528 lines
18 KiB
C++
528 lines
18 KiB
C++
// -*- C++ -*-
|
|
//===---------------------------- numeric ---------------------------------===//
|
|
//
|
|
// The LLVM Compiler Infrastructure
|
|
//
|
|
// This file is dual licensed under the MIT and the University of Illinois Open
|
|
// Source Licenses. See LICENSE.TXT for details.
|
|
//
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
#ifndef _LIBCPP_NUMERIC
|
|
#define _LIBCPP_NUMERIC
|
|
|
|
/*
|
|
numeric synopsis
|
|
|
|
namespace std
|
|
{
|
|
|
|
template <class InputIterator, class T>
|
|
T
|
|
accumulate(InputIterator first, InputIterator last, T init);
|
|
|
|
template <class InputIterator, class T, class BinaryOperation>
|
|
T
|
|
accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
|
|
|
|
template<class InputIterator>
|
|
typename iterator_traits<InputIterator>::value_type
|
|
reduce(InputIterator first, InputIterator last); // C++17
|
|
|
|
template<class InputIterator, class T>
|
|
T
|
|
reduce(InputIterator first, InputIterator last, T init); // C++17
|
|
|
|
template<class InputIterator, class T, class BinaryOperation>
|
|
T
|
|
reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17
|
|
|
|
template <class InputIterator1, class InputIterator2, class T>
|
|
T
|
|
inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
|
|
|
|
template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
|
|
T
|
|
inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
|
|
T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
|
|
|
|
|
|
template<class InputIterator1, class InputIterator2, class T>
|
|
T
|
|
transform_reduce(InputIterator1 first1, InputIterator1 last1,
|
|
InputIterator2 first2, T init); // C++17
|
|
|
|
template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
|
|
T
|
|
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>
|
|
T
|
|
transform_reduce(InputIterator first, InputIterator last, T init,
|
|
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
|
|
|
|
template <class InputIterator, class OutputIterator>
|
|
OutputIterator
|
|
partial_sum(InputIterator first, InputIterator last, OutputIterator result);
|
|
|
|
template <class InputIterator, class OutputIterator, class BinaryOperation>
|
|
OutputIterator
|
|
partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
|
|
|
|
template<class InputIterator, class OutputIterator, class T>
|
|
OutputIterator
|
|
exclusive_scan(InputIterator first, InputIterator last,
|
|
OutputIterator result, T init); // C++17
|
|
|
|
template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
|
|
OutputIterator
|
|
exclusive_scan(InputIterator first, InputIterator last,
|
|
OutputIterator result, T init, BinaryOperation binary_op); // C++17
|
|
|
|
template<class InputIterator, class OutputIterator>
|
|
OutputIterator
|
|
inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17
|
|
|
|
template<class InputIterator, class OutputIterator, class BinaryOperation>
|
|
OutputIterator
|
|
inclusive_scan(InputIterator first, InputIterator last,
|
|
OutputIterator result, BinaryOperation binary_op); // C++17
|
|
|
|
template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
|
|
OutputIterator
|
|
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>
|
|
OutputIterator
|
|
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>
|
|
OutputIterator
|
|
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>
|
|
OutputIterator
|
|
transform_inclusive_scan(InputIterator first, InputIterator last,
|
|
OutputIterator result,
|
|
BinaryOperation binary_op, UnaryOperation unary_op,
|
|
T init); // C++17
|
|
|
|
template <class InputIterator, class OutputIterator>
|
|
OutputIterator
|
|
adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);
|
|
|
|
template <class InputIterator, class OutputIterator, class BinaryOperation>
|
|
OutputIterator
|
|
adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
|
|
|
|
template <class ForwardIterator, class T>
|
|
void 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
|
|
|
|
} // std
|
|
|
|
*/
|
|
|
|
#include <__config>
|
|
#include <iterator>
|
|
#include <limits> // for numeric_limits
|
|
#include <functional>
|
|
#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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
|
|
{
|
|
for (; __first != __last; ++__first)
|
|
__init = __init + *__first;
|
|
return __init;
|
|
}
|
|
|
|
template <class _InputIterator, class _Tp, class _BinaryOperation>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
|
|
{
|
|
