Hardware/Software Codesign

Hardware/Software Codesign 3. Partitioning Marco Platzner Lothar Thiele by the authors 1 Overview A Model for System Synthesis The Partitioning Problem General Partitioning Methods HW/SW-Partitioning Methods Case Studies 2

A Model for System Synthesis Synthesis = Allocation + Binding + Scheduling on the System Level: Partitioning = Allocation + Binding Graph Models Œ Problem Graph» vertices: functional and communication objects» edges: dependencies Œ Architecture Graph» vertices: functional and communication resources» edges: directed communication channels Œ Specification Graph» problem graph + architecture graph + possible mappings 3 Problem Graph task graph problem graph 1 2 1 2 5 3 3 6 4 communication 7 4 4

Architecture Graph target architecture architecture graph RISC v RISC bus v bus HWM1 HWM2 v HWM1 point-to-point link v ptp v HWM2 5 Specification Graph 1 5 3 v RISC v bus 7 v HWM1 2 v ptp 6 v HWM2 4 6

Allocation, Binding 1 5 v RISC v bus 3 7 v HWM1 2 v ptp 6 v HWM2 4 7 Example: homogeneous Multiprocessor Allocation given find Binding and Schedule with Πminimal latency or Πguaranteed deadlines v PE1 v PE2 v PE3 M PE1 M PE2 M PE3 bus v bus 8

Example: Hw/Sw Partitioning in its simplest form only two blocks: SW and HW (bi-partitioning) processor v processor bus v bus ASIC v ASIC 9 Partitioning Levels of Abstractions Œ structural partitioning: at the register transfer (RTL) level, at the netlist level» split a digitial circuit and map it to several devices (FPGAs, ASICs)» system parameters are relatively well-known (area, delay)» no more comparison of design alternatives possible Œ functional partitioning: at the system level» comparison of design alternatives possible (design space exploration)» system parameters are unknown Å estimation (analysis, simulation, rapid prototyping) 10

The Partitioning Problem Definition: The partitioning problem is to assign n objects O ={o 1,..., o n } to m blocks (also called partitions) P={p 1,..., p m }, such that l p 1 p 2... p m = O l l p i p j = { } i,j: i j and cost c(p) are minimized. the general partitioning problem is NP-complete 11 Cost Metrics - Example cost function : f(c, L, P) = k 1 h C (C,C) + k 2 h L (L,L) + k 3 h P (P,P) C system cost in [$] L execution time in [sec] P power consumption in [W] h C, h L, h P functions that determine how much C, L, P violate the design constraints C, L, P (penalty) k 1, k 2, k 3 weighting and normalization 12

General Partitioning Methods exact methods Œ enumeration Œ Integer Linear Programs (ILP) heuristic methods Œ constructive methods» random mapping» hierarchical clustering Œ iterative methods» Kernighan-Lin Algorithm» Simulated Annealing» Evolutionary Algorithms (EA) 13 Integer Linear Programs (1) binary variables x i,k Œ x i,k = 1: object o i in block p k Œ x i,k = 0: object o i not in block p k cost c i,k, if object o i is in block p k integer linear program: x i, k m k= 1 x { 0,1} i, k = 1 minimize 1 i n,1 k m 1 i n m n k= 1i= 1 x i, k c i, k 1 k m,1 i n 14

Integer Linear Programs (2) additional constraints Πexample: maximum number of h k objects in block k n xi, k hk 1 i= 1 k m ILP is NP-complete Πin the worst-case exponential runtime Πsolved by branch&bound algorithms Πformulation gets difficult when constraints are non-linear 15 Constructive Methods random mapping Πeach object is assigned to a block randomly hierarchical clustering Πstepwise grouping of objects Πcloseness function determines how desirable it is to group two objects constructive methods Πare often used to generate a starting partition for iterative methods Πshow the difficulty of finding proper closeness functions 16

Hierarchical Clustering - Example (1) v 5 = v 1 v 3 v 2 10 10 v 1 8 20 v 3 v 2 10 v 5 7 4 6 v 4 4 v 4 closeness function: arithmetic mean of weights 17 Hierarchical Clustering - Example (2) v 6 = v 2 v 5 v 5 10 v 6 v 2 7 5.5 4 v 4 v 4 18

Hierarchical Clustering - Example (3) v 6 5.5 v 7 = v 6 v 4 v 7 v 4 19 Hierarchical Clustering - Example (4) step 3: v 7 = v 6 v 4 step 2: v 6 = v 2 v 5 cut lines (partitions) step 1: v 5 = v 1 v 3 v 1 v 2 v 3 v 4 20

Iterative Methods - Kernighan-Lin (1) Generation of bi-partitions: re-group the object which leads to the largest gain in cost v 6 v 1 v 3 v 2 v 4 v 5 v 7 v 8 v 9 example: cost = number of edges crossing the partitions 21 Iterative Methods - Kernighan-Lin (2) Extensions Œ re-group the object which leads to the largest gain in cost or the smallest loss in cost» as long as a better partition is found: from all n objects, virtually re-group the best, then from the remaining n-1 objects again the best, etc., until all objects have been re-grouped from this n partitions take that with smallest cost and actually perform the corresponding re-group operations» escapes from global minima» asymptotic complexity O(n 3 ) Œ partitioning into m blocks: O(mn 3 ) 22

