any FVIM incidence, say in function f, with a variable index defined by

a range with upper limit offset from U. decoupling will not hold for

that function index. The reason is that, for iz=Li the first pass

through the "ii loop," the function f will require values of x for all

values of ii. This being the case these values must be supplied by

tearing x, hence decoupling could not hold. An analogous condition

holds for the function index being decremented rather than incremented.

Another "shortcut" is to note that, if for some variable type all

variable indices depending upon a particular function index are the

same, decoupling cannot occur for that function index.

 Figure 4-1 presents an example problem to which the decoupling

algorithm will be applied. The first step is to produce the FVIM, which

is at the top of the figure. No assignments need be broken as none have

been made. Choose ascending order for both indices initially. The

function and variable types are untagged. Now the algorithm begins in

earnest. The FVIM does not fully precedence order, so the algorithm

skips to step IV.A. The following steps are then carried out:

 IV. A. Choose x. Tag x.

 IV. B. Choose f. Tag f.

 IV. C. Legal output; continue.

 V. A. Choose ii.

 VI. A. No decoupling (all variable indices are j1). Tag i

 V. B. Choose i2.

 VI. A. No decoupling (U. =U. ). Tag i .
 34 12
 V. B. No more function indices.

 IV. B. Choose g. Tag g.

 IV. C. Legal output; continue.


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