# 1.3 Reduction¶

The following program shows how to fix the integration example using the `omp atomic`

pragma.

Take a look at the updated program below:

Note

the keyword `private`

indicates that each thread will have its own copy of the variable i, whereas `shared`

is indicating that the variables a, n, h, and integral will be shared in memory by all of the threads.

Another way to solve this issue is to employ the concept of **reduction**. The notion of a reduction comes from the mathematical operation
*reduce*, in which a collection of values are combined into a single value via a common mathematical function. Summing up a collection of
values is therefore a natural example of reduction. OpenMP provides the `reduction`

clause for the `omp parallel for`

pragma to show
that reduction should be used. The following example shows the integration example fixed using `reduction`

clause:

The reduction clause (`reduction(+: integral)`

) indicates that the addition operation should be used for reduction, and that the final reduced value will be stored in the variable `integral`

.

Note

The `integral`

variable is not included in the ``shared`

clause when moved to the reduction clause.

## 1.3.1 Fix the array sum program¶

Now that you have learned what the reduction clause is, modify the array example to use reduction:

## 1.3.2 Summary¶

So far, we have introduced three different ways to deal with race conditions:

use the

`omp critical`

pragmause the

`omp atomic`

pragmause a

`reduction`

clause

OpenMP offers programmers multiple ways to deal with race conditions, because some techniques may be faster in different contexts. In the next section, we will discuss how to measure performance.