Reaching definition
Encyclopedia
In compiler theory, a reaching definition for a given instruction is another instruction, the target variable of which may reach the given instruction without an intervening assignment. For example, in the following code:
d1 : y := 3
d2 : x := y
d1 : y := 3
d2 : y := 4
d3 : x := y
which statically determines which definitions may reach a given point in the code. Because of its simplicity, it is often used as the canonical example of a data-flow analysis in textbooks. The data-flow confluence operator used is set union, and the analysis is forward flow. Reaching definitions are used to compute use-def chains and def-use chains.
The data-flow equations used for a given basic block
in reaching definitions are:
In other words, the set of reaching definitions going into
are all of the reaching definitions from 
's predecessors, 
. 
consists of all of the basic blocks that come before 
in the control flow graph
. The reaching definitions coming out of
are all reaching definitions of its predecessors minus those reaching definitions whose variable is killed by 
plus any new definitions generated within 
.
For a generic instruction, we define the
and 
sets as follows:
where
is the set of all definitions that assign to the variable 
. Here 
is a unique label attached to the assigning instruction; thus, the domain of values in reaching definitions are these instruction labels.
d1 : y := 3
d2 : x := y
d1 is a reaching definition at d2. In the following, example, however:d1 : y := 3
d2 : y := 4
d3 : x := y
d1 is no longer a reaching definition at d3, because d2 kills its reach.As analysis
The similarly named reaching definitions is a data-flow analysisData-flow analysis
Data-flow analysis is a technique for gathering information about the possible set of values calculated at various points in a computer program. A program's control flow graph is used to determine those parts of a program to which a particular value assigned to a variable might propagate. The...
which statically determines which definitions may reach a given point in the code. Because of its simplicity, it is often used as the canonical example of a data-flow analysis in textbooks. The data-flow confluence operator used is set union, and the analysis is forward flow. Reaching definitions are used to compute use-def chains and def-use chains.
The data-flow equations used for a given basic block
in reaching definitions are:
In other words, the set of reaching definitions going into
are all of the reaching definitions from 's predecessors, . consists of all of the basic blocks that come before in the control flow graphControl flow graph
A control flow graph in computer science is a representation, using graph notation, of all paths that might be traversed through a program during its execution.- Overview :...
. The reaching definitions coming out of
are all reaching definitions of its predecessors minus those reaching definitions whose variable is killed by plus any new definitions generated within .For a generic instruction, we define the
and sets as follows:
where
is the set of all definitions that assign to the variable . Here is a unique label attached to the assigning instruction; thus, the domain of values in reaching definitions are these instruction labels.