mirror of
https://github.com/ziglang/zig.git
synced 2024-11-17 01:23:54 +00:00
590 lines
20 KiB
C++
590 lines
20 KiB
C++
// -*- C++ -*-
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//===---------------------------- numeric ---------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef _LIBCPP_NUMERIC
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#define _LIBCPP_NUMERIC
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/*
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numeric synopsis
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namespace std
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{
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template <class InputIterator, class T>
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T
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accumulate(InputIterator first, InputIterator last, T init);
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template <class InputIterator, class T, class BinaryOperation>
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T
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accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
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template<class InputIterator>
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typename iterator_traits<InputIterator>::value_type
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reduce(InputIterator first, InputIterator last); // C++17
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template<class InputIterator, class T>
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T
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reduce(InputIterator first, InputIterator last, T init); // C++17
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template<class InputIterator, class T, class BinaryOperation>
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T
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reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17
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template <class InputIterator1, class InputIterator2, class T>
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T
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inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
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template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
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T
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inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
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T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
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template<class InputIterator1, class InputIterator2, class T>
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T
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transform_reduce(InputIterator1 first1, InputIterator1 last1,
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InputIterator2 first2, T init); // C++17
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template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
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T
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transform_reduce(InputIterator1 first1, InputIterator1 last1,
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InputIterator2 first2, T init,
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BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); // C++17
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template<class InputIterator, class T, class BinaryOperation, class UnaryOperation>
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T
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transform_reduce(InputIterator first, InputIterator last, T init,
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BinaryOperation binary_op, UnaryOperation unary_op); // C++17
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template <class InputIterator, class OutputIterator>
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OutputIterator
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partial_sum(InputIterator first, InputIterator last, OutputIterator result);
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template <class InputIterator, class OutputIterator, class BinaryOperation>
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OutputIterator
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partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
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template<class InputIterator, class OutputIterator, class T>
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OutputIterator
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exclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result, T init); // C++17
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template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
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OutputIterator
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exclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result, T init, BinaryOperation binary_op); // C++17
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template<class InputIterator, class OutputIterator>
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OutputIterator
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inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17
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template<class InputIterator, class OutputIterator, class BinaryOperation>
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OutputIterator
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inclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result, BinaryOperation binary_op); // C++17
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template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
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OutputIterator
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inclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result, BinaryOperation binary_op, T init); // C++17
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template<class InputIterator, class OutputIterator, class T,
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class BinaryOperation, class UnaryOperation>
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OutputIterator
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transform_exclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result, T init,
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BinaryOperation binary_op, UnaryOperation unary_op); // C++17
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template<class InputIterator, class OutputIterator,
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class BinaryOperation, class UnaryOperation>
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OutputIterator
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transform_inclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result,
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BinaryOperation binary_op, UnaryOperation unary_op); // C++17
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template<class InputIterator, class OutputIterator,
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class BinaryOperation, class UnaryOperation, class T>
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OutputIterator
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transform_inclusive_scan(InputIterator first, InputIterator last,
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OutputIterator result,
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BinaryOperation binary_op, UnaryOperation unary_op,
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T init); // C++17
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template <class InputIterator, class OutputIterator>
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OutputIterator
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adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);
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template <class InputIterator, class OutputIterator, class BinaryOperation>
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OutputIterator
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adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
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template <class ForwardIterator, class T>
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void iota(ForwardIterator first, ForwardIterator last, T value);
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template <class M, class N>
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constexpr common_type_t<M,N> gcd(M m, N n); // C++17
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template <class M, class N>
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constexpr common_type_t<M,N> lcm(M m, N n); // C++17
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integer midpoint(integer a, integer b); // C++20
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pointer midpoint(pointer a, pointer b); // C++20
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floating_point midpoint(floating_point a, floating_point b); // C++20
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} // std
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*/
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#include <__config>
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#include <iterator>
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#include <limits> // for numeric_limits
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#include <functional>
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#include <cmath> // for isnormal
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#include <version>
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
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#pragma GCC system_header
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#endif
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_LIBCPP_PUSH_MACROS
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#include <__undef_macros>
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_LIBCPP_BEGIN_NAMESPACE_STD
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template <class _InputIterator, class _Tp>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
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{
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for (; __first != __last; ++__first)
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__init = __init + *__first;
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return __init;
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}
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template <class _InputIterator, class _Tp, class _BinaryOperation>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
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{
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for (; __first != __last; ++__first)
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__init = __binary_op(__init, *__first);
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return __init;
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}
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#if _LIBCPP_STD_VER > 14
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template <class _InputIterator, class _Tp, class _BinaryOp>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
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{
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for (; __first != __last; ++__first)
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__init = __b(__init, *__first);
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return __init;
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}
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template <class _InputIterator, class _Tp>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
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{
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return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
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}
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template <class _InputIterator>
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inline _LIBCPP_INLINE_VISIBILITY
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typename iterator_traits<_InputIterator>::value_type
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reduce(_InputIterator __first, _InputIterator __last)
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{
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return _VSTD::reduce(__first, __last,
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typename iterator_traits<_InputIterator>::value_type{});
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}
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#endif
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template <class _InputIterator1, class _InputIterator2, class _Tp>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
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{
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for (; __first1 != __last1; ++__first1, (void) ++__first2)
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__init = __init + *__first1 * *__first2;
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return __init;
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}
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template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
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_Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
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{
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for (; __first1 != __last1; ++__first1, (void) ++__first2)
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__init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
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return __init;
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}
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#if _LIBCPP_STD_VER > 14
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template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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transform_reduce(_InputIterator __first, _InputIterator __last,
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_Tp __init, _BinaryOp __b, _UnaryOp __u)
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{
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for (; __first != __last; ++__first)
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__init = __b(__init, __u(*__first));
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return __init;
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}
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template <class _InputIterator1, class _InputIterator2,
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class _Tp, class _BinaryOp1, class _BinaryOp2>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
