Predicated Execution: Effective Compiler Support using Hyperblock - Prof. Scott Mahlke, Study notes of Electrical and Electronics Engineering

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EECS 583 – Class 4 If-conversion

University of Michigan January 19, 2005

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Reading Material^ Y^ Today’s class

»^ “The Program Dependence Graph and Its Use in Optimization”,^ J. Ferrante, K. Ottenstein, and J. Warren, ACM TOPLAS, 1987 »^ “On Predicated Execution”, Park and Schlansker, HPL TechnicalReport, 1991. Y Material for the next lecture »^ "Effective Compiler Support for Predicated Execution using theHyperblock", S. Mahlke et al., MICRO-25, 1992. »^ "Control CPR: A Branch Height Reduction Optimization forEPIC Processors", M. Schlansker et al., PLDI-99, 1999.

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Recap: CMPP Action Specifiers

Guarding^ predicate^0011

Compare^ Result^0101

UN^ UC^0001

ON 0 0 1 0

OC -^ - -^ - -^11 -

AN^ AC^ -^ -^0 -

• • • 0

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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Recap: 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 p

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

Talk about these later – used for control height reduction

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Class Problem^ w = w + 1^ if (a == 0 || b <= 1)

x = x + 1 else if (c != -1) y = y + 1 } z = z + 1

a.^ Draw the CFG b.^ Predicate the code removing^ all branches c.^ Where could you use AND-type^ predicates to potentially speed things up?

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

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

»^ If not a loop body

Æ^ skip this step

Y^ 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

Y^ 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

BB2c > 0^ c <= 0 b <= 13

c <= 25^

c > 25 d++ b++^

c++

c > 25 c <= 25 c++

BB

BB6 BB

BB

BB1 b < 0 b >= 0^ BB3^ BB b > 13

e < 34 e >= 34 a++

e++^ BB

BB2c > 0^ c <= 0 BB4b <= 13^ BB

BB

BB

BB1 b < 0 b >= 0^ BB

e++

b > 13 b++

d++^ BB^

a++ e < 34

e >= 34

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Control Dependences^ Y^ 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 Y 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 Y 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 T BB4^ BB5 BB

T^ F

F

BB^

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

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

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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^ Entry

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

b < 0^

b >= 0 BB2c > 0^ c <= 0 b <= 13

c <= 25^

c > 25 d++

e++ BB3 (^) c++

BB4 b > 13 BB^

BB

b++

BB

a++^ BB

e < 34^

BB

Exit

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Running Example – CDs Via Algorithm (2)

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)

Entry^

BB1 b < 0 b >= 0 BB2 c <= 0 c > 0

b <= 13

c <= 25^

c > 25 d++

e++ BB3 (^) c++

BB4 b > 13 BB^

BB

b++

BB^

Class Problem: 1

Æ^ 3 edge (aka 1)

a++^ BB

e < 34^

BB

Exit

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Running Example – CDs Via Algorithm (3)^ Entry

BB

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

b < 0^

b >= 0 BB2c > 0^ c <= 0 b <= 13

c <= 25^

c > 25 d++

e++ BB3 (^) c++

BB4 b > 13 BB^

BB

b++

BB

a++^ BB

e < 34^

BB

Exit