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EECS 583 – Lecture 13 Classical, ILP Optimization

University of Michigan February 19, 2003

• 1 -

Constant Combining

Y

Combine 2 dependent ops into 1by combining the literals

r1 = r2 + 4

r5 = r1 - 9

Æ

r5 = r2 – 5

Y

First op often becomes dead

Y

Rules (ops X and Y in same BB)

X is of the form rx +- K

dest(X) != src1(X)

Y is of the form ry +- K(comparison also ok)

Y consumes dest(X)

src1(X) not modified in (X…Y)

r1 = r2 + 4 r3 = r1 < 0 r2 = r3 + 6 r7 = r1 – 3 r8 = r7 + 5

• 3 -

Loop Optimizations

Y

The most important set of optimizations

Because programs spend so much time in loops

Y

Optimize given that you know a sequence of code will berepeatedly executed

Y

Optis

Invariant code removal

Global variable migration

Induction variable strength reduction

Induction variable elimination

• 4 -

Recall Loop Terminology

• r1, r4 are basic induction variables - r7 is a derived induction variable

r1 = 3

r2 = 10

loop preheader

r4 = r4 + 1 r7 = r4 * 3

r2 = 0

r3 = r2 + 1

r1 = r1 + 2

store (r1, r3)

loop header

exit BB

backedge BB

• 6 -

Global Variable Migration

Y

Assign a global variabletemporarily to a register for theduration of the loop

Load in preheader

Store at exit points

Y

Rules

X is a load or store

address(X) not modified in theloop

if X not executed on everyiteration, then X must provablynot cause an exception

All memory ops in loop whoseaddress can equal address(X)must always have the sameaddress as X

r4 = load(r5)

r4 = r4 + 1

r8 = load(r5)

r7 = r8 * r

store(r5, r4)

store(r5,r7)

• 7 -

Class Problem

Optimize this applying 1. loop invariant removal 2. global variable migration + other optis

r2 = 10

r7 = r4 * r

r6 = load(r10)

r3 = 1 / r

r3 = r4 * r r3 = r3 + r

r2 = r2 + 1

store(r10,r3) store (r2, r3)

• 9 -

Induction Variable Elimination

Y

Remove unnecessary basicinduction variables from theloop by substituting uses withanother BIV

Y

Rules (same init val, same inc)

Find 2 basic induction varsx,y

x,y in same family

y

incremented in same places

increments equal

initial values equal

x not live when you exit loop

for each BB where x isdefined, there are no uses of xbetween first/last defn of xand last/first defn of y

r1 = r1 - 1r2 = r2 - 1

r9 = r2 + r

r7 = r1 * r

r4 = load(r1)

store(r2, r7)

• 10 -

Induction Variable Elimination (2)

Y

5 variants discussed in thesis

1. Trivial – induction variable that is never used except by theincrements themselves, not live at loop exit

2. Same increment, same initial value

3. Same increment, initial values are a known constant offsetfrom one another

4. Same increment, no nothing about relation of initial values

5. Different increments, no nothing about initial values

Y

The higher the number, the more complex the elimination

Also, the more expensive it is

1,2 are basically free, so always should be done

3-5 require preheader operations

• 12 -

ILP Optimization

Y

Traditional optimizations

Redundancy elimination

Reducing operation count

Y

ILP (instruction-level parallelism) optimizations

Increase the amount of parallelism and the ability to overlapoperations

Operation count is secondary, often trade parallelism for extrainstructions (avoid code explosion)

Y

ILP increased by breaking dependences

True or flow = read after write dependence

False or (anti/output) = write after read, write after write

• 13 -

Register Renaming

Y

Remove dependences causedby variable re-use

Re-use of source variables

Re-use of temporaries

Anti, output dependences

Y

Create a new variable to holdeach unique life time

Y

Very simple transformationwith straight-line code

Make each def a uniqueregister

Substitute new name intosubsequent uses

a: r1 = r2 + r3b: r3 = r4 + r5c: r1 = r7 * r8d: r7 = r1 + r5e: r1 = r3 + 4f: r4 = r7 + 4

a: r1 = r2 + r3b: r13 = r4 + r5c: r11 = r7 * r8d: r17 = r11 + r5e: r21 = r13 + 4f: r14 = r17 + 4

• 15 -

Rename with Copy

Y

Renaming within a web

The worst case is a web spansall defs/uses

Want to enable some of thedefs within the web to bereordered or executed inparallel

Y

Xform

Rename def

Rename uses for which def isthe the only reaching def

Insert copy

y

orig_dest = new_dest

y =

= y

y = = y

= y

y =

= y

= y

• 16 -

Predicate Promotion

Y

Predicate promotion or predicatespeculation

Remove dependence betweenCMPP and predicated operation

Modify predicate of an operationto an ancestor predicate

Operation executes more oftenthan it should, “speculated”

Y

x = … if p

Æ

if p

Where p2 is an ancestor of p

Legal if x not live on p2 – p

And, op will not cause aspurious exception

r1 = r2 + r3 r7 = 0 p1,p2 = CMPP.UN.UC(r1 < r5) r4 = r5 * r6 if p1 r7 = r8 + r9 if p2 r10 = r4 + 4 if p1 r11 = r7 + 1 if T

• 18 -

Class Problem

1. Promote everything to its highest predicate w/o renaming 2. Promote any defs of r1, r2 that remain predicated to True

using promotion with renaming

r1 = 0 if T p1 = CMPP.UN(r3 < r4) if T r2 = r6 + 3 if p1 p2,p3 = CMPP.UN.UC(r5 < r6) if p1 r1 = r5 + 1 if p2 r10 = r2 + r3 if p2 r1 = r3 * 3 if p3 r11 = load(r1) if p3 store (r1, r10) if T store (r3, r11) if T

• 19 -

Back Substitution

Y

Generation of expressions bycompiler frontends is verysequential

Account for operatorprecedence

Apply left-to-right withinsame precedence

Y

Back substitution

Create larger expressions

y

Iteratively substitute RHSexpression for LHS variable

Note – may correspond tomultiple source statements

Enable subsequent optis

Y

Optimization

Re-compute expression in amore favorable manner

y = a + b + c – d + e – f;

r9 = r1 + r2 r10 = r9 + r3 r11 = r10 - r4 r12 = r11 + r5 r13 = r12 – r

Subs r12:

r13 = r11 + r5 – r

Subs r11:

r13 = r10 – r4 + r5 – r

Subs r

r13 = r9 + r3 – r4 + r5 – r

Subs r

r13 = r1 + r2 + r3 – r4 + r5 – r