704 lines
24 KiB
C++
704 lines
24 KiB
C++
// <numeric> -*- C++ -*-
|
|
|
|
// Copyright (C) 2001-2019 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/>.
|
|
|
|
/*
|
|
*
|
|
* Copyright (c) 1994
|
|
* Hewlett-Packard Company
|
|
*
|
|
* Permission to use, copy, modify, distribute and sell this software
|
|
* and its documentation for any purpose is hereby granted without fee,
|
|
* provided that the above copyright notice appear in all copies and
|
|
* that both that copyright notice and this permission notice appear
|
|
* in supporting documentation. Hewlett-Packard Company makes no
|
|
* representations about the suitability of this software for any
|
|
* purpose. It is provided "as is" without express or implied warranty.
|
|
*
|
|
*
|
|
* Copyright (c) 1996,1997
|
|
* Silicon Graphics Computer Systems, Inc.
|
|
*
|
|
* Permission to use, copy, modify, distribute and sell this software
|
|
* and its documentation for any purpose is hereby granted without fee,
|
|
* provided that the above copyright notice appear in all copies and
|
|
* that both that copyright notice and this permission notice appear
|
|
* in supporting documentation. Silicon Graphics makes no
|
|
* representations about the suitability of this software for any
|
|
* purpose. It is provided "as is" without express or implied warranty.
|
|
*/
|
|
|
|
/** @file include/numeric
|
|
* This is a Standard C++ Library header.
|
|
*/
|
|
|
|
#ifndef _GLIBCXX_NUMERIC
|
|
#define _GLIBCXX_NUMERIC 1
|
|
|
|
#pragma GCC system_header
|
|
|
|
#include <bits/c++config.h>
|
|
#include <bits/stl_iterator_base_types.h>
|
|
#include <bits/stl_numeric.h>
|
|
|
|
#ifdef _GLIBCXX_PARALLEL
|
|
# include <parallel/numeric>
|
|
#endif
|
|
|
|
/**
|
|
* @defgroup numerics Numerics
|
|
*
|
|
* Components for performing numeric operations. Includes support for
|
|
* complex number types, random number generation, numeric (n-at-a-time)
|
|
* arrays, generalized numeric algorithms, and mathematical special functions.
|
|
*/
|
|
|
|
#if __cplusplus >= 201402L
|
|
#include <type_traits>
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
namespace __detail
|
|
{
|
|
// std::abs is not constexpr and doesn't support unsigned integers.
|
|
template<typename _Tp>
|
|
constexpr
|
|
enable_if_t<__and_<is_integral<_Tp>, is_signed<_Tp>>::value, _Tp>
|
|
__abs_integral(_Tp __val)
|
|
{ return __val < 0 ? -__val : __val; }
|
|
|
|
template<typename _Tp>
|
|
constexpr
|
|
enable_if_t<__and_<is_integral<_Tp>, is_unsigned<_Tp>>::value, _Tp>
|
|
__abs_integral(_Tp __val)
|
|
{ return __val; }
|
|
|
|
void __abs_integral(bool) = delete;
|
|
|
|
template<typename _Mn, typename _Nn>
|
|
constexpr common_type_t<_Mn, _Nn>
|
|
__gcd(_Mn __m, _Nn __n)
|
|
{
|
|
return __m == 0 ? __detail::__abs_integral(__n)
|
|
: __n == 0 ? __detail::__abs_integral(__m)
|
|
: __detail::__gcd(__n, __m % __n);
|
|
}
|
|
|
|
/// Least common multiple
|
|
template<typename _Mn, typename _Nn>
|
|
constexpr common_type_t<_Mn, _Nn>
|
|
__lcm(_Mn __m, _Nn __n)
|
|
{
|
|
return (__m != 0 && __n != 0)
|
|
? (__detail::__abs_integral(__m) / __detail::__gcd(__m, __n))
|
|
* __detail::__abs_integral(__n)
|
|
: 0;
|
|
}
|
|
} // namespace __detail
|
|
|
|
#if __cplusplus >= 201703L
|
|
|
|
#define __cpp_lib_gcd_lcm 201606
|
|
// These were used in drafts of SD-6:
|
|
#define __cpp_lib_gcd 201606
|
|
#define __cpp_lib_lcm 201606
|
|
|
|
/// Greatest common divisor
|
|
template<typename _Mn, typename _Nn>
