1 Fine Slicing: Theory and Applications for Computation Extraction Aharon Abadi,Ran Ettinger,Yishai...

1

Fine Slicing:Theory and Applications for Computation Extraction

Aharon Abadi,Ran Ettinger,Yishai A. FeldmanIBM Research – Haifa

2

Program Slicing

Program

x := expStart Slice x := exp

Slice

The same sequence of values

3

Example

x := 6y := 3f(x,y)x := 9y : = 2w : = x*y

x := 9y : = 2w : = x*y

x := 6y := 3

w : = x*y

w := 18x := 6y := 2f(x,y)x := 9y : = 2w : = x*yz := w

x := 9y : = 2w : = x*yz := w

w := 18

z := w

4

A:Z0A:Z0

Control-Flow Path Compression

go-to Bgo-to B

if-zero-go-to A

test X

Work in two stages:- Compute the ‘traditional’ slice

- Control dependences- Data Dependences

- Compute the necessary branches to prevent infeasible control paths

test X

if-zero-go-to A

. . .

L:test Y

if-zero-

. . .

go-to L

B:

. . .

B:

5

A:Z0

go-to B

if-zero-go-to A

test X

This algorithm:- preserves behavior- yields a sub-program

- one version may turn conditional branches into unconditional ones (“rhetorization”)

B:go-to Bgo-to B

test X test X

. . .

L:test Y

if-zero-

. . .

go-to L

B:

. . .

if-zero-go-to A

A:Z0

Control-Flow Path Compression

6

Data-Flow Path Compression

The result is too large

The value of R7 does not depend on the loop

R7:=exp1Out: R0:=R7 + 1

Out: R0:= R7 + 1

Start:R2:=0

R7:=exp1

Loop: R2:=R2 + 1

compare R2, R9

if-not-less-go-to Out

use R7

Temp:=R7; spill R7 to memory

… ; code that uses

; all registers

R7:=Temp; restore R7

go-to Loop

Start:R2:=0 R7:=exp1Loop: R2:=R2 + 1 compare R2, R9 if-not-less-go-to Out Temp:=R7 R7:=Temp go-to Loop Out: R0:=R7 + 1

7

Control-Flow Path Compressionx<11

F T

x:=x+1 goto A4

goto A2

y<TT F

y:=y-1

goto A

print(x)

x<9T F

x:=x-1x:=x+2

goto A2

goto A3

if (x<11)

x := x+1

goto A2

A1: if (y<T)

y := y–1

goto A1

goto A2

goto A4

x := x-1

A4: if (x<9) goto A3

A3: x := x+2

A2: print(x)

8

Compute the ‘Traditional’ Slicex<11

F T

x:=x+1 goto A4

goto A2

y<TT F

y:=y-1

goto A

print(x)

x<9T F

x:=x-1x:=x+2

goto A2

goto A3

if (x<11)

x := x+1

goto A2

A1: if (y<T)

y := y–1

goto A1

goto A2

goto A4

x := x-1

A4: if (x<9) goto A3

A3: x := x+2

print(x)

A2: print(x)

x:=x+1

x:=x+2 x:=x-1

x<11

x<9

y<T

9

Completing Control Flow Paths:Main Lemma

• precisely identifies the possible sets of branches that may be added to the slice

• any path in the original program can be chosen

• optimizations can be performed

All paths from the same point in the slice enter the slice at a single point

10

Compute the Necessary Branchesx<11

F T

x:=x+1 goto A4

goto A2

y<TT F

y:=y-1

goto A

print(x)

x<9T F

x:=x-1x:=x+2

goto A2

goto A3

if(x<11)

x:=x+1

goto A2

A1: if(y<T)

y:=y–1

goto A1

goto A2

goto A4

x:=x-1

A4: if(x<9) goto A3

A3: x:=x+2

A2: print(x)

11

Start:R2:=0 R7:=exp1Loop: R2:=R2 + 1 compare R2, R9 if-not-less-go-to Out use R7 Temp:=R7; spill R7 to ;memory … ; code that uses ;all registers R7:=Temp; restore R7 go-to Loop Out: R0:=R7 + 1


