1 / 21

OPTIMIZATION

OPTIMIZATION. Chuen-Liang Chen Department of Computer Science and Information Engineering National Taiwan University Taipei, TAIWAN. Introduction. local optimization within a basic block may be accompanying with code generation e.g., peephole optimization global optimization

brendaz
Download Presentation

OPTIMIZATION

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. OPTIMIZATION Chuen-Liang Chen Department of Computer Science and Information Engineering National Taiwan University Taipei, TAIWAN

  2. Introduction • local optimization • within a basic block • may be accompanying with code generation • e.g., peephole optimization • global optimization • over more than one basic blocks • e.g., loop optimization data flow analysis (a technique)

  3. Peephole optimization (1/2) • modify particular pattern in a small window (peephole; 2-3 instructions) • may on intermediate or target code • constant folding (evaluate constant expressions in advance) • ( +, Lit1, Lit2, Result ) Þ( :=, Lit1+Lit2, Result ) • ( :=, Lit1, Result1 ), ( +, Lit2, Result1, Result2 )Þ( :=, Lit1, Result1 ), ( :=, Lit1+Lit2, Result2 ) • strength reduction (replace slow operations with faster equivalents) • ( *, Operand, 2, Result ) Þ( ShiftLeft, Operand, 1, Result ) • ( *, Operand, 4, Result ) Þ( ShiftLeft, Operand, 2, Result ) • null sequences (delete useless operations) • ( +, Operand, 0, Result ) Þ( :=, Operand, Result ) • ( *, Operand, 1, Result ) Þ ( :=, Operand, Result )

  4. Peephole optimization (2/2) • combine operations (replace several operations with one equivalent) • Load A, Rj; Load A+1, Rj+1ÞDoubleLoad A, Rj • BranchZero L1, R1; Branch L2; L1: ÞBranchNotZero L2, R1 • Subtract #1, R1; BranchZero L1, R1 ÞSubtractOneBranch L1, R1 • algebraic laws (use algebraic laws to simplify or reorder instructions) • ( +, Lit, Operand, Result ) Þ( +, Operand, Lit, Result ) • ( -, 0, Operand, Result ) Þ( Negate, Operand, Result ) • special case instructions (use instructions designed for special operand cases) • Subtract #1, R1 Þ Decrement R1 • Add #1, R1 Þ Increment R1 • Load #0, R1; Store A, R1 ÞClear A • address mode operations (use address modes to simplify code) • Load A, R1; Add 0(R1), R2 ÞAdd @A, R2 • Subtract #2, R1; Clear 0(R1) ÞClear -(R1)

  5. Loop optimization (1/6) • due to 90 / 10 rule • example -- for l in 1..100 loop for J in 1..100 loop T1 := Adr( A(l)(J) ); T2 := I * J; for K in 1..100 loop T1(K) := T2 * K; end loop; end loop; end loop; loop invariant expression factorization for l in 1..100 loop for J in 1..100 loop for K in 1..100 loop A(l)(J)(K) := ( I * J ) * K; end loop; end loop; end loop; for l in 1..100 loop T3 := Adr( A(I) ); for J in 1..100 loop T1 :=Adr( T3(J) ); T2 := I * J; for K in 1..100 loop T1(K) := T2 * K; end loop; end loop; end loop; loop invariant expression factorization

  6. Loop optimization (2/6) for l in 1..100 loop T3 := Adr( A(I) ); for J in 1..100 loop T1 :=Adr( T3(J) ); T2 := I * J; for K in 1..100 loop T1(K) := T2 * K; end loop; end loop; end loop; for l in 1..100 loop T3 := Adr( A(I) ); T4 := I; -- Initial value of l*J for J in 1..100 loop T1 := Adr( T3(J) ); T2 := T4; -- T4 holds I*J T5 := T2; -- Initial value of T2*K for K in 1..100 loop T1(K) := T5; -- T5 holds T2*K = I*J*K T5 := T5 + T2; end loop; T4 := T4 + I; end loop; end loop; induction variable elimination

  7. Loop optimization (3/6) for l in 1..100 loop T3 := Adr( A(I) ); T4 := I; for J in 1..100 loop T1 := Adr( T3(J) ); T2 := T4; T5 := T2; for K in 1..100 loop T1(K) := T5; T5 := T5 + T2; end loop; T4 := T4 + I; end loop; end loop; for l in 1..100 loop T3 := Adr( A(I) ); T4 := I; -- Initial value of l*J for J in 1..100 loop T1 := Adr( T3(J) ); T5 := T4; -- Initial value of T2*K for K in 1..100 loop T1(K) := T5; -- T5 holds T2*K = I*J*K T5 := T5 + T4; end loop; T4 := T4 + I; end loop; end loop; copy propagation

  8. Loop optimization (4/6) for l in 1..100 loop T3 := Adr( A(I) ); T4 := I; for J in 1..100 loop T1 := Adr( T3(J) ); T5 := T4; for K in 1..100 loop T1(K) := T5; T5 := T5 + T4; end loop; T4 := T4 + I; end loop; end loop; for l in 1..100 loop T3 := A0 + ( 10000 * l ) - 10000; T4 := I; -- Initial value of l*J for J in 1..100 loop T1 := T3 + ( 100 * J ) - 100; T5 := T4; -- Initial value of T4*K for K in 1..100 loop (T1+K-1)­:= T5; -- T5 holds T4*K = I*J*K T5 := T5 + T4; end loop; T4 := T4 + I; end loop; end loop; subscripting code expansion

