1// <numeric> -*- C++ -*-
2
3// Copyright (C) 2001-2019 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/*
26 *
27 * Copyright (c) 1994
28 * Hewlett-Packard Company
29 *
30 * Permission to use, copy, modify, distribute and sell this software
31 * and its documentation for any purpose is hereby granted without fee,
32 * provided that the above copyright notice appear in all copies and
33 * that both that copyright notice and this permission notice appear
34 * in supporting documentation. Hewlett-Packard Company makes no
35 * representations about the suitability of this software for any
36 * purpose. It is provided "as is" without express or implied warranty.
37 *
38 *
39 * Copyright (c) 1996,1997
40 * Silicon Graphics Computer Systems, Inc.
41 *
42 * Permission to use, copy, modify, distribute and sell this software
43 * and its documentation for any purpose is hereby granted without fee,
44 * provided that the above copyright notice appear in all copies and
45 * that both that copyright notice and this permission notice appear
46 * in supporting documentation. Silicon Graphics makes no
47 * representations about the suitability of this software for any
48 * purpose. It is provided "as is" without express or implied warranty.
49 */
50
51/** @file include/numeric
52 * This is a Standard C++ Library header.
53 */
54
55#ifndef _GLIBCXX_NUMERIC
56#define _GLIBCXX_NUMERIC 1
57
58#pragma GCC system_header
59
60#include <bits/c++config.h>
61#include <bits/stl_iterator_base_types.h>
62#include <bits/stl_numeric.h>
63#include <ext/numeric_traits.h>
64
65#ifdef _GLIBCXX_PARALLEL
66# include <parallel/numeric>
67#endif
68
69/**
70 * @defgroup numerics Numerics
71 *
72 * Components for performing numeric operations. Includes support for
73 * complex number types, random number generation, numeric (n-at-a-time)
74 * arrays, generalized numeric algorithms, and mathematical special functions.
75 */
76
77#if __cplusplus >= 201402L
78#include <type_traits>
79
80namespace std _GLIBCXX_VISIBILITY(default)
81{
82_GLIBCXX_BEGIN_NAMESPACE_VERSION
83
84namespace __detail
85{
86 // std::abs is not constexpr, doesn't support unsigned integers,
87 // and std::abs(std::numeric_limits<T>::min()) is undefined.
88 template<typename _Up, typename _Tp>
89 constexpr _Up
90 __absu(_Tp __val)
91 {
92 static_assert(is_unsigned<_Up>::value, "result type must be unsigned");
93 static_assert(sizeof(_Up) >= sizeof(_Tp),
94 "result type must be at least as wide as the input type");
95 return __val < 0 ? -(_Up)__val : (_Up)__val;
96 }
97
98 template<typename _Up> void __absu(bool) = delete;
99
100 // GCD implementation
101 template<typename _Tp>
102 constexpr _Tp
103 __gcd(_Tp __m, _Tp __n)
104 {
105 static_assert(is_unsigned<_Tp>::value, "type must be unsigned");
106 return __m == 0 ? __n
107 : __n == 0 ? __m
108 : __detail::__gcd(__n, _Tp(__m % __n));
109 }
110
111 // LCM implementation
112 template<typename _Tp>
113 constexpr _Tp
114 __lcm(_Tp __m, _Tp __n)
115 {
116 return (__m != 0 && __n != 0)
117 ? (__m / __detail::__gcd(__m, __n)) * __n
118 : 0;
119 }
120} // namespace __detail
121
122#if __cplusplus >= 201703L
123
124#define __cpp_lib_gcd_lcm 201606
125// These were used in drafts of SD-6:
126#define __cpp_lib_gcd 201606
127#define __cpp_lib_lcm 201606
128
129 /// Greatest common divisor
