Reliable Embedded Multimedia Systems?

Transcription

1 2 Overview Reliable Embedded Multimedia Systems? Twan Basten Joint work with Marc Geilen, AmirHossein Ghamarian, Hamid Shojaei, Sander Stuijk, Bart Theelen, and others Embedded Multi-media Analysis of Synchronous Dataflow Graphs Throughput Analysis Throughput-Storage Trade-off Analysis Scenario-aware Analysis Run-time Adaptation Looking Forward Funding: NWO PROMES EC FP6 Betsy, FP7 MNEMEE Knowing is not understanding. Charles Kettering 3 Embedded Multi-media 4 Embedded Multi-media Trends Concurrency Connectedness Interaction Variability

2 5 Embedded Multi-media 6 Embedded Multi-media 7 Approach: Models of Computation (MoCs) 8 Essential Challenges on the interface between science and engineering Basic dimensions Aspects essential for predictability Metrics predictability and efficiency processing communication storage functionality concurrency timing energy quality functionality concurrency timing energy quality execution time energy dissipation perceived quality reconfiguration time are contradictory

3 9 Scenario-aware H.263 Decoder Model (FSM-based Scenario-Aware DataFlow (SADF)) Control channel Fixed rate Kernel Data channel VLD d d d IDCT Parameterized rate a c c b e FD MC RC Detector... I P 99 P 99 P Tokens 3 x={3,4,5,6,7,8,99} Rate I P x P a b x c 99 x d e 99 x Execution time VLD P others 4 IDCT P others 7 I, P P 3 9 P 4 45 MC P 5 9 P P P 8 3 P I 35 P RC P 3, P 4, P 5 25 P 6 3 P 7, P 8, P FD All MEMOCODE 26 The Goal: Scenario-aware Flow extract application model keep trade-offs select operating point and switch dynamically Overview Embedded Multi-media Analysis of Synchronous Dataflow Graphs Throughput Analysis Throughput-Storage Trade-off Analysis Scenario-aware Analysis Run-time Adaptation Looking Forward 2 Synchronous Data Flow Graphs (SDFGs [Lee 986]) rate token actor channel execution time A, B,2 C,2 Throughput: average number of actor firings over time Iteration: smallest non-empty set of actor firings that does not change the token distribution (example: A:3, B:2, C:) ACSD 26 emb. mm throughput storage

4 3 Our Throughput Analysis Method 4 Throughput Analysis: Our Result Self-timed execution: Each actor fires as soon as it can fire Known to maximize throughput Execution state: distribution of tokens + remaining execution times Execution: transient + periodic phase A A Transient Phase Throughput can be calculated from the periodic phase A, C B A, C Periodic Phase B B A B MP3 dec. Modem Sample Rate Satellite H.263 decoder State Space Traditional methods, all using conversion to Homogeneous SDFGs Dasdan Gupta >8 >8 >8 Howard >8 >8 >8 Runtimes of various throughput analysis methods (in seconds) Young Tarjan Orlin >8 >8 >8 Efficient implementation Consider one designated firing per iteration only to detect a recurrent state emb. mm throughput storage emb. mm throughput storage 5 Overview 6 Trade-off: Storage vs. Throughput Embedded Multi-media Analysis of Synchronous Dataflow Graphs Throughput Analysis.25 multi-media applications ` Throughput-Storage Trade-off Analysis Scenario-aware Analysis Run-time Adaptation Looking Forward throughput DSP synthesis storage DAC 26, IEEE T on Comp 28

5 7 Storage Distribution 2 α 3 β 2 A, B,2 C,2 Tokens on channels must be stored in memory. Separate memory for each channel. Storage distribution, for example, α,β 4,2 8 Problem Definition throughput 2 α 3 β 2 A, B,2 C, ,2 5,3 6,3 6,2 7, distribution size Find all minimal storage distributions for any possible throughput 9 Dependency Graph 2 Dependency Graph 2 α 3 β 2 A, B,2 C,2 Storage distribution α,β 4,2 resolving storage dependencies may increase throughput firings in one period sp(β) tk(β) C dependency: an actor firing start may depend on an actor firing end firings in one period sp(β) tk(β) C dependency: an actor firing start may depend on an actor firing end B sp - space tk - token A 2 tk(α) B tk(α) A 3 A tk(a) 4 cycles denote storage dependencies B sp - space tk - token A 2 tk(α) B tk(α) A 3 A tk(a) 4 cycles denote storage dependencies

