Ohio State University Department of Computer Science and Engineering Data-Centric Transformations on...
-
Upload
allen-mccarthy -
Category
Documents
-
view
217 -
download
1
Transcript of Ohio State University Department of Computer Science and Engineering Data-Centric Transformations on...
Ohio State University Department of Computer Science and Engineering
Data-Centric Transformations on Data-Centric Transformations on Non-Integer Iteration SpacesNon-Integer Iteration Spaces
Swarup Kumar Sahoo
Gagan Agrawal
The Ohio State University
Ohio State University Department of Computer Science and Engineering
RoadmapRoadmap• Motivation • Background• System Overview• XQuery, Low and High Level schema and Mapping
schema• Compiler Analysis and Algorithm• Parallelization• Experiment • Summary and Future Work
Ohio State University Department of Computer Science and Engineering
MotivationMotivation
• Declarative and application specific languages – Uses high-level abstractions
– Simplifies development of applications
• Use of restructuring transformations– Difficult due to these abstractions
• Goal : Apply data-centric transformations– On integer and non-integer based iteration space while providing
high-level abstractions/virtual view of underlying datasets.
Ohio State University Department of Computer Science and Engineering
BackgroundBackground
• Data-centric transformation :– Input data is brought into memory/cache in chunks or
shackles and then corresponding program fragments or loop iterations requiring access to these data are executed.
– Helps in improving data locality.• Integer based iteration space
– Loop takes integer values with constant step-size between a lower and upper bound.
• Non-integer based iteration space– Loop takes values from a sequence or set of real numbers,
strings, or any other data types.– Easily expressible in declarative languages
Ohio State University Department of Computer Science and Engineering
Example: Data-centric Example: Data-centric transformationtransformation
for i:= 1 to 3
{
Count the number of occurrences of i in a list of digits }
Ohio State University Department of Computer Science and Engineering
Naïve Strategy Naïve Strategy
DatasetOutput
0
2
2
224
1
11
1 1
5
33
33
336
Requires 3 Scans
Counter
Ohio State University Department of Computer Science and Engineering
Data Centric StrategyData Centric Strategy
DatasetOutput
0 0 0
2
2
224
1
11
1 1
5
33
33
336
Requires just one scan
Counter1 Counter2 Counter3
21 11
Ohio State University Department of Computer Science and Engineering
Example: Data-centric Example: Data-centric transformation with non-integer transformation with non-integer
iteration spaceiteration space
for each distinct color (green, blue, pink) {
with that color }
Ohio State University Department of Computer Science and Engineering
Naïve Strategy Naïve Strategy
DatasetOutput
000
Requires 3 Scans
555
Counter
Ohio State University Department of Computer Science and Engineering
Data Centric StrategyData Centric Strategy
DatasetsOutput
0 0 0
Requires just one scan
Counter1 Counter2 Counter3
Mapping
5 5 51 112
Ohio State University Department of Computer Science and Engineering
Previous work and ContributionsPrevious work and Contributions
• Related Work– Data-centric multilevel blocking (Pingali et. al., PLDI 1997)– Sparse matrix code synthesis from high-level specifications
(Pingali et. al., SC 2000)– Supporting XML Based high-level abstraction on flat-file
datasets (LCPC 2003, XIME-P 2004)• Contributions of this paper
– An improved data- centric transformation algorithm which works on both integer and non-integer based iteration spaces.
– Handling of out-of-core computations involving multi-dimensional datasets, without limiting the organization of low-level datasets.
– Automatic parallelization of the considered class of application.
Ohio State University Department of Computer Science and Engineering
System OverviewSystem OverviewHigh levelXML Schema
Mapping Schema
Dataset
CompilerMapping Service
System OverviewSystem Overview
Low levelXML Schema
Low-level Library
Cluster with Disk
XQuery Source Code
Ohio State University Department of Computer Science and Engineering
XQuery and XML SchemasXQuery and XML Schemas
• High-level declarative languages ease application development– XQuery is a high-level language for processing XML datasets– Derived from database, declarative, and functional languages!
• High-level schema– XML is used to provide a virtual view of the dataset
• Low-level schema – reflects actual physical layout.
