pass: tweak ordering in liveness analysis

Previously we updated the set of live in registers before live out. This
was extremely inefficient, since on each pass through live in depends on
live out.

We also change to processing the instructions in reverse order, which is
more likely to be efficient, although we should replace this with
topological sort order soon.

pass/reg.go

@@ -15,9 +15,15 @@ func Liveness(fn *avo.Function) error {
 
 	is := fn.Instructions()
 
-	// Initialize to empty sets.
+	// Process instructions in reverse: poor approximation to topological sort.
+	// TODO(mbm): process instructions in topological sort order
+	for l, r := 0, len(is)-1; l < r; l, r = l+1, r-1 {
+		is[l], is[r] = is[r], is[l]
+	}
+
+	// Initialize.
 	for _, i := range is {
-		i.LiveIn = reg.NewEmptySet()
+		i.LiveIn = reg.NewSetFromSlice(i.InputRegisters())
 		i.LiveOut = reg.NewEmptySet()
 	}
 
@@ -26,15 +32,6 @@ func Liveness(fn *avo.Function) error {
 		changes := false
 
 		for _, i := range is {
-			// in[n] = use[n] UNION (out[n] - def[n])
-			nin := len(i.LiveIn)
-			i.LiveIn.Update(reg.NewSetFromSlice(i.InputRegisters()))
-			def := reg.NewSetFromSlice(i.OutputRegisters())
-			i.LiveIn.Update(i.LiveOut.Difference(def))
-			if len(i.LiveIn) != nin {
-				changes = true
-			}
-
 			// out[n] = UNION[s IN succ[n]] in[s]
 			nout := len(i.LiveOut)
 			for _, s := range i.Succ {
@@ -46,6 +43,19 @@ func Liveness(fn *avo.Function) error {
 			if len(i.LiveOut) != nout {
 				changes = true
 			}
+
+			// in[n] = use[n] UNION (out[n] - def[n])
+			nin := len(i.LiveIn)
+			def := reg.NewSetFromSlice(i.OutputRegisters())
+			i.LiveIn.Update(i.LiveOut.Difference(def))
+			for r := range i.LiveOut {
+				if _, found := def[r]; !found {
+					i.LiveIn.Add(r)
+				}
+			}
+			if len(i.LiveIn) != nin {
+				changes = true
+			}
 		}
 
 		if !changes {