\section{Reduction}

\label{sec:reduction}

This section covers ways to perform reductions in parallel, task, taskloop, and SIMD regions.

\subsection{The \code{reduction} Clause}

\label{subsec:reduction}

The following example demonstrates the \code{reduction} clause; note that some

reductions can be expressed in the loop in several ways, as shown for the \code{max}

and \code{min} reductions below:

\cexample{reduction}{1}

\ffreeexample{reduction}{1}

A common implementation of the preceding example is to treat it as if it had been

written as follows:

\cexample{reduction}{2}

\ffreenexample{reduction}{2}

The following program is non-conforming because the reduction is on the

\emph{intrinsic procedure name} \code{MAX} but that name has been redefined to be the variable

named \code{MAX}.

\ffreenexample{reduction}{3}

\begin{figure}[t!]

\linewitharrows{-1}{dashed}{Fortran (cont.)}{8em}

\end{figure}

The following conforming program performs the reduction using the

\emph{intrinsic procedure name} \code{MAX} even though the intrinsic \code{MAX} has been renamed

to \code{REN}.

\ffreenexample{reduction}{4}

The following conforming program performs the reduction using

\plc{intrinsic procedure name} \code{MAX} even though the intrinsic \code{MAX} has been renamed

to \code{MIN}.

\ffreenexample{reduction}{5}

The following example is non-conforming because the initialization (\code{a =

0}) of the original list item \code{a} is not synchronized with the update of

\code{a} as a result of the reduction computation in the \code{for} loop. Therefore,

the example may print an incorrect value for \code{a}.

To avoid this problem, the initialization of the original list item \code{a}

should complete before any update of \code{a} as a result of the \code{reduction}

clause. This can be achieved by adding an explicit barrier after the assignment

\code{a = 0}, or by enclosing the assignment \code{a = 0} in a \code{single}

directive (which has an implied barrier), or by initializing \code{a} before

the start of the \code{parallel} region.

\cexample{reduction}{6}

\fexample{reduction}{6}

The following example demonstrates the reduction of array \plc{a}. In C/C++ this is illustrated by the explicit use of an array section \plc{a[0:N]} in the \code{reduction} clause. The corresponding Fortran example uses array syntax supported in the base language. As of the OpenMP 4.5 specification the explicit use of array section in the \code{reduction} clause in Fortran is not permitted. But this oversight will be fixed in the next release of the specification.

\cexample{reduction}{7}

\ffreeexample{reduction}{7}

\subsection{Task Reduction}

\label{subsec:task_reduction}

The following C/C++ and Fortran examples show how to implement

a task reduction over a linked list.

Task reductions are supported by the \code{task\_reduction} clause which can only be

applied to the \code{taskgroup} directive, and a \code{in\_reduction} clause

which can be applied to the \code{task} construct among others.

The \code{task\_reduction} clause on the \code{taskgroup} construct is used to

define the scope of a new reduction, and after the \code{taskgroup}

region the original variable will contain the final value of the reduction.

In the task-generating while loop the \code{in\_reduction} clause of the \code{task}

construct is used to specify that the task participates "in" the reduction.

Note: The \plc{res} variable is private in the \plc{linked\_list\_sum} routine

and is not required to be shared (as in the case of a \code{parallel} construct

reduction).

\cexample{task_reduction}{1}

\ffreeexample{task_reduction}{1}

\subsection{Taskloop Reduction}

\label{subsec:taskloop_reduction}

In the OpenMP 5.0 Specification the \code{taskloop} construct

was extended to include the reductions.

The following two examples show how to implement a reduction over an array

using taskloop reduction in two different ways.

In the first

example we apply the \code{reduction} clause to the \code{taskloop} construct. As it was

explained above in the task reduction examples, a reduction over tasks is

divided in two components: the scope of the reduction, which is defined by a

\code{taskgroup} region, and the tasks that participate in the reduction. In this

example, the \code{reduction} clause defines both semantics. First, it specifies that

the implicit \code{taskgroup} region associated with the \code{taskloop} construct is the scope of the

reduction, and second, it defines all tasks created by the \code{taskloop} construct as

participants of the reduction. About the first property, it is important to note

that if we add the \code{nogroup} clause to the \code{taskloop} construct the code will be

nonconforming, basically because we have a set of tasks that participate in a

reduction that has not been defined.

