = __x.intervals();
__os << __int.size() - 1;
for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
__os << __space << *__xit;
std::vector<double> __den = __x.densities();
for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
__os << __space << *__dit;
__os.flags(__flags);
__os.fill(__fill);
__os.precision(__precision);
return __os;
}
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
piecewise_linear_distribution<_RealType>& __x)
{
using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
const typename __ios_base::fmtflags __flags = __is.flags();
__is.flags(__ios_base::dec | __ios_base::skipws);
size_t __n;
if (__is >> __n)
{
vector<_RealType> __int_vec;
if (__detail::__extract_params(__is, __int_vec, __n + 1))
{
vector<double> __den_vec;
if (__detail::__extract_params(__is, __den_vec, __n + 1))
{
__x.param({ __int_vec.begin(), __int_vec.end(),
__den_vec.begin() });
}
}
}
__is.flags(__flags);
return __is;
}
template<typename _IntType, typename>
seed_seq::seed_seq(std::initializer_list<_IntType> __il)
{
_M_v.reserve(__il.size());
for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
_M_v.push_back(__detail::__mod<result_type,
__detail::_Shift<result_type, 32>::__value>(*__iter));
}
template<typename _InputIterator>
seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
{
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wc++17-extensions" // if constexpr
if constexpr (__is_random_access_iter<_InputIterator>::value)
_M_v.reserve(std::distance(__begin, __end));
#pragma GCC diagnostic pop
for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
_M_v.push_back(__detail::__mod<result_type,
__detail::_Shift<result_type, 32>::__value>(*__iter));
}
template<typename _RandomAccessIterator>
void
seed_seq::generate(_RandomAccessIterator __begin,
_RandomAccessIterator __end)
{
typedef typename iterator_traits<_RandomAccessIterator>::value_type
_Type;
if (__begin == __end)
return;
std::fill(__begin, __end, _Type(0x8b8b8b8bu));
const size_t __n = __end - __begin;
const size_t __s = _M_v.size();
const size_t __t = (__n >= 623) ? 11
: (__n >= 68) ? 7
: (__n >= 39) ? 5
: (__n >= 7) ? 3
: (__n - 1) / 2;
const size_t __p = (__n - __t) / 2;
const size_t __q = __p + __t;
const size_t __m = std::max(size_t(__s + 1), __n);
#ifndef __UINT32_TYPE__
struct _Up
{
_Up(uint_least32_t v) : _M_v(v & 0xffffffffu) { }
operator uint_least32_t() const { return _M_v; }
uint_least32_t _M_v;
};
using uint32_t = _Up;
#endif
// k == 0, every element in [begin,end) equals 0x8b8b8b8bu
{
uint32_t __r1 = 1371501266u;
uint32_t __r2 = __r1 + __s;
__begin[__p] += __r1;
__begin[__q] = (uint32_t)__begin[__q] + __r2;
__begin[0] = __r2;
}
for (size_t __k = 1; __k <= __s; ++__k)
{
const size_t __kn = __k % __n;
const size_t __kpn = (__k + __p) % __n;
const size_t __kqn = (__k + __q) % __n;
uint32_t __arg = (__begin[__kn]
^ __begin[__kpn]
^ __begin[(__k - 1) % __n]);
uint32_t __r1 = 1664525u * (__arg ^ (__arg >> 27));
uint32_t __r2 = __r1 + (uint32_t)__kn + _M_v[__k - 1];
__begin[__kpn] = (uint32_t)__begin[__kpn] + __r1;
__begin[__kqn] = (uint32_t)__begin[__kqn] + __r2;
__begin[__kn] = __r2;
}
for (size_t __k = __s + 1; __k < __m; ++__k)
{
const size_t __kn = __k % __n;
const size_t __kpn = (__k + __p) % __n;
const size_t __kqn = (__k + __q) % __n;
uint32_t __arg = (__begin[__kn]
^ __begin[__kpn]
^ __begin[(__k - 1) % __n]);
uint32_t __r1 = 1664525u * (__arg ^ (__arg >> 27));
uint32_t __r2 = __r1 + (uint32_t)__kn;
__begin[__kpn] = (uint32_t)__begin[__kpn] + __r1;
__begin[__kqn] = (uint32_t)__begin[__kqn] + __r2;
__begin[__kn] = __r2;
}
for (size_t __k = __m; __k < __m + __n; ++__k)
{
const size_t __kn = __k % __n;
const size_t __kpn = (__k + __p) % __n;
const size_t __kqn = (__k + __q) % __n;
uint32_t __arg = (__begin[__kn]
+ __begin[__kpn]
+ __begin[(__k - 1) % __n]);
uint32_t __r3 = 1566083941u * (__arg ^ (__arg >> 27));
uint32_t __r4 = __r3 - __kn;
__begin[__kpn] ^= __r3;
__begin[__kqn] ^= __r4;
__begin[__kn] = __r4;
}
}
// [rand.util.canonical]
// generate_canonical(RNG&)
#ifndef _GLIBCXX_USE_OLD_GENERATE_CANONICAL
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wc++14-extensions" // for variable templates
#pragma GCC diagnostic ignored "-Wc++17-extensions" // if constexpr
// __generate_canonical_pow2 is used when Urbg::max()-Urbg::min() is
// a power of two less 1. It works by calling urng() as many times as
// needed to fill the target mantissa, accumulating entropy into an
// integer value, converting that to the float type, and then dividing
// by the range of the integer value (a constexpr power of 2,
// so only adjusts the exponent) to produce a result in [0..1].
