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From Novel Mathematics to Efficient Algorithms. Do We Have Proper SD

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From Novel Mathematics to Efficient Algorithms. Do We Have Proper SD F.V.Tkachov TalkatComputerParticlePhysics(CPP2001),28-30November2001,Tokyo 1 Fromnovelmathematicstoefficientalgorithms. DowehaveproperSDfoundationtobuildfuture? AlbertaThy03-02 hep-ph/0202033 FyodorV.Tkachov INRRAS,Moscow117312Russia;UniversityofAlberta,Edmonton,T6J2J1Canada Computerimplementationofsophisticatedalgorithmsforphysicsapplicationsisgreatlyfacilitatedbythenew generationofcomponent-orientedSDtechnologiespioneeredbyWirth'sOberonandembracedbythesoftware industry(Sun'sJavaandMicrosoft'sC#).InastarkcontrastwiththedeeplyflawedC++,theOberontechnolo- gies(specifically,theComponentPascalandtheBlackBoxdevelopmentenvironment)offeranunparalleledSD platformforbuildingscientificapplicationsfromsophisticateddataprocessingtodemandingsymboliccalcula- tions.Specificexamplesarediscussed. Thisworkshopistakingplaceagainstthebackdropofa • the state of the art in SD is not the amateurish and theoreticalcrisiswithcalculationsforthe existing and fu- deeply flawed C++ [10] but Oberon-2 [11] (the best sup- ture colliders; theorists are behind experimentalists preci- portedimplementationknownasComponentPascal[12]); sion-wise,anditisnotclearwhen(andif)thegapwillbe • i significantly narrowed. The theory for LEP1 [1] was im- theOberon technologies have ushered in what may be plementedwithintheframeworkofthecalculationalpara- calledthemodernstandardSDparadigm;theparadigmen- digmbasedontheuseof Schoonschip and derivatives [2] compassesthetwodominantmega-projectsofthesoftware for vector and spinor algebra; dilogarithms for (one loop) industry:Sun’sJavaandMicrosoft’s.NET; integrals [3]; and FORTRAN for numerical calculations; • but Oberon-2/Component Pascal, while capable of with the different pieces connected [4] by a tremendous peaceful coexistence with both Java and C#, remains the amountofhandwork.Butalreadytheone-loopcalculations bestfoundationforcomplexscientificapplications. forLEP2arefarfrombeingcomplete.What about 2 loop Threecausesofthecalculationalcrisis calculations in the Standard Model that are needed for theoreticalnumberstomatchdataprecision-wise? First, there is the problem of politics around research Thepurposeofthisworkshopasexplicitlyset forth by fundallocation,andthe research community has not done theorganizersinthefirstbulletinwassupposedtobe enoughtominimizeitsadverseeffectsontheefficiencyof research. Politics means desinformation (which spans the “tosetupthebasesfora morecoherentand entirerangefromomissionstoplagiarism),andso“stifles professional approachofouractivitiesboth communication,breedingdistrustandinefficiency…”—in at the theoretical as well as the technical the final respect, causing a crippling misallocation of re- level.” searchfunds ii .Atatechnicallevel,theresource allocation Toappreciatewhat morecoherent meanshere,consider politics obstructs component software iii : why should one thefactthatthisworkshophasseenpresentationsfromthe bothertomakepublic a software component for, say, fast GRACE [5], CompHEP [6], OMEGA [7], and GiNaC [8] Diractracecalculationsifthereisnocredittobegottenfor projects — all featuring different and incompatible sym- it? bolicalgebraengines,withoutanywaytoshareapplication- Second,thetheoreticalcommunity’scommandofmathe- specificalgorithmsexceptbyrewritingsourcecode.Clearly matical methods seems to be below what’s required by coherence betweenalltheseprojectsislackingtoaworry- perturbativequantumfieldtheory—notinregardofcom- ingdegree. binatorial complexity but in regard of the conceptual arXiv:hep-ph/0202033 v2 11 Feb 2002 Professional is,inessence,aboutefficiency:itistheef- framework.ItisprofoundlymisleadingtoregardFeynman ficiencyinperformingataskthatdifferentiatesprofession- diagramsasordinaryintegrals;theyaregeneralizedobjects alsfromamateurs.Mostimportantly,aprofessionalisseen and should be treated as such, with full understanding of bythetoolss/heuses. theconceptsandmethodsofdistributiontheory(Idiscussed Itis perfectly obvious that many of the problems theo- this in [13]). Generalized solutions, regularization (in the ristsareencounteringresult from a lack of a proper com- sense of numerical methods), etc. are key concepts here. monSDfoundationforthealgorithmdesignwork.Yetsur- prisingly little has been said about this at this workshop: i For simplicity, I will not explicitly distinguish Oberon (1986) and D. Perret-Gallixmentionedtheproblemofstandardsinhis Oberon-2(1991),andwillalwayshaveinviewthelatter. introduction, and A.Kryukov discussed a technology that ii One can invent calculational methods on which a whole calcula- couldhelpeliminateredundanteffortinfieldtheorymodel tional industry would thrive, with the results receiving thousands of