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std::reduce

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:

#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

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)