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Showing content from https://en.cppreference.com/w/cpp/iterator/../algorithm/partial_sum.html below:

std::partial_sum - cppreference.com

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

Otherwise, performs the following operations in order:

1. Creates an accumulator acc, whose type is the value type of InputIt, and initializes it with *first.
2. Assigns acc to *d_first.
3. 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.

Assigns

to

, where

is the next

iterator of

.

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].

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

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. ​

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

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

1) Exactly \(\scriptsize N-1\)N-1 applications of operator+.

2) Exactly \(\scriptsize N-1\)N-1 applications of the binary function op.

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<>());
}

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;
}

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>{});

#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

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

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