std::reduce

 

C++

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Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Technical Specifications

 

Algorithm library

Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms: std::ranges::copy, std::ranges::sort, ...
Execution policies (C++17)
is_execution_policy (C++17)	execution::seqexecution::parexecution::par_unseqexecution::unseq (C++17)(C++17)(C++17)(C++20)	execution::sequenced_policyexecution::parallel_policyexecution::parallel_unsequenced_policyexecution::parallel_unsequenced (C++17)(C++17)(C++17)(C++20)
Non-modifying sequence operations
all_ofany_ofnone_of (C++11)(C++11)(C++11) for_each for_each_n (C++17)	countcount_if mismatch equal adjacent_find	findfind_iffind_if_not (C++11) find_end find_first_of	search search_n lexicographical_compare lexicographical_compare_three_way (C++20)
Modifying sequence operations
copycopy_if (C++11) copy_n (C++11) copy_backward move (C++11) move_backward (C++11) shift_leftshift_right (C++20)(C++20) transform	fill fill_n generate generate_n swap iter_swap swap_ranges sample (C++17)	removeremove_if replacereplace_if reverse rotate unique random_shuffle (until C++17)	remove_copyremove_copy_if replace_copyreplace_copy_if reverse_copy rotate_copy unique_copy shuffle (C++11)
Operations on uninitialized storage
uninitialized_copy uninitialized_move (C++17) uninitialized_fill destroy (C++17)	uninitialized_copy_n (C++11) uninitialized_move_n (C++17) uninitialized_fill_n destroy_n (C++17)	uninitialized_default_construct (C++17) uninitialized_value_construct (C++17) destroy_at (C++17)	uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17) construct_at (C++20)
Partitioning operations
is_partitioned (C++11) partition_point (C++11)	partition partition_copy (C++11)	stable_partition
Sorting operations
is_sorted (C++11) is_sorted_until (C++11)	sort stable_sort	partial_sort partial_sort_copy	nth_element
Binary search operations
lower_bound	upper_bound	binary_search	equal_range
Set operations (on sorted ranges)
merge inplace_merge	set_difference set_intersection	set_symmetric_difference set_union	includes
Heap operations
is_heap (C++11) is_heap_until (C++11)	make_heap sort_heap	push_heap pop_heap
Minimum/maximum operations
max max_element	min min_element	minmax (C++11) minmax_element (C++11)	clamp (C++17)
Permutations
is_permutation (C++11)	next_permutation	prev_permutation
Numeric operations
iota (C++11) inner_product adjacent_difference	accumulate reduce (C++17) transform_reduce (C++17)	partial_sum inclusive_scan (C++17) exclusive_scan (C++17)	transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
C library
qsort	bsearch

 

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>> (until C++20) std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> (since C++20) 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 <chrono>
#include <execution>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <utility>
#include <vector>
 
int main()
{
    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::fixed << std::setprecision(1) << name << " result "
                  << result << " took " << 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(std::execution::seq, v.cbegin(), v.cend())}; } );
        eval([&v]{ return std::pair{"std::reduce (par, double)",
            std::reduce(std::execution::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(), 0)}; } );
        eval([&v]{ return std::pair{"std::reduce (seq, long)",
            std::reduce(std::execution::seq, v.cbegin(), v.cend())}; } );
        eval([&v]{ return std::pair{"std::reduce (par, long)",
            std::reduce(std::execution::par, v.cbegin(), v.cend())}; } );
    }
}

Possible output:

std::accumulate (double) result 10000000.7 took 163.6 ms
std::reduce (seq, double) result 10000000.7 took 162.9 ms
std::reduce (par, double) result 10000000.7 took 97.5 ms
std::accumulate (long) result 100000007 took 62.3 ms
std::reduce (seq, long) result 100000007 took 64.3 ms
std::reduce (par, long) result 100000007 took 49.0 ms

See also

accumulate	sums up 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)