130 template<typename _Mn, typename _Nn>
131 constexpr common_type_t<_Mn, _Nn>
132 gcd(_Mn __m, _Nn __n) noexcept
133 {
134 static_assert(is_integral_v<_Mn>, "std::gcd arguments must be integers");
135 static_assert(is_integral_v<_Nn>, "std::gcd arguments must be integers");
136 static_assert(_Mn(2) != _Mn(1), "std::gcd arguments must not be bool");
137 static_assert(_Nn(2) != _Nn(1), "std::gcd arguments must not be bool");
138 using _Up = make_unsigned_t<common_type_t<_Mn, _Nn>>;
139 return __detail::__gcd(__detail::__absu<_Up>(__m),
140 __detail::__absu<_Up>(__n));
141 }
142
143 /// Least common multiple
144 template<typename _Mn, typename _Nn>
145 constexpr common_type_t<_Mn, _Nn>
146 lcm(_Mn __m, _Nn __n) noexcept
147 {
148 static_assert(is_integral_v<_Mn>, "std::lcm arguments must be integers");
149 static_assert(is_integral_v<_Nn>, "std::lcm arguments must be integers");
150 static_assert(_Mn(2) == 2, "std::lcm arguments must not be bool");
151 static_assert(_Nn(2) == 2, "std::lcm arguments must not be bool");
152 using _Up = make_unsigned_t<common_type_t<_Mn, _Nn>>;
153 return __detail::__lcm(__detail::__absu<_Up>(__m),
154 __detail::__absu<_Up>(__n));
155 }
156
157#endif // C++17
158
159_GLIBCXX_END_NAMESPACE_VERSION
160} // namespace std
161
162#endif // C++14
163
164#if __cplusplus > 201703L
165#include <limits>
166
167namespace std _GLIBCXX_VISIBILITY(default)
168{
169_GLIBCXX_BEGIN_NAMESPACE_VERSION
170 // midpoint
171# define __cpp_lib_interpolate 201902L
172
173 template<typename _Tp>
174 constexpr
175 enable_if_t<__and_v<is_arithmetic<_Tp>, is_same<remove_cv_t<_Tp>, _Tp>,
176 __not_<is_same<_Tp, bool>>>,
177 _Tp>
178 midpoint(_Tp __a, _Tp __b) noexcept
179 {
180 if constexpr (is_integral_v<_Tp>)
181 {
182 using _Up = make_unsigned_t<_Tp>;
183
184 int __k = 1;
185 _Up __m = __a;
186 _Up __M = __b;
187 if (__a > __b)
188 {
189 __k = -1;
190 __m = __b;
191 __M = __a;
192 }
193 return __a + __k * _Tp(_Up(__M - __m) / 2);
194 }
195 else // is_floating
196 {
197 constexpr _Tp __lo = numeric_limits<_Tp>::min() * 2;
198 constexpr _Tp __hi = numeric_limits<_Tp>::max() / 2;
199 const _Tp __abs_a = __a < 0 ? -__a : __a;
200 const _Tp __abs_b = __b < 0 ? -__b : __b;
201 if (__abs_a <= __hi && __abs_b <= __hi) [[likely]]
202 return (__a + __b) / 2; // always correctly rounded
203 if (__abs_a < __lo) // not safe to halve __a
204 return __a + __b/2;
205 if (__abs_b < __lo) // not safe to halve __b
206 return __a/2 + __b;
207 return __a/2 + __b/2; // otherwise correctly rounded
208 }
209 }
210
211 template<typename _Tp>
212 constexpr
213 enable_if_t<__and_v<is_object<_Tp>, bool_constant<sizeof(_Tp) != 0>>, _Tp*>
214 midpoint(_Tp* __a, _Tp* __b) noexcept
215 {
216 return __a + (__b - __a) / 2;
217 }
218_GLIBCXX_END_NAMESPACE_VERSION
219} // namespace std
220
221#endif // C++20
222
223#if __cplusplus > 201402L
224#include <bits/stl_function.h>
225
226namespace std _GLIBCXX_VISIBILITY(default)
227{
228_GLIBCXX_BEGIN_NAMESPACE_VERSION
229
230 /// @addtogroup numeric_ops
231 /// @{
232
233 /// @cond undocumented
234 template<typename _It, typename _Traits = iterator_traits<_It>,
235 typename _Cat = typename _Traits::iterator_category>
236 using __is_random_access_iter
237 = is_base_of<random_access_iterator_tag, _Cat>;
238 /// @endcond
239
240 /**
241 * @brief Calculate reduction of values in a range.
