1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
|
// -*- C++ -*-
//===---------------------------- numeric ---------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#ifndef _LIBCPP_NUMERIC
#define _LIBCPP_NUMERIC
/*
numeric synopsis
namespace std
{
template <class InputIterator, class T>
T
accumulate(InputIterator first, InputIterator last, T init);
template <class InputIterator, class T, class BinaryOperation>
T
accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
template<class InputIterator>
typename iterator_traits<InputIterator>::value_type
reduce(InputIterator first, InputIterator last); // C++17
template<class InputIterator, class T>
T
reduce(InputIterator first, InputIterator last, T init); // C++17
template<class InputIterator, class T, class BinaryOperation>
T
reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17
template <class InputIterator1, class InputIterator2, class T>
T
inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
T
inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
template<class InputIterator1, class InputIterator2, class T>
T
transform_reduce(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init); // C++17
template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
T
transform_reduce(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init,
BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); // C++17
template<class InputIterator, class T, class BinaryOperation, class UnaryOperation>
T
transform_reduce(InputIterator first, InputIterator last, T init,
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
template <class InputIterator, class OutputIterator>
OutputIterator
partial_sum(InputIterator first, InputIterator last, OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator
partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
template<class InputIterator, class OutputIterator, class T>
OutputIterator
exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, T init); // C++17
template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
OutputIterator
exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, T init, BinaryOperation binary_op); // C++17
template<class InputIterator, class OutputIterator>
OutputIterator
inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17
template<class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator
inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op); // C++17
template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
OutputIterator
inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op, T init); // C++17
template<class InputIterator, class OutputIterator, class T,
class BinaryOperation, class UnaryOperation>
OutputIterator
transform_exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result, T init,
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
template<class InputIterator, class OutputIterator,
class BinaryOperation, class UnaryOperation>
OutputIterator
transform_inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
BinaryOperation binary_op, UnaryOperation unary_op); // C++17
template<class InputIterator, class OutputIterator,
class BinaryOperation, class UnaryOperation, class T>
OutputIterator
transform_inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
BinaryOperation binary_op, UnaryOperation unary_op,
T init); // C++17
template <class InputIterator, class OutputIterator>
OutputIterator
adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator
adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
template <class ForwardIterator, class T>
void iota(ForwardIterator first, ForwardIterator last, T value);
template <class M, class N>
constexpr common_type_t<M,N> gcd(M m, N n); // C++17
template <class M, class N>
constexpr common_type_t<M,N> lcm(M m, N n); // C++17
} // std
*/
#include <__config>
#include <iterator>
#include <limits> // for numeric_limits
#include <functional>
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif
_LIBCPP_PUSH_MACROS
#include <__undef_macros>
_LIBCPP_BEGIN_NAMESPACE_STD
template <class _InputIterator, class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
{
for (; __first != __last; ++__first)
__init = __init + *__first;
return __init;
}
template <class _InputIterator, class _Tp, class _BinaryOperation>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
{
for (; __first != __last; ++__first)
__init = __binary_op(__init, *__first);
return __init;
}
#if _LIBCPP_STD_VER > 14
template <class _InputIterator, class _Tp, class _BinaryOp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
{
for (; __first != __last; ++__first)
__init = __b(__init, *__first);
return __init;
}
template <class _InputIterator, class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
{
return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
}
template <class _InputIterator>
inline _LIBCPP_INLINE_VISIBILITY
typename iterator_traits<_InputIterator>::value_type
reduce(_InputIterator __first, _InputIterator __last)
{
return _VSTD::reduce(__first, __last,
typename iterator_traits<_InputIterator>::value_type{});
}
#endif
template <class _InputIterator1, class _InputIterator2, class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
{
for (; __first1 != __last1; ++__first1, (void) ++__first2)
__init = __init + *__first1 * *__first2;
return __init;
}
template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
_Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
{
for (; __first1 != __last1; ++__first1, (void) ++__first2)
__init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
return __init;
}
#if _LIBCPP_STD_VER > 14
template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
transform_reduce(_InputIterator __first, _InputIterator __last,
_Tp __init, _BinaryOp __b, _UnaryOp __u)
{
for (; __first != __last; ++__first)
__init = __b(__init, __u(*__first));
return __init;
}
template <class _InputIterator1, class _InputIterator2,