• Mapping schema:– describes mapping between each element of high-level
schema and low-level schema
Ohio State University Department of Computer Science and Engineering
Oil Reservoir SimulationOil Reservoir Simulation• Support cost-effective Oil
Production• Simulations on a 3-D grid• 17 variables and cell
locations in 3-D grid at each time step
• Computation of bypassed regions– Expression to determine if a
cell is bypassed for a time-step– Within a spatial region and
range of time steps– Grid cells that are bypassed for
every time-step in the rangeOil Reservoir management
Ohio State University Department of Computer Science and Engineering
High-Level SchemaHigh-Level Schema< xs:element name="data" maxOccurs="unbounded" >
< xs:complexType > < xs:sequence (unique x,y,z,t) >
< xs:element name="x" type="xs:integer"/ > < xs:element name="y" type="xs:integer"/ > < xs:element name="z" type="xs:integer"/ > < xs:element name="time" type="xs:integer"/ > < xs:element name="velocity" type="xs:float"/ > < xs:element name="mom" type="xs:float"/ >
< /xs:sequence >
< /xs:complexType >
< /xs:element >
Ohio State University Department of Computer Science and Engineering
High-Level XQuery Code Of Oil High-Level XQuery Code Of Oil Reservoir managementReservoir management
unordered( for $i in ($x1 to $x2)
for $j in ($y1 to $y2) for $k in ($z1 to $z2)
let $p := document("OilRes.xml")/datawhere ($p/x=$i) and ($p/y = $j) and ($p/z = $k) and ($p/time >= $tmin) and ($p/time <= $tmax) return <info> <coord> {$i, $j, $k} </x-coord> <summary> { analyze($p) } </summary> </info>
)
Ohio State University Department of Computer Science and Engineering
Low-Level SchemaLow-Level Schema<file name="info">
<sequence> <group name="data">
<attribute name="time"> <datatype> integer </datatype> <dataspace> <rank> 1 </rank> <dimension> [1] </dimension> </dataspace> </attribute>
<dataset name="velocity"> <datatype> float </datatype> <dataspace> <rank> 1 </rank> <dimension> [x] </dimension> </dataspace> </dataset>
..............
</group> </sequence>
</file>
Ohio State University Department of Computer Science and Engineering
Mapping SchemaMapping Schema
//high/data/velocity //low/info/data/velocity
//high/data/time //low/info/data/time
//high/data/mom //low/info/data/mom [index(//low/info/data/velocity, 1)]
//high/data/x //low/coord/x [index(//low/info/data/velocity, 1)]
Ohio State University Department of Computer Science and Engineering
Modified Oil Reservoir management Modified Oil Reservoir management with non-integer iteration spacewith non-integer iteration space
let $src = document(“Oil.xml”)//data/x,y,z
Let $coord = distinct-values($src)
unordered(
for $C in $coord
let $p := document("OilRes.xml")/datawhere ($p/x=$C/x) and ($p/y = $C/y) and ($p/z = $C/z)
and ($p/time >= $tmin) and ($p/time <= $tmax)
return
<info>
<coord> {$C/x, $C/y, $C/z} </x-coord>
<summary> { analyze($p) } </summary>
</info>
)
Ohio State University Department of Computer Science and Engineering
Basic steps in our Data Centric Basic steps in our Data Centric Transformation algorithmTransformation algorithm
• Mapping Function T :Iteration space → High-Level data
• Mapping Function C : High-Level data → Low-Level data
• Mapping Function C · T = M : Iteration space → Low-Level data
• Our Goal is to compute M-1 and use the following steps– Iterate over each data element in actual storage – Find out iterations of the original loop in which they are accessed
using M-1.– Access required elements of other datasets.– Execute computation corresponding to those iterations.
Ohio State University Department of Computer Science and Engineering
Handling non-integer based iteration Handling non-integer based iteration space with hash-tablespace with hash-table
• Abstract integer iteration space:– Based on the unique sequence number of each element
in the actual iteration space.
