Fine Slicing:
Theory and Applications for Computation Extraction
Aharon Abadi,Ran Ettinger,Yishai A. Feldman
IBM Research – Haifa
1
Program Slicing
Program
Slice
Start Slice
x := exp
The same sequence of values
2
Example
x := 6
y := 3
f(x,y)
x := 9
y:=2
w : = x*y
w := 18
x := 6
y := 2
f(x,y)
x := 9
y:=2
w : = x*y
z := w
x := 6
y := 3
x := 9
y:=2
w : = x*y
w : = x*y
w := 18
x := 9
y:=2
w : = x*y
z := w
z := w
3
Control-Flow Path Compression
test X
if-zero-go-to A
. . .
L:test Y
if-zero- go-to B
. . .
go-to L
A:Z0
. . .
B:
Work in two stages:
- Compute the ‘traditional’ slice
- Control dependences
- Data Dependences
- Compute the necessary branches
to prevent infeasible control paths
4
Control-Flow Path Compression
test X
test X
if-zero-go-to A
if-zero-go-to A
. . .
go-to B
A:Z0
L:test Y
if-zero- go-to B
B:
. . .
go-to L
A:Z0
. . .
B:
This algorithm:
- preserves behavior
- yields a sub-program
- one version may turn conditional branches into
unconditional ones (“rhetorization”)
5
Data-Flow Path Compression
Start:R2:=0
Start:R2:=0
R7:=exp1
Loop: R2:=R2 + 1
Loop: R2:=R2 + 1
compare R2, R9
compare R2, R9
R7:=exp1
if-not-less-go-to Out
if-not-less-go-to Out
Out: R0:=R7
+ 1
Temp:=R7
use R7
R7:=Temp
Temp:=R7; spill R7 to memory
go-to Loop
Out: R0:=R7 + 1
…
; code that uses
R7:=exp1
; all registers
R7:=Temp; restore R7
go-to Loop
Out:
R0:= R7 + 1
The result is too large
The value of R7 does
not depend on the loop
6
Control-Flow Path Compression
if (x<11) goto A4
F
x := x+1
goto A2
A4: if (x<9) goto A3
x := x-1
A1: if (y<T) goto A2
x<11
T
goto A4
x:=x+1
T
goto A2
x<9
F
goto A3
x:=x+2
x:=x-1
y := y–1
goto A1
T
A3: x := x+2
y<T
F
goto A2
A2: print(x)
print(x)
y:=y-1
goto A
7
Compute the ‘Traditional’ Slice
if (x<11) goto A4
F
x := x+1
goto A2
A4: if (x<9) goto A3
x := x-1
A1: if (y<T) goto A2
x<11
T
goto A4
x:=x+1
T
goto A2
x<9
F
goto A3
x:=x+2
y := y–1
x:=x-1
goto A1
T
A3: x := x+2
y<T
F
goto A2
A2: print(x)
print(x)
y:=y-1
goto A
8
Completing Control Flow Paths:
Main Lemma
All paths from the same point in the slice enter the
slice at a single point
• 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
9
Compute the Necessary Branches
F
if(x<11) goto A4
x:=x+1
goto A2
A4: if(x<9) goto A3
x:=x-1
A1: if(y<T) goto A2
x<11
T
x:=x+1
goto A4
goto A2
T
x<9
F
goto A3
x:=x+2
x:=x-1
y:=y–1
goto A1
T
A3: x:=x+2
y<T
F
goto A2
A2: print(x)
print(x)
y:=y-1
goto A
10
Data-Flow Path Compression
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
Out: R0:=R7 + 1
R2:=0
R7:=exp1
R2:=R2+1
compare R2,R9
if-not-less
use R7
go-to Out
Temp:=R7
R7:=exp1
Out:R0:=R7 + 1
+1
R0:=R7+1
R7:=Temp
goto Loop
exit
11
Data-Flow Path Compression
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
Out: R0:=R7+1
R2:=0
0
d1
d2
R7:=exp1
exp1
d1
R2:=R2+1
++
in data port
holds the
next value
compare R2,R9
out data port
holds the last value
if-not-less
use R7
go-to Out
Temp:=R7
• The Plan Calculus:
The Programmer’s Apprentice,
Rich and Waters, 1990
• R7,Temp carry the value of exp1
R7:=R7+1
++
R7:=Temp
• Use data edges instead of variables
goto-Loop
exit
12
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