242 *
243 * @param __first Start of range.
244 * @param __last End of range.
245 * @param __init Starting value to add other values to.
246 * @param __binary_op A binary function object.
247 * @return The final sum.
248 *
249 * Reduce the values in the range `[first,last)` using a binary operation.
250 * The initial value is `init`. The values are not necessarily processed
251 * in order.
252 *
253 * This algorithm is similar to `std::accumulate` but is not required to
254 * perform the operations in order from first to last. For operations
255 * that are commutative and associative the result will be the same as
256 * for `std::accumulate`, but for other operations (such as floating point
257 * arithmetic) the result can be different.
258 */
259 template<typename _InputIterator, typename _Tp, typename _BinaryOperation>
260 _Tp
261 reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
262 _BinaryOperation __binary_op)
263 {
264 using value_type = typename iterator_traits<_InputIterator>::value_type;
265 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>);
266 static_assert(is_convertible_v<value_type, _Tp>);
267 if constexpr (__is_random_access_iter<_InputIterator>::value)
268 {
269 while ((__last - __first) >= 4)
270 {
271 _Tp __v1 = __binary_op(__first[0], __first[1]);
272 _Tp __v2 = __binary_op(__first[2], __first[3]);
273 _Tp __v3 = __binary_op(__v1, __v2);
274 __init = __binary_op(__init, __v3);
275 __first += 4;
276 }
277 }
278 for (; __first != __last; ++__first)
279 __init = __binary_op(__init, *__first);
280 return __init;
281 }
282
283 /**
284 * @brief Calculate reduction of values in a range.
285 *
286 * @param __first Start of range.
287 * @param __last End of range.
288 * @param __init Starting value to add other values to.
289 * @return The final sum.
290 *
291 * Reduce the values in the range `[first,last)` using addition.
292 * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`.
293 */
294 template<typename _InputIterator, typename _Tp>
295 inline _Tp
296 reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
297 { return std::reduce(__first, __last, std::move(__init), plus<>()); }
298
299 /**
300 * @brief Calculate reduction of values in a range.
301 *
302 * @param __first Start of range.
303 * @param __last End of range.
304 * @return The final sum.
305 *
306 * Reduce the values in the range `[first,last)` using addition, with
307 * an initial value of `T{}`, where `T` is the iterator's value type.
308 * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`.
309 */
310 template<typename _InputIterator>
311 inline typename iterator_traits<_InputIterator>::value_type
312 reduce(_InputIterator __first, _InputIterator __last)
313 {
314 using value_type = typename iterator_traits<_InputIterator>::value_type;
315 return std::reduce(__first, __last, value_type{}, plus<>());
316 }
317
318 /**
319 * @brief Combine elements from two ranges and reduce
320 *
321 * @param __first1 Start of first range.
322 * @param __last1 End of first range.
323 * @param __first2 Start of second range.
324 * @param __init Starting value to add other values to.
325 * @param __binary_op1 The function used to perform reduction.
326 * @param __binary_op2 The function used to combine values from the ranges.
327 * @return The final sum.
328 *
329 * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)`
330 * and then use `binary_op1` to reduce the values returned by `binary_op2`
331 * to a single value of type `T`.
332 *
333 * The range beginning at `first2` must contain at least `last1-first1`
334 * elements.
335 */
336 template<typename _InputIterator1, typename _InputIterator2, typename _Tp,
337 typename _BinaryOperation1, typename _BinaryOperation2>
338 _Tp
339 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
340 _InputIterator2 __first2, _Tp __init,
341 _BinaryOperation1 __binary_op1,
342 _BinaryOperation2 __binary_op2)
343 {
344 if constexpr (__and_v<__is_random_access_iter<_InputIterator1>,
345 __is_random_access_iter<_InputIterator2>>)
346 {
347 while ((__last1 - __first1) >= 4)
348 {
349 _Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]),
350 __binary_op2(__first1[1], __first2[1]));
351 _Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]),
352 __binary_op2(__first1[3], __first2[3]));
353 _Tp __v3 = __binary_op1(__v1, __v2);
354 __init = __binary_op1(__init, __v3);
355 __first1 += 4;
356 __first2 += 4;
357 }
358 }
359 for (; __first1 != __last1; ++__first1, (void) ++__first2)
360 __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
361 return __init;
362 }
363
364 /**
365 * @brief Combine elements from two ranges and reduce
366 *
367 * @param __first1 Start of first range.
