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authordgp@users.sourceforge.net <dgp>2015-10-20 18:32:25 (GMT)
committerdgp@users.sourceforge.net <dgp>2015-10-20 18:32:25 (GMT)
commit9aa93b55692af9e4c8b34f44c1f4ba06dfc8230e (patch)
treeeec76819493f794df45194cbc87e7e3bef721177
parent55c12125b94505972f15686ea3b60f0498f8cdd6 (diff)
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Adaptation of re-better-fixempties.patch from Tom Lane @ postgres.
-rw-r--r--generic/regc_nfa.c265
-rw-r--r--generic/regcomp.c6
2 files changed, 136 insertions, 135 deletions
diff --git a/generic/regc_nfa.c b/generic/regc_nfa.c
index 0f572b8..5582e4e 100644
--- a/generic/regc_nfa.c
+++ b/generic/regc_nfa.c
@@ -603,44 +603,6 @@ hasnonemptyout(
}
/*
- - nonemptyouts - count non-EMPTY out arcs of a state
- ^ static int nonemptyouts(struct state *);
- */
-static int
-nonemptyouts(
- 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(
- 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);
@@ -1897,6 +1859,12 @@ fixempties(
struct state *nexts;
struct arc *a;
struct arc *nexta;
+ int totalinarcs;
+ struct arc **inarcsorig;
+ struct arc **arcarray;
+ int arccount;
+ int prevnins;
+ int nskip;
/*
* First, get rid of any states whose sole out-arc is an EMPTY,
@@ -1942,42 +1910,129 @@ fixempties(
dropstate(nfa, s);
}
+ if (NISERR()) {
+ return;
+ }
+
/*
- * 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.
+ * For each remaining NFA state, find all other states from which it is
+ * reachable by a chain of one or more EMPTY arcs. Then generate new arcs
+ * that eliminate the need for each such chain.
+ *
+ * We could replace a chain of EMPTY arcs that leads from a "from" state
+ * to a "to" state either by pushing non-EMPTY arcs forward (linking
+ * directly from "from"'s predecessors to "to") or by pulling them back
+ * (linking directly from "from" to "to"'s successors). We choose to
+ * always do the former; this choice is somewhat arbitrary, but the
+ * approach below requires that we uniformly do one or the other.
+ *
+ * Suppose we have a chain of N successive EMPTY arcs (where N can easily
+ * approach the size of the NFA). All of the intermediate states must
+ * have additional inarcs and outarcs, else they'd have been removed by
+ * the steps above. Assuming their inarcs are mostly not empties, we will
+ * add O(N^2) arcs to the NFA, since a non-EMPTY inarc leading to any one
+ * state in the chain must be duplicated to lead to all its successor
+ * states as well. So there is no hope of doing less than O(N^2) work;
+ * however, we should endeavor to keep the big-O cost from being even
+ * worse than that, which it can easily become without care. In
+ * particular, suppose we were to copy all S1's inarcs forward to S2, and
+ * then also to S3, and then later we consider pushing S2's inarcs forward
+ * to S3. If we include the arcs already copied from S1 in that, we'd be
+ * doing O(N^3) work. (The duplicate-arc elimination built into newarc()
+ * and its cohorts would get rid of the extra arcs, but not without cost.)
+ *
+ * We can avoid this cost by treating only arcs that existed at the start
+ * of this phase as candidates to be pushed forward. To identify those,
+ * we remember the first inarc each state had to start with. We rely on
+ * the fact that newarc() and friends put new arcs on the front of their
+ * to-states' inchains, and that this phase never deletes arcs, so that
+ * the original arcs must be the last arcs in their to-states' inchains.
+ *
+ * So the process here is that, for each state in the NFA, we gather up
+ * all non-EMPTY inarcs of states that can reach the target state via
+ * EMPTY arcs. We then sort, de-duplicate, and merge these arcs into the
+ * target state's inchain. (We can safely use sort-merge for this as long
+ * as we update each state's original-arcs pointer after we add arcs to
+ * it; the sort step of mergeins probably changed the order of the old
+ * arcs.)
*
- * 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.
+ * Another refinement worth making is that, because we only add non-EMPTY
+ * arcs during this phase, and all added arcs have the same from-state as
+ * the non-EMPTY arc they were cloned from, we know ahead of time that any
+ * states having only EMPTY outarcs will be useless for lack of outarcs
+ * after we drop the EMPTY arcs. (They cannot gain non-EMPTY outarcs if
+ * they had none to start with.) So we need not bother to update the
+ * inchains of such states at all.
*/
+
+ /* Remember the states' first original inarcs */
+ /* ... and while at it, count how many old inarcs there are altogether */
+ inarcsorig = (struct arc **) MALLOC(nfa->nstates * sizeof(struct arc *));
+ if (inarcsorig == NULL) {
+ NERR(REG_ESPACE);
+ return;
+ }
+ totalinarcs = 0;
+ for (s = nfa->states; s != NULL; s = s->next) {
+ inarcsorig[s->no] = s->ins;
+ totalinarcs += s->nins;
+ }
+
+ /*
+ * Create a workspace for accumulating the inarcs to be added to the
+ * current target state. totalinarcs is probably a considerable
+ * overestimate of the space needed, but the NFA is unlikely to be large
+ * enough at this point to make it worth being smarter.
