Scalar Optimisation - Compiler Optimisation - Lecture Slides, Slides of Computer Science

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Scalar Optimisation Part 1^ Michael O’BoyleJanuary, 2013 M. O’Boyle Scalar Optimisation^

January, 2013

1 Course Structure • L1 Introduction and Recap • 4/5 lectures on classical optimisation– 2 lectures on scalar optimisation – Today example optimisations – Next lecture dataflow framework and SSA • 5 lectures on high level approaches • 4-5 lectures on adaptive compilation M. O’Boyle Scalar Optimisation^

January, 2013

3 Optimisation Classification • Machine independent vs dependent - not always a clear distinction.

Main trends in architecture increased memory latency and exploitation of ILP aremachine dependent • Machine independent applicable to all.

Eliminate redundant work, accesses. Use less expensive operations where possible • Optimisation can be performed at source, IR, assembler, machine code level. • Concentrate on machine independent scalar optimisation - IR level. • Optimisation = analysis + transformation. Form depends on IR - impact oncomplexity. M. O’Boyle^ Scalar Optimisation

January, 2013

4 Redundant expression elimination An expression x + y is redundant if already evaluated and not redefinedValue numbering: Associate numbers with operators/operands and hash lookupin table Hash (+,x,y) return value numberIf value number already there replace with reference to variable (^3 1 23 1 2312) a= x+ y a=^ x+^ y^ a=^ x+^ y^0 0 04 1 24 3412 b= x+ y b=^ a^ b=^ x+^ y^0 0 03 3 3 a= 17 a= 17^ a= 17^1 5 1 25 3512 c= x+ y c=^ a!!^ c=^ x+^ y^0 0

(^312) a=^ x+^ y (^0 0 043) b=^ a (^0 034) a= 17 (^1 53) c=^ a 0 0 Can be extended to handle larger scope based on dominators.

Fails in presence of general control-flow M. O’Boyle^ Scalar Optimisation

January, 2013

6 Super Local Value numbering SVN Basic blocks(BB) have just one entry and exit. • Extended BB: (EBB) A tree of BBs^ {B,... , B}^ where^1 n

Bmay have multiple^1 predecessors. • All others have a single unique predecessor but possibly multiple exits. • This tree is only entered at the root.In our example 3 EBBs (A,B,C,D,E), (F), (G)SVN considers each path within an EBB as single blockSo (A,B), (A,C,D), (A,C,E) are considered paths for LVN M. O’Boyle^ Scalar Optimisation

January, 2013

7 Example: Extended Basic Blocks.^ m = a+b^ ALn = a+bp = c + d^ q = a+b B^ CSr = c + dr = c+dL e = b + 18e = a + 17ED^ s = a + bt = c + du = e + fu = e + f v = a + bF^? w = c + d?x = e + f? y = a + bG? z = c + d?

SS M. O’Boyle^ Scalar Optimisation

January, 2013

9 Example: Dominator value numbering.^ m = a+b^ An = a+bL p = c + d^ q = a+b^ B^ CS r = c + dr = c+dL e = b + 18e = a + 17ED^ s = a + bt = c + du = e + fu = e + f v = a + bF w = c + dx = e + f^? y = a + bGz = c + d?

SS DD D What about the remaining two ?s in G and F? M. O’Boyle^ Scalar Optimisation

January, 2013

(^10) Dataflow analysis

-^ A formal program analysis that has a wide range of application. •^ Described property of a program at a particular point in set based recurrenceequations •^ Assumes a control-flow graph(CFG) consisting of nodes (basic blocks) andedges: control-flow •^ Determines property at a point in the program as a function of local informationand approximation of global information •^ Approx solutions will converge to exact solution in finite number of iterationsfor finite lattices - more detail next lecture M. O’Boyle^ Scalar Optimisation

January, 2013

12 Find available expressions part 1 Node A^ B^ C^ D^ E^

F^ G

pred^ -^ A^ A^ C^

C^ D,E^ B,F

DEExpr^ a+b^ c+d^ a+b^ b+

a+17^ a+b^ a+b c+d a+b c+d^ c+d^ c+d e+f e+f^ e+f Kill^ e+f

e+f Calculate Avail(b) for each Basic Block b starting at block A AV AIL(B) = (DEExpr(A)^ ∪^ (AV AIL(A

)^ ∩^ N OT KILLED(A)))

=^ {a^ +^ b} ∪^ (∅ ∩^ U^ ) =^ {a^ +^ b} AV AIL(C) = (DEExpr(A)^ ∪^ (AV AIL

(A)^ ∩^ N OT KILLED(A)))

=^ {a^ +^ b} ∪^ (∅ ∩^ U^ ) =^ {a^ +^ b} M. O’Boyle^ Scalar Optimisation

January, 2013

13 Find available expressions part 2 D and E are the same AV AIL(D) = (DEExpr(C)^ ∪^ (AV AIL(C)^ ∩^ N OT KILLED

(C)))

=^ {a^ +^ b, c^ +^ d} ∪^ ({a^ +^ b} ∩^ U^ ) =

{a^ +^ b, c^ +^ d} AV AIL(E) = (DEExpr(C)^ ∪^ (AV AIL

(C)^ ∩^ N OT KILLED(C)))

=^ {a^ +^ b, c^ +^ d} ∪^ ({a^ +^ b} ∩^ U^ ) =

{a^ +^ b, c^ +^ d} F is a join point: 2 predecessors AV AIL(F^ ) = (DEExpr(D)^ ∪^ (AV AIL

(D)^ ∩^ N OT KILLED(D)))

⋂(DEExpr(E)^ ∪^ (AV AIL(E)^ ∩

N OT KILLED(E)) =

{b^ + 18, a^ +^ b, e^ +^ f^ } ∪^ ({a^ +^ b,^ c

+^ d} ∩^ U^ − {e^ +^ f^ }) ⋂{a^ + 17, c^ +^ d, e^ +^ f^ } ∪^ ({a^ +^ b

,^ c^ +^ d} ∩^ U^ − {e^ +^ f^ }) =^ {a^ +^ b, c^ +^ d, e^ +^ f^ } M. O’Boyle^ Scalar Optimisation

January, 2013

15 Example: Global redundancy elim using AVAIL()^ m = a+bn = a+bp = c + d^ q = a+br = c + dr = c+de = b + 18s = a + bu = e + f AL B C^ SL e = a + 17ED^ t = c + dSS u = e + f v = a + bFDw = c + dDx = e + fG y = a + bGDz = c + dG M. O’Boyle^ Scalar Optimisation

January, 2013

(^16) Summary

-^ Levels of optimisations •^ Redundant expression elimination •^ LVN, SVN, DVN •^ Introduced dataflow as a generic optimisation framework •^ Iterative solution to equations •^ Next time: More detailed examination of dataflow and SSA M. O’Boyle^ Scalar Optimisation

January, 2013