libstdc++
numeric
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1 // <numeric> -*- C++ -*-
2 
3 // Copyright (C) 2001-2021 Free Software Foundation, Inc.
4 //
5 // This file is part of the GNU ISO C++ Library. This library is free
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15 
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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 
64 #ifdef _GLIBCXX_PARALLEL
65 # include <parallel/numeric>
66 #endif
67 
68 #if __cplusplus >= 201402L
69 # include <type_traits>
70 # include <bit>
71 #endif
72 
73 #if __cplusplus >= 201703L
74 # include <bits/stl_function.h>
75 #endif
76 
77 #if __cplusplus > 201703L
78 # include <limits>
79 #endif
80 
81 /**
82  * @defgroup numerics Numerics
83  *
84  * Components for performing numeric operations. Includes support for
85  * complex number types, random number generation, numeric (n-at-a-time)
86  * arrays, generalized numeric algorithms, and mathematical special functions.
87  */
88 
89 namespace std _GLIBCXX_VISIBILITY(default)
90 {
91 _GLIBCXX_BEGIN_NAMESPACE_VERSION
92 
93 #if __cplusplus >= 201402L
94 namespace __detail
95 {
96  // std::abs is not constexpr, doesn't support unsigned integers,
97  // and std::abs(std::numeric_limits<T>::min()) is undefined.
98  template<typename _Up, typename _Tp>
99  constexpr _Up
100  __absu(_Tp __val)
101  {
102  static_assert(is_unsigned<_Up>::value, "result type must be unsigned");
103  static_assert(sizeof(_Up) >= sizeof(_Tp),
104  "result type must be at least as wide as the input type");
105  return __val < 0 ? -(_Up)__val : (_Up)__val;
106  }
107 
108  template<typename _Up> void __absu(bool) = delete;
109 
110  // GCD implementation, using Stein's algorithm
111  template<typename _Tp>
112  constexpr _Tp
113  __gcd(_Tp __m, _Tp __n)
114  {
115  static_assert(is_unsigned<_Tp>::value, "type must be unsigned");
116 
117  if (__m == 0)
118  return __n;
119  if (__n == 0)
120  return __m;
121 
122  const int __i = std::__countr_zero(__m);
123  __m >>= __i;
124  const int __j = std::__countr_zero(__n);
125  __n >>= __j;
126  const int __k = __i < __j ? __i : __j; // min(i, j)
127 
128  while (true)
129  {
130  if (__m > __n)
131  {
132  _Tp __tmp = __m;
133  __m = __n;
134  __n = __tmp;
135  }
136 
137  __n -= __m;
138 
139  if (__n == 0)
140  return __m << __k;
141 
142  __n >>= std::__countr_zero(__n);
143  }
144  }
145 
146  // LCM implementation
147  template<typename _Tp>
148  constexpr _Tp
149  __lcm(_Tp __m, _Tp __n)
150  {
151  return (__m != 0 && __n != 0)
152  ? (__m / __detail::__gcd(__m, __n)) * __n
153  : 0;
154  }
155 } // namespace __detail
156 
157 #if __cplusplus >= 201703L
158 
159 #define __cpp_lib_gcd_lcm 201606
160 // These were used in drafts of SD-6:
161 #define __cpp_lib_gcd 201606
162 #define __cpp_lib_lcm 201606
163 
164  /// Greatest common divisor
165  template<typename _Mn, typename _Nn>
166  constexpr common_type_t<_Mn, _Nn>
167  gcd(_Mn __m, _Nn __n) noexcept
168  {
169  static_assert(is_integral_v<_Mn>, "std::gcd arguments must be integers");
170  static_assert(is_integral_v<_Nn>, "std::gcd arguments must be integers");
171  static_assert(_Mn(2) != _Mn(1), "std::gcd arguments must not be bool");
172  static_assert(_Nn(2) != _Nn(1), "std::gcd arguments must not be bool");
