Mapping and architecture exploration

Transcription

1 Mapping and architecture exploration onfigure the resources, e.g. the size of an internal memory, width of a bus. Map the processes to the resources. ompile the processes in terms of the services provided by the mapped resources: SP PU HW HW ffective scheduling of process operations mapped to a PU is a key issue: reduce the context-switching between tasks for efficient execution increase data coherency among processes for efficient memory usage

2 Scheduling lassification ynamic scheduling Make all scheduling decisions at run-time ontext switch overhead Static scheduling Make all scheduling decisions at compile-time Reduce context switch overhead Restricted to specification without data-dependent controls (e.g. if-then-else) Quasi-static scheduling llow specification to have data-dependent controls Perform static scheduling as much as possible Leave data-dependent choices resolved at run-time

3 Quasi-static scheduling QSS Sequentialize concurrent operations as much as possible. better starting point for code generation technologies: Straight-line code across function blocks ounded memory usage during the code execution

4 Scheduling concurrent programs T STRT T while(1){ read(t, d, 1); = d * d; write(port,, 1); PORT IN STRT while(1){ read(strt, N, 1); for(i=0,y=0;i<n;i++){ read(in, x, 2); y = y+x[0]+2*x[1]; write(out, y, 1); OUT while(1){ read(strt, N, 1); for(i=0,y=0;i<n;i++){ read(t, d, 1); = d * d; x[0] = ; read(t, d, 1); = d * d; x[1] = ; y = y+x[0]+2*x[1]; write(out, y, 1); OUT

5 Outline The problem and an approach Petri Net: a model for capturing the behavior of a program efinition of a schedule n algorithm n application to MP2 decoder The effectiveness The outstanding problem: alse Path Problem pproaches for the alse Path Problem ong s observation uture directions

6 Scheduling concurrent programs STRT T while(1){ read(t, d, 1); = d * d; write(port,, 1); PORT IN while(1){ read(strt, N, 1); for(i=0,y=0;i<n;i++){ read(in, x, 2); y = y+x[0]+2*x[1]; write(out, y, 1); OUT STRT T PORT and are in conflict. We call {, an qual hoice Set (S). IN 2 OUT

7 Scheduling concurrent programs STRT T while(1){ read(t, d, 1); = d * d; write(port,, 1); PORT IN while(1){ read(strt, N, 1); for(i=0,y=0;i<n;i++){ read(in, x, 2); y = y+x[0]+2*x[1]; write(out, y, 1); OUT STRT T 2 OUT and are in conflict. We call {, an qual hoice Set (S).

8 Scheduling concurrent programs STRT 1 T OUT T 3,8 1,2,8 STRT 2,6 2,5,6 2,7 2,8 2,6,9 OUT 2,4,8 T 1,2, 4,8 3,4,8 2,4 4,8 One node r associated with the initial marking. ll and only transitions of an enabled S from each node. path to the node r from each node.

9 inding a schedule on the Petri net STRT p1 T p3 p4 2 p2 p5 p7 p8 p6 p9 OUT : r : r : r : v2 r (p2 p6) STRT v1 (p2 p5 p6) Two checks when a node is created: v2 (p2 p7) 1. Termination conditions 2. v5 ncestor (p2 p8) with v3 (p2 the p6 same p9) marking T OUT v4 (p2 p6) : r : r T : v2 : v2 v6 (p2 p4 p4 p8) v7 (p2 p7) : the node at which a cycle was found.

10 inding a schedule on the Petri net STRT p5 p6 r (p2 p6) STRT v1 (p2 p5 p6) OUT p7 v2 (p2 p7) p1 T p3 p2 p4 2 p8 p9 OUT v5 (p2 p8) T v3 (p2 p6 p9) T v6 (p2 p4 p4 p8)

11 enerating code from a schedule r (p2 p6) STRT v1 (p2 p5 p6) OUT T STRT T v2 (p2 p7) v5 (p2 p8) v3 (p2 p6 p9) T Start: read(strt, N, 1); i=0; y=0; : if(i < N){ read(t, d, 1); = d*d; x[0] = ; read(t, d, 1); = d*d; x[1] = ; y=y+x[0]+2*x[1]; i++; goto ; else{ write(out, y, 1); goto Start; v6 (p2 p4 p4 p8) OUT

12 Properties of the algorithm laim1: If the algorithm terminates successfully, a schedule is obtained. - The schedule provides an upper bound on memories required for communicating data. laim2: If the algorithm does NOT terminate successfully, no schedule exists under given termination conditions.

