COMPILER TECHNIQUES FOR MATLAB PROGRAMS ... - CiteSeerX

avariable previously dened in lexicographic order, or a forward denition if it points to a
variable denition that post-dominates the function.
Our functions are classied into two groups, according to the kind of construction
required by the function. The rst group of functions, which we redene as functions,
replaces the functions required at the end of conditional statements and loops.
Both
parameters of functions have backward denitions. The other group of functions, which
we redene as ' functions, replaces the functions required at the beginning of loops. '
functions have one forward denition and one backward denition.
In some cases, the use of a variable may nothave a previous denition in the lexicographic
order of the program, as for example variable y in Statement S3 in the code segment
presented in Figure 4.5(a).
In these cases, when generating the and ' functions, the
corresponding backward denitions are assumed to be null, as exemplied by Statement
P1 in Figure 4.5(b) that presents the SSA representation for the same program. Thus, as
shown in Statement P2, the ' function will have two parameters however, one points to an
\actual" assignment, while the other points to an \articial" assignment tonull. These
articial assignments are not necessary for the static inference mechanism, as the ' function
could have just the forward parameter. However, its use facilitates the implementation by
forcing all ' functions to have two parameters. It is also helpful during the dynamic phase,
as discussed in Chapter 6.
4.2.3 Extension of the SSA Representation to Support Indexed
Array Assignments
While it is easy to determine which denitions cover a given use in the case of scalars and
full array assignments using the SSA representation, indexed array assignments require a
more complex approach involving a new function. Consider, for example, the MATLAB
code segment presented in Figure 4.6, and assume that A is assigned in statements S2 and
S4 only. In this code segment, S1 creates a matrix Z lled with zeros S2 creates a matrix
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