# std::experimental::parallel::reduce

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< cpp‎ | experimental

Defined in header `<experimental/numeric>` |  |
template<class InputIt> typename std::iterator_traits<InputIt>::value_type reduce( InputIt first, InputIt last); | (1) | (parallelism TS)
template<class ExecutionPolicy, class InputIterator> typename std::iterator_traits<InputIt>::value_type reduce( ExecutionPolicy&& policy, InputIt first, InputIt last); | (2) | (parallelism TS)
template<class InputIt, class T> T reduce(InputIt first, InputIt last, T init); | (3) | (parallelism TS)
template<class ExecutionPolicy, class InputIt, class T> T reduce(ExecutionPolicy&& policy, InputIt first, InputIt last, T init); | (4) | (parallelism TS)
template<class InputIt, class T, class BinaryOp> T reduce(InputIt first, InputIt last, T init, BinaryOp binary_op); | (5) | (parallelism TS)
template<class ExecutionPolicy, class InputIt, class T, class BinaryOp> T reduce(ExecutionPolicy&& policy, InputIt first, InputIt last, T init, BinaryOp binary_op); | (6) | (parallelism TS)

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`

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).

### Parameters

first, last | - | the range of elements to apply the algorithm to
init | - | the initial value of the generalized sum
policy | - | the execution policy
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`.

### 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, the elements of the range may be grouped and rearranged in arbitrary order

### Complexity

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

### Exceptions

- If execution of a function invoked as part of the algorithm throws an exception,

  - if `policy` is `parallel_vector_execution_policy`, std::terminate is called
  - if `policy` is `sequential_execution_policy` or `parallel_execution_policy`, the algorithm exits with an `exception_list` containing all uncaught exceptions. If there was only one uncaught exception, the algorithm may rethrow it without wrapping in `exception_list`. It is unspecified how much work the algorithm will perform before returning after the first exception was encountered.
  - if `policy` is some other type, the behavior is implementation-defined

- If the algorithm fails to allocate memory (either for itself or to construct an `exception_list` when handling a user exception), std::bad_alloc is thrown.

### Notes

If the range is empty, `init` is returned, unmodified

- If `policy` is an instance of `sequential_execution_policy`, all operations are performed in the calling thread.
- If `policy` is an instance of `parallel_execution_policy`, operations may be performed in unspecified number of threads, indeterminately sequenced with each other
- If `policy` is an instance of `parallel_vector_execution_policy`, execution may be both parallelized and vectorized: function body boundaries are not respected and user code may be overlapped and combined in arbitrary manner (in particular, this implies that a user-provided Callable must not acquire a mutex to access a shared resource)

### Example

reduce is the out-of-order version of std::accumulate:

Run this code

    #include <iostream>
    #include <chrono>
    #include <vector>
    #include <numeric>
    #include <experimental/execution_policy>
    #include <experimental/numeric>

    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::experimental::parallel::reduce(
                                std::experimental::parallel::par,
                                v.begin(), v.end());
            auto t2 = std::chrono::high_resolution_clock::now();
            std::chrono::duration<double, std::milli> ms = t2 - t1;
            std::cout << "parallel::reduce result "
                      << result << " took " << ms.count() << " ms\n";
        }
    }

Possible output:

    std::accumulate result 5000003.50000 took 12.7365 ms
    parallel::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 (parallelism TS) | applies a functor, then reduces out of order (function template)

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