libstdc++
numeric
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1 // <numeric> -*- C++ -*-
2 
3 // Copyright (C) 2001-2020 Free Software Foundation, Inc.
4 //
5 // This file is part of the GNU ISO C++ Library. This library is free
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9 // any later version.
10 
11 // This library is distributed in the hope that it will be useful,
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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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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 /**
69  * @defgroup numerics Numerics
70  *
71  * Components for performing numeric operations. Includes support for
72  * complex number types, random number generation, numeric (n-at-a-time)
73  * arrays, generalized numeric algorithms, and mathematical special functions.
74  */
75 
76 #if __cplusplus >= 201402L
77 #include <type_traits>
78 
79 namespace std _GLIBCXX_VISIBILITY(default)
80 {
81 _GLIBCXX_BEGIN_NAMESPACE_VERSION
82 
83 namespace __detail
84 {
85  // std::abs is not constexpr and doesn't support unsigned integers.
86  template<typename _Tp>
87  constexpr
88  enable_if_t<__and_<is_integral<_Tp>, is_signed<_Tp>>::value, _Tp>
89  __abs_integral(_Tp __val)
90  { return __val < 0 ? -__val : __val; }
91 
92  template<typename _Tp>
93  constexpr
94  enable_if_t<__and_<is_integral<_Tp>, is_unsigned<_Tp>>::value, _Tp>
95  __abs_integral(_Tp __val)
96  { return __val; }
97 
98  void __abs_integral(bool) = delete;
99 
100  template<typename _Mn, typename _Nn>
101  constexpr common_type_t<_Mn, _Nn>
102  __gcd(_Mn __m, _Nn __n)
103  {
104  return __m == 0 ? __detail::__abs_integral(__n)
105  : __n == 0 ? __detail::__abs_integral(__m)
106  : __detail::__gcd(__n, __m % __n);
107  }
108 
109  /// Least common multiple
110  template<typename _Mn, typename _Nn>
111  constexpr common_type_t<_Mn, _Nn>
112  __lcm(_Mn __m, _Nn __n)
113  {
114  return (__m != 0 && __n != 0)
115  ? (__detail::__abs_integral(__m) / __detail::__gcd(__m, __n))
116  * __detail::__abs_integral(__n)
117  : 0;
118  }
119 } // namespace __detail
120 
121 #if __cplusplus >= 201703L
122 
123 #define __cpp_lib_gcd_lcm 201606
124 // These were used in drafts of SD-6:
125 #define __cpp_lib_gcd 201606
126 #define __cpp_lib_lcm 201606
127 
128  /// Greatest common divisor
129  template<typename _Mn, typename _Nn>
130  constexpr common_type_t<_Mn, _Nn>
131  gcd(_Mn __m, _Nn __n)
132  {
133  static_assert(is_integral_v<_Mn>, "gcd arguments are integers");
134  static_assert(is_integral_v<_Nn>, "gcd arguments are integers");
135  static_assert(!is_same_v<remove_cv_t<_Mn>, bool>,
136  "gcd arguments are not bools");
137  static_assert(!is_same_v<remove_cv_t<_Nn>, bool>,
138  "gcd arguments are not bools");
139  return __detail::__gcd(__m, __n);
140  }
141 
142  /// Least common multiple
143  template<typename _Mn, typename _Nn>
144  constexpr common_type_t<_Mn, _Nn>
145  lcm(_Mn __m, _Nn __n)
146  {
147  static_assert(is_integral_v<_Mn>, "lcm arguments are integers");
148  static_assert(is_integral_v<_Nn>, "lcm arguments are integers");
149  static_assert(!is_same_v<remove_cv_t<_Mn>, bool>,
150  "lcm arguments are not bools");
151  static_assert(!is_same_v<remove_cv_t<_Nn>, bool>,
152  "lcm arguments are not bools");
153  return __detail::__lcm(__m, __n);
154  }
155 
156 #endif // C++17
157 
158 _GLIBCXX_END_NAMESPACE_VERSION
159 } // namespace std
160 
161 #endif // C++14
162 
163 #if __cplusplus > 201703L
164 #include <limits>
165 
166 namespace std _GLIBCXX_VISIBILITY(default)
167 {
168 _GLIBCXX_BEGIN_NAMESPACE_VERSION
169  // midpoint
170 # define __cpp_lib_interpolate 201902L
171 
172  template<typename _Tp>
173  constexpr
174  enable_if_t<__and_v<is_arithmetic<_Tp>, is_same<remove_cv_t<_Tp>, _Tp>,
175  __not_<is_same<_Tp, bool>>>,
176  _Tp>
177  midpoint(_Tp __a, _Tp __b) noexcept
