Fast Computation of Database Operations using Graphics Processors Naga K. Govindaraju Univ. of North Carolina Modified By, Mahendra Chavan forCS632

Fast Computation of Database Operations using Graphics Processors

Fast Computation of Database Operations using Graphics Processors

Naga K. Govindaraju

Univ. of North Carolina

Modified By,

Mahendra Chavan for CS632

GoalGoal

• Utilize graphics processors for fast computation of common database operations

Motivation: Fast operationsMotivation: Fast operations

• Increasing database sizes

• Faster processor speeds but low improvement in query execution time– Memory stalls– Branch mispredictions– Resource stalls Eg. Instruction dependency

• Utilize the available architectural features and exploit parallel execution possibilities

Graphics ProcessorsGraphics Processors

• Present in almost every PC

• Have multiple vertex and pixel processing engines running parallel

• Can process tens of millions of geometric primitives per second

• Peak Perf. Of GPU is increasing at the rate of 2.5-3 times a year!

• Programmable- fragment programs – executed on pixel processing engines

Main ContributionsMain Contributions

• Algorithms for predicates, boolean combinations and aggregations

• Utilize SIMD capabilities of pixel processing engines

• They have used these algorithms for selection queries on one or more attributes and aggregate queries

Related WorkRelated Work

• Hardware Acceleration for DB operations– Vector processors for relational DB operations

[Meki and Kambayashi 2000]– SIMD instructions for relational DB operations

[ Zhou and Ross 2002]– GPUs for spatial selections and joins [Sun et al. 2003]

Graphics Processors: Design IssuesGraphics Processors: Design Issues

• Programming model is limited due to lack of random access writes– Design algorithms avoiding data rearrangements

• Programmable pipeline has poor branching– Design algorithms without branching in programmable

pipeline - evaluate branches using fixed function tests

Frame BufferFrame Buffer

• Pixels stored on graphics card in a frame buffer.

• Frame buffer conceptually divided into:

• Color Buffer– Stores color component of each pixel in the frame buffer

• Depth Buffer– Stores depth value associated with each pixel. The depth is

used to determine surface visibility

• Stencil Buffer– Stores stencil value for each pixel . Called Stencil because, it

is typically used for enabling/disabling writes to frame buffer

Graphics PipelineGraphics Pipeline

Vertices

Vertex Processing

Engine

Vertex Processing

Engine

Pixel processing

EngineSetupEngine Alpha TestAlpha Test

Stencil TestStencil Test

Depth TestDepth Test

Graphics PipelineGraphics Pipeline

• Vertex Processing Engine – Transforms vertices to points on screen

• Setup Engine– Generates Info. For color, depth etc. associated with primitive

vertices

• Pixel processing Engines– Fragment processors, performs a series of tests before

writing the fragments to frame buffer

Pixel processing EnginesPixel processing Engines

• Alpha Test– Compares fragments alpha value to user-specified reference

value

• Stencil Test– Compares fragments’ pixel’s stencil value to user-specified

reference value

• Depth Test– Compares depth value of the fragment to the reference depth

value.

OperatorsOperators

• =

• <

• >

• <=

• >=

• Never

• Always

Occlusion Query Occlusion Query

• Users can supply custom fragment programs on each fragment

Fragment ProgramsFragment Programs

•Gives no. of fragments that pass different no. of tests

Radeon R770 GPU by AMD Graphics Product Group

Data Representation on GPUsData Representation on GPUs

• Textures – 2 D arrays- may have multiple channels

• We store data in textures in floating point formats

• To perform computations on the values, render the quadrilateral, generate fragments, run fragment programs and perform tests!

