[PDF] - A F amily of Data P a rallel Derivations Maurice Clint PDF Document

SLIDE 1 A F amily

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Data P a rallel Derivations Maurice Clint Stephen Fitzpatrick T erence J Ha rmer P eter L Kilpatrick Depa rtment

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Computer Science The Queens Universit y

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Belfast Belfast No rthern Ireland UK James M Bo yle Mathematics and Computer Science Division Argonne National Lab

rato

ry Argonne USA This w

rk

is supp

rted

b y SERC Grant GRG

b

y a resea rch studentship from the Depa rtment

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Education fo r No rthern Ireland and b y the Oce

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Scientic Computing US Depa rtment

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Energy

under

Contract WEng

SLIDE 2 Cla rit y V Eciency Highlevel a rchitectureindep endent p rograms

Easier

to construct

Easier

to understand

P
rtable

Ecient p rograms

T

ailo red to pa rticula r machine nonp

rtable
Aw

ash with details

Dicult

to construct

Dicult

to understand

SLIDE 3 Example T ransp

se
f

a Matrix Denition transp

se

A T

f

mn matrix A is an nm matrix such that i j

A

T i j Aj i Highlevel implementation function transpose A m n

generate

n m f n i j A j i

Ecient

sequential implementation fo r squa re matrix m

n

SUBROUTINE transpose An

DO

in DO jin t

Aij

Aij

Aji

Aji

t

END END

SLIDE 4 Our resolution Programmer constructs sp ecication and implementation automatically derived Sp ecication language F unctional p rogramming language

Mathematically

based

Simple

semantics easily understo

d
Useful

mathematical p rop erties

Executable

p rotot yp es Implementation language Whatever required b y implementation environ ment usually version

f

F

rtran
r

C

Ecient
Go
d

vendo r supp

rt
Mo

re convenient than machine language Derivation b y p rogram transfo rmation

SLIDE 5 Program T ransfo rmations Program rewrite rules patter n r epl acement All

ccurrences
f

patter n in p rogram changed to r epl acement

Achieves

a small lo cal change

Based
n

fo rmal p rop erties Clea rly p reserves meaning

f

p rogram

F
rmally

dened in wide sp ectrum gram ma r

F
rmal

p ro

f

p

ssible

Derivations Sequences

f

transfo rmations

Complete

metamo rphosis through many ap plications

f

many transfo rmations

Automatically

applied b y T AMPR system

SLIDE 6 F amily

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Derivations Derivation p erfo rmed in steps

Subderivations
Intermediate

fo rms b et w een sp ecication and implementation languages F

r

example SML

calculus
F
rtran

Same intermediate fo rm fo r

ther

sp ecication languages

ther

a rchitecturesimplementation languages Combinations have included SML Lisp Miranda

calculus
F
rtran

CRA Y F

rtran

D AP F

rtran

C

SLIDE 7 Other subderivationsintermediate fo rms fo r

Optimization

eg function unfolding common sub exp ression elimination

T

ailo ring fo r pa rticula r fo rms

f

data eg spa rse matrices

SML Lisp λ-calculus Evaluated Unfolded Processes Shared Memory Processes & Communication Distributed Memory Sectioned Array Form Common Subexpression DAP Fortran Fortran90 Fortran77 Common Subexpression CRAY Sparse

SLIDE 8 Example Matrixvecto r multiplication

a

b c d

a
b
c
d
fun

timesUve ct

r

V ve ct

r
ve

ct

r
generates

iz e U fn i i nt

U
i

V i

fun

sumUvect

r
re

al

reduceU
fun

innerprodu ct U v ect

r

V v ec to r r ea l

sumtimes

U V

fun

mvmultAm at ri x Vv ec to r v ec to r

generates

iz e A

fniint
in

ne rpr

d

uc t ro w A i V

SML

sp ecication Data pa rallel functions

generate

denes vecto rmatrix

reduce

combines elements

f

vecto rmatrix into single value

SLIDE 9 Optimize generate n i reducen j realtimes

elementA

i j

elementV

j

realplus
SequentialCRA

Y implementation generate and reduce implemented as lo

ps

DO in AVi DO jn AViAVi A i j

Vj
ENDDO

ENDDO D AP implementation wholea rra y

p

erations AVsumcA ma tr V n

SLIDE 10 Assessment T echniques have b een applied to mo re com plex algo rithms fo r sequentialvecto r a rra y and sha redmemo ry a rchitectures Compa ring with indep endent manually con structed implementations

Derived

implementations simila r

Execution

p erfo rmance equal

r

b etter T echniques a re b eing extended fo r y et mo re complex algo rithms fo r distributed and sha red memo ry pa rallel a rchitectures and fo r further sp ecial data structures

SLIDE 11 With derivational app roach p rogrammer

develops

implementation techniques

enco

des techniques as derivations Reusabilit y Multiple sp ecications Multiple implementations

f

each Algo rithm mo died mo dify sp ecication and reapply derivation Extensibilit y New

ptimization

technique

r

new a rchitecture

r

new data rep resentation slot in new subderivation T ransferabilit y Subderivation requires no exp ertise to use One p rogrammer ma y use anothers w

rk

Co rrectness Co rrectness

f

transfo rmations implies co rrectness

f

implementation