368 * @param __last1 End of first range.
369 * @param __first2 Start of second range.
370 * @param __init Starting value to add other values to.
371 * @return The final sum.
372 *
373 * Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then
374 * use addition to sum those products to a single value of type `T`.
375 *
376 * The range beginning at `first2` must contain at least `last1-first1`
377 * elements.
378 */
379 template<typename _InputIterator1, typename _InputIterator2, typename _Tp>
380 inline _Tp
381 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
382 _InputIterator2 __first2, _Tp __init)
383 {
384 return std::transform_reduce(__first1, __last1, __first2,
385 std::move(__init),
386 plus<>(), multiplies<>());
387 }
388
389 /**
390 * @brief Transform the elements of a range and reduce
391 *
392 * @param __first Start of range.
393 * @param __last End of range.
394 * @param __init Starting value to add other values to.
395 * @param __binary_op The function used to perform reduction.
396 * @param __unary_op The function used to transform values from the range.
397 * @return The final sum.
398 *
399 * Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then
400 * use `binary_op` to reduce the values returned by `unary_op`
401 * to a single value of type `T`.
402 */
403 template<typename _InputIterator, typename _Tp,
404 typename _BinaryOperation, typename _UnaryOperation>
405 _Tp
406 transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
407 _BinaryOperation __binary_op, _UnaryOperation __unary_op)
408 {
409 if constexpr (__is_random_access_iter<_InputIterator>::value)
410 {
411 while ((__last - __first) >= 4)
412 {
413 _Tp __v1 = __binary_op(__unary_op(__first[0]),
414 __unary_op(__first[1]));
415 _Tp __v2 = __binary_op(__unary_op(__first[2]),
416 __unary_op(__first[3]));
417 _Tp __v3 = __binary_op(__v1, __v2);
418 __init = __binary_op(__init, __v3);
419 __first += 4;
420 }
421 }
422 for (; __first != __last; ++__first)
423 __init = __binary_op(__init, __unary_op(*__first));
424 return __init;
425 }
426
427 /** @brief Output the cumulative sum of one range to a second range
428 *
429 * @param __first Start of input range.
430 * @param __last End of input range.
431 * @param __result Start of output range.
432 * @param __init Initial value.
433 * @param __binary_op Function to perform summation.
434 * @return The end of the output range.
435 *
436 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
437 * to the output range. Each element of the output range contains the
438 * running total of all earlier elements (and the initial value),
439 * using `binary_op` for summation.
440 *
441 * This function generates an "exclusive" scan, meaning the Nth element
442 * of the output range is the sum of the first N-1 input elements,
443 * so the Nth input element is not included.
444 */
445 template<typename _InputIterator, typename _OutputIterator, typename _Tp,
446 typename _BinaryOperation>
447 _OutputIterator
448 exclusive_scan(_InputIterator __first, _InputIterator __last,
449 _OutputIterator __result, _Tp __init,
450 _BinaryOperation __binary_op)
451 {
452 while (__first != __last)
453 {
454 auto __v = __init;
455 __init = __binary_op(__init, *__first);
456 ++__first;
457 *__result++ = std::move(__v);
458 }
459 return __result;
460 }
461
462 /** @brief Output the cumulative sum of one range to a second range
463 *
464 * @param __first Start of input range.
465 * @param __last End of input range.
466 * @param __result Start of output range.
467 * @param __init Initial value.
468 * @return The end of the output range.
469 *
470 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
471 * to the output range. Each element of the output range contains the
472 * running total of all earlier elements (and the initial value),
473 * using `std::plus<>` for summation.
