Factorial calculation using Scala actors

Question

Problem

You have to split up your input in partial products. This partial products can then be calculated in parallel. The partial products are then multiplied to get the final product.

This can be reduced to a broader class of problems: The so called Parallel prefix calculation. You can read up about it on Wikipedia.

Short version: When you calculate a*b*c*d with an associative operation _ * _, you can structure the calculation a*(b*(c*d)) or (a*b)*(c*d). With the second approach, you can then calculate a*b and c*d in parallel and then calculate the final result from these partial results. Of course you can do this recursively, when you have a bigger number of input values.

Solution

Disclaimer

This sounds a little bit like a homework assignment. So I will provide a solution that has two properties:

It contains a small bug
It shows how to solve parallel prefix in general, without solving the problem directly

So you can see how the solution should be structured, but no one can use it to cheat on her homework.

Solution in detail

First I need a few imports

import akka.event.Logging import java.util.concurrent.TimeUnit import scala.concurrent.duration.FiniteDuration import akka.actor._

Then I create some helper classes for the communication between the actors

case class Calculate[T](values : Seq[T], segment : Int, parallelLimit : Int, fn : (T,T) => T)

trait CalculateResponse
case class CalculationResult[T](result : T, index : Int) extends CalculateResponse
case object Busy extends CalculateResponse

Instead of telling the receiver you are busy, the actor could also use the stash or implement its own queue for partial results. But in this case I think the sender shoudl decide how much parallel calculations are allowed.

Now I create the actor:

class ParallelPrefixActor[T] extends Actor {
  val log = Logging(context.system, this)
  val subCalculation = Props(classOf[ParallelPrefixActor[BigInt]])
  val fanOut = 2
  def receive = waitForCalculation

  def waitForCalculation : Actor.Receive = {
    case c : Calculate[T] =>
      log.debug(s"Start calculation for ${c.values.length} values, segment nr. ${c.index}, from ${c.values.head} to ${c.values.last}")
      if (c.values.length < c.parallelLimit) {
        log.debug("Calculating result direct")
        val result = c.values.reduceLeft(c.fn)
        sender ! CalculationResult(result, c.index)
      }else{
        val groupSize: Int = Math.max(1, (c.values.length / fanOut) + Math.min(c.values.length % fanOut, 1))
        log.debug(s"Splitting calculation for ${c.values.length} values up to ${fanOut} children, ${groupSize} elements each, limit ${c.parallelLimit}")
        def segments=c.values.grouped(groupSize)
        log.debug("Starting children")
        segments.zipWithIndex.foreach{case (values, index) =>
          context.actorOf(subCalculation) ! c.copy(values = values, index = index)
        }
        val partialResults: Vector[T] = segments.map(_.head).to[Vector]
        log.debug(s"Waiting for ${partialResults.length} results (${partialResults.indices})")
        context.become(waitForResults(segments.length, partialResults, c, sender), discardOld = true)
      }
  }
  def waitForResults(outstandingResults : Int, partialResults : Vector[T], originalRequest : Calculate[T], originalSender : ActorRef) : Actor.Receive = {
    case c : Calculate[_] => sender ! Busy
    case r : CalculationResult[T] =>
      log.debug(s"Putting result ${r.result} on position ${r.index} in ${partialResults.length}")
      val updatedResults = partialResults.updated(r.index, r.result)
      log.debug("Killing sub-worker")
      sender ! PoisonPill
      if (outstandingResults==1) {
        log.debug("Calculating result from partial results")
        val result = updatedResults.reduceLeft(originalRequest.fn)
        originalSender ! CalculationResult(result, originalRequest.index)
        context.become(waitForCalculation, discardOld = true)
      }else{
        log.debug(s"Still waiting for ${outstandingResults-1} results")
        // For fanOut > 2 one could here already combine consecutive partial results
        context.become(waitForResults(outstandingResults-1, updatedResults, originalRequest, originalSender), discardOld = true)
      }
  }
}

Optimizations

Using parallel prefix calculation is not optimal. The actors calculating the the product of the bigger numbers will do much more work than the actors calculating the product of the smaller numbers (e.g. when calculating 1 * ... * 100 , it is faster to calculate 1 * ... * 10 than 90 * ... * 100). So it might be a good idea to shuffle the numbers, so big numbers will be mixed with small numbers. This works in this case, because we use an commutative operation. Parallel prefix calculation in general only needs an associative operation to work.

