xref: /freebsd/contrib/llvm-project/libcxx/include/numeric (revision 13ec1e3155c7e9bf037b12af186351b7fa9b9450) 
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 <__debug>
149#include <cmath> // for isnormal
150#include <functional>
151#include <iterator>
152#include <limits> // for numeric_limits
153#include <version>
154
155#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
156#pragma GCC system_header
157#endif
158
159_LIBCPP_PUSH_MACROS
160#include <__undef_macros>
161
162_LIBCPP_BEGIN_NAMESPACE_STD
163
164template <class _InputIterator, class _Tp>
165_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
166_Tp
167accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
168{
169    for (; __first != __last; ++__first)
170#if _LIBCPP_STD_VER > 17
171        __init = _VSTD::move(__init) + *__first;
172#else
173        __init = __init + *__first;
174#endif
175    return __init;
176}
177
178template <class _InputIterator, class _Tp, class _BinaryOperation>
179_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
180_Tp
181accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
182{
183    for (; __first != __last; ++__first)
184#if _LIBCPP_STD_VER > 17
185        __init = __binary_op(_VSTD::move(__init), *__first);
186#else
187        __init = __binary_op(__init, *__first);
188#endif
189    return __init;
190}
191
192#if _LIBCPP_STD_VER > 14
193template <class _InputIterator, class _Tp, class _BinaryOp>
194_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
195_Tp
196reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
197{
198    for (; __first != __last; ++__first)
199        __init = __b(__init, *__first);
200    return __init;
201}
202
203template <class _InputIterator, class _Tp>
204_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
205_Tp
206reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
207{
208    return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
209}
210
211template <class _InputIterator>
212_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
213typename iterator_traits<_InputIterator>::value_type
214reduce(_InputIterator __first, _InputIterator __last)
215{
216    return _VSTD::reduce(__first, __last,
217       typename iterator_traits<_InputIterator>::value_type{});
218}
219#endif
220
221template <class _InputIterator1, class _InputIterator2, class _Tp>
222_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
223_Tp
224inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
225{
226    for (; __first1 != __last1; ++__first1, (void) ++__first2)
227#if _LIBCPP_STD_VER > 17
228        __init = _VSTD::move(__init) + *__first1 * *__first2;
229#else
230        __init = __init + *__first1 * *__first2;
231#endif
232    return __init;
233}
234
235template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
236_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
237_Tp
238inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
239              _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
240{
241    for (; __first1 != __last1; ++__first1, (void) ++__first2)
242#if _LIBCPP_STD_VER > 17
243        __init = __binary_op1(_VSTD::move(__init), __binary_op2(*__first1, *__first2));
244#else
245        __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
246#endif
247    return __init;
248}
249
250#if _LIBCPP_STD_VER > 14
251template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
252_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
253_Tp
254transform_reduce(_InputIterator __first, _InputIterator __last,
255           _Tp __init,  _BinaryOp __b, _UnaryOp __u)
256{
257    for (; __first != __last; ++__first)
258        __init = __b(__init, __u(*__first));
259    return __init;
260}
261
262template <class _InputIterator1, class _InputIterator2,
263          class _Tp, class _BinaryOp1, class _BinaryOp2>
264_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
265_Tp
266transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
267                 _InputIterator2 __first2, _Tp __init,  _BinaryOp1 __b1, _BinaryOp2 __b2)
268{
269    for (; __first1 != __last1; ++__first1, (void) ++__first2)
270        __init = __b1(__init, __b2(*__first1, *__first2));
271    return __init;
272}
273
274template <class _InputIterator1, class _InputIterator2, class _Tp>
275_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
276_Tp
277transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
278                 _InputIterator2 __first2, _Tp __init)
279{
280    return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
281                                   _VSTD::plus<>(), _VSTD::multiplies<>());
282}
283#endif
284
285template <class _InputIterator, class _OutputIterator>
286_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
287_OutputIterator
288partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
289{
290    if (__first != __last)
291    {
292        typename iterator_traits<_InputIterator>::value_type __t(*__first);
293        *__result = __t;
294        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
295        {
296#if _LIBCPP_STD_VER > 17
297            __t = _VSTD::move(__t) + *__first;
298#else
299            __t = __t + *__first;
300#endif
301            *__result = __t;
302        }
303    }
304    return __result;
305}
306
307template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
308_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
309_OutputIterator
310partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
311              _BinaryOperation __binary_op)
