Reaching definition explained

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.

As analysis

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.

in reaching definitions are:

{\rmREACH}_\rm[S]=cup_p{\rmREACH}_\rm[p]

{\rmREACH}_\rm[S]={\rmGEN}[S]\cup({\rmREACH}_\rm[S]-{\rmKILL}[S])

In other words, the set of reaching definitions going into

are all of the reaching definitions from

's predecessors,

pred[S]

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

{\rmGEN}

and

{\rmKILL}

sets as follows:

{\rmGEN}[d:y\leftarrowf(x_{1, … ,x}_n)]=\{d\}

, a set of locally available definitions in a basic block

{\rmKILL}[d:y\leftarrowf(x_{1, … ,x}_n)]={\rmDEFS}[y]-\{d\}

, a set of definitions (not locally available, but in the rest of the program) killed by definitions in the basic block.

where

{\rmDEFS}[y]

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.

Worklist algorithm

Reaching definition is usually calculated using an iterative worklist algorithm.

Input: control-flow graph CFG = (Nodes, Edges, Entry, Exit)// Initializefor 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)

Reaching definition explained

As analysis

Worklist algorithm

See also

Further reading