xref: /freebsd/contrib/llvm-project/libcxx/include/numeric (revision f976241773df2260e6170317080761d1c5814fe5) 
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    T
21    accumulate(InputIterator first, InputIterator last, T init);
22
23template <class InputIterator, class T, class BinaryOperation>
24    T
25    accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
26
27template<class InputIterator>
28    typename iterator_traits<InputIterator>::value_type
29    reduce(InputIterator first, InputIterator last);  // C++17
30
31template<class InputIterator, class T>
32    T
33    reduce(InputIterator first, InputIterator last, T init);  // C++17
34
35template<class InputIterator, class T, class BinaryOperation>
36    T
37    reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);  // C++17
38
39template <class InputIterator1, class InputIterator2, class T>
40    T
41    inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
42
43template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
44    T
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    T
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    T
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    T
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    OutputIterator
67    partial_sum(InputIterator first, InputIterator last, OutputIterator result);
68
69template <class InputIterator, class OutputIterator, class BinaryOperation>
70    OutputIterator
71    partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
72
73template<class InputIterator, class OutputIterator, class T>
74    OutputIterator
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    OutputIterator
80    exclusive_scan(InputIterator first, InputIterator last,
81                   OutputIterator result, T init, BinaryOperation binary_op); // C++17
82
83template<class InputIterator, class OutputIterator>
84    OutputIterator
85    inclusive_scan(InputIterator first, InputIterator last, OutputIterator result);  // C++17
86
87template<class InputIterator, class OutputIterator, class BinaryOperation>
88    OutputIterator
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    OutputIterator
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    OutputIterator
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    OutputIterator
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    OutputIterator
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    OutputIterator
121    adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);
122
123template <class InputIterator, class OutputIterator, class BinaryOperation>
124    OutputIterator
125    adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
126
127template <class ForwardIterator, class T>
128    void iota(ForwardIterator first, ForwardIterator last, T value);
129
130template <class M, class N>
131    constexpr common_type_t<M,N> gcd(M m, N n);    // C++17
132
133template <class M, class N>
134    constexpr common_type_t<M,N> lcm(M m, N n);    // C++17
135
136integer         midpoint(integer a, integer b);                  // C++20
137pointer         midpoint(pointer a, pointer b);                  // C++20
138floating_point  midpoint(floating_point a, floating_point b);    // C++20
139
140}  // std
141
142*/
143
144#include <__config>
145#include <iterator>
146#include <limits> // for numeric_limits
147#include <functional>
148#include <cmath> // for isnormal
149#include <version>
150
151#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
152#pragma GCC system_header
153#endif
154
155_LIBCPP_PUSH_MACROS
156#include <__undef_macros>
157
158_LIBCPP_BEGIN_NAMESPACE_STD
159
160template <class _InputIterator, class _Tp>
161inline _LIBCPP_INLINE_VISIBILITY
162_Tp
163accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
164{
165    for (; __first != __last; ++__first)
166        __init = __init + *__first;
167    return __init;
168}
169
170template <class _InputIterator, class _Tp, class _BinaryOperation>
171inline _LIBCPP_INLINE_VISIBILITY
172_Tp
173accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
174{
175    for (; __first != __last; ++__first)
176        __init = __binary_op(__init, *__first);
177    return __init;
178}
179
180#if _LIBCPP_STD_VER > 14
181template <class _InputIterator, class _Tp, class _BinaryOp>
182inline _LIBCPP_INLINE_VISIBILITY
183_Tp
184reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
185{
186    for (; __first != __last; ++__first)
187        __init = __b(__init, *__first);
188    return __init;
189}
190
191template <class _InputIterator, class _Tp>
192inline _LIBCPP_INLINE_VISIBILITY
193_Tp
194reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
195{
196    return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
197}
198
199template <class _InputIterator>
200inline _LIBCPP_INLINE_VISIBILITY
201typename iterator_traits<_InputIterator>::value_type
202reduce(_InputIterator __first, _InputIterator __last)
203{
204    return _VSTD::reduce(__first, __last,
205       typename iterator_traits<_InputIterator>::value_type{});
206}
207#endif
208
209template <class _InputIterator1, class _InputIterator2, class _Tp>
210inline _LIBCPP_INLINE_VISIBILITY
211_Tp
212inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
213{
214    for (; __first1 != __last1; ++__first1, (void) ++__first2)
215        __init = __init + *__first1 * *__first2;
216    return __init;
217}
218
219template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
220inline _LIBCPP_INLINE_VISIBILITY
221_Tp
222inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
223              _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
224{
225    for (; __first1 != __last1; ++__first1, (void) ++__first2)
226        __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
227    return __init;
228}
229
230#if _LIBCPP_STD_VER > 14
231template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