178  {
179  if constexpr (is_integral_v<_Tp>)
180  {
181  using _Up = make_unsigned_t<_Tp>;
182 
183  int __k = 1;
184  _Up __m = __a;
185  _Up __M = __b;
186  if (__a > __b)
187  {
188  __k = -1;
189  __m = __b;
190  __M = __a;
191  }
192  return __a + __k * _Tp(_Up(__M - __m) / 2);
193  }
194  else // is_floating
195  {
196  constexpr _Tp __lo = numeric_limits<_Tp>::min() * 2;
197  constexpr _Tp __hi = numeric_limits<_Tp>::max() / 2;
198  const _Tp __abs_a = __a < 0 ? -__a : __a;
199  const _Tp __abs_b = __b < 0 ? -__b : __b;
200  if (__abs_a <= __hi && __abs_b <= __hi) [[likely]]
201  return (__a + __b) / 2; // always correctly rounded
202  if (__abs_a < __lo) // not safe to halve __a
203  return __a + __b/2;
204  if (__abs_b < __lo) // not safe to halve __b
205  return __a/2 + __b;
206  return __a/2 + __b/2; // otherwise correctly rounded
207  }
208  }
209 
210  template<typename _Tp>
211  constexpr enable_if_t<is_object_v<_Tp>, _Tp*>
212  midpoint(_Tp* __a, _Tp* __b) noexcept
213  {
214  static_assert( sizeof(_Tp) != 0, "type must be complete" );
215  return __a + (__b - __a) / 2;
216  }
217 _GLIBCXX_END_NAMESPACE_VERSION
218 } // namespace std
219 
220 #endif // C++20
221 
222 #if __cplusplus > 201402L
223 #include <bits/stl_function.h>
224 
225 namespace std _GLIBCXX_VISIBILITY(default)
226 {
227 _GLIBCXX_BEGIN_NAMESPACE_VERSION
228 
229 #if __cplusplus > 201703L
230 #define __cpp_lib_constexpr_numeric 201911L
231 #endif
232 
233  /// @addtogroup numeric_ops
234  /// @{
235 
236  /**
237  * @brief Calculate reduction of values in a range.
238  *
239  * @param __first Start of range.
240  * @param __last End of range.
241  * @param __init Starting value to add other values to.
242  * @param __binary_op A binary function object.
243  * @return The final sum.
244  *
245  * Reduce the values in the range `[first,last)` using a binary operation.
246  * The initial value is `init`. The values are not necessarily processed
247  * in order.
248  *
249  * This algorithm is similar to `std::accumulate` but is not required to
250  * perform the operations in order from first to last. For operations
251  * that are commutative and associative the result will be the same as
252  * for `std::accumulate`, but for other operations (such as floating point
253  * arithmetic) the result can be different.
254  */
255  template<typename _InputIterator, typename _Tp, typename _BinaryOperation>
256  _GLIBCXX20_CONSTEXPR
257  _Tp
258  reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
259  _BinaryOperation __binary_op)
260  {
261  using value_type = typename iterator_traits<_InputIterator>::value_type;
262  static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>);
263  static_assert(is_convertible_v<value_type, _Tp>);
264  if constexpr (__is_random_access_iter<_InputIterator>::value)
265  {
266  while ((__last - __first) >= 4)
267  {
268  _Tp __v1 = __binary_op(__first[0], __first[1]);
269  _Tp __v2 = __binary_op(__first[2], __first[3]);
270  _Tp __v3 = __binary_op(__v1, __v2);
271  __init = __binary_op(__init, __v3);
272  __first += 4;
273  }
274  }
275  for (; __first != __last; ++__first)
276  __init = __binary_op(__init, *__first);
277  return __init;
278  }
279 
280  /**
281  * @brief Calculate reduction of values in a range.
282  *
283  * @param __first Start of range.
284  * @param __last End of range.
285  * @param __init Starting value to add other values to.
286  * @return The final sum.
287  *
288  * Reduce the values in the range `[first,last)` using addition.
289  * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`.
290  */
291  template<typename _InputIterator, typename _Tp>
292  _GLIBCXX20_CONSTEXPR
293  inline _Tp
294  reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
295  { return std::reduce(__first, __last, std::move(__init), plus<>()); }
296 
297  /**
298  * @brief Calculate reduction of values in a range.
