xref: /freebsd/contrib/llvm-project/libcxx/include/numeric (revision 19261079b74319502c6ffa1249920079f0f69a72) 
1// -*- C++ -*-
2//===---------------------------- numeric ---------------------------------===//
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
11#define _LIBCPP_NUMERIC
12
13/*
14    numeric synopsis
15
16namespace std
17{
18
19template <class InputIterator, class T>
20    constexpr T  // constexpr since C++20
21    accumulate(InputIterator first, InputIterator last, T init);
22
23template <class InputIterator, class T, class BinaryOperation>
24    constexpr T  // constexpr since C++20
25    accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
26
27template<class InputIterator>
28    constexpr typename iterator_traits<InputIterator>::value_type  // constexpr since C++20
29    reduce(InputIterator first, InputIterator last);  // C++17
30
31template<class InputIterator, class T>
32    constexpr T  // constexpr since C++20
33    reduce(InputIterator first, InputIterator last, T init);  // C++17
34
35template<class InputIterator, class T, class BinaryOperation>
36    constexpr T  // constexpr since C++20
37    reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);  // C++17
38
39template <class InputIterator1, class InputIterator2, class T>
40    constexpr T  // constexpr since C++20
41    inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
42
43template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
44    constexpr T  // constexpr since C++20
45    inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
46                  T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
47
48
49template<class InputIterator1, class InputIterator2, class T>
50    constexpr T  // constexpr since C++20
51    transform_reduce(InputIterator1 first1, InputIterator1 last1,
52                     InputIterator2 first2, T init);  // C++17
53
54template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
55    constexpr T  // constexpr since C++20
56    transform_reduce(InputIterator1 first1, InputIterator1 last1,
57                     InputIterator2 first2, T init,
58                     BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);  // C++17
59
60template<class InputIterator, class T, class BinaryOperation, class UnaryOperation>
61    constexpr T  // constexpr since C++20
62    transform_reduce(InputIterator first, InputIterator last, T init,
63                     BinaryOperation binary_op, UnaryOperation unary_op);  // C++17
64
65template <class InputIterator, class OutputIterator>
66    constexpr OutputIterator  // constexpr since C++20
67    partial_sum(InputIterator first, InputIterator last, OutputIterator result);
68
69template <class InputIterator, class OutputIterator, class BinaryOperation>
70    constexpr OutputIterator  // constexpr since C++20
71    partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
72
73template<class InputIterator, class OutputIterator, class T>
74    constexpr OutputIterator  // constexpr since C++20
75    exclusive_scan(InputIterator first, InputIterator last,
76                   OutputIterator result, T init); // C++17
77
78template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
79    constexpr OutputIterator  // constexpr since C++20
80    exclusive_scan(InputIterator first, InputIterator last,
81                   OutputIterator result, T init, BinaryOperation binary_op); // C++17
82
83template<class InputIterator, class OutputIterator>
84    constexpr OutputIterator  // constexpr since C++20
85    inclusive_scan(InputIterator first, InputIterator last, OutputIterator result);  // C++17
86
87template<class InputIterator, class OutputIterator, class BinaryOperation>
88    constexpr OutputIterator  // constexpr since C++20
89    inclusive_scan(InputIterator first, InputIterator last,
90                   OutputIterator result, BinaryOperation binary_op);  // C++17
91
92template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
93    constexpr OutputIterator  // constexpr since C++20
94    inclusive_scan(InputIterator first, InputIterator last,
95                   OutputIterator result, BinaryOperation binary_op, T init);  // C++17
96
97template<class InputIterator, class OutputIterator, class T,
98         class BinaryOperation, class UnaryOperation>
99    constexpr OutputIterator  // constexpr since C++20
100    transform_exclusive_scan(InputIterator first, InputIterator last,
101                             OutputIterator result, T init,
102                             BinaryOperation binary_op, UnaryOperation unary_op);  // C++17
103
104template<class InputIterator, class OutputIterator,
105         class BinaryOperation, class UnaryOperation>
106    constexpr OutputIterator  // constexpr since C++20
107    transform_inclusive_scan(InputIterator first, InputIterator last,
108                             OutputIterator result,
109                             BinaryOperation binary_op, UnaryOperation unary_op);  // C++17
110
111template<class InputIterator, class OutputIterator,
112         class BinaryOperation, class UnaryOperation, class T>
113    constexpr OutputIterator  // constexpr since C++20
114    transform_inclusive_scan(InputIterator first, InputIterator last,
115                             OutputIterator result,
116                             BinaryOperation binary_op, UnaryOperation unary_op,
117                             T init);  // C++17
118
119template <class InputIterator, class OutputIterator>
120    constexpr OutputIterator  // constexpr since C++20
121    adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);
122
123template <class InputIterator, class OutputIterator, class BinaryOperation>
