Kwangil Choi, Hyunok Oh Hanyang University

 Introduction ◦ Non-volatile Memory (NVM) ◦ Synchronous dataflow (SDF)  Problem Definition  Answer Set Programming  Experiment  Conclusion

 Non-Volatile Memory (NVM)  Replace DRAM for main memory Type Phase change RAM (PRAM) Spin-transfer torque magneto resistive RAM (STT-MRAM) Ferroelectric RAM(FRAM) Pros High density Low static energy consumption Cons High write energy consumption Poor write performance

( * MTJ : Magnetic Tunnel Junction) current free layer tunnel oxide fixed layer Gate SourceDrain Synthetic Anti ferromagnetic (SyAF) structure Bottom Electrode(substrate) Tunnel Barrier Free Layer Pinned Layer Seed Layer Capping Layer Spacing Layer Top AF Layer Top Electrode Bottom AF Layer Buffer Layer MTJ*

The reduction of the retention time contributes the cell density, leakage power, dynamic power consumption, and performance.

STT1STT2STT3 Cell size (F 2 ) T retention 26.5μs3.24s4.27yr Lat R (ns) Lat w (ns) Dyn R (nJ) Dyn W (nJ) P leak (mW)

26.5μs 3.24s 4.27y processor STT1 memory STT2 memory STT3 memory

 Synchronous dataflow (SDF) ◦ represents streaming applications like multimedia that require frequent memory access ◦ Node(Actor) - functional algorithm ◦ Edge - communication between two actors ◦ Producing / Consuming rate  the number of produced and consumed samples ◦ Rate is fixed A A B B 32

1ms } T retention = 1 ms 16 refresh operations T retention = 4 ms no refresh operation

 Introduction ◦ Non-volatile Memory (NVM) ◦ Synchronous dataflow (SDF)  Problem Definition  Answer Set Programming  Experiment  Conclusion

 Input ◦ Target architecture: A system with multiple relaxed reten tion time STT-MRAM modules. Note that the memory ref reshes memory cells containing valid data. ◦ Characteristics of STT-MRAM : retention time, read/write energy, and refresh energy. ◦ Application : An application is specified in SDF model. A schedule and the execution time of each node are given.  Goal ◦ Minimization the total energy consumption on the memo ry system for the application.  Output ◦ The mapping of buffers to STT-MRAM modules.

A A B B 32 SDF graph, schedule and execution time are given A system with multiple retention time memories Map the buffer to memory to minimize the energy consumption

1. Construct a schedule AACBDDFEEEE 2. Build lifetime chart STT- Short STT- Short STT- Long STT- Long 3. Determine buffer mapping Energy consumption = Energy consumption = 15033

 Write energy  Refresh energy  Total energy = write energy+refresh energy  ConstraintMeaning lt(t j )The lifetime of token belonging to buffer map(b i )The mapped memory for buffer rt(m)The retention time of memory bibi The buffer size on edge E ref (m)The refresh energy for a token in memory

 Introduction ◦ Non-volatile Memory (NVM) ◦ Synchronous dataflow (SDF)  Problem Definition  Answer Set Programming  Experiment  Conclusion

 Declarative approach for NP problems  Problem - logic predicates “ AND”  Solutions - answer sets  Easy to understand the formulation  Fast ASP solvers have been introduced

A B node(1..2). edge(1,1,2,3,3,3).edge(2,2,1,2,2,5). repetition(1,1).repetition(2,1). lifetime(E,Inv, Duration) :- fire(A,S), fire(B,F), edge(E,A,B, P,C,I), numFiredBefore(A,S,SN), numFiredBefore( B,F,FN), Inv=FN*C-C+1..FN*C, SN*P-P 0, Inv> 0, Inv<= R*P,repetition(A,R), S<F, extime(A,ATime). buffer_energy(E,Write*P*Rep+Refresh*Energy) :- Energy = [lifetime(E,T,Duration)=Duration/Retention+1], ed ge(E,A,_,P,_,I), retention(Type,Retention), memory _type(M,Type), map(E,M), refresh_energy(Type,Re fresh), write_energy(Type,Write), repetition(A,Rep). 1 { memory_type(M,T) : retention(T,_) } 1 :- memory(M). 1 { map(E,M) : memory(M) } 1 :- edge(E,_,_,_,_,_).sample (E,S-C,T) :- fire(B,T), edge(E,_,B,P,C,I), sample(E, S,T-1), S>= C, time(T). #minimize [buffer_energy(E,Energy)=Energy : edge(E,_,_,_,_,_)]. Answer: 1 memory_type(2,1) memory_type(1,1) map(8,2) map(7,2) map(6,2) map(5,2) map(4,2) map(3,2) map(2,2) map(1,2) buffer_energy(8,3123) buffer_energy(7,11196) buffer_energy(6,12438) buffer_energy(5,4850) buffer_energy(4,11196) buffer_energy(3,11196) buffer_energy(2,11196) buffer_energy(1,19269) Optimization: Answer: 2 memory_type(2,2) memory_type(1,1) map(8,2) map(7,2) map(6,2) map(5,2) map(4,2) map(3,2) map(2,2) map(1,2) buffer_energy(8,5004) buffer_energy(7,5994) buffer_energy(6,5994) buffer_energy(5,6660) buffer_energy(4,5994) buffer_energy(3,5994) buffer_energy(2,5994) buffer_energy(1,5994) Optimization: Answer: 3 memory_type(2,2) memory_type(1,1) map(8,2) map(7,2) map(6,2) map(5,1) map(4,2) map(3,2) map(2,2) map(1,2) buffer_energy(8,5004) buffer_energy(7,5994) buffer_energy(6,5994) buffer_energy(5,4850) buffer_energy(4,5994) buffer_energy(3,5994) buffer_energy(2,5994) buffer_energy(1,5994) Optimization: OPTIMUM FOUND SDF GraphASP formulationResult

 Introduction ◦ Non-volatile Memory (NVM) ◦ Synchronous dataflow (SDF)  Problem Definition  Answer Set Programming  Experiments  Conclusion

 Synthetic examples ◦ 7 randomly generated examples ◦ 3 to 7 actors  Real-life applications ◦ Part of CELP ◦ H.263 encoder / decoder ◦ MP3 decoder  Each node n has the execution time ◦ T(n) = k*T i (n) ◦ where k represents the scale factor, T i (n) the initial execution ti me, and T(n) the execution time of node n. CPUIntel i5 RAM8GB OSUbuntu Linux ASP SolverClingo 3.0

Scale factor = 1Scale factor = 10 Scale factor = 1000 Scale factor = 50000

scale factor ratio

Scale factor=1Scale factor=10

 Buffer mapping algorithm for a system with multiple retention STT-MRAM memories can reduce the energy consumption by 30~70%.  The mapped STT-MRAM memory is dependent on the variable lifetime.