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-rw-r--r--generic/regc_nfa.c349
1 files changed, 258 insertions, 91 deletions
diff --git a/generic/regc_nfa.c b/generic/regc_nfa.c
index 459968a..11fd49b 100644
--- a/generic/regc_nfa.c
+++ b/generic/regc_nfa.c
@@ -460,6 +460,42 @@ struct arc *victim;
}
/*
+ - nonemptyouts - count non-EMPTY out arcs of a state
+ ^ static int nonemptyouts(struct state *);
+ */
+static int
+nonemptyouts(s)
+struct state *s;
+{
+ int n = 0;
+ struct arc *a;
+
+ for (a = s->outs; a != NULL; a = a->outchain) {
+ if (a->type != EMPTY)
+ n++;
+ }
+ return n;
+}
+
+/*
+ - nonemptyins - count non-EMPTY in arcs of a state
+ ^ static int nonemptyins(struct state *);
+ */
+static int
+nonemptyins(s)
+struct state *s;
+{
+ int n = 0;
+ struct arc *a;
+
+ for (a = s->ins; a != NULL; a = a->inchain) {
+ if (a->type != EMPTY)
+ n++;
+ }
+ return n;
+}
+
+/*
- findarc - find arc, if any, from given source with given type and color
* If there is more than one such arc, the result is random.
^ static struct arc *findarc(struct state *, int, pcolor);
@@ -538,6 +574,26 @@ struct state *new;
}
/*
+ - copynonemptyins - as above, but ignore empty arcs
+ ^ static void copynonemptyins(struct nfa *, struct state *, struct state *);
+ */
+static VOID
+copynonemptyins(nfa, oldState, newState)
+struct nfa *nfa;
+struct state *oldState;
+struct state *newState;
+{
+ struct arc *a;
+
+ assert(oldState != newState);
+
+ for (a=oldState->ins ; a!=NULL ; a=a->inchain) {
+ if (a->type != EMPTY)
+ cparc(nfa, a, a->from, newState);
+ }
+}
+
+/*
- moveouts - move all out arcs of a state to another state
^ static VOID moveouts(struct nfa *, struct state *, struct state *);
*/
@@ -574,6 +630,26 @@ struct state *new;
for (a = old->outs; a != NULL; a = a->outchain)
cparc(nfa, a, new, a->to);
}
+
+/*
+ - copynonemptyouts - as above, but ignore empty arcs
+ ^ static void copynonemptyouts(struct nfa *, struct state *, struct state *);
+ */
+static VOID
+copynonemptyouts(nfa, oldState, newState)
+struct nfa *nfa;
+struct state *oldState;
+struct state *newState;
+{
+ struct arc *a;
+
+ assert(oldState != newState);
+
+ for (a=oldState->outs ; a!=NULL ; a=a->outchain) {
+ if (a->type != EMPTY)
+ cparc(nfa, a, newState, a->to);
+ }
+}
/*
- cloneouts - copy out arcs of a state to another state pair, modifying type
@@ -1137,103 +1213,194 @@ fixempties(nfa, f)
struct nfa *nfa;
FILE *f; /* for debug output; NULL none */
{
- struct state *s;
- struct state *nexts;
- struct state *to;
- struct arc *a;
- struct arc *nexta;
- int progress;
-
- /* find and eliminate empties until there are no more */
- do {
- progress = 0;
- for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
- nexts = s->next;
- for (a = s->outs; a != NULL && !NISERR();
- a = a->outchain)
- if (a->type == EMPTY)
- /* Mark a for deletion; copy arcs
- * to preserve graph connectivity
- * after it is gone. */
- unempty(nfa, a);
-
- /* Now pass through and delete the marked arcs.
- * Doing all the deletion after all the marking
- * prevents arc copying from resurrecting deleted
- * arcs which can cause failure to converge.
