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# COMPILER CONSTRUCTION CS 201

UCR
GPA 3.88

Rajiv Gupta

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COURSE
PROF.
Rajiv Gupta
TYPE
Class Notes
PAGES
7
WORDS
KARMA
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## Popular in ComputerScienence

This 7 page Class Notes was uploaded by Adele Schaden MD on Thursday October 29, 2015. The Class Notes belongs to CS 201 at University of California Riverside taught by Rajiv Gupta in Fall. Since its upload, it has received 67 views. For similar materials see /class/231744/cs-201-university-of-california-riverside in ComputerScienence at University of California Riverside.

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Date Created: 10/29/15
4109 CS 201 Compiler Construction Lecture 4 Data Flow Framework Data Flow Framework The various problems considered have things in common Transfer functions Confluence Operator Direction of Propagation These problems can be treated in a unified way 9 data flow framework is an algebraic structure used to encode and solve data flow problems Monotone Data Flow Framework Components of the framework 1 Information Set L 2 Effect of joining paths meet operator 3 Effect of basic blocks fn monotone transfer func 4 Iterative Solution can be shown to terminate Lisasemilattice st V a be 5L 1 a a a idempotent 2 a b b a commutative 3 a b c a b c assocative Bottom Element L st V a 5 L a J J TopElement T stVaeLaTa If top amp bottom elements exist they are unique Contd Relation i is a partial order on L aSb E a b a Can similarly define lt gt 2 relations A semilattice is bounded iff V a 8 L there exists a constant ca st length of chain beginning at a is at a most ca Max C AK l 4109 Monotonic Functions Effec r of each basic block is modeled by a Transfer func rion f L 9 L Func rion f mus r be mono ronic A ro ral func rion f L L is mono39ronic iff V a b E L faAb S fa fb Dis rr ibu rive func rion faAb fa fb For mono ronic func rions a g b gt fa g fb Coan For monotonic functions a S b gt fa S fb Proof aAb S fa fb Defn of Monotonioity f faAbfafb faAb Defn of S aAba fafafb fa GivenaSb a ba fa fb fa fafa fa idempotenoe Hal 5 fb Defn of S 4109 FixpoinT A fixpoinT of a monoTonic funcTion f L 9 L is a value a e L such that fa a TgtfTgtffTgtfffT Ther e exisTsTsuch ThanfTfT ff T is The gr39eaTesT fixpoinT of f MonoTone FuncTion Space A monoTone funcTion space for a semilaTTice is a seT F of monoTonic funcTions which 1 ConTains The idenTiTy funcTion id basic blocks may noT modify infor maTion Is closed under funcTion composiTion To model The effecTs of paThs For each a E L Ther e exisTs f E F sT fi 2 a To model gen funcTions N A A disTr ibuTive funcTion space is a monoTone funcTion space in which all funcTions ar e disTr ibuTive 4109 A MonoTone DaTa Flow SysTem A monoTone daTa flow sysTem is a Tuple ltL A F G FMgt 1 L is a bounded semilaTTice wiTh T d L 2 is The monoTone funcTion space 3 G N E s is The program flow graph 4 FM N 9 F is a ToTa funcTion ThaT associaTes a funcTion from F wiTh each basic block MeeT Over All PaThs SoluTion MeeT over all paThs souTion MOP of a daTa flow sysTem MOP N 9 L MOPs NULL NULL is The elemenT in L which represenTs no informaTion W e in 53 Mo n Ln NULL TT39 6 Pa x n f 1 is composiTion of funcTions from nodes along paTh 7r excluding node n n19n29n399nk19nk fnk o fnkloo i n201 n1 10 4109 MOP SoluTion Finding MOP solu rion is undecidable ie There does no r exis r a general algor39i rhm ThaT compu res MOP soluTion for39 all mono rone daTa flow sysTems LeT X N 9 L denoTe a To ral func rion ThaT associa res nodes wi rh Ia r rice elemen rs X is conserva rive or39 safe iff Vn 8 N Xn s MOPn I rer39a rive algori rhm compu res conserva rive approxima rion of MOP For39 dis rr39ibu rive da ra flow sysTems i r compu res soluTion ThaT is iden rical To MOP solu rion 11 ITer39aTive Algori rhm NULL 6 mm X39CnT Vepeai 8562i hm 2193 7 6 N39 3 in d0 XLni new 71 X 539 in E1 H hi shed 6 44 X03 LBJ if new 7 X017 ken fr 69w 846413 a Bake 15004 elf4717M Link mm 4109 4109 Reaching Definitions oars sea4 019 me L 170935 I A u iDEF5i390UJL9v L 75 C3939 iUTa i l inx X KIM nu U ewm mum di39d EDEF39J h MMMea vamaak 4454 73 J GENO 2 d 7 me cu39n Mimi1 J wA cA rad 0 Ma q Con rd T r39f at 3 1 id I W1 d h M 53 cub1 as Ed 4 d J nr rJ 39 14 avg 4 Cquot AE if A Ha fab 39 0 Uh mu U FN CaMILL u 6 ran when V leLLI EV U 6 kLLU f 39 m u 5 X39L39r r T nuu Wquot U H burs u 6mm Fti vurm 14

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