Stencil TestsStencil Tests

• Fragments failing Stencil test are rejected from the rasterization pipeline

• Stencil Operations– KEEP: keep the stencil value in the stencil buffer– INCR: stencil value ++– DECR: stencil value –– ZERO: stencil value = 0 – REPLACE: stencil value = reference value– INVERT: bitwise invert (stencil value)

Stencil and Depth TestsStencil and Depth Tests

• We can setup the stencilOP routine as below

• For each fragment , three possible outcomes, based on the outcome, corresponding stencil op. is executed

• Op1: when a fragment fails stencil test

• Op2: when a fragment passes stencil test but fails depth test

• Op3: when a fragment passes stencil and depth test

OutlineOutline

• Database Operations on GPUs

• Implementation & Results

• Analysis

• Conclusions

OutlineOutline



• Analysis

• Conclusions

OverviewOverview

• Database operations require comparisons

• Utilize depth test functionality of GPUs for performing comparisons– Implements all possible comparisons <, <=, >=, >, ==, !=,

ALWAYS, NEVER

• Utilize stencil test for data validation and storing results of comparison operations

Basic OperationsBasic Operations

Basic SQL query

Select A

From T

Where C

A= attributes or aggregations (SUM, COUNT, MAX etc)

T=relational table

C= Boolean Combination of Predicates (using operators AND, OR, NOT)

Outline: Database OperationsOutline: Database Operations

• Predicate Evaluation– (a op constant) – depth test and stencil test– (a op b) = (a-b op 0 ) – can be executed on GPUs

• Boolean Combinations of Predicates– Express as CNF and repetitively use stencil tests

• Aggregations– Occlusion queries


• Predicate Evaluation

• Boolean Combinations of Predicates

• Aggregations

Basic OperationsBasic Operations

• Predicates – ai op constant or ai op aj

– Op is one of <,>,<=,>=,!=, =, TRUE, FALSE

• Boolean combinations – Conjunctive Normal Form (CNF) expression evaluation

• Aggregations – COUNT, SUM, MAX, MEDIAN, AVG

Predicate EvaluationPredicate Evaluation

• ai op constant (d)

– Copy the attribute values ai into depth buffer

– Define the comparison operation using depth test– Draw a screen filling quad at depth d

Screen

PIf ( ai op d )

pass fragment

Else

reject fragment

ai op d

d

Predicate EvaluationPredicate Evaluation

• ai op aj

– Treat as (ai – aj) op 0

• Semi-linear queries– Defined as linear combination of attribute values compared

against a constant– Linear combination is computed as a dot product of two

vectors– Utilize the vector processing capabilities of GPUs

Data ValidationData Validation

• Performed using stencil test

• Valid stencil values are set to a given value “s”

• Data values that fail predicate evaluation are set to “zero”




• Aggregations

Boolean CombinationsBoolean Combinations

• Expression provided as a CNF

• CNF is of form (A1 AND A2 AND … AND Ak)

where Ai = (Bi1 OR Bi

2 OR … OR Bimi )

• CNF does not have NOT operator– If CNF has a NOT operator, invert comparison operation to

eliminate NOT

Eg. NOT (ai < d) => (ai >= d)

Boolean CombinationBoolean Combination

• We will focus on (A1 AND A2)

• All cases are considered

– A1 = (TRUE AND A1)

– If Ei = (A1 AND A2 AND … AND Ai-1 AND Ai),

Ei = (Ei-1 AND Ai)

• Clear stencil value to 1

• For each Ai , i=1,….,k

• do

– if (mod(I,2)) /* Valid stencil value is 1 */• Stencil test to pass if stencil value is equal to 1• StencilOp (KEEP,KEPP, INCR)

– Else• Stencil test to pass if stencil value is equal to 2• StencilOp (KEEP,KEPP, DECR)

– Endif

– For each Bij, j=1,…..,mi– Do

• Perform Bij using COMPARE /* depth test */– End for

– If (mod(I,2)) /* valid stencil value is 2 */• If stencil value on screen is 1 , REPLACE with 0

– Else /* valid stencil value is 1 */• If stencil value on screen is 2, REPLACE with 0

– Endif

• End For

A1 AND A2A1 AND A2

A1

B21

B22

B23

A1 AND A2A1 AND A2

Stencil value = 1

A1 AND A2A1 AND A2

A1

Stencil value = 1

A1 AND A2A1 AND A2

A1

Stencil value = 0

Stencil value = 2

A1 AND A2A1 AND A2

A1

St = 0

B21

St=1

B22

St=1

B23

St=1

St=0St=2

A1 AND A2A1 AND A2

A1

Stencil = 0

St = 0

B21

B22

B23

St=1

St=1

St=1

A1 AND A2A1 AND A2

St = 0

St=1A1 AND B2

1

St = 1A1 AND B2

2 St=1

A1 AND B23

Range QueryRange Query

• Compute ai within [low, high]

