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.

For more information on the algorithm and how we can use Phasers to make it better, review Topic 3.5 from the RiceX course.

Background

Check out the reference page on phasers

Guide to the Java Phaser

class Phaser

bulkRegister

arriveAndAwaitAdvance

arriveAndDeregister (note: not required for this studio, but good to know about.)

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.

The Core Questions

• What are the tasks?
• What is the data?
• Is the data mutable?
• If so, how is it shared?

Code to Investigate

class AbstractPhasable<T>

getSrcForPhase(phaseIndex)

getDstForPhase(phaseIndex)

class PhasableDoubleArrays extends AbstractPhasable<double[]>

new PhasableDoubleArrays(originalData)

class Ranges

slice(min, maxExclusive, numSlices)

class Range

getMinInclusive()

getMaxExclusive()

getIndexId()

forEachIndex(body)

Code to Implement

Warmup

class:	SequentialIterativeAverager.java	DEMO:
methods:	iterativelyAverage
package:	iterativeaveraging.warmup
source folder:	src//java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) (sequential implementation only)

Studio

IterativeAveragingUtils

class:	IterativeAveragingUtils.java
methods:	sliceDoubleArrayIntoRangesForIterativeAveraging
package:	iterativeaveraging.optional
source folder:	student/src/main/java

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)

Tip: Use PhasableDoubleArrays

Warning: Do NOT use SwappableDoubleArrays

Parallel

class:	ParallelIterativeAverager.java
methods:	iterativelyAverage
package:	iterativeaveraging.studio
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 Iterative Averaging algorithm shown above sequentially. 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

PhasedParallel

class:	PhasedParallelIterativeAverager.java
methods:	iterativelyAverage
package:	iterativeaveraging.studio
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 RiceX 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. 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

FuzzyPhasedParallel

class:	FuzzyPhasedParallelIterativeAverager.java
methods:	iterativelyAverage
package:	iterativeaveraging.studio
source folder:	student/src/main/java

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

Which indices must be complete before neighboring tasks can proceed? Which indices have more flexibility?

create phaser
register phaser for each task
parallel loop
    sequential loop
        shared work
        arrive on phaser
        local work
        await advance (must specify the phase) on phaser

Optional Challenge

PointToPointPhasedParallel

class:	PointToPointPhasedParallelIterativeAverager.java
methods:	iterativelyAverage
package:	iterativeaveraging.challenge
source folder:	student/src/main/java

Testing Your Solution

Correctness

class:	IterativeAveragingTestSuite.java
package:	iterativeaveraging.studio
source folder:	testing/src/test/java

Performance

class:	IterativeAveragingTiming.java
package:	iterativeaveraging.studio
source folder:	src/main/java