std::reduce

From cppreference.com

Defined in header `<numeric>`
template<class InputIt> typename std::iterator_traits<InputIt>::value_type reduce( InputIt first, InputIt last);	(1)	(since C++17)
template<class ExecutionPolicy, class ForwardIt> typename std::iterator_traits<ForwardIt>::value_type reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last);	(2)	(since C++17)
template<class InputIt, class T> T reduce(InputIt first, InputIt last, T init);	(3)	(since C++17)
template<class ExecutionPolicy, class ForwardIt, class T> T reduce(ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init);	(4)	(since C++17)
template<class InputIt, class T, class BinaryOp> T reduce(InputIt first, InputIt last, T init, BinaryOp binary_op);	(5)	(since C++17)
template<class ExecutionPolicy, class ForwardIt, class T, class BinaryOp> T reduce(ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init, BinaryOp binary_op);	(6)	(since C++17)

1) same as reduce(first, last, typename std::iterator_traits<InputIt>::value_type{})

3) same as reduce(first, last, init, std::plus<>())

5) Reduces the range

[first; last)

, possibly permuted and aggregated in unspecified manner, along with the initial value init over binary_op.

2,4,6) Same as (1,3,5), but executed according to policy. This overload only participates in overload resolution if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true

The behavior is non-deterministic if binary_op is not associative or not commutative.

The behavior is undefined if binary_op modifies any element or invalidates any iterator in $[first; last]$ , including the end iterator.

Parameters

first, last	-	the range of elements to apply the algorithm to
init	-	the initial value of the generalized sum
policy	-	the execution policy to use. See execution policy for details.
binary_op	-	binary `FunctionObject` that will be applied in unspecified order to the result of dereferencing the input iterators, the results of other `binary_op` and `init`.
Type requirements
- `InputIt` must meet the requirements of `InputIterator`.
- `ForwardIt` must meet the requirements of `ForwardIterator`.
- `T` must meet the requirements of `MoveConstructible`. and `binary_op(init, first)`, `binary_op(first, init)`, `binary_op(init, init)`, and `binary_op(first, first)` must be convertible to `T`.

Return value

Generalized sum of init and *first, *(first+1), ... *(last-1) over binary_op,

where generalized sum $GSUM(op, a 1, ..., a N)$ is defined as follows:

if $N=1$ , $a 1$
if $N > 1$ , $op(GSUM(op, b 1, ..., b K), GSUM(op, b M, ..., b N))$ where

$b 1, ..., b N$ may be any permutation of $a1, ..., aN$ and
$1 < K+1 = M \leq N$

in other words, reduce behaves like std::accumulate except the elements of the range may be grouped and rearranged in arbitrary order

Complexity

$O(last - first)$ applications of binary_op.

Exceptions

The overloads with a template parameter named ExecutionPolicy report errors as follows:

If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the three standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined.
If the algorithm fails to allocate memory, std::bad_alloc is thrown.

Notes

If the range is empty, init is returned, unmodified

Example

side-by-side comparison between reduce and std::accumulate:

Run this code

#include <iostream>
#include <chrono>
#include <vector>
#include <numeric>
#include <execution>
 
int main()
{
    std::vector<double> v(10'000'007, 0.5);
 
    {
        auto t1 = std::chrono::high_resolution_clock::now();
        double result = std::accumulate(v.begin(), v.end(), 0.0);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::chrono::duration<double, std::milli> ms = t2 - t1;
        std::cout << std::fixed << "std::accumulate result " << result
                  << " took " << ms.count() << " ms\n";
    }
 
    {
        auto t1 = std::chrono::high_resolution_clock::now();
        double result = std::reduce(std::execution::par, v.begin(), v.end());
        auto t2 = std::chrono::high_resolution_clock::now();
        std::chrono::duration<double, std::milli> ms = t2 - t1;
        std::cout << "std::reduce result "
                  << result << " took " << ms.count() << " ms\n";
    }
}

Possible output:

std::accumulate result 5000003.50000 took 12.7365 ms
std::reduce result 5000003.50000 took 5.06423 ms

Language
Standard library headers
Concepts
Utilities library
Strings library
Containers library
Algorithms library
Iterators library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications

accumulate	sums up a range of elements (function template)
transform	applies a function to a range of elements (function template)
transform_reduce (C++17)	applies a functor, then reduces out of order (function template)