Bit Vector Problems
The examples above are problems in which the data-flow value is a set, e.g. the set of reaching definitions (Using a bit for a definition position in the program), or the set of live variables. These sets can be represented efficiently as bit vectors, in which each bit represents set membership of one particular element. Using this representation, the join and transfer functions can be implemented as bitwise logical operations. The join operation is typically union or intersection, implemented by bitwise logical or and logical and. The transfer function for each block can be decomposed in so-called gen and kill sets.
As an example, in live-variable analysis, the join operation is union. The kill set is the set of variables that are written in a block, whereas the gen set is the set of variables that are read without being written first. The data-flow equations become
In logical operations, this reads as
- out(b) = 0
- for s in succ(b)
- out(b) = out(b) or in(s)
- in(b) = (out(b) and not kill(b)) or gen(b)
Read more about this topic: Data-flow Analysis
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