1// -*- C++ -*-
2//===----------------------------------------------------------------------===//
3//
4// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5// See https://llvm.org/LICENSE.txt for license information.
6// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7//
8//===----------------------------------------------------------------------===//
9
10#ifndef _LIBCPP___NUMERIC_MIDPOINT_H
11#define _LIBCPP___NUMERIC_MIDPOINT_H
12
13#include <__config>
14#include <__cstddef/ptrdiff_t.h>
15#include <__type_traits/enable_if.h>
16#include <__type_traits/is_floating_point.h>
17#include <__type_traits/is_integral.h>
18#include <__type_traits/is_null_pointer.h>
19#include <__type_traits/is_object.h>
20#include <__type_traits/is_pointer.h>
21#include <__type_traits/is_same.h>
22#include <__type_traits/is_void.h>
23#include <__type_traits/make_unsigned.h>
24#include <__type_traits/remove_pointer.h>
25#include <limits>
26
27#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
28# pragma GCC system_header
29#endif
30
31_LIBCPP_PUSH_MACROS
32#include <__undef_macros>
33
34_LIBCPP_BEGIN_NAMESPACE_STD
35
36#if _LIBCPP_STD_VER >= 20
37template <class _Tp>
38_LIBCPP_HIDE_FROM_ABI constexpr enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
39midpoint(_Tp __a, _Tp __b) noexcept _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK {
40 using _Up = make_unsigned_t<_Tp>;
41 constexpr _Up __bitshift = numeric_limits<_Up>::digits - 1;
42
43 _Up __diff = _Up(__b) - _Up(__a);
44 _Up __sign_bit = __b < __a;
45
46 _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff);
47
48 return __a + __half_diff;
49}
50
51template <class _Tp, enable_if_t<is_object_v<_Tp> && !is_void_v<_Tp> && (sizeof(_Tp) > 0), int> = 0>
52_LIBCPP_HIDE_FROM_ABI constexpr _Tp* midpoint(_Tp* __a, _Tp* __b) noexcept {
53 return __a + std::midpoint(ptrdiff_t(0), __b - __a);
54}
55
56template <typename _Tp>
57_LIBCPP_HIDE_FROM_ABI constexpr int __sign(_Tp __val) {
58 return (_Tp(0) < __val) - (__val < _Tp(0));
59}
60
61template <typename _Fp>
62_LIBCPP_HIDE_FROM_ABI constexpr _Fp __fp_abs(_Fp __f) {
63 return __f >= 0 ? __f : -__f;
64}
65
66template <class _Fp>
67_LIBCPP_HIDE_FROM_ABI constexpr enable_if_t<is_floating_point_v<_Fp>, _Fp> midpoint(_Fp __a, _Fp __b) noexcept {
68 constexpr _Fp __lo = numeric_limits<_Fp>::min() * 2;
69 constexpr _Fp __hi = numeric_limits<_Fp>::max() / 2;
70
71 // typical case: overflow is impossible
72 if (std::__fp_abs(__a) <= __hi && std::__fp_abs(__b) <= __hi)
73 return (__a + __b) / 2; // always correctly rounded
74 if (std::__fp_abs(__a) < __lo)
75 return __a + __b / 2; // not safe to halve a
76 if (std::__fp_abs(__b) < __lo)
77 return __a / 2 + __b; // not safe to halve b
78
79 return __a / 2 + __b / 2; // otherwise correctly rounded
80}
81
82#endif // _LIBCPP_STD_VER >= 20
83
84_LIBCPP_END_NAMESPACE_STD
85
86_LIBCPP_POP_MACROS
87
88#endif // _LIBCPP___NUMERIC_MIDPOINT_H
89