for (; __first != __last; ++__first)
|
|
__init = __binary_op(__init, *__first);
|
|
return __init;
|
|
}
|
|
|
|
#if _LIBCPP_STD_VER > 14
|
|
template <class _InputIterator, class _Tp, class _BinaryOp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
|
|
{
|
|
return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
|
|
}
|
|
|
|
template <class _InputIterator>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
|
|
{
|
|
for (; __first1 != __last1; ++__first1, (void) ++__first2)
|
|
__init = __init + *__first1 * *__first2;
|
|
return __init;
|
|
}
|
|
|
|
template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
|
|
_Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
|
|
{
|
|
for (; __first1 != __last1; ++__first1, (void) ++__first2)
|
|
__init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
|
|
return __init;
|
|
}
|
|
|
|
#if _LIBCPP_STD_VER > 14
|
|
template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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)
|
|
{
|
|
__t = __t + *__first;
|
|
*__result = __t;
|
|
}
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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)
|
|
{
|
|
__t = __binary_op(__t, *__first);
|
|
*__result = __t;
|
|
}
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
#if _LIBCPP_STD_VER > 14
|
|
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_OutputIterator
|
|
exclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _Tp __init, _BinaryOp __b)
|
|
{
|
|
if (__first != __last)
|
|
{
|
|
_Tp __saved = __init;
|
|
do
|
|
{
|
|
__init = __b(__init, *__first);
|
|
*__result = __saved;
|
|
__saved = __init;
|
|
++__result;
|
|
} while (++__first != __last);
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
template <class _InputIterator, class _OutputIterator, class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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>
|
|
_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>
|
|
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _BinaryOp __b)
|
|
{
|
|
if (__first != __last) {
|
|
typename std::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>
|
|
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result)
|
|
{
|
|
return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
|
|
}
|
|
|
|
template <class _InputIterator, class _OutputIterator, class _Tp,
|
|
class _BinaryOp, class _UnaryOp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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>
|
|
_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>
|
|
_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
|
|
{
|
|
if (__first != __last) {
|
|
typename std::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>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_OutputIterator
|
|
adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
|
|
{
|
|
if (__first != __last)
|
|
{
|
|
typename iterator_traits<_InputIterator>::value_type __t1(*__first);
|
|
*__result = __t1;
|
|
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
|
|
{
|
|
typename iterator_traits<_InputIterator>::value_type __t2(*__first);
|
|
*__result = __t2 - __t1;
|
|
__t1 = _VSTD::move(__t2);
|
|
}
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_OutputIterator
|
|
adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
|
|
_BinaryOperation __binary_op)
|
|
{
|
|
if (__first != __last)
|
|
{
|
|
typename iterator_traits<_InputIterator>::value_type __t1(*__first);
|
|
*__result = __t1;
|
|
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
|
|
{
|
|
typename iterator_traits<_InputIterator>::value_type __t2(*__first);
|
|
*__result = __binary_op(__t2, __t1);
|
|
__t1 = _VSTD::move(__t2);
|
|
}
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
template <class _ForwardIterator, class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
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 __abs;
|
|
|
|
template <typename _Result, typename _Source>
|
|
struct __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 __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>(__abs<_Rp, _Tp>()(__m)),
|
|
static_cast<_Wp>(__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 = __abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
|
|
_Rp __val2 = __abs<_Rp, _Up>()(__n);
|
|
_LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
|
|
return __val1 * __val2;
|
|
}
|
|
|
|
#endif /* _LIBCPP_STD_VER > 14 */
|
|
|
|
_LIBCPP_END_NAMESPACE_STD
|
|
|
|
_LIBCPP_POP_MACROS
|
|
|
|
#endif // _LIBCPP_NUMERIC
|