173  using _Up = make_unsigned_t<common_type_t<_Mn, _Nn>>;
174  return __detail::__gcd(__detail::__absu<_Up>(__m),
175  __detail::__absu<_Up>(__n));
176  }
177 
178  /// Least common multiple
179  template<typename _Mn, typename _Nn>
180  constexpr common_type_t<_Mn, _Nn>
181  lcm(_Mn __m, _Nn __n) noexcept
182  {
183  static_assert(is_integral_v<_Mn>, "std::lcm arguments must be integers");
184  static_assert(is_integral_v<_Nn>, "std::lcm arguments must be integers");
185  static_assert(_Mn(2) == 2, "std::lcm arguments must not be bool");
186  static_assert(_Nn(2) == 2, "std::lcm arguments must not be bool");
187  using _Up = make_unsigned_t<common_type_t<_Mn, _Nn>>;
188  return __detail::__lcm(__detail::__absu<_Up>(__m),
189  __detail::__absu<_Up>(__n));
190  }
191 
192 #endif // C++17
193 #endif // C++14
194 
195 #if __cplusplus > 201703L
196 
197  // midpoint
198 # define __cpp_lib_interpolate 201902L
199 
200  template<typename _Tp>
201  constexpr
202  enable_if_t<__and_v<is_arithmetic<_Tp>, is_same<remove_cv_t<_Tp>, _Tp>,
203  __not_<is_same<_Tp, bool>>>,
204  _Tp>
205  midpoint(_Tp __a, _Tp __b) noexcept
206  {
207  if constexpr (is_integral_v<_Tp>)
208  {
209  using _Up = make_unsigned_t<_Tp>;
210 
211  int __k = 1;
212  _Up __m = __a;
213  _Up __M = __b;
214  if (__a > __b)
215  {
216  __k = -1;
217  __m = __b;
218  __M = __a;
219  }
220  return __a + __k * _Tp(_Up(__M - __m) / 2);
221  }
222  else // is_floating
223  {
224  constexpr _Tp __lo = numeric_limits<_Tp>::min() * 2;
225  constexpr _Tp __hi = numeric_limits<_Tp>::max() / 2;
226  const _Tp __abs_a = __a < 0 ? -__a : __a;
227  const _Tp __abs_b = __b < 0 ? -__b : __b;
228  if (__abs_a <= __hi && __abs_b <= __hi) [[likely]]
229  return (__a + __b) / 2; // always correctly rounded
230  if (__abs_a < __lo) // not safe to halve __a
231  return __a + __b/2;
232  if (__abs_b < __lo) // not safe to halve __b
233  return __a/2 + __b;
234  return __a/2 + __b/2; // otherwise correctly rounded
235  }
236  }
237 
238  template<typename _Tp>
239  constexpr enable_if_t<is_object_v<_Tp>, _Tp*>
240  midpoint(_Tp* __a, _Tp* __b) noexcept
241  {
242  static_assert( sizeof(_Tp) != 0, "type must be complete" );
243  return __a + (__b - __a) / 2;
244  }
245 #endif // C++20
246 
247 #if __cplusplus >= 201703L
248 
249 #if __cplusplus > 201703L
250 #define __cpp_lib_constexpr_numeric 201911L
251 #endif
252 
253  /// @addtogroup numeric_ops
254  /// @{
255 
256  /**
257  * @brief Calculate reduction of values in a range.
258  *
259  * @param __first Start of range.
260  * @param __last End of range.
261  * @param __init Starting value to add other values to.
262  * @param __binary_op A binary function object.
263  * @return The final sum.
264  *
265  * Reduce the values in the range `[first,last)` using a binary operation.
266  * The initial value is `init`. The values are not necessarily processed
267  * in order.
268  *
269  * This algorithm is similar to `std::accumulate` but is not required to
270  * perform the operations in order from first to last. For operations
271  * that are commutative and associative the result will be the same as
272  * for `std::accumulate`, but for other operations (such as floating point
273  * arithmetic) the result can be different.