232inline _LIBCPP_INLINE_VISIBILITY
233_Tp
234transform_reduce(_InputIterator __first, _InputIterator __last,
235           _Tp __init,  _BinaryOp __b, _UnaryOp __u)
236{
237    for (; __first != __last; ++__first)
238        __init = __b(__init, __u(*__first));
239    return __init;
240}
241
242template <class _InputIterator1, class _InputIterator2,
243          class _Tp, class _BinaryOp1, class _BinaryOp2>
244inline _LIBCPP_INLINE_VISIBILITY
245_Tp
246transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
247                 _InputIterator2 __first2, _Tp __init,  _BinaryOp1 __b1, _BinaryOp2 __b2)
248{
249    for (; __first1 != __last1; ++__first1, (void) ++__first2)
250        __init = __b1(__init, __b2(*__first1, *__first2));
251    return __init;
252}
253
254template <class _InputIterator1, class _InputIterator2, class _Tp>
255inline _LIBCPP_INLINE_VISIBILITY
256_Tp
257transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
258                 _InputIterator2 __first2, _Tp __init)
259{
260    return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
261                                   _VSTD::plus<>(), _VSTD::multiplies<>());
262}
263#endif
264
265template <class _InputIterator, class _OutputIterator>
266inline _LIBCPP_INLINE_VISIBILITY
267_OutputIterator
268partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
269{
270    if (__first != __last)
271    {
272        typename iterator_traits<_InputIterator>::value_type __t(*__first);
273        *__result = __t;
274        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
275        {
276            __t = __t + *__first;
277            *__result = __t;
278        }
279    }
280    return __result;
281}
282
283template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
284inline _LIBCPP_INLINE_VISIBILITY
285_OutputIterator
286partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
287              _BinaryOperation __binary_op)
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            __t = __binary_op(__t, *__first);
296            *__result = __t;
297        }
298    }
299    return __result;
300}
301
302#if _LIBCPP_STD_VER > 14
303template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
304inline _LIBCPP_INLINE_VISIBILITY
305_OutputIterator
306exclusive_scan(_InputIterator __first, _InputIterator __last,
307               _OutputIterator __result, _Tp __init, _BinaryOp __b)
308{
309    if (__first != __last)
310    {
311        _Tp __saved = __init;
312        do
313        {
314            __init = __b(__init, *__first);
315            *__result = __saved;
316            __saved = __init;
317            ++__result;
318        } while (++__first != __last);
319    }
320    return __result;
321}
322
323template <class _InputIterator, class _OutputIterator, class _Tp>
324inline _LIBCPP_INLINE_VISIBILITY
325_OutputIterator
326exclusive_scan(_InputIterator __first, _InputIterator __last,
327               _OutputIterator __result, _Tp __init)
328{
329    return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
330}
331
332template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
333_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
334                               _OutputIterator __result, _BinaryOp __b,  _Tp __init)
335{
336    for (; __first != __last; ++__first, (void) ++__result) {
337        __init = __b(__init, *__first);
338        *__result = __init;
339        }
340    return __result;
341}
342
343template <class _InputIterator, class _OutputIterator, class _BinaryOp>
344_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
345                               _OutputIterator __result, _BinaryOp __b)
346{
347    if (__first != __last) {
348        typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
349        *__result++ = __init;
350        if (++__first != __last)
351            return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
352        }
353
354    return __result;
355}
356
357template <class _InputIterator, class _OutputIterator>
358_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
359                               _OutputIterator __result)
360{
361    return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
362}
363
364template <class _InputIterator, class _OutputIterator, class _Tp,
365          class _BinaryOp, class _UnaryOp>
366inline _LIBCPP_INLINE_VISIBILITY
367_OutputIterator
368transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
369                           _OutputIterator __result, _Tp __init,
370                           _BinaryOp __b, _UnaryOp __u)
371{
372    if (__first != __last)
373    {
374        _Tp __saved = __init;
375        do
376        {
377            __init = __b(__init, __u(*__first));
378            *__result = __saved;
379            __saved = __init;
380            ++__result;
381        } while (++__first != __last);
382    }
383    return __result;
384}
385
386template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
387_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
388                           _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
389{
390    for (; __first != __last; ++__first, (void) ++__result) {
391        __init = __b(__init, __u(*__first));
392        *__result = __init;
393        }
394
395    return __result;
396}
397
398template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
399_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
400                               _OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
401{
402    if (__first != __last) {
403        typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
404        *__result++ = __init;
405        if (++__first != __last)
406            return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
407        }
408
409    return __result;
410}
411#endif
412