474 *
475 * This function generates an "exclusive" scan, meaning the Nth element
476 * of the output range is the sum of the first N-1 input elements,
477 * so the Nth input element is not included.
478 */
479 template<typename _InputIterator, typename _OutputIterator, typename _Tp>
480 inline _OutputIterator
481 exclusive_scan(_InputIterator __first, _InputIterator __last,
482 _OutputIterator __result, _Tp __init)
483 {
484 return std::exclusive_scan(__first, __last, __result, std::move(__init),
485 plus<>());
486 }
487
488 /** @brief Output the cumulative sum of one range to a second range
489 *
490 * @param __first Start of input range.
491 * @param __last End of input range.
492 * @param __result Start of output range.
493 * @param __binary_op Function to perform summation.
494 * @param __init Initial value.
495 * @return The end of the output range.
496 *
497 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
498 * to the output range. Each element of the output range contains the
499 * running total of all earlier elements (and the initial value),
500 * using `binary_op` for summation.
501 *
502 * This function generates an "inclusive" scan, meaning the Nth element
503 * of the output range is the sum of the first N input elements,
504 * so the Nth input element is included.
505 */
506 template<typename _InputIterator, typename _OutputIterator,
507 typename _BinaryOperation, typename _Tp>
508 _OutputIterator
509 inclusive_scan(_InputIterator __first, _InputIterator __last,
510 _OutputIterator __result, _BinaryOperation __binary_op,
511 _Tp __init)
512 {
513 for (; __first != __last; ++__first)
514 *__result++ = __init = __binary_op(__init, *__first);
515 return __result;
516 }
517
518 /** @brief Output the cumulative sum of one range to a second range
519 *
520 * @param __first Start of input range.
521 * @param __last End of input range.
522 * @param __result Start of output range.
523 * @param __binary_op Function to perform summation.
524 * @return The end of the output range.
525 *
526 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
527 * to the output range. Each element of the output range contains the
528 * running total of all earlier elements, using `binary_op` for summation.
529 *
530 * This function generates an "inclusive" scan, meaning the Nth element
531 * of the output range is the sum of the first N input elements,
532 * so the Nth input element is included.
533 */
534 template<typename _InputIterator, typename _OutputIterator,
535 typename _BinaryOperation>
536 _OutputIterator
537 inclusive_scan(_InputIterator __first, _InputIterator __last,
538 _OutputIterator __result, _BinaryOperation __binary_op)
539 {
540 if (__first != __last)
541 {
542 auto __init = *__first;
543 *__result++ = __init;
544 ++__first;
545 if (__first != __last)
546 __result = std::inclusive_scan(__first, __last, __result,
547 __binary_op, std::move(__init));
548 }
549 return __result;
550 }
551
552 /** @brief Output the cumulative sum of one range to a second range
553 *
554 * @param __first Start of input range.
555 * @param __last End of input range.
556 * @param __result Start of output range.
557 * @return The end of the output range.
558 *
559 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
560 * to the output range. Each element of the output range contains the
561 * running total of all earlier elements, using `std::plus<>` for summation.
562 *
563 * This function generates an "inclusive" scan, meaning the Nth element
564 * of the output range is the sum of the first N input elements,
565 * so the Nth input element is included.
566 */
567 template<typename _InputIterator, typename _OutputIterator>
568 inline _OutputIterator
569 inclusive_scan(_InputIterator __first, _InputIterator __last,
570 _OutputIterator __result)
571 { return std::inclusive_scan(__first, __last, __result, plus<>()); }
572
573 /** @brief Output the cumulative sum of one range to a second range
574 *
575 * @param __first Start of input range.
576 * @param __last End of input range.
577 * @param __result Start of output range.
578 * @param __init Initial value.
579 * @param __binary_op Function to perform summation.
580 * @param __unary_op Function to transform elements of the input range.
581 * @return The end of the output range.
582 *
583 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
584 * to the output range. Each element of the output range contains the
585 * running total of all earlier elements (and the initial value),
586 * using `__unary_op` to transform the input elements
587 * and using `__binary_op` for summation.