Out: R0:=R7 + 1
entry
exp1
0
R2
R9
R2
++
R7
compare R2,R9
if-not-less
R7:= exp1
R0:=R7 + 1
T
F
use R7
++
R0
exit
13
Decompression
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
Out: R0:=R7 + 1
entry
exp1
0
R2
R9
R2
++
R7
compare R2,R9
if-not-less
T
R7:=exp1
F
use R7
go-to Out
Out: R0:=R7 + 1
++
R0
exit
14
If(q) goto Skip
If(q)
i := 0
x := 1
i := 0
i
x := 1
Loop: If(i>10) goto Out
i := i + 1
goto loop
If(q) goto Skip
0
i := 0
x := 1
x := 1
goto Skip
goto Out
Skip: x := 2
Out: print(x)
2
Skip: x := 2
Out: print(x)
x := 2
If(i>10)
1
+
goto out
x := 2
x := 1
print(x)
15
Fine Slicing Motivating Example
Automatically extracts
Out computation
(The view model)
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) {
out.println("<table border=0>");
for (int i = start; i < end; i++) {
printPicture(out,pictures.remove());
}
out.println("</table>");
}
16
slice (v.): to cut with or as
if with a knife
slice (n.): a thin flat piece
cut from something
17
Merriam-Webster
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
18
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
19
entry
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>");
"<table border=0>"
out
println
page
Token
Semantics
20
*
start
+
out
album
out
getPictures
i
size
end
min
getPicture
p2
p1
end
"</table>"
out
i
out
p2 p1
<
println
printPicture
T
++
F
exit
20
entry
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>");
"<table border=0>"
out
println
page
Fine
Slicing
20
*
start
+
out
album
out
getPictures
i
size
end
min
getPicture
end
"</table>"
out
i
out
<
println
printPicture
T
++
F
exit
21
entry
out.println("<table border=0>");
for (int i = start; i < end; i++) {
printPicture(out, picture);
}
out.println("</table>");
"<table border=0>"
out
println
start
picture p1 p2 p3
end
The Fine
Slice
out
out
i
"</table>"
out
i
out
<
println
printPicture
T
++
F
exit
22
entry
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>");
"<table border=0>"
out
println
Co-Slicing
page
20
*
start
+
out
album
out
getPictures
i
size
end
min
getPicture
end
"</table>"
out
i
out
<
println
printPicture
T
++
F
exit
23
entry
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);
}
The CoSlice
page
20
*
start
+
album
getPictures
i
size
end
min
getPicture
i
start
picture
out
<
end
T
++
F
exit
24
entry
Co-slice
Fine slice
page
entry
20
"<table border=0>"
*
out
start
println
+
end
start
picture
album
getPictures
i
end
size
min
getPicture
p1 p2 p3
picture
start
i
i
out
<
"</table>"
<
printPicture
end
out
T
println
T
++
F
out
exit
++
F
A place for
The call
25
exit
How do we distinguish between sequence of values and single value?
entry
"<table border=0>"
out
println
page
20
*
start
+
out
album
out
Every cycle of control
that passes through
entry
out
din does not pass through println
dout
Therefore
din requires single
value
start
picture
getPictures
"<table border=0>"
end
out
out
i
i
size
end
min
getPicture
end
"</table>"
"</table>"
out
i
out
i
out
out
<
printPicture
<
printPicture
++
println
T
T
println
F
F
exit
++
exit
26
How do we distinguish between sequence of values and single value?