\cexample{taskloop_reduction}{1}

\ffreeexample{taskloop_reduction}{1}

The second example computes exactly the same value as in the preceding\plc{taskloop\_reduction.1} code section,

but in a very different way.

First, in the \plc{array\_sum} function a \code{taskgroup} region is created

that defines the scope of a new reduction using the \code{task\_reduction} clause.

After that, a task and also the tasks generated by a taskloop participate in

that reduction by using the \code{in\_reduction} clause on the \code{task}

and \code{taskloop} constructs, respectively.

Note that the \code{nogroup} clause was added to the \code{taskloop} construct.

This is allowed because what is expressed with the \code{in\_reduction} clause

is different from what is expressed with the \code{reduction} clause.

In one case the generated tasks are specified to participate in a previously

declared reduction (\code{in\_reduction} clause) whereas in the other case

creation of a new reduction is specified and also that all tasks generated

by the taskloop will participate on it.

\cexample{taskloop_reduction}{2}

\ffreeexample{taskloop_reduction}{2}

In the OpenMP 5.0 Specification, \code{reduction} clauses for the

\code{taskloop}~\code{ simd} construct were also added.

The examples below compare reductions for the \code{taskloop} and the \code{taskloop}~\code{simd} constructs.

These examples illustrate the use of \code{reduction} clauses within

"stand-alone" \code{taskloop} constructs, and the use of \code{in\_reduction} clauses for tasks of taskloops to participate

with other reductions within the scope of a parallel region.

\textbf{taskloop reductions:}

In the \plc{taskloop reductions} section of the example below,

\plc{taskloop 1} uses the \code{reduction} clause

in a \code{taskloop} construct for a sum reduction, accumulated in \plc{asum}.

The behavior is as though a \code{taskgroup} construct encloses the

taskloop region with a \code{task\_reduction} clause, and each taskloop

task has an \code{in\_reduction} clause with the specifications

of the \code{reduction} clause.

At the end of the taskloop region \plc{asum} contains the result of the reduction.

The next taskloop, \plc{taskloop 2}, illustrates the use of the

\code{in\_reduction} clause to participate in a previously defined

reduction scope of a \code{parallel} construct.

The task reductions of \plc{task 2} and \plc{taskloop 2} are combined

across the \code{taskloop} construct and the single \code{task} construct, as specified

in the \code{reduction(task,}~\code{+:asum)} clause of the \code{parallel} construct.

At the end of the parallel region \plc{asum} contains the combined result of all reductions.

\textbf{taskloop simd reductions:}

Reductions for the \code{taskloop}~\code{simd} construct are shown in the second half of the code.

Since each component construct, \code{taskloop} and \code{simd},

can accept a reduction-type clause, the \code{taskloop}~\code{simd} construct

is a composite construct, and the specific application of the reduction clause is defined

within the \code{taskloop}~\code{simd} construct section of the OpenMP 5.0 Specification.

The code below illustrates use cases for these reductions.

In the \plc{taskloop simd reduction} section of the example below,

\plc{taskloop simd 3} uses the \code{reduction} clause

in a \code{taskloop}~\code{simd} construct for a sum reduction within a loop.

For this case a \code{reduction} clause is used, as one would use

for a \code{simd} construct.

The SIMD reductions of each task are combined, and the results of these tasks are further

combined just as in the \code{taskloop} construct with the \code{reduction} clause for \plc{taskloop 1}.

At the end of the taskloop region \plc{asum} contains the combined result of all reductions.

If a \code{taskloop}~\code{simd} construct is to participate in a previously defined

reduction scope, the reduction participation should be specified with

a \code{in\_reduction} clause, as shown in the \code{parallel} region enclosing

\plc{task 4} and \plc{taskloop simd 4} code sections.

Here the \code{taskloop}~\code{simd} construct's

\code{in\_reduction} clause specifies participation of the construct's tasks as

a task reduction within the scope of the parallel region.

That is, the results of each task of the \code{taskloop} construct component

contribute to the reduction in a broader level, just as in \plc{parallel reduction a} code section above.

Also, each \code{simd}-component construct

occurs as if it has a \code{reduction} clause, and the

SIMD results of each task are combined as though to form a single result for

each task (that participates in the \code{in\_reduction} clause).

At the end of the parallel region \plc{asum} contains the combined result of all reductions.

\cexample{taskloop_simd_reduction}{1}

\ffreeexample{taskloop_simd_reduction}{1}