Fast Design Space Exploration using Hierarchies

1. Fast Design Space Exploration using Hierarchies Patrick de la Hamette, Marco Wirz

2. Overview • motivation • ad hoc approach • formalized approach- decomposition, composition- simple example- validity function- component level filtering- common /partial validity filter- quality filter- example Design Space Exploration

3. motivation: DSE in large systems large system design: • evaluation criteria: e =(cost, time) (performance-1) • many design parameters… (cache_size, cache_associativity, cache_ports, cpu_instruction_size…) • Problems: - design space D {d1,…,dn} is huge(all parameter combinations)- evaluation D e complicated (slow)- infeasible… RAM Bus CPU Cache Goal: reduce number of designs to be evaluated, with no loss in accuracy Design Space Exploration

4. approach Problem: produces non optimal results if interactions between subsystems are complicated… big system ad hoc approach Formalizedapproach • - split system into subsystems that interact little • evaluate isolated subsystems • recombine optimal subsystems Design Space Exploration

5. formalized approach • formal method for dividing a system into subsystems (components), which are separately evaluated • reduces design space(s) in a systematic way, using different filtering steps. • only a limited number of system combinations have to be evaluated • guarantees optimality of final designs (pareto set) systemcomposition system validity and optimality filtering Component 1 Design space D1 componentfiltering decomposition system ... Component n Design space Dn Design Space Exploration

6. decomposition: definition a decomposition of the design space partitions a system S into the components C1 ..Cn, with: • design spaces Di for all components Ci, ( ) with different component designs di,n , their evaluation functions e and a decomposition function, mapping a system to a set of components • validity function V: (D1X D2…X Dn)  [TRUE, FALSE]e.g. V(d1, …,di)=true for a valid system (=combination of component designs) • composition function : (D1X D2…X Dn)  [D,‡], mapping all sets of component design to system design, or to ‡ for invalid combination Design Space Exploration

7. simple, inefficient example • no component level filtering! • output = pareto set • Nc all combinations e.g. 10.000 • Nv valid combinations e.g. 1.000 • Np pareto comb. e.g. 100 • (“start with empty pareto set, and check for every new valid combination, if it is dominated. If not, add to pareto set, and remove elements that are dominated”) Goal: reduce Nc and Nv before final evalution, by filtering component design space! Design Space Exploration

8. Validity Function • System Validity function: V: (D1×D2×… ×Dn)  [true, false] reduced to canonical AND-OR form:V()=((a  b  c) v (a  d  e)) • Common expression: term appearing in all AND expressions (here: a)Can be factored out:V()=a  ((b  c) v (d  e)) • V() = CE  PSOPCE: Common Expression (a)PSOP: Partial Sum Of Products: (bc) v (de) Design Space Exploration

9. Component-level Filtering Design Space Exploration

10. Common Validity Filter • For each design space Di there is a common expression CEi (can be as simple as TRUE) • V() is the conjunction of all CEi: • If CEi is FALSE for a design di, then V() is FALSE for all designs containing di • Eliminate all di that do not satisfy CEi Design Space Exploration

11. Partial Validity Filter • V() = CE  PSOP • PSOP = ((b  c) v (d  e)) = • CPEij: Part of expression associated with component Ci • Eliminate all di that do not satisfy any CPEi Design Space Exploration

12. Quality Filter • PSi is the set of designs di which satisfy CEi and CPEi • Evaluate component designs di in PSi • Choose quality (Pareto) set QSi of di • Idea:A system design containing a component di in PSi but not in QSi can always be improved by substituting a design dp in QSi if the evaluation functions are perfectly correlated. Design Space Exploration

13. Component-level Filtering Design Space Exploration

14. Example • Processor / mem design • 100 designs each: total Nc = 10.000 • Simple System: • Validity: Nv = 1.000 • Quality: Np = 100 • Hierarchical system: • C[CE]: 40 of 100 processors: Nc = 4.000 • V[CPE] (4 sets): 12 Proc, 50 Mem: NC = 2.400 • Q (4 sets): 5 Proc, 10 Mem: Nc = 200 • Only 200 instead of 10.000 systems have to be evaluated. Design Space Exploration