Compilation 2007 Optimization Michael I. Schwartzbach BRICS, University of Aarhus

2 Optimization Optimization  The optimizer aims at: reducing the runtime reducing the code size  These goals often conflict, since a larger program may in fact be faster  The best optimizations achive both goals  An optimizer may also have more esoteric aims: reducing energy consumption reducing chip area

3 Optimization Optimizations for Space  Were historically important, because memory was small and expensive  When memory became large and cheap, optimizing compilers traded space for time  Java compilers do not optimize much, but JVM bytecodes are designed to be small  When Java is targeted at mobile devices, space optimizations are again important

4 Optimization Optimizations for Speed  Were historically important to gain acceptance for the introduction of high-level languages  Are still important, since the software always strains the limits of the hardware  Are challenged by ever higher abstractions in programming languages and must constantly adapt to changing microprocessor architecures  Java compilers do not optimize much, since the JVM kicks in with the JIT compiler

5 Optimization Opportunities for Optimization  At the source code level  At an intermediate low level  At the binary machine code level  At runtime (JIT compilers)  At the hardware level  An aggressive optimization requires many small contributions from all levels

6 Optimization Optimizers Must Undo Abstractions  Variables abstract away from registers, so the optimizer must find an efficient mapping  Control structures abstract away from gotos, so the optimizer must simplify a goto graph  Data structures abstract away from memory, so the optimizer must find an efficient layout...  Method invocations abstract away from procedure calls, so the optimizer must efficiently determine the intended implementation

7 Optimization Difficult Compromises  A high abstraction level makes the development time cheaper, but the runtime more expensive  An optimizing compiler makes runtime more efficient, but compile time less efficient  Optimizations for speed and size may conflict  Different applications may require different choices at different times

8 Optimization Examples of Optimizations  Strength reduction  Loop unrolling  Common subexpression elimination  Loop invariant code motion  Inline expansion  These may take place either at the source level or at the bytecode level  Most require information from static analyses

9 Optimization Strength Reduction  Replace expensive operations with cheap ones: for (i = 0; i < a.length; i++) a[i] = a[i] + i/4; for (i = 0; i < a.length; i++) a[i] += (i >> 2);

10 Optimization Loop Unrolling  Unfold a loop to save condition tests: for (i = 0; i < 100; i++) g(i); for (i = 0; i < 100; i += 2) { g(i); g(i+1); }

11 Optimization Common Subexpression Elimination  Avoid redundant computations: double d = a * Math.sqrt(c); double e = b * Math.sqrt(c); double tmp = Math.sqrt(c); double d = a * tmp; double e = b * tmp;

12 Optimization Loop Invariant Code Motion  Move constant valued expressions outside loops: for (i = 0; i < a.length; i++) b[i] = a[i] + c * d; int tmp1 = a.length; int tmp2 = c * d; for (i = 0; i < tmp1; i++) b[i] = a[i] + tmp2;

13 Optimization Inline Expansion  Replace method invocations with copies: int pred(int x) { if (x == 0) return x; else return x-1; } int f(int y) { return pred(y) + pred(0) + pred(y+1); } int f(int y) { int tmp = 0; if (y == 0) tmp += 0; else tmp += y-1; if (0 == 0) tmp += 0; else tmp += 0-1; if (y+1 ==0 ) tmp += 0; else tmp += (y+1)-1; return tmp; }

14 Optimization Collaborating Optimizations  Optimizations may enable other optimizations: int f(int y) { int tmp = 0; if (y == 0) tmp += 0; else tmp += y-1; if (0 == 0) tmp += 0; else tmp += 0-1; if (y+1 == 0) tmp += 0; else tmp += (y+1)-1; return tmp; } int f(int y) { if (y == 0) return 0; else if (y == -1) return -2; else return y+y-1; }

