Hardware-Software Codesign 4. System Partitioning Lothar Thiele - PowerPoint PPT Presentation

Hardware-Software Codesign 4. System Partitioning Lothar Thiele Swiss Federal Computer Engineering 4 - 1 Institute of Technology and Networks Laboratory

System Design specification system synthesis estimation SW-compilation instruction set HW-synthesis intellectual intellectual prop. code prop. block machine code net lists Swiss Federal Computer Engineering 4 - 2 Institute of Technology and Networks Laboratory

Mapping Mapping transforms behavior into structure and execution: allocation : select components partitioning binding : assign functions to components mapping scheduling : determine execution order … finally, synthesis results into implementation Swiss Federal Computer Engineering 4 - 3 Institute of Technology and Networks Laboratory

Levels of Abstractions Mapping can be done at low level: register transfer level (RTL) or netlist level  e.g., split a digital circuit and map it to several devices (FPGAs, ASICs)  system parameters (e.g., area, delay) relatively easy to determine p0 p3 p1 p2 at high level: system level CPU0 CPU2 CPU1 CPU3  comparison of design alternatives for optimality (design space exploration) bus … OR ?  system parameters are unknown and difficult to determine p0 p3 p1 p2  to be estimated via analysis, simulation, (rapid) prototyping CPU0 CPU2 CPU1 CPU3 Swiss Federal Computer Engineering bus 4 - 4 Institute of Technology and Networks Laboratory

Model-Based Synthesis – Example optimal C: N:1 mapping p0 p3 p1 p2 optimal L: 1:1 mapping CPU0 CPU1 CPU2 CPU3 bus considered performance  cost C: cost of allocated components, e.g., sum  latency L: due to scheduling (resource sharing) conflicting design goals and constraints  feasible schedule L ≤ Lmax  feasible allocation C ≤ Cmax Swiss Federal Computer Engineering 4 - 5 Institute of Technology and Networks Laboratory

Example – Alternatives p0 p3 p1 p2 CPU0 p0 p1 p2 p3 latency CPU0 CPU2 CPU1 CPU3 L MAX bus optimal C: N:1 mapping optimal L: 1:1 mapping CPU0 p0 p0 p3 p1 p2 p1 CPU1 CPU2 p2 CPU0 CPU2 CPU1 CPU3 CPU3 p3 bus latency L MAX Swiss Federal Computer Engineering 4 - 6 Institute of Technology and Networks Laboratory

Cost Functions Quantitatively measure performance of a design point  system cost C[$]  latency L[sec]  power consumption P[W]  … Estimation is required to find C,L,P values, for each design point  example: linear cost (preference) function with penalty f(C,L,P)= k 1 ·h C (C,C max )+ k 2 ·h L (L,L max )+ k 3 ·h P (P,P max )  h C , h L , h P … denote how strong C, L, P violate design constraints C max , L max , P max  k 1 , k 2 , k 3 … weighting and normalization Swiss Federal Computer Engineering 4 - 7 Institute of Technology and Networks Laboratory

The Formal Partitioning Problem assign n objects O={o 1 ,...,o n } to m blocks (also called partitions) P={p 1 ,...,p m } , such that  p 1  p 2  ...  p m =O (all objects are assigned –mapped)  p i  p j ={ }  i,j:i  j (an object is not assigned or “mapped” twice)  and costs c(P) are minimized note: in system synthesis (simple model) objects O p0 p3 p1 p2 objects = process network graph nodes partitions p blocks = architecture graph nodes cost = measured/estimated with blocks m dedicated cost functions (e.g., latency, CPU0 CPU1 power, hardware cost) bus Swiss Federal Computer Engineering 4 - 8 Institute of Technology and Networks Laboratory

Partitioning Methods Exact methods  enumeration  integer linear programs (ILP) (  see next slides) Heuristic methods  constructive methods • random mapping • hierarchical clustering  iterative methods • Kernighan-Lin algorithm • simulated annealing • evolutionary algorithms Swiss Federal Computer Engineering 4 - 9 Institute of Technology and Networks Laboratory

Integer Programming Model Ingredients:  objective function (cost) involving linear expressions of integer variables from a set X  constraints     objective C a x with a R , x N ( 1 ) i i i i  x X i      j J : b x c with b , c R ( 2 ) constraints i , j i j i , j j  x X i Integer programming (IP) problem: minimize objective function (1) subject to constraints (2) note: if all x i are constrained to be either 0 or 1 , the IP problem is said to be a 0/1 integer programming problem Swiss Federal Computer Engineering 4 - 10 Institute of Technology and Networks Laboratory

