Predicated Execution and Control Dependence Analysis - Prof. Scott Mahlke, Assignments of Electrical and Electronics Engineering

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EECS 583 – Lecture 5 If-conversion

University of Michigan January 22, 2003

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Homework 1^ Y^ Due next Monday (1/27) @11:59pm^ Y^ Check out the class newsgroup for help/info^ Y^ Notes

»^ My soln is ~400 lines »^ Please delete the original code in loopdet.cpp when you turn inthe HWth^ »^4 testcase not ready yet, will be soon

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Recap: Predicated Execution Example^ a = b + c^ if (a > 0)^ e = f + g^ else^ e = f / g^ h = i - j

BB1 BB1 BB3 BB3 BB2 BB

add a, b, c bgt a, 0, L1 div e, f, g jump L2 L1: add e, f, g L2: sub h, i, j

BB1 BB2^ BB3^ BB

Traditional branching code^ BB1^ BB1^ BB1^ BB3^ BB2^ BB

add a, b, c if T p2 = a > 0 if T p3 = a <= 0 if T div e, f, g if p3 add e, f, g if p2 sub h, i, j if T

BB1 BB2 BB3 BB

p2^ Æ^ BB2 p3^ Æ^ BB

Predicated code

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Compare-to-Predicate Operations (CMPPs)^ Y^ How do we compute predicates

»^ Compare registers/literals like a branch would do »^ Efficiency, code size, nested conditionals, etc Y 2 targets for computing taken/fall-through conditions with1 operation

p1, p2 = CMPP.cond.D1a.D2a (r1, r2) if p3 p1 = first destination predicate p2 = second destination predicate cond = compare condition (ie EQ, LT, GE, …) D1a = action specifier for first destination D2a = action specifier for second destination (r1,r2) = data inputs to be compared (ie r1 < r2) p3 = guarding predicate

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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 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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Use of OR-type Predicates^ a = b + c^ if (a > 0 && b > 0)^ e = f + g^ else^ e = f / g^ h = i - j

BB1 BB1 BB5 BB2 BB2 BB3 BB

add a, b, c ble a, 0, L1 ble b, 0, L1 add e, f, g jump L2 L1: div e, f, g L2: sub h, i, j

BB1 BB5 BB

BB

Traditional branching code

BB

BB1 BB1 BB5 BB3 BB2 BB

add a, b, c if T p3, p5 = cmpp.ON.UC a <= 0 if T p3, p2 = cmpp.ON.UC b <= 0 if p5 div e, f, g if p3 add e, f, g if p2 sub h, i, j if T

BB1 BB5 BB2 BB3 BB

p2^ Æ^ BB2 p3^ Æ^ BB3 p5^ Æ^ BB

Predicated code

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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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Running Example – Initial State^ do {^ b = load(a)^ if (b < 0) {

if ((c > 0) && (b > 13))^ b = b + 1 else^ c = c + 1 d = d + 1 } else { e = e + 1 if (c > 25) continue } a = a + 1 } while (e < 34)

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

BB

BB

BB1 b < 0 b >= 0

e+ BB3+ c > 25 c <= 25 c++

b > 13 b++

d++^ BB^

a++ e < 34

e >= 34

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Running Example – Backedge Coalescing

b < 0^

b >= 0 c <= 0 c > 0

b <= 13

c <= 25^

c > 25 d++

e++

b++^

c++

b < 0^

b >= 0 c <= 0 c > 0 b <= 13

e++ c > 25c <= 25 c++

BB2 BB4^ BB

BB

BB

BB1^ BB3^ BB

b > 13

e < 34 e >= 34 a++

BB

BB1 BB2 BB

BB4 b > 13 BB^

BB

b++

BB^

d++^ BB^

a++ e < 34

e >= 34

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Step 2: Control Dependence Analysis (CD)^ Y^ Control flow – Execution transfer from 1 BB to anothervia a taken branch or fallthrough path^ Y^ Dependence – Ordering constraint between 2 operations

»^ Must execute in proper order to achieve the correct result »^ O1: a = b + c »^ O2: d = a – e »^ O2 dependent on O1 Y Control dependence – One operation controls theexecution of another »^ O1: blt a, 0, SKIP »^ O2: b = c + d »^ SKIP: »^ O2 control dependent on O1 Y Control dependence analysis derives these dependences

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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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Running Example – CDs^ Entry

First, nuke backedge(s) Second, nuke exit edges Then, Add pseudo entry/exit nodes^ - Entry

Æ^ nodes with no predecessors - Exit Æ^ nodes with no successors

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

b <= 13

c <= 25^

c > 25 d++

e++ c++ BB^

BB

BB^

Control deps (left is taken) BB1: BB2: BB3: BB4: BB5: BB6: BB7: BB8: BB9:

b > 13^ BB

BB

b++

BB

a++^ BB

e < 34^

BB

Exit

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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 c <= 0 c > 0

b <= 13

c <= 25^

c > 25 d++

e++ c++ BB^

BB

BB4 b > 13 BB^

BB

b++

BB

a++^ BB

e < 34^

BB

Exit

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Running Example – CDs Via Algorithm

c <= 0 c > 0

b <= 13

c <= 25^

c > 25 d++

e++ c++ BB2 BB4^ BB

BB

BB

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

e < 34 a++ b++

x = 1e = taken edge 1

Æ^2

y = 2y not in pdom(x)lub = 9x_id = -1t = 22 != 9cd(2) += -1t = 77 != 9cd(7) += -1t = 88 != 9cd(8) += -1t = 99 == 9 1 Æ^ 2 edge (aka –1)

Entry

BB

Exit