.bp
.NH 1
Cross jumping
.NH 2
Introduction
.PP
The "Cross Jumping" optimization technique (CJ)
.[
wulf design optimizing compiler
.]
is basically a space optimization technique. It looks for pairs of
basic blocks (B1,B2), for which:
.DS
SUCC(B1) = SUCC(B2) = {S}
.DE
(So B1 and B2 both have one and the same successor).
If the last few non-branch instructions are the same for B1 and B2,
one such sequence can be eliminated.
.DS
Pascal:

if cond then
    S1
    S3
else
    S2
    S3

(pseudo) EM:

TEST COND		TEST COND
BNE *1			BNE *1
S1			S1
S3	   --->		BRA *2
BRA *2			1:
1:			S2
S2			2:
S3			S3
2:

Fig. 9.1 An example of Cross Jumping
.DE
As the basic blocks have the same successor,
at least one of them ends in an unconditional branch instruction (BRA).
Hence no extra branch instruction is ever needed, just the target
of an existing branch needs to be changed; neither the program size
nor the execution time will ever increase.
In general, the execution time will remain the same, unless
further optimizations can be applied because of this optimization.
.PP
This optimization is particularly effective,
because it cannot always be done by the programmer at the source level,
as demonstrated by the Fig. 8.2.
.DS
	Pascal:

	if cond then
	   x := f(4)
	else
	   x := g(5)


	EM:

	...                     ...
	LOC 4			LOC 5
	CAL F			CAL G
	ASP 2			ASP 2
	LFR 2			LFR 2
	STL X			STL X

Fig. 9.2 Effectiveness of Cross Jumping
.DE
At the source level there is no common tail,
but at the EM level there is a common tail.
.NH 2
Implementation
.PP
The implementation of cross jumping is rather straightforward.
The technique is applied to one procedure at a time.
The control flow graph of the procedure 
is scanned for pairs of basic blocks
with the same (single) successor and with common tails.
Note that there may be more than two such blocks (e.g. as the result
of a case statement).
This is dealt with by repeating the entire process until no
further optimizations can de done for the current procedure.
.sp
If a suitable pair of basic blocks has been found, the control flow
graph must be altered. One of the basic
blocks must be split into two.
The control flow graphs before and after the optimization are shown
in Fig. 9.3 and Fig. 9.4.
.DS

	--------				--------
	|      |				|      |
	| S1   |			        | S2   |
	| S3   |   				| S3   |
	|      |				|      |
	--------				--------
	   |					   |
	   |------------------|--------------------|
			      |
			      v

Fig. 9.3 CFG before optimization
.DE
.DS

	--------				--------
	|      |				|      |
	| S1   |			        | S2   |
	|      |				|      |
	--------				--------
	   |					   |
	   |--------------------<------------------|
	   v
	--------
	|      |
	| S3   |
	|      |
	--------
	   |
	   v

Fig. 9.4 CFG after optimization
.DE
Some attributes of the three resulting blocks (such as immediate dominator)
are updated.
.PP
In some cases, cross jumping might split the computation of an expression
into two, by inserting a branch somewhere in the middle.
Most code generators will generate very poor assembly code when
presented with such EM code. 
Therefor, cross jumping is not performed in these cases.