// In case of an exact 1.0 result, we re-try.
//
// It needs to work even when the integer type used is only as big
// as the float mantissa, such as uint64_t for long double. So,
// commented-out assignments represent computations the Standard
// prescribes but cannot be performed, or are not used. Names are
// chosen to match the description in the Standard.
//
// When the result is close to zero, the strict Standard-prescribed
// calculation may leave more low-order zeros in the mantissa than
// is usually necessary. When spare entropy has been extracted, as
// is usual for float and double, some or all of the spare entropy
// can commonly be pulled into the result for better randomness.
// Defining _GLIBCXX_GENERATE_CANONICAL_STRICT discards it instead.
//
// When k calls to urng() yield more bits of entropy, log2_Rk_max,
// than fit into UInt, we discard some of it by overflowing, which
// is OK. On converting the integer representation of the sample
// to the float value, we must divide out the (possibly-truncated)
// size log2_Rk.
//
// This implementation works with std::bfloat16, which can exactly
// represent 2^32, but not with std::float16_t, limited to 2^15.
template<typename _RealT, size_t __d, typename _Urbg>
_RealT
__generate_canonical_pow2(_Urbg& __urng)
{
using _UInt = typename __detail::_Select_uint_least_t<__d>::type;
// Parameter __d is the actual target number of bits.
// Commented-out assignments below are of values specified in
// the Standard, but not used here for reasons noted.
// r = 2; // Redundant, we only support radix 2.
using _Rng = decltype(_Urbg::max());
const _Rng __rng_range_less_1 = _Urbg::max() - _Urbg::min();
// R = _UInt(__rng_range_less_1) + 1; // May wrap to 0.
const auto __log2_R = __builtin_popcountg(__rng_range_less_1);
const auto __log2_uint_max = sizeof(_UInt) * __CHAR_BIT__;
// rd = _UInt(1) << __d; // Could overflow, UB.
const unsigned __k = (__d + __log2_R - 1) / __log2_R;
const unsigned __log2_Rk_max = __k * __log2_R;
const unsigned __log2_Rk = // Bits of entropy actually obtained:
__log2_uint_max < __log2_Rk_max ? __log2_uint_max : __log2_Rk_max;
// Rk = _UInt(1) << __log2_Rk; // Likely overflows, UB.
_GLIBCXX14_CONSTEXPR const _RealT __Rk
= _RealT(_UInt(1) << (__log2_Rk - 1)) * _RealT(2.0);
#if defined(_GLIBCXX_GENERATE_CANONICAL_STRICT)
const unsigned __log2_x = __log2_Rk - __d; // # of spare entropy bits.
