29 Numerics library [numerics]

29.8 Generalized numeric operations [numeric.ops]

29.8.10 Transform inclusive scan [transform.inclusive.scan]

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

Requires:

(1.1)
If init is provided, T shall be MoveConstructible (Table 23); otherwise, ForwardIterator1's value type shall be MoveConstructible.
(1.2)
If init is provided, all of
- (1.2.1)
  binary_op(init, init),
- (1.2.2)
  binary_op(init, unary_op(*first)), and
- (1.2.3)
  binary_op(unary_op(*first), unary_op(*first))
shall be convertible to T; otherwise, binary_op(unary_op(*first), unary_op(*first)) shall be convertible to ForwardIterator1's value type.
(1.3)
Neither unary_op nor binary_op shall 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

(2.1)
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))
if init is provided, or
(2.2)
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))
otherwise.

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

Complexity: $O (last - first)$ applications each of unary_op and binary_op.

Remarks: result may be equal to first.

[ Note: The difference between transform_exclusive_scan and transform_inclusive_scan is that transform_inclusive_scan includes the $i^{th}$ input element in the $i^{th}$ sum. If binary_op is not mathematically associative, the behavior of transform_inclusive_scan may be nondeterministic. transform_inclusive_scan does not apply unary_op to init. — end note ]