entry
"<table border=0>"
out
println
page
20
*
start
+
out
album
out
There is a cycle of
control that passes
through din and dout
Therefore
din may require multiple
single value
picture
getPictures
entry
out
"<table border=0>"
println
start
end
out
out
i
i
size
end
min
getPicture
end
"</table>"
"</table>"
out
i
out
i
out
out
<
printPicture
<
printPicture
++
println
T
T
println
F
F
exit
++
exit
27
Adding Container
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>");
void display(PrintStream out, int start,
int end, Picture picture) {
out.println("<table border=0>");
for (int i = start; i < end; i++) {
printPicture(out,picture);
}
out.println("</table>");
}
out.println("<table border=0>");
int start = page * 20;
void display(PrintStream out, int start,
int end = start + 20;
int end, Queue<Picture> pictures) {
end = Math.min(end,
out.println("<table border=0>");
album.getPictures().size());
Queue<Picture> pictures = new LinkedList<Picture>(); for (int i = start; i < end; i++) {
for (int i = start; i < end; i++) {
printPicture(out,pictures.remove());
Picture picture = album.getPicture(i);
}
pictures.add(picture);
out.println("</table>");
printPicture(out,pictures.remove());
}
}
out.println("</table>");
28
Adding Container
out.println("<table border=0>");
void display(PrintStream out, int start,
int start = page * 20;
int end, Queue<Picture> pictures) {
int end = start + 20;
out.println("<table border=0>");
end = Math.min(end,
for (int i = start; i < end; i++) {
album.getPictures().size());
printPicture(out,pictures.remove());
Queue<Picture> pictures = new LinkedList<Picture>();
for (int i = start; i < end; i++) {
}
Picture picture = album.getPicture(i);
out.println("</table>");
pictures.add(picture);
}
printPicture(out,pictures.remove());
}
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);
29
out.println("<table border=0>");
entry
"<table border=0>"
int start = page * 20;
out
int end = start + 20;
println
end = Math.min(end,
album.getPictures().size());
page
20
Queue<Picture> pictures = new LinkedList<Picture>();
for (int i = start; i < end; i++) {
*
Picture picture = album.getPicture(i);
start
pictures.add(picture);
printPicture(out,pictures.remove());
}
+
out
album
out.println("</table>");
out
Adding a
Container
getPictures
i
pictures
size
end
min
getPicture
new
pictures
picture
pictures
add
end
pictures
remove
"</table>"
out
i
out
picture
<
println
printPicture
T
++
F
exit
30
entry
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>");
}
"<table border=0>"
out
The Fine
Slice
println
end
start
pictures
out
out
i
pictures
pictures
"</table>"
remove
out
i
out
picture
<
println
printPicture
T
++
F
exit
31
out.println("<table border=0>");
entry
"<table border=0>"
int start = page * 20;
out
int end = start + 20;
println
end = Math.min(end,
album.getPictures().size());
page
20
Queue<Picture> pictures = new LinkedList<Picture>();
for (int i = start; i < end; i++) {
*
Picture picture = album.getPicture(i);
start
pictures.add(picture);
printPicture(out,pictures.remove());
}
+
out
album
out.println("</table>");
out
Program
with
Container
getPictures
i
pictures
size
end
min
getPicture
new
pictures
picture
pictures
add
end
pictures
remove
"</table>"
out
i
out
picture
<
println
printPicture
T
++
F
exit
32
int start = page * 20;
entry
int end = start + 20;
end = Math.min(end,
album.getPictures().size());
Queue<Picture> pictures = new LinkedList<Picture>(); page
for (int i = start; i < end; i++) {
Picture picture = album.getPicture(i);
pictures.add(picture);
}
display(out, start, end, pictures);
out
The CoSlice
20
*
start
+
album
getPictures
start
i
pictures
size
end
min
getPicture
new
pictures
picture
add
pictures
end
pictures
pictures
i
<
display
out
T
++
F
exit
33
Fine Slicing Motivating Example
Automatically extracts
Out computation
(The view model)
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) {
out.println("<table border=0>");
for (int i = start; i < end; i++) {
printPicture(out,pictures.remove());
}
out.println("</table>");
}
34
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.
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>");
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.
Stat1;
if(q){
x = x + 1;;
}else{
y = x + 2;
stat1;
x = x + 1;;
y = x + 2;
}
36
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
37