274  */
275  template<typename _InputIterator, typename _Tp, typename _BinaryOperation>
276  _GLIBCXX20_CONSTEXPR
277  _Tp
278  reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
279  _BinaryOperation __binary_op)
280  {
281  using value_type = typename iterator_traits<_InputIterator>::value_type;
282  static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>);
283  static_assert(is_convertible_v<value_type, _Tp>);
284  if constexpr (__is_random_access_iter<_InputIterator>::value)
285  {
286  while ((__last - __first) >= 4)
287  {
288  _Tp __v1 = __binary_op(__first[0], __first[1]);
289  _Tp __v2 = __binary_op(__first[2], __first[3]);
290  _Tp __v3 = __binary_op(__v1, __v2);
291  __init = __binary_op(__init, __v3);
292  __first += 4;
293  }
294  }
295  for (; __first != __last; ++__first)
296  __init = __binary_op(__init, *__first);
297  return __init;
298  }
299 
300  /**
301  * @brief Calculate reduction of values in a range.
302  *
303  * @param __first Start of range.
304  * @param __last End of range.
305  * @param __init Starting value to add other values to.
306  * @return The final sum.
307  *
308  * Reduce the values in the range `[first,last)` using addition.
309  * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`.
310  */
311  template<typename _InputIterator, typename _Tp>
312  _GLIBCXX20_CONSTEXPR
313  inline _Tp
314  reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
315  { return std::reduce(__first, __last, std::move(__init), plus<>()); }
316 
317  /**
318  * @brief Calculate reduction of values in a range.
319  *
320  * @param __first Start of range.
321  * @param __last End of range.
322  * @return The final sum.
323  *
324  * Reduce the values in the range `[first,last)` using addition, with
325  * an initial value of `T{}`, where `T` is the iterator's value type.
326  * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`.
327  */
328  template<typename _InputIterator>
329  _GLIBCXX20_CONSTEXPR
330  inline typename iterator_traits<_InputIterator>::value_type
331  reduce(_InputIterator __first, _InputIterator __last)
332  {
333  using value_type = typename iterator_traits<_InputIterator>::value_type;
334  return std::reduce(__first, __last, value_type{}, plus<>());
335  }
336 
337  /**
338  * @brief Combine elements from two ranges and reduce
339  *
340  * @param __first1 Start of first range.
341  * @param __last1 End of first range.
342  * @param __first2 Start of second range.
343  * @param __init Starting value to add other values to.
344  * @param __binary_op1 The function used to perform reduction.
345  * @param __binary_op2 The function used to combine values from the ranges.
346  * @return The final sum.
347  *
348  * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)`
349  * and then use `binary_op1` to reduce the values returned by `binary_op2`
350  * to a single value of type `T`.
351  *
352  * The range beginning at `first2` must contain at least `last1-first1`
353  * elements.
354  */
355  template<typename _InputIterator1, typename _InputIterator2, typename _Tp,
356  typename _BinaryOperation1, typename _BinaryOperation2>
357  _GLIBCXX20_CONSTEXPR
358  _Tp
359  transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
360  _InputIterator2 __first2, _Tp __init,
361  _BinaryOperation1 __binary_op1,
362  _BinaryOperation2 __binary_op2)
363  {
364  if constexpr (__and_v<__is_random_access_iter<_InputIterator1>,
365  __is_random_access_iter<_InputIterator2>>)
366  {
367  while ((__last1 - __first1) >= 4)
368  {
369  _Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]),
370  __binary_op2(__first1[1], __first2[1]));
371  _Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]),
372  __binary_op2(__first1[3], __first2[3]));
373  _Tp __v3 = __binary_op1(__v1, __v2);
374  __init = __binary_op1(__init, __v3);
375  __first1 += 4;
376  __first2 += 4;
377  }
378  }
379  for (; __first1 != __last1; ++__first1, (void) ++__first2)
380  __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
381  return __init;
382  }
383 
384  /**
385  * @brief Combine elements from two ranges and reduce
386  *
387  * @param __first1 Start of first range.
388  * @param __last1 End of first range.
389  * @param __first2 Start of second range.
390  * @param __init Starting value to add other values to.
391  * @return The final sum.
