Program Optimization 1 Today Overview Generally Useful Optimizations Code motion precomputation Strength reduction Sharing of common subexpressions Removing unnecessary procedure calls Optimization Blockers Procedure calls Memory aliasing Exploiting Instruction Level Parallelism Dealing with Conditionals 2 Performance Realities There s more to performance than asymptotic complexity Constant factors matter too Easily see 10 1 performance range depending on how code is written Must optimize at multiple levels algorithm data representations procedures and loops Must understand system to optimize performance How programs are compiled and executed How to measure program performance and identify bottlenecks How to improve performance without destroying code modularity and generality 3 Optimizing Compilers Provide efficient mapping of program to machine register allocation code selection and ordering scheduling dead code elimination eliminating minor inefficiencies Don t usually improve asymptotic efficiency up to programmer to select best overall algorithm big O savings are often more important than constant factors but constant factors also matter Have difficulty overcoming optimization blockers potential memory aliasing potential procedure side effects 4 Limitations of Optimizing Compilers Operate under fundamental constraint Must not cause any change in program behavior Often prevents it from making optimizations when would only affect behavior under pathological conditions Behavior that may be obvious to the programmer can be obfuscated by languages and coding styles e g Data ranges may be more limited than variable types suggest Most analysis is performed only within procedures Whole program analysis is too expensive in most cases Most analysis is based only on static information Compiler has difficulty anticipating run time inputs When in doubt the compiler must be conservative 5 Generally Useful Optimizations Optimizations that you or the compiler should do regardless of processor compiler Code Motion Reduce frequency with which computation performed If it will always produce same result Especially moving code out of loop void set row double a double b long i long n long j for j 0 j n j a n i j b j long j int ni n i for j 0 j n j a ni j b j 6 Compiler Generated Code Motion void set row double a double b long i long n long j for j 0 j n j a n i j b j long j long ni n i double rowp a ni for j 0 j n j rowp b j Where are the FP operations set row testq rcx rcx Test n jle L4 If 0 goto done movq rcx rax rax n imulq rdx rax rax i leaq rdi rax 8 rdx rowp A n i 8 movl 0 r8d j 0 L3 loop movq rsi r8 8 rax t b j movq rax rdx rowp t addq 1 r8 j addq 8 rdx rowp cmpq r8 rcx Compare n j jg L3 If goto loop L4 done rep ret 7 Reduction in Strength Replace costly operation with simpler one Shift add instead of multiply or divide 16 x x 4 Utility machine dependent Depends on cost of multiply or divide instruction On Intel Nehalem integer multiply requires 3 CPU cycles Recognize sequence of products for i 0 i n i for j 0 j n j a n i j b j int ni 0 for i 0 i n i for j 0 j n j a ni j b j ni n 8 Share Common Subexpressions Reuse portions of expressions Compilers often not very sophisticated in exploiting arithmetic properties Sum neighbors of i j up val i 1 n j down val i 1 n j left val i n j 1 right val i n j 1 sum up down left right 3 multiplications i n i 1 n i 1 n leaq leaq imulq imulq imulq addq addq addq 1 rsi rax 1 rsi r8 rcx rsi rcx rax rcx r8 rdx rsi rdx rax rdx r8 i 1 i 1 i n i 1 n i 1 n i n j i 1 n j i 1 n j long inj i n j up val inj n down val inj n left val inj 1 right val inj 1 sum up down left right 1 multiplication i n imulq rcx rsi i n addq rdx rsi i n j movq rsi rax i n j subq rcx rax i n j n leaq rsi rcx rcx i n j n 9 Optimization Blocker 1 Procedure Calls Procedure to Convert String to Lower Case void lower char s int i for i 0 i strlen s i if s i A s i Z s i A a Extracted from 213 lab submissions Fall 1998 10 Lower Case Conversion Performance CPU seconds Time quadruples when double string length Quadratic performance lower 200 180 160 140 120 100 80 60 40 20 0 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000 String length 11 Convert Loop To Goto Form void lower char s int i 0 if i strlen s goto done loop if s i A s i Z s i A a i if i strlen s goto loop done strlen executed every iteration 12 Calling Strlen My version of strlen size t strlen const char s size t length 0 while s 0 s length return length Strlen performance Only way to determine length of string is to scan its entire length looking for null character Overall performance string of length N N calls to strlen Require times N N 1 N 2 1 Overall O N2 performance 13 Improving Performance void lower char s int i int len strlen s for i 0 i len i if s i A s i Z s i A a Move call to strlen outside of loop Since result does not change from one iteration to another Form of code motion 14 Lower Case Conversion Performance CPU seconds Time doubles when double string length Linear performance of lower2 200 180 160 140 120 lower 100 80 60 40 20 lower2 0 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000 String length 15 Optimization Blocker Procedure Calls Why couldn t compiler move strlen out of inner loop Procedure may have side effects Alters global state each time called Function may not return same value for given arguments Depends on other parts of global state Procedure lower could interact with strlen Warning Compiler treats procedure call as a black box Weak optimizations near them int lencnt 0 Remedies size t strlen const char s Use of inline functions GCC does this with O2 See web aside ASM OPT Do your own code motion size t length 0 while s 0 s length lencnt length return length 16 Memory Matters Sum rows is of n X n matrix a and store in vector b void sum rows1 double a double b long n long i j for i 0 i n i b i 0 for j 0 j n j b i a i n j sum rows1 inner loop L53 addsd rcx xmm0 addq 8 rcx decq rax movsd xmm0 rsi r8 8 jne L53 FP add FP store Code updates b i on every iteration …