Application of rule rewriting system to software automated tuning

Transcription

1 Applicatio of rule rewritig system to software automated tuig Ivaeko P.A., Dorosheko A.Y. Istitute of Software Systems of Natioal Academy of Scieces of Ukraie, Glushkov av. 40, Kyiv, Ukraie Abstract. This paper presets a techical report o developmet of auto-tuig framework TuigGeie for parallel programs performace acceleratio. The framework works with source code of software ad performs code-to-code trasformatios by utilizig facilities of rule-based rewritig system. Such approach gais higher flexibility comparig to existig solutios. This paper explais the framework s lifecycle, offers toolset for optimizatio, basics of architecture, ad presets demo examples with results of tuig computatioally complex parallel program. Keywords Software automated tuig, rule rewritig systems, parallel software optimizatio. 1 Itroductio Curret ad emergig scietific ad idustrial applicatios require sigificat computatio power provided by parallel platforms such as multicore, clusters, Grids, cloud computig ad GPGPU. Therefore, optimizig applicatio code for a give parallel platform is a sigificat part of developmet process. The problem is that powerful computatio platform does ot guaratee applicatio performace: developer effort is required to achieve it. Programmig efficiet algorithm has always bee a challegig task. It is made eve harder by widespread use of multicore processors. The performace growth of a multithreaded program is limited by Amdahl's law [1], so efficiet programs should miimize the fractio of sequetial computatio as well as sychroizatio ad commuicatio overhead. Such optimizatios are usually hardware platform-depedet, ad the program that was optimized for oe problem is likely ot optimal o aother platform. Therefore there is a eed of tools that could perform such adaptatio to cocrete platform i automated mode. Oe traditioal solutio of this problem is provided by parallelizig compilers [2-3]. The quality of automated parallelizatio has icreased recetly; still, such tools are oly applicable to programs with simple structure of computatio. The reasos iclude the complexity of static aalysis of large codebases, icreasig complexity of parallel architectures, as well as their diversity. A alterative to parallelizig compilers is provided by auto-tuig [4] a method that has already prove its efficiecy ad versatility. It ca automate the search for the optimal program variat out of set of provided possibilities, by ruig each cadidate ad measurig its performace o a give parallel architecture. Its mai beefit is high level of abstractio program is optimized without explicit kowledge of hardware implemetatio details, such as umber of cores, cache size or memory access speed o various levels. Istead, the parallel program uses subject domai cocepts such as umber ad size of idepedet tasks, or algorithm details such as data traversal methods. The drawbacks of auto-tuig approach iclude sigificat oe-time costs of optimizatio process itself: if the umber of program variats is large eough, the optimizatio process may ru for may hours ad eve days. Also there is a additioal developmet overhead creatio of auto-tuer applicatio. This paper cosiders a uiversal framework for automated geeratio of auto-tuer applicatios from source code. Proposed approach solves may of the described drawbacks ad is versatile eough to be applied i ay subject domai

2 2 Framework overview TuigGeie framework optimizes programs by geeratig a stad-aloe tuer applicatio. This approach allows ecapsulatig the optimizatio logic i auto-tuer, simplifyig developmet ad maiteace for the target applicatio. To avoid the auto-tuig problems described i Sectio 1, the framework works with program source code usig expert kowledge of a developer ad automatio facilities from the framework. Developers add metadata to the source code i form of special commets-pragmas or Java aotatios. Such expert kowledge reduces umber of program variats to be evaluated ad therefore icreases optimizatio speed. Also such approach allows TuigGeie to provide domaiidepedet optimizatio, ulike may existig specialized tools like ATLAS [5] ad FFTW [6]. Our TuigGeie framework is quite similar to Atue-IL [7] a laguage extesio for auto-tuig. The mai differece of TuigGeie is due to term rewritig egie that is used for source code trasformatio. Represetig program code as a term allows modifyig program structure i a declarative way. This feature sigificatly icreases the capabilities of auto-tuig framework. 