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
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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,
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33  * that both that copyright notice and this permission notice appear
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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
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46  * in supporting documentation. Silicon Graphics makes no
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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 __ref = typename iterator_traits<_InputIterator>::reference;
265  static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, __ref>);
266  static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, __ref, _Tp&>);
267  static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>);
268  static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, __ref, __ref>);
269  if constexpr (__is_random_access_iter<_InputIterator>::value)
270  {
271  while ((__last - __first) >= 4)
272  {
273  _Tp __v1 = __binary_op(__first[0], __first[1]);
274  _Tp __v2 = __binary_op(__first[2], __first[3]);
275  _Tp __v3 = __binary_op(__v1, __v2);
276  __init = __binary_op(__init, __v3);
277  __first += 4;
278  }
279  }
280  for (; __first != __last; ++__first)
281  __init = __binary_op(__init, *__first);
282  return __init;
283  }
284 
285  /**
286  * @brief Calculate reduction of values in a range.
287  *
288  * @param __first Start of range.
289  * @param __last End of range.
290  * @param __init Starting value to add other values to.
291  * @return The final sum.
292  *
293  * Reduce the values in the range `[first,last)` using addition.
294  * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`.
295  */
296  template<typename _InputIterator, typename _Tp>
297  inline _Tp
298  reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
299  { return std::reduce(__first, __last, std::move(__init), plus<>()); }
300 
301  /**
302  * @brief Calculate reduction of values in a range.
303  *
304  * @param __first Start of range.
305  * @param __last End of range.
306  * @return The final sum.
307  *
308  * Reduce the values in the range `[first,last)` using addition, with
309  * an initial value of `T{}`, where `T` is the iterator's value type.
310  * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`.
311  */
312  template<typename _InputIterator>
313  inline typename iterator_traits<_InputIterator>::value_type
314  reduce(_InputIterator __first, _InputIterator __last)
315  {
316  using value_type = typename iterator_traits<_InputIterator>::value_type;
317  return std::reduce(__first, __last, value_type{}, plus<>());
318  }
319 
320  /**
321  * @brief Combine elements from two ranges and reduce
322  *
323  * @param __first1 Start of first range.
324  * @param __last1 End of first range.
325  * @param __first2 Start of second range.
326  * @param __init Starting value to add other values to.
327  * @param __binary_op1 The function used to perform reduction.
328  * @param __binary_op2 The function used to combine values from the ranges.
329  * @return The final sum.
330  *
331  * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)`
332  * and then use `binary_op1` to reduce the values returned by `binary_op2`
333  * to a single value of type `T`.
334  *
335  * The range beginning at `first2` must contain at least `last1-first1`
336  * elements.
337  */
338  template<typename _InputIterator1, typename _InputIterator2, typename _Tp,
339  typename _BinaryOperation1, typename _BinaryOperation2>
340  _Tp
341  transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
342  _InputIterator2 __first2, _Tp __init,
343  _BinaryOperation1 __binary_op1,
344  _BinaryOperation2 __binary_op2)
345  {
346  if constexpr (__and_v<__is_random_access_iter<_InputIterator1>,
347  __is_random_access_iter<_InputIterator2>>)
348  {
349  while ((__last1 - __first1) >= 4)
350  {
351  _Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]),
352  __binary_op2(__first1[1], __first2[1]));
353  _Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]),
354  __binary_op2(__first1[3], __first2[3]));
355  _Tp __v3 = __binary_op1(__v1, __v2);
356  __init = __binary_op1(__init, __v3);
357  __first1 += 4;
358  __first2 += 4;
359  }
360  }
361  for (; __first1 != __last1; ++__first1, (void) ++__first2)
362  __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
363  return __init;
364  }
365 
366  /**
367  * @brief Combine elements from two ranges and reduce
368  *
369  * @param __first1 Start of first range.
370  * @param __last1 End of first range.
371  * @param __first2 Start of second range.
372  * @param __init Starting value to add other values to.
373  * @return The final sum.
374  *
375  * Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then
376  * use addition to sum those products to a single value of type `T`.
377  *
378  * The range beginning at `first2` must contain at least `last1-first1`
379  * elements.
380  */
381  template<typename _InputIterator1, typename _InputIterator2, typename _Tp>
382  inline _Tp
383  transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
384  _InputIterator2 __first2, _Tp __init)
385  {
386  return std::transform_reduce(__first1, __last1, __first2,
387  std::move(__init),
388  plus<>(), multiplies<>());
389  }
390 
391  /**
392  * @brief Transform the elements of a range and reduce
393  *
394  * @param __first Start of range.
395  * @param __last End of range.