312{
313    if (__first != __last)
314    {
315        typename iterator_traits<_InputIterator>::value_type __t(*__first);
316        *__result = __t;
317        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
318        {
319#if _LIBCPP_STD_VER > 17
320            __t = __binary_op(_VSTD::move(__t), *__first);
321#else
322            __t = __binary_op(__t, *__first);
323#endif
324            *__result = __t;
325        }
326    }
327    return __result;
328}
329
330#if _LIBCPP_STD_VER > 14
331template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
332_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
333_OutputIterator
334exclusive_scan(_InputIterator __first, _InputIterator __last,
335               _OutputIterator __result, _Tp __init, _BinaryOp __b)
336{
337    if (__first != __last)
338    {
339        _Tp __tmp(__b(__init, *__first));
340        while (true)
341        {
342            *__result = _VSTD::move(__init);
343            ++__result;
344            ++__first;
345            if (__first == __last)
346                break;
347            __init = _VSTD::move(__tmp);
348            __tmp = __b(__init, *__first);
349        }
350    }
351    return __result;
352}
353
354template <class _InputIterator, class _OutputIterator, class _Tp>
355_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
356_OutputIterator
357exclusive_scan(_InputIterator __first, _InputIterator __last,
358               _OutputIterator __result, _Tp __init)
359{
360    return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
361}
362
363template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
364_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
365_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
366                               _OutputIterator __result, _BinaryOp __b,  _Tp __init)
367{
368    for (; __first != __last; ++__first, (void) ++__result) {
369        __init = __b(__init, *__first);
370        *__result = __init;
371    }
372    return __result;
373}
374
375template <class _InputIterator, class _OutputIterator, class _BinaryOp>
376_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
377_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
378                               _OutputIterator __result, _BinaryOp __b)
379{
380    if (__first != __last) {
381        typename iterator_traits<_InputIterator>::value_type __init = *__first;
382        *__result++ = __init;
383        if (++__first != __last)
384            return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
385    }
386
387    return __result;
388}
389
390template <class _InputIterator, class _OutputIterator>
391_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
392_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
393                               _OutputIterator __result)
394{
395    return _VSTD::inclusive_scan(__first, __last, __result, _VSTD::plus<>());
396}
397
398template <class _InputIterator, class _OutputIterator, class _Tp,
399          class _BinaryOp, class _UnaryOp>
400_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
401_OutputIterator
402transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
403                           _OutputIterator __result, _Tp __init,
404                           _BinaryOp __b, _UnaryOp __u)
405{
406    if (__first != __last)
407    {
408        _Tp __saved = __init;
409        do
410        {
411            __init = __b(__init, __u(*__first));
412            *__result = __saved;
413            __saved = __init;
414            ++__result;
415        } while (++__first != __last);
416    }
417    return __result;
418}
419
420template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
421_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
422_OutputIterator
423transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
424                           _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
425{
426    for (; __first != __last; ++__first, (void) ++__result) {
427        __init = __b(__init, __u(*__first));
428        *__result = __init;
429        }
430
431    return __result;
432}
433
434template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
435_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
436_OutputIterator
437transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
438                               _OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
439{
440    if (__first != __last) {
441        typename iterator_traits<_InputIterator>::value_type __init = __u(*__first);
442        *__result++ = __init;
443        if (++__first != __last)
444            return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
445    }
446
447    return __result;
448}
449#endif
450
451template <class _InputIterator, class _OutputIterator>
452_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
453_OutputIterator
454adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
455{
456    if (__first != __last)
457    {
458        typename iterator_traits<_InputIterator>::value_type __acc(*__first);
459        *__result = __acc;
460        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
461        {
462            typename iterator_traits<_InputIterator>::value_type __val(*__first);
463#if _LIBCPP_STD_VER > 17
464            *__result = __val - _VSTD::move(__acc);
465#else
466            *__result = __val - __acc;
467#endif
468            __acc = _VSTD::move(__val);
469        }
470    }
471    return __result;
472}
473
474template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