Iterative Methods - Simulated Annealing (1) from Physics: Œ metal and gas take on a minimal-energy state during cooling down (under certain constraints):» at each temperature, the system reaches a thermodynamic equilibrium» the temperature is decreased sufficiently slowly Œ probability that a particle jumps to a higher-energy state: P( e, e, T ) = e i j ei e k T B j application to Combinatorial Optimization Œ energy = cost of a solution (partition) Œ cost decreases with temperature, sometimes (with a certain probability) increases in cost are accepted 23 Iterative Methods - Simulated Annealing (2) temp = temp_start; cost = c(p); while (Frozen() == FALSE) { while (Equilibrium() == FALSE) { P = RandomMove(P); cost = c(p ); deltacost = cost - cost; if (Accept(deltacost, temp) > random[0,1)) { P = P ; cost = cost ; } } temp = DecreaseTemp (temp); } Accept() = min(1, e deltacost k temp ) 24

Iterative Methods - Simulated Annealing (3) Cooling Down: DecreaseTemp(), Frozen()» temp_start = 1.0» temp = α temp (typical: 0.8 α 0.99)» terminate when temp < temp_min or there is no more improvement Equilibrium: Equilibrium()» after defined number of iterations or when there is no more improvement Complexity Œ from exponential to constant, depending on the implementation of the functions Equilibrium(), DecreaseTemp(), and Frozen() Œ the longer the runtime, the better the quality of results Œ typical: construct functions to get polynomial runtimes 25 Iterative Methods - EA (1) Principles of Evolution å Selection Cross-over ê Mutation 26

Iterative Methods - EA (2) minimize g(x) = x² =one solution fitnesscalculation fitness = 9 selection next generation mutation cross-over 27 Applications Domain of EA Problem is: GLIIXVH FRPSOH[ Œ Examples:» system synthesis» route planning in robotics» container loading Multi criteria optimization Œ multiple criteria that are conflicting» example: performance vs. cost vs. power consumption Œ EA find Pareto-fronts (set of Pareto points) 28

Dominance, Pareto Points (1) Definition: A (design) point J i is dominated by J k, if J k is better or equal than J i in each criteria. Ji f J k Definition: A point is Pareto-optimal or a Pareto-point, if it is not dominated. 29 Dominance, Pareto Points (2) execution time 1 3 2 4 5 6 cost 30

Pareto-Ranking Fitness function: execution time = = 1: Ji p J F ( J ) i 1.. N, J 0 : else J i 1 2 4 3 5 6 F (1) = 0 F (2) = 1 F (3) = 2 F (4) = 0 F (5) = 0 F (6) = 5 cost 31 EA - Case Study (1) 32

EA - Case Study (2) 33 EA - Case Study (3) frame memory dual ported frame memory block matching module input module subtract/add module DCT/IDCT module 34 output module Huffman encoder

HW/SW Partitioning simplest case: bi-partitioning (processor-asic system) P = {p SW, p HW } software-oriented approach: P = {O, {}} Πin software we can realize all functions Πbut the performance may be inacceptably low migrate objects into hardware to improve performance hardware-oriented approach: P = {{}, O} Πin hardware the performance is sufficient Πbut the cost might be too high migrate objects into software to lower cost 35 Greedy Algorithms Migration of objects into the other block (hw/sw), until there is no more improvement repeat { P old = P; for i = 1 to n { if (f(move(p, o i )) < f(p)) { P = Move(P, o i ); } } until (P == P old ) cost function 36

Yorktown Silicon Compiler (YSC) functional partitioning of hardware Πinput: functional description at the level of arithmetic and logic expressions Πpartitioning into functional units of a datapath (ALUs, register) Πmethod: hierarchical clustering Πcloseness function: Closeness( p, p min i j maxsize sharedwires( pi, p ) = maxwires( P) c 3 2 ) { size( p ), ( )} ( ) + ( ) i size p j size pi size p j j maxsize c 37 Hw/Sw Partitioning - Vulcan Input: program in HardwareC ΠC extended by a process concept and inter process communication Πspecification with constraits (min/max-times and rates) Target architecture: single-processor / single-asic Πone global bus, one global memory Πprocessor is the bus master Abstraction level: basic blocks and operations Πderministic computation times Πinternal/external non-deterministic computation times Method: HW-oriented Greedy-Algorithm Πcost function includes HW-cost, memory requirement, performance, and synchronization effort 38

Hw/Sw Partitioning - Cosyma Input: Program in C x ΠC extended by a process concept and inter process communication Πspecification with min/max-times Target architecture: processor + coprocessor Πcoupled by shared memory Πcomputations on the processor and on the coprocessor may not overlap Abstraction level: basic blocks Method: SW-oriented, 2 loops: Πinner loop: Simulated Annealing with cost function that measures the gain in computation time for a hardware-realization of a block Πouter loop: synthesis to get estimations for the inner loop 39