29 Numerics library [numerics]

29.8 Generalized numeric operations [numeric.ops]

29.8.8 Inclusive scan [inclusive.scan]

template<class InputIterator, class OutputIterator>
  OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                OutputIterator result);

Effects: Equivalent to:

return inclusive_scan(first, last, result, plus<>());

template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
  ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec,
                                ForwardIterator1 first, ForwardIterator1 last,
                                ForwardIterator2 result);

Effects: Equivalent to:

return inclusive_scan(std::forward<ExecutionPolicy>(exec), first, last, result, plus<>());

template<class InputIterator, class OutputIterator, class BinaryOperation>
  OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                OutputIterator result,
                                BinaryOperation binary_op);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
         class BinaryOperation>
  ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec,
                                  ForwardIterator1 first, ForwardIterator1 last,
                                  ForwardIterator2 result,
                                  BinaryOperation binary_op);

template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
  OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                OutputIterator result,
                                BinaryOperation binary_op, T init);
template<class ExecutionPolicy,
         class ForwardIterator1, class ForwardIterator2, class BinaryOperation, class T>
  ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec,
                                  ForwardIterator1 first, ForwardIterator1 last,
                                  ForwardIterator2 result,
                                  BinaryOperation binary_op, T init);

Requires:

(3.1)
If init is provided, T shall be MoveConstructible (Table 23); otherwise, ForwardIterator1's value type shall be MoveConstructible.
(3.2)
If init is provided, all of binary_op(init, init), binary_op(init, *first), and binary_op(*first, *first) shall be convertible to T; otherwise, binary_op(*first, *first) shall be convertible to ForwardIterator1's value type.
(3.3)
binary_op shall neither invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].

Effects: For each integer K in [0, last - first) assigns through result + K the value of

(4.1)
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init, *(first + 0), *(first + 1), ..., *(first + K))
if init is provided, or
(4.2)
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, *(first + 0), *(first + 1), ..., *(first + K))
otherwise.

Returns: The end of the resulting range beginning at result.

Complexity: applications of binary_op.

Remarks: result may be equal to first.

[ Note

The difference between exclusive_scan and inclusive_scan is that inclusive_scan includes the ith input element in the ith sum.

If binary_op is not mathematically associative, the behavior of inclusive_scan may be nondeterministic.

— end note

]