Common subexpression

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

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

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. 

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. 

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]. 

Often the chip architecture produced by behavioral synthesis tools such as VSS contain inefficiencies such as constants that can be propagated through a design, and common subexpressions that appear multiple times in the design, each time with replicated hardware. These can partly result from the fashion in which the user wrote the behavioral description. Also, optimization must modify the design in the direction of meeting time and area constraints. Tradeoffs must be made along different paths. On critical paths optimizations that reduce... 

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