building[9].Andthatwasit. citations—andthenbetoldthatone“isnotdoinganyphysics”andbe deniedanessentialsupport. Thepresenttalkarguesthat: iii Componentsoftwareimpliesthatonecanreplaceamoduleencap- • physicistsasa community are actually well behind the sulating,say,analgorithmfordoingDiractracesandconformingto state of the art in software engineering; the circumstance pre-definedinterfacespecifications,inone’ssystembypassingunnec- resultsinahugeandcontinuingwasteofresources,bound essaryencumbranceslikethelinkingstepandmaintenanceofheader files,andimmediatelystartusingthemodulewithoutrewriting/recom- tocontinueintothefuture; piling/relinkingone’sapplicationprogramwrittentothesamespecifi- cations.ThisconceptisimplementedinOberon,JavaandC#—butis impossiblewithFORTRAN,CandC++. F.V.Tkachov TalkatComputerParticlePhysics(CPP2001),28-30November2001,Tokyo 2 Examples of constructive solutions of this kind from my YetthecomplexityofTeXtendstobe(unconsciously)re- own experience are: the asymptotic operation [14]; the gardedasasourceofpridebyTeXnicians.(Asimilarsen- gauge-invariant perturbation theory with unstable fields timentseemstoprevailinregardofC++.)Ipersonallydo [15]; algebraic (a.k.a. integration-by-parts) algorithms for notfeelIhaveenoughbrainpowertowastewithTeX.On multiloopcalculations[16];quasi-optimalobservables[17]. thetechnicalside,TeXisaonewaystreet:itwasdesigned Buthowtoimplementallthatwonderfulmathematicsas with, essentially, the sole goal in view (eliminating the workingalgorithms?Quiteoften,thisrequires much more typesetterbyplacingtheburdenontheauthor),anditistoo experimentationandsafeflexibilityofdatastructuresthan complex to be a standard for exchange of convertible what’sofferedbythedominantSDplatforms(FORTRAN, mathematical information. Even for exchange of papers C/C++). In other words, the dominating SD platform im- postscript proves to be a preferred solution. (Most people posesseverepenaltiesonthealgorithmicdesign. seem to prefer to download postscript from the arXive to Onemightsaythatthisiswhatdivisionoflaborisfor. avoidthehasslesofTeX.Ontheotherhand,theemerging However,thereisanobjectiveandasubjectiveobjectionto MathML standard addresses the need of mathematical in- this. Subjectively, as experience proves, whoever controls formation exchange with not just form but also meaning the software tends to dictate the rules of collaboration, preserved[18].) which was seen to be disastrous in the long run. Objec- • Thenthereisthisproblemofmonolithicsoftwareinca- tively, experimenting with sophisticated algorithms may pableofgenuineextension(see[8]forsimilararguments): requireamuchmorerapidcycleandbroader-bandfeedback trytoimplementafastbit-manipulatingalgorithminMaple thanwhat’susuallypossiblewithinateamofspecialists;in orSchoonschip(anexampleisthealgorithmforevaluation other words, the best results are achieved when formulae ofDiractraces,seebelow). andtheiralgorithmicimplementationco-evolveinthesame At this point I note that the variety of efficient algo- head.DuetothesereasonsIhadbeenfora lo-o-ong time rithmic solutions needed for advanced pQFT calculations seekingsimpleyetpowerfulSDtoolsthatwouldallowme spans the entire spectrum from old-fashioned numerical tostayincontrolofmyalgorithms,intellectually and oth- calculations to dynamical Lisp-like data structures to bit- erwise. wise manipulation usually considered to be a feature of Thethirdcauseofthecalculationalcrisisisagrosslyin- system-level programming. One needs genuine procedures adequateSDfoundation.Brieflyput,physicists’SD,onthe withvariousparameter-passingmechanisms,etc.Inshort: whole,isinthestoneage. • The computer revolution evolves too fast, affecting too Oneneedsthefullpowerofageneral-purposesys- much.Thisbyitselfcreatesmyths.Physicistsaremoresus- temprogramminglanguage. ceptibletosuchmythsbecausetheyhavephysicstoworry Onealsoneedstobeabletomixsoftwarecomponentsre- about,fulltime. sponsiblefordifferentaspectsofthecalculationinanarbi- • Thespeedof computer revolution exacerbates the phe- traryfashion,inaseasyanderror-safefashionaspossible. nomenon of effective incompetence of scientific elite . Iwon’tdiscussthedyingFORTRANmonster.So: (Itishardtostayonthecuttingedgeeveninone’sfieldof specialization.Asteportwoupinthehierarchy,anditbe- What’swrongwithC/C++? comes impossible to have one’s own expertly opinion on Twothingsarewrongwiththesepopularlanguages: therangeofsubjectsoneissupposedtosupervise.Another (i) Programmers’ productivity isunnecessarilylow. stepup,andonenolongerreallyneedstobeanexpertin anythingbutpublicrelations.) (ii) Theresultingsoftware’s quality isunnecessarilylow. • Economicprinciplesdonotworkas elsewhere because (WearetalkinghereaboutaBIGfactor,notjustafew%, it is hard to match the “product’s” value against invest- andaboutlargerprojectswheretheseeffectsaremanifest.) ment. Therearemountainsofevidence for this. The problem • So there is platform
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