299  *
300  * @param __first Start of range.
301  * @param __last End of range.
302  * @return The final sum.
303  *
304  * Reduce the values in the range `[first,last)` using addition, with
305  * an initial value of `T{}`, where `T` is the iterator's value type.
306  * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`.
307  */
308  template<typename _InputIterator>
309  _GLIBCXX20_CONSTEXPR
310  inline typename iterator_traits<_InputIterator>::value_type
311  reduce(_InputIterator __first, _InputIterator __last)
312  {
313  using value_type = typename iterator_traits<_InputIterator>::value_type;
314  return std::reduce(__first, __last, value_type{}, plus<>());
315  }
316 
317  /**
318  * @brief Combine elements from two ranges and reduce
319  *
320  * @param __first1 Start of first range.
321  * @param __last1 End of first range.
322  * @param __first2 Start of second range.
323  * @param __init Starting value to add other values to.
324  * @param __binary_op1 The function used to perform reduction.
325  * @param __binary_op2 The function used to combine values from the ranges.
326  * @return The final sum.
327  *
328  * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)`
329  * and then use `binary_op1` to reduce the values returned by `binary_op2`
330  * to a single value of type `T`.
331  *
332  * The range beginning at `first2` must contain at least `last1-first1`
333  * elements.
334  */
335  template<typename _InputIterator1, typename _InputIterator2, typename _Tp,
336  typename _BinaryOperation1, typename _BinaryOperation2>
337  _GLIBCXX20_CONSTEXPR
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  _GLIBCXX20_CONSTEXPR
381  inline _Tp
382  transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
383  _InputIterator2 __first2, _Tp __init)
384  {
385  return std::transform_reduce(__first1, __last1, __first2,
386  std::move(__init),
387  plus<>(), multiplies<>());
388  }
389 
390  /**
391  * @brief Transform the elements of a range and reduce
392  *
393  * @param __first Start of range.
394  * @param __last End of range.
395  * @param __init Starting value to add other values to.
396  * @param __binary_op The function used to perform reduction.
397  * @param __unary_op The function used to transform values from the range.
398  * @return The final sum.
399  *
400  * Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then
401  * use `binary_op` to reduce the values returned by `unary_op`
402  * to a single value of type `T`.
403  */
404  template<typename _InputIterator, typename _Tp,
405  typename _BinaryOperation, typename _UnaryOperation>
406  _GLIBCXX20_CONSTEXPR
407  _Tp
408  transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init,
409  _BinaryOperation __binary_op, _UnaryOperation __unary_op)
410  {
411  if constexpr (__is_random_access_iter<_InputIterator>::value)
412  {
413  while ((__last - __first) >= 4)
414  {
415  _Tp __v1 = __binary_op(__unary_op(__first[0]),
416  __unary_op(__first[1]));
417  _Tp __v2 = __binary_op(__unary_op(__first[2]),
418  __unary_op(__first[3]));
419  _Tp __v3 = __binary_op(__v1, __v2);
420  __init = __binary_op(__init, __v3);
421  __first += 4;
422  }
423  }
424  for (; __first != __last; ++__first)
425  __init = __binary_op(__init, __unary_op(*__first));
426  return __init;
427  }
428 
429  /** @brief Output the cumulative sum of one range to a second range
430  *
431  * @param __first Start of input range.
432  * @param __last End of input range.
433  * @param __result Start of output range.
434  * @param __init Initial value.
435  * @param __binary_op Function to perform summation.
436  * @return The end of the output range.
437  *
438  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
439  * to the output range. Each element of the output range contains the
440  * running total of all earlier elements (and the initial value),
441  * using `binary_op` for summation.
442  *
443  * This function generates an "exclusive" scan, meaning the Nth element
444  * of the output range is the sum of the first N-1 input elements,
445  * so the Nth input element is not included.
446  */
447  template<typename _InputIterator, typename _OutputIterator, typename _Tp,
448  typename _BinaryOperation>
449  _GLIBCXX20_CONSTEXPR
450  _OutputIterator
451  exclusive_scan(_InputIterator __first, _InputIterator __last,
452  _OutputIterator __result, _Tp __init,
453  _BinaryOperation __binary_op)
454  {
455  while (__first != __last)
456  {
457  auto __v = __init;
458  __init = __binary_op(__init, *__first);
459  ++__first;
460  *__result++ = std::move(__v);
461  }
462  return __result;
463  }
464 
465  /** @brief Output the cumulative sum of one range to a second range
466  *
467  * @param __first Start of input range.