392  *
393  * Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then
394  * use addition to sum those products to a single value of type `T`.
395  *
396  * The range beginning at `first2` must contain at least `last1-first1`
397  * elements.
398  */
399  template<typename _InputIterator1, typename _InputIterator2, typename _Tp>
400  _GLIBCXX20_CONSTEXPR
401  inline _Tp
402  transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
403  _InputIterator2 __first2, _Tp __init)
404  {
405  return std::transform_reduce(__first1, __last1, __first2,
406  std::move(__init),
407  plus<>(), multiplies<>());
408  }
409 
410  /**
411  * @brief Transform the elements of a range and reduce
412  *
413  * @param __first Start of range.
414  * @param __last End of range.
415  * @param __init Starting value to add other values to.
416  * @param __binary_op The function used to perform reduction.
417  * @param __unary_op The function used to transform values from the range.
418  * @return The final sum.
419  *
420  * Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then
421  * use `binary_op` to reduce the values returned by `unary_op`
422  * to a single value of type `T`.
423  */
424  template<typename _InputIterator, typename _Tp,
425  typename _BinaryOperation, typename _UnaryOperation>
426  _GLIBCXX20_CONSTEXPR
427  _Tp
428  transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
429  _BinaryOperation __binary_op, _UnaryOperation __unary_op)
430  {
431  if constexpr (__is_random_access_iter<_InputIterator>::value)
432  {
433  while ((__last - __first) >= 4)
434  {
435  _Tp __v1 = __binary_op(__unary_op(__first[0]),
436  __unary_op(__first[1]));
437  _Tp __v2 = __binary_op(__unary_op(__first[2]),
438  __unary_op(__first[3]));
439  _Tp __v3 = __binary_op(__v1, __v2);
440  __init = __binary_op(__init, __v3);
441  __first += 4;
442  }
443  }
444  for (; __first != __last; ++__first)
445  __init = __binary_op(__init, __unary_op(*__first));
446  return __init;
447  }
448 
449  /** @brief Output the cumulative sum of one range to a second range
450  *
451  * @param __first Start of input range.
452  * @param __last End of input range.
453  * @param __result Start of output range.
454  * @param __init Initial value.
455  * @param __binary_op Function to perform summation.
456  * @return The end of the output range.
457  *
458  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
459  * to the output range. Each element of the output range contains the
460  * running total of all earlier elements (and the initial value),
461  * using `binary_op` for summation.
462  *
463  * This function generates an "exclusive" scan, meaning the Nth element
464  * of the output range is the sum of the first N-1 input elements,
465  * so the Nth input element is not included.
466  */
467  template<typename _InputIterator, typename _OutputIterator, typename _Tp,
468  typename _BinaryOperation>
469  _GLIBCXX20_CONSTEXPR
470  _OutputIterator
471  exclusive_scan(_InputIterator __first, _InputIterator __last,
472  _OutputIterator __result, _Tp __init,
473  _BinaryOperation __binary_op)
474  {
475  while (__first != __last)
476  {
477  auto __v = __init;
478  __init = __binary_op(__init, *__first);
479  ++__first;
480  *__result++ = std::move(__v);
481  }
482  return __result;
483  }
484 
485  /** @brief Output the cumulative sum of one range to a second range
486  *
487  * @param __first Start of input range.
488  * @param __last End of input range.
489  * @param __result Start of output range.
490  * @param __init Initial value.
491  * @return The end of the output range.
492  *
493  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
494  * to the output range. Each element of the output range contains the
495  * running total of all earlier elements (and the initial value),
496  * using `std::plus<>` for summation.
497  *
498  * This function generates an "exclusive" scan, meaning the Nth element
499  * of the output range is the sum of the first N-1 input elements,
500  * so the Nth input element is not included.
501  */
502  template<typename _InputIterator, typename _OutputIterator, typename _Tp>
503  _GLIBCXX20_CONSTEXPR
504  inline _OutputIterator
505  exclusive_scan(_InputIterator __first, _InputIterator __last,
506  _OutputIterator __result, _Tp __init)
507  {
508  return std::exclusive_scan(__first, __last, __result, std::move(__init),
509  plus<>());
510  }
511 
512  /** @brief Output the cumulative sum of one range to a second range
513  *
514  * @param __first Start of input range.