Small Example of 0/1 IP    C 5 x 6 x 4 x minimize: 1 2 3    x x x 2 subject to: 1 2 3  x , x , x { 0 , 1 } 1 2 3 C optimal (minimal) Swiss Federal Computer Engineering 4 - 11 Institute of Technology and Networks Laboratory

Integer Linear Program for Partitioning Binary variables x i,k  x i,k = 1: object o i in block p k  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 0 , 1 1 i n , 1 k m i , k m    x 1 1 i n  i , k  k 1 m n      minimize x c 1 k m , 1 i n   i , k i , k   k 1 i 1 Swiss Federal Computer Engineering 4 - 12 Institute of Technology and Networks Laboratory

Example – Partitioning t0 t3 t1 t2 task t0 t1 t2 t3 PE PE0 1 1 0 0 PE1 0 0 1 1 PE0 PE1 bus e.g., optimized for a load balanced system load balancing: exe. t0 t1 t2 t3 time load PE0 = 5+15 PE0 5 15 10 30 load PE1 = 10+10 PE1 10 20 10 10 Swiss Federal Computer Engineering 4 - 13 Institute of Technology and Networks Laboratory

Variations in ILP Additional constraints:  e.g., maximum h k objects in block k n    x h 1 k m  i , k k  i 1 Maximizing the cost function:  can be done by setting C’= -C in a minimization problem Swiss Federal Computer Engineering 4 - 14 Institute of Technology and Networks Laboratory

ILP for synthesis Solving the synthesis problem with ILP is very popular:  If not solving to optimality, runtimes are acceptable and a solution with guaranteed quality can be determined.  Scheduling can be integrated.  Various additional constraints can be added.  However, finding the right equations to model the constraints is an art. Swiss Federal Computer Engineering 4 - 15 Institute of Technology and Networks Laboratory

Remarks on Integer Programming Integer programming is NP-complete  In practice, runtimes can increase exponentially with the size of the problem.  But problems of some thousands of variables can still be solved with commercial solvers (depending on the size/structure of the problem) or approximation algorithms (heuristics).  IP models can be a good starting point for designing heuristic optimization methods. Swiss Federal Computer Engineering 4 - 16 Institute of Technology and Networks Laboratory

Partitioning Methods exact methods  enumeration  integer linear programs (ILP) heuristic methods  constructive methods (  see next slides) • random mapping • hierarchical clustering  iterative methods • Kernighan-Lin algorithm • simulated annealing • evolutionary algorithms Swiss Federal Computer Engineering 4 - 17 Institute of Technology and Networks Laboratory

Constructive Methods Examples  random mapping • each object is assigned to a block randomly  hierarchical clustering • stepwise grouping of (e.g., two) objects • and evaluate closeness function (how desirable it is to group objects) Constructive methods are often used to generate a starting partition for iterative methods Swiss Federal Computer Engineering 4 - 18 Institute of Technology and Networks Laboratory

Hierarchical Clustering Example (1) v 5 = v 1  v 3 v 1 v 5 20 10 10 8 10 7 v 2 v 2 v 3 4 4 6 v 4 v 4 closeness function: arithmetic mean of weights Swiss Federal Computer Engineering 4 - 19 Institute of Technology and Networks Laboratory

Hierarchical Clustering Example (2) v 6 = v 2  v 5 v 5 v 6 10 7 5.5 v 2 4 v 4 v 4 Swiss Federal Computer Engineering 4 - 20 Institute of Technology and Networks Laboratory

Hierarchical Clustering Example (3) v 6 v 7 = v 6  v 4 v 7 5.5 v 4 Swiss Federal Computer Engineering 4 - 21 Institute of Technology and Networks Laboratory

Hierarchical Clustering – Summary cut lines step 3: v 7 {v 7 } v 7 = v 6  v 4 (partitions) {v 4 ,v 6 } v 6 step 2: v 6 = v 2  v 5 {v 2 ,v 4 ,v 5 } step 1: v 5 v 5 = v 1  v 3 {v 1 ,v 2 ,v 3 ,v 4 } v 1 v 2 v 3 v 4 step 0: Swiss Federal Computer Engineering 4 - 22 Institute of Technology and Networks Laboratory

Partitioning Methods exact methods  enumeration  integer linear programs (ILP) heuristic methods  constructive methods • random mapping • hierarchical clustering  iterative methods (  see next slides) • Kernighan-Lin algorithm • simulated annealing • evolutionary algorithms Swiss Federal Computer Engineering 4 - 23 Institute of Technology and Networks Laboratory