396  * @param __init Starting value to add other values to.
397  * @param __binary_op The function used to perform reduction.
398  * @param __unary_op The function used to transform values from the range.
399  * @return The final sum.
400  *
401  * Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then
402  * use `binary_op` to reduce the values returned by `unary_op`
403  * to a single value of type `T`.
404  */
405  template<typename _InputIterator, typename _Tp,
406  typename _BinaryOperation, typename _UnaryOperation>
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  _OutputIterator
450  exclusive_scan(_InputIterator __first, _InputIterator __last,
451  _OutputIterator __result, _Tp __init,
452  _BinaryOperation __binary_op)
453  {
454  while (__first != __last)
455  {
456  auto __v = __init;
457  __init = __binary_op(__init, *__first);
458  ++__first;
459  *__result++ = std::move(__v);
460  }
461  return __result;
462  }
463 
464  /** @brief Output the cumulative sum of one range to a second range
465  *
466  * @param __first Start of input range.
467  * @param __last End of input range.
468  * @param __result Start of output range.
469  * @param __init Initial value.
470  * @return The end of the output range.
471  *
472  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
473  * to the output range. Each element of the output range contains the
474  * running total of all earlier elements (and the initial value),
475  * using `std::plus<>` for summation.
476  *
477  * This function generates an "exclusive" scan, meaning the Nth element
478  * of the output range is the sum of the first N-1 input elements,
479  * so the Nth input element is not included.
480  */
481  template<typename _InputIterator, typename _OutputIterator, typename _Tp>
482  inline _OutputIterator
483  exclusive_scan(_InputIterator __first, _InputIterator __last,
484  _OutputIterator __result, _Tp __init)
485  {
486  return std::exclusive_scan(__first, __last, __result, std::move(__init),
487  plus<>());
488  }
489 
490  /** @brief Output the cumulative sum of one range to a second range
491  *
492  * @param __first Start of input range.
493  * @param __last End of input range.
494  * @param __result Start of output range.
495  * @param __binary_op Function to perform summation.
496  * @param __init Initial value.
497  * @return The end of the output range.
498  *
499  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
500  * to the output range. Each element of the output range contains the
501  * running total of all earlier elements (and the initial value),
502  * using `binary_op` for summation.
503  *
504  * This function generates an "inclusive" scan, meaning the Nth element
505  * of the output range is the sum of the first N input elements,
506  * so the Nth input element is included.
507  */
508  template<typename _InputIterator, typename _OutputIterator,
509  typename _BinaryOperation, typename _Tp>
510  _OutputIterator
511  inclusive_scan(_InputIterator __first, _InputIterator __last,
512  _OutputIterator __result, _BinaryOperation __binary_op,
513  _Tp __init)
514  {
515  for (; __first != __last; ++__first)
516  *__result++ = __init = __binary_op(__init, *__first);
517  return __result;
518  }
519 
520  /** @brief Output the cumulative sum of one range to a second range
521  *
522  * @param __first Start of input range.
523  * @param __last End of input range.
524  * @param __result Start of output range.
525  * @param __binary_op Function to perform summation.
526  * @return The end of the output range.
527  *
528  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
529  * to the output range. Each element of the output range contains the
530  * running total of all earlier elements, using `binary_op` for summation.
531  *
532  * This function generates an "inclusive" scan, meaning the Nth element
533  * of the output range is the sum of the first N input elements,
534  * so the Nth input element is included.
535  */
536  template<typename _InputIterator, typename _OutputIterator,
537  typename _BinaryOperation>
538  _OutputIterator
539  inclusive_scan(_InputIterator __first, _InputIterator __last,
540  _OutputIterator __result, _BinaryOperation __binary_op)
541  {
542  if (__first != __last)
543  {
544  auto __init = *__first;
545  *__result++ = __init;
546  ++__first;
547  if (__first != __last)
548  __result = std::inclusive_scan(__first, __last, __result,
549  __binary_op, std::move(__init));
550  }
551  return __result;
552  }
553 
554  /** @brief Output the cumulative sum of one range to a second range
555  *
556  * @param __first Start of input range.
557  * @param __last End of input range.
558  * @param __result Start of output range.
559  * @return The end of the output range.
560  *
561  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
562  * to the output range. Each element of the output range contains the
563  * running total of all earlier elements, using `std::plus<>` for summation.
564  *
565  * This function generates an "inclusive" scan, meaning the Nth element
566  * of the output range is the sum of the first N input elements,
567  * so the Nth input element is included.