– Evaluated as ( ai >= low ) AND ( ai <= high )




• Aggregations

AggregationsAggregations

• COUNT, MAX, MIN, SUM, AVG

• No data rearrangements

COUNTCOUNT

• Use occlusion queries to get pixel pass count

• Syntax:– Begin occlusion query– Perform database operation– End occlusion query– Get count of number of attributes that passed database

operation

• Involves no additional overhead!

MAX, MIN, MEDIANMAX, MIN, MEDIAN

• We compute Kth-largest number

• Traditional algorithms require data rearrangements

• We perform no data rearrangements, no frame buffer readbacks

K-th Largest NumberK-th Largest Number

• Say vk is the k-th largest number

• How do we generate a number m equal to vk?

– Without knowing vk’s bit-representation and using comparisons

Our algorithmOur algorithm

• b_max = max. no. of bits in the values in tex

• x=0

• For i= b_max-1 down to 0– Count = Compare (text >= x + 2^i)– If Count > k-1

• x=x+2^i

• Return x

K-th Largest NumberK-th Largest Number

• Lemma: Let vk be the k-th largest number. Let count

be the number of values >= m

– If count > (k-1): m<= vk

– If count <= (k-1): m>vk

• Apply the earlier algorithm ensuring that count >(k-1)

ExampleExample

• Vk = 11101001

• M = 00000000

ExampleExample

• Vk = 11101001

• M = 10000000

• M <= Vk

ExampleExample

• Vk = 11101001

• M = 11000000

• M <= Vk

ExampleExample

• Vk = 11101001

• M = 11100000

• M <= Vk

ExampleExample

• Vk = 11101001

• M = 11110000

• M > Vk

Make the bit 0

M = 11100000

ExampleExample

• Vk = 11101001

• M = 11101000

• M <= Vk

ExampleExample

• Vk = 11101001

• M = 11101100

• M > Vk

• Make this bit 0

• M = 11101000

ExampleExample

• Vk = 11101001

• M = 11101010

• M > Vk

• M = 11101000

ExampleExample

• Vk = 11101001

• M = 11101001

• M <= Vk

ExampleExample

• Integers ranging from 0 to 255

• Represent them in depth buffer– Idea – Use depth functions to perform comparisons– Use NV_occlusion_query to determine maximum

Example: Parallel MaxExample: Parallel Max• S={10,24,37,99,192,200,200,232}

• Step 1: Draw Quad at 128– S = {10,24,37,99,192,200,200,232}

• Step 2: Draw Quad at 192– S = {10,24,37,192,200,200,232}


• Step 4: Draw Quad at 240 – No values pass


• Step 6,7,8: Draw Quads at 236,234,233 – No values pass

• Max is 232

SUM and AVGSUM and AVG

• Mipmaps – multi resolution textures consisting of multiple levels

• Highest level contains average of all values at lowest level

• SUM = AVG * COUNT

• Problems with mipmaps

– If we want sum of a subset of values then we have to introduce conditions in the fragment programs

– Floating point representations may have problems

AccumulatorAccumulator

• Data representation is of form

• ak 2k + ak-1 2k-1 + … + a0

Sum = sum(ak) 2k+ sum(ak-1) 2k-1+…+sum(a0)

Current GPUs support no bit-masking operations

AVG = SUM/COUNT

TestBitTestBit

• Read the data value from texture, say ai

• F= frac(ai/2k+1)

• If F>=0.5, then k-th bit of ai is 1

• Set F to alpha value. Alpha test passes a fragment if alpha value>=0.5

OutlineOutline



• Analysis

• Conclusions

ImplementationImplementation

• Dell Precision Workstation with Dual 2.8GHz Xeon Processor

• NVIDIA GeForce FX 5900 Ultra GPU

• 2GB RAM

ImplementationImplementation

• CPU – Intel compiler 7.1 with hyperthreading, multi-threading, SIMD optimizations