+ */
+ arcarray = (struct arc **) MALLOC(totalinarcs * sizeof(struct arc *));
+ if (arcarray == NULL) {
+ NERR(REG_ESPACE);
+ FREE(inarcsorig);
+ return;
+ }
+
+ /* And iterate over the target states */
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 || hasnonemptyout(s2)) {
- replaceempty(nfa, s, s2);
+ /* Ignore target states without non-EMPTY outarcs, per note above */
+ if (!s->flag && !hasnonemptyout(s)) {
+ continue;
+ }
+
+ /* Find predecessor states and accumulate their original inarcs */
+ arccount = 0;
+ for (s2 = emptyreachable(nfa, s, s, inarcsorig); s2 != s; s2 = nexts) {
+ /* Add s2's original inarcs to arcarray[], but ignore empties */
+ for (a = inarcsorig[s2->no]; a != NULL; a = a->inchain) {
+ if (a->type != EMPTY) {
+ arcarray[arccount++] = a;
+ }
}
+
+ /* Reset the tmp fields as we walk back */
+ nexts = s2->tmp;
+ s2->tmp = NULL;
+ }
+ s->tmp = NULL;
+ assert(arccount <= totalinarcs);
- /* Reset the tmp fields as we walk back */
- nexts = s2->tmp;
- s2->tmp = NULL;
+ /* Remember how many original inarcs this state has */
+ prevnins = s->nins;
+
+ /* Add non-duplicate inarcs to target state */
+ mergeins(nfa, s, arcarray, arccount);
+
+ /* Now we must update the state's inarcsorig pointer */
+ nskip = s->nins - prevnins;
+ a = s->ins;
+ while (nskip-- > 0) {
+ a = a->inchain;
}
- s->tmp = NULL;
+ inarcsorig[s->no] = a;
}
+
+ FREE(arcarray);
+ FREE(inarcsorig);
+
if (NISERR()) {
return;
}
@@ -2013,90 +2068,38 @@ fixempties(
}
/*
- - emptyreachable - recursively find all states reachable from s by EMPTY arcs
+ - emptyreachable - recursively find all states that can reach 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.
+ *
+ * Since this is only used in fixempties(), we pass in the inarcsorig[] array
+ * maintained by that function. This lets us skip over all new inarcs, which
+ * are certainly not EMPTY arcs.
+ *
* 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.
+ * the NFA, and in practice will be less than that.
^ static struct state *emptyreachable(struct state *, struct state *);
*/
static struct state *
emptyreachable(
+ struct nfa *nfa,
struct state *s,
- struct state *lastfound)
+ struct state *lastfound,
+ struct arc **inarcsorig)
{
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);
+ for (a = inarcsorig[s->no]; a != NULL; a = a->inchain) {
+ if (a->type == EMPTY && a->from->tmp == NULL) {
+ lastfound = emptyreachable(nfa, a->from, lastfound, inarcsorig);
}
}
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(
- struct nfa *nfa,
- struct state *from,
- struct state *to)
-{
- 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) {
- copyouts(nfa, to, from, 0);
- return;
- }
- if (fromouts < toins) {
- copyins(nfa, from, to, 0);
- 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) {
- copyouts(nfa, to, from, 0);
- return;
- }
-
- copyins(nfa, from, to, 0);
-}
/*
* isconstraintarc - detect whether an arc is of a constraint type
diff --git a/generic/regcomp.c b/generic/regcomp.c
index b01311b..985cb93 100644
--- a/generic/regcomp.c
+++ b/generic/regcomp.c
@@ -124,8 +124,6 @@ static struct arc *allocarc(struct nfa *, struct state *);
static void freearc(struct nfa *, struct arc *);
static void changearctarget(struct arc *, struct state *);
static int hasnonemptyout(struct state *);
-static int nonemptyouts(struct state *);
-static int nonemptyins(struct state *);
static struct arc *findarc(struct state *, int, pcolor);
static void cparc(struct nfa *, struct arc *, struct state *, struct state *);
static void sortins(struct nfa *, struct state *);
@@ -154,8 +152,8 @@ static int push(struct nfa *, struct arc *);
#define COMPATIBLE 3 /* compatible but not satisfied yet */
static int combine(struct arc *, struct arc *);
static void fixempties(struct nfa *, FILE *);
-static struct state *emptyreachable(struct state *, struct state *);
-static void replaceempty(struct nfa *, struct state *, struct state *);
+static struct state *emptyreachable(struct nfa *, struct state *,
+ struct state *, struct arc **);
static int isconstraintarc(struct arc *);
static int hasconstraintout(struct state *);
static void fixconstraintloops(struct nfa *, FILE *);