568  */
569  template<typename _InputIterator, typename _OutputIterator>
570  inline _OutputIterator
571  inclusive_scan(_InputIterator __first, _InputIterator __last,
572  _OutputIterator __result)
573  { return std::inclusive_scan(__first, __last, __result, plus<>()); }
574 
575  /** @brief Output the cumulative sum of one range to a second range
576  *
577  * @param __first Start of input range.
578  * @param __last End of input range.
579  * @param __result Start of output range.
580  * @param __init Initial value.
581  * @param __binary_op Function to perform summation.
582  * @param __unary_op Function to transform elements of the input 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 (and the initial value),
588  * using `__unary_op` to transform the input elements
589  * and using `__binary_op` for summation.
590  *
591  * This function generates an "exclusive" scan, meaning the Nth element
592  * of the output range is the sum of the first N-1 input elements,
593  * so the Nth input element is not included.
594  */
595  template<typename _InputIterator, typename _OutputIterator, typename _Tp,
596  typename _BinaryOperation, typename _UnaryOperation>
597  _OutputIterator
598  transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
599  _OutputIterator __result, _Tp __init,
600  _BinaryOperation __binary_op,
601  _UnaryOperation __unary_op)
602  {
603  while (__first != __last)
604  {
605  auto __v = __init;
606  __init = __binary_op(__init, __unary_op(*__first));
607  ++__first;
608  *__result++ = std::move(__v);
609  }
610  return __result;
611  }
612 
613  /** @brief Output the cumulative sum of one range to a second range
614  *
615  * @param __first Start of input range.
616  * @param __last End of input range.
617  * @param __result Start of output range.
618  * @param __binary_op Function to perform summation.
619  * @param __unary_op Function to transform elements of the input range.
620  * @param __init Initial value.
621  * @return The end of the output range.
622  *
623  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
624  * to the output range. Each element of the output range contains the
625  * running total of all earlier elements (and the initial value),
626  * using `__unary_op` to transform the input elements
627  * and using `__binary_op` for summation.
628  *
629  * This function generates an "inclusive" scan, meaning the Nth element
630  * of the output range is the sum of the first N input elements,
631  * so the Nth input element is included.
632  */
633  template<typename _InputIterator, typename _OutputIterator,
634  typename _BinaryOperation, typename _UnaryOperation, typename _Tp>
635  _OutputIterator
636  transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
637  _OutputIterator __result,
638  _BinaryOperation __binary_op,
639  _UnaryOperation __unary_op,
640  _Tp __init)
641  {
642  for (; __first != __last; ++__first)
643  *__result++ = __init = __binary_op(__init, __unary_op(*__first));
644  return __result;
645  }
646 
647  /** @brief Output the cumulative sum of one range to a second range
648  *
649  * @param __first Start of input range.
650  * @param __last End of input range.
651  * @param __result Start of output range.
652  * @param __binary_op Function to perform summation.
653  * @param __unary_op Function to transform elements of the input range.
654  * @return The end of the output range.
655  *
656  * Write the cumulative sum (aka prefix sum, aka scan) of the input range
657  * to the output range. Each element of the output range contains the
658  * running total of all earlier elements,
659  * using `__unary_op` to transform the input elements
660  * and using `__binary_op` for summation.
661  *
662  * This function generates an "inclusive" scan, meaning the Nth element
663  * of the output range is the sum of the first N input elements,
664  * so the Nth input element is included.
665  */
666  template<typename _InputIterator, typename _OutputIterator,
667  typename _BinaryOperation, typename _UnaryOperation>
668  _OutputIterator
669  transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
670  _OutputIterator __result,
671  _BinaryOperation __binary_op,
672  _UnaryOperation __unary_op)
673  {
674  if (__first != __last)
675  {
676  auto __init = __unary_op(*__first);
677  *__result++ = __init;
678  ++__first;
679  if (__first != __last)
680  __result = std::transform_inclusive_scan(__first, __last, __result,
681  __binary_op, __unary_op,
682  std::move(__init));
683  }
684  return __result;
685  }
686 
687  /// @} group numeric_ops
688 
689 _GLIBCXX_END_NAMESPACE_VERSION
690 } // namespace std
691 
692 // Parallel STL algorithms
693 # if __PSTL_EXECUTION_POLICIES_DEFINED
694 // If <execution> has already been included, pull in implementations
695 # include <pstl/glue_numeric_impl.h>
696 # else
697 // Otherwise just pull in forward declarations
698 # include <pstl/glue_numeric_defs.h>
699 # define __PSTL_NUMERIC_FORWARD_DECLARED 1
700 # endif
701 
702 // Feature test macro for parallel algorithms
703 # define __cpp_lib_parallel_algorithm 201603L
704 #endif // C++17
705 
706 #endif /* _GLIBCXX_NUMERIC */