COMPILER TECHNIQUES FOR MATLAB PROGRAMS ... - CiteSeerX

S1: Ap = A p
S2: alpha = (r' p) / (p' Ap)
S3: x = x + alpha p
S4: r = r + alpha Ap
Figure 3.5: MATLAB code segment to compute conjugate gradient.
A simpler approach would be to consider all variables that cannot have their type inferred
statically by the compiler as having intrinsic type complex One problem with this approach
is that for each of these undened variables, the type will have to be propagated as a
complex variable, and this propagation will tend to perturb the inference process.
For
example, consider the MATLAB code segment from a function that computes conjugate
gradient, as presented in Figure 3.5.
Suppose that the type of A is unknown and that the compiler assumes it to be of type
complex. Assume also that all other variables are known to be of type real. We notice
that the variable A appears only once in this code segment however, the compiler will have
to consider Ap, alpha, x, and r as complex variables because of its assumption about the
type of A.
The generation of dynamic code is avoided whenever there is an assignment that redenes
avariable, changing its intrinsic type. To this end, the variable is renamed and a second
declaration for the variable is generated. Thus, for example, for the pseudo-code presented
in Figure 3.6, the compiler will declare statically three instances of the variable, one for each
intrinsic type assumed by thevariable, and generate the code as shown in gure 3.7.
Dynamic Shape and Rank Inference
The second step of the dynamic phase is the dynamic shape and rank inference. During
this step, dynamic code is generated to compute during run-time the necessary space for the
dynamic allocation. To thisend,two shadowvariables are used to keep track ofvariable
dimensions during execution-time. So, for example, if the shape of B in an assignment of
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