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- // <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 */
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