- * [Tcl Bug 3604074] */
- for (a = s->outs; a != NULL; a = nexta) {
- nexta = a->outchain;
- if (a->from == NULL) {
- progress = 1;
- to = a->to;
- a->from = s;
- freearc(nfa, a);
- if (to->nins == 0) {
- while ((a = to->outs))
- freearc(nfa, a);
- if (nexts == to)
- nexts = to->next;
- freestate(nfa, to);
- }
- if (s->nouts == 0) {
- while ((a = s->ins))
- freearc(nfa, a);
- freestate(nfa, s);
- }
- }
- }
- }
- if (progress && f != NULL)
- dumpnfa(nfa, f);
- } while (progress && !NISERR());
+ struct state *s;
+ struct state *s2;
+ struct state *nexts;
+ struct arc *a;
+ struct arc *nexta;
+
+ /*
+ * First, get rid of any states whose sole out-arc is an EMPTY, since
+ * they're basically just aliases for their successor. The parsing
+ * algorithm creates enough of these that it's worth special-casing this.
+ */
+ for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
+ nexts = s->next;
+ if (s->nouts == 1 && !s->flag) {
+ a = s->outs;
+ assert(a != NULL && a->outchain == NULL);
+ if (a->type == EMPTY) {
+ if (s != a->to)
+ moveins(nfa, s, a->to);
+ dropstate(nfa, s);
+ }
+ }
+ }
+
+ /*
+ * Similarly, get rid of any state with a single EMPTY in-arc, by folding
+ * it into its predecessor.
+ */
+ for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
+ nexts = s->next;
+ /* while we're at it, ensure tmp fields are clear for next step */
+ s->tmp = NULL;
+ if (s->nins == 1 && !s->flag) {
+ a = s->ins;
+ assert(a != NULL && a->inchain == NULL);
+ if (a->type == EMPTY) {
+ if (s != a->from)
+ moveouts(nfa, s, a->from);
+ dropstate(nfa, s);
+ }
+ }
+ }
+
+ /*
+ * For each remaining NFA state, find all other states that are reachable
+ * from it by a chain of one or more EMPTY arcs. Then generate new arcs
+ * that eliminate the need for each such chain.
+ *
+ * If we just do this straightforwardly, the algorithm gets slow in
+ * complex graphs, because the same arcs get copied to all intermediate
+ * states of an EMPTY chain, and then uselessly pushed repeatedly to the
+ * chain's final state; we waste a lot of time in newarc's duplicate
+ * checking. To improve matters, we decree that any state with only EMPTY
+ * out-arcs is "doomed" and will not be part of the final NFA. That can be
+ * ensured by not adding any new out-arcs to such a state. Having ensured
+ * that, we need not update the state's in-arcs list either; all arcs that
+ * might have gotten pushed forward to it will just get pushed directly to
+ * successor states. This eliminates most of the useless duplicate arcs.
+ */
+ for (s = nfa->states; s != NULL && !NISERR(); s = s->next) {
+ for (s2 = emptyreachable(s, s); s2 != s && !NISERR(); s2 = nexts) {
+ /*
+ * If s2 is doomed, we decide that (1) we will always push arcs
+ * forward to it, not pull them back to s; and (2) we can optimize
+ * away the push-forward, per comment above. So do nothing.
+ */
+ if (s2->flag || nonemptyouts(s2) > 0)
+ replaceempty(nfa, s, s2);
+
+ /* Reset the tmp fields as we walk back */
+ nexts = s2->tmp;
+ s2->tmp = NULL;
+ }
+ s->tmp = NULL;
+ }
+
+ /*
+ * Now remove all the EMPTY arcs, since we don't need them anymore.
+ */
+ for (s = nfa->states; s != NULL && !NISERR(); s = s->next) {
+ for (a = s->outs; a != NULL; a = nexta) {
+ nexta = a->outchain;
+ if (a->type == EMPTY)
+ freearc(nfa, a);
+ }
+ }
+
+ /*
+ * And remove any states that have become useless. (This cleanup is not
+ * very thorough, and would be even less so if we tried to combine it with
+ * the previous step; but cleanup() will take care of anything we miss.)
+ */
+ for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
+ nexts = s->next;
+ if ((s->nins == 0 || s->nouts == 0) && !s->flag)
+ dropstate(nfa, s);
+ }
+
+ if (f != NULL && !NISERR())
+ dumpnfa(nfa, f);
}
-
+
/*
- - unempty - optimize out an EMPTY arc, if possible
- * Actually, as it stands this function always succeeds, but the return
- * value is kept with an eye on possible future changes.
