std::transform_reduce() algorithm

since C++20

// (1)
template< class InputIt1, class InputIt2, class T >
constexpr T transform_reduce( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init );

// (2)
template< class InputIt1, class InputIt2, class T, class BinaryReductionOp, class BinaryTransformOp >
constexpr T transform_reduce( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init,
                              BinaryReductionOp reduce, BinaryTransformOp transform );

// (3)
template< class InputIt, class T, class BinaryReductionOp, class UnaryTransformOp >
constexpr T transform_reduce( InputIt first, InputIt last, T init, BinaryReductionOp reduce,
                              UnaryTransformOp transform );

// (4)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T >
constexpr T transform_reduce( ExecutionPolicy&& policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2,
                              T init );

// (5)
template< class ExecutionPolicy,
          class ForwardIt1,
          class ForwardIt2,
          class T,
          class BinaryReductionOp,
          class BinaryTransformOp >
T transform_reduce( ExecutionPolicy&& policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, T init,
                    BinaryReductionOp reduce, BinaryTransformOp transform );

// (6)
template< class ExecutionPolicy, class ForwardIt, class T, class BinaryReductionOp, class UnaryTransformOp >
T transform_reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init,
                    BinaryReductionOp reduce, UnaryTransformOp transform );

since C++17

// (1)
template< class InputIt1, class InputIt2, class T >
T transform_reduce( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init );

// (2)
template< class InputIt1, class InputIt2, class T, class BinaryReductionOp, class BinaryTransformOp >
T transform_reduce( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init,
                    BinaryReductionOp reduce, BinaryTransformOp transform );

// (3)
template< class InputIt, class T, class BinaryReductionOp, class UnaryTransformOp >
T transform_reduce( InputIt first, InputIt last, T init, BinaryReductionOp reduce, UnaryTransformOp transform );

// (4)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T >
T transform_reduce( ExecutionPolicy&& policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, T init );

// (5)
template< class ExecutionPolicy,
          class ForwardIt1,
          class ForwardIt2,
          class T,
          class BinaryReductionOp,
          class BinaryTransformOp >
T transform_reduce( ExecutionPolicy&& policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, T init,
                    BinaryReductionOp reduce, BinaryTransformOp transform );

// (6)
template< class ExecutionPolicy, class ForwardIt, class T, class BinaryReductionOp, class UnaryTransformOp >
T transform_reduce( ExecutionPolicy&& policy, ForwardIt first, ForwardIt last, T init,
                    BinaryReductionOp reduce, UnaryTransformOp transform );

• (1) Equivalent to std::transform_reduce(first1, last1, first2, init, std::plus<>(), std::multiplies<>()), effectively parallelized version of the default std::inner_product.

• (2) Applies transform to each pair of elements from the ranges [first; last) and the range starting at first2 and reduces the results (possibly permuted and aggregated in unspecified manner) along with the initial value init over reduce.

• (3) 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

• (4 - 6) Same as (1 - 3), but executed according to policy.

  Overload Resolution

  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)

The behavior is non-deterministic if reduce is not associative or not commutative.

Undefined Behaviour

The behavior is undefined

if reduce or transform modifies any element or invalidates any iterator in the input ranges, including their end iterators.

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.
reduce	Binary FunctionObject that will be applied in unspecified order to the result of transform, the results of other reduce and init.
transform	Binary FunctionObject that will be applied to each element in the input range(s).

Type requirements

InputIt	LegacyInputIterator
ForwardIt	LegacyForwardIterator

• (3, 6):

  T	MoveConstructible

  The following expressions have to be convertible to T:

  • reduce(init, transform(*first))
  • reduce(transform(*first), init)
  • reduce(init, init)
  • reduce(transform(*first), transform(*first))

• (2, 5):

  T	MoveConstructible

  The following expressions have to be convertible to T:

  • reduce(init, transform(*first1, *first2))
  • reduce(transform(*first1, *first2), init)
  • reduce(init, init)
  • reduce(transform(*first1, *first2)
  • transform(*first1, *first2))

Return value

• (2) Generalized sum of init and transform(*first, *first2), transform(*(first + 1), *(first2 + 1)), ..., over reduce.
• (3) Generalized sum of init and transform(*first), transform(*(first + 1)), ... transform(*(last - 1)) over reduce.

The results of transform or of reduce may be grouped and arranged in arbitrary order.

Formallly, the generalized sum GSUM(op, a1, ..., aN) is defined as follows:

• If N = 1, a1
• If N > 1, op(GSUM(op, b 1, ..., b K), GSUM(op, b M, ..., b N)) where
  • b1, ..., bN may be any permutation of a1, ..., aN
  • and 1 < K + 1 = M ≤ N

important

If first == last or first1 == last1, init is returned, unmodified.

Complexity

• (1, 2, 4, 5) O(last1 - first1) applications each of reduce and transform.
• (3, 6) O(last - first) applications each of transform and reduce.

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

In the unary-binary overload (3, 6), transform is not applied to init.

Examples

Main.cpp

#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