15 Optimization Optimization in Joos public int foo(int a, int b, int c) { c = a*b+c; if (c<a) a = a+b*113; while (b>0) { a = a*c; b = b-1; } return a; } iload_1 iload_2 imul iload_3 iadd dup istore_3 pop iload_3 iload_1 if_icmplt true1 iconst_0 goto end2 true1: iconst_1 end2: ifeq false0 iload_1 iload_2 imul iload_3 iadd istore_3 iload_3 iload_1 if_icmpge cond4 iload_1 iload_2 bipush 113 imul iadd istore_1 goto cond4 loop3: iload_1 iload_3 imul istore_1 iinc 2 -1 cond4: iload_2 ifgt loop3 iload_1 ireturn iload_1 iload_2 bipush 113 imul iadd dup istore_1 pop false0: goto cond4 loop3: iload_1 iload_3 imul dup istore_1 pop iload_2 iconst_1 isub dup istore_2 pop cond4: iload_2 iconst_0 if_icmpgt true5 iconst_0 goto end6 true5: iconst_1 end6: ifne loop3 iload_1 ireturn 52 bytecodes 27 bytecodes

16 Optimization Peephole Optimizations  Make local improvements in bytecode sequences  The optimizers considers only finite windows of the sequence  When the pattern "clicks", the optimizer rewrites a part of the code using a template: dup istore 3 istore 3 pop

17 Optimization Peephole Transitions  Let P be a collection of peephole patterns  It defines a transition relation on sequences of bytecodes: B 1 B 2 meaning that p  P clicked at some position in the sequence B 1 and produced the sequence B 2 p

18 Optimization Termination  A collection of peephole patterns must terminate  This means that for the collection P, there must not exist an infinite sequence: B 0 B 1 B 2 B 3... for any B 0 and p i  P p1p1 p2p2 p3p3 p4p4

19 Optimization Soundness (1/2)  Every peephole pattern must preserve semantics  Assume the pattern p transforms a bytecode sequence B 1 into the sequence B 2  Consider now any bytecode context C  If C[B 1 ] emits the verifiable code E 1, then C[B 2 ] must emit some verifiable code E 2 with the same semantics

20 Optimization Soundness (2/2)   C  B 1 :C B 1 B 2 E 1 E 2 p emit 

21 Optimization A Peephole Pattern Language  Joos has a domain-specific language for specifying peephole patterns  The Joos compiler contains an interpreter for this peephole language  It is invoked with the option -O patternfile  It will try all patterns in an unspecified order until no pattern clicks anywhere

22 Optimization Pattern Syntax pattern → pattern name var : exp -> intconst templates  The exp determines whether the pattern clicks  The intconst tells how many bytecodes to replace  The template specifies the new bytecodes  The evaluation of exp produces a set of bindings that may be used inside the templates and later in the expression

23 Optimization Expression Types  The following types are possible results: int label type-signature field-signature method-signature string condition bytecodes boolean  The notation inst(σ 1,..., σ k ) means that the given instruction has these arguments in the JVM specification

24 Optimization exp intop exp | exp intcomp exp | exp comp exp | exp ~ peepholes | ! exp | exp && exp | exp || exp | intconst | condconst Pattern Expressions exp →var | degree var | target var | formals var | returns var | negate exp | commute exp |

25 Optimization Peepholes and Templates peepholes →peephole* peephole →instruction | instruction ( vars ) | * |(any single instruction) var : (label binder) template →template* template →instruction | instruction ( exps ) condconst → eq | ne | lt | le | gt | ge | aeq | ane intop → + | - | * | / | % intcomp → | >= comp → == | !=

26 Optimization Peephole Judgements  The judgement: |- E: σ[  →  '] means that the expression E: evaluates to a result of type σ consumes the bindings  produces the bindings  '  The judgement: |- X: [  →  '] similarly describes peepholes, templates, and patterns

27 Optimization Expression Well-Formedness (1/5)  (x) = σ |- x: σ[  →  ]  (x) = label |- degree x: int[  →  ]  (x) = label |- target x: bytecodes[  →  ]  (x) = method-signature |- formals x: int[  →  ]

28 Optimization Expression Well-Formedness (2/5) |- E: condition[  →  '] |- negate E: condition[  →  ']  (x)= method-signature |- returns x: int[  →  ] |- E: condition[  →  '] |- commute E: condition[  →  ']

29 Optimization Expression Well-Formedness (3/5) |- E 1 : int[  →  '] |- E 2 : int[  ' →  ''] |- E 1 intop E 2 : int[  →  ''] |- E 1 : int[  →  '] |- E 2 : int[  '→  ''] |- E 1 intcomp E 2 : boolean[  →  ''] |- E 1 : σ[  →  '] |- E 2 : σ[  '→  ''] |- E 1 comp E 2 : boolean[  →  '']

