Early Program Optimizations Chapter 12 Mooly Sagiv

Outline Constant Folding Scalar Replacement of Aggregates Algebraic Simplification and Reassociation Value Numbering –Basic blocks –Procedure based data flow analysis Sparse conditional constant propagation

Constant Folding Evaluate expressions with constant value inside basic blocks Invoked at all levels Computations need to be conducted according to target machine Need to take care of overflow exceptions –Very problematic in floating point arithmetic

Scalar replacement of aggregates Replace structure elements by scalars Very simple but not common Depends on aliasing Makes other optimizations applicable

typedef enum { APPLE, BANANA, ORANGE} VARIETY; typedef enum { LONG, ROUND} SHAPE; typedef struct fruit { VARIETY variety; SHAPE shape ; } FRUIT;

char * Red = “red”; char * Yellow = “yellow”; char * Orange = “orange”; char * color(FRUIT CurrentFruit); { switch (currentFruit->variety) { case APPLE: return Red; break; case BANANA: return Yellow; break; case ORANGE: return Orange; }} main() { FRUIT snack; snack.variety = APPLE; snack.shape = ROUND; printf(“%s\n”, color(&snack));} char * Red = “red”; char * Yellow = “yellow”; char * Orange = “orange”; main() { FRUIT snack; VARIETY t1; SHAPE t2; COLOR t3; t1 = APPLE; t2 = ROUND; switch (t1) { case APPLE: t3= Red; break; case BANANA: t3=Yellow; break; case ORANGE: t3=Orange; }} printf(“%s\n”, t3);}

char * Red = “red”; char * Yellow = “yellow”; char * Orange = “orange”; main() { FRUIT snack; VARIETY t1; SHAPE t2; COLOR t3; t1 = APPLE; t2 = ROUND; switch (t1) { case APPLE: t3= Red; break; case BANANA: t3=Yellow; break; case ORANGE: t3=Orange; }} printf(“%s\n”, t3);} main() { printf(“%s\n”, “red”);}

Algebraic Simplification and Reassociations Use algebraic properties of operators in basic block Invoked at all levels Convert (HIR, MIR, LIR) in a basic block into a tree  rewrite trees according to rules (in an efficient way) Mainly for integer and address arithmetic

0/1/false/true Simplification

Simplifying Unary Operators

Simplifying Shift Operators

Strength Reduction in Operators t  i *5 t  i shl 2 t  t +i t  i *7 t  i shl 3 t  t - i

Commutativity and Associativity

Algebraic Simplifications of Addressing Expressions Cannot raise overflow Important for array references Use canonizations Integrate with other optimizations

var a:array[lo1..hi1, lo2..hi2] of eltype; i, j: integer;... for j :=lo2 to hi2 do a[i,j] := b+a[i, j]; end

Algebraic Simplifications of Floating Point Expressions Almost always impossible Removal of type coercions can be done eps:=1.0 ; while eps+1.0>1.0 do oldeps := eps; eps := 0.5*eps; od

Summary Algebraic association and constant folding are useful Compiler need to take into account the exact semantics Example: Floating point –IEEE Standards, C, Fortran77, Ada, Java