13 Improving efficiency Which transition to choose at each node? ind sequences of transitions to create cycles. T-invariants: a basis of the linear system x = 0 r (p2 p6) STRT v1 (p2 p5 p6) v2 (p2 p7) [i, j]: # of tokens produced to the i-th place by the j-th transition. v3 (p2 p6 p9) OUT T-invariants: T STRT OUT [ ] [ ] STRT hoose a T-invariant using a heuristic, and use it as much as possible. p1 T p3 p4 2 p2 p5 p7 p8 p6 p9 OUT

14 inding a schedule on the Petri net STRT p5 p6 r (p2 p6) STRT v1 (p2 p5 p6) OUT p7 v2 (p2 p7) p1 T p3 p2 p4 2 p8 p9 OUT v5 (p2 p8) T v3 (p2 p6 p9) T v6 (p2 p4 p4 p8)

15 The MP2 decoder Part of a complete commercial video decoder escribed in YPI (developed at Philips) based on Kahn Process Network partially translated into low to apply QSS 11 processes 5000 lines of code of ++ code 45 IOs Hdr Vld ecmv Predict Mem Out ISIQ IT dd WriteM Manager

16 The MP2 decoder mbout Predict smbc = prop.skipped_cnt; while (smbc > 0) { opredictionskipped(<params>); Write(mbOut, mb_p); smbc--; /* Other Predict stuff here */ mbin dd mb_dout smbc = mb_prop.skipped_cnt; while (smbc > 0) { Read(mbIn, mb_p); Write(mb_dOut, mb_p); smbc--; /* Other dd stuff here */

17 The MP2 decoder smbc = prop.skipped_cnt; while (smbc > 0) { opredictionskipped(<params>); Write(mbOut, mb_p); smbc--; /* Other Predict stuff here */ smbc = mb_prop.skipped_cnt; while (smbc > 0) { Read(mbIn, mb_p); Write(mb_dOut, mb_p); smbc--; /* Other dd stuff here */ Various optimizations still possible: remove unused variables remove unused communications Predict_smbc = Predict_prop.skipped_cnt; dd_smbc = dd_ mb_prop.skipped_cnt looplabel: (void) (dd_smbc > 0); if (Predict_smbc > 0) { opredictionskipped(<params>); Write(mbOut, Predict_mb_p, 1); Read(mbIn, dd_mb_p, 1); Write(mb_dOut, dd_mb_p, 1); Predict_smbc--; dd_smbc--; goto looplabel; else if (!(Predict_smbc > 0) {

18 The MP2 decoder Total MP Testench OS Total vld+hdr 5 blocks Philips QSS blocks Total omputation ommunication Philips QSS Performance improved by 45% reduction of communication (no internal IOs between statically scheduled processes) reduction of run-time scheduling (OS) no reduction in computation

19 Outline The problem and an approach Petri Net: a model for capturing the behavior of a program efinition of a schedule n algorithm n application to MP2 decoder The effectiveness The outstanding problem: alse Path Problem pproaches for the alse Path Problem onventional approaches ong s observation uture directions

20 alse paths in scheduling concurrent programs IN while(1){ N=read(IN); write(x, N); for(i=0;i<n;i++){ write(y, [i]); X Y X Y while(1){ M=read(X); for(j=0;j<m;j++){ [j]=read(y); X Y H

21 alse paths in scheduling concurrent programs X Y H j<m? alse state 1,6 1,4 N=read(IN); write(x,n); i=0; 2,X,4 M=read(X); j=0; 2,5 i<n? 1,5 3,Y,5 3,Y,6 j<m? 3,Y,4 i=i+1; 2,Y,6 H j=j+1; alse state The false path problem arises very often in practice. With this problem, the scheduling algorithm blows up, or produces huge schedules...

22 Our previous approach for the false path problem 1. Manually change the input program to eliminate the false paths: [rrigoni et. al, 2002] 1 2 X Y one Loop 4 5 1,4 2,X,4 2,5 3 H 6 1,,5 3,Y,L,5 3,Y,6 2,Y,6 H ffective if specified correctly. The additional burden to the user may not be practical.

