# Taskflow Algorithms » Parallel Reduction

Taskflow provides template function that constructs a task to perform parallel reduction over a range of items.

## Include the Header

You need to include the header file, `taskflow/algorithm/reduce.hpp`, for creating a parallel-reduction task.

    #include <taskflow/algorithm/reduce.hpp>

## Create a Parallel-Reduction Task

The reduction task created by tf::Taskflow::reduce(B first, E last, T& result, O bop, P&& part) performs parallel reduction over a range of elements specified by `[first, last)` using the binary operator `bop` and stores the reduced result in `result`. It represents the parallel execution of the following reduction loop:

    for(auto itr=first; itr<last; itr++) {
      result = bop(result, *itr);
    }

At runtime, the reduction task spawns a subflow to perform parallel reduction. The reduced result is stored in `result` that will be captured by reference in the reduction task. It is your responsibility to ensure `result` remains alive during the parallel execution.

    int sum = 100;
    std::vector<int> vec = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

    tf::Task task = taskflow.reduce(vec.begin(), vec.end(), sum,
      [] (int l, int r) { return l + r; }  // binary reducer operator
    );
    executor.run(taskflow).wait();

    assert(sum == 100 + 55);

The order in which the binary operator is applied to pairs of elements is unspecified. In other words, the elements of the range may be grouped and rearranged in arbitrary order. The result and the argument types of the binary operator must be consistent with the input data type.

## Capture Iterators by Reference

You can pass iterators by reference using std::ref to marshal parameter update between dependent tasks. This is especially useful when the range is unknown at the time of creating a parallel-reduction task, but needs initialization from another task.

    int sum = 100;
    std::vector<int> vec;
    std::vector<int>::iterator first, last;

    tf::Task init = taskflow.emplace([&](){
      vec   = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
      first = vec.begin();
      last  = vec.end();
    });

    tf::Task task = taskflow.reduce(std::ref(first), std::ref(last), sum,
      [] (int l, int r) { return l + r; }  // binary reducer operator
    );

    // wrong! must use std::ref, or first and last are captured by copy
    // tf::Task task = taskflow.reduce(first, last, sum, [] (int l, int r) {
    //   return l + r;    // binary reducer operator
    // });

    init.precede(task);

    executor.run(taskflow).wait();

    assert(sum == 100 + 55);

In the above example, when `init` finishes, `vec` has been initialized to 10 elements with `first` and `last` pointing to the data range of `vec`. The reduction task will then work on this initialized range as a result of passing iterators by reference.

## Create a Parallel-Transform-Reduction Task

It is common to transform each element into a new data type and then perform reduction on the transformed elements. Taskflow provides a method, tf::Taskflow::transform_reduce(B first, E last, T& result, BOP bop, UOP uop, P&& part), that applies `uop` to transform each element in the specified range and then perform parallel reduction over `result` and transformed elements. It represents the parallel execution of the following reduction loop:

    for(auto itr=first; itr<last; itr++) {
      result = bop(result, uop(*itr));
    }

The example below transforms each digit in a string to an integer number and then sums up all integers in parallel.

    std::string str = "12345678";
    int sum {0};
    tf::Task task = taskflow.transform_reduce(str.begin(), str.end(), sum,
      [] (int a, int b) {      // binary reduction operator
        return a + b;
      },
      [] (char c) -> int {     // unary transformation operator
        return c - '0';
      }
    );
    executor.run(taskflow).wait();
    assert(sum == 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8);  // sum will be 36

The order in which we apply the binary operator on the transformed elements is unspecified. It is possible that the binary operator will take r-value in both arguments, for example, `bop(uop(*itr1), uop(*itr2))`, due to the transformed temporaries. When data passing is expensive, you may define the result type `T` to be move-constructible.

## Configure a Partitioner

You can configure a partitioner for parallel-reduction tasks to run with different scheduling methods, such as guided partitioning, dynamic partitioning, and static partitioning. The following example creates two parallel-reduction tasks using two different partitioners, one with the static partitioning algorithm and another one with the guided partitioning algorithm:

    tf::StaticPartitioner static_partitioner;
    tf::GuidedPartitioner guided_partitioner;

    int sum1 = 100, sum2 = 100;
    std::vector<int> vec = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

    // create a parallel-reduction task with static partitioner
    taskflow.reduce(vec.begin(), vec.end(), sum1,
      [] (int l, int r) { return l + r; },
      static_partitioner
    );

    // create a parallel-reduction task with guided partitioner
    taskflow.reduce(vec.begin(), vec.end(), sum2,
      [] (int l, int r) { return l + r; },
      guided_partitioner
    );

#### Note

By default, parallel-reduction tasks use tf::DefaultPartitioner if no partitioner is specified.

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