std::reduce

Defined in header `<numeric>`
template< class InputIt > typename std::iterator_traits<InputIt>::value_type reduce( InputIt first, InputIt last );	(1)	(since 哋它亢++17) (constexpr since 哋它亢++20)
template< class ExecutionPolicy, class ForwardIt > typename std::iterator_traits<ForwardIt>::value_type reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last );	(2)	(since 哋它亢++17)
template< class InputIt, class T > T reduce( InputIt first, InputIt last, T init );	(3)	(since 哋它亢++17) (constexpr since 哋它亢++20)
template< class ExecutionPolicy, class ForwardIt, class T > T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init );	(4)	(since 哋它亢++17)
template< class InputIt, class T, class BinaryOp > T reduce( InputIt first, InputIt last, T init, BinaryOp op );	(5)	(since 哋它亢++17) (constexpr since 哋它亢++20)
template< class ExecutionPolicy, class ForwardIt, class T, class BinaryOp > T reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init, BinaryOp op );	(6)	(since 哋它亢++17)

1) Equivalent to reduce(first, last, typename std::iterator_traits<InputIt>::value_type{}).

3) Equivalent to 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 op.

2,4,6) Same as (1,3,5), but executed according to policy.

These overloads participate in overload resolution only if

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

Given binary_op as the actual binary operation:

The result is non-deterministic if the binary_op is not associative or not commutative (such as floating-point addition).

If any of the following values is not convertible to T, the program is ill-formed:

binary_op(init, *first)
binary_op(*first, init)
binary_op(init, init)
binary_op(*first, *first)

If any of the following conditions is satisfied, the behavior is undefined:

T is not MoveConstructible.
binary_op modifies any element of [first, last).
binary_op invalidates any iterator or subrange of [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 to use. See execution policy for details.
op	-	binary FunctionObject that will be applied in unspecified order to the result of dereferencing the input iterators, the results of other op and init.
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator.
- `ForwardIt` must meet the requirements of LegacyForwardIterator.

Return value

1-4) The generalized sum of init and the elements of [first, last) over std::plus<>().

5,6) The generalized sum of init and the elements of [first, last) over op.

The generalized sum of a group of elements over an binary operation binary_op is defined as follows:

If the group only has one element, the sum is the value of the element.
Otherwise, performs the following operations in order:

Takes any two elements elem1 and elem2 from the group.
Calculates binary_op(elem1, elem2) and puts the result back to the group.
Repeats steps 1 and 2 until there is only one element in the group.

Complexity

Given $\scriptsize N$ $N$ as std::distance(first, last):

1-4)

O(N)

applications of std::plus<>().

5,6)

O(N)

applications of 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

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

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=哋它亢++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=哋它亢++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

Compiler support
Freestanding and hosted
Language
Standard library
Standard library headers
Named requirements
Feature test macros (哋它亢++20)
Language support library
Concepts library (哋它亢++20)
Metaprogramming library (哋它亢++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (哋它亢++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (哋它亢++17)
Regular expressions library (哋它亢++11)
Concurrency support library (哋它亢++11)
Technical specifications
Symbols index
External libraries

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 (哋它亢++17)	applies an invocable, then reduces out of order (function template)
ranges::fold_left (哋它亢++23)	left-folds a range of elements (niebloid)