#else
const unsigned __log2_x = 0;
#endif
_GLIBCXX14_CONSTEXPR const _UInt __x = _UInt(1) << __log2_x;
_GLIBCXX14_CONSTEXPR const _RealT __rd = __Rk / _RealT(__x);
// xrd = __x << __d; // Could overflow.
while (true)
{
_UInt __sum = _UInt(__urng() - _Urbg::min());
for (unsigned __i = __k - 1, __shift = 0; __i > 0; --__i)
{
__shift += __log2_R;
__sum |= _UInt(__urng() - _Urbg::min()) << __shift;
}
const _RealT __ret = _RealT(__sum >> __log2_x) / _RealT(__rd);
if (__ret < _RealT(1.0))
return __ret;
}
}
template<typename _UInt>
struct __gen_canon_log_res
{
unsigned __floor_log;
_UInt __floor_pow;
constexpr __gen_canon_log_res
update(_UInt __base) const
{ return {__floor_log + 1, __floor_pow * __base}; }
};
template <typename _UInt1, typename _UInt2,
typename _UComm = __conditional_t<(sizeof(_UInt2) > sizeof(_UInt1)),
_UInt2, _UInt1>>
constexpr __gen_canon_log_res<_UInt1>
__gen_canon_log(_UInt1 __val, _UInt2 __base)
{
#if __cplusplus >= 201402L
__gen_canon_log_res<_UInt1> __res{0, _UInt1(1)};
if (_UComm(__base) > _UComm(__val))
return __res;
const _UInt1 __base1(__base);
do
{
__val /= __base1;
__res = __res.update(__base1);
}
while (__val >= __base1);
return __res;
#else
return (_UComm(__val) >= _UComm(__base))
? __gen_canon_log(__val / _UInt1(__base), _UInt1(__base))
.update(_UInt1(__base))
: __gen_canon_log_res<_UInt1>{0, _UInt1(1)};
#endif
}
// This version must be used when the range of possible RNG results,
// Urbg::max()-Urbg::min(), is not a power of two less one. The UInt
// type passed must be big enough to represent Rk, R^k, a power of R
// (the range of values produced by the rng) up to twice the length
// of the mantissa.
template<typename _RealT, size_t __d, typename _Urbg>
_RealT
__generate_canonical_any(_Urbg& __urng)
{
// Names below are chosen to match the description in the Standard.
// Parameter d is the actual target number of bits.
#if (__cplusplus >= 201402L) || defined(__SIZEOF_INT128__)
# define _GLIBCXX_GEN_CANON_CONST constexpr
#else
# define _GLIBCXX_GEN_CANON_CONST const
#endif
using _UIntR = typename make_unsigned<decltype(_Urbg::max())>::type;
// Cannot overflow, as _Urbg::max() - _Urbg::min() is not power of
// two minus one
constexpr _UIntR __R = _UIntR(_Urbg::max() - _Urbg::min()) + 1;
constexpr unsigned __log2R
= sizeof(_UIntR) * __CHAR_BIT__ - __builtin_clzg(__R) - 1;
// We overstimate number of required bits, by computing
// r such that l * log2(R) >= d, so:
// R^l >= (2 ^ log2(R)) ^ l == 2 ^ (log2(r) * l) >= 2^d
// And then requiring l * bit_width(R) bits.
constexpr unsigned __l = (__d + __log2R - 1) / __log2R;
constexpr unsigned __bits = (__log2R + 1) * __l;
using _UInt = typename __detail::_Select_uint_least_t<__bits>::type;
_GLIBCXX_GEN_CANON_CONST _UInt __rd = _UInt(1) << __d;
_GLIBCXX_GEN_CANON_CONST auto __logRrd = __gen_canon_log(__rd, __R);
_GLIBCXX_GEN_CANON_CONST unsigned __k
= __logRrd.__floor_log + (__rd > __logRrd.__floor_pow);
_GLIBCXX_GEN_CANON_CONST _UInt __Rk
= (__k > __logRrd.__floor_log)
? _UInt(__logRrd.__floor_pow) * _UInt(__R)
: _UInt(__logRrd.__floor_pow);
_GLIBCXX_GEN_CANON_CONST _UInt __x = __Rk / __rd;
while (true)
{
_UInt __Ri{1};
_UInt __sum(__urng() - _Urbg::min());
for (int __i = __k - 1; __i > 0; --__i)
{
__Ri *= _UInt(__R);
__sum += _UInt(__urng() - _Urbg::min()) * __Ri;
}
const _RealT __ret = _RealT(__sum / __x) / _RealT(__rd);
if (__ret < _RealT(1.0))
return __ret;
}
#undef _GLIBCXX_GEN_CANON_CONST
}
#if !defined(_GLIBCXX_GENERATE_CANONICAL_STRICT)
template <typename _Tp>
const bool __is_rand_dist_float_v = is_floating_point<_Tp>::value;
#else
template <typename _Tp> const bool __is_rand_dist_float_v = false;
template <> const bool __is_rand_dist_float_v<float> = true;
template <> const bool __is_rand_dist_float_v<double> = true;
template <> const bool __is_rand_dist_float_v<long double> = true;
#endif
// Note, this works even when (__range + 1) overflows:
template <typename _Rng>
constexpr bool __is_power_of_2_less_1(_Rng __range)
{ return ((__range + 1) & __range) == 0; };
_GLIBCXX_BEGIN_INLINE_ABI_NAMESPACE(_V2)
/** Produce a random floating-point value in the range [0..1)
*
* The result of `std::generate_canonical<RealT,digits>(urng)` is a
* random floating-point value of type `RealT` in the range [0..1),
* using entropy provided by the uniform random bit generator `urng`.
