// findCandidates recursively locates potential node pairs (g and s) for an
// isomorphism of sub in graph and adds them to c.
func (eq *equation) findCandidates(g, s *dot.Node, sub *graphs.SubGraph) {
// Exit early for impossible node pairs.
if !isPotential(g, s, sub) {
return
}
// Prevent infinite cycles.
if _, ok := eq.c[s.Name]; ok {
if eq.c[s.Name][g.Name] {
return
}
}
// Add node pair candidate.
if _, ok := eq.c[s.Name]; !ok {
eq.c[s.Name] = make(map[string]bool)
} else if s.Name == sub.Entry() {
// Locate candidates for the entry node and its immediate successors
// exactly once.
return
}
eq.c[s.Name][g.Name] = true
// Recursively locate candidate successor pairs.
for _, ssucc := range s.Succs {
for _, gsucc := range g.Succs {
eq.findCandidates(gsucc, ssucc, sub)
}
}
}
// candidates locates node pair candidates for an isomorphism of sub in graph
// which starts at the entry node.
func candidates(graph *dot.Graph, entry string, sub *graphs.SubGraph) (*equation, error) {
// Sanity checks.
g, ok := graph.Nodes.Lookup[entry]
if !ok {
return nil, errutil.Newf("unable to locate entry node %q in graph", entry)
}
s, ok := sub.Nodes.Lookup[sub.Entry()]
if !ok {
panic(fmt.Sprintf("unable to locate entry node %q in sub", sub.Entry()))
}
if !isPotential(g, s, sub) {
return nil, errutil.Newf("invalid entry node candidate %q; expected %d successors, got %d", g.Name, len(s.Succs), len(g.Succs))
}
// Locate candidate node pairs.
eq := &equation{
c: make(map[string]map[string]bool),
m: make(map[string]string),
}
eq.findCandidates(g, s, sub)
if len(eq.c) != len(sub.Nodes.Nodes) {
return nil, errutil.Newf("incomplete candidate mapping; expected %d map entites, got %d", len(sub.Nodes.Nodes), len(eq.c))
}
return eq, nil
}
// isPotential returns true if the graph node g is a potential candidate for the
// sub node s, and false otherwise.
func isPotential(g, s *dot.Node, sub *graphs.SubGraph) bool {
// Verify predecessors.
if s.Name != sub.Entry() && len(g.Preds) != len(s.Preds) {
return false
}
// Verify successors.
if s.Name != sub.Exit() && len(g.Succs) != len(s.Succs) {
return false
}
return true
}
// printMapping prints the mapping from sub node name to graph node name for an
// isomorphism of sub in graph.
func printMapping(graph *dot.Graph, sub *graphs.SubGraph, m map[string]string) {
entry := m[sub.Entry()]
var snames []string
for sname := range m {
snames = append(snames, sname)
}
sort.Strings(snames)
fmt.Printf("Isomorphism of %q found at node %q:\n", sub.Name, entry)
for _, sname := range snames {
fmt.Printf(" %q=%q\n", sname, m[sname])
}
}
// Merge merges the nodes of the isomorphism of sub in graph into a single node.
// If successful it returns the name of the new node.
func Merge(graph *dot.Graph, m map[string]string, sub *graphs.SubGraph) (name string, err error) {
var nodes []*dot.Node
for _, gname := range m {
node, ok := graph.Nodes.Lookup[gname]
if !ok {
return "", errutil.Newf("unable to locate mapping for node %q", gname)
}
nodes = append(nodes, node)
}
name = uniqName(graph, sub.Name)
entry, ok := graph.Nodes.Lookup[m[sub.Entry()]]
if !ok {
return "", errutil.Newf("unable to locate mapping for entry node %q", sub.Entry())
}
exit, ok := graph.Nodes.Lookup[m[sub.Exit()]]
if !ok {
return "", errutil.Newf("unable to locate mapping for exit node %q", sub.Exit())
}
err = graph.Replace(nodes, name, entry, exit)
if err != nil {
return "", errutil.Err(err)
}
return name, nil
}
// isValid returns true if m is a valid mapping, from sub node name to graph
// node name, for an isomorphism of sub in graph considering all nodes and edges
// except predecessors of entry and successors of exit.
func (eq *equation) isValid(graph *dot.Graph, sub *graphs.SubGraph) bool {
if len(eq.m) != len(sub.Nodes.Nodes) {
return false
}
// Check for duplicate values.
if hasDup(eq.m) {
return false
}
// Verify that the entry node dominates the exit node.
entry, ok := graph.Nodes.Lookup[eq.m[sub.Entry()]]
if !ok {
return false
}
exit, ok := graph.Nodes.Lookup[eq.m[sub.Exit()]]
if !ok {
return false
}
// TODO: Figure out how to handle find the if-statement in the following graph:
// digraph bar {
// E -> F
// E -> J
// F -> G
// F -> E
// G -> I
// I -> E
// E [label="entry"]
// F
// G
// I
// J [label="exit"]
// }
//
// ref: https://github.com/decomp/decompilation/issues/172
if !entry.Dominates(exit) {
return false
}
// Sort keys to make the algorithm deterministic.
var snames []string
for sname := range eq.m {
snames = append(snames, sname)
}
sort.Strings(snames)
for _, sname := range snames {
gname := eq.m[sname]
s, ok := sub.Nodes.Lookup[sname]
if !ok {
panic(fmt.Sprintf("unable to locate node %q in sub", sname))
}
g, ok := graph.Nodes.Lookup[gname]
if !ok {
panic(fmt.Sprintf("unable to locate node %q in graph", gname))
}
// Verify predecessors.
if s.Name != sub.Entry() {
if len(s.Preds) != len(g.Preds) {
return false
}
for _, spred := range s.Preds {
found := false
for _, gpred := range g.Preds {
if gpred.Name == eq.m[spred.Name] {
found = true
break
}
}
if !found {
return false
}
}
}
// Verify successors.
if s.Name != sub.Exit() {
if len(s.Succs) != len(g.Succs) {
return false
}
for _, ssucc := range s.Succs {
found := false
for _, gsucc := range g.Succs {
if gsucc.Name == eq.m[ssucc.Name] {
found = true
break
}
}
if !found {
return false
}
}
}
}
// Isomorphism found!
return true
}