588 *
589 * This function generates an "exclusive" scan, meaning the Nth element
590 * of the output range is the sum of the first N-1 input elements,
591 * so the Nth input element is not included.
592 */
593 template<typename _InputIterator, typename _OutputIterator, typename _Tp,
594 typename _BinaryOperation, typename _UnaryOperation>
595 _OutputIterator
596 transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
597 _OutputIterator __result, _Tp __init,
598 _BinaryOperation __binary_op,
599 _UnaryOperation __unary_op)
600 {
601 while (__first != __last)
602 {
603 auto __v = __init;
604 __init = __binary_op(__init, __unary_op(*__first));
605 ++__first;
606 *__result++ = std::move(__v);
607 }
608 return __result;
609 }
610
611 /** @brief Output the cumulative sum of one range to a second range
612 *
613 * @param __first Start of input range.
614 * @param __last End of input range.
615 * @param __result Start of output range.
616 * @param __binary_op Function to perform summation.
617 * @param __unary_op Function to transform elements of the input range.
618 * @param __init Initial value.
619 * @return The end of the output range.
620 *
621 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
622 * to the output range. Each element of the output range contains the
623 * running total of all earlier elements (and the initial value),
624 * using `__unary_op` to transform the input elements
625 * and using `__binary_op` for summation.
626 *
627 * This function generates an "inclusive" scan, meaning the Nth element
628 * of the output range is the sum of the first N input elements,
629 * so the Nth input element is included.
630 */
631 template<typename _InputIterator, typename _OutputIterator,
632 typename _BinaryOperation, typename _UnaryOperation, typename _Tp>
633 _OutputIterator
634 transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
635 _OutputIterator __result,
636 _BinaryOperation __binary_op,
637 _UnaryOperation __unary_op,
638 _Tp __init)
639 {
640 for (; __first != __last; ++__first)
641 *__result++ = __init = __binary_op(__init, __unary_op(*__first));
642 return __result;
643 }
644
645 /** @brief Output the cumulative sum of one range to a second range
646 *
647 * @param __first Start of input range.
648 * @param __last End of input range.
649 * @param __result Start of output range.
650 * @param __binary_op Function to perform summation.
651 * @param __unary_op Function to transform elements of the input range.
652 * @return The end of the output range.
653 *
654 * Write the cumulative sum (aka prefix sum, aka scan) of the input range
655 * to the output range. Each element of the output range contains the
656 * running total of all earlier elements,
657 * using `__unary_op` to transform the input elements
658 * and using `__binary_op` for summation.
659 *
660 * This function generates an "inclusive" scan, meaning the Nth element
661 * of the output range is the sum of the first N input elements,
662 * so the Nth input element is included.
663 */
664 template<typename _InputIterator, typename _OutputIterator,
665 typename _BinaryOperation, typename _UnaryOperation>
666 _OutputIterator
667 transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
668 _OutputIterator __result,
669 _BinaryOperation __binary_op,
670 _UnaryOperation __unary_op)
671 {
672 if (__first != __last)
673 {
674 auto __init = __unary_op(*__first);
675 *__result++ = __init;
676 ++__first;
677 if (__first != __last)
678 __result = std::transform_inclusive_scan(__first, __last, __result,
679 __binary_op, __unary_op,
680 std::move(__init));
681 }
682 return __result;
683 }
684
685 /// @} group numeric_ops
686
687_GLIBCXX_END_NAMESPACE_VERSION
688} // namespace std
689
690// Parallel STL algorithms
691# if __PSTL_EXECUTION_POLICIES_DEFINED
692// If <execution> has already been included, pull in implementations
693# include <pstl/glue_numeric_impl.h>
694# else
695// Otherwise just pull in forward declarations
696# include <pstl/glue_numeric_defs.h>
697# define __PSTL_NUMERIC_FORWARD_DECLARED 1
698# endif
699
700// Feature test macro for parallel algorithms
701# define __cpp_lib_parallel_algorithm 201603L
702#endif // C++17
703
704#endif /* _GLIBCXX_NUMERIC */
705