Efficient Compiler Support: Predicated Execution & Control Analysis - Prof. Scott Mahlke, Papers of Electrical and Electronics Engineering

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EECS 583 – Class 4 If-conversion

University of Michigan September 17, 2007

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Reading Material^ ™^ Today’s class

»^ “The Program Dependence Graph and Its Use in Optimization”,^ J. Ferrante, K. Ottenstein, and J. Warren, ACM TOPLAS, 1987^ y^

This is a long paper – the part we care about is the controldependence stuff. The PDG is interesting and you shouldskim it over, but we will not talk about it now

»^ “On Predicated Execution”, Park and Schlansker, HPL TechnicalReport, 1991. ™ Next class »^ "Effective Compiler Support for Predicated Execution using theHyperblock", S. Mahlke et al., MICRO-25, 1992. »^ “Profiled Guided Code Positioning”,^ K. Pettis and R. Hansen, Proc. PLDI-90, 1999.

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CMPP Action Specifiers

Guarding^ predicate^0011

Compare^ Result^0101

UN^ UC^0001

ON 0 0 1 0

OC -^ - -^ - -^11 -

AN^ AC^ -^ -^0 -

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UN/UC = Unconditional normal/complement

This is what we used in the earlier examples guard = 0, both outputs are 0 guard = 1, UN = Compare result, UC = opposite

ON/OC = OR-type normal/complement AN/AC = AND-type normal/complement

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OR-type, AND-type Predicates^ p1 = 0^ p1 = cmpp_ON (r1 < r2) if T^ p1 = cmpp_OC (r3 < r4) if T^ p1 = cmpp_ON (r5 < r6) if T^ p1 = (r1 < r2) | (!(r3 < r4)) |^ (r5 < r5)^ Wired-OR into p

p1 = 1 p1 = cmpp_AN (r1 < r2) if T p1 = cmpp_AC (r3 < r4) if T p1 = cmpp_AN (r5 < r6) if T p1 = (r1 < r2) & (!(r3 < r4)) &^ (r5 < r5) Wired-AND into p1 Talk about these later – used for control height reduction

Generating predicated code for some source code requires OR-type predicates

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Class Problem^ if (a > 0) {

if (b > 0)^ r = t + s else^ u = v + 1 y = x + 1 } a. Draw the CFG b. Predicate the code removing all branches

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If-conversion^ ™^ Algorithm for generating predicated code

»^ Automate what we’ve been doing by hand »^ Handle arbitrary complex graphs^ y^

But, acyclic subgraph only!! y Need a branch to get you back to the top of a loop

»^ Efficient ™ Roots are from Vector computer days »^ Vectorize a loop with an if-statement in the body ™ 4 steps »^ 1. Loop backedge coalescing »^ 2. Control dependence analysis »^ 3. Control flow substitution »^ 4. CMPP compaction ™ My version of Park & Schlansker

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Step 1: Backedge Coalescing^ ™^ Recall – Loop backedge is branch from inside the loopback to the loop header^ ™^ This step only applicable for a loop body

»^ If not a loop body

Æ^ skip this step

™^ Process^ »^

Create a new basic block^ y^ New BB contains an unconditional branch to the loop header » Adjust all other backedges to go to new BB rather than header

™^ Why do this?^ »^

Heuristic step – Not essential for correctness^ y^ If-conversion cannot remove backedges (only forward edges)^ y^ But this allows the control logic to figure out which backedge youtake to be eliminated » Generally this is a good thing to do

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Running Example – Backedge Coalescing

BB2 BB4^ BB

BB

BB

BB1 b < 0 b >= 0^ BB3c <= 0^ BB c > 0

b <= 13

c <= 25^

c > 25 e < 34 d++ b++^

c++

b > 13

e >= 34 a++

e++^ BB

BB2 BB4^ BB

BB

BB

BB1 b < 0 b >= 0^ BB3c <= 0^ BB c > 0 b <= 13

c > 25c <= 25

b++^

c++

b > 13

e < 34

d++^ a++^ e >= 34

e++

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Control Dependences^ ™^ Recall

»^ Post dominator – BBX is post dominated by BBY if every pathfrom BBX to EXIT contains BBY »^ Immediate post dominator – First breadth first successor of ablock that is a post dominator ™ Control dependence – BBY is control dependent on BBXiff »^ 1. There exists a directed path P from BBX to BBY with anyBBZ in P (excluding BBX and BBY) post dominated by BBY »^ 2. BBX is not post dominated by BBY ™ In English, »^ A BB is control dependent on the closest BB(s) that determine(s)its execution »^ Its actually not a BB, it’s a control flow edge coming out of a BB

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Control Dependence Example

BB2 BB4^ BB5 BB

BB

BB

BB

Control dependences BB1: BB2: BB3: BB4: BB5: BB6: BB7:

T^

F

T^

F

Notation positive BB number = fallthru direction^ negative BB number = taken direction

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Algorithm for Control Dependence Analysis^ for each

basic block x in region for each^ outgoing control flow edge e of x y = destination basic block of e if (y not in pdom(x)) then lub = ipdom(x) if^ (e corresponds to a taken branch) then^ x_id = -x.id else^ x_id = x.id endif t = y while^ (t != lub) do^ cd(t) += x_id;^ t = ipdom(t) endwhile endif endfor endfor

Notes Compute cd(x) which contains those BBs which x is control dependent on^ Iterate on per edge basis, adding^ edge to each cd set it is a member of

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Running Example – Post Dominators

BB2 BB4^ BB

BB

BB

BB1 b < 0 b >= 0^ BB3c <= 0^ BB c > 0

b <= 13

c <= 25^

c > 25 e < 34 d++

c++

b > 13

a++

e++

b++

BB

pdom^

ipdom

BB1:^

1, 9, ex

BB2:^

2, 7, 8, 9, ex

BB3:^

3, 9, ex

BB4:^

4, 7, 8, 9, ex

BB5:^

5, 7, 8, 9, ex

BB6:^

6, 7, 8, 9, ex

BB7:^

7, 8, 9, ex

BB8:^

8, 9, ex

BB9:^

9, ex^

ex

Entry

Exit

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Running Example – CDs Via Algorithm (2)

BB2 BB4^ BB

BB

BB

BB1 b < 0 b >= 0^ BB3c <= 0^ BB c > 0

b <= 13

c <= 25^

c > 25 e < 34 d++

c++

b > 13

a++

e++

b++

BB

Entry

Exit

x = 3e = taken edge 3

Æ^8

y = 8y not in pdom(x)lub = 9x_id = -3t = 88 != 9cd(8) += -3t = 99 == 9 3 Æ^ 8 edge (aka -3)^ Class Problem: 1

Æ^ 3 edge (aka 1)

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Running Example – CDs Via Algorithm (3)

BB2 BB4^ BB

BB

BB

BB1 b < 0 b >= 0^ BB3c <= 0^ BB c > 0

b <= 13

c <= 25^

c > 25 e < 34 d++

c++

b > 13

a++

e++

b++

BB

Entry

Exit

Control deps (left is taken) BB1: none BB2: -1 BB3: 1 BB4: -2 BB5: -4 BB6: 2, 4 BB7: -1 BB8: -1, -3 BB9: none