# std::partial_sum

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< cpp‎ | algorithm

Defined in header `<numeric>` |  |
| (1) |
template< class InputIt, class OutputIt > OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first ); |  | (until C++20)
template< class InputIt, class OutputIt > constexpr OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first ); |  | (since C++20)
| (2) |
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op ); |  | (until C++20)
template< class InputIt, class OutputIt, class BinaryOperation > constexpr OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op ); |  | (since C++20)

If `[`first`,` last`)` is not empty, computes the partial sums of the elements in its subranges and writes the sums to the range beginning at d_first, both applying `std::move` to their operands on the left hand side (since C++11).

Internally, a variable acc, whose type is the value type of `InputIt`, is used as accumulator for intermediate results.

1) Uses operator+ to sum up the elements. Equivalent to:

    std::iterator_traits<InputIt>::value_type acc = *first;
    *d_first = acc;

    acc = std::move(acc) + *(first + 1);
    *(d_first + 1) = acc;

    acc = std::move(acc) + *(first + 2);
    *(d_first + 2) = acc;

    acc = std::move(acc) + *(first + 3);
    *(d_first + 3) = acc;
    // ...

2) Uses the given binary function op. Equivalent to:

    std::iterator_traits<InputIt>::value_type acc = *first;
    *d_first = acc;

    acc = op(std::move(acc), *(first + 1));
    *(d_first + 1) = acc;

    acc = op(std::move(acc), *(first + 2));
    *(d_first + 2) = acc;

    acc = op(std::move(acc), *(first + 3));
    *(d_first + 3) = acc;
    // ...

If op invalidates any iterators (including the end iterators) or modifies any elements of the range involved, the behavior is undefined.

### Parameters

first, last | - | the range of elements to sum
d_first | - | the beginning of the destination range; may be equal to first
op | - | binary operation function object that will be applied. The signature of the function should be equivalent to the following: Ret fun(const Type1 &a, const Type2 &b); The signature does not need to have const &. The type Type1 must be such that an object of type std::iterator_traits<InputIt>::value_type can be implicitly converted to Type1. The type Type2 must be such that an object of type InputIt can be dereferenced and then implicitly converted to Type2. The type Ret must be such that an object of type InputIt can be dereferenced and assigned a value of type Ret. ​
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator. Its value type must be constructible from *first.
- `OutputIt` must meet the requirements of LegacyOutputIterator. acc (defined above) must be writable to d_first.

### Return value

Iterator to the element past the last element written, or d_first if `[`first`,` last`)` is empty.

### Complexity

Given `N` as std::distance(first, last) - 1:

1) exactly `N` applications of operator+
2) exactly `N` applications of the binary function op

### Possible implementation

partial_sum (1)
    template<class InputIt, class OutputIt>
    constexpr // since C++20
    OutputIt partial_sum(InputIt first, InputIt last, OutputIt d_first)
    {
        if (first == last)
            return d_first;

        typename std::iterator_traits<InputIt>::value_type sum = *first;
        *d_first = sum;

        while (++first != last)
        {
            sum = std::move(sum) + *first; // std::move since C++11
            *++d_first = sum;
        }

        return ++d_first;

        // or, since C++14:
        // return std::partial_sum(first, last, d_first, std::plus<>());
    }
partial_sum (2)
    template<class InputIt, class OutputIt, class BinaryOperation>
    constexpr // since C++20
    OutputIt partial_sum(InputIt first, InputIt last,
                         OutputIt d_first, BinaryOperation op)
    {
        if (first == last)
            return d_first;

        typename std::iterator_traits<InputIt>::value_type acc = *first;
        *d_first = acc;

        while (++first != last)
        {
            acc = op(std::move(acc), *first); // std::move since C++11
            *++d_first = acc;
        }

        return ++d_first;
    }

### Notes

acc was introduced because of the resolution of LWG issue 539. The reason of using acc rather than directly summing up the results (i.e. *(d_first + 2) = (*first + *(first + 1)) + *(first + 2);) is because the semantic of the latter is confusing if the following types mismatch:

- the value type of `InputIt`
- the writable type(s) of `OutputIt`
- the types of the parameters of operator+ or op
- the return type of operator+ or op

acc serves as the intermediate object to store and provide the values for each step of the computation:

- its type is the value type of `InputIt`
- it is written to d_first
- its value is passed to operator+ or op
- it stores the return value of operator+ or op

    enum not_int { x = 1, y = 2 };

    char i_array[4] = {100, 100, 100, 100};
    not_int e_array[4] = {x, x, y, y};
    int  o_array[4];

    // OK: uses operator+(char, char) and assigns char values to int array
    std::partial_sum(i_array, i_array + 4, o_array);

    // Error: cannot assign not_int values to int array
    std::partial_sum(e_array, e_array + 4, o_array);

    // OK: performs conversions when needed
    // 1. creates `acc` of type char (the value type)
    // 2. the char arguments are used for long multiplication (char -> long)
    // 3. the long product is assigned to `acc` (long -> char)
    // 4. `acc` is assigned to an element of `o_array` (char -> int)
    // 5. go back to step 2 to process the remaining elements in the input range
    std::partial_sum(i_array, i_array + 4, o_array, std::multiplies<long>{});

### Example

Run this code

    #include <functional>
    #include <iostream>
    #include <iterator>
    #include <numeric>
    #include <vector>

    int main()
    {
        std::vector<int> v(10, 2); // v = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

        std::cout << "The first " << v.size() << " even numbers are: ";
        // write the result to the cout stream
        std::partial_sum(v.cbegin(), v.cend(),
                         std::ostream_iterator<int>(std::cout, " "));
        std::cout << '\n';

        // write the result back to the vector v
        std::partial_sum(v.cbegin(), v.cend(),
                         v.begin(), std::multiplies<int>());

        std::cout << "The first " << v.size() << " powers of 2 are: ";
        for (int n : v)
            std::cout << n << ' ';
        std::cout << '\n';
    }

Output:

    The first 10 even numbers are: 2 4 6 8 10 12 14 16 18 20
    The first 10 powers of 2 are: 2 4 8 16 32 64 128 256 512 1024

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 242 | C++98 | op could not have side effects | it cannot modify the ranges involved
LWG 539 | C++98 | the type requirements needed for the result evaluations and assignments to be valid were missing | added
LWG 2055 (P0616R0) | C++11 | acc was not moved while being accumulated | it is moved

### See also

adjacent_difference | computes the differences between adjacent elements in a range (function template)
accumulate | sums up or folds a range of elements (function template)
inclusive_scan (C++17) | similar to std::partial_sum, includes the ith input element in the ith sum (function template)
exclusive_scan (C++17) | similar to std::partial_sum, excludes the ith input element from the ith sum (function template)

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