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// -*- C++ -*-
//===---------------------------- numeric ---------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef _LIBCPP_NUMERIC
#define _LIBCPP_NUMERIC
/*
numeric synopsis
namespace std
{
template <class InputIterator, class T>
constexpr T // constexpr since C++20
accumulate(InputIterator first, InputIterator last, T init);
template <class InputIterator, class T, class BinaryOperation>
constexpr T // constexpr since C++20
accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
template<class InputIterator>
constexpr typename iterator_traits<InputIterator>::value_type // constexpr since C++20
reduce(InputIterator first, InputIterator last); // C++17
template<class InputIterator, class T>
constexpr T // constexpr since C++20
reduce(InputIterator first, InputIterator last, T init); // C++17
template<class InputIterator, class T, class BinaryOperation>
constexpr T // constexpr since C++20
reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17
template <class InputIterator1, class InputIterator2, class T>
constexpr T // constexpr since C++20
inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
constexpr T // constexpr since C++20
inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
template<class InputIterator1, class InputIterator2, class T>
constexpr T // constexpr since C++20
transform_reduce(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init); // C++17
template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
constexpr T // constexpr since C++20
transform_reduce(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init,
BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); // C++17
template<class InputIterator, class T, class BinaryOperation, class UnaryOperation>
constexpr T // constexpr since C++20
transform_reduce(InputIterator first, InputIterator last, T init,
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
template <class InputIterator, class OutputIterator>
constexpr OutputIterator // constexpr since C++20
partial_sum(InputIterator first, InputIterator last, OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
constexpr OutputIterator // constexpr since C++20
partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
template<class InputIterator, class OutputIterator, class T>
constexpr OutputIterator // constexpr since C++20
exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, T init); // C++17
template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
constexpr OutputIterator // constexpr since C++20
exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, T init, BinaryOperation binary_op); // C++17
template<class InputIterator, class OutputIterator>
constexpr OutputIterator // constexpr since C++20
inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17
template<class InputIterator, class OutputIterator, class BinaryOperation>
constexpr OutputIterator // constexpr since C++20
inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op); // C++17
template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
constexpr OutputIterator // constexpr since C++20
inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op, T init); // C++17
template<class InputIterator, class OutputIterator, class T,
class BinaryOperation, class UnaryOperation>
constexpr OutputIterator // constexpr since C++20
transform_exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, T init,
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
template<class InputIterator, class OutputIterator,
class BinaryOperation, class UnaryOperation>
constexpr OutputIterator // constexpr since C++20
transform_inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
template<class InputIterator, class OutputIterator,
class BinaryOperation, class UnaryOperation, class T>
constexpr OutputIterator // constexpr since C++20
transform_inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
BinaryOperation binary_op, UnaryOperation unary_op,
T init); // C++17
template <class InputIterator, class OutputIterator>
constexpr OutputIterator // constexpr since C++20
adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
constexpr OutputIterator // constexpr since C++20
adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
template <class ForwardIterator, class T>
constexpr void // constexpr since C++20
iota(ForwardIterator first, ForwardIterator last, T value);
template <class M, class N>
constexpr common_type_t<M,N> gcd(M m, N n); // C++17
template <class M, class N>
constexpr common_type_t<M,N> lcm(M m, N n); // C++17
template<class T>
constexpr T midpoint(T a, T b) noexcept; // C++20
template<class T>
constexpr T* midpoint(T* a, T* b); // C++20
} // std
*/
#include <__config>
#include <iterator>
#include <limits> // for numeric_limits
#include <functional>
#include <cmath> // for isnormal
#include <version>
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif
_LIBCPP_PUSH_MACROS
#include <__undef_macros>
_LIBCPP_BEGIN_NAMESPACE_STD
template <class _InputIterator, class _Tp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
{
for (; __first != __last; ++__first)
#if _LIBCPP_STD_VER > 17
