Scan

Motivation

Scan, also known as parallel prefix, is a fundamental and useful operation in parallel programming. We will gain experience in building Hillis & Steele scan with an optional work efficient Blellock scan.

Further, the dependencies in scan:

$y_{i}=y_{i-1}+x_{i}$

make it seem to have little hope for parallelism. However, simple yet clever approaches can achieve $\log n$ critical path lengths.

While we will simply implement prefix sum, scan can be used for other associative operations.

Background

Prefix Sum

Hillis-Steele Prefix Sum

Hillis and Steele Algorithm

Data parallel algorithms

(Optional) Work-efficient Blelloch Scan

Blelloch Algorithm

Scan Primitives for Vector Computers

Prefix Sums and Their Applications

Code To Investigate

class ArraysHolder

getSrc()

getDst()

nextSrcAndDst()

class PowersOfTwoLessThan implements Iterable<Integer>

The Core Questions

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

Code To Implement

Sequential Scan

class:	SequentialScan.java
methods:	sumScanInclusive
package:	scan.studio
source folder:	student/src/main/java

method: public static int[] sumScanInclusive(SwappableIntArrays swappable) (sequential implementation only)

SwappableIntArrays

One of the downsides to parallel scan requires memory. For our scans we add the additional requirement that we will not mutate the incoming array parameter. We could create log(n) arrays, one for each level but that would be wasteful. If we create two array buffers and switch which is the source to read from and which is the destination to write from at each power of two level of the scan, we should be good to go.

The table below shows which array will be passed back for each offset if swap used appropriately from a parallel scan.

	1	2	4	8	16
src:	data	a	b	a	b
dst:	a	b	a	b	a

NOTE: think about which array is the correct one to return from your scan method given how you write your code.

class:	DefaultArraysHolder.java
methods:	getSrc getDst nextSrcAndDst size
package:	scan.studio
source folder:	student/src/main/java

Hillis and Steele Parallel Scan

class:	StepEfficientParallelScan.java
methods:	sumScanInclusive
package:	scan.studio
source folder:	student/src/main/java

method: public int[] sumScan(int[] data) (parallel implementation required)

(Optional) Blelloch Work Efficient Scan

class:	WorkEfficientParallelScan.java
methods:	sumScanExclusiveInPlace
package:	scan.challenge
source folder:	student/src/main/java

method: public static void sumScanExclusiveInPlace(int[] data) (parallel implementation required)

Testing Your Solution

Correctness

Required

class:	ScanTestSuite.java
package:	scan.studio
source folder:	testing/src/test/java

Optional Work Efficient

class:	WorkEfficientScanTestSuite.java
package:	scan.challenge
source folder:	testing/src/test/java