23 Our previous approach for the false path problem 2. ompute sets of values of variables at each state: [ousot, 1976] j<m? 1,6 1,4 N=read(IN); write(x,n); i=0; 2,X,4 M=read(X); j=0; 0 i, 0 j 2,5 i<n? i = j, M = N 1,5 3,Y,5 3,Y,6 j<m? 3,Y,4 i=i+1; 2,Y,6 H j=j+1; 0 i < N 0 i < N, i N The convex hull computation at {2,5 j 1 1 i Restrictions on arithmetic operations to be handled. Restrictions on the problem sizes.

24 Outline The problem and an approach Petri Net: a model for capturing the behavior of a program efinition of a schedule n algorithm n application to MP2 decoder The effectiveness The outstanding problem: alse Path Problem pproaches for the alse Path Problem onventional approaches ong s observation uture directions

25 ong s observation certain pattern exists beyond the false states in the reachability tree: The pattern is observed in typical dataflow applications we have in practice. The pattern makes a scheduler fail to find a (finite) schedule. The pattern is caused by a structural property of the input Petri net X Y H ,6. 1,4 2,X,4 2,5 1,5 3,Y,5 3,Y,6 2,Y,6 H 3,Y,4.

26 ong s observation 1, Y Z H ,Z,4 2,Y,4 2,5 3,5 2,Y,5 3,6 2,Z,6 2,Y,Z,4 H.

27 ong s observation Transition dependency transition s requires a transition t, s t, if for any T-invariant of the Petri net, if it contains s, then it also contains t. T-invariant: a solution of the marking equations. I.e., a set of instances of transitions such that if all and only the instances of the set are fired, the resulting marking is same as before Y Z H T-invariants (minimal): {,,,, {,, H S1={, and S2={, are recurrent: and and Recurrent S es Two distinct S es, S1 and S2, are recurrent if there exist distinct elements {si, sj S1 and {tk, tl S2, such that si tk and tl sj.

28 ong s observation Proposition No schedule of a given Petri net contains recurrent S es. Proof: What to show: any attempt to include one of recurrent S es in a schedule leads to either a deadlock or infinite paths. Say S1 and S2 are recurrent, with {si, sj S1 and {tk, tl S2 and si tk and tl sj. schedule needs to include all resolutions of an S contained in it. ny instance of S1 in the reachability tree has a path such that the path starts with si, and tk and sj do not appear in the path, and the path ends with a deadlock, or else is infinite (no repeated marking in the path). Had a schedule contained S1, there is its instance for which the path above does not have any marking repeated in the pre-history of the path in the schedule.

29 ong s observation 1, Y Z H ,Z,4 2,Y,4 2,5 3,5 2,Y,5 3,6 2,Z,6 2,Y,Z,4 H S1={, and S2={, are recurrent: 1. and 2. and.

30 ong s observation: summary Recurrent S es lead the schedule search to either deadlock or endless. The recurrence between S es is a structural property of a Petri net. The proposition holds regardless of markings. The property can be found with a structural analysis. irections of research with ong s observation: 1. pplication to the false path problem 2. pplication to the schedulability analysis 3. xtension of the notion of recurrent S es

31 irections of research with ong s observation 1. pplication to the false path problem X Y H j<m? alse state 1,6 1,4 N=read(IN); write(x,n); i=0; 2,X,4 M=read(X); j=0; 2,5 i<n? 1,5 3,Y,5 3,Y,6 j<m? 3,Y,4 i=i+1; 2,Y,6 H j=j+1; alse state..

32 oncluding remarks Static scheduling of concurrent programs finds attractive applications in practice. Petri nets with abstracted control flow seem to be a reasonable model, but the false path problem stands as a showstopper. Previous attempts directly looked at data-value analysis. ong s observation deals with structural properties of the Petri nets: strong proposition, independent of markings mechanism of a failure of a schedule search revealed While not directly applicable to the false path problem, it may lead to an effective way to address the problem.

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34 irections of research with ong s observation 2. pplication to the schedulability problem Question: when does the other direction of ong s proposition hold? I.e. iven two distinct S es, suppose that no schedule contains either of them. re these S es recurrent then?

35 irections of research with ong s observation 3. xtension of the notion of recurrent S es H

36 irections of research with ong s observation 3. xtension of the notion of recurrent S es H S1={,, S2={I,J, S3={,, S4={L,M I L I J I L I K L J L M M J N M None of them is recurrent to each other.