3 Tuig lifecycle The software implemetatio of the auto-tuig system is based o rewritig rules system TermWare[8-9]. TermWare implemets a cocept of termial systems, i.e. object structures ad rewritig rules with explicit actios that iteract with the kowledge base. Thaks to this system, TuigGeie ca extract expert kowledge from program source code ad geerate a ew versio of program o each tuig iteratio. TermWare traslates source code ito a term ad provides trasformatio tools based o rewritig rules. Therefore TuigGeie ca perform structural chages i program computatios usig declarative style (without explicit chages to source code). This property distiguishes TuigGeie from similar systems, such as AtueIL[7]; it is quite useful whe there is a eed to optimize large existig parallel programs. Curret versio of TermWare cotais compoets for iteractio with Java ad C# laguages. To support other laguages, a parser to traslate source code ito TermWare laguage ad a pretty-priter should be implemeted. Curret versio of TuigGeie supports Java programs. The commo workflow of the TuigGeie framework is show o Fig. 1. Fig. 1. Tuig workflow TuigGeie accepts as a iput Java source code marked with so-called "pragmas". Pragmas describe cofiguratios ad trasformatios of program that affect its performace. Pragmas are specified maually by program developers, usig Java commets of a special form. Durig the parsig of source code ito a term, the auto-tuer builds a set of cofiguratios based o these expert data. The these cofiguratios are traslated ito rewritig rules. Also o this "prelimiary" stage some values of program parameters are calculated (see the "calculatedvalue" pragma i Sectio 4). The results of this stage iclude a

3 program term, a set of parameterized rewritig rules ad a set of rule cofiguratios C that specify the cocrete parameter values. Each of these cofiguratios specifies a uique variat of iput program. steps: The TuigGeie searches for the most efficiet cofiguratio C opt C, by iteratively performig the followig 1. Select a cofiguratio to test С * C 2. Geerate ad compile the correspodig program variat. The parameters from a give cofiguratio are substituted ito the rules; the these rules are executed o the source term of the parallel program. After the trasformatio is complete, the term is trasformed ito Java source code usig TermWare facilities. The code is compiled usig commo JDK tools. The result of this step is a ew versio of the program ready for performace measuremet. 3. Execute the program ad evaluate its performace. A small laucher class is geerated automatically. It * rus the program ad measures its executio time, therefore computig f ( С ) = t 4. If all cofiguratios from the set C have bee evaluated or if the optimizatio process has used up all the allotted time go to step 5. Else go to step The optimal cofiguratio is selected from a set of all cofiguratio that have bee * * evaluated: C opt = C : f ( C ) = fmi. For this cofiguratio, a optimal program versio is geerated, as i step 2. The program obtaied as a result of steps 1-5 is saved ad executed i a target eviromet. This program is cosidered optimal for a give architecture. 4 TuigGeie facilities As already metioed i sectio 3, the expert kowledge about subject domai ad implemetatio is saved i source code as a special directives called "pragmas" (by aalogy with C laguage). "Pragmas" are actually commets of a special form, therefore they are igored by compiler. Addig pragmas does ot chage the structure of computatio, ad such istrumeted program ca be compiled by ay compiler without additioal libraries. Curretly the TuigGeie framework supports three kids of pragmas: tueableparam specifies a search domai for a optimal value of a umeric variable. E.g. the followig pragma sets the possible values for a threadcout variable as a rage [ ] with