124    constexpr OutputIterator  // constexpr since C++20
125    adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
126
127template <class ForwardIterator, class T>
128    constexpr void  // constexpr since C++20
129    iota(ForwardIterator first, ForwardIterator last, T value);
130
131template <class M, class N>
132    constexpr common_type_t<M,N> gcd(M m, N n);    // C++17
133
134template <class M, class N>
135    constexpr common_type_t<M,N> lcm(M m, N n);    // C++17
136
137template<class T>
138    constexpr T midpoint(T a, T b) noexcept;  // C++20
139
140template<class T>
141    constexpr T* midpoint(T* a, T* b);        // C++20
142
143}  // std
144
145*/
146
147#include <__config>
148#include <iterator>
149#include <limits> // for numeric_limits
150#include <functional>
151#include <cmath> // for isnormal
152#include <version>
153
154#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
155#pragma GCC system_header
156#endif
157
158_LIBCPP_PUSH_MACROS
159#include <__undef_macros>
160
161_LIBCPP_BEGIN_NAMESPACE_STD
162
163template <class _InputIterator, class _Tp>
164_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
165_Tp
166accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
167{
168    for (; __first != __last; ++__first)
169#if _LIBCPP_STD_VER > 17
170        __init = _VSTD::move(__init) + *__first;
171#else
172        __init = __init + *__first;
173#endif
174    return __init;
175}
176
177template <class _InputIterator, class _Tp, class _BinaryOperation>
178_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
179_Tp
180accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
181{
182    for (; __first != __last; ++__first)
183#if _LIBCPP_STD_VER > 17
184        __init = __binary_op(_VSTD::move(__init), *__first);
185#else
186        __init = __binary_op(__init, *__first);
187#endif
188    return __init;
189}
190
191#if _LIBCPP_STD_VER > 14
192template <class _InputIterator, class _Tp, class _BinaryOp>
193_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
194_Tp
195reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
196{
197    for (; __first != __last; ++__first)
198        __init = __b(__init, *__first);
199    return __init;
200}
201
202template <class _InputIterator, class _Tp>
203_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
204_Tp
205reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
206{
207    return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
208}
209
210template <class _InputIterator>
211_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
212typename iterator_traits<_InputIterator>::value_type
213reduce(_InputIterator __first, _InputIterator __last)
214{
215    return _VSTD::reduce(__first, __last,
216       typename iterator_traits<_InputIterator>::value_type{});
217}
218#endif
219
220template <class _InputIterator1, class _InputIterator2, class _Tp>
221_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
222_Tp
223inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
224{
225    for (; __first1 != __last1; ++__first1, (void) ++__first2)
226#if _LIBCPP_STD_VER > 17
227        __init = _VSTD::move(__init) + *__first1 * *__first2;
228#else
229        __init = __init + *__first1 * *__first2;
230#endif
231    return __init;
232}
233
234template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
235_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
236_Tp
237inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
238              _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
239{
240    for (; __first1 != __last1; ++__first1, (void) ++__first2)
241#if _LIBCPP_STD_VER > 17
242        __init = __binary_op1(_VSTD::move(__init), __binary_op2(*__first1, *__first2));
243#else
244        __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
245#endif
246    return __init;
247}
248
249#if _LIBCPP_STD_VER > 14
250template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
251_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
252_Tp
253transform_reduce(_InputIterator __first, _InputIterator __last,
254           _Tp __init,  _BinaryOp __b, _UnaryOp __u)
255{
256    for (; __first != __last; ++__first)
257        __init = __b(__init, __u(*__first));
258    return __init;
259}
260
261template <class _InputIterator1, class _InputIterator2,
262          class _Tp, class _BinaryOp1, class _BinaryOp2>
263_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
264_Tp
265transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
266                 _InputIterator2 __first2, _Tp __init,  _BinaryOp1 __b1, _BinaryOp2 __b2)
267{
268    for (; __first1 != __last1; ++__first1, (void) ++__first2)
269        __init = __b1(__init, __b2(*__first1, *__first2));
270    return __init;
271}
272
273template <class _InputIterator1, class _InputIterator2, class _Tp>
274_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
275_Tp
276transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
277                 _InputIterator2 __first2, _Tp __init)
278{
279    return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
280                                   _VSTD::plus<>(), _VSTD::multiplies<>());
281}
282#endif
283
284template <class _InputIterator, class _OutputIterator>
285_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
286_OutputIterator
287partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
288{
289    if (__first != __last)
290    {
291        typename iterator_traits<_InputIterator>::value_type __t(*__first);
292        *__result = __t;
293        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
294        {
295#if _LIBCPP_STD_VER > 17
296            __t = _VSTD::move(__t) + *__first;
297#else
298            __t = __t + *__first;
