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doc/ego/ud/ud2

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+.NH 2
+Data flow information
+.PP
+.NH 3
+Use-Definition information
+.PP
+A \fIdefinition\fR of a variable A is an assignment to A.
+A definition is said to \fIreach\fR a point p if there is a
+path in the control flow graph from the definition to p, such that
+A is not redefined on that path.
+.PP
+For every basic block B, we define the following sets:
+.IP GEN[b] 9
+the set of definitions in b that reach the end of b.
+.IP KILL[b]
+the set of definitions outside b that define a variable that
+is changed in b.
+.IP IN[b]
+the set of all definitions reaching the beginning of b.
+.IP OUT[b]
+the set of all definitions reaching the end of b.
+.LP
+GEN and KILL can be determined by inspecting the code of the procedure.
+IN and OUT are computed by solving the following data flow equations:
+.DS
+(1)    OUT[b] = IN[b] - KILL[b] + GEN[b]
+(2)    IN[b]  = OUT[p1] + ... + OUT[pn],
+	 where PRED(b) = {p1, ... , pn}
+.DE
+.NH 3
+Copy information
+.PP
+A \fIcopy\fR is a definition of the form "A := B".
+A copy is said to be \fIgenerated\fR in a basic block n if
+it occurs in n and there is no subsequent assignment to B in n.
+A copy is said to be \fIkilled\fR in n if:
+.IP (i)
+it occurs in n and there is a subsequent assignment to B within n, or
+.IP (ii)
+it occurs outside n, the definition A := B reaches the beginning of n
+and B is changed in n (note that a copy also is a definition).
+.LP
+A copy \fIreaches\fR a point p, if there are no assignments to B
+on any path in the control flow graph from the copy to p.
+.PP
+We define the following sets:
+.IP C_GEN[b] 11
+the set of all copies in b generated in b.
+.IP C_KILL[b]
+the set of all copies killed in b.
+.IP C_IN[b]
+the set of all copies reaching the beginning of b.
+.IP C_OUT[b]
+the set of all copies reaching the end of b.
+.LP
+C_IN and C_OUT are computed by solving the following equations:
+(root is the entry node of the current procedure; '*' denotes
+set intersection)
+.DS
+(1)    C_OUT[b] = C_IN[b] - C_KILL[b] + C_GEN[b]
+(2)    C_IN[b]  = C_OUT[p1] * ... * C_OUT[pn],
+	 where PRED(b) = {p1, ... , pn} and b /= root
+       C_IN[root] = {all copies}
+.DE