|
|
constexpr common_type_t<_Mn, _Nn>
|
|
gcd(_Mn __m, _Nn __n)
|
|
{
|
|
static_assert(is_integral_v<_Mn>, "gcd arguments are integers");
|
|
static_assert(is_integral_v<_Nn>, "gcd arguments are integers");
|
|
static_assert(!is_same_v<remove_cv_t<_Mn>, bool>,
|
|
"gcd arguments are not bools");
|
|
static_assert(!is_same_v<remove_cv_t<_Nn>, bool>,
|
|
"gcd arguments are not bools");
|
|
return __detail::__gcd(__m, __n);
|
|
}
|
|
|
|
/// Least common multiple
|
|
template<typename _Mn, typename _Nn>
|
|
constexpr common_type_t<_Mn, _Nn>
|
|
lcm(_Mn __m, _Nn __n)
|
|
{
|
|
static_assert(is_integral_v<_Mn>, "lcm arguments are integers");
|
|
static_assert(is_integral_v<_Nn>, "lcm arguments are integers");
|
|
static_assert(!is_same_v<remove_cv_t<_Mn>, bool>,
|
|
"lcm arguments are not bools");
|
|
static_assert(!is_same_v<remove_cv_t<_Nn>, bool>,
|
|
"lcm arguments are not bools");
|
|
return __detail::__lcm(__m, __n);
|
|
}
|
|
|
|
#endif // C++17
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace std
|
|
|
|
#endif // C++14
|
|
|
|
#if __cplusplus > 201703L
|
|
#include <limits>
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
// midpoint
|
|
# define __cpp_lib_interpolate 201902L
|
|
|
|
template<typename _Tp>
|
|
constexpr
|
|
enable_if_t<__and_v<is_arithmetic<_Tp>, is_same<remove_cv_t<_Tp>, _Tp>,
|
|
__not_<is_same<_Tp, bool>>>,
|
|
_Tp>
|
|
midpoint(_Tp __a, _Tp __b) noexcept
|
|
{
|
|
if constexpr (is_integral_v<_Tp>)
|
|
{
|
|
using _Up = make_unsigned_t<_Tp>;
|
|
|
|
int __k = 1;
|
|
_Up __m = __a;
|
|
_Up __M = __b;
|
|
if (__a > __b)
|
|
{
|
|
__k = -1;
|
|
__m = __b;
|
|
__M = __a;
|
|
}
|
|
return __a + __k * _Tp(_Up(__M - __m) / 2);
|
|
}
|
|
else // is_floating
|
|
{
|
|
constexpr _Tp __lo = numeric_limits<_Tp>::min() * 2;
|
|
constexpr _Tp __hi = numeric_limits<_Tp>::max() / 2;
|
|
const _Tp __abs_a = __a < 0 ? -__a : __a;
|
|
const _Tp __abs_b = __b < 0 ? -__b : __b;
|
|
if (__abs_a <= __hi && __abs_b <= __hi) [[likely]]
|
|
return (__a + __b) / 2; // always correctly rounded
|
|
if (__abs_a < __lo) // not safe to halve __a
|
|
return __a + __b/2;
|
|
if (__abs_b < __lo) // not safe to halve __b
|
|
return __a/2 + __b;
|
|
return __a/2 + __b/2; // otherwise correctly rounded
|
|
}
|
|
}
|
|
|
|
template<typename _Tp>
|
|
constexpr
|
|
enable_if_t<__and_v<is_object<_Tp>, bool_constant<sizeof(_Tp) != 0>>, _Tp*>
|
|
midpoint(_Tp* __a, _Tp* __b) noexcept
|
|
{
|
|
return __a + (__b - __a) / 2;
|
|
}
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace std
|
|
|
|
#endif // C++20
|
|
|
|
#if __cplusplus > 201402L
|
|
#include <bits/stl_function.h>
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
/// @addtogroup numeric_ops
|
|
/// @{
|
|
|
|
/// @cond undocumented
|
|
template<typename _It, typename _Traits = iterator_traits<_It>,
|
|
typename _Cat = typename _Traits::iterator_category>
|
|
using __is_random_access_iter
|
|
= is_base_of<random_access_iterator_tag, _Cat>;
|
|
/// @endcond
|
|
|
|
/**
|
|
* @brief Calculate reduction of values in a range.
|
|
*
|
|
* @param __first Start of range.
|
|
* @param __last End of range.
|
|
* @param __init Starting value to add other values to.
|
|
* @param __binary_op A binary function object.
|
|
* @return The final sum.
|
|
*
|
|
* Reduce the values in the range `[first,last)` using a binary operation.
|
|
* The initial value is `init`. The values are not necessarily processed
|
|
* in order.
