# std::reduce

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< cpp‎ | algorithm

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 LegacyInputIterator.
- `ForwardIt` must meet the requirements of LegacyForwardIterator.
- `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 ≤ 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 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

### See also

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)

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