6 2 Abstract Dependency Graph dependencies between actors B A B C tk(α) tk(β) tk(a) sp(β) tk(β) A 2 tk(α) B sp(β) C abstract dependency graph contains all storage dependencies A 3 A tk(a) 4 easily constructed from state-space exploration 22 Design-Space Exploration Algorithm Given an SDFG G with storage distribution δ. Compute throughput and abstract dependency graph for G with δ 2. For each channel c with a storage dependency in Create new storage distribution by enlarging c 3. Repeat steps -2 All minimal storage distributions are found when starting from storage distribution,..., dependency graph may be very large tk(α) 23 Experimental Results 24 Conclusions Trade-off Analysis #actors #channels min throughput > Example 3 2 /7 Satellite MP3 3 2 /37 H /2876 Exact minimum memory requirements for any possible throughput Technique can be combined with heuristics to prune the search space if necessary Technique can be generalized to other types of resources and performance metrics Distr. size Max throughput Distr. size #Pareto points Approximation /4.23 /32 increase buffers with 544 n times 6 the minimal step size / #Distributions Exec. time ms 7ms 2ms 53min

7 25 Overview Embedded Multi-media Analysis of Synchronous Dataflow Graphs Throughput Analysis Throughput-Storage Trade-off Analysis Scenario-aware Analysis Run-time Adaptation Looking Forward 26 Scenario-aware H.263 Decoder Model (FSM-based Scenario-Aware DataFlow (SADF)) Control channel Fixed rate Kernel Data channel VLD d d d IDCT Parameterized rate a c c b e FD MC RC Detector... I P 99 P 99 P Tokens 3 x={3,4,5,6,7,8,99} Rate I P x P a b x c 99 x d e 99 x Execution time VLD P others 4 IDCT P others 7 I, P P 3 9 P 4 45 MC P 5 9 P P P 8 3 P I 35 P RC P 3, P 4, P 5 25 P 6 3 P 7, P 8, P FD All MEMOCODE Scenario-aware Performance Analysis 28 Overview SDF-based throughput analysis considers worst-case actor times Scenario-aware throughput analysis considers worst-case actor times per scenario, but it must consider scenario transitions Embedded Multi-media Analysis of Synchronous Dataflow Graphs Throughput Analysis Throughput-Storage Trade-off Analysis Scenario-aware Analysis Run-time Adaptation Looking Forward Analyzing all scenario transitions separately can be avoided Separate scenario transitions with an invariant reference schedule ACM TECS DAC 29

8 29 Run-time Application Management 3 Pareto Algebra - Applications starting/stopping over time - 6 procs, slow (ck) and fast clocks (ck2) - Minimize energy under time constraints Energy (3,ck2) (2,ck2) (5,ck) (4,ck) Const (,ck2) (3,ck) (3,ck2) (2,ck2) (5,ck) (4,ck) (6,ck2) (,ck2) (3,ck) (5,ck2) (4,ck2) JCM (9,ck2) (8,ck2) (7,ck2) (6,ck2) Goal: Compositional computation of trade-offs Completion time (,ck) (9,ck) (3,ck2) (2,ck2) (5,ck) (4,ck) (,ck2) (3,ck) Join Const Min enforce the same clock (8,ck) Gantt chart 3 Pareto Algebra The elements: sets of configurations (Relevant) operators: Minimization Gives the Pareto points (optimal trade-offs) Product Cartesian product of configurations e.g. application and platform configurations Constraint Selects solutions according to constraints e.g. all application configurations with some minimal quality Abstraction Discards information about solutions e.g. bandwidth usage in bandwidth energy quality configurations Derived metric Derive a new metric from other metrics e.g. total power from power of components energy better better prerequisite monotonicity time 32 Pareto-Algebraic Characterization of run-time component trade-off spaces product - derive constrain abstract - minimize adapt select and configure system trade-off space (at the time of a change)