|
|
*
|
|
* This algorithm is similar to `std::accumulate` but is not required to
|
|
* perform the operations in order from first to last. For operations
|
|
* that are commutative and associative the result will be the same as
|
|
* for `std::accumulate`, but for other operations (such as floating point
|
|
* arithmetic) the result can be different.
|
|
*/
|
|
template<typename _InputIterator, typename _Tp, typename _BinaryOperation>
|
|
_Tp
|
|
reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
|
|
_BinaryOperation __binary_op)
|
|
{
|
|
using value_type = typename iterator_traits<_InputIterator>::value_type;
|
|
static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>);
|
|
static_assert(is_convertible_v<value_type, _Tp>);
|
|
if constexpr (__is_random_access_iter<_InputIterator>::value)
|
|
{
|
|
while ((__last - __first) >= 4)
|
|
{
|
|
_Tp __v1 = __binary_op(__first[0], __first[1]);
|
|
_Tp __v2 = __binary_op(__first[2], __first[3]);
|
|
_Tp __v3 = __binary_op(__v1, __v2);
|
|
__init = __binary_op(__init, __v3);
|
|
__first += 4;
|
|
}
|
|
}
|
|
for (; __first != __last; ++__first)
|
|
__init = __binary_op(__init, *__first);
|
|
return __init;
|
|
}
|
|
|
|
/**
|
|
* @brief Calculate reduction of values in a range.
|
|
*
|
|
* @param __first Start of range.
|
|
* @param __last End of range.
|
|
* @param __init Starting value to add other values to.
|
|
* @return The final sum.
|
|
*
|
|
* Reduce the values in the range `[first,last)` using addition.
|
|
* Equivalent to calling `std::reduce(first, last, init, std::plus<>())`.
|
|
*/
|
|
template<typename _InputIterator, typename _Tp>
|
|
inline _Tp
|
|
reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
|
|
{ return std::reduce(__first, __last, std::move(__init), plus<>()); }
|
|
|
|
/**
|
|
* @brief Calculate reduction of values in a range.
|
|
*
|
|
* @param __first Start of range.
|
|
* @param __last End of range.
|
|
* @return The final sum.
|
|
*
|
|
* Reduce the values in the range `[first,last)` using addition, with
|
|
* an initial value of `T{}`, where `T` is the iterator's value type.
|
|
* Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`.
|
|
*/
|
|
template<typename _InputIterator>
|
|
inline typename iterator_traits<_InputIterator>::value_type
|
|
reduce(_InputIterator __first, _InputIterator __last)
|
|
{
|
|
using value_type = typename iterator_traits<_InputIterator>::value_type;
|
|
return std::reduce(__first, __last, value_type{}, plus<>());
|
|
}
|
|
|
|
/**
|
|
* @brief Combine elements from two ranges and reduce
|
|
*
|
|
* @param __first1 Start of first range.
|
|
* @param __last1 End of first range.
|
|
* @param __first2 Start of second range.
|
|
* @param __init Starting value to add other values to.
|
|
* @param __binary_op1 The function used to perform reduction.
|
|
* @param __binary_op2 The function used to combine values from the ranges.
|
|
* @return The final sum.
|
|
*
|
|
* Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)`
|
|
* and then use `binary_op1` to reduce the values returned by `binary_op2`
|
|
* to a single value of type `T`.
|
|
*
|
|
* The range beginning at `first2` must contain at least `last1-first1`
|
|
* elements.
|
|
*/
|
|
template<typename _InputIterator1, typename _InputIterator2, typename _Tp,
|
|
typename _BinaryOperation1, typename _BinaryOperation2>
|
|
_Tp
|
|
transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
|
|
_InputIterator2 __first2, _Tp __init,
|
|
_BinaryOperation1 __binary_op1,
|
|
_BinaryOperation2 __binary_op2)
|
|
{
|
|
if constexpr (__and_v<__is_random_access_iter<_InputIterator1>,
|
|
__is_random_access_iter<_InputIterator2>>)
|
|
{
|
|
while ((__last1 - __first1) >= 4)
|
|
{
|
|
_Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]),
|
|
__binary_op2(__first1[1], __first2[1]));
|
|
_Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]),
|
|
__binary_op2(__first1[3], __first2[3]));
|
|
_Tp __v3 = __binary_op1(__v1, __v2);
|
|
__init = __binary_op1(__init, __v3);
|
|
__first1 += 4;
|
|
__first2 += 4;
|
|
}
|
|
}
|
|
for (; __first1 != __last1; ++__first1, (void) ++__first2)
|
|
__init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
|
|
return __init;
|
|
}
|
|
|
|
/**
|
|
* @brief Combine elements from two ranges and reduce
|
|
*
|
|
* @param __first1 Start of first range.