Performance

In theory

Performance of the actor solution is worse than the "naive" solution (using parallel collections) for small amounts of data. The actor solution will shine, when you make complex calculations or distribute your calculation on specialized hardware (e.g. graphics card or FPGA) or on multiple machines. With the actor you can control, who does which calculation and you can even restart "hanging calculations". This can give a big speed up.

On a single machine, the actor solution might help when you have a non-uniform memory architecture. You could then organize the actors in a way that pins memory to a certain processor.

Some measurement

I did some real performance measurement using a Scala worksheet in IntelliJ IDEA.

First I set up the actor system:

// Setup the actor system
val system = ActorSystem("root")
// Start one calculation actor
val calculationStart = Props(classOf[ParallelPrefixActor[BigInt]])


val calcolon = system.actorOf(calculationStart, "Calcolon-BigInt")

val inbox = Inbox.create(system)

Then I defined a helper method to measure time:

// Helper function to measure time
def time[A] (id : String)(f: => A) = {
  val start = System.nanoTime()
  val result = f
  val stop = System.nanoTime()
  println(s"""Time for "${id}": ${(stop-start)*1e-6d}ms""")
  result
}

And then I did some performance measurement:

// Test code
val limit = 10000
def testRange = (1 to limit).map(BigInt(_))

time("par product")(testRange.par.product)
val timeOut = FiniteDuration(240, TimeUnit.SECONDS)
inbox.send(calcolon, Calculate[BigInt]((1 to limit).map(BigInt(_)), 0, 10, _ * _))
time("actor product")(inbox.receive(timeOut))

time("par sum")(testRange.par.sum)
inbox.send(calcolon, Calculate[BigInt](testRange, 0, 5, _ + _))
time("actor sum")(inbox.receive(timeOut))

I got the following results

> Time for "par product": 134.38289ms
  res0: scala.math.BigInt = 284625968091705451890641321211986889014805140170279923
  079417999427441134000376444377299078675778477581588406214231752883004233994015
  351873905242116138271617481982419982759241828925978789812425312059465996259867
  065601615720360323979263287367170557419759620994797203461536981198970926112775
  004841988454104755446424421365733030767036288258035489674611170973695786036701
  910715127305872810411586405612811653853259684258259955846881464304255898366493
  170592517172042765974074461334000541940524623034368691540594040662278282483715
  120383221786446271838229238996389928272218797024593876938030946273322925705554
  596900278752822425443480211275590191694254290289169072190970836905398737474524
  833728995218023632827412170402680867692104515558405671725553720158521328290342
  799898184493136...

  Time for "actor product": 1310.217247ms
  res2: Any = CalculationResult(28462596809170545189064132121198688901480514017027
  992307941799942744113400037644437729907867577847758158840621423175288300423399
  401535187390524211613827161748198241998275924182892597878981242531205946599625
  986706560161572036032397926328736717055741975962099479720346153698119897092611
  277500484198845410475544642442136573303076703628825803548967461117097369578603
  670191071512730587281041158640561281165385325968425825995584688146430425589836
  649317059251717204276597407446133400054194052462303436869154059404066227828248
  371512038322178644627183822923899638992827221879702459387693803094627332292570
  555459690027875282242544348021127559019169425429028916907219097083690539873747
  452483372899521802363282741217040268086769210451555840567172555372015852132829
  034279989818449...

> Time for "par sum": 6.488620999999999ms
  res3: scala.math.BigInt = 50005000

> Time for "actor sum": 657.752832ms
  res5: Any = CalculationResult(50005000,0)

You can easily see that the actor version is much slower than using parallel collections.