std::reduce(3)

NAME
std::reduce - std::reduce

Synopsis
   Defined in header <numeric>
   template< class InputIt > (since
                        C++17)
   typename std::iterator_traits<InputIt>::value_type (until
                        C++20)
   reduce( InputIt first, InputIt last );
   template< class InputIt >
   constexpr typename (since
   std::iterator_traits<InputIt>::value_type C++20)
   reduce( InputIt first, InputIt last );
   template< class ExecutionPolicy, class ForwardIt >
   typename std::iterator_traits<ForwardIt>::value_type (2) (since
   reduce( ExecutionPolicy&& policy, C++17)
   ForwardIt first, ForwardIt last );
                        (since
   template< class InputIt, class T > C++17)
   T reduce( InputIt first, InputIt last, T init ); (until
                        C++20)
   template< class InputIt, class T > (1) (since
   constexpr T reduce( InputIt first, InputIt last, T C++20)
   init );
   template< class ExecutionPolicy, class ForwardIt,
   class T >
                        (4) (since
   T reduce( ExecutionPolicy&& policy, C++17)
   ForwardIt first, ForwardIt last, T init );
   template< class InputIt, class T, class BinaryOp > (3) (since
   T reduce( InputIt first, InputIt last, T init, C++17)
   BinaryOp binary_op ); (until
                        C++20)
   template< class InputIt, class T, class BinaryOp > (since
   constexpr T reduce( InputIt first, InputIt last, T C++20)
   init, BinaryOp binary_op ); (5)
   template< class ExecutionPolicy, class ForwardIt,
   class T, class BinaryOp >
                        (since
   T reduce( ExecutionPolicy&& policy, (6) C++17)
   ForwardIt first, ForwardIt last, T init, BinaryOp
   binary_op );
   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 FunctionObject that will be applied in unspecified order
   binary_op - 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)
                    applies a function to a range of elements, storing results in a
   transform destination range
                    (function template)
   transform_reduce applies an invocable, then reduces out of order
   (C++17) (function template)