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 (1) (constexpr since
                        C++20)
       reduce( InputIt first, InputIt last );
   template< class ExecutionPolicy, class ForwardIt >
   typename std::iterator_traits<ForwardIt>::value_type (2) (since C++17)
       reduce( ExecutionPolicy&& policy,
               ForwardIt first, ForwardIt last );
   template< class InputIt, class T > (since C++17)
   T reduce( InputIt first, InputIt last, T init ); (3) (constexpr since
                        C++20)
   template< class ExecutionPolicy, class ForwardIt, class T >
   T reduce( ExecutionPolicy&& policy, (4) (since C++17)
             ForwardIt first, ForwardIt last, T init );
   template< class InputIt, class T, class BinaryOp > (since C++17)
   T reduce( InputIt first, InputIt last, T init, BinaryOp op ); (5) (constexpr since
                        C++20)
   template< class ExecutionPolicy,
             class ForwardIt, class T, class BinaryOp >
   T reduce( ExecutionPolicy&& policy, (6) (since C++17)
             ForwardIt first, ForwardIt last, T init, BinaryOp op
   );
   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
                        C++20)
   std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. (since
                        C++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.
                 binary FunctionObject that will be applied in unspecified order to the
   op - 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:
    1. Takes any two elements elem1 and elem2 from the group.
    2. Calculates binary_op(elem1, elem2) and puts the result back to the group.
    3. 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) \(\scriptsize O(N)\)O(N) applications of std::plus<>().
   5,6) \(\scriptsize O(N)\)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=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

See also
   accumulate sums up or folds 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)
   ranges::fold_left left-folds a range of elements
   (C++23) (niebloid)