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 __saved = __init;
339        do
340        {
341            __init = __b(__init, *__first);
342            *__result = __saved;
343            __saved = __init;
344            ++__result;
345        } while (++__first != __last);
346    }
347    return __result;
348}
349
350template <class _InputIterator, class _OutputIterator, class _Tp>
351_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
352_OutputIterator
353exclusive_scan(_InputIterator __first, _InputIterator __last,
354               _OutputIterator __result, _Tp __init)
355{
356    return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
357}
358
359template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
360_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
361_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
362                               _OutputIterator __result, _BinaryOp __b,  _Tp __init)
363{
364    for (; __first != __last; ++__first, (void) ++__result) {
365        __init = __b(__init, *__first);
366        *__result = __init;
367    }
368    return __result;
369}
370
371template <class _InputIterator, class _OutputIterator, class _BinaryOp>
372_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
373_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
374                               _OutputIterator __result, _BinaryOp __b)
375{
376    if (__first != __last) {
377        typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
378        *__result++ = __init;
379        if (++__first != __last)
380            return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
381    }
382
383    return __result;
384}
385
386template <class _InputIterator, class _OutputIterator>
387_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
388_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
389                               _OutputIterator __result)
390{
391    return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
392}
393
394template <class _InputIterator, class _OutputIterator, class _Tp,
395          class _BinaryOp, class _UnaryOp>
396_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
397_OutputIterator
398transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
399                           _OutputIterator __result, _Tp __init,
400                           _BinaryOp __b, _UnaryOp __u)
401{
402    if (__first != __last)
403    {
404        _Tp __saved = __init;
405        do
406        {
407            __init = __b(__init, __u(*__first));
408            *__result = __saved;
409            __saved = __init;
410            ++__result;
411        } while (++__first != __last);
412    }
413    return __result;
414}
415
416template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
417_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
418_OutputIterator
419transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
420                           _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
421{
422    for (; __first != __last; ++__first, (void) ++__result) {
423        __init = __b(__init, __u(*__first));
424        *__result = __init;
425        }
426
427    return __result;
428}
429
430template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
431_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
432_OutputIterator
433transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
434                               _OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
435{
436    if (__first != __last) {
437        typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
438        *__result++ = __init;
439        if (++__first != __last)
440            return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
441    }
442
443    return __result;
444}
445#endif
446
447template <class _InputIterator, class _OutputIterator>
448_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
449_OutputIterator
450adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
451{
452    if (__first != __last)
453    {
454        typename iterator_traits<_InputIterator>::value_type __acc(*__first);
455        *__result = __acc;
456        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
457        {
458            typename iterator_traits<_InputIterator>::value_type __val(*__first);
459#if _LIBCPP_STD_VER > 17
460            *__result = __val - _VSTD::move(__acc);
461#else
462            *__result = __val - __acc;
463#endif
464            __acc = _VSTD::move(__val);
465        }
466    }
467    return __result;
468}
469
470template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
471_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
472_OutputIterator
473adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
474                      _BinaryOperation __binary_op)
475{
476    if (__first != __last)
477    {
478        typename iterator_traits<_InputIterator>::value_type __acc(*__first);
479        *__result = __acc;
480        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
481        {
482            typename iterator_traits<_InputIterator>::value_type __val(*__first);
483#if _LIBCPP_STD_VER > 17
484            *__result = __binary_op(__val, _VSTD::move(__acc));
485#else
486            *__result = __binary_op(__val, __acc);
487#endif
488            __acc = _VSTD::move(__val);
489        }
490    }
491    return __result;
492}
493
494template <class _ForwardIterator, class _Tp>
495_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
496void
497iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
498{
499    for (; __first != __last; ++__first, (void) ++__value_)
500        *__first = __value_;
501}
502
503
504#if _LIBCPP_STD_VER > 14
505template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs;
506
507template <typename _Result, typename _Source>
508struct __ct_abs<_Result, _Source, true> {
509    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
510    _Result operator()(_Source __t) const noexcept
511    {
512        if (__t >= 0) return __t;
513        if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
514        return -__t;
515    }
516};
517
518template <typename _Result, typename _Source>
519struct __ct_abs<_Result, _Source, false> {
520    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
521    _Result operator()(_Source __t) const noexcept { return __t; }
522};
523
524
525template<class _Tp>
526_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
527_Tp __gcd(_Tp __m, _Tp __n)
528{
529    static_assert((!is_signed<_Tp>::value), "");
530    return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
531}
532
533
534template<class _Tp, class _Up>
535_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
536common_type_t<_Tp,_Up>
537gcd(_Tp __m, _Up __n)
538{
539    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
540    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
541    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
542    using _Rp = common_type_t<_Tp,_Up>;
543    using _Wp = make_unsigned_t<_Rp>;
544    return static_cast<_Rp>(_VSTD::__gcd(
545        static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)),
546        static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
547}
548
549template<class _Tp, class _Up>
550_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
551common_type_t<_Tp,_Up>
552lcm(_Tp __m, _Up __n)
553{
554    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
555    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
556    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
557    if (__m == 0 || __n == 0)
558        return 0;
559
560    using _Rp = common_type_t<_Tp,_Up>;
561    _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
562    _Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
563    _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
564    return __val1 * __val2;
565}
566
567#endif /* _LIBCPP_STD_VER > 14 */
568
569#if _LIBCPP_STD_VER > 17
570template <class _Tp>
571_LIBCPP_INLINE_VISIBILITY constexpr
572enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
573midpoint(_Tp __a, _Tp __b) noexcept
574_LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
575{
576    using _Up = std::make_unsigned_t<_Tp>;
577    constexpr _Up __bitshift = std::numeric_limits<_Up>::digits - 1;
578
579    _Up __diff = _Up(__b) - _Up(__a);
580    _Up __sign_bit = __b < __a;
581
582    _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff);
583
584    return __a + __half_diff;
585}
586
587
588template <class _TPtr>
589_LIBCPP_INLINE_VISIBILITY constexpr
590enable_if_t<is_pointer_v<_TPtr>
591             && is_object_v<remove_pointer_t<_TPtr>>
592             && ! is_void_v<remove_pointer_t<_TPtr>>
593             && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr>
594midpoint(_TPtr __a, _TPtr __b) noexcept
595{
596    return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a);
597}
598
599
600template <typename _Tp>
601constexpr int __sign(_Tp __val) {
602    return (_Tp(0) < __val) - (__val < _Tp(0));
603}
604
605template <typename _Fp>
606constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; }
607
608template <class _Fp>
609_LIBCPP_INLINE_VISIBILITY constexpr
610enable_if_t<is_floating_point_v<_Fp>, _Fp>
611midpoint(_Fp __a, _Fp __b) noexcept
612{
613	constexpr _Fp __lo = numeric_limits<_Fp>::min()*2;
614	constexpr _Fp __hi = numeric_limits<_Fp>::max()/2;
615    return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ?  // typical case: overflow is impossible
616      (__a + __b)/2 :                                        // always correctly rounded
617      __fp_abs(__a) < __lo ? __a + __b/2 :                   // not safe to halve a
618      __fp_abs(__b) < __lo ? __a/2 + __b :                   // not safe to halve b
619      __a/2 + __b/2;                                         // otherwise correctly rounded
620}
621
622#endif // _LIBCPP_STD_VER > 17
623
624_LIBCPP_END_NAMESPACE_STD
625
626_LIBCPP_POP_MACROS
627
628#if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17
629#   include <__pstl_numeric>
630#endif
631
632#endif  // _LIBCPP_NUMERIC
633