Subexpressions

The modified model guarantees only one adder and the multiplexers at the input ports of the adder are implied by the i f statement. The original example may synthesize with three adders. 

It is often useful in practice to identify common subexpressions and to reuse computed values where possible. Here is a simple example. 

II Assume that the second assignment is executed every // time the first statement is executed. Note that this // assumption may not be true if either of the statements //is inside an if statement or a case statement. 

The problem of identifying common subexpressions becomes more important if larger blocks such as multipliers are used. 

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The last two CGC in Eq. (12) evidently dictate that rather different partial wave interference contributions are made to each of the angular parameters. This will impact on the dynamical information conveyed by each one. Equally important, the phase subexpression... 

Substituting this ( subexpression back into Eq. (A.l 1) finally yields... 

Some expressions may have undefined values—for example, attributes of null, daft arithmetic expressions such as 0/0, or parameterized attributes whose precondition is false. Generally, an expression is undefined if any of its subexpressions is undefined. However, some operators do not depend on one of their inputs under certain circumstances 0 n is well defined even if you don t know n so is n 0. The same applies to (true b) and (false b), again no matter what the order of the operands. (This works no matter which way you write the operands—we re not writing a program.)... 

In conventional programs, you split a big program into subroutines so that common routines can be invoked individually and so that the program is easier to understand. In 00 programming, the process goes even further. For eveiy statement, you think, Which object should this be attached to Which object has the information and the other operations most strongly relevant to this Then you send a message to the appropriate object. Actually, that s not for every statement rather, it s for every subexpression. 

Notes Every diagram can have embedded informal notes. Any syntactical construct— for example, a type, an attribute, a postcondition, a subexpression, or a variable—can also have an informal note. A note can appear in addition to or instead of the more formal statement. 

Given some expression P involving some subexpression,... 

Common factoring is the extraction of common subexpressions in mutually-exclusive branches of an i f statement or a case statement. Here is an example. 

In certain cases, it may be necessary to perform commutative operations before performing some of the earlier mentioned optimizations. Here is an example where performing a commutative operation before common subexpression identification helps in identifying common subexpressions. 

Applying commutativity rales to the expression R2 + Rl helps in identifying the common subexpression Rl + R2 that is also used in the first assignment. 

Notice that applying associativity and commutativity rules on the expression in the first statement identifies C + A as a common subexpression. After subexpression identification, the example appears like this. 

If associativity and commutativity are not used, a synthesis tool may generate three adders and one subtracter after subexpression identification, it may generate only two adders and one subtracter, thus providing increased savings in logic. 

What do we need to know if the oexp consists of two arithmetic expressions combined by + We need to find out whether the two subexpressions are numbered. 

What is the natural value of an arithmetic expression that consists of two arithmetic expressions combined by + [f we had the natural value of the two subexpressions we could just add up the two values. 

As nested mappings factor out common subexpressions, there are many benefits in their use (1) it is possible to produce more efficient translation queries by reducing the number of passes over the source (2) the generated data have less redundancy as the same data are not mapped repeatedly by s-t tgds sharing common parts. 

DDD is a transformation system that operates on expressions of these forms. It as a first-order reasoning tool in which implementation proofs are presented as algebraic derivations. It is proficient at the large-scale formal manipulations involved as structure is imposed on a behavioral specification and as concrete data representations are introduced. A proof consists of an initial expression and a sequence of constructions and transformations together with any side conditions they generate. In practice, one also needs the intermediate expressions in order to address the subexpressions to be manipulated. 

Prom the upper left, clockwise, are the derivation management window, con-taining a command menu, derivation history, and current command editing subwindow the current expression window, used to address subexpressions a control window for animating the model a window showing signal wave forms and a window for input to the model. 

Supports behavioral transformations, primarily to improve the efficiency of the control structure constant folding, common subexpression elimination, dead procedure elimination, inline expansion and formation of procedures, code motion into and out of the branches of decoding operations, and loop unrolling. 

Compiler-like transformations, including constant folding, code motion, global common-subexpression elimination, expression factoring, and redundant code elimination. 

Performs common subexpression elimination, and substitutes logically equivalent structures when doing so will reduce the number of components. 

Performs constant folding and common subexpression elimination. 

Automatic transformations include constant and variable folding, common subexpression elimination, dead code... 

Figure 7-4 shows a flow chart of the transformations. Only the behavioral partitioning transformation is described in the remainder of this section. In-line expansion of procedure calls, constant folding and common subexpression are described in Chapter 3 or in [WalkerSS]. Map transformation and truncation transformation were defined by Oakley and are described in [Oakley79]. 

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