9 33 Pareto-Algebraic Characterization of run-time 34 Complexity n components with p Pareto points each components product - derive constrain abstract - minimize select and configure X derive constrain abstract min component trade-off spaces take a product and on-the-fly derive constrain abstract - minimize adapt O(p 2n ) system trade-off space (at the time of a change) 35 Complexity n components with p Pareto points each take a product and on-the-fly derive constrain abstract - minimize O(p 2n ) 36 Complexity Control keep n and p small Compositional reasoning, among others Approximate Pareto sets y/x = c 2 components X constrain derive-abstract min y = x = y/x = c 4 motivation Pareto algebra cmp wsn conclusions

10 37 Multi-dimensional Multiple-choice Knapsack Problem MMKP NP hard - One optimization objective (value) - Multiple resource dimensions with capacity constraints - Multiple independent applications - Multiple independent configurations per application Pick one configuration per application optimizing value within constraints 38 A Parameterized Compositional Heuristic product constrain derive abstract minimize Project all resource dimensions into one dimension Approximate Pareto set in 2-dimensional space Compute product while on-the-fly Applying resource constraints Computing values, projecting all resource dimensions into one (taking simply the sum) Minimizing the configuration set in 2-dimensional space product-constrain-derive-abstract-minimize 39 A Parameterized Compositional Heuristic Project all resource dimensions into one dimension Approximate Pareto set in 2-dimensional space 4 A Parameterized Compositional Heuristic Project all resource dimensions into one dimension Approximate Pareto set in 2-dimensional space y/x = c 2 parameter p: maintain (at most) p Pareto points y = y/x = c 4 Allows to budget analysis time analysis time c n p 2 (n number of applications; c platform constant) x = product-constrain-derive-abstract-minimize product-constrain-derive-abstract-minimize

11 4 Controlling Time Budgets 42 Compositionality par p time budgets T=ms t=5ms T=2ms t=ms values I I2 I3 I4 I5 I6 time(ms) Applications start at various times 5 at a time (a), at a time (b) IMEC values 2353 Pareto # of active applications 3224 what about applications stopping? MMKP benchmark: Always within budget Good values Similar results to the IMEC, SOC 26, non-compositional state-of-the-art heuristic SimIt-ARM simulator 26 Mhz StrongARM time(ms).5 values always at least as good as IMEC heuristic # of active applications 43 Conclusions Run-time Adaptation 44 Overview Run-time : product - derive constrain abstract - minimize select and configure Parameterized compositional method Allows to trade off quality with analysis time Allows to bound analysis time Open question: components leaving the composition? Embedded Multi-media Analysis of Synchronous Dataflow Graphs Throughput Analysis Throughput-Storage Trade-off Analysis Scenario-aware Analysis Run-time Adaptation Looking Forward Feasible for resource-constrained embedded systems Wide variety of applications

12 45 Dataflow MoCs Expressiveness Hierarchy BDF and larger: Turing complete Better notions of expressiveness needed Unification needed RPN: Reactive Process Networks KPN: Kahn Process Networks DF: DataFlow DDF: Dynamic DF BDF: Boolean DF CSDF: Cyclo-Static DF SDF: Synchronous DF HSDF: Homogeneous SDF 46 Challenges Suitable notions of expressivity Expressivity while maintaining analyzability and synthesizability Abstraction without loosing accuracy Composability and compositionality MoCs for non-functional aspects Unification of MoCs Multi-objective trade-off analysis Parametric analysis Model-driven design and synthesis flows Model-driven run-time systems 47 Thank you! Questions? More info: SDF3 toolkit: Pareto calculator: An understanding of the natural world and what's in it is a source of not only a great curiosity but great fulfillment. David Attenborough