Harsh Reality 15 213 There There s more to performance than asymptotic complexity The course that gives CMU its Zip Code Optimization I Nov 25 2008 Constant factors matter too Easily see 10 1 performance range depending on how code is written Must optimize at multiple levels z algorithm data representations procedures and loops Topics Machine Independent Optimizations Must understand system to optimize performance z Basic optimizations z Optimization blockers 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 08 2 class25 ppt Optimizing Compilers Limitations of Optimizing Compilers Provide efficient mapping of program to machine Operate under fundamental constraint register allocation code selection and ordering scheduling dead code elimination eliminating minor inefficiencies Behavior that may be obvious to the programmer can be obfuscated by languages and coding styles Don Don t usually improve asymptotic efficiency up to programmer to select best overall algorithm big O savings are often more important than constant factors Have difficulty overcoming optimization blockers blockers potential memory aliasing potential procedure side effects e g Data ranges may be more limited than variable types suggest Most analysis is performed only within procedures z but constant factors also matter 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 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 3 15 213 F 08 4 15 213 F 08 Machine Independent Optimizations 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 Optimizations that you or the compiler should do regardless of processor compiler long j long ni n i double rowp a ni for j 0 j n j rowp b j Code Motion Where are the FP operations Reduce frequency with which computation performed set row z If it will always produce same result z 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 15 213 F 08 Reduction in Strength Replace costly operation with simpler one Shift add instead of multiply or divide 7 movq incq movq addq cmpq jl rsi r8 8 rax r8 rax rdx 8 rdx rcx r8 L5 L7 6 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 08 return Share Common Subexpressions 16 x x 4 z Utility machine dependent z Depends on cost of multiply or divide instruction On Pentium IV integer multiply requires 10 CPU cycles On Core 2 requires 3 cycles Recognize sequence of products for i 0 i n i for j 0 j n j a n i j b j r8d r8d rcx r8 L7 rcx rax rdx rax rdi rax 8 rdx L5 long j int ni n i for j 0 j n j a ni j b j 5 xorl cmpq jge movq imulq leaq 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 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 08 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 08 Optimization Blocker 1 Procedure Calls Lower Case Conversion Performance Procedure to Convert String to Lower Case Quadratic performance 15 213 F 08 9 Convert Loop To Goto Form 256k 64k 32k 16k 8k 4k 2k 128k 15 213 F 08 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 strlen executed every iteration 11 1k String Length 10 Calling Strlen 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 512 Extracted from 213 lab submissions Fall 1998 256 Time quadruples when double string length 1000 100 10 1 0 1 0 01 0 001 0 0001 CPU Seconds void lower char s int i for i 0 i strlen s i if s i A s i Z s i A a 15 213 F 08 12 N calls to strlen Require times N N 1 N 2 1 Overall O N2 performance 15 213 F 08 Improving Performance Lower Case Conversion 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 Time doubles when double string length Linear performance of lower2 10000 lower1 0 0001 15 213 F 08 13 Optimization Blocker Procedure Calls Why couldn couldn t compiler move strlen out of inner loop Procedure may have side effects Function may not return same value for given arguments z Depends on other parts of global state z 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 256k 128k 64k 32k 16k String Length 14 15 213 F 08 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 z Alters global state each time called 8k 0 000001 4k Form of code motion 2k 0 01 1k Since result does not change from one iteration to another 512 Move call to strlen outside of loop lower2 1 256 …
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