std::inclusive_scan

Creates a sequence which is formed by the elements of [first, iter] in order, where iter is the next ith iterator of first.
Computes the generalized noncommutative sum of the sequence over op.
Assigns the result to *dest, where dest is the next ith iterator of d_first.

5) Same as (3), but each sequence created is formed by init followed by the elements of [first, iter] in order.

2,4,6) Same as (1,3,5), but executed according to policy.

These overloads participate in overload resolution only if all following conditions are satisfied:

std::is_execution_policy_v <std::decay_t <ExecutionPolicy>> is true.

(until C++20)

std::is_execution_policy_v <std::remove_cvref_t <ExecutionPolicy>> is true.

(since C++20)

The generalized, noncommutative sum of a sequence of elements over a binary operation binary_op is defined as follows:

If the sequence only has one element, the sum is the value of the element.
Otherwise, performs the following operations in order:

Selects any two adjacent elements elem1 and elem2 from the sequence.
Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence with the result.
Repeats steps 1 and 2 until there is only one element in the sequence.

Given binary_op as the actual binary operation:

The result is non-deterministic if the binary_op is not associative (such as floating-point addition).

For overloads (1-4), if binary_op(*first, *first) is not convertible to the value type of decltype(first), the program is ill-formed.

For overloads (5,6), if any of the following values is not convertible to T, the program is ill-formed:

binary_op(init, *first)
binary_op(init, init)
binary_op(*first, *first)

If any of the following conditions is satisfied, the behavior is undefined:

For overloads (1-4), the value type of decltype(first) is not MoveConstructible.
For overloads (5,6), T is not MoveConstructible.
binary_op modifies any element of [first, last).
binary_op invalidates any iterator or subrange of [first, last].

If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined.
If the algorithm fails to allocate memory, std::bad_alloc is thrown.

[edit] Example

Run this code

#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <vector>
 
int main()
{
 std::vector data{3, 1, 4, 1, 5, 9, 2, 6};
 
 std::cout << "Exclusive sum: ";
 std::exclusive_scan (data.begin(), data.end(),
 std::ostream_iterator <int>(std::cout, " "),
 0);
 
 std::cout << "\nInclusive sum: ";
 std::inclusive_scan(data.begin(), data.end(),
 std::ostream_iterator <int>(std::cout, " "));
 
 std::cout << "\n\nExclusive product: ";
 std::exclusive_scan (data.begin(), data.end(),
 std::ostream_iterator <int>(std::cout, " "),
 1, std::multiplies <>{});
 
 std::cout << "\nInclusive product: ";
 std::inclusive_scan(data.begin(), data.end(),
 std::ostream_iterator <int>(std::cout, " "),
 std::multiplies <>{});
}

Output:

Exclusive sum: 0 3 4 8 9 14 23 25
Inclusive sum: 3 4 8 9 14 23 25 31
 
Exclusive product: 1 3 3 12 12 60 540 1080
Inclusive product: 3 3 12 12 60 540 1080 6480