std::reduce() algorithm

since C++20

// (1)
template< class InputIt >
constexpr typename std::iterator_traits<InputIt>::value_type
    reduce( InputIt first, InputIt last );

// (2)
template< class InputIt, class T >
constexpr T reduce( InputIt first, InputIt last, T init );

// (3)
template< class InputIt, class T, class BinaryOp >
constexpr T reduce( InputIt first, InputIt last, T init, BinaryOp binary_op );

// (4)
template< class ExecutionPolicy, class ForwardIt >
typename std::iterator_traits<ForwardIt>::value_type
    reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last );

// (5)
template< class ExecutionPolicy, class ForwardIt, class T >
T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init );

// (6)
template< class ExecutionPolicy, class ForwardIt, class T, class BinaryOp >
T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init, BinaryOp binary_op );

since C++17

// (1)
template< class InputIt >
typename std::iterator_traits<InputIt>::value_type
    reduce( InputIt first, InputIt last );

// (2)
template< class InputIt, class T >
T reduce( InputIt first, InputIt last, T init );

// (3)
template< class InputIt, class T, class BinaryOp >
T reduce( InputIt first, InputIt last, T init, BinaryOp binary_op );

// (4)
template< class ExecutionPolicy, class ForwardIt >
typename std::iterator_traits<ForwardIt>::value_type
    reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last );

// (5)
template< class ExecutionPolicy, class ForwardIt, class T >
T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init );

// (6)
template< class ExecutionPolicy, class ForwardIt, class T, class BinaryOp >
T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init, BinaryOp binary_op );

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

• (2) Same as reduce(first, last, init, std::plus<>())

• (3) Reduces the range [first; last), possibly permuted and aggregated in unspecified manner, along with the initial value init over binary_op.

• (4 - 6) Same as (1 - 3), but executed according to policy.

  Overload Resolution

  These overloads participate in overload resolution only if 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.

Undefined Behaviour

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	LegacyInputIterator
ForwardIt	LegacyForwardIterator
T	MoveAssignable MoveConstructible

• The following expressions must be convertible to T:
  • binary_op(init, *first)
  • binary_op(*first, init)
  • binary_op(init, init)
  • binary_op(*first, *first)

Return value

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

Behaves like std::reduce except the elements of the range may be grouped and rearranged in arbitrary order.

Formallly, the generalized sum GSUM(op, a1, ..., aN) is defined as follows:

• If N = 1, a1
• If N > 1, op(GSUM(op, b 1, ..., b K), GSUM(op, b M, ..., b N)) where
  • b1, ..., bN may be any permutation of a1, ..., aN
  • and 1 < K + 1 = M ≤ N

important

If the range is empty, init is returned, unmodified

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.

Examples

Main.cpp

#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::reduce (double)",
            std::reduce(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::reduce (long)",
            std::reduce(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::reduce (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::reduce (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::reduce (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::reduce (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