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_InputIterator2 __first2, _Tp __init, _BinaryOp1 __b1, _BinaryOp2 __b2)
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{
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for (; __first1 != __last1; ++__first1, (void) ++__first2)
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__init = __b1(__init, __b2(*__first1, *__first2));
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return __init;
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}
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template <class _InputIterator1, class _InputIterator2, class _Tp>
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inline _LIBCPP_INLINE_VISIBILITY
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_Tp
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transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
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_InputIterator2 __first2, _Tp __init)
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{
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return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
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_VSTD::plus<>(), _VSTD::multiplies<>());
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}
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#endif
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template <class _InputIterator, class _OutputIterator>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
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{
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if (__first != __last)
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{
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typename iterator_traits<_InputIterator>::value_type __t(*__first);
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*__result = __t;
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for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
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{
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__t = __t + *__first;
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*__result = __t;
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}
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
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_BinaryOperation __binary_op)
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{
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if (__first != __last)
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{
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typename iterator_traits<_InputIterator>::value_type __t(*__first);
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*__result = __t;
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for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
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{
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__t = __binary_op(__t, *__first);
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*__result = __t;
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}
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}
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return __result;
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}
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#if _LIBCPP_STD_VER > 14
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template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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exclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _Tp __init, _BinaryOp __b)
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{
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if (__first != __last)
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{
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_Tp __saved = __init;
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do
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{
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__init = __b(__init, *__first);
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*__result = __saved;
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__saved = __init;
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++__result;
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} while (++__first != __last);
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator, class _Tp>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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exclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _Tp __init)
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{
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return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
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}
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template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
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_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _BinaryOp __b, _Tp __init)
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{
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for (; __first != __last; ++__first, (void) ++__result) {
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__init = __b(__init, *__first);
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*__result = __init;
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator, class _BinaryOp>
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_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _BinaryOp __b)
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{
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if (__first != __last) {
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typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
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*__result++ = __init;
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if (++__first != __last)
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return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator>
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_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result)
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{
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return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
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}
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template <class _InputIterator, class _OutputIterator, class _Tp,
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class _BinaryOp, class _UnaryOp>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _Tp __init,
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_BinaryOp __b, _UnaryOp __u)
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{
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if (__first != __last)
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{
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_Tp __saved = __init;
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do
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{
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__init = __b(__init, __u(*__first));
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*__result = __saved;
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__saved = __init;
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++__result;
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} while (++__first != __last);
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
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_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
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{
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for (; __first != __last; ++__first, (void) ++__result) {
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__init = __b(__init, __u(*__first));
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*__result = __init;
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
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_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
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_OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
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{
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if (__first != __last) {
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typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
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*__result++ = __init;
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if (++__first != __last)
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return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
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}
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return __result;
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}
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#endif
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template <class _InputIterator, class _OutputIterator>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
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{
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if (__first != __last)
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{
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typename iterator_traits<_InputIterator>::value_type __t1(*__first);
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*__result = __t1;
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for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
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{
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typename iterator_traits<_InputIterator>::value_type __t2(*__first);
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*__result = __t2 - __t1;
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__t1 = _VSTD::move(__t2);
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}
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}
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return __result;
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}
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template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
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inline _LIBCPP_INLINE_VISIBILITY
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_OutputIterator
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adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
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_BinaryOperation __binary_op)
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{
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if (__first != __last)
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{
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typename iterator_traits<_InputIterator>::value_type __t1(*__first);
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*__result = __t1;
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for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
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{
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typename iterator_traits<_InputIterator>::value_type __t2(*__first);
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*__result = __binary_op(__t2, __t1);
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__t1 = _VSTD::move(__t2);
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}
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}
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return __result;
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}
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template <class _ForwardIterator, class _Tp>
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inline _LIBCPP_INLINE_VISIBILITY
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void
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iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
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{
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for (; __first != __last; ++__first, (void) ++__value_)
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*__first = __value_;
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}
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#if _LIBCPP_STD_VER > 14
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template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs;
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template <typename _Result, typename _Source>
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struct __ct_abs<_Result, _Source, true> {
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_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
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_Result operator()(_Source __t) const noexcept
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{
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if (__t >= 0) return __t;
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if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
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return -__t;
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}
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};
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template <typename _Result, typename _Source>
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struct __ct_abs<_Result, _Source, false> {
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_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
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_Result operator()(_Source __t) const noexcept { return __t; }
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};
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template<class _Tp>
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_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
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_Tp __gcd(_Tp __m, _Tp __n)
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{
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static_assert((!is_signed<_Tp>::value), "");
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return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
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}
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template<class _Tp, class _Up>
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_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
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common_type_t<_Tp,_Up>
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gcd(_Tp __m, _Up __n)
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{
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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 = std::make_unsigned_t<_Tp>;
|
|
|
|
int __sign = 1;
|
|
_Up __m = __a;
|
|
_Up __M = __b;
|
|
if (__a > __b)
|
|
{
|
|
__sign = -1;
|
|
__m = __b;
|
|
__M = __a;
|
|
}
|
|
return __a + __sign * _Tp(_Up(__M-__m) >> 1);
|
|
}
|
|
|
|
|
|
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(__a) < __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
|
|
|
|
#endif // _LIBCPP_NUMERIC
|