PAP: Power Aware Partitioning of Reconfigurable Systems Vijay R. P. Kappagantula Rabi Mahapatra Texas A&M University College Station, TX 77843
Outline ! Introduction ! Related Work ! PAP: Power Aware Partitioning ! MPAP: PAP for multifunctional systems ! Experiments ! Summary SSRS - Feb 08 2003 2
Introduction HW/SW Codesign: Key Issues ! Partitioning ! Synthesis ! Co-simulation ! Partitioning problem : Non-trivial ! Application - 100 tasks , 3 different HW/SW ! implementations (2* 3)^ 100! possible partitioning solutions SSRS - Feb 08 2003 3
Objective ! Given (Inputs) ! Application(s) descriptions (system level) ! Target Architecture (CPU, FPGA, P max , Ah total ) ! Task’s metrics ( P s , T s , P h , T h , A h ) Determine suitable partitioning framework that will map and schedule the application(s) on target architecture so as to meet ! The Deadline & Power Constraints SSRS - Feb 08 2003 4
Partitioning Mapping & Scheduling CPU StrongArm-1100 (Software) Memory PCI FPGA Xilinx XCV4000 (Hardware) System Components System System Description Architecture SSRS - Feb 08 2003 5
Related Work Heuristic Based ! Asawaree Kalavade and P.A. Subramanyam 1998 ! “Global Criticality/Local Phase (GCLP) Heuristic” ! System Power not considered I terative improvement techniques ! Huiqun Liu and D.F. Wong 1998 ! “Integrated Partitioning & Scheduling (IPS) algorithm” ! Uniform SW and negligible HW execution times ! No power consideration Power-Aware Scheduling ! J. Liu, P.H. Chou, N. Bagherzadeh and F. Kurdahi 2001 ! “Power-Aware Scheduling using timing Constraints” ! Use initial schedule assumption – may be inflexible SSRS - Feb 08 2003 6
Contributions ! Considered power as important constraint during partitioning step, (in hybrid systems) ! Concurrent Mapping and Scheduling of tasks with non-uniform execution times – for Real-Time Applications, ! Used Reconfigurable systems for performance tuning through task migration SSRS - Feb 08 2003 7
PAP Algorithm Overview Iterative improvement technique. ! Initial mapping: All Software ! Every iteration, one software task is selected for hardware ! mapping ! Tasks mobility indices ! Task Selection Routine Reschedule the tasks ! Schedule is verified to see if it meets its timing and power ! requirements. SSRS - Feb 08 2003 8
Task Mobility ! Parallelism ! Schedule Dependent ! Time Interval (E i ,L i ) defined by mobility is used to schedule task i in hardware ! E i is the earliest possible start time in HW E i = max ( η (k) ) k ∈ pred(i) pred(i) is the immediate predecessor set of task i η (k) : start time of task k SSRS - Feb 08 2003 9
Task Mobility Contd. ! L i is the latest possible finish time of task i in HW L i = min ( η (k) – ts i ) k ∈ succ(i) succ(i) is the immediate successor set of task i ts i is the execution time of task i in SW ! Task Mobility of task i µ (i) is determined as follows: µ (i) = 1, L i > E i 0, L i = E i SSRS - Feb 08 2003 10
Task Selection Routine N s : Set of software tasks in application S.1 Rank the tasks in N s in the order of decreasing software execution times ts i S.2 Compute the mobility µ (i) for all i ∈ N s S.3 If µ (i) = 0 for all i ∈ N s Task i with maximum execution time ts i is selected Else Task i ∈ N s with maximum execution time ts i and non-zero mobility is selected SSRS - Feb 08 2003 11
Definition: Time Valid Schedule ! T exec : The finish time of a single iteration of the application ! T exec = max ( η (i) + t i ), for all i ∈ N N is the set of tasks in the application ! Schedule: Time-Valid If T exec ≤ D, D is the application deadline SSRS - Feb 08 2003 12
Power Valid (Definitions) ! Power Profile (P σ ) ! P σ (t) = Σ P(i), for all i ∈ set of active tasks at time instant t ! Power Spike ! P σ (t) > P max ! Power-Valid ! P σ (t) ≤ P max , 0 ≤ t ≤ T exec SSRS - Feb 08 2003 13
Communication Model ! 32 bit 33 MHz PCI ! Delay Computation P.V. Knudsen and Jan Madsen, 1998. CC * N + sample t comm = AC N bus F ! Power Dissipation J.Buck, S. Ha, E.A. Lee, and D.G. Messerschmit, April 1994. 1 × P bus = 2 C bus V mn 2 SSRS - Feb 08 2003 14
Scheduling the Bus communication ! No bus conflict is assumed. ! The execution of the hardware task and its communications should lie within the interval defined by its mobility . SSRS - Feb 08 2003 15