468  * @param __last End of input range.
469  * @param __result Start of output range.
470  * @param __init Initial value.
471  * @return The end of the output range.
472  *
473  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
474  * to the output range. Each element of the output range contains the
475  * running total of all earlier elements (and the initial value),
476  * using `std::plus<>` for summation.
477  *
478  * This function generates an "exclusive" scan, meaning the Nth element
479  * of the output range is the sum of the first N-1 input elements,
480  * so the Nth input element is not included.
481  */
482  template<typename _InputIterator, typename _OutputIterator, typename _Tp>
483  _GLIBCXX20_CONSTEXPR
484  inline _OutputIterator
485  exclusive_scan(_InputIterator __first, _InputIterator __last,
486  _OutputIterator __result, _Tp __init)
487  {
488  return std::exclusive_scan(__first, __last, __result, std::move(__init),
489  plus<>());
490  }
491 
492  /** @brief Output the cumulative sum of one range to a second range
493  *
494  * @param __first Start of input range.
495  * @param __last End of input range.
496  * @param __result Start of output range.
497  * @param __binary_op Function to perform summation.
498  * @param __init Initial value.
499  * @return The end of the output range.
500  *
501  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
502  * to the output range. Each element of the output range contains the
503  * running total of all earlier elements (and the initial value),
504  * using `binary_op` for summation.
505  *
506  * This function generates an "inclusive" scan, meaning the Nth element
507  * of the output range is the sum of the first N input elements,
508  * so the Nth input element is included.
509  */
510  template<typename _InputIterator, typename _OutputIterator,
511  typename _BinaryOperation, typename _Tp>
512  _GLIBCXX20_CONSTEXPR
513  _OutputIterator
514  inclusive_scan(_InputIterator __first, _InputIterator __last,
515  _OutputIterator __result, _BinaryOperation __binary_op,
516  _Tp __init)
517  {
518  for (; __first != __last; ++__first)
519  *__result++ = __init = __binary_op(__init, *__first);
520  return __result;
521  }
522 
523  /** @brief Output the cumulative sum of one range to a second range
524  *
525  * @param __first Start of input range.
526  * @param __last End of input range.
527  * @param __result Start of output range.
528  * @param __binary_op Function to perform summation.
529  * @return The end of the output range.
530  *
531  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
532  * to the output range. Each element of the output range contains the
533  * running total of all earlier elements, using `binary_op` for summation.
534  *
535  * This function generates an "inclusive" scan, meaning the Nth element
536  * of the output range is the sum of the first N input elements,
537  * so the Nth input element is included.
538  */
539  template<typename _InputIterator, typename _OutputIterator,
540  typename _BinaryOperation>
541  _GLIBCXX20_CONSTEXPR
542  _OutputIterator
543  inclusive_scan(_InputIterator __first, _InputIterator __last,
544  _OutputIterator __result, _BinaryOperation __binary_op)
545  {
546  if (__first != __last)
547  {
548  auto __init = *__first;
549  *__result++ = __init;
550  ++__first;
551  if (__first != __last)
552  __result = std::inclusive_scan(__first, __last, __result,
553  __binary_op, std::move(__init));
554  }
555  return __result;
556  }
557 
558  /** @brief Output the cumulative sum of one range to a second range
559  *
560  * @param __first Start of input range.
561  * @param __last End of input range.
562  * @param __result Start of output range.
563  * @return The end of the output range.
564  *
565  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
566  * to the output range. Each element of the output range contains the
567  * running total of all earlier elements, using `std::plus<>` for summation.
568  *
569  * This function generates an "inclusive" scan, meaning the Nth element
570  * of the output range is the sum of the first N input elements,
571  * so the Nth input element is included.
572  */
573  template<typename _InputIterator, typename _OutputIterator>
574  _GLIBCXX20_CONSTEXPR
575  inline _OutputIterator
576  inclusive_scan(_InputIterator __first, _InputIterator __last,
577  _OutputIterator __result)
578  { return std::inclusive_scan(__first, __last, __result, plus<>()); }
579 
580  /** @brief Output the cumulative sum of one range to a second range
581  *
582  * @param __first Start of input range.
583  * @param __last End of input range.
584  * @param __result Start of output range.
585  * @param __init Initial value.
586  * @param __binary_op Function to perform summation.
587  * @param __unary_op Function to transform elements of the input range.