__init = _VSTD::move(__init) + *__first;
#else
__init = __init + *__first;
#endif
return __init;
}
template <class _InputIterator, class _Tp, class _BinaryOperation>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
{
for (; __first != __last; ++__first)
#if _LIBCPP_STD_VER > 17
__init = __binary_op(_VSTD::move(__init), *__first);
#else
__init = __binary_op(__init, *__first);
#endif
return __init;
}
#if _LIBCPP_STD_VER > 14
template <class _InputIterator, class _Tp, class _BinaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
{
for (; __first != __last; ++__first)
__init = __b(__init, *__first);
return __init;
}
template <class _InputIterator, class _Tp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
{
return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
}
template <class _InputIterator>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
typename iterator_traits<_InputIterator>::value_type
reduce(_InputIterator __first, _InputIterator __last)
{
return _VSTD::reduce(__first, __last,
typename iterator_traits<_InputIterator>::value_type{});
}
#endif
template <class _InputIterator1, class _InputIterator2, class _Tp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
{
for (; __first1 != __last1; ++__first1, (void) ++__first2)
#if _LIBCPP_STD_VER > 17
__init = _VSTD::move(__init) + *__first1 * *__first2;
#else
__init = __init + *__first1 * *__first2;
#endif
return __init;
}
template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
_Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
{
for (; __first1 != __last1; ++__first1, (void) ++__first2)
#if _LIBCPP_STD_VER > 17
__init = __binary_op1(_VSTD::move(__init), __binary_op2(*__first1, *__first2));
#else
__init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
#endif
return __init;
}
#if _LIBCPP_STD_VER > 14
template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
transform_reduce(_InputIterator __first, _InputIterator __last,
_Tp __init, _BinaryOp __b, _UnaryOp __u)
{
for (; __first != __last; ++__first)
__init = __b(__init, __u(*__first));
return __init;
}
template <class _InputIterator1, class _InputIterator2,
class _Tp, class _BinaryOp1, class _BinaryOp2>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
_InputIterator2 __first2, _Tp __init, _BinaryOp1 __b1, _BinaryOp2 __b2)
{
for (; __first1 != __last1; ++__first1, (void) ++__first2)
__init = __b1(__init, __b2(*__first1, *__first2));
return __init;
}
template <class _InputIterator1, class _InputIterator2, class _Tp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_Tp
transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
_InputIterator2 __first2, _Tp __init)
{
return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
_VSTD::plus<>(), _VSTD::multiplies<>());
}
#endif
template <class _InputIterator, class _OutputIterator>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __t(*__first);
*__result = __t;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
#if _LIBCPP_STD_VER > 17
__t = _VSTD::move(__t) + *__first;
#else
__t = __t + *__first;
#endif
*__result = __t;
}
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
_BinaryOperation __binary_op)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __t(*__first);
*__result = __t;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
#if _LIBCPP_STD_VER > 17
__t = __binary_op(_VSTD::move(__t), *__first);
#else
__t = __binary_op(__t, *__first);
#endif
*__result = __t;
}
}
return __result;
}
#if _LIBCPP_STD_VER > 14
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
exclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp __init, _BinaryOp __b)
{
if (__first != __last)
{
_Tp __tmp(__b(__init, *__first));
while (true)
{
*__result = _VSTD::move(__init);
++__result;
++__first;
if (__first == __last)
break;
__init = _VSTD::move(__tmp);
__tmp = __b(__init, *__first);
}
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _Tp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
exclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp __init)
{
return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
}
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b, _Tp __init)
{
for (; __first != __last; ++__first, (void) ++__result) {
__init = __b(__init, *__first);
*__result = __init;
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b)
{
if (__first != __last) {
typename iterator_traits<_InputIterator>::value_type __init = *__first;
*__result++ = __init;
if (++__first != __last)
return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
}
return __result;
}
template <class _InputIterator, class _OutputIterator>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result)
{
return _VSTD::inclusive_scan(__first, __last, __result, _VSTD::plus<>());
}
template <class _InputIterator, class _OutputIterator, class _Tp,
class _BinaryOp, class _UnaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp __init,
_BinaryOp __b, _UnaryOp __u)
{
if (__first != __last)
{
_Tp __saved = __init;
do
{
__init = __b(__init, __u(*__first));
*__result = __saved;
__saved = __init;
++__result;
} while (++__first != __last);
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
