COMPILER TECHNIQUES FOR MATLAB PROGRAMS ... - CiteSeerX

S1: if (A D1 .ne. B D1 .or. A D2 .ne. B D2) then
S2: if (ALLOCATED(A)) DEALLOCATE(A)
S3: A D1 = B D1
S4: A D2 = B D2
S5: ALLOCATE(A(A D1,A D2))
S6: end if
S7: A = B + 0.5
Figure 3.8: Example of shadow variables for shape.
the form A=B+0.5 were unknown at compile time, the compiler would generate the code
presented in Figure 3.8, which uses shadow variables A D1, A D2, B D1, and B D2, to
store the run-time information about the dimensions of A and B. These shadow variables
are initialized to zero at the beginning of the program. This gure shows the general form
for the dynamic allocation. However, only the necessary statements are generated. So, for
example, if this is the rst denition of variable A, statements S1 and S2 are not generated 5 .
Dynamic rank inference is also generated for the correct execution of the code. Consider
again a multiplication of two variables being assigned to a third variable: c = a b. Suppose
that both variables a and b are of type real, but have unknown shape at the end of
the static analysis phase.
The simple solution of generating a single matrix multiplication statement for this expression
(e.g., c = MATMUL(a,b) ) is not possible due to performance and conformability
considerations. Thus, dynamic rank inference is performed in order to select the appropriate
functions to perform the operations according to the rank of a and b. The resulting
Fortran 90 code would be the code sequence 6 shown in Figure 3.9.
The shadow variables of a and b are used to infer the rank of the variables during
execution time. The shadow variable for c is updated according to the operation that is
5 If this denition occurs inside a loop, it is not considered the rst denition because there will be an
articial assignment tonull outside the loop, as described in Section 4.2.2.
6 The compiler assumes the correctness of the original program. It uses the BLAS routines DDOT, DGEMV,
and DGEMM for dot-product, matrix-vector multiplication, and matrix multiplication respectively.
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