a step 10: //tueableparam ame=threadcout start=50 stop=100 step=10 it threadcout = 1; The tueableparam pragma is applicable to the algorithms that use geometrical parallelizatio: it allows to fid the optimal decompositio of computatios by estimatig the size of a block that executes o a sigle processor. It also ca be applied whe we eed to estimate the optimal umber of some limited resources like size of caches or umber of used threads to be used i a program. Aother use of the tueableparam pragma is to fid a optimal threshold value to switch to a differet algorithm. Cosider a sort algorithm that uses QuickSort or MergeSort for large arrays ad applies the same sort recursively to sub-arrays. For some small size of sub-array, it is more efficiet to switch to aother sortig algorithm, such as IsertioSort. The optimal threshold value depeds o processor architecture ad ca be determied experimetally. TuigGeie framework allows fidig this value with miimal chages to source code:. //tueableparam ame=threshold start=10 stop=100 step=5 it threshold = 1; if (high - low < threshold) { isertiosort(array, low, high); } else { addpartitioforquicksort(array, low, high) }. calculatedvalue pragma evaluates some fuctio i a target eviromet ad assigs the resultig value to a give variable: //calculatedvalue ame=hdreadspeed method= //"org.tuig.eviromutils.gethdreadspeed()" it hdkbpersec= 1; This pragma ca be used if some algorithm parameters deped o executio eviromet details, such as executio times of arithmetic operatios or memory access o various levels. All such values are

4 calculated before auto-tuig process starts ad saved i TermWare kowledge base. The data stored i kowledge base is accessible from rewritig rules, so calculatedvalue ca specify the value rage for the tueableparam pragma. I this way, the developer ca ru a small test program to reduce the search domai ad improve auto-tuig speed. The similar approach for GPU computig is described i [10]. bidirectioalcycle ca be used to specify loops were the iteratios ca be ru i ay order. I the followig example TuigGeie will evaluate both icremet (0 to SIZE-1) ad decremet (SIZE-1 to 0) versios: it[] data = ew it[size]; //bidirectioalcycle for (it i=0; i <SIZE; i++) { dosomethigwith(data[i]); } Chagig iteratio order ca affects cache efficiecy ad might sigificatly improve executio time. 5 Case study 5.1 Problem defiitio This sectio presets a case study o the performace tuig of a applicatio for short-term atmospheric circulatio modellig (from hours to several days). Full defiitio of model ad method for umerical solutio ca be foud i [11]. Here we ll show simplified problem defiitio to give a geeral idea. Cosidered model describes macro-scale processes. Their usual horizotal extet is of the order of thousads of kilometers. Typical examples of such processes are equatorial ad mosooal currets, log Rossby waves [12], cycloes ad aticycloes, ridges at etc. Model is based o spherical coordiate system. This work cosiders twodimesioal simplified case that models wid characteristics (directio ad force). Hece model cosists of two evolutio equatios to calculate horizotal compoets of wid force. Model takes state of atmosphere State ( T 0 ) at some momet T 0 as a iput. Suppose we wat to get predictio of state at some momet i future - State( Tm ), Tm > T0. To calculate this program performs series of smaller predictios with time step t << T m T0. So we have recurrece relatio betwee iteratios: State( T ) m = Pr edictio ( State ( T )), m 1 Tm = Tm 1 + t. Note that iteratio step t should be chose from the iterval [5, 20] miutes to provide acceptable accuracy of the result. For the experimet iitial coditios for model were take from a electroic archive of regioal forecastig ceter "Offebach" [13]. Method for umerical solutio of described model allows parallelize computatio o three levels: evolutio equatio level - each of equatio ca be solved idepedetly i scope of oe iteratio; geometric decompositio iput data ca be decomposed for parallel processig; by utilizig a modified additive-averaged operator splittig algorithm [14] it is possible to expad idepedet processig of subtasks to several calculatio iteratios without sigificat loss i accuracy of result Fig. 2 shows how each evolutio equatio is parallelized Fig. 2. Parallelizatio scheme

