| // -*- C++ -*- |
| //===---------------------------- numeric ---------------------------------===// |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #ifndef _LIBCPP_NUMERIC |
| #define _LIBCPP_NUMERIC |
| |
| /* |
| numeric synopsis |
| |
| namespace std |
| { |
| |
| template <class InputIterator, class T> |
| 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 |
| |
| integer midpoint(integer a, integer b); // C++20 |
| pointer midpoint(pointer a, pointer b); // C++20 |
| floating_point midpoint(floating_point a, floating_point b); // C++20 |
| |
| } // std |
| |
| */ |
| |
| #include <__config> |
| #include <iterator> |
| #include <limits> // for numeric_limits |
| #include <functional> |
| #include <cmath> // for isnormal |
| #include <version> |
| |
| #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
| #pragma GCC system_header |
| #endif |
| |
| _LIBCPP_PUSH_MACROS |
| #include <__undef_macros> |
| |
| _LIBCPP_BEGIN_NAMESPACE_STD |
| |
| template <class _InputIterator, class _Tp> |
| 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 __ct_abs; |
| |
| template <typename _Result, typename _Source> |
| struct __ct_abs<_Result, _Source, true> { |
| _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
| _Result operator()(_Source __t) const noexcept |
| { |
| if (__t >= 0) return __t; |
| if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t); |
| return -__t; |
| } |
| }; |
| |
| template <typename _Result, typename _Source> |
| struct __ct_abs<_Result, _Source, false> { |
| _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
| _Result operator()(_Source __t) const noexcept { return __t; } |
| }; |
| |
| |
| template<class _Tp> |
| _LIBCPP_CONSTEXPR _LIBCPP_HIDDEN |
| _Tp __gcd(_Tp __m, _Tp __n) |
| { |
| static_assert((!is_signed<_Tp>::value), ""); |
| return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n); |
| } |
| |
| |
| template<class _Tp, class _Up> |
| _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
| common_type_t<_Tp,_Up> |
| gcd(_Tp __m, _Up __n) |
| { |
| static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types"); |
| static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" ); |
| static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" ); |
| using _Rp = common_type_t<_Tp,_Up>; |
| using _Wp = make_unsigned_t<_Rp>; |
| return static_cast<_Rp>(_VSTD::__gcd( |
| static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), |
| static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n)))); |
| } |
| |
| template<class _Tp, class _Up> |
| _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
| common_type_t<_Tp,_Up> |
| lcm(_Tp __m, _Up __n) |
| { |
| static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types"); |
| static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" ); |
| static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" ); |
| if (__m == 0 || __n == 0) |
| return 0; |
| |
| using _Rp = common_type_t<_Tp,_Up>; |
| _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n); |
| _Rp __val2 = __ct_abs<_Rp, _Up>()(__n); |
| _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm"); |
| return __val1 * __val2; |
| } |
| |
| #endif /* _LIBCPP_STD_VER > 14 */ |
| |
| #if _LIBCPP_STD_VER > 17 |
| template <class _Tp> |
| _LIBCPP_INLINE_VISIBILITY constexpr |
| enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp> |
| midpoint(_Tp __a, _Tp __b) noexcept |
| _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK |
| { |
| using _Up = std::make_unsigned_t<_Tp>; |
| constexpr _Up __bitshift = std::numeric_limits<_Up>::digits - 1; |
| |
| _Up __diff = _Up(__b) - _Up(__a); |
| _Up __sign_bit = __b < __a; |
| |
| _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff); |
| |
| return __a + __half_diff; |
| } |
| |
| |
| template <class _TPtr> |
| _LIBCPP_INLINE_VISIBILITY constexpr |
| enable_if_t<is_pointer_v<_TPtr> |
| && is_object_v<remove_pointer_t<_TPtr>> |
| && ! is_void_v<remove_pointer_t<_TPtr>> |
| && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr> |
| midpoint(_TPtr __a, _TPtr __b) noexcept |
| { |
| return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a); |
| } |
| |
| |
| template <typename _Tp> |
| constexpr int __sign(_Tp __val) { |
| return (_Tp(0) < __val) - (__val < _Tp(0)); |
| } |
| |
| template <typename _Fp> |
| constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; } |
| |
| template <class _Fp> |
| _LIBCPP_INLINE_VISIBILITY constexpr |
| enable_if_t<is_floating_point_v<_Fp>, _Fp> |
| midpoint(_Fp __a, _Fp __b) noexcept |
| { |
| constexpr _Fp __lo = numeric_limits<_Fp>::min()*2; |
| constexpr _Fp __hi = numeric_limits<_Fp>::max()/2; |
| return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ? // typical case: overflow is impossible |
| (__a + __b)/2 : // always correctly rounded |
| __fp_abs(__a) < __lo ? __a + __b/2 : // not safe to halve a |
| __fp_abs(__b) < __lo ? __a/2 + __b : // not safe to halve b |
| __a/2 + __b/2; // otherwise correctly rounded |
| } |
| |
| #endif // _LIBCPP_STD_VER > 17 |
| |
| _LIBCPP_END_NAMESPACE_STD |
| |
| _LIBCPP_POP_MACROS |
| |
| #if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17 |
| # include <__pstl_numeric> |
| #endif |
| |
| #endif // _LIBCPP_NUMERIC |