  9. Loop optimization (5/6) for l in 1..100 loop T3 := A0 + ( 10000 * l ) - 10000; T4 := I; for J in 1..100 loop T1 := T3 + ( 100 * J ) - 100; T5 := T4; for K in 1..100 loop (T1+K-1)­ := T5; T5 := T5 + T4; end loop; T4 := T4 + I; end loop; end loop; T6 := A0 ; -- Initial value of Adr(A(I)) for l in 1..100 loop T3 := T6; T4 := I; -- Initial value of l*J T7 := T3; -- Initial value of Adr(A(l)(J)) for J in 1..100 loop T1 := T7; T5 := T4; -- Initial value of T4*K T8 := T1; -- Initial value of Adr(A(l)(J)(K)) for K in 1..100 loop T8­ := T5; -- T5 holds T4*K = I*J*K T5 := T5 + T4; T8 := T8 + 1; end loop; T4 := T4 + I; T7 := T7 + 100; end loop; T6 := T6 + 10000; end loop; induction variable elimination

  10. Loop optimization (6/6) T6 := A0 ; for l in 1..100 loop T3 := T6; T4 := I; T7 := T3; for J in 1..100 loop T1 := T7; T5 := T4; T8 := T1; for K in 1..100 loop T8­ := T5; T5 := T5 + T4; T8 := T8 + 1; end loop; T4 := T4 + I; T7 := T7 + 100; end loop; T6 := T6 + 10000; end loop; T6 := A0 ; -- Initial value of Adr(A(I)) for l in 1..100 loop T4 := I; -- Initial value of l*J T7 := T6; -- Initial value of Adr(A(l)(J)) for J in 1..100 loop T5 := T4; -- Initial value of T4*K T8 := T7; -- Initial value of Adr(A(l)(J)(K)) for K in 1..100 loop T8­ := T5; -- T5 holds T4*K = I*J*K T5 := T5 + T4; T8 := T8 + 1; end loop; T4 := T4 + I; T7 := T7 + 100; end loop; T6 := T6 + 10000; end loop; copy propa- gation

  11. 0 Read(Limit) I := 1 1 I > Limit 2 Read(J) I = 1 3 4 Sum := J Sum := Sum + J 5 I := I + 1 6 Write(Sum) Global data flow analysis (1/2) • to fetch information for global structure, not only for a basic block • data flow graph • node -- basic block • example -- Read ( Limit ) ; for I in 1 .. Limit loop Read ( J ) ; if I = 1 then Sum := J ; else Sum := Sum + J ; end if ; end loop ; Write ( Sum ) ;

  12. Global data flow analysis (2/2) • classification of data flow analyses • any-path v.s. all-path • forward-flow v.s. backward-flow • dependent on different types of information • data flow equations • each basic block has 4 sets, IN, OUT, KILLED, and GEN, whose relationships are specified by data flow equations • equations for all basic blocks need to be satisfied simultaneously • may not unique solution • solution • iterative method • structure method

  13. p p b s s Any-path forward-flow analysis • example -- uninitialized variable (used but undefined) • IN -- uninitialized just before this basic block • OUT -- uninitialized before (including) this basic block • KILLED -- defined • GEN -- out of scope • data flow equations -- • IN(b) = È iÎP(b) OUT(i) • OUT(b) = GEN(b) È ( IN(b) - KILLED(b) ) • IN(first) = universal set • initial condition, i.e., IN(first), is case by case

  14. p p b s s Any-path backward-flow analysis • example -- live variable • OUT -- will be used just after this basic block • IN -- will be used after (including) this basic block • KILLED -- defined • GEN -- used • data flow equations -- • OUT(b) = È iÎS(b) IN(i) • IN(b) = GEN(b) È ( OUT(b) - KILLED(b) ) • OUT(last) = f

  15. p p b s s All-path forward-flow analysis • example -- available expression (to check redundant computation) • IN -- already computed just before this basic block • OUT -- already computed before (including) this basic block • KILLED -- one of operands is re-defined • GEN -- computed subexpression • data flow equations -- • IN(b) = Ç iÎP(b) OUT(i) • OUT(b) = GEN(b) È ( IN(b) - KILLED(b) ) • IN(first) = f

  16. p p b s s All-path backward-flow analysis • example -- very busy expression (worth storing on register) • OUT -- will be used for all cases just after this basic block • IN -- will be used for all cases after (including) this basic block • KILLED -- defined • GEN -- used • data flow equations -- • OUT(b) = Ç iÎS(b) IN(i) • IN(b) = GEN(b) È ( OUT(b) - KILLED(b) ) • OUT(last) = f

  17. S1 S2 S1 S2 Structure method of data flow solution (1/4) • for backward analysis -- I Û O • for forward analysis • I = I1 O = ( I2 - K2 ) È G2 = ( ((I1-K1)ÈG1) - K2 ) È G2 = ( I - (K1ÈK2) ) È (G1-K2)ÈG2 K = K1È K2 G = ( G1 - K2 ) È G2 • I = I1 = I2 O = O1È O2 = ((I1-K1)ÈG1) È ((I2-K2)ÈG2) = ( I - (K1ÇK2) ) È (G1ÈG2) K = K1Ç K2 G = G1È G2 (any path)

  18. S1 S2 (all path) S1 S1 S2 S1 S2 S1 Structure method of data flow solution (2/4) • I = I1 = I2 O = O1Ç O2 = ((I1-K1)ÈG1) Ç ((I2-K2)ÈG2) = × × × = ( I - (K1ÈK2) ) È (G1ÇG2) K = K1È K2 G = G1Ç G2 • any path K = K1– all path K = K1È K2 G = ( G2 - K1 ) È G1 G = G1

  19. 0 Read(Limit) I := 1 1 I > Limit 2 Read(J) I = 1 3 4 Sum := J Sum := Sum + J 5 I := I + 1 6 Write(Sum) Structure method of data flow solution (3/4) • example -- uninitialized variable

  20. Structure method of data flow solution (4/4)

  21. Applications of data flow analyses

More Related