Synthesis of certified programs in fixed-point arithmetic, and its application to linear algebra basic

81 Pages·2017·2.72 MB·English

by  Mohamed Amine Najahi

Synthesis of certified programs in fixed-point arithmetic,
and its application to linear algebra basic blocks
Mohamed Amine Najahi
To cite this version:
Mohamed Amine Najahi. Synthesis of certified programs in fixed-point arithmetic, and its application
to linear algebra basic blocks. RAIM: Rencontres Arithmétiques de l’Informatique Mathématique,
Apr 2015, Rennes, France. 7ème Rencontres Arithmétiques de l’Informatique Mathématique, 2015.
￿lirmm-01277374￿
HAL Id: lirmm-01277374
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01277374
Submitted on 22 Feb 2016
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est
archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents
entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non,
lished or not. The documents may come from émanant des établissements d’enseignement et de
teaching and research institutions in France or recherche français ou étrangers, des laboratoires
abroad, or from public or private research centers. publics ou privés.
7èmeRencontresArithmétiquesdel’InformatiqueMathématique(RAIM2015)
Rennes,7-9april2015
Synthesis of certified programs in fixed-point
arithmetic, and its application to
linear algebra basic blocks
AmineNajahi
Univ.PerpignanViaDomitia,DALIproject-team
Univ.Montpellier2,LIRMM,UMR5506
CNRS,LIRMM,UMR5506
DALI
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 1/25
• >50%ofdesigntime[Wil98]
(cid:169) Easyandfasttoimplement (cid:167) Tediousandtimeconsumingtoimplement
(cid:169)
Easilyportable[IEEE754]
(cid:167) Requiresdedicatedhardware (cid:169) Reliesonlyonintegerinstructions
(cid:167) Slowifemulatedinsoftware (cid:169) Efficient
Embeddedsystemstargets
→
haveefficientintegerinstructions
µ-controllers DSPs FPGAs
Fixed-pointarithmeticiswellsuitedforembeddedsystems
But,howtomakeiteasy,fast,andnumericallysafetousebynon-expertprogrammers?
Which arithmetic for computational tasks?
Floating-pointcomputations Fixed-pointcomputations
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 2/25
(cid:167) Requiresdedicatedhardware (cid:169) Reliesonlyonintegerinstructions
(cid:167) Slowifemulatedinsoftware (cid:169) Efficient
Embeddedsystemstargets
→
haveefficientintegerinstructions
µ-controllers DSPs FPGAs
Fixed-pointarithmeticiswellsuitedforembeddedsystems
But,howtomakeiteasy,fast,andnumericallysafetousebynon-expertprogrammers?
Which arithmetic for computational tasks?
Floating-pointcomputations Fixed-pointcomputations
(cid:169) Easyandfasttoimplement (cid:167) Tediousandtimeconsumingtoimplement
(cid:169) Easilyportable[IEEE754] • >50%ofdesigntime[Wil98]
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 2/25
Embeddedsystemstargets
→
haveefficientintegerinstructions
µ-controllers DSPs FPGAs
Fixed-pointarithmeticiswellsuitedforembeddedsystems
But,howtomakeiteasy,fast,andnumericallysafetousebynon-expertprogrammers?
Which arithmetic for computational tasks?
Floating-pointcomputations Fixed-pointcomputations
(cid:169) Easyandfasttoimplement (cid:167) Tediousandtimeconsumingtoimplement
(cid:169) Easilyportable[IEEE754] • >50%ofdesigntime[Wil98]
(cid:167) Requiresdedicatedhardware (cid:169) Reliesonlyonintegerinstructions
(cid:167) Slowifemulatedinsoftware (cid:169) Efficient
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 2/25
But,howtomakeiteasy,fast,andnumericallysafetousebynon-expertprogrammers?
Which arithmetic for computational tasks?
Floating-pointcomputations Fixed-pointcomputations
(cid:169) Easyandfasttoimplement (cid:167) Tediousandtimeconsumingtoimplement
(cid:169) Easilyportable[IEEE754] • >50%ofdesigntime[Wil98]
(cid:167) Requiresdedicatedhardware (cid:169) Reliesonlyonintegerinstructions
(cid:167) Slowifemulatedinsoftware (cid:169) Efficient
Embeddedsystemstargets
→
haveefficientintegerinstructions
µ-controllers DSPs FPGAs
Fixed-pointarithmeticiswellsuitedforembeddedsystems
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 2/25