|
|
* @param __last1 End of first range.
|
|
* @param __first2 Start of second range.
|
|
* @param __init Starting value to add other values to.
|
|
* @return The final sum.
|
|
*
|
|
* Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then
|
|
* use addition to sum those products to a single value of type `T`.
|
|
*
|
|
* The range beginning at `first2` must contain at least `last1-first1`
|
|
* elements.
|
|
*/
|
|
template<typename _InputIterator1, typename _InputIterator2, typename _Tp>
|
|
inline _Tp
|
|
transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
|
|
_InputIterator2 __first2, _Tp __init)
|
|
{
|
|
return std::transform_reduce(__first1, __last1, __first2,
|
|
std::move(__init),
|
|
plus<>(), multiplies<>());
|
|
}
|
|
|
|
/**
|
|
* @brief Transform the elements of a range and reduce
|
|
*
|
|
* @param __first Start of range.
|
|
* @param __last End of range.
|
|
* @param __init Starting value to add other values to.
|
|
* @param __binary_op The function used to perform reduction.
|
|
* @param __unary_op The function used to transform values from the range.
|
|
* @return The final sum.
|
|
*
|
|
* Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then
|
|
* use `binary_op` to reduce the values returned by `unary_op`
|
|
* to a single value of type `T`.
|
|
*/
|
|
template<typename _InputIterator, typename _Tp,
|
|
typename _BinaryOperation, typename _UnaryOperation>
|
|
_Tp
|
|
transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
|
|
_BinaryOperation __binary_op, _UnaryOperation __unary_op)
|
|
{
|
|
if constexpr (__is_random_access_iter<_InputIterator>::value)
|
|
{
|
|
while ((__last - __first) >= 4)
|
|
{
|
|
_Tp __v1 = __binary_op(__unary_op(__first[0]),
|
|
__unary_op(__first[1]));
|
|
_Tp __v2 = __binary_op(__unary_op(__first[2]),
|
|
__unary_op(__first[3]));
|
|
_Tp __v3 = __binary_op(__v1, __v2);
|
|
__init = __binary_op(__init, __v3);
|
|
__first += 4;
|
|
}
|
|
}
|
|
for (; __first != __last; ++__first)
|
|
__init = __binary_op(__init, __unary_op(*__first));
|
|
return __init;
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __init Initial value.
|
|
* @param __binary_op Function to perform summation.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements (and the initial value),
|
|
* using `binary_op` for summation.
|
|
*
|
|
* This function generates an "exclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N-1 input elements,
|
|
* so the Nth input element is not included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator, typename _Tp,
|
|
typename _BinaryOperation>
|
|
_OutputIterator
|
|
exclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _Tp __init,
|
|
_BinaryOperation __binary_op)
|
|
{
|
|
while (__first != __last)
|
|
{
|
|
auto __v = __init;
|
|
__init = __binary_op(__init, *__first);
|
|
++__first;
|
|
*__result++ = std::move(__v);
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __init Initial value.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements (and the initial value),
|
|
* using `std::plus<>` for summation.
|
|
*
|
|
* This function generates an "exclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N-1 input elements,
|
|
* so the Nth input element is not included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator, typename _Tp>
|
|
inline _OutputIterator
|
|
exclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _Tp __init)
|
|
{
|
|
return std::exclusive_scan(__first, __last, __result, std::move(__init),
|
|
plus<>());
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __binary_op Function to perform summation.
|
|
* @param __init Initial value.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements (and the initial value),
|
|
* using `binary_op` for summation.
|
|
*
|
|
* This function generates an "inclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N input elements,
|
|
* so the Nth input element is included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator,
|
|
typename _BinaryOperation, typename _Tp>
|
|
_OutputIterator
|
|
inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _BinaryOperation __binary_op,
|
|
_Tp __init)
|
|
{
|
|
for (; __first != __last; ++__first)
|
|
*__result++ = __init = __binary_op(__init, *__first);
|
|
return __result;
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __binary_op Function to perform summation.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements, using `binary_op` for summation.
|
|
*
|
|
* This function generates an "inclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N input elements,
|
|
* so the Nth input element is included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator,
|
|
typename _BinaryOperation>
|
|
_OutputIterator
|
|
inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _BinaryOperation __binary_op)
|
|
{
|
|
if (__first != __last)
|
|
{
|
|
auto __init = *__first;
|
|
*__result++ = __init;
|
|
++__first;
|
|
if (__first != __last)
|
|
__result = std::inclusive_scan(__first, __last, __result,
|
|
__binary_op, std::move(__init));
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements, using `std::plus<>` for summation.