R7:=exp1Out:R0:=R7 + 1 +1

R7:=exp1

exit

R0:=R7+1

R2:=0

R2:=R2+1

compare R2,R9

if-not-less

use R7

Temp:=R7

R7:=Temp

goto Loop

go-to Out

12

++

++

exp1


R7:=exp1

exit

R7:=R7+1

R2:=0

R2:=R2+1

compare R2,R9

if-not-less

use R7

Temp:=R7

R7:=Temp

goto-Loop

• R7,Temp carry the value of exp1

• Use data edges instead of variables

go-to Out

out data portholds the last valuein data port

holds the next value

d1 d2

d1

Start:R2:=0 R7:=exp1Loop: R2:=R2 + 1 compare R2, R9 if-not-less-go-to Out use R7 Temp:=R7; spill R7 to ; memory … ; code that uses ; all registers R7:=Temp; restore R7 go-to Loop Out: R0:=R7+1

0

• The Plan Calculus:The Programmer’s Apprentice,Rich and Waters, 1990

13

exp1

entry

0

exit

++

R7

R0

R9

R2

++

R2

T F

compare R2,R9

R7:= exp1R0:=R7 + 1

Start:R2:=0

Loop: R2:=R2 + 1 compare R2, R9 if-not-less-go-to Out use R7 Temp:=R7; spill R7 to ; memory … ; code that uses ; all registers R7:=Temp; restore R7 go-to Loop Out: R0:=R7 + 1

R7:=exp1

Out: R0:=R7 + 1

R7:=exp1

if-not-less

use R7

14

exp1

0

exit

++

R7

R0

R9

R2

++

R2

T F

compare R2,R9

Start:R2:=0

Loop:R2:=R2 + 1 compare R2, R9 if-not-less- use R7 ; spill R7 to ; memory … ; code that uses ; all registers ; restore R7 go-to Loop Out: R0:=R7 + 1

R7:=exp1

if-not-less

use R7

Decompression

go-to Out

Temp:=R7

R7:=Temp

R7:=exp1

R0:=R7 + 1

go-to Out

entry

Out:

15

If(q)

print(x)

If(i>10)

+

If(q)

If(q) goto Skip

x := 1

goto Outx := 2Skip:

Out: print(x)

x := 1

If(i>10) goto Out

i := i + 1

goto loop

x := 2

If(q) goto Skip

print(x)

Loop:

Skip:

Out: print(x)

2

1

goto Skip

goto out x := 2

x := 1

0ix := 1

x := 2

x := 1

i := 0i := 0

i := 0

16

out.println("<table border=0>");

int start = page * 20;

int end = start + 20;

end = Math.min(end,

album.getPictures().size());

for (int i = start; i < end; i++) {

Picture picture = album.getPicture(i);

printPicture(out, picture);

}

out.println("</table>");

int start = page * 20;int end = start + 20;end = Math.min(end,

album.getPictures().size());Queue<Picture> pictures = new LinkedList<Picture>();for (int i = start; I < end; i++) { Picture picture = album.getPicture(i); pictures.add(picture); }display(out, start, end, pictures);

void display(PrintStream out, int start,

int end, Queue<Picture> pictures) {



printPicture(out,pictures.remove());

}


}

Fine Slicing Motivating Example

Automatically extracts Out computation (The view model)

17

slice (v.): to cut with or as if with a knife

Merriam-Webster

slice (n.): a thin flat piece cut from something

18

Fine Slicing

• A generalization of traditional program slicing• Fine slices can be precisely bounded

– Slicing criteria include set of data and control dependences to ignore

• Fine slices are executable and extractable• Complement slices (co-slices) are also fine

slices• Oracle-based semantics for fine slices• Algorithm for computing data-structure

representing the oracle

19

Extract Computation

• A new refactoring• Extracts a fine slice into contiguous code• Computes the co-slice• Computation can then be extracted into a

separate method using Extract Method• Passes necessary “oracle” variables between

slice and co-slice• Generates new containers if series of values

need to be passed

20++

out.println("<table border=0>");int start = page * 20;int end = start + 20;end = Math.min(end, album.getPictures().size());for (int i = start; i < end; i++) { Picture picture = album.getPicture(i); printPicture(out, picture);}out.println("</table>");

entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

p1

p1

p2

p2

Token Semantics

21++


entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

printPicture

Fine Slicing

22++

out.println("<table border=0>");for (int i = start; i < end; i++) { printPicture(out, picture);}out.println("</table>");

entry

println

out

out

T F

>

i

out

end

printPicture

out

out

println

i

"<table border=0>"

"</table>"

exit

printPicture

startpicture

The Fine Slice

p1 p2 p3

23++


entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

printPicture

Co-Slicing

24++

int start = page * 20;int end = start + 20;end = Math.min(end, album.getPictures().size());for (int i = start; i < end; i++) { Picture picture = album.getPicture(i); }

entry

*

album

getPictures

size

page

min

+

start

end

T F

>

getPicture

i

end

out

i

20

exit

startpicture

The Co-Slice

25++

entry

*

album

getPictures

size

page

min

+

start

end

T F

>

getPicture

i

end

out

i

20

exit

startpicture

++

entry

println

out

T F

>

end

out

println

i

"<table border=0>"

"</table>"

exit

printPicture

startpicture

Fine slice Co-slice

out

p1 p2 p3

A place forThe call

26

How do we distinguish between sequence of values and single value?

