Spring 20092009 Lecture 9:9: IntroductionIntroduction toto Program Analysis and Optimization Outline • Introduction • Basic Blocks • Common Subexpression Elimination • Copy P ropa gatition •Dead CCodeode Eliminatation • Algebraic Simplification • Summary Prog ram Analysis • Compile-time reasoning about run-time behavior of program – Can discover things that are always true: • “ x is al ways 1 in thth e s tatemen t y = x + z” • “the pointer p always points into array a” • “the statement return 5 can never execute” – Can infer things that are likely to be true: • “the reference r usually refers to an object of class C” • “thethe statement a=b+ca = b + c appears ttoo eexecutexecute more frequently than the statement x = y + z” – Distinction between data and control-flow properties Saman Amarasinghe 3 6.035 ©MIT Fall 1998 Transformations • Use analysis results to transform program • Overall goal: improve some aspect of program • Traditional goals: – RdReduce number of execute d i nstruct ions – Reduce overall code size • Other goalsgoals emerge as space becomesbecomes more complex – Reduce number of cycles • Use vector or DSP instructions • Improve instruction or data cache hit rate – Reduce power consumption – Reduce memory usage Saman Amarasinghe 4 6.035 ©MIT Fall 1998 Outline • Introduction • Basic Blocks • Common Subexpression Elimination • Copy P ropa gatition •Dead CCodeode Eliminatation • Algebraic Simplification • Summary Control Flow Graph • Nodes Rep resent Comp utation – Each Node is a Basic Block –Basic Block is a Seququ ence of Instructions with • No Branches Out Of Middle of Basic Block • No Branches Into Middle of Basic Block • Basic Blocks should be maximal – Execution of basic block starts with first instruction – Includes all instructions in basic block •Edges Represent Control Flow Saman Amarasinghe 6 6.035 ©MIT Fall 1998 Control Flow Grap h s = 0; a = 4; into add(n, k) { i = 0; s = 0; a = 4; i = 0; k == 0 if (k == 0) b = 1; else b = 2; b = 1; b=b = 2;2; while (i < n) { i < n s = s + a*b; s = s +*+ a*bb; i = i + 1; return s; i = i + 1; } return s; } Saman Amarasinghe 7 6.035 ©MIT Fall 1998 Basic Block Construction • Start with instruction control-flow ggpraph • Visit all edges in graph • Merge aadjacentdjacent nnodesodes if – Only one edge from first node – Only oneone edge into second node s = 0; s = 0; a = 4; a = 4; Saman Amarasinghe 8 6.035 ©MIT Fall 1998 s = 0; s = 0; a = 4; a = 4; i = 0; k==0 b = 2; b = 1; i < n s = s + a*b; return s; iii+1; = i+1; Saman Amarasinghe 9 6.035 ©MIT Fall 2006 s = 0; s = 0; a = 4; a = 4; i = 0; i = 0; k==0 b = 2; b = 1; i < n s = s + a*b; return s; iii+1; = i+1; Saman Amarasinghe 10 6.035 ©MIT Fall 2006 s = 0; s = 0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; i < n s = s + a*b; return s; iii+1; = i+1; Saman Amarasinghe 11 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; i < n s = s + a*b; return s; iii+1; = i+1; Saman Amarasinghe 12 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; i < n i < n s = s + a*b; return s; iii+1; = i+1; Saman Amarasinghe 13 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; i < n i < n s = s + a*b; s = s + a*b; return s; iii+1; = i+1; Saman Amarasinghe 14 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; i < n i < n s = s + a*b; s = s + a*b; return s; i = i + 1; i = i + 1; Saman Amarasinghe 15 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; i < n i < n s = s + a*b; s = s + a*b; return s; i = i + 1; iii+1; = i+1; Saman Amarasinghe 16 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; i < n i < n s = s + a*b; s = s + a*b; return s; return s; i = i + 1; iii+1; = i+1; Saman Amarasinghe 17 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; b = 1; i < n i < n s = s + a*b; s = s + a*b; return s; return s; i = i + 1; iii+1; = i+1; Saman Amarasinghe 18 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; b = 1; i < n i < n s = s + a*b; s = s + a*b; return s; return s; i = i + 1; iii+1; = i+1; Saman Amarasinghe 19 6.035 ©MIT Fall 2006 s = 0; s=0; a = 4; a = 4; i = 0; k==0 i = 0; k==0 b = 2; b = 1; b = 2; b = 1; i < n i < n s = s + a*b; s = s + a*b; return s; return s; i = i + 1; iii+1; = i+1; Saman Amarasinghe 20 6.035 ©MIT Fall 2006 Program Points, Split and Join Points • One program point before and after each statement in program • Split point has multiple successors – conditional branch statements only split points • Merge point has multiple predecessors • Each basic block – Either starts with a merge point or its predecessor ends with a split point – Either ends with a split point or its successor stttarts wiithth a merge point Saman Amarasinghe 