Pack

Motivation

One of the applications for scan is the pack operation. Given an input array, the operation produces an output array containing only the elements that satisfy some specified predicate.

The problem with parallelizing pack is that although it is easy to determine whether an element should be filtered out into the output, we can't know where to put the element in the output array. It seems that placing an element into the output requires knowledge of the placement of the previous elements. This is where prefix sum becomes very useful.

Think about quick sort. In the partition step, we are given a pivot and need to separate the array by the predicate of whether an element is larger than the pivot. This is the perfect place to use the pack operation. You are going to build a more general pack filter in this studio, but you can still attempt the parallel partitioner challenge here: Quicksort Parallel Partitioner.

Background

For example, if you have a String array input:

Africa

Asia

SouthAmerica

NorthAmerica

Europe

Australia

Antarctica

You want to filter out all Strings which do not contain "c". You can first create a flag array in which all the indices where arr[index] contains an "c" is flagged as "1" and all other positions are marked as "0".

1

0

1

1

0

0

1

The prefix sum of this flag array is:

1

1

2

3

3

3

4

Notice how each position that that was flagged now has a distinct number assigned to it in the prefix sum array. We can use this to help us index the output array.

Africa

SouthAmerica

NorthAmerica

Antarctica

Code To Investigate and Implement

ParallelPacker

class:	ParallelPacker.java
methods:	inclusiveSumScanner arrayGenerator
package:	pack.exercise
source folder:	student/src/main/java

constructor

constructor
public ParallelPacker(OutOfPlaceSumScanner inclusiveSumScanner, IntFunction<C[]> arrayGenerator) { if (inclusiveSumScanner.isInclusive()) { this.inclusiveSumScanner = inclusiveSumScanner; } else { throw new IllegalArgumentException(); } this.arrayGenerator = arrayGenerator; }

pack

method: public static <T> T[] pack(Class<T[]> arrayType, T[] arr, Predicate<T> predicate) (parallel implementation required)

Applications which use scan tend to have step after step each with $\log n$ CPL. Pack is no different. Each step can be parallelized.

Be sure to invoke your parallel scan from the Scan studio.

isChangedFromNeighborOnTheLeft

Invoking isChangedFromNeighborOnTheLeft is optional but still worth investigating. Since our implementation of Hillis and Steele scan does not mutate the input data, it is not required. If you were to use a scan which mutated the input, you could still divine whether or not to copy the value into the packed array by using this method on the sum scan.

<syntaxhighlight lang="java"> private static boolean isChangedFromNeighborOnTheLeft(int[] prefixSum, int index) { if (index > 0) { return prefixSum[index - 1] < prefixSum[index]; } else { return prefixSum[0] == 1; } } </syntaxhighlight lang="java">

Testing Your Solution

class:	PackTestSuite.java
package:	pack.studio
source folder:	testing/src/test/java

Output

class:	ParallelPackOutput.java	EXAMPLE
methods:	main
package:	pack.output
source folder:	src/main/java

String[] continentNames = { "Africa", "Asia", "SouthAmerica", "NorthAmerica", "Europe", "Australia", "Antarctica" };
launchApp(() -> {
	String[] packedNamesWhichContainC = ParallelPack.pack(String[].class, continentNames, (continentName) -> {
		return continentName.contains("c");
	});
	System.out.println(Arrays.toString(continentNames));
	System.out.println(Arrays.toString(packedNamesWhichContainC));
});

produces the output:

[Africa, Asia, SouthAmerica, NorthAmerica, Europe, Australia, Antarctica]
[Africa, SouthAmerica, NorthAmerica, Antarctica]