5 1. We have some State T ) as a iput ad we wat to calculate our predictio for some meteorological ( characteristic u (humidity, horizotal wid speed etc.). T ) State gives us ( u - value of our characteristic at momet T. 2. By utilizig modified additive-averaged operator splittig algorithm we are capable to compute predictio q gives us possibility to compute predictio u + without exchagig itermediate results. So these q steps we are isolated from other sub-tasks. Such approach spares time o sychroizatio but itroduces additioal iaccuracy of results. We defie boudary coditios for momet T + ad iitial coditios. They are costat for steps 3, 4 ad 5. Sice our model is two-dimesioal, calculatio of u is split by special directio o calculatio of u ad 1 u. Each directio is calculated 2 idepedetly. 3. Here geometric decompositio is applied for each directio. Iput area is split o s sub-regios so we have 2 s idepedet sub-tasks. Each subtask iteratively calculates progosis for momets T, T T + q 4. Calculated progoses for T + q from previous steps are eutralized by arithmetical mea. 5. Results from previous step are aggregated ad we derive It s worth metioig, that model is highly scalable sice subtasks with equal size (after decompositio) require equal amout of work idepedetly of what type of physical characteristics is computed. q u + q 5.2 Performace tuig Sectio Tuig facilities provides examples of usig tueableparam ad calculatedvalue pragmas. Let s describe how the third pragma bidirectioalcycle was used i our case study. Moder strategies of workig with processor's cache icrease efficiecy of traversig applicatio's data by precachig eighbourig values. For istace, whe program reads first elemet of array followig elemets also are fetched to fast L1 cache. So whe ext iteratio starts required data might be already i cache. That's why sequetial iteratio over arrays is sigificatly faster. Cout of pre-fetched elemets depeds o size of elemet ad size of cache lie. Basic cocepts of CPU cachig ca be foud at [16]. As already said, everythig should be good whe you access data i array sequetially (eve i iverse order). But i some cases, logically sequetial iteratio is ot sequetial from the data represetatio poit of view. For istace, you ca have Matrix<Iteger> data structure that represets some usual two-dimesioal data (grid) with access by two idexes 'i ' ad 'j'. If itegers are stored i liearized form i oe-dimesioal array the oe of columwise ad row-wise iteratio strategies lead to jumpig amog array elemets, hece high rate of cache misses. With right strategy simple summatio of all elemets of square matrix with 4*10^8 itegers was costatly faster by 6% o my laptop with Core i7-4850hq CPU (32k L1 cache, 256k L2 cache, 6MB L3 Cache). So if your algorithm does a lot of iteratio over big data collectio ad reversig cycle's directio ca lead to data beig accessed i sequetial maer pragma bidirectioalcycle ca speed-up it. For our case study, a applicatio for short-term atmospheric circulatio modellig, the differece due to such chage was almost 15%. Overall performace of parallel program mostly depeds o graularity of data decompositio sice it defies amout of calculatio per subtask hece size of plai parallel sectio. It s reasoable to assume that coarse-graied decompositio will be the most efficiet oe. Let s idetify umber of subdomais as S ad umber of available processors as N. Search area ca be arrowed to values of. Experimet validated assumptio about decompositio of multiprocessor speedup fuctio: T W ( N) = T 0 S N, for istace S [ Ndiv4,4 N] S = N beig the most efficiet oe but also revealed other bedig poit This poit represeted decompositio of iput data ito very small subdomais (about a hudred elemets). Such result ca be explaied by suggestio that all data etirely fit processor caches providig additioal acceleratio of computatio. It s worth metioig that preseted framework eases so-called program s behavior aalysis. Sice it

