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
Famous quotes containing the words bit and/or problems:
“Take a decayed Christian ... and the remains of a Stoic; mix thoroughly with good manners, a bit of money and an old-fashioned education; simmer for several years in a university. Result: a scholar and a gentleman. Well, there were worse types of human being.”
—Aldous Huxley (1894–1963)
“I have said many times, and it is literally true, that there is absolutely nothing that could keep me in business, if my job were simply business to me. The human problems which I deal with every day—concerning employees as well as customers—are the problems that fascinate me, that seem important to me.”
—Hortense Odlum (1892–?)