# std::reduce

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< cpp‎ | algorithm

Defined in header `<numeric>` |  |
| (1) |
template< class InputIt > typename std::iterator_traits<InputIt>::value_type reduce( InputIt first, InputIt last ); |  | (since C++17) (until C++20)
template< class InputIt > constexpr typename std::iterator_traits<InputIt>::value_type reduce( InputIt first, InputIt last ); |  | (since C++20)
template< class ExecutionPolicy, class ForwardIt > typename std::iterator_traits<ForwardIt>::value_type reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last ); | (2) | (since C++17)
| (3) |
template< class InputIt, class T > T reduce( InputIt first, InputIt last, T init ); |  | (since C++17) (until C++20)
template< class InputIt, class T > constexpr T reduce( InputIt first, InputIt last, T init ); |  | (since C++20)
template< class ExecutionPolicy, class ForwardIt, class T > T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init ); | (4) | (since C++17)
| (5) |
template< class InputIt, class T, class BinaryOp > T reduce( InputIt first, InputIt last, T init, BinaryOp binary_op ); |  | (since C++17) (until C++20)
template< class InputIt, class T, class BinaryOp > constexpr T reduce( InputIt first, InputIt last, T init, BinaryOp binary_op ); |  | (since C++20)
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. These overloads do not participate in overload resolution unless

std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true. | (until C++20)
std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. | (since C++20)

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 `std::reduce` and std::accumulate:

Run this code

    #if PARALLEL
    #include <execution>
    #define SEQ std::execution::seq,
    #define PAR std::execution::par,
    #else
    #define SEQ
    #define PAR
    #endif

    #include <chrono>
    #include <iomanip>
    #include <iostream>
    #include <numeric>
    #include <utility>
    #include <vector>

    int main()
    {
        std::cout.imbue(std::locale("en_US.UTF-8"));
        std::cout << std::fixed << std::setprecision(1);
        auto eval = [](auto fun)
        {
            const auto t1 = std::chrono::high_resolution_clock::now();
            const auto [name, result] = fun();
            const auto t2 = std::chrono::high_resolution_clock::now();
            const std::chrono::duration<double, std::milli> ms = t2 - t1;
            std::cout << std::setw(28) << std::left << name << "sum: "
                      << result << "\t time: " << ms.count() << " ms\n";
        };
        {
            const std::vector<double> v(100'000'007, 0.1);

            eval([&v]{ return std::pair{"std::accumulate (double)",
                std::accumulate(v.cbegin(), v.cend(), 0.0)}; } );
            eval([&v]{ return std::pair{"std::reduce (seq, double)",
                std::reduce(SEQ v.cbegin(), v.cend())}; } );
            eval([&v]{ return std::pair{"std::reduce (par, double)",
                std::reduce(PAR v.cbegin(), v.cend())}; } );
        }
        {
            const std::vector<long> v(100'000'007, 1);

            eval([&v]{ return std::pair{"std::accumulate (long)",
                std::accumulate(v.cbegin(), v.cend(), 0l)}; } );
            eval([&v]{ return std::pair{"std::reduce (seq, long)",
                std::reduce(SEQ v.cbegin(), v.cend())}; } );
            eval([&v]{ return std::pair{"std::reduce (par, long)",
                std::reduce(PAR v.cbegin(), v.cend())}; } );
        }
    }

Possible output:

    // POSIX: g++ -std=c++23 ./example.cpp -ltbb -O3; ./a.out
    std::accumulate (double)    sum: 10,000,000.7    time: 356.9 ms
    std::reduce (seq, double)   sum: 10,000,000.7    time: 140.1 ms
    std::reduce (par, double)   sum: 10,000,000.7    time: 140.1 ms
    std::accumulate (long)      sum: 100,000,007     time: 46.0 ms
    std::reduce (seq, long)     sum: 100,000,007     time: 67.3 ms
    std::reduce (par, long)     sum: 100,000,007     time: 63.3 ms

    // POSIX: g++ -std=c++23 ./example.cpp -ltbb -O3 -DPARALLEL; ./a.out
    std::accumulate (double)    sum: 10,000,000.7    time: 353.4 ms
    std::reduce (seq, double)   sum: 10,000,000.7    time: 140.7 ms
    std::reduce (par, double)   sum: 10,000,000.7    time: 24.7 ms
    std::accumulate (long)      sum: 100,000,007     time: 42.4 ms
    std::reduce (seq, long)     sum: 100,000,007     time: 52.0 ms
    std::reduce (par, long)     sum: 100,000,007     time: 23.1 ms

### See also

accumulate | sums up or folds a range of elements (function template)
transform | applies a function to a range of elements, storing results in a destination range (function template)
transform_reduce (C++17) | applies an invocable, then reduces out of order (function template)
ranges::fold_left (C++23) | left-folds a range of elements (niebloid)

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