NAME¶

std::partial_sum - std::partial_sum

Synopsis¶

Defined in header <numeric>
template< class InputIt, class OutputIt >

OutputIt partial_sum( InputIt first, InputIt last, (1) (constexpr since C++20)

OutputIt d_first );
template< class InputIt, class OutputIt, class BinaryOp
>
(2) (constexpr since C++20)
OutputIt partial_sum( InputIt first, InputIt last,

OutputIt d_first, BinaryOp op );

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++11)
std::move(acc) + *iter
(since C++11), where iter is the next i
th iterator of first.
b) Assigns the result to acc.
c) Assigns acc^[1] to *dest, where dest is the next i
th iterator of d_first.
2) Same as (1), but computes
op(acc, *iter)
(until C++11)
op(std::move(acc), *iter)
(since C++11) 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++11)
binary_op(std::move(acc), *iter)
(since C++11) 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.

Parameters¶

first, last - the range of elements to sum
d_first - the beginning of the destination range; may be equal to first
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);

op - 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 \(\scriptsize N-1\)N-1 applications of operator+.
2) Exactly \(\scriptsize N-1\)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++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 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++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
the type requirements needed for the
LWG 539 C++98 result added
evaluations and assignments to be valid
were missing
LWG 2055 C++11 acc was not moved while being accumulated it is moved
(P0616R0)

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 similar to std::partial_sum, includes the i^th input element in
(C++17) the i^th sum
(function template)
exclusive_scan similar to std::partial_sum, excludes the i^th input element
(C++17) from the i^th sum
(function template)