15 213 The course that gives CMU its Zip Code Optimization I September 22 2006 Topics Machine Independent Optimizations Basic optimizations Optimization blockers class08 ppt Harsh Reality 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 2 How programs are compiled and executed How to measure program performance and identify bottlenecks How to improve performance without destroying code modularity and generality 15 213 F 06 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 3 potential memory aliasing potential procedure side effects 15 213 F 06 Limitations of Optimizing Compilers Operate under fundamental constraint Must not cause any change in program behavior under any possible condition 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 4 15 213 F 06 Machine Independent 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 5 long j int ni n i for j 0 j n j a ni j b j 15 213 F 06 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 xorl cmpq jge movq imulq leaq r8d r8d rcx r8 L7 rcx rax rdx rax rdi rax 8 rdx movq incq movq addq cmpq jl rsi r8 8 rax r8 rax rdx 8 rdx rcx r8 L5 L5 6 L7 rep ret j 0 j n if goto done n n i outside of inner loop rowp A n i 8 loop t b j j rowp t rowp j n if goot loop done 15 213 F 06 return 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 Pentium IV integer multiply requires 10 CPU cycles Recognize sequence of products for i 0 i n i for j 0 j n j a n i j b j 7 int ni 0 for i 0 i n i for j 0 j n j a ni j b j ni n 15 213 F 06 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 8 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 int inj i n up val inj down val inj left val inj right val inj sum up down j n n 1 1 left right 1 multiplication i n imulq addq movq subq leaq rcx rsi i n rdx rsi i n j rsi rax i n j rcx rax i n j n rsi rcx rcx i n j n 15 213 F 06 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 Remedies Use of inline functions Do your own code motion 15 int lencnt 0 size t strlen const char s size t length 0 while s 0 s length lencnt length return length 15 213 F 06 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 16 Code updates b i on every iteration Why couldn t compiler optimize this away FP add FP store 15 213 F 06 Memory Aliasing 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 Value of B double A 9 0 1 2 4 8 16 32 64 128 init double B 3 A 3 i 1 3 22 16 sum rows1 A B 3 i 2 3 22 224 17 4 8 16 i 0 3 8 16 Code updates b i on every iteration Must consider possibility that these updates will affect program behavior 15 213 F 06 Removing Aliasing Sum rows is of n X n matrix a and store in vector b void sum rows2 double a double b long n long i j for i 0 i n i double val 0 for j 0 j n j val a i n j b i val sum rows2 inner loop L66 addsd rcx xmm0 addq 8 rcx decq rax jne L66 18 FP Add No need to store intermediate results 15 213 F 06 Unaliased Version Sum rows is of n X n matrix a and store in vector b void sum rows2 double a double b long n long i j for i 0 i n i double val 0 for j 0 j n j val a i n j b i val Value of B double A 9 0 1 2 4 8 16 …
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