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