Dataflow Networks, Intuitive and Formal Semantics - Lecture Slides | CPSC 489, Study notes of Computer Science

Download Dataflow Networks, Intuitive and Formal Semantics - Lecture Slides | CPSC 489 and more Study notes Computer Science in PDF only on Docsity! 1 1 Dataflow Networks • Dataflow Networks • Syntax and Semantics – actor, tokens and firing • Static scheduling • Other dataflow models slide -ASV-UCB 2 Dataflow network a A data-flow network is a collection of functional nodes which are connected ‘and,communicate over unbounded FIFO queues a Nodes are commonly called-actors a The bits of information that are communicated over the queues are commonly called tokens slide -ASV-UCB Intuitive Semantics a Unbounded FIFOs perform communication via sequences-of tokens carrying values « integer, (loa, fixed point + matrix of integer, float, fixed point, « image of pixels a Slate implemented as-self-loop. a Determinacy: « unique output sequences given unique input sequences « Sutticient condition: blvcking read (process cannot test input queues for emptiness) slide -ASV-UCB  + singh + single o slide -ASV-UCB « singl « single o ¢ o(n) =cl ifn 10 slide -ASV-UCB  « sing] + single vo ¢ o(n) =cl ifn slide -ASV-UCB + singh + single o1 + o(n) =cl i 2 slide -ASV-UCB  ¢ singh a Exal + single o1 + o(n) = el ifn 13 slide -ASV-UCB * singl + single o « o(n) = cl i(n! “ slide -ASV-UCB  Chains of-sequences Consider the set Sof all finite and infinite sequences of tokens a This set is partially orderedsby the prefix order a A subset C of Sis called.a chaimill all pairs of elements of C are comparable If Cis a chain, then it must be.a linear order inside S (hence the name chain) mw Example: { [ x, ], [ x, x, ], Pp X93 |, ... } is a chain a Example: { [ x, ], [ x, x, ],[ x4], «.. } is not a chain slide -ASV-UCB 19 (Least) Upper. Bound Givena suhset Y of Span upper bound-of ¥ is an element of S such thatz.is larger than all elements of ¥ Consider now-the set -4,(subsetiof' S) of allthe upper bounds of Y If Z has a least element, then u is:called the least upper bound (lub) of Y a The least upper bound, if it exists, is unique a Note: u might not he in Y (if itis; then it is the largest value of Y) slide -ASV-UCB 20 10  Complete Partia-Order a Every chainin S has@least upper bound a Because of this property, 'S is called‘a Complete Partial Order a Notation: if Cisachain, weindicate the leastupper bound of’ C by lubCC} a Note: the least upper bound may be thought of as the limit of the the chain slide -ASV-UCB 21 Processes = Process: function from a p-tuple of sequences to a q- tuple of sequences F : Sp=pes4 Tuples have the induced pointwise order: Y=(Yp..s¥ph Y°S(Y pastay’y) in SP: ¥ <= Y’ iff y; <=y?; forall [<=i<= p a Given a chain C in SP, FCC) may or may not be a chain in S4 a We are interested in conditions that make that true slide -ASV-UCB 2 11 12 slide -ASV-UCB 23 Mahapatra- Texas A&M- Fall00 24 Summary of function class • Summary of function class and their relationship for the function F: Sp → Sq Sequential ⇒ continuous ⇒ monotonic Static scheduling-of DF = Key property. of DFnctworks: outputscquences do not dependon timeof firing-of actors a SDF networkscambe statically scheduled abcompile- time + execute an actor when itis.knewnto. be fireable * no overhead due fosequencing of coneurrency « static buffer sizing a Different schedules yield-different + code size « buffer size slide -ASV-UCB 2» Static scheduling of. SDF Based only on process graph (ignores-tunctionality) Network state: numberof tokens in FIFOs Objective: tind schedule that is valid, isec + admissible (only fires actors when fireable). perivdic (brings network back4o initial state by firing each actor at least once) Optimize cost function overadmissible schedules slide -ASV-UCB 30 15  —_== —=_ ~ —_== m Repetitions (or firing f schedule S: number of firings of each actor in Ss ~~ > m yo(A) n= v,(B) n, — must be satisfied for each edge ~~ slide -ASV-UCB 31 a Balance for each edges - + 39(A)- YD) <0 + ¥B)-¥(C)=0 0 + 2vfA)- v(C) =0 — . . 7 # 2v(A)- v0) =0 = ww slide -ASV-UCB 32 16 17 slide -ASV-UCB 33 Mahapatra-Texas A&M-Fall’00 34 Tagged Token DFM • Arvind and Gostelow 80’s • Each token has a tag, firing is enabled when tokens have matching tags. – No need of FIFO discipline in the channel