Input Specification : Task graph (TG) deadline ‘D’, P max and Ah total PAP ALGORITHM (All tasks mapped to SW) Software and hardware task's metrics. Test schedulability . Select a new task using Task Compute T exec , finish time of one Selection Routine for hardware iteration mapping Compute the Power Profile (P σ σ ) of σ σ the schedule and the total hardware used (Ah) Invalidate for all no future cycles Is (Ah <= Ah total ) yes Invalidate no for the next cycle Is (P σ <= P max ) End of PAP algorithm yes no Is T exec <= D yes SSRS - Feb 08 2003 16
Example of PAP algorithm 1 0 2 Application specified as a 7 task graph 4 3 6 5 P max D P(t) 4 6 3 5 2 7 0 1 a. Initial schedule on CPU (all software) SSRS - Feb 08 2003 17
Example contd. D P(t) P max 1 t 3 2 5 6 0 4 2 3 6 5 4 3 b. Schedule after iteration1 2 P(t) Power Spike 1 6 3 5 t 0 4 2 3 5 4 3 c. Schedule during iteration2 (Time-valid, Power-invalid ) P(t) No Power Spike 2 1 3 0 4 6 5 t 2 3 5 4 3 d . Schedule after iteration2 (Time-valid, Power-valid) SSRS - Feb 08 2003 18
Partitioning of Multifunctional Systems ! Multifunctional systems- Support a set of applications. ! Set of active applications - Combined task graph (CTG). ! PAP extended to include information ! Similar tasks ! Hardware re-use ! Modified PAP applied to CTG SSRS - Feb 08 2003 19
Application Criticality ! The set of active applications { A 1 , A 2 ,...,A n } is ordered based on the criticalities. T CTG ! AC i = D i T CTG : Finish time of a single iteration of the CTG D i : Deadline of Application A i SSRS - Feb 08 2003 20
Modified Task Selection Routine ! All software tasks of CTG labeled with self and shared priorities. ! Self-Priority : Information about parallelism within ‘own’ application ! Shared-Priority : Information about similar tasks across the set of applications and hardware re-use. ! Combined-priority: Task selection index SSRS - Feb 08 2003 21
Self-Priority: Computation Compute the mobility µ (i) for all i ∈ N s , N s is set S.1 of software tasks in application A k Determine N s1 ∈ N s , set of all software tasks with S.2 non zero mobility. Similarly N s2 ∈ N s , set of all software tasks with zero mobility. S.3 Initialize counter Count = 0 SSRS - Feb 08 2003 22
Self-Priority Contd. S.4 Extract task i, i ∈ N s1 with maximum execution time tsi N − Count S.4.1 Compute SeP(i) = for all j ∈ N s s N s S.4.2 Increment Count S.4.3 Remove task i from N s1 S.4.4 Go to Step S.4 S.5 Extract task i, i ∈ N s2 with maximum execution time tsi N − Count S.5.1 SeP(i) = for all j ∈ N s s N s S.5.2 Increment Count S.5.3 Remove task i from N s2 S.5.4 Go to Step S.5 SSRS - Feb 08 2003 23
Shared-Priority Computation ! Num i - Total Number of hardware implementations of similar tasks of task i in current iteration. Num i ! The shared-priority ShP(i) = for all j ∈ N s max Num j N s : Set of Software tasks of application A k SSRS - Feb 08 2003 24
MPAP Algorithm Inputs : Set {A 1 , A 2 ,...,A n } , Deadlines , Ah total and P max Output s: Time and Power valid schedules for the set of applications S.1 Set of applications is aggregated to form a single task graph CTG. All tasks are initially mapped to software. Schedule is assumed to be Power-Valid SSRS - Feb 08 2003 25
MPAP contd. S.2 The Application Criticalities for {A 1 , A 2 ,...,A n } are computed. S.3 Application with maximum application criticality is considered first. S.4 Task selected - Modified Task Selection Routine Test Schedulability & Power Profile Repeat for other applications in the ordered set {A 1 , A 2 ,..., A n }. SSRS - Feb 08 2003 26
MPAP Contd. S.5 If all applications have time and power-valid schedules Terminate Algorithm Else Repeat from step S.2 SSRS - Feb 08 2003 27
MPAP: Complexity Task’s mobility computation: Ο (N) ! The self and combined priorities: Ο (N) ! Sorting: Ο (NlogN) ! ∴ Modified task selection routine: Ο (NlogN) time. ! Rescheduling takes Ο (N) time. ! Initial all software schedule: Ο (N 2 ) ! At most N iterations ! Therefore, MPAP algorithm: Ο (N 2 logN) time ! SSRS - Feb 08 2003 28
Case Studies Applications: 8 kHz 16-QAM Modem and DTMF Codec ! Specified in CGC domain of the Ptolemy system ! SW Processor: StrongARM SA-1100 ! SW Estimates: ! Timing and Power using JouleTrack (MIT) ! HW Resource: Xilinx-Virtex2 (XCV4000). ! Estimates: Xilinx ISE 4.2 simulator ! Timing and Area using PAR ! Power using XPower ! SSRS - Feb 08 2003 29
Experiment1: PAP Vs Extensive Search ! Case Studies: 16-QAM and DTMF Codec ! Periodic Deadline (D): 800 µ s. ! Applied PAP for 3 different P max (8W, 6W, 2W) ! Performed Extensive search for P max = 8W SSRS - Feb 08 2003 30
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