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Scalably verifiable dynamic power management. Opeoluwa Matthews, Meng Zhang, and Daniel J. Sorin 20th International Symposium on High Performance Computer Architecture (HPCA) Orlando, Florida, February 17-19, 2014. - Krishnaprasad K and Yashas Krishna. Some Background.
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Scalably verifiable dynamic power management Opeoluwa Matthews, Meng Zhang, and Daniel J. Sorin 20th International Symposium on High Performance Computer Architecture (HPCA) Orlando, Florida, February 17-19, 2014 - Krishnaprasad K and Yashas Krishna
Some Background • Current day biggest problem • Power Management • Managing power each Component gets • When power is given • How system gets power when needed • Etc .. • Power management • Static Power Management • Pre allocate power to each component • Dynamic Power Management • Allocate power when needed • Eg : Dynamic Voltage / frequency scaling
Problems with DPM • Designing DPM is Difficult • Because of Increasing scale of Computer Systems • Cores / Processor increases • Processors /System Increasing • Challenge to efficient DPM: • Scalability • Scalable to large-scale systems • Verifiability • Verify correctness in all situations • Scalability affects Verifiability • But no automated methods to Verify DPM
Important Factors in DOM • Scalability Factor • Scalability proportional to Power Consumption • High Scale = High Power Req. • Low Scale = Low Power Req. • Verification Of DPM and Benefits • Find Bugs in DPM • To Prove Correctness of DPM • If not Done : • Component Overheat • System Failure and Damage • So a Scalably verifiable DPM is needed
Contents • Existing System Model and Issues • Introducing new DPM system : Fractal DPM • How verification possible in new System ? • Fractal DPM vs Performance : Tradeoffs • New System Evaluation • Implementation Strategy • Comparison to Prior works • Conclusion
Initial System Model • DPM Model • Dynamically allocate power to each component Ci • Power Allotted proportional to Current performance Xi • Xi = function of ( Current power Allocation Pi & Current unconstrained perf (Xmaxi).) • Initial Setting : • Set a power Budget • Allot power to Components satisfying Budget • Maximize Xi • Sum(Pi) < Budget • Power Performance Model • 5 possible power settings for each Ci • Low ( L) • Medium_Low (ML) • Medium (M) • Medium_High (MH) • High ( H )
Initial Model : Issues • Design Using Existing tools • Fully automated Formal verification Methodologies • Tool : MurΦ Model Checker • Exhaustive State Space search • Checks Invariant Satisfied or not • Issue : State Space Explosion problems • As Ci increase : States Increase • Infeasible to traverse all states • For Eg: 5 C and 5 setting means 5^5 states • Typical Solution: • Check for small scale and if satisfied , assume Large scale also satisfies • Need not be true always
Fractal DPM Design • Fractal Design • A design in which system behaves the same at every scale • This makes Inductive verification possible • Base case: Verify that the minimum system satisfies its power constraints • Inductive step: Verify that larger systems are equivalent to smaller systems • Both done Using MurΦ
Fractal System organization • Hierarchical Structure : Binary tree model • Leaves : Computing Resource ( CR ) • Intermediate Nodes : DPM Controllers • Records Power states of Child Nodes • Handles power requests of CRs • Power Requests • CR can request more power • Sending req to DMP controller ( Parent ) • DMP Controller Responds • Either directly • Or Passing the req to Its parent Controller • A DMP Controller and Its Two Child considered a single “Node” like a Single CR • Each such Node has a combined Power Setting • Average of Child Nodes L:R
Fractal System organization • Eg : If Child are H and L , then average is MH • L:R format represents power setting of Left child : power setting of right child
Fractal Power Invariant • The Invariant Must be fractal • Applicable on all scales of System • Plus point of Fractal DPM : makes its unique from other DPMs • Fractal Invariant • It is impossible for both children of a DPM controller to be at the High power setting at the same time • Why? • Good for cases when Sum(Pi) > Budget • Limits System Wide power consumption • Limitation • Other Invariants are not considered or Compared : Future Work
Fractal DPM : Specification • Table based specification Method • Each entry in the table corresponds to a state/event combination, and the entry specifies what happens in that situation.
