std::partial_sum() algorithm

od C++20

// (1)
template< class InputIt, class OutputIt >
constexpr OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first );

// (2)
template< class InputIt, class OutputIt, class BinaryOperation >
constexpr OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );

do C++20

// (1)
template< class InputIt, class OutputIt >
OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first );

// (2)
template< class InputIt, class OutputIt, class BinaryOperation >
OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );

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 (od C++11).

• (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;
// ...

Undefined Behaviour

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 fold.
init	Initial value of the fold.
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 it. The type Type2 must be such that an object of type InputIt can be dereferenced and then implicitly converted to it. The type Ret must be such that an object of type InputIt can be dereferenced and assigned a value of it's type.

Type requirements

InputIt	LegacyInputIterator
OutputIt	LegacyOutputIterator

• InputIt's value type must be constructible from *first.
• acc 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.

Exceptions

(none)

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 calculating the differences 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 cache values of the iterated elements:

• Its type is the value type of InputIt
• The value written to d_first (which is the return value of operator- or op) is assigned to it
• Its value is passed to 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>{});

Examples

Main.cpp

#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