588  * @return The end of the output range.
589  *
590  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
591  * to the output range. Each element of the output range contains the
592  * running total of all earlier elements (and the initial value),
593  * using `__unary_op` to transform the input elements
594  * and using `__binary_op` for summation.
595  *
596  * This function generates an "exclusive" scan, meaning the Nth element
597  * of the output range is the sum of the first N-1 input elements,
598  * so the Nth input element is not included.
599  */
600  template<typename _InputIterator, typename _OutputIterator, typename _Tp,
601  typename _BinaryOperation, typename _UnaryOperation>
602  _GLIBCXX20_CONSTEXPR
603  _OutputIterator
604  transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
605  _OutputIterator __result, _Tp __init,
606  _BinaryOperation __binary_op,
607  _UnaryOperation __unary_op)
608  {
609  while (__first != __last)
610  {
611  auto __v = __init;
612  __init = __binary_op(__init, __unary_op(*__first));
613  ++__first;
614  *__result++ = std::move(__v);
615  }
616  return __result;
617  }
618 
619  /** @brief Output the cumulative sum of one range to a second range
620  *
621  * @param __first Start of input range.
622  * @param __last End of input range.
623  * @param __result Start of output range.
624  * @param __binary_op Function to perform summation.
625  * @param __unary_op Function to transform elements of the input range.
626  * @param __init Initial value.
627  * @return The end of the output range.
628  *
629  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
630  * to the output range. Each element of the output range contains the
631  * running total of all earlier elements (and the initial value),
632  * using `__unary_op` to transform the input elements
633  * and using `__binary_op` for summation.
634  *
635  * This function generates an "inclusive" scan, meaning the Nth element
636  * of the output range is the sum of the first N input elements,
637  * so the Nth input element is included.
638  */
639  template<typename _InputIterator, typename _OutputIterator,
640  typename _BinaryOperation, typename _UnaryOperation, typename _Tp>
641  _GLIBCXX20_CONSTEXPR
642  _OutputIterator
643  transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
644  _OutputIterator __result,
645  _BinaryOperation __binary_op,
646  _UnaryOperation __unary_op,
647  _Tp __init)
648  {
649  for (; __first != __last; ++__first)
650  *__result++ = __init = __binary_op(__init, __unary_op(*__first));
651  return __result;
652  }
653 
654  /** @brief Output the cumulative sum of one range to a second range
655  *
656  * @param __first Start of input range.
657  * @param __last End of input range.
658  * @param __result Start of output range.
659  * @param __binary_op Function to perform summation.
660  * @param __unary_op Function to transform elements of the input range.
661  * @return The end of the output range.
662  *
663  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
664  * to the output range. Each element of the output range contains the
665  * running total of all earlier elements,
666  * using `__unary_op` to transform the input elements
667  * and using `__binary_op` for summation.
668  *
669  * This function generates an "inclusive" scan, meaning the Nth element
670  * of the output range is the sum of the first N input elements,
671  * so the Nth input element is included.
672  */
673  template<typename _InputIterator, typename _OutputIterator,
674  typename _BinaryOperation, typename _UnaryOperation>
675  _GLIBCXX20_CONSTEXPR
676  _OutputIterator
677  transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
678  _OutputIterator __result,
679  _BinaryOperation __binary_op,
680  _UnaryOperation __unary_op)
681  {
682  if (__first != __last)
683  {
684  auto __init = __unary_op(*__first);
685  *__result++ = __init;
686  ++__first;
687  if (__first != __last)
688  __result = std::transform_inclusive_scan(__first, __last, __result,
689  __binary_op, __unary_op,
690  std::move(__init));
691  }
692  return __result;
693  }
694 
695  // @} group numeric_ops
696 
697 _GLIBCXX_END_NAMESPACE_VERSION
698 } // namespace std
699 
700 // Parallel STL algorithms
701 # if _PSTL_EXECUTION_POLICIES_DEFINED
702 // If <execution> has already been included, pull in implementations
703 # include <pstl/glue_numeric_impl.h>
704 # else
705 // Otherwise just pull in forward declarations
706 # include <pstl/glue_numeric_defs.h>
707 # define _PSTL_NUMERIC_FORWARD_DECLARED 1
708 # endif
709 
710 // Feature test macro for parallel algorithms
711 # define __cpp_lib_parallel_algorithm 201603L
712 #endif // C++17
713 
714 #endif /* _GLIBCXX_NUMERIC */