Specification Continued • Special States : • Pend-* • family of pending states in which the computing resource has requested a new power state and is waiting for a response • Block-* • family includes states such as block-L:ML, in which the DPM controller granted or denied a request to a child and is blocked waiting on the Ackfrom the child and will then go to state L:ML • Specification Of root DPM • Same as Non Root DPM except Root has no parent DPM to request power • No Pending States , Only Block States • Non root DPM passes to parent DPM only if : • It handles req by itself ( but Node state unchanged ) • 4 Exceptions : Invariant not satisfied
Fractal DPM : Scalability Issues • When High Scalability • Tree height Increase • Request from leaves to root take more time • Latency Issues • More hops • Possible Solution • Multi Degree Tree : Reduces Height of Tree • Prob : MurΦ doesn’t support this ; Couldn't verify • Scalability Issues : No big Concern • latency of DPM itself is not critical. • many requests can be satisfied without traveling far up the tree • Experimental results on a real system (modestly sized system (16 computing resources)) • latencies are reasonable.
Verification of Fractal DPM • Scalably Verify • Verification Effort : Independent of number of CR • Steps • Base Case Verification • Induction Step Verification • Base Case :Minimum System verification • Base system must be complete • Include all basic components • Incomplete base system • When some elements not considered • Gives incomplete verification : Spurious Actions • MurΦ verifies whether Invariants satisfied
Verification of Fractal DPM • Inductive Step : Equivalence Verification • Observation Equivalence verification chosen • Only outside behavior of system of diff. scale considered • No internal Actions considered • Considers only how system reacts to inputs • Two Perspectives • Looking Down • When system scaled Downwards • Looking Up • When system scaled Upwards • In both case , verify the larger system behaves same as sub system . • Tool : MurΦis used • Using same tool for both steps decrease transitional errors • On-The-Fly Mode : No extra state space
Power management Efficiency • System wide power consumption : upper bounded • Max power consumed : ( C-1) MH + H • As C approach Infinity • Max Average power of CR = MH • F-DPM allows all CR to be in MH • Do not permit certain cases • Causes Inefficiency But Tradeoff between this and Fractal Invariance • But Rare and Inefficiency caused is small • Another Inefficiency : F-DPM forces on CR of H to MH
Evaluation of System • Goal • Fractal DPM actually does its Job well ? • In allocating power to CRs Dynamically and Efficiently • Simulation Methodology • Dynamically set Xmaxi to all CRs • Keep it changing at Time steps • Give weights to power settings • Model behavior of CRs and DPMCs • Specification Tables • Computes performance of each CR • Function of power it is granted by DPM per Time Steps
Performance Modeling • How determine performance of a given CR at a given power setting ? • Each CR can use power different way • May achieve different performance at same setting • Abstract way : as a function of Pi and Xmaxi • Two Functions : • Perf1: • Decreasing marginal performance benefit • E.g. using more power to enable a faster core clock frequency helps performance but eventually performance becomes memory-bound • Perf2: • Linear Performance benefit • E.g. ideal voltage/frequency scaling
Performance Comparison and Results • Compare Against Implementable Oracle ( Ideal DPM) • Gives best possible allocations , even H:H allocations • Results ( give #CRs = 8) : • In majority of the time steps (>72%) : performance(FDPM) = performance(Oracle) • the performance gap is never more than 37% for perf1 and 46% for perf2 • Performance difference greater for Perf2 • perf2 models greater performance at higher power states, and thus being at a lower power state (to maintain the fractal invariant) is somewhat more costly • Thus : amount of performance sacrificed = Small
Implementation Strategy • Dynamic Voltage/Frequency Scaling as Power adjustment strategy • V/F adjusted on a core-pair ( Granularity ) • Possible because of fractal structure • CR and DPMC using Linux Daemons • Communication through Sockets • Optimization : OptiFDPM • CR re-requests next lower power setting if current request rejected • Optimized version holds scalable verifiability of FDPM
Evaluation of Implementation • Compare the power and performance of fractal DPM against an un-implementable oracle DPM scheme that always assigns the optimal power levels to core pairs. • Compare the power and performance of fractal DPM against a provably correct power management scheme that statically sets all cores to a given power level. • Determine the latency to service requests for new power levels
Evaluation of Implementation • Comparison to Oracle Power Management
Evaluation of Implementation • Comparison to Static Power Management
Evaluation of Implementation • Latency
Comparison : Previous Works • Lungu et al.’s research on verifiable DPM for multicore processors [9] • Observed DPM schemes cannot be verified on Large Scale • Showed State space explosion • Zhang et al.’s works on Fractal Coherence [14] • Derived idea of Fractal design • First time used for DPM • Others Works on DMP [10][8][6] • Did not use Verification
Conclusion • Design of Scalably verifiable DPM • Using Fractal Design for Verifiability • Small performance in efficiency only • Par with Oracle Model
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