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...nal re-engineered loop has the ideal reachability ratio of 1. We therefore suggest that as an indicator of branch structure quality this semantic-based index is far more useful than the McCabe Number =-=[24]-=- because it indicates an ideal and how the structure might be improved to realize the ideal. We have shown elsewhere how BSG have an important role to play in developing a theory of normal forms for p...

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...est precondition under which each assignment may execute. Imposing this requirement also effectively collapses complex branch structures within a loop to a simple uniform form. Using guarded commands =-=[19]-=- we call this structure the multiply branched statement (MBS) form, i.e: do G 3 if C1 3 S1 [] C2 3 S2 []....[]Cn3Snfiod R E-ENGINEERING LOOPS A loop that has undergone transformation to the MBS form e...

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... in this loop structure. Both procedures share the same input x but while the output fx is always produced during iteration, the output fd is not (this leads to an inhomogeneous loop invariant defect =-=[6]-=-). This discrepancy in the relationship between fx and fd arises because of the exit branch 3 zerodivattempted X� state zerodivinf. It is necessary to remove this inconsistency, by grouping the two pr...

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...ture that is being transformed—such benefits are not possible using simple transformation-based restructuring methods. The only other recent formal work on exits has been published by King and Morgan =-=[26]-=-. The focus of that work is upon formally accommodating exits and exceptions. These objectives are quite different from what we have tried to do here. The processes we have developed can be used to de...

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...oop to which they have been propagated. To illustrate how the overall process is applied we will transform the following nested multiple-exit C loop structure which has been taken from the literature =-=[10]-=-: NoReply � TRUE; do { if (SendMessage(RequestMsg)<0)) { printf(‘‘Bad send\n’’); return(RPC-FAILED); }; while (NoReply) if ((status � ReceiveMessage(ReplyMsg,10*Seconds))<0) { if (status �� TIMEOUT) {...

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... a read(s) or procedure(s) or loop(s) in both S and SXe. For instance, do G(x,y) 3 read(x); if C(x) 3 S1; break [] XC(x) 3 read(y); S2 fiodis a typical example. From the viewpoint of software quality =-=[21, 22]-=- this sort of loop has an inconsistent (inhomogeneous) invariant which should always be avoided. Because the exiting branch C e 3 S e is executed only once, it should not be in the loop structure. For...

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...tion formally. We may use this information to construct the branch successor graph (BSG) for the loop (see Figure 2). The BSG may be used to both assess and improve the structural quality of programs =-=[20]-=-. Important logical (semantic) and structural characteristics of a loop may be conveniently interpreted in terms of features of the BSG. Well-structured loops have a BSG where each node (corresponding...

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... return statements. After removal of gotos from a loop body only breaks, returns and the statements that make the loop guard false are left to cause multiple-exits. Generally, the last kind of ‘exit’ =-=[4]-=- may not be detected by pure syntactic analysis, because it is often difficult to neatly capture in a powerful pattern description all possible forms that a particular kind of statement might assume. ...

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...t directly following the loop; F return transfers control directly out of the function/procedure that encapsulates it. F 2.1. Preliminary transformations We have previously developed a formal process =-=[16]-=- to eliminate all gotos from any program. Here, we will therefore focus only upon removal of break and return statements. After removal of gotos from a loop body only breaks, returns and the statement...

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...onds to the inner loop. 6.3. Removal of guard-terminating branches We now consider an example (in a Pascal-like language) proposed by Atkinson [4] that was put forward as a strategy for handling MELs =-=[7, 15, 18, 25]-=-. According to our earlier definition the proposed solution is still a MEL. It has the following form: ...... PROCEDURE Evaluatef(x: real; VAR f:real; VAR zerodiv:boolean); ...... PROCEDURE Evaluatefd...

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...onds to the inner loop. 6.3. Removal of guard-terminating branches We now consider an example (in a Pascal-like language) proposed by Atkinson [4] that was put forward as a strategy for handling MELs =-=[7, 15, 18, 25]-=-. According to our earlier definition the proposed solution is still a MEL. It has the following form: ...... PROCEDURE Evaluatef(x: real; VAR f:real; VAR zerodiv:boolean); ...... PROCEDURE Evaluatefd...

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...onds to the inner loop. 6.3. Removal of guard-terminating branches We now consider an example (in a Pascal-like language) proposed by Atkinson [4] that was put forward as a strategy for handling MELs =-=[7, 15, 18, 25]-=-. According to our earlier definition the proposed solution is still a MEL. It has the following form: ...... PROCEDURE Evaluatef(x: real; VAR f:real; VAR zerodiv:boolean); ...... PROCEDURE Evaluatefd...

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...R E-ENGINEERING LOOPS }while ((Op �� Opl)�(Op �� Ops)); if (Op �� Opq) { QFlag � TRUE; Error � TRUE; } elsif (Op ! � ERROR) && (Op ! � Opq)&& (Op ! � Opl)&& (Op ! � Ops)) {Error � TRUE; } } Elsewhere =-=[23]-=- we have shown how a property of the BSG provides an excellent metric for assessing the quality of branched loop structures. The ideal for a multiple-branched loop structure is that in passing from on...