6 empirically evaluates all cosidered program variatios it s easy to discover tued parameter s impact o overall performace. 5.3 Experimet results This paper does t aalyze coformity of derived meteorological progosis results. Performed research focuses o achievig maximal multiprocessor speedup while preservig acceptable accuracy of results i compariso with sequetial versio. Tab.1. Eviromet cofiguratio Operatig system Width Processors 2хItel Xeo Processor E5405 Quad Core Total cores um. 8 L2-cache capacity 12 Mb RAM 16 Gb A experimet lasted about two hours. Iput data was iterpolated up to size 600x600 to load available computatioal resources. Still, distace betwee poits was about 10 km. Search for optimal value of S was carried by auto-tuer utilizig ad the followig chart describes how log it takes to calculate 24-hour progosis depedig o value of S. It s sigificat to metio that with S = 1 parallel algorithm geerates 4 sub-tasks: 2 equstios 2spartial _ directios. Fig. 3. Time to S relatio Optimized program showed multiprocessor speedup of ( 8) = Coclusio W ad efficiecy ( 8) = 47.75% E. Developmet of efficiet parallel software is a complex task. World-kow thesis states that program is symbiosis of algorithms ad data structures [15]. Parallel programmig model cosiderably complicates both compoets ad the most efficiet programs are derived from their best combiatio. Variety of moder hardware architectures leads to differet combiatios beig optimal for various computatioal eviromets. Thus optimizatio phase cosumes sizeable amout of time ad efforts i developmet of parallel programs. Auto-tuig methodology helps to automate process but i geeral requires creatio of additioal software that performs tuig (tuer) or sigificat chages i software beig optimized. This article itroduced framework for automated geeratio of such tuer-apps. It was desiged with emphasis o miimizatio of required source code chages i optimized program. Mostly such chages are declarative ad do ot affect iitial sources. Such flexibility is reached by utilizig rule-rewritig approach for code trasformatio which sigificatly differs from related solutios

7 Curret TuigGeie versio cotais quite a extesive toolset so reducig time costs of optimizatio is a mai priority i further developmet. There are several promisig directios like itroducig fuctioality for defiig relatio betwee pragmas to reduce amout of probed cofiguratios or partial executio of optimized program. Refereces [1] Amdahl, Gee M.: Validity of the Sigle Processor Approach to Achievig Large-Scale Computig Capabilities. AFIPS Coferece Proceedigs (30): , [2] Oracle Solaris Studio [3] Itel Parallel Compilers [4] Naoo K., Teraishi K., Cavazos J., Suda R. Software Automatic Tuig From Cocepts to State-of-the-Art Results. Spriger, p., [5] R. Whaley, A. Petitet, J. J. Dogarra, Automated em-pirical optimizatios of software ad the ATLAS project. Parallel Computig (1-2), pp.3-35., [6] M. Frigo ad S. Johso, FFTW: A adaptive software architecture for the FF. Acoustics, Speech ad Sigal Processig vol. 3, pp , [7] Schaefer C.A., Pakratius V., ad Tichy W. F. Atue-IL: A istrumetatio laguage for auto-tuig parallel applicatios. Euro-Par '09 Proc. 15th It.Euro-Par Cof. o Parallel Processig Spriger-Verlag Berli, Heidelberg pp. 9-20, [8] TermWare framework [9] Dorosheko, A., Shevcheko, R.: A Rewritig Framework for Rule-Based Programmig Dyamic Applicatios. Fudameta Iformaticae. 72, 1, , [10]Ma W., Krishamoorthy S., Agrawal G. Parameterized Micro-bechmarkig: A Auto-tuig Approach for Complex Applicatios. Proceedigs of the 9th coferece o Computig Frotiers pp , [11]V. A. Prusov, A. E. Dorosheko, R. I. Cherysh, L. N. Guk: Theoretical study of a umerical method to solve a diffusio-covectio problem. Cyberetics ad Systems Aalysis, Volume 44 Issue 2., [12]P. N. Belov, E. P. Borisekov, ad B. D. Pai, Numerical Methods of Weather Predictio {i Russia}, Gidrometeoizdat, Leigrad, [13]Database of regioal meteorological ceter Offebach ftp://ftp-outgoig.dwd.de. [14]V. A. Prusov, A. E. Dorosheko, R. I. Cherysh: A method for umerical solutio of a multidimesioal covectio-diffusio problem. Cyberetics ad Systems Aalysis, Volume 45 Issue 1., [15]Algorithms + Data Structures = Programs Pretice Hall PTR Upper Saddle River, NJ, USA, [16]Harvey G. Crago.: Joes & Bartlett Learig; 1st editio,