– One-to-one correspondence between actual and abstract iteration space
» Hash table can be used to create this mapping
» Sequence number in the hash table indicates the iteration instance in abstract iteration space
Ohio State University Department of Computer Science and Engineering
Template for Generated Code using Template for Generated Code using hash tablehash table
Generated_Query { Go through the datasets and create a list of tuples, each denoting an
iterationForeach i in the list of tuples { apply hash function on i If i is not present in hash table, enter i into hash table and store its
sequence number and the corresponding output element }
For k = 1, …, NO_OF_CHUNKS { Read kth chunk of dataset S1 using HDF5 functions. Foreach of the other datasets S2, … , Sn
access the required chunk of the dataset. Foreach data element in the chunks of data {
compute the iteration instance i. apply the hash function and determine the corresponding output element.
apply the reduction computation and update the output. } }
}
Ohio State University Department of Computer Science and Engineering
Handling non-integer based iteration Handling non-integer based iteration space without hash-tablespace without hash-table
• Find out the two choices required for construction of actual iteration space
• Determine the procedure to construct the actual iteration space
• From High-level schema, select the attributes forming unique set of tuples (V)
• Consider the set of attributes forming the iteration space as P.
• If P is not a subset of V, we use hash table.• Else if P = V, transformation is done without hash
table.• Else if P is a proper subset of V, then the choice
depends on the presence of duplicate tuples.
Ohio State University Department of Computer Science and Engineering
ParallelizationParallelization• Two obvious ways to parallelize
– First one is to parallelize the for loop going through different chunks
– Second one is to parallelize the for loop going through data in each chunk
• Choose the method depending on the number of chunks and chunk size.
• Reduction operation required to combine values from different processors.
Ohio State University Department of Computer Science and Engineering
Experimental test bedExperimental test bed• HDF5 version 1.6.3 ( uses MPI-I/O for parallel I/O )
• Sequential experiments - 700 MHz PIII machine,1GB memory, Linux version 2.4.18
• Parallel Experiments – Itanium 2 cluster with dual 1.3 Ghz Itanium 2 processor nodes, 4 GB RAM, 80 GB hard drive
• Four applications– Transaction database analysis
– Original Oil reservoir simulation
– Modified Oil reservoir simulation
– Virtual microscope
Ohio State University Department of Computer Science and Engineering
Experimental resultExperimental resultVirtual Microscope
Oil Reservoir Simulation
Modified Oil Reservoir Simulation
Transaction database Analysis
With DCT without hash table
1.32 2.64 2.08 -
With DCT using hash table
- - 2.97 7.57
Without DCT
10.65 27.13 23.69 96.11
Execution time (sec.) using different versions of transformation algorithm
Ohio State University Department of Computer Science and Engineering
Experimental resultExperimental result
Parallel Performance of Virtual
Microscope
0
20
40
60
80
100
1 2 4 8
Number of Processors
Ex
ec
uti
on
Tim
e (
Se
c)
Ohio State University Department of Computer Science and Engineering
Experimental resultExperimental result
Parallel Performance of Oil Reservoir
Simulation
010203040506070
1 2 4 8
Number of Processors
Ex
ec
uti
on
Tim
e (
se
c)
Ohio State University Department of Computer Science and Engineering
Experimental resultExperimental resultParallel Performance of Modified Oil
Reservoir Simulation
0
10
20
30
40
1 2 4 8
Number of Processors
Ex
ec
uti
on
Tim
e (
se
c)
Ohio State University Department of Computer Science and Engineering
Experimental resultExperimental result
Parallel Performance of Transaction
Database Analysis
010203040506070
1 2 4 8
Number of Processors
Ex
ec
uti
on
Tim
e (
se
c)
Ohio State University Department of Computer Science and Engineering
SummarySummary• Compiler techniques
– Perform data centric transformations automatically on integer and non-integer based iteration space.
– More efficient method without using has table for data centric transformation on non-integer based iteration space.
– Support High-level abstractions on complex low-level data formats.
– Parallelization of the considered class of queries.• Future Work
– Experimental results on more applications.– Compare performance with manual implementations – Formalize the mapping schema.– Extend applicability of the algorithm to more general class of
queries.