- ^ static int unempty(struct nfa *, struct arc *);
+ - emptyreachable - recursively find all states reachable from s by EMPTY arcs
+ * The return value is the last such state found. Its tmp field links back
+ * to the next-to-last such state, and so on back to s, so that all these
+ * states can be located without searching the whole NFA.
+ * The maximum recursion depth here is equal to the length of the longest
+ * loop-free chain of EMPTY arcs, which is surely no more than the size of
+ * the NFA, and in practice will be a lot less than that.
+ ^ static struct state *emptyreachable(struct state *, struct state *);
*/
-static int /* 0 couldn't, 1 could */
-unempty(nfa, a)
+static struct state *
+emptyreachable(s, lastfound)
+struct state *s;
+struct state *lastfound;
+{
+ struct arc *a;
+
+ s->tmp = lastfound;
+ lastfound = s;
+ for (a = s->outs; a != NULL; a = a->outchain) {
+ if (a->type == EMPTY && a->to->tmp == NULL)
+ lastfound = emptyreachable(a->to, lastfound);
+ }
+ return lastfound;
+}
+
+/*
+ - replaceempty - replace an EMPTY arc chain with some non-empty arcs
+ * The EMPTY arc(s) should be deleted later, but we can't do it here because
+ * they may still be needed to identify other arc chains during fixempties().
+ ^ static void replaceempty(struct nfa *, struct state *, struct state *);
+ */
+static VOID
+replaceempty(nfa, from, to)
struct nfa *nfa;
-struct arc *a;
+struct state *from;
+struct state *to;
{
- struct state *from = a->from;
- struct state *to = a->to;
-
- assert(a->type == EMPTY);
- assert(from != nfa->pre && to != nfa->post);
-
- if (from == to) { /* vacuous loop */
- freearc(nfa, a);
- return 1;
- }
-
- /* Mark arc for deletion */
- a->from = NULL;
-
- if (from->nouts > to->nins) {
- copyouts(nfa, to, from);
- return 1;
- }
- if (from->nouts < to->nins) {
- copyins(nfa, from, to);
- return 1;
- }
-
- /* from->nouts == to->nins */
- /* decide on secondary issue: move/copy fewest arcs */
- if (from->nins > to->nouts) {
- copyouts(nfa, to, from);
- return 1;
- }
-
- copyins(nfa, from, to);
- return 1;
+ int fromouts;
+ int toins;
+
+ assert(from != to);
+
+ /*
+ * Create replacement arcs that bypass the need for the EMPTY chain. We
+ * can do this either by pushing arcs forward (linking directly from
+ * "from"'s predecessors to "to") or by pulling them back (linking
+ * directly from "from" to "to"'s successors). In general, we choose
+ * whichever way creates greater fan-out or fan-in, so as to improve the
+ * odds of reducing the other state to zero in-arcs or out-arcs and
+ * thereby being able to delete it. However, if "from" is doomed (has no
+ * non-EMPTY out-arcs), we must keep it so, so always push forward in that
+ * case.
+ *
+ * The fan-out/fan-in comparison should count only non-EMPTY arcs. If
+ * "from" is doomed, we can skip counting "to"'s arcs, since we want to
+ * force taking the copynonemptyins path in that case.
+ */
+ fromouts = nonemptyouts(from);
+ toins = (fromouts == 0) ? 1 : nonemptyins(to);
+
+ if (fromouts > toins) {
+ copynonemptyouts(nfa, to, from);
+ return;
+ }
+ if (fromouts < toins) {
+ copynonemptyins(nfa, from, to);
+ return;
+ }
+
+ /*
+ * fromouts == toins. Decide on secondary issue: copy fewest arcs.
+ *
+ * Doesn't seem to be worth the trouble to exclude empties from these
+ * comparisons; that takes extra time and doesn't seem to improve the
+ * resulting graph much.
+ */
+ if (from->nins > to->nouts) {
+ copynonemptyouts(nfa, to, from);
+ return;
+ } else {
+ copynonemptyins(nfa, from, to);
+ return;
+ }
}
-
+
/*
- cleanup - clean up NFA after optimizations
^ static VOID cleanup(struct nfa *);