class _Tp, class _BinaryOp1, class _BinaryOp2>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
_InputIterator2 __first2, _Tp __init, _BinaryOp1 __b1, _BinaryOp2 __b2)
{
for (; __first1 != __last1; ++__first1, (void) ++__first2)
__init = __b1(__init, __b2(*__first1, *__first2));
return __init;
}
template <class _InputIterator1, class _InputIterator2, class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
_InputIterator2 __first2, _Tp __init)
{
return _VSTD::transform_reduce(__first1, __last1, __first2, __init,
_VSTD::plus<>(), _VSTD::multiplies<>());
}
#endif
template <class _InputIterator, class _OutputIterator>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __t(*__first);
*__result = __t;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
__t = __t + *__first;
*__result = __t;
}
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
_BinaryOperation __binary_op)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __t(*__first);
*__result = __t;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
__t = __binary_op(__t, *__first);
*__result = __t;
}
}
return __result;
}
#if _LIBCPP_STD_VER > 14
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
exclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp __init, _BinaryOp __b)
{
if (__first != __last)
{
_Tp __saved = __init;
do
{
__init = __b(__init, *__first);
*__result = __saved;
__saved = __init;
++__result;
} while (++__first != __last);
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
exclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp __init)
{
return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
}
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b, _Tp __init)
{
for (; __first != __last; ++__first, (void) ++__result) {
__init = __b(__init, *__first);
*__result = __init;
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOp>
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b)
{
if (__first != __last) {
typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
*__result++ = __init;
if (++__first != __last)
return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
}
return __result;
}
template <class _InputIterator, class _OutputIterator>
_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result)
{
return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
}
template <class _InputIterator, class _OutputIterator, class _Tp,
class _BinaryOp, class _UnaryOp>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp __init,
_BinaryOp __b, _UnaryOp __u)
{
if (__first != __last)
{
_Tp __saved = __init;
do
{
__init = __b(__init, __u(*__first));
*__result = __saved;
__saved = __init;
++__result;
} while (++__first != __last);
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
{
for (; __first != __last; ++__first, (void) ++__result) {
__init = __b(__init, __u(*__first));
*__result = __init;
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
{
if (__first != __last) {
typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
*__result++ = __init;
if (++__first != __last)
return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
}
return __result;
}
#endif
template <class _InputIterator, class _OutputIterator>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __t1(*__first);
*__result = __t1;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
typename iterator_traits<_InputIterator>::value_type __t2(*__first);
*__result = __t2 - __t1;
__t1 = _VSTD::move(__t2);
}
}
return __result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
inline _LIBCPP_INLINE_VISIBILITY
_OutputIterator
adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
_BinaryOperation __binary_op)
{
if (__first != __last)
{
typename iterator_traits<_InputIterator>::value_type __t1(*__first);
*__result = __t1;
for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
{
typename iterator_traits<_InputIterator>::value_type __t2(*__first);
*__result = __binary_op(__t2, __t1);
__t1 = _VSTD::move(__t2);
}
}
return __result;
}
template <class _ForwardIterator, class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
void
iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
{
for (; __first != __last; ++__first, (void) ++__value_)
*__first = __value_;
}
#if _LIBCPP_STD_VER > 14
template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __abs;
template <typename _Result, typename _Source>
struct __abs<_Result, _Source, true> {
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
_Result operator()(_Source __t) const noexcept
{
if (__t >= 0) return __t;
if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
return -__t;
}
};
template <typename _Result, typename _Source>
struct __abs<_Result, _Source, false> {
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
_Result operator()(_Source __t) const noexcept { return __t; }
};
template<class _Tp>
_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
_Tp __gcd(_Tp __m, _Tp __n)
{
static_assert((!is_signed<_Tp>::value), "");
return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
}
template<class _Tp, class _Up>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
common_type_t<_Tp,_Up>
gcd(_Tp __m, _Up __n)
{
static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
using _Rp = common_type_t<_Tp,_Up>;
using _Wp = make_unsigned_t<_Rp>;
return static_cast<_Rp>(_VSTD::__gcd(
static_cast<_Wp>(__abs<_Rp, _Tp>()(__m)),
static_cast<_Wp>(__abs<_Rp, _Up>()(__n))));
}
template<class _Tp, class _Up>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
common_type_t<_Tp,_Up>
lcm(_Tp __m, _Up __n)
{
static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
if (__m == 0 || __n == 0)
return 0;
using _Rp = common_type_t<_Tp,_Up>;
_Rp __val1 = __abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
_Rp __val2 = __abs<_Rp, _Up>()(__n);
_LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
return __val1 * __val2;
}
#endif /* _LIBCPP_STD_VER > 14 */
_LIBCPP_END_NAMESPACE_STD
_LIBCPP_POP_MACROS
#endif // _LIBCPP_NUMERIC
|