299#endif
300            *__result = __t;
301        }
302    }
303    return __result;
304}
305
306template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
307_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
308_OutputIterator
309partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
310              _BinaryOperation __binary_op)
311{
312    if (__first != __last)
313    {
314        typename iterator_traits<_InputIterator>::value_type __t(*__first);
315        *__result = __t;
316        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
317        {
318#if _LIBCPP_STD_VER > 17
319            __t = __binary_op(_VSTD::move(__t), *__first);
320#else
321            __t = __binary_op(__t, *__first);
322#endif
323            *__result = __t;
324        }
325    }
326    return __result;
327}
328
329#if _LIBCPP_STD_VER > 14
330template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
331_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
332_OutputIterator
333exclusive_scan(_InputIterator __first, _InputIterator __last,
334               _OutputIterator __result, _Tp __init, _BinaryOp __b)
335{
336    if (__first != __last)
337    {
338        _Tp __tmp(__b(__init, *__first));
339        while (true)
340        {
341            *__result = _VSTD::move(__init);
342            ++__result;
343            ++__first;
344            if (__first == __last)
345                break;
346            __init = _VSTD::move(__tmp);
347            __tmp = __b(__init, *__first);
348        }
349    }
350    return __result;
351}
352
353template <class _InputIterator, class _OutputIterator, class _Tp>
354_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
355_OutputIterator
356exclusive_scan(_InputIterator __first, _InputIterator __last,
357               _OutputIterator __result, _Tp __init)
358{
359    return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
360}
361
362template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
363_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
364_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
365                               _OutputIterator __result, _BinaryOp __b,  _Tp __init)
366{
367    for (; __first != __last; ++__first, (void) ++__result) {
368        __init = __b(__init, *__first);
369        *__result = __init;
370    }
371    return __result;
372}
373
374template <class _InputIterator, class _OutputIterator, class _BinaryOp>
375_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
376_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
377                               _OutputIterator __result, _BinaryOp __b)
378{
379    if (__first != __last) {
380        typename iterator_traits<_InputIterator>::value_type __init = *__first;
381        *__result++ = __init;
382        if (++__first != __last)
383            return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
384    }
385
386    return __result;
387}
388
389template <class _InputIterator, class _OutputIterator>
390_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
391_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
392                               _OutputIterator __result)
393{
394    return _VSTD::inclusive_scan(__first, __last, __result, _VSTD::plus<>());
395}
396
397template <class _InputIterator, class _OutputIterator, class _Tp,
398          class _BinaryOp, class _UnaryOp>
399_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
400_OutputIterator
401transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
402                           _OutputIterator __result, _Tp __init,
403                           _BinaryOp __b, _UnaryOp __u)
404{
405    if (__first != __last)
406    {
407        _Tp __saved = __init;
408        do
409        {
410            __init = __b(__init, __u(*__first));
411            *__result = __saved;
412            __saved = __init;
413            ++__result;
414        } while (++__first != __last);
415    }
416    return __result;
417}
418
419template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
420_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
421_OutputIterator
422transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
423                           _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
424{
425    for (; __first != __last; ++__first, (void) ++__result) {
426        __init = __b(__init, __u(*__first));
427        *__result = __init;
428        }
429
430    return __result;
431}
432
433template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
434_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
435_OutputIterator
436transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
437                               _OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
438{
439    if (__first != __last) {
440        typename iterator_traits<_InputIterator>::value_type __init = __u(*__first);
441        *__result++ = __init;
442        if (++__first != __last)
443            return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
444    }
445
446    return __result;
447}
448#endif
449
450template <class _InputIterator, class _OutputIterator>
451_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
452_OutputIterator
453adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
454{
455    if (__first != __last)
456    {
457        typename iterator_traits<_InputIterator>::value_type __acc(*__first);
458        *__result = __acc;
459        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
460        {
461            typename iterator_traits<_InputIterator>::value_type __val(*__first);
462#if _LIBCPP_STD_VER > 17
463            *__result = __val - _VSTD::move(__acc);
464#else
