std::partial_sum

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

1) If [first, last) is empty, does nothing.

Otherwise, performs the following operations in order:

Creates an accumulator acc, whose type is the value type of InputIt, and initializes it with *first.
Assigns acc to *d_first.
For each integer i in [1, std::distance(first, last)), performs the following operations in order:

a) Computes acc + *iter(until C++20)std::move(acc) + *iter(since C++20), where iter is the next ith iterator of first.

b) Assigns the result to acc.

c) Assigns acc^[1] to *dest, where dest is the next ith iterator of d_first.

2) Same as (1), but computes op(acc, *iter)(until C++20)op(std::move(acc), *iter)(since C++20) instead.

Given binary_op as the actual binary operation:

If any of the following conditions is satisfied, the program is ill-formed:

The value type of InputIt is not constructible from *first.
acc is not writable to d_first.
The result of binary_op(acc, *iter)(until C++20)binary_op(std::move(acc), *iter)(since C++20) is not implicitly convertible to the value type of InputIt.

Given d_last as the iterator to be returned, if any of the following conditions is satisfied, the behavior is undefined:

binary_op modifies any element of [first, last) or [d_first, d_last).
binary_op invalidates any iterator or subrange in [first, last] or [d_first, d_last].

↑ The actual value to be assigned is the result of the assignment in the previous step. We assume the assignment result is acc here.

Parameters

first, last	-	the pair of iterators defining 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.
- `OutputIt` must meet the requirements of LegacyOutputIterator.

Return value

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

Complexity

Given $\scriptsize N$ $N$ as std::distance(first, last):

1) Exactly

N-1

applications of operator+.

2) Exactly

N-1

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++20
        *++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 BinaryOp>
constexpr // since C++20
OutputIt partial_sum(InputIt first, InputIt last, 
                     OutputIt d_first, BinaryOp 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++20
        *++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

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External libraries

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

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