* A value for `digits` may be passed to limit the precision of the
* result to so many bits, but normally `-1u` is passed to get the
* native precision of `RealT`. As many `urng()` calls are made as
* needed to obtain the required entropy. On rare occasions, more
* `urng()` calls are used. It is fastest when the value of
* `Urbg::max()` is a power of two less one, such as from a
* `std::philox4x32` (for `float`) or `philox4x64` (for `double`).
*
* @since C++11
*/
template<typename _RealT, size_t __digits,
typename _Urbg>
_RealT
generate_canonical(_Urbg& __urng)
{
#ifdef __glibcxx_concepts
static_assert(uniform_random_bit_generator<_Urbg>);
#endif
static_assert(__is_rand_dist_float_v<_RealT>,
"template argument must be a floating point type");
static_assert(__digits != 0 && _Urbg::max() > _Urbg::min(),
"random samples with 0 bits are not meaningful");
static_assert(std::numeric_limits<_RealT>::radix == 2,
"only base-2 float types are supported");
#if defined(__STDCPP_FLOAT16_T__)
static_assert(! is_same_v<_RealT, _Float16>,
"float16_t type is not supported, consider using bfloat16_t");
#endif
const unsigned __d_max = std::numeric_limits<_RealT>::digits;
const unsigned __d = __digits > __d_max ? __d_max : __digits;
// If the RNG range is a power of 2 less 1, the float type mantissa
// is enough bits. If not, we need more.
if constexpr (__is_power_of_2_less_1(_Urbg::max() - _Urbg::min()))
return __generate_canonical_pow2<_RealT, __d>(__urng);
else // Need up to 2x bits.
return __generate_canonical_any<_RealT, __d>(__urng);
}
_GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)
#pragma GCC diagnostic pop
#else // _GLIBCXX_USE_OLD_GENERATE_CANONICAL
// This is the pre-P0952 definition, to reproduce old results.
template<typename _RealType, size_t __bits,
typename _UniformRandomNumberGenerator>
_RealType
generate_canonical(_UniformRandomNumberGenerator& __urng)
{
static_assert(std::is_floating_point<_RealType>::value,
"template argument must be a floating point type");
const size_t __b
= std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
__bits);
const long double __r = static_cast<long double>(__urng.max())
- static_cast<long double>(__urng.min()) + 1.0L;
const size_t __log2r = std::log(__r) / std::log(2.0L);
const size_t __m = std::max<size_t>(1UL,
(__b + __log2r - 1UL) / __log2r);
_RealType __ret;
_RealType __sum = _RealType(0);
_RealType __tmp = _RealType(1);
for (size_t __k = __m; __k != 0; --__k)
{
__sum += _RealType(__urng() - __urng.min()) * __tmp;
__tmp *= __r;
}
__ret = __sum / __tmp;
if (__builtin_expect(__ret >= _RealType(1), 0))
{
# if _GLIBCXX_USE_C99_MATH_FUNCS
__ret = std::nextafter(_RealType(1), _RealType(0));
# else
__ret = _RealType(1)
- std::numeric_limits<_RealType>::epsilon() / _RealType(2);
# endif
}
return __ret;
}
#endif // _GLIBCXX_USE_OLD_GENERATE_CANONICAL
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
#endif