30 Optimization Expression Well-Formedness (4/5) |- E: bytecodes[  →  '] |- P[  '→  ''] |- E ~ P: boolean[  →  ''] |- E: boolean[  →  '] |- ! E: boolean[  →  ] |- E 1 : boolean[  →  '] |- E 2 : boolean[  '→  ''] |- E 1 && E 2 : boolean[  →  '']

31 Optimization Expression Well-Formedness (5/5) |- E 1 : boolean[  →  '] |- E 2 : boolean[  →  '']  x:  '(x)=  '   ''(x)=  ''   ' =  '' |- E 1 || E 2 : boolean[  →  '   ''] |- k: int[  →  ] |- cond: condition[  →  ]

32 Optimization Peephole Well-Formedness (1/2) |- P i [  i →  i+1 ] |- P 1 P 2...P k [  1 →  k+1 ] |- inst: [  →  ] x i ≠ x j x i  inst(σ 1,..., σ k ) |- inst(x 1,...,x k )[  →  [x i →σ i ]]

33 Optimization Peephole Well-Formedness (2/2) |- * : [  →  ] |- x : : [  →  [x→label]] |- label (x) : [  →  [x→label]]

34 Optimization Template Well-Formedness |- T i : [  i →  i+1 ] |- T 1 T 2...T k : [  1 →  k+1 ] |- inst: [  →  ] |- E i : σ i [  i →  i+1 ] inst(σ 1,..., σ k ) |- inst(E 1,...,E k )[  1 →  k+1 ] |- E: label [  1 →  2 ] |- E:inst: [  1 →  2 ]

35 Optimization Pattern Well-Formedness |- E: boolean[[x→bytecodes] →  ] |- T[  →  '] |- pattern n x : E -> k T: [[]→  ']

36 Optimization Pattern Examples (1/4) pattern dup_istore_pop x: x ~ dup istore (i0) pop -> 3 istore (i0)  This pattern is relevant for code like: x = a*b;

37 Optimization Pattern Examples (2/4) pattern goto_label x: x ~ goto (l1) label (l2) && l1 == l2 -> 1  This pattern arises during optimization of nested control structures

38 Optimization Pattern Examples (3/4) pattern constant_iadd_residue x: x ~ ldc_int (i0) iadd ldc_int (i1) iadd -> 4 ldc_int (i0+i1) iadd  This pattern is relevant for code like: a+5+7

39 Optimization Pattern Examples (4/4) pattern goto_goto x: x ~ goto (l0) && target l0 ~ goto (l1) && ! (target l1 ~ goto (l2)) && ! (target l1 ~ label (l3)) -> 1 goto (l1)  This pattern arises during optimization of nested control structures

40 Optimization Proving Termination  We want to avoid infinite sequences like: B 0 B 1 B 2 B 3...  Define an integer valued function  such that:  B:  (B)  0  p  P: B 1 B 2   (B 2 ) <  (B 1 ) p1p1 p2p2 p3p3 p4p4 p

41 Optimization Termination Function Example  For our 4 example patterns we define:  (B) = # dup + # goto + # iadd + ???  What gets smaller in the goto_goto pattern?

42 Optimization Termination Function Example  For our 4 example patterns we define:  (B) = # dup + # goto + # iadd + ???  What gets smaller in the goto_goto pattern? label (l 1 )  B l 1 → l 2 → l 3 →... → l k l i ≠ l j  goto k

43 Optimization A Non-Terminating Pattern pattern bad_goto_goto x: x ~ goto (l0) && target l0 ~ goto (l1) -> 1 goto (l1) foo: goto bar bar: goto foo

44 Optimization Proving Soundness  A formal proof of soundness for a collection of patterns requires a full formal semantics of: bytecode sequences peephole patterns bytecode contexts code emission the complete JVM  The pitfall is usually the universal quantification of contexts: does this really always work?

45 Optimization An Unsound Pattern pattern idiv_pop x: x ~ idiv pop -> 1 pop  This pattern may actually click  And the resulting bytecode will always verify  But the semantics is not preserved, since it may remove a java.lang.ArithmeticException