std::transform_reduce(3)

NAME
std::transform_reduce - std::transform_reduce

Synopsis
   Defined in header <numeric>
   template< class InputIt1, class InputIt2, class T >
                        (since C++17)
   T transform_reduce( InputIt1 first1, InputIt1 last1, (1) (constexpr since C++20)
                       InputIt2 first2, T init );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2, class T >
   T transform_reduce( ExecutionPolicy&& policy, (2) (since C++17)
                       ForwardIt1 first1, ForwardIt1 last1,
                       ForwardIt2 first2, T init );
   template< class InputIt1, class InputIt2, class T,
             class BinaryOp1, class BinaryOp2 >
   T transform_reduce( InputIt1 first1, InputIt1 last1, (3) (since C++17)
                       InputIt2 first2, T init, (constexpr since C++20)
                       BinaryOp1 reduce, BinaryOp2
   transform );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2, class T,
             class BinaryOp1, class BinaryOp2 >
   T transform_reduce( ExecutionPolicy&& policy, (4) (since C++17)
                       ForwardIt1 first1, ForwardIt1 last1,
                       ForwardIt2 first2, T init,
                       BinaryOp1 reduce, BinaryOp2
   transform );
   template< class InputIt, class T,
             class BinaryOp, class UnaryOp > (since C++17)
   T transform_reduce( InputIt first, InputIt last, T init, (5) (constexpr since C++20)
                       BinaryOp reduce, UnaryOp transform
   );
   template< class ExecutionPolicy,
             class ForwardIt, class T,
             class BinaryOp, class UnaryOp >
   T transform_reduce( ExecutionPolicy&& policy, (6) (since C++17)
                       ForwardIt first, ForwardIt last, T
   init,
                       BinaryOp reduce, UnaryOp transform
   );
   1) Equivalent to transform_reduce(first1, last1, first2, init,
                    std::plus<>(), std::multiplies<>()), effectively parallelized
   version of the default std::inner_product.
   3) Applies transform to each pair of elements from the ranges [first1, last1) and
   the range of std::distance(first1, last1) elements starting from first2 and reduces
   the results (possibly permuted and aggregated in unspecified manner) along with the
   initial value init over reduce.
   The result is non-deterministic if the reduce 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:
     * reduce(init, init)
     * reduce(init, transform(*first1, *first2))
     * reduce(transform(*first1, *first2), init)
     * reduce(transform(*first1, *first2), transform(*first1, *first2))
   Given last2 as the std::distance(first1, last1)
   th next iterator of first2, if any of the following conditions is satisfied, the
   behavior is undefined:
     * T is not MoveConstructible.
     * transform or reduce modifies any element of [first1, last1) or [first2, last2).
     * transform or reduce invalidates any iterator or subrange of [first1, last1] or
       [first2, last2].
   5) Applies transform to each element in the range [first, last) and reduces the
   results (possibly permuted and aggregated in unspecified manner) along with the
   initial value init over reduce.
   The result is non-deterministic if the reduce 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:
     * reduce(init, init)
     * reduce(init, transform(*first))
     * reduce(transform(*first), init)
     * reduce(transform(*first), transform(*first))
   If any of the following conditions is satisfied, the behavior is undefined:
     * T is not MoveConstructible.
     * transform or reduce modifies any element of [first, last).
     * transform or reduce invalidates any iterator or subrange of [first, last].
   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)

Parameters
   first1, last1 - the range of elements to be taken as the left operand of transform
   first2 - the start of range of elements to be taken as the right operand of
                   transform
   first, last - the range of elements to be taken as the operand of transform
   init - the initial value of the generalized sum
   policy - the execution policy to use. See execution policy for details.
   reduce - binary FunctionObject that will be applied in unspecified order to
                   the results of transform, the results of other reduce and init.
                   unary or binary FunctionObject that will be applied to each element
   transform - of the input range(s). The return type must be acceptable as input
                   to reduce.

Type requirements
   -
   InputIt1, InputIt2, InputIt must meet the requirements of LegacyInputIterator.
   -
   ForwardIt1, ForwardIt2, ForwardIt must meet the requirements of
   LegacyForwardIterator.

Return value
   1,2) The generalized sum of init and values over std::plus<>(), where values are the
   values transformed by std::multiplies<>(), each value is transformed from a pair of
   elements from the two input ranges.
   3,4) The generalized sum of init and values over reduce, where values are the values
   transformed by transform, each value is transformed from a pair of elements from the
   two input ranges.
   5,6) The generalized sum of init and values over reduce, where values are the values
   transformed by transform, each value is transformed from an element from the input
   range.
   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(first1, last1) (or std::distance(first,
   last) for overloads (5,6)):
   1,2) \(\scriptsize O(N)\)O(N) applications of std::plus<>() and std::multiplies<>()
   respectively.
   3-6) \(\scriptsize O(N)\)O(N) applications of reduce and transform respectively.

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
   transform is never applied to init.
   If first == last or first1 == last1, init is returned, unmodified.

Example
   transform_reduce can be used to parallelize std::inner_product. Some systems may
   need additional support to get advantages of parallel execution. E.g., on GNU/Linux,
   the Intel TBB be installed and -ltbb option be provided to gcc/clang compiler. // Run this code
 #if PARALLEL
 #include <execution>
 #define PAR std::execution::par,
 #else
 #define PAR
 #endif
 #include <algorithm>
 #include <functional>
 #include <iostream>
 #include <iterator>
 #include <locale>
 #include <numeric>
 #include <vector>
 // to parallelize non-associate accumulative operation, you'd better choose
 // transform_reduce instead of reduce; e.g., a + b * b != b + a * a
 void print_sum_squared(long const num)
 {
     std::cout.imbue(std::locale{"en_US.UTF8"});
     std::cout << "num = " << num << '\n';
     // create an immutable vector filled with pattern: 1,2,3,4, 1,2,3,4 ...
     const std::vector<long> v{[n = num * 4] {
         std::vector<long> v;
         v.reserve(n);
         std::generate_n(std::back_inserter(v), n,
             [i = 0]() mutable { return 1 + i++ % 4; });
         return v;
     }()};
     auto squared_sum = [](auto sum, auto val) { return sum + val * val; };
     auto sum1 = std::accumulate(v.cbegin(), v.cend(), 0L, squared_sum);
     std::cout << "accumulate(): " << sum1 << '\n';
     auto sum2 = std::reduce(PAR v.cbegin(), v.cend(), 0L, squared_sum);
     std::cout << "reduce(): " << sum2 << '\n';
     auto sum3 = std::transform_reduce(PAR v.cbegin(), v.cend(), 0L, std::plus{},
                        [](auto val) { return val * val; });
     std::cout << "transform_reduce(): " << sum3 << "\n\n";
 }
 int main()
 {
     print_sum_squared(1);
     print_sum_squared(1'000);
     print_sum_squared(1'000'000);
 }

Possible output:
 num = 1
 accumulate(): 30
 reduce(): 30
 transform_reduce(): 30
 num = 1,000
 accumulate(): 30,000
 reduce(): -7,025,681,278,312,630,348
 transform_reduce(): 30,000
 num = 1,000,000
 accumulate(): 30,000,000
 reduce(): -5,314,886,882,370,003,032
 transform_reduce(): 30,000,000
 // Compile-options for parallel execution on POSIX:
 // g++ -O2 -std=c++17 -Wall -Wextra -pedantic -DPARALLEL ./example.cpp -ltbb -o tr; ./tr

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)
   reduce similar to std::accumulate, except out of order
   (C++17) (function template)