{
for (; __first != __last; ++__first, (void) ++__result) {
__init = __b(__init, __u(*__first));
*__result = __init;
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
{
if (__first != __last) {
typename iterator_traits<_InputIterator>::value_type __init = __u(*__first);
*__result++ = __init;
if (++__first != __last)
return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
}
return __result;
}
#endif
template <class _InputIterator, class _OutputIterator>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __acc(*__first);
*__result = __acc;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
typename iterator_traits<_InputIterator>::value_type __val(*__first);
#if _LIBCPP_STD_VER > 17
*__result = __val - _VSTD::move(__acc);
#else
*__result = __val - __acc;
#endif
__acc = _VSTD::move(__val);
}
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
_OutputIterator
adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
_BinaryOperation __binary_op)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __acc(*__first);
*__result = __acc;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
typename iterator_traits<_InputIterator>::value_type __val(*__first);
#if _LIBCPP_STD_VER > 17
*__result = __binary_op(__val, _VSTD::move(__acc));
#else
*__result = __binary_op(__val, __acc);
#endif
__acc = _VSTD::move(__val);
}
}
return __result;
}
template <class _ForwardIterator, class _Tp>
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
void
iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
{
for (; __first != __last; ++__first, (void) ++__value_)
*__first = __value_;
}
#if _LIBCPP_STD_VER > 14
template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs;
template <typename _Result, typename _Source>
struct __ct_abs<_Result, _Source, true> {
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
_Result operator()(_Source __t) const noexcept
{
if (__t >= 0) return __t;
if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
return -__t;
}
};
template <typename _Result, typename _Source>
struct __ct_abs<_Result, _Source, false> {
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
_Result operator()(_Source __t) const noexcept { return __t; }
};
template<class _Tp>
_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
_Tp __gcd(_Tp __m, _Tp __n)
{
static_assert((!is_signed<_Tp>::value), "");
return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
}
template<class _Tp, class _Up>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
common_type_t<_Tp,_Up>
gcd(_Tp __m, _Up __n)
{
static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
using _Rp = common_type_t<_Tp,_Up>;
using _Wp = make_unsigned_t<_Rp>;
return static_cast<_Rp>(_VSTD::__gcd(
static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)),
static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
}
template<class _Tp, class _Up>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
common_type_t<_Tp,_Up>
lcm(_Tp __m, _Up __n)
{
static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
if (__m == 0 || __n == 0)
return 0;
using _Rp = common_type_t<_Tp,_Up>;
_Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
_Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
_LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
return __val1 * __val2;
}
#endif /* _LIBCPP_STD_VER > 14 */
#if _LIBCPP_STD_VER > 17
template <class _Tp>
_LIBCPP_INLINE_VISIBILITY constexpr
enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
midpoint(_Tp __a, _Tp __b) noexcept
_LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
{
using _Up = make_unsigned_t<_Tp>;
constexpr _Up __bitshift = numeric_limits<_Up>::digits - 1;
_Up __diff = _Up(__b) - _Up(__a);
_Up __sign_bit = __b < __a;
_Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff);
return __a + __half_diff;
}
template <class _TPtr>
_LIBCPP_INLINE_VISIBILITY constexpr
enable_if_t<is_pointer_v<_TPtr>
&& is_object_v<remove_pointer_t<_TPtr>>
&& ! is_void_v<remove_pointer_t<_TPtr>>
&& (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr>
midpoint(_TPtr __a, _TPtr __b) noexcept
{
return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a);
}
template <typename _Tp>
constexpr int __sign(_Tp __val) {
return (_Tp(0) < __val) - (__val < _Tp(0));
}
template <typename _Fp>
constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; }
template <class _Fp>
_LIBCPP_INLINE_VISIBILITY constexpr
enable_if_t<is_floating_point_v<_Fp>, _Fp>
midpoint(_Fp __a, _Fp __b) noexcept
{
constexpr _Fp __lo = numeric_limits<_Fp>::min()*2;
constexpr _Fp __hi = numeric_limits<_Fp>::max()/2;
return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ? // typical case: overflow is impossible
(__a + __b)/2 : // always correctly rounded
__fp_abs(__a) < __lo ? __a + __b/2 : // not safe to halve a
__fp_abs(__b) < __lo ? __a/2 + __b : // not safe to halve b
__a/2 + __b/2; // otherwise correctly rounded
}
#endif // _LIBCPP_STD_VER > 17
_LIBCPP_END_NAMESPACE_STD
_LIBCPP_POP_MACROS
#if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17
# include <__pstl_numeric>
#endif
#endif // _LIBCPP_NUMERIC
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