++

entry

println

out

out

T F

>

i

out

end

printPicture

out

out

println

i

"<table border=0>"

"</table>"

exit

printPicture

startpicture

++

entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

Every cycle of controlthat passes through din does not pass through dout

Therefore

din requires singlevalue

27

++

entry

println

out

out

T F

>

i

out

end

printPicture

out

out

println

i

"<table border=0>"

"</table>"

exit

printPicture

startpicture

++

entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

There is a cycle of control that passes through din and dout

Thereforedin may require multiplesingle value

How do we distinguish between sequence of values and single value?

28


Adding Container


int end, Picture picture) {



printPicture(out,picture);

}


}

out.println("<table border=0>");int start = page * 20;int end = start + 20;end = Math.min(end, album.getPictures().size());Queue<Picture> pictures = new LinkedList<Picture>();for (int i = start; i < end; i++) { Picture picture = album.getPicture(i); pictures.add(picture); printPicture(out,pictures.remove());}out.println("</table>");







}


}

29

Adding Containerout.println("<table border=0>");int start = page * 20;int end = start + 20;end = Math.min(end, album.getPictures().size());Queue<Picture> pictures = new LinkedList<Picture>();for (int i = start; i < end; i++) { Picture picture = album.getPicture(i); pictures.add(picture); printPicture(out,pictures.remove());}out.println("</table>");






}


}



30++

println

>

remove

printPicture println

++


entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

new

remove

add

picture

pictures

picture

pictures

pictures

Adding a Container

pictures

31++

println

<

remove


++

void display(PrintStream out, int start, int end, Queue<Picture> pictures){ out.println("<table border=0>"); for (int i = start; i < end; i++) { printPicture(out, pictures.remove()); } out.println("</table>");}

entry

println

out

out

start

T F

>

out

end

printPicture

out

println

i

"<table border=0>"

"</table>"

exit

pictures

remove

entry

i

out

The Fine Slice

pictures

pictures

picture

32++

println

>

remove


++

entry

println

out

*

album

getPictures

size

page

min

+ out

start

end

T F

>

getPicture

i

out

end

printPicture

out

out

println

i

"<table border=0>"

20

"</table>"

exit

new

remove

add


Program with

Container

pictures

pictures

pictures

pictures

picture

picture

33++

>

++

int start = page * 20;int end = start + 20;end = Math.min(end, album.getPictures().size());Queue<Picture> pictures = new LinkedList<Picture>();for (int i = start; i < end; i++) { Picture picture = album.getPicture(i); pictures.add(picture); }display(out, start, end, pictures);

entry

*

album

getPictures

size

page

min

+

out

start

end

T F

>

getPicture

i

end

i

20

exit

newpictures

add

display

pictures

start

out

The Co-Slice

pictures

pictures

pictures

picture

34




end = Math.min(end,





}









}


}

Fine Slicing Motivating Example

Automatically extracts Out computation (The view model)

35

Fine Slicing Algorithm

• Compute the core slice by following unfiltered data and control dependence relations backwards in the plan.

• (Semantic Restoration) Add necessary tests to make the slice executable.




end = Math.min(end,





}


36

Stat1;

if(q){

x = x + 1;;

}else{

y = x + 2;

}

Fine Slicing Algorithm

• Compute the core slice by following unfiltered data and control dependence relations backwards in the plan.

• (Semantic Restoration) Add necessary tests to make the slice executable.

stat1;

x = x + 1;;

y = x + 2;

Stat1;

if(q){

x = x + 1;;

}else{

y = x + 2;

}

37

Extract Computation

• Get as input the program (P) and slicing criteria (SC)

• Compute the fine slice (FS) corresponding to P and SC

• Compute the Co-Slice:– Compute fine slice starting from P\FS – Disconnect the return values according to SC

• Add containers to the fine slice and co-slice• Add the call from co-slice to the fine slice

Date post:	13-Jan-2016
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