• GPU – NVIDIA Cg Compiler

BenchmarksBenchmarks

• TCP/IP database with 1 million records and four attributes

• Census database with 360K records

Copy TimeCopy Time

Predicate Evaluation (3 times faster)Predicate Evaluation (3 times faster)

Range Query(5.5 times faster)Range Query(5.5 times faster)

Multi-Attribute Query (2 times)Multi-Attribute Query (2 times)

Semi-linear Query (9 times faster)Semi-linear Query (9 times faster)

COUNTCOUNT

• Same timings for GPU implementation

Kth-Largest for median(2.5 times)Kth-Largest for median(2.5 times)

Kth-LargestKth-Largest

Kth-Largest conditionalKth-Largest conditional

Accumulator(20 times slower!)Accumulator(20 times slower!)

OutlineOutline



• Analysis

• Conclusions

Analysis: IssuesAnalysis: Issues

• Precision – Currently depth buffer has only 24 bit precision , inadequate

• Copy time– Copy from texture to depth buffer – no mechanism in GPU

• Integer arithmetic– Not enough arithmetic inst. In pixel processing engines

• Depth compare masking– Useful to have comparison mask for depth function

Analysis: IssuesAnalysis: Issues

• Memory management– Current GPUS have 512 MB video memory, we may use the

out-of–core techniques and swap

• No random writes– No data re-arrangements possible

Analysis: PerformanceAnalysis: Performance

• Relative Performance Gain– High Performance – Predicate evaluation, multi-attribute

queries, semi-linear queries, count– Medium Performance – Kth-largest number– Low Performance - Accumulator

High PerformanceHigh Performance

• Parallel pixel processing engines

• Pipelining– Multi-attribute queries get advantage

• Early Depth culling– Before passing through the pixel processing engine

• Eliminate branch mispredictions

Medium PerformanceMedium Performance

• Parallelism

• FX 5900 has clock speed 450MHz, 8 pixel processing engines

• Rendering single 1000x1000 quad takes 0.278ms

• Rendering 19 such quads take 5.28ms. Observed time is 6.6ms

• 80% efficiency in parallelism!!

Low PerformanceLow Performance

• No gain over SIMD based CPU implementation

• Two main reasons:– Lack of integer-arithmetic– Clock rate

OutlineOutline



• Analysis

• Conclusions

ConclusionsConclusions

• Novel algorithms to perform database operations on GPUs

– Evaluation of predicates, boolean combinations of predicates, aggregations

• Algorithms take into account GPU limitations– No data rearrangements– No frame buffer readbacks

ConclusionsConclusions

• Preliminary comparisons with optimized CPU implementations is promising

• Discussed possible improvements on GPUs

• GPU as a useful co-processor

Relational JoinsRelational Joins

• Modern GPUs have thread groups

• Each thread group have several threads

• Data Parallel primitives– Map– Scatter – scatters the Data of a relation with respect to an

array L– Gather – reverse of scatter– Split – Divides the relation into a number of disjoint partitions

with a given partitioning function

NINLJNINLJ

R

S

Thread Group 1

Thread Group j

Thread Group i

Thread Group Bp

INLJINLJ

• Used Cache Optimized Search Trees (CSS trees) for index structure

• Inner relation as the CSS tree

• Multiple keys are searched in parallel on the tree

Sort Merge joinSort Merge join

• Merge step is done in parallel

• 3 steps– Divide relation S into Q chunks Q= ||S|| / M– Find the corresponding matching chunks from R by using the

start and end of each chunk of S– Merge each pair of S and R chunk in parallel. 1 thread group

per pair.

Hash joinHash join

• Partitioning– Use the Split primitive to partition both the relations

• Matching– Read the inner relation in memory relation– Each tuple from the outer relation uses sequential/binary

search on the inner relation– For binary search, the inner relation will be sorted using

bitonic sort.

Documents

Fast Computation of Database Operations using Graphics Processors Naga K. Govindaraju Univ. of North Carolina Modified By, Mahendra Chavan forCS632