Which arithmetic for computational tasks?
Floating-pointcomputations Fixed-pointcomputations
(cid:169) Easyandfasttoimplement (cid:167) Tediousandtimeconsumingtoimplement
(cid:169) Easilyportable[IEEE754] • >50%ofdesigntime[Wil98]
(cid:167) Requiresdedicatedhardware (cid:169) Reliesonlyonintegerinstructions
(cid:167) Slowifemulatedinsoftware (cid:169) Efficient
Embeddedsystemstargets
→
haveefficientintegerinstructions
µ-controllers DSPs FPGAs
Fixed-pointarithmeticiswellsuitedforembeddedsystems
But,howtomakeiteasy,fast,andnumericallysafetousebynon-expertprogrammers?
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 2/25
(cid:207) Ourapproach(DALI,Univ.Perpignan):
• certifiedfixed-pointsynthesisfor:
• FinegrainedIPblocks:dot-products,
polynomials,...
• HighlevelIPblocks:matrixmultiplication,
triangularmatrixinversion,Choleskydecomposition
Application description
B1 B4
B3 B6
B2
B5
FloaCt icnogd-peoint ParIaPm belotecrkiszed
Co(cid:207)(cid:207)mbMDiinédeni••easracrdceouodtteoeanmtlvg.aaeel(t.niPrcse(ECflriQaooAUtanIiRoAt-nNNato,,fn-oUUfidrnnxtiivvhIc..PeoRPnlaebivnrneilesnor)eascsr[iko)LfinH[lstMeDyrCn1IPCt4h]Sb:el0os2ciks]: ArAccocmhncituosetrdoSrcaeayptciulsyntrt itememiz aletivoenl OVapltiidmaFiItzWWioaDtnLLioy & eDDnn vtaeemramattlSeaenu2itrsrcaiSfmmo ot Rniriioa-nnnnaae gAttvieicaooc lunnugaerSatnpbicoeelyonrc acitfkii co n optimizationlevel Algorithm Infrastructure for the design of fixed-point system
s
Back-end
Fixed-point C code
Im
HSyignht hleevseisl Compiler tools plementation
Longtermobjective: codesynthesisformatrixinversion Architecture
The DEFIS approach
DEFIS(ANR,2011-2015)
Goal: developtechniquesandtoolstoautomate
fixed-pointprogramming
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 3/25
(cid:207) Ourapproach(DALI,Univ.Perpignan):
• certifiedfixed-pointsynthesisfor:
• FinegrainedIPblocks:dot-products,
polynomials,...
• HighlevelIPblocks:matrixmultiplication,
triangularmatrixinversion,Choleskydecomposition
Longtermobjective: codesynthesisformatrixinversion
The DEFIS approach Application description
B1 B4
B3 B6
DEFIS(ANR,2011-2015) B2 B5
Goal: developtechniquesandtoolstoautomate FloaCt icnogd-peoint ParIaPm belotecrkiszed
fixed-pointprogramming
Co(cid:207)(cid:207)mbDMiinédeni••easracrdceouodtteoeanmtlvg.aaeel(t.niPrcse(ECflriQaooAUtanIiRoAt-nNNato,,fn-oUUfidrnnxtiivvhIc..PeoRPnlaebivnrneilesnor)eascsr[iko)LfinH[lstMeDyrCn1IPCt4h]Sb:el0os2ciks]: ArAccocmhncituosetrdoSrcaeayptciulsyntrt itememiz aletivoenl OVapltiidmaFiItzWWioaDtnLLioy & eDDnn vtaeemramattlSeaenu2itrsrcaiSfmmo ot Rniriioa-nnnnaae gAttvieicaooc lunnugaerSatnpbicoeelyonrc acitfkii co n optimizationlevel Algorithm Infrastructure for the design of fixed-point system
s
Back-end
Fixed-point C code
Im
HSyignht hleevseisl Compiler tools plementation
Architecture
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 3/25
Longtermobjective: codesynthesisformatrixinversion
The DEFIS approach Application description
B1 B4
B3 B6
DEFIS(ANR,2011-2015) B2 B5
Goal: developtechniquesandtoolstoautomate FloaCt icnogd-peoint ParIaPm belotecrkiszed
fixed-pointprogramming
Co(cid:207)(cid:207)(cid:207)mbDOMiinuédreni••eaasracprdceoupodttreoeoanmtalvg.aaceel(t.hniPrcse(E(CflriDQaooAAUtanIiLRoAtI-nNN,atoU,,fn-oUUnfidrinnvxt.iivvhIcP..PeoeRPnrlaebipvnrnieilgesnorn)eascasr[inko)Lfi)nH[l:stMeDyrCn1IPCt4h]Sb:el0os2ciks]: ArAccocmhncituosetrdoSrcaeayptciulsyntrt itememiz aletivoenl OVapltiidmaFiItzWWioaDtnLLioy & eDDnn vtaeemramattlSeaenu2itrsrcaiSfmmo ot Rniriioa-nnnnaae gAttvieicaooc lunnugaerSatnpbicoeelyonrc acitfkii co n optimizationlevel Algorithm Infrastructure for the design of fixed-point systems
Back-end
• certifiedfixed-pointsynthesisfor:
• FinegrainedIPblocks:dot-products, Fixed-point C code
• pHtroiialgynnhgoulmleaivraemlsl,aI.tP.r.ixbinlovecrkssio:n,mCahtroixlemskuyltidpeliccoamtiopno,sition HSyignht hleevseisl Compiler tools Implementation
Architecture
M.A.Najahi(DALIUPVD/LIRMM,UM2,CNRS) Synthesisofcertifiedprogramsinfixed-pointarithmetic,anditsapplicationtolinearalgebrabasicblocks 3/25