465            *__result = __val - __acc;
466#endif
467            __acc = _VSTD::move(__val);
468        }
469    }
470    return __result;
471}
472
473template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
474_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
475_OutputIterator
476adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
477                      _BinaryOperation __binary_op)
478{
479    if (__first != __last)
480    {
481        typename iterator_traits<_InputIterator>::value_type __acc(*__first);
482        *__result = __acc;
483        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
484        {
485            typename iterator_traits<_InputIterator>::value_type __val(*__first);
486#if _LIBCPP_STD_VER > 17
487            *__result = __binary_op(__val, _VSTD::move(__acc));
488#else
489            *__result = __binary_op(__val, __acc);
490#endif
491            __acc = _VSTD::move(__val);
492        }
493    }
494    return __result;
495}
496
497template <class _ForwardIterator, class _Tp>
498_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
499void
500iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
501{
502    for (; __first != __last; ++__first, (void) ++__value_)
503        *__first = __value_;
504}
505
506
507#if _LIBCPP_STD_VER > 14
508template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs;
509
510template <typename _Result, typename _Source>
511struct __ct_abs<_Result, _Source, true> {
512    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
513    _Result operator()(_Source __t) const noexcept
514    {
515        if (__t >= 0) return __t;
516        if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
517        return -__t;
518    }
519};
520
521template <typename _Result, typename _Source>
522struct __ct_abs<_Result, _Source, false> {
523    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
524    _Result operator()(_Source __t) const noexcept { return __t; }
525};
526
527
528template<class _Tp>
529_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
530_Tp __gcd(_Tp __m, _Tp __n)
531{
532    static_assert((!is_signed<_Tp>::value), "");
533    return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
534}
535
536
537template<class _Tp, class _Up>
538_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
539common_type_t<_Tp,_Up>
540gcd(_Tp __m, _Up __n)
541{
542    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
543    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
544    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
545    using _Rp = common_type_t<_Tp,_Up>;
546    using _Wp = make_unsigned_t<_Rp>;
547    return static_cast<_Rp>(_VSTD::__gcd(
548        static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)),
549        static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
550}
551
552template<class _Tp, class _Up>
553_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
554common_type_t<_Tp,_Up>
555lcm(_Tp __m, _Up __n)
556{
557    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
558    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
559    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
560    if (__m == 0 || __n == 0)
561        return 0;
562
563    using _Rp = common_type_t<_Tp,_Up>;
564    _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
565    _Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
566    _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
567    return __val1 * __val2;
568}
569
570#endif /* _LIBCPP_STD_VER > 14 */
571
572#if _LIBCPP_STD_VER > 17
573template <class _Tp>
574_LIBCPP_INLINE_VISIBILITY constexpr
575enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
576midpoint(_Tp __a, _Tp __b) noexcept
577_LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
578{
579    using _Up = make_unsigned_t<_Tp>;
580    constexpr _Up __bitshift = numeric_limits<_Up>::digits - 1;
581
582    _Up __diff = _Up(__b) - _Up(__a);
583    _Up __sign_bit = __b < __a;
584
585    _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff);
586
587    return __a + __half_diff;
588}
589
590
591template <class _TPtr>
592_LIBCPP_INLINE_VISIBILITY constexpr
593enable_if_t<is_pointer_v<_TPtr>
594             && is_object_v<remove_pointer_t<_TPtr>>
595             && ! is_void_v<remove_pointer_t<_TPtr>>
596             && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr>
597midpoint(_TPtr __a, _TPtr __b) noexcept
598{
599    return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a);
600}
601
602
603template <typename _Tp>
604constexpr int __sign(_Tp __val) {
605    return (_Tp(0) < __val) - (__val < _Tp(0));
606}
607
608template <typename _Fp>
609constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; }
610
611template <class _Fp>
612_LIBCPP_INLINE_VISIBILITY constexpr
613enable_if_t<is_floating_point_v<_Fp>, _Fp>
614midpoint(_Fp __a, _Fp __b) noexcept
615{
616	constexpr _Fp __lo = numeric_limits<_Fp>::min()*2;
617	constexpr _Fp __hi = numeric_limits<_Fp>::max()/2;
618    return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ?  // typical case: overflow is impossible
619      (__a + __b)/2 :                                        // always correctly rounded
620      __fp_abs(__a) < __lo ? __a + __b/2 :                   // not safe to halve a
621      __fp_abs(__b) < __lo ? __a/2 + __b :                   // not safe to halve b
622      __a/2 + __b/2;                                         // otherwise correctly rounded
623}
624
625#endif // _LIBCPP_STD_VER > 17
626
627_LIBCPP_END_NAMESPACE_STD
628
629_LIBCPP_POP_MACROS
630
631#if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17
632#   include <__pstl_numeric>
633#endif
634
635#endif  // _LIBCPP_NUMERIC
636