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In compiler theory, a reaching definition for a given instruction is an earlier instruction whose target variable can reach (be assigned to) the given one without an intervening assignment. For example, in the following code:
d1 : y := 3 d2 : x := y
d1
is a reaching definition for d2
. In the following, example, however:
d1 : y := 3 d2 : y := 4 d3 : x := y
d1
is no longer a reaching definition for d3
, because d2
kills its reach: the value defined in d1
is no longer available and cannot reach d3
.
The similarly named reaching definitions is a data-flow analysis 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.
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.
Reaching definition is usually calculated using an iterative worklist algorithm.
Input: control-flow graph CFG = (Nodes, Edges, Entry, Exit)
// Initialize
for all CFG nodes n in N,
OUT[n] = emptyset; // can optimize by OUT[n] = GEN[n];
// put all nodes into the changed set
// N is all nodes in graph,
Changed = N;
// Iterate
while (Changed != emptyset)
{
choose a node n in Changed;
// remove it from the changed set
Changed = Changed -{ n };
// init IN[n] to be empty
IN[n] = emptyset;
// calculate IN[n] from predecessors' OUT[p]
for all nodes p in predecessors(n)
IN[n] = IN[n] Union OUT[p];
oldout = OUT[n]; // save old OUT[n]
// update OUT[n] using transfer function f_n ()
OUT[n] = GEN[n] Union (IN[n] -KILL[n]);
// any change to OUT[n] compared to previous value?
if (OUT[n] changed) // compare oldout vs. OUT[n]
{
// if yes, put all successors of n into the changed set
for all nodes s in successors(n)
Changed = Changed U { s };
}
}
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