libstdc++
numeric
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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
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18 // 3.1, as published by the Free Software Foundation.
19 
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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 
80 namespace std _GLIBCXX_VISIBILITY(default)
81 {
82 _GLIBCXX_BEGIN_NAMESPACE_VERSION
83 
84 namespace __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 
167 namespace 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 
226 namespace 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 */