Iterative Averaging

Motivation

Iterative Averaging is the process of updating an array to so that each index becomes the average of the indices one before and one after it. After repeating this for many iterations, the array may converge to one set of numbers. For example, when given the following array, we can perform iterations of this algorithm until the array eventually converges:

[0]	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]
0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0
0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.5	1.0
0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.25	0.5	1.0
0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.125	0.25	0.625	1.0
0.0	0.0	0.0	0.0	0.0	0.0	0.0625	0.125	0.375	0.625	1.0
0.0	0.0	0.0	0.0	0.0	0.03125	0.0625	0.21875	0.375	0.6875	1.0
0.0	0.0	0.0	0.0	0.015625	0.03125	0.125	0.21875	0.453125	0.6875	1.0
0.0	0.0	0.0	0.0078125	0.015625	0.0703125	0.125	0.2890625	0.453125	0.7265625	1.0
0.0	0.0	0.00390625	0.0078125	0.0390625	0.0703125	0.1796875	0.2890625	0.5078125	0.7265625	1.0
0.0	0.001953125	0.00390625	0.021484375	0.0390625	0.109375	0.1796875	0.34375	0.5078125	0.75390625	1.0
0.0	0.001953125	0.01171875	0.021484375	0.0654296875	0.109375	0.2265625	0.34375	0.548828125	0.75390625	1.0
0.0	$\vdots$									1.0
0.0	$\vdots$									1.0
0.0	$\vdots$									1.0
0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0

X10-like Phasers have been added to Java since JDK7. We will gain some experience with using Phasers in a parallel for-loop context. Phasers allow us to change the structure of our loops and reduce overhead in the algorithm.

Background

Java Phaser

Check out the reference page on phasers

Guide to the Java Phaser

class Phaser

bulkRegister (also see instructions on ForkLoopWithPhaserIterativeAverager)

arriveAndAwaitAdvance

Warning: Our use of the forall loop with Phasers does not accurately convey their finicky nature. More than other features, Phasers seem to require more care to get performance improvements.

PhasableDoubleArrays

• class AbstractPhasable<T>
  • getSrcForPhase(phaseIndex)
  • getDstForPhase(phaseIndex)
• class PhasableDoubleArrays extends AbstractPhasable<double[]>
  • new PhasableDoubleArrays(originalData, initializerFunction)

Ranges

Ranges (Previous Exercise To Use)

Code to Implement

IterativeAveragingUtils

class:	IterativeAveragingUtils.java
methods:	slice createPhasableDoubleArrays
package:	iterativeaveraging.util.exercise
source folder:	student/src/main/java

slice

Each IterativeAverager should slice the data into ranges. The constructor for each IterativeAverager is passed the number of slices to create.

Tip: Use Ranges.slice(min, maxExclusive, numSlices)

If you are to create 3 slices an array of length 11:

the slices should have these properties:

	sliceID	minInclusive	maxExclusive
sliceA	0	1	4
sliceB	1	4	7
sliceC	2	7	10

createPhasableDoubleArrays

TL;DR: Initialize a double[] and make sure to copy over the original data's 0th and last index's value.

LoopOfForkLoopsIterativeAverager

class:	LoopOfForkLoopsIterativeAverager.java
methods:	sliceCount iterativelyAverage
package:	iterativeaveraging.exercise
source folder:	student/src/main/java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) (parallel implementation required)

For this method, you should not be using Phasers. Instead, implement a parallel version of the Sequential Iterative Averaging warm up. Make use of the PhasableDoubleArrays class. The return value should be the current version of the array after it has gone through the number of iterations passed in the method.

sequential loop
    parallel loop
        work

What is the work for each task?

X10PhasedForkLoopIterativeAverager

class:	X10PhasedForkLoopIterativeAverager.java
methods:	x10 sliceCount iterativelyAverage
package:	iterativeaveraging.exercise
source folder:	student/src/main/java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) (parallel implementation required)

x10 phased parallel loop
    sequential loop
        work
        arrive and await advance on phaser

What is the work for each iteration of a task?

ForkLoopWithPhaserIterativeAverager

class:	ForkLoopWithPhaserIterativeAverager.java
methods:	phaserCreator sliceCount iterativelyAverage
package:	iterativeaveraging.exercise
source folder:	student/src/main/java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) (parallel implementation required)

Before you get started on this, make sure you review the Background section in order to understand how to utilize Phasers (it will look different than the X10 implementation). This time, we will use Phasers to create a parallel version of the algorithm that has less overhead. Here are a few notes to keep in mind when working on this assignment:

• Think carefully as to how the loops in this version will be structured. Drawing out the computation graph may help
• Bulk registering a Phaser indicates how many times phaser.arriveAndAwaitAdvance() needs to be called before any of the threads are able to move on. In other words, it equals to how many threads need to arive at the checkpoint before moving on. Make sure to register the right number!

create phaser
register phaser for each task
parallel loop
    sequential loop
        work
        arrive and await advance on phaser

What is the work for each iteration of a task?

Testing Your Solution

Correctness

class:	__RigidIterativeAveragingTestSuite.java
package:	iterativeaveraging.rigid.exercise
source folder:	testing/src/test/java

class:	_IterativeAveragingUtilsTestSuite.java
package:	iterativeaveraging.util.exercise
source folder:	testing/src/test/java

class:	_LoopOfForkLoopsIterativeAveragerTestSuite.java
package:	iterativeaveraging.rigid.exercise
source folder:	testing/src/test/java

class:	_X10PhasedForkLoopIterativeAveragerTestSuite.java
package:	iterativeaveraging.rigid.exercise
source folder:	testing/src/test/java

class:	_ForkLoopWithPhaserIterativeAveragerTestSuite.java
package:	iterativeaveraging.rigid.exercise
source folder:	testing/src/test/java