1 Topics (cont) Loop Transformations VI. Parallelism and Locality - PowerPoint PPT Presentation

Final Review Questions to think about Today Possible big picture questions – Overview of what we have learned so far – For this class, which of the five criteria for evaluating optimizations have – SSA review we used and how? (safety, profitability, opportunity, compile-time, – pointer and alias analysis implementation complexity) – interprocedural analysis and optimization – What is the scope of different analyses/optimizations that we have – loop transformations and Fourier-Motzkin studied? (peep hole, local, global, interprocedural) – affine partitionings for parallelism – Where could a representation for loops (polyhedral or presburger sets) fit – induction variable elimination review into the MiniJava compiler? – How would you design an experiment to compare a set of alias/pointer Studying analysis algorithms? – make sure to review terminology – (i.e. what does flow-sensitive mean?) – do lots of examples CS553 Lecture Final Review 1 CS553 Lecture Final Review 2 Structure of the MiniJava Compiler (CodeGenAssem.java) Topics I. Introduction Analysis Synthesis – Scanning and parsing character stream II. Compiling for OOP and Garbage Collection III. Low-Level Optimizations Lexer Translate lexical analysis IR code generation – Register allocation – Instruction scheduling tokens “words” IRT Tree/ IV. Data-Flow and Control-Flow Analysis and Optimization instruction selection Mips/Codegen Parser.parse() syntactic analysis – Dataflow analysis – Theoretic framework built on lattices AST “sentences” Assem – Control flow analysis: control-flow graphs, dominators, dominance frontiers, Project 4 irreducibility BuildSymTable semantic analysis optimization CheckTypes – Program optimizations: dead-code elimination, constant propagation, CSE, loop- Assem invariant code motion, copy propagation, PRE, induction variable elimination (*) CodeGenAssem V. Static Single Assignment (*) AST and symbol table code generation – SSA Form: types of data dependences, how to translate to minimal SSA minijava.node/ MIPS – global value numbering SymTable/ CS553 Lecture Final Review 3 CS553 Lecture Final Review 4 1

Topics (cont) Loop Transformations VI. Parallelism and Locality (*) Original code – Dependence analysis do i = 1,6 – Loop transformations do j = 1,5 – unimodular transformation framework j A(i,j) = A(i-1,j+1)+1 i – Kelly and Pugh transformation framework enddo – Tiling and Unroll and Jam: when is tiling legal? enddo – Fourier Motzkin elimination for code generation – Affine partitionings for parallelism (1, -1) Distance vector: Which loop can we parallelize and why? IV. Interprocedural Analysis and Optimization (*) What transformation can enable parallelism? – Aliases – how do data-flow analysis algorithms use aliasing information? What is a synchronization-free affine partitioning for this loop? – how do we characterize alias analysis algorithms? – Interprocedural Analysis – how do different levels of context information affect analysis results? CS553 Lecture Final Review 5 CS553 Lecture Final Review 6 Synchronization-free parallelism SSA do i = 1 to N f = read() x = 3 do j = 0 to M y = 5 A(i,j) = A(i-1,j) if (f>6) z = 7 else z = 0 x = y - 2 print x+y+z CS553 Lecture Final Review 7 CS553 Lecture Final Review 8 2

Induction Variable Elimination Jump Functions for Figure 12.11 in book i = 0 int id(int p) { return p; } j = 0 k = 0 if (a==1) { x = id(2); y=id(3); } loop: else { x = id(3); y=id(2); } i = i + 1 z = x+y; j = i*4 k = i+10 if i<10 goto loop exit: CS553 Lecture Final Review 9 CS553 Lecture Final Review 10 Alias/Pointer Analysis Example Example (Data dependence analysis main() { Sample code int *a,*b,c,d; do i = 1,6 a = &c; do j = 1,5 b = &d; A(2i,j) = A(i,j-1) foo(&a,&a); enddo foo(&b,&a); enddo } j void boo(int** x, int **y){ *x = *y; Dependence i **x = 3; – 2i 1 -i 2 = 0, j 1 = j 2 - 1, solution: YES } void foo(int** p, int **q){ Distance/Direction Vector boo(p,q); } – (i 1 , j 1 ) + (d i , d j ) = (i 2 , j 2 ), d j = 1, d i = ?, d = (<,1) Which analyses are relevant? FICI, FICS, FSCI, and/or FSCS Dependence Relation How do the analysis results differ based on a call stack size of 0, 1, or 2? – { [i, j] -> [2i, j +1 ]| 1<=i<=3 && 1<=j<=4 } CS553 Lecture Final Review 11 CS553 Lecture Final Review 12 3

Tiling Sample code do i = 1,6 do j = 1,5 A(2i,j) = A(i,j-1) enddo enddo j Dependence Relation i – { [i, j] -> [2i, j +1 ]| 1<=i<=3 && 1<=j<=4 } Tiling Both Loops with tile size 4 – { [i, j] -> [(j-1)/4, (i-1)/4, i,j]} CS553 Lecture Final Review 13 4