515  * @param __last End of input range.
516  * @param __result Start of output range.
517  * @param __binary_op Function to perform summation.
518  * @param __init Initial value.
519  * @return The end of the output range.
520  *
521  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
522  * to the output range. Each element of the output range contains the
523  * running total of all earlier elements (and the initial value),
524  * using `binary_op` for summation.
525  *
526  * This function generates an "inclusive" scan, meaning the Nth element
527  * of the output range is the sum of the first N input elements,
528  * so the Nth input element is included.
529  */
530  template<typename _InputIterator, typename _OutputIterator,
531  typename _BinaryOperation, typename _Tp>
532  _GLIBCXX20_CONSTEXPR
533  _OutputIterator
534  inclusive_scan(_InputIterator __first, _InputIterator __last,
535  _OutputIterator __result, _BinaryOperation __binary_op,
536  _Tp __init)
537  {
538  for (; __first != __last; ++__first)
539  *__result++ = __init = __binary_op(__init, *__first);
540  return __result;
541  }
542 
543  /** @brief Output the cumulative sum of one range to a second range
544  *
545  * @param __first Start of input range.
546  * @param __last End of input range.
547  * @param __result Start of output range.
548  * @param __binary_op Function to perform summation.
549  * @return The end of the output range.
550  *
551  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
552  * to the output range. Each element of the output range contains the
553  * running total of all earlier elements, using `binary_op` for summation.
554  *
555  * This function generates an "inclusive" scan, meaning the Nth element
556  * of the output range is the sum of the first N input elements,
557  * so the Nth input element is included.
558  */
559  template<typename _InputIterator, typename _OutputIterator,
560  typename _BinaryOperation>
561  _GLIBCXX20_CONSTEXPR
562  _OutputIterator
563  inclusive_scan(_InputIterator __first, _InputIterator __last,
564  _OutputIterator __result, _BinaryOperation __binary_op)
565  {
566  if (__first != __last)
567  {
568  auto __init = *__first;
569  *__result++ = __init;
570  ++__first;
571  if (__first != __last)
572  __result = std::inclusive_scan(__first, __last, __result,
573  __binary_op, std::move(__init));
574  }
575  return __result;
576  }
577 
578  /** @brief Output the cumulative sum of one range to a second range
579  *
580  * @param __first Start of input range.
581  * @param __last End of input range.
582  * @param __result Start of output range.
583  * @return The end of the output range.
584  *
585  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
586  * to the output range. Each element of the output range contains the
587  * running total of all earlier elements, using `std::plus<>` for summation.
588  *
589  * This function generates an "inclusive" scan, meaning the Nth element
590  * of the output range is the sum of the first N input elements,
591  * so the Nth input element is included.
592  */
593  template<typename _InputIterator, typename _OutputIterator>
594  _GLIBCXX20_CONSTEXPR
595  inline _OutputIterator
596  inclusive_scan(_InputIterator __first, _InputIterator __last,
597  _OutputIterator __result)
598  { return std::inclusive_scan(__first, __last, __result, plus<>()); }
599 
600  /** @brief Output the cumulative sum of one range to a second range
601  *
602  * @param __first Start of input range.
603  * @param __last End of input range.
604  * @param __result Start of output range.
605  * @param __init Initial value.
606  * @param __binary_op Function to perform summation.
607  * @param __unary_op Function to transform elements of the input range.
608  * @return The end of the output range.
609  *
610  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
611  * to the output range. Each element of the output range contains the
612  * running total of all earlier elements (and the initial value),
613  * using `__unary_op` to transform the input elements
614  * and using `__binary_op` for summation.
615  *
616  * This function generates an "exclusive" scan, meaning the Nth element
617  * of the output range is the sum of the first N-1 input elements,
618  * so the Nth input element is not included.