413template <class _InputIterator, class _OutputIterator>
414inline _LIBCPP_INLINE_VISIBILITY
415_OutputIterator
416adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
417{
418    if (__first != __last)
419    {
420        typename iterator_traits<_InputIterator>::value_type __t1(*__first);
421        *__result = __t1;
422        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
423        {
424            typename iterator_traits<_InputIterator>::value_type __t2(*__first);
425            *__result = __t2 - __t1;
426            __t1 = _VSTD::move(__t2);
427        }
428    }
429    return __result;
430}
431
432template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
433inline _LIBCPP_INLINE_VISIBILITY
434_OutputIterator
435adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
436                      _BinaryOperation __binary_op)
437{
438    if (__first != __last)
439    {
440        typename iterator_traits<_InputIterator>::value_type __t1(*__first);
441        *__result = __t1;
442        for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
443        {
444            typename iterator_traits<_InputIterator>::value_type __t2(*__first);
445            *__result = __binary_op(__t2, __t1);
446            __t1 = _VSTD::move(__t2);
447        }
448    }
449    return __result;
450}
451
452template <class _ForwardIterator, class _Tp>
453inline _LIBCPP_INLINE_VISIBILITY
454void
455iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
456{
457    for (; __first != __last; ++__first, (void) ++__value_)
458        *__first = __value_;
459}
460
461
462#if _LIBCPP_STD_VER > 14
463template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs;
464
465template <typename _Result, typename _Source>
466struct __ct_abs<_Result, _Source, true> {
467    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
468    _Result operator()(_Source __t) const noexcept
469    {
470    if (__t >= 0) return __t;
471    if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
472    return -__t;
473    }
474};
475
476template <typename _Result, typename _Source>
477struct __ct_abs<_Result, _Source, false> {
478    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
479    _Result operator()(_Source __t) const noexcept { return __t; }
480};
481
482
483template<class _Tp>
484_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
485_Tp __gcd(_Tp __m, _Tp __n)
486{
487    static_assert((!is_signed<_Tp>::value), "");
488    return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
489}
490
491
492template<class _Tp, class _Up>
493_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
494common_type_t<_Tp,_Up>
495gcd(_Tp __m, _Up __n)
496{
497    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
498    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
499    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
500    using _Rp = common_type_t<_Tp,_Up>;
501    using _Wp = make_unsigned_t<_Rp>;
502    return static_cast<_Rp>(_VSTD::__gcd(
503        static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)),
504        static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
505}
506
507template<class _Tp, class _Up>
508_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
509common_type_t<_Tp,_Up>
510lcm(_Tp __m, _Up __n)
511{
512    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
513    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
514    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
515    if (__m == 0 || __n == 0)
516        return 0;
517
518    using _Rp = common_type_t<_Tp,_Up>;
519    _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
520    _Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
521    _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
522    return __val1 * __val2;
523}
524
525#endif /* _LIBCPP_STD_VER > 14 */
526
527#if _LIBCPP_STD_VER > 17
528template <class _Tp>
529_LIBCPP_INLINE_VISIBILITY constexpr
530enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
531midpoint(_Tp __a, _Tp __b) noexcept
532_LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
533{
534    using _Up = std::make_unsigned_t<_Tp>;
535
536    int __sign = 1;
537    _Up __m = __a;
538    _Up __M = __b;
539    if (__a > __b)
540    {
541        __sign = -1;
542        __m = __b;
543        __M = __a;
544    }
545     return __a + __sign * _Tp(_Up(__M-__m) >> 1);
546}
547
548
549template <class _TPtr>
550_LIBCPP_INLINE_VISIBILITY constexpr
551enable_if_t<is_pointer_v<_TPtr>
552             && is_object_v<remove_pointer_t<_TPtr>>
553             && ! is_void_v<remove_pointer_t<_TPtr>>
554             && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr>
555midpoint(_TPtr __a, _TPtr __b) noexcept
556{
557    return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a);
558}
559
560
561template <typename _Tp>
562constexpr int __sign(_Tp __val) {
563    return (_Tp(0) < __val) - (__val < _Tp(0));
564}
565
566template <typename _Fp>
567constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; }
568
569template <class _Fp>
570_LIBCPP_INLINE_VISIBILITY constexpr
571enable_if_t<is_floating_point_v<_Fp>, _Fp>
572midpoint(_Fp __a, _Fp __b) noexcept
573{
574	constexpr _Fp __lo = numeric_limits<_Fp>::min()*2;
575	constexpr _Fp __hi = numeric_limits<_Fp>::max()/2;
576    return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ?  // typical case: overflow is impossible
577      (__a + __b)/2 :                                        // always correctly rounded
578      __fp_abs(__a) < __lo ? __a + __b/2 :                   // not safe to halve a
579      __fp_abs(__a) < __lo ? __a/2 + __b :                   // not safe to halve b
580      __a/2 + __b/2;                                         // otherwise correctly rounded
581}
582
583#endif // _LIBCPP_STD_VER > 17
584
585_LIBCPP_END_NAMESPACE_STD
586
587_LIBCPP_POP_MACROS
588
589#endif  // _LIBCPP_NUMERIC
590