|
|
*
|
|
* This function generates an "inclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N input elements,
|
|
* so the Nth input element is included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator>
|
|
inline _OutputIterator
|
|
inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result)
|
|
{ return std::inclusive_scan(__first, __last, __result, plus<>()); }
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __init Initial value.
|
|
* @param __binary_op Function to perform summation.
|
|
* @param __unary_op Function to transform elements of the input range.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements (and the initial value),
|
|
* using `__unary_op` to transform the input elements
|
|
* and using `__binary_op` for summation.
|
|
*
|
|
* This function generates an "exclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N-1 input elements,
|
|
* so the Nth input element is not included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator, typename _Tp,
|
|
typename _BinaryOperation, typename _UnaryOperation>
|
|
_OutputIterator
|
|
transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result, _Tp __init,
|
|
_BinaryOperation __binary_op,
|
|
_UnaryOperation __unary_op)
|
|
{
|
|
while (__first != __last)
|
|
{
|
|
auto __v = __init;
|
|
__init = __binary_op(__init, __unary_op(*__first));
|
|
++__first;
|
|
*__result++ = std::move(__v);
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __binary_op Function to perform summation.
|
|
* @param __unary_op Function to transform elements of the input range.
|
|
* @param __init Initial value.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements (and the initial value),
|
|
* using `__unary_op` to transform the input elements
|
|
* and using `__binary_op` for summation.
|
|
*
|
|
* This function generates an "inclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N input elements,
|
|
* so the Nth input element is included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator,
|
|
typename _BinaryOperation, typename _UnaryOperation, typename _Tp>
|
|
_OutputIterator
|
|
transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result,
|
|
_BinaryOperation __binary_op,
|
|
_UnaryOperation __unary_op,
|
|
_Tp __init)
|
|
{
|
|
for (; __first != __last; ++__first)
|
|
*__result++ = __init = __binary_op(__init, __unary_op(*__first));
|
|
return __result;
|
|
}
|
|
|
|
/** @brief Output the cumulative sum of one range to a second range
|
|
*
|
|
* @param __first Start of input range.
|
|
* @param __last End of input range.
|
|
* @param __result Start of output range.
|
|
* @param __binary_op Function to perform summation.
|
|
* @param __unary_op Function to transform elements of the input range.
|
|
* @return The end of the output range.
|
|
*
|
|
* Write the cumulative sum (aka prefix sum, aka scan) of the input range
|
|
* to the output range. Each element of the output range contains the
|
|
* running total of all earlier elements,
|
|
* using `__unary_op` to transform the input elements
|
|
* and using `__binary_op` for summation.
|
|
*
|
|
* This function generates an "inclusive" scan, meaning the Nth element
|
|
* of the output range is the sum of the first N input elements,
|
|
* so the Nth input element is included.
|
|
*/
|
|
template<typename _InputIterator, typename _OutputIterator,
|
|
typename _BinaryOperation, typename _UnaryOperation>
|
|
_OutputIterator
|
|
transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
|
|
_OutputIterator __result,
|
|
_BinaryOperation __binary_op,
|
|
_UnaryOperation __unary_op)
|
|
{
|
|
if (__first != __last)
|
|
{
|
|
auto __init = __unary_op(*__first);
|
|
*__result++ = __init;
|
|
++__first;
|
|
if (__first != __last)
|
|
__result = std::transform_inclusive_scan(__first, __last, __result,
|
|
__binary_op, __unary_op,
|
|
std::move(__init));
|
|
}
|
|
return __result;
|
|
}
|
|
|
|
// @} group numeric_ops
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace std
|
|
|
|
// Parallel STL algorithms
|
|
# if __PSTL_EXECUTION_POLICIES_DEFINED
|
|
// If <execution> has already been included, pull in implementations
|
|
# include <pstl/glue_numeric_impl.h>
|
|
# else
|
|
// Otherwise just pull in forward declarations
|
|
# include <pstl/glue_numeric_defs.h>
|
|
# define __PSTL_NUMERIC_FORWARD_DECLARED 1
|
|
# endif
|
|
|
|
// Feature test macro for parallel algorithms
|
|
# define __cpp_lib_parallel_algorithm 201603L
|
|
#endif // C++17
|
|
|
|
#endif /* _GLIBCXX_NUMERIC */
|