619  */
620  template<typename _InputIterator, typename _OutputIterator, typename _Tp,
621  typename _BinaryOperation, typename _UnaryOperation>
622  _GLIBCXX20_CONSTEXPR
623  _OutputIterator
624  transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
625  _OutputIterator __result, _Tp __init,
626  _BinaryOperation __binary_op,
627  _UnaryOperation __unary_op)
628  {
629  while (__first != __last)
630  {
631  auto __v = __init;
632  __init = __binary_op(__init, __unary_op(*__first));
633  ++__first;
634  *__result++ = std::move(__v);
635  }
636  return __result;
637  }
638 
639  /** @brief Output the cumulative sum of one range to a second range
640  *
641  * @param __first Start of input range.
642  * @param __last End of input range.
643  * @param __result Start of output range.
644  * @param __binary_op Function to perform summation.
645  * @param __unary_op Function to transform elements of the input range.
646  * @param __init Initial value.
647  * @return The end of the output range.
648  *
649  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
650  * to the output range. Each element of the output range contains the
651  * running total of all earlier elements (and the initial value),
652  * using `__unary_op` to transform the input elements
653  * and using `__binary_op` for summation.
654  *
655  * This function generates an "inclusive" scan, meaning the Nth element
656  * of the output range is the sum of the first N input elements,
657  * so the Nth input element is included.
658  */
659  template<typename _InputIterator, typename _OutputIterator,
660  typename _BinaryOperation, typename _UnaryOperation, typename _Tp>
661  _GLIBCXX20_CONSTEXPR
662  _OutputIterator
663  transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
664  _OutputIterator __result,
665  _BinaryOperation __binary_op,
666  _UnaryOperation __unary_op,
667  _Tp __init)
668  {
669  for (; __first != __last; ++__first)
670  *__result++ = __init = __binary_op(__init, __unary_op(*__first));
671  return __result;
672  }
673 
674  /** @brief Output the cumulative sum of one range to a second range
675  *
676  * @param __first Start of input range.
677  * @param __last End of input range.
678  * @param __result Start of output range.
679  * @param __binary_op Function to perform summation.
680  * @param __unary_op Function to transform elements of the input range.
681  * @return The end of the output range.
682  *
683  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
684  * to the output range. Each element of the output range contains the
685  * running total of all earlier elements,
686  * using `__unary_op` to transform the input elements
687  * and using `__binary_op` for summation.
688  *
689  * This function generates an "inclusive" scan, meaning the Nth element
690  * of the output range is the sum of the first N input elements,
691  * so the Nth input element is included.
692  */
693  template<typename _InputIterator, typename _OutputIterator,
694  typename _BinaryOperation, typename _UnaryOperation>
695  _GLIBCXX20_CONSTEXPR
696  _OutputIterator
697  transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
698  _OutputIterator __result,
699  _BinaryOperation __binary_op,
700  _UnaryOperation __unary_op)
701  {
702  if (__first != __last)
703  {
704  auto __init = __unary_op(*__first);
705  *__result++ = __init;
706  ++__first;
707  if (__first != __last)
708  __result = std::transform_inclusive_scan(__first, __last, __result,
709  __binary_op, __unary_op,
710  std::move(__init));
711  }
712  return __result;
713  }
714 
715  // @} group numeric_ops
716 #endif // C++17
717 
718 _GLIBCXX_END_NAMESPACE_VERSION
719 } // namespace std
720 
721 #if __cplusplus >= 201703L
722 // Parallel STL algorithms
723 # if _PSTL_EXECUTION_POLICIES_DEFINED
724 // If <execution> has already been included, pull in implementations
725 # include <pstl/glue_numeric_impl.h>
726 # else
727 // Otherwise just pull in forward declarations
728 # include <pstl/glue_numeric_defs.h>
729 # define _PSTL_NUMERIC_FORWARD_DECLARED 1
730 # endif
731 
732 // Feature test macro for parallel algorithms
733 # define __cpp_lib_parallel_algorithm 201603L
734 #endif // C++17
735 
736 #endif /* _GLIBCXX_NUMERIC */