21 6.035 ©MIT Fall 1998 Basic Block Optimizations • Common SSubub - • Copy Propagation Expression Elimination – a=x+y; b=a; c=b+z; –a=(x+y) y)+z; b=x+y; – a=x+y; b=a; c=a+z; – t=x+y; a=t+z; b=t; • Constant Pr opagation • Dead Code Elimination –x=5; b=x+y; – a=x+y; b=a; b=a+z; –x=5; b=5+y; y; – a=x+y; b=a+z • Algebraic Identities • Strength Reduction – a=x*1; – tit=i*4*4; –a=x; – t=i<<2; Saman Amarasinghe 22 6.035 ©MIT Fall 1998 Basic Block Analysis App pproach • Assume normalized basic block - all statements are of the form – var = var op var (where op is a binary operator) – var = op var (where op is a unary operator) – var = var • Simulate a symbolic execution of basic block – Reason about values of variables (or other aspects of computation) – Derive property of interest Saman Amarasinghe 23 6.035 ©MIT Fall 1998 Two Kinds of Variables • Temp oraries Introduced By Comp iler – Transfer values only within basic block –Introduced as papa rt of instruction flattening – Introduced by optimizations/transformations – Typically assigned to only once • Program Variables – Declared in original program – May be assigned to multiple times – May t rans fer va lues between basic blbl ock s Saman Amarasinghe 24 6.035 ©MIT Fall 1998 Outline • Introduction • Basic Blocks • Common Subexpression Elimination • Copy P ropa gatition •Dead CCodeode Eliminatation • Algebraic Simplification • Summary Value Numbering • Reason about values of variables and expressions in the program – SimulateSimulate executionexecution ofof basicbasic blockblock – Assign virtual value to each variable and expression • Discovered pproperty:roperty: which vvariablesariables and eexpressionsxpressions have the same value • Standarduse: – Common subexpression elimination – Typically combined with transformation that • Saves computed values in temporaries • Replaces expressions with temporaries when value of expression previously computed Saman Amarasinghe 26 6.035 ©MIT Fall 1998 New Basic Original Basic Block Block a = x+y a = x+y t1 = a b = aaz+z b=b = a+za+z b = b+y t2 = b c = a+z b = b+y t3 = b Var to Val c = t2 x v1 y v2 Exp to Val Exp to Tmp a v3 v1+v2 v3 v1+v2 t1 z v4 v3+v4 v5 v3+v4 t2 b v5v6 v5+v2 t6 c v5 v5+v2 v6 Saman Amarasinghe 27 6.035 ©MIT Fall 1998 Value Numbering Summary • Forward symbolic execution of basic block • Each new value assigned to temporary – a=x+y; becomes a=x+y; t=a; – Temporary ppreservesreserves value fforor use llaterater in program eevenven if original variable rewritten • a=x+y; a=a+z; b=x+y becomes • a=x+y; t=a; a=a+z; b=t; • Maps – VtVar to Val – specifies symbolic value for eachvar iable – Exp to Val – specifies value of each evaluated expression – Exp toto TmpTmp – specifies tmp tthathat hholdsolds value ofof eacheach evaluated expression Saman Amarasinghe 28 6.035 ©MIT Fall 1998 Map Usage •Var to Val – Used to compute symbolic value of y and z when processing statement offf form x = y + z •Exp to Tmp – Used to determine which tmp to use if value(y) + value(z) previously computed when processing statement ooff fformorm x = y + z •Exp to Val – Used to update Var to Val when • processing statement of the form x = y + z, and • value(y) + value(z)value(z) previouslypreviously computedcomputed Saman Amarasinghe 29 6.035 ©MIT Fall 1998 Interesting Properties • Finds common subexpressions even if they use diff erent vari ables in expressions – y=a+b; x=b; z=a+x becomes – y= aa+b;+b;t t= y;y; x= b;b;z z= t – Why? Because computes with symbolic values • Finds ccommonommon subexpressions eveneven iiff vvariableariable that originally held the value was overwritten – yya=a+b;+b; y1y=1;; zaz =a+b+b becomes – y=a+b; t=y; y=1; z=t –Why ? Because saves values away in temporaries Saman Amarasinghe 30 6.035 ©MIT Fall 1998 One More Interesting Property • Flattening and CSE combine to capture partial and arbitrarily complex common subexpressions w=(a+b)+c; y=(a+x)+c; z=a+b; – After flattening: t1=a+b; wtw=t1+c;1+c; xbx=b;; t2 =a+x; yty=t2+c;2+c; z =aa+b;+b; x=b; – CSE algorithm notices that •t1+c andt 2+c compute same value • In the statement z = a+b, a+b has already been computed so generated code can reuse the result t1=a+b; w=t1+c; t3=w; x=b; t2=t1; y=t3; z=t1; Saman Amarasinghe 31 6.035 ©MIT Fall 1998 Problems I • Algorithm has a temporary for each new value – a=x+y; t1=a; •Introduces – lots of temporaries – lots of copy statements to temporaries • In many cases, temporaries and copy statements are unnecessary • S o we ellii mina te ththem withith copy propagation and dead code elimination Saman Amarasinghe 32 6.035 ©MIT Fall 1998 Problems II • Expressions have to be identical –