Presburger Arithmetic and Its Use in Verification

2.2. MULTICORE PARALLELISM ON .NET FRAMEWORK
algorithms. Using Task is rather simple; however, to achieve good efficiency, tasks
should be created only when computation is heavier than overheads of creating and
coordinating tasks.
2.2.4 Asynchronous computation as parallelization
F# has very good support of asynchronous computation by the notion of Asynchronous
Workflow. ThiscomponentisbuiltforF#onlyandhasconvenientuseby
the syntax of async{...}. Certainly, Asynchronous Workflow best fits IO-bound
computation where tasks are executed and are not blocked to wait for the final result.
Using asynchronous computation, operations are going to run asynchronously,
and resources will not be wasted. In some cases, asynchronous computation could
bring benefits to CPU-bound tasks as the following example of computing first 46
Fibonacci numbers:
let rec fib x = if x fib(i)) [|0..45|];;
let pfibs =
Async.Parallel [| for i in 0..45 −> async { return fib(i) }|]
|> Async.RunSynchronously;;
In this example, functions are turned to be asynchronous by using async keyword.
While these functions are marked for parallel execution by Async.Parallel
and Async.RunSynchronously, .NETframeworkwilldothejobofdistributing
them to available cores and running them effectively. Our benchmark shows that
the asynchronous variant is 2.5× faster than the sequential one. A better speedup
can be achieved by using Task instead of Asynchronous Workflow, however,itisa
good idea to use Asynchronous Workflow if the computation consists of both CPUbound
tasks and IO-bound tasks where using Task only could be bad due to the
blocking property of IO operations. With the presence of Asynchronous Workflow,
we show that F# has very rich support of parallel constructs. There are many
primitives to employ for each algorithm, choosing constructs really depends on the
nature of problem and operations required.
2.2.5 Other parallel constructs
The Array.Parallel and PSeq Module
The Array.Parallel module is a thin wrapper around Parallel.For(Each) constructs,
the purpose is providing a convenient interface for parallel operations on
Array. Array.Parallel is easy to use because its signature is exactly the same
as Array correspondent. Employing this module, we can clearly see the benefit of
wrapping imperative parallel constructs by high order functions to hide side effects.
Similar to above module, the PSeq module based on PLINQ constructs to provide
high order functions for parallel processing on sequences. Input for this mod-
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