475_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
476_OutputIterator
477adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
478                      _BinaryOperation __binary_op)
479{
480    if (__first != __last)
481    {
482        typename iterator_traits<_InputIterator>::value_type __acc(*__first);
483        *__result = __acc;
484        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
485        {
486            typename iterator_traits<_InputIterator>::value_type __val(*__first);
487#if _LIBCPP_STD_VER > 17
488            *__result = __binary_op(__val, _VSTD::move(__acc));
489#else
490            *__result = __binary_op(__val, __acc);
491#endif
492            __acc = _VSTD::move(__val);
493        }
494    }
495    return __result;
496}
497
498template <class _ForwardIterator, class _Tp>
499_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
500void
501iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
502{
503    for (; __first != __last; ++__first, (void) ++__value_)
504        *__first = __value_;
505}
506
507
508#if _LIBCPP_STD_VER > 14
509template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs;
510
511template <typename _Result, typename _Source>
512struct __ct_abs<_Result, _Source, true> {
513    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
514    _Result operator()(_Source __t) const noexcept
515    {
516        if (__t >= 0) return __t;
517        if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
518        return -__t;
519    }
520};
521
522template <typename _Result, typename _Source>
523struct __ct_abs<_Result, _Source, false> {
524    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
525    _Result operator()(_Source __t) const noexcept { return __t; }
526};
527
528
529template<class _Tp>
530_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
531_Tp __gcd(_Tp __m, _Tp __n)
532{
533    static_assert((!is_signed<_Tp>::value), "");
534    return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
535}
536
537
538template<class _Tp, class _Up>
539_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
540common_type_t<_Tp,_Up>
541gcd(_Tp __m, _Up __n)
542{
543    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
544    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
545    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
546    using _Rp = common_type_t<_Tp,_Up>;
547    using _Wp = make_unsigned_t<_Rp>;
548    return static_cast<_Rp>(_VSTD::__gcd(
549        static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)),
550        static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
551}
552
553template<class _Tp, class _Up>
554_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
555common_type_t<_Tp,_Up>
556lcm(_Tp __m, _Up __n)
557{
558    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
559    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
560    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
561    if (__m == 0 || __n == 0)
562        return 0;
563
564    using _Rp = common_type_t<_Tp,_Up>;
565    _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
566    _Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
567    _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
568    return __val1 * __val2;
569}
570
571#endif /* _LIBCPP_STD_VER > 14 */
572
573#if _LIBCPP_STD_VER > 17
574template <class _Tp>
575_LIBCPP_INLINE_VISIBILITY constexpr
576enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
577midpoint(_Tp __a, _Tp __b) noexcept
578_LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
579{
580    using _Up = make_unsigned_t<_Tp>;
581    constexpr _Up __bitshift = numeric_limits<_Up>::digits - 1;
582
583    _Up __diff = _Up(__b) - _Up(__a);
584    _Up __sign_bit = __b < __a;
585
586    _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff);
587
588    return __a + __half_diff;
589}
590
591
592template <class _TPtr>
593_LIBCPP_INLINE_VISIBILITY constexpr
594enable_if_t<is_pointer_v<_TPtr>
595             && is_object_v<remove_pointer_t<_TPtr>>
596             && ! is_void_v<remove_pointer_t<_TPtr>>
597             && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr>
598midpoint(_TPtr __a, _TPtr __b) noexcept
599{
600    return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a);
601}
602
603
604template <typename _Tp>
605constexpr int __sign(_Tp __val) {
606    return (_Tp(0) < __val) - (__val < _Tp(0));
607}
608
609template <typename _Fp>
610constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; }
611
612template <class _Fp>
613_LIBCPP_INLINE_VISIBILITY constexpr
614enable_if_t<is_floating_point_v<_Fp>, _Fp>
615midpoint(_Fp __a, _Fp __b) noexcept
616{
617    constexpr _Fp __lo = numeric_limits<_Fp>::min()*2;
618    constexpr _Fp __hi = numeric_limits<_Fp>::max()/2;
619    return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ?  // typical case: overflow is impossible
620      (__a + __b)/2 :                                        // always correctly rounded
621      __fp_abs(__a) < __lo ? __a + __b/2 :                   // not safe to halve a
622      __fp_abs(__b) < __lo ? __a/2 + __b :                   // not safe to halve b
623      __a/2 + __b/2;                                         // otherwise correctly rounded
624}
625
626#endif // _LIBCPP_STD_VER > 17
627
628_LIBCPP_END_NAMESPACE_STD
629
630_LIBCPP_POP_MACROS
631
632#if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17
633#   include <__pstl_numeric>
634#endif
635
636#endif // _LIBCPP_NUMERIC
637