postgres/src/backend/regex/regc_nfa.c

/*
 * NFA utilities.
 * This file is #included by regcomp.c.
 *
 * Copyright (c) 1998, 1999 Henry Spencer.  All rights reserved.
 *
 * Development of this software was funded, in part, by Cray Research Inc.,
 * UUNET Communications Services Inc., Sun Microsystems Inc., and Scriptics
 * Corporation, none of whom are responsible for the results.  The author
 * thanks all of them.
 *
 * Redistribution and use in source and binary forms -- with or without
 * modification -- are permitted for any purpose, provided that
 * redistributions in source form retain this entire copyright notice and
 * indicate the origin and nature of any modifications.
 *
 * I'd appreciate being given credit for this package in the documentation
 * of software which uses it, but that is not a requirement.
 *
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
 * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
 * AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL
 * HENRY SPENCER BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
 * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
 * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
 * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
 * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * src/backend/regex/regc_nfa.c
 *
 *
 * One or two things that technically ought to be in here
 * are actually in color.c, thanks to some incestuous relationships in
 * the color chains.
 */

#define NISERR()	VISERR(nfa->v)
#define NERR(e)		VERR(nfa->v, (e))


/*
 * newnfa - set up an NFA
 */
static struct nfa *				/* the NFA, or NULL */
newnfa(struct vars *v,
	   struct colormap *cm,
	   struct nfa *parent)		/* NULL if primary NFA */
{
	struct nfa *nfa;

	nfa = (struct nfa *) MALLOC(sizeof(struct nfa));
	if (nfa == NULL)
	{
		ERR(REG_ESPACE);
		return NULL;
	}

	/* Make the NFA minimally valid, so freenfa() will behave sanely */
	nfa->states = NULL;
	nfa->slast = NULL;
	nfa->freestates = NULL;
	nfa->freearcs = NULL;
	nfa->lastsb = NULL;
	nfa->lastab = NULL;
	nfa->lastsbused = 0;
	nfa->lastabused = 0;
	nfa->nstates = 0;
	nfa->cm = cm;
	nfa->v = v;
	nfa->bos[0] = nfa->bos[1] = COLORLESS;
	nfa->eos[0] = nfa->eos[1] = COLORLESS;
	nfa->flags = 0;
	nfa->minmatchall = nfa->maxmatchall = -1;
	nfa->parent = parent;		/* Precedes newfstate so parent is valid. */

	/* Create required infrastructure */
	nfa->post = newfstate(nfa, '@');	/* number 0 */
	nfa->pre = newfstate(nfa, '>'); /* number 1 */
	nfa->init = newstate(nfa);	/* may become invalid later */
	nfa->final = newstate(nfa);
	if (ISERR())
	{
		freenfa(nfa);
		return NULL;
	}
	rainbow(nfa, nfa->cm, PLAIN, COLORLESS, nfa->pre, nfa->init);
	newarc(nfa, '^', 1, nfa->pre, nfa->init);
	newarc(nfa, '^', 0, nfa->pre, nfa->init);
	rainbow(nfa, nfa->cm, PLAIN, COLORLESS, nfa->final, nfa->post);
	newarc(nfa, '$', 1, nfa->final, nfa->post);
	newarc(nfa, '$', 0, nfa->final, nfa->post);

	if (ISERR())
	{
		freenfa(nfa);
		return NULL;
	}
	return nfa;
}

/*
 * freenfa - free an entire NFA
 */
static void
freenfa(struct nfa *nfa)
{
	struct statebatch *sb;
	struct statebatch *sbnext;
	struct arcbatch *ab;
	struct arcbatch *abnext;

	for (sb = nfa->lastsb; sb != NULL; sb = sbnext)
	{
		sbnext = sb->next;
		nfa->v->spaceused -= STATEBATCHSIZE(sb->nstates);
		FREE(sb);
	}
	nfa->lastsb = NULL;
	for (ab = nfa->lastab; ab != NULL; ab = abnext)
	{
		abnext = ab->next;
		nfa->v->spaceused -= ARCBATCHSIZE(ab->narcs);
		FREE(ab);
	}
	nfa->lastab = NULL;

	nfa->nstates = -1;
	FREE(nfa);
}

/*
 * newstate - allocate an NFA state, with zero flag value
 */
static struct state *			/* NULL on error */
newstate(struct nfa *nfa)
{
	struct state *s;

	/*
	 * This is a handy place to check for operation cancel during regex
	 * compilation, since no code path will go very long without making a new
	 * state or arc.
	 */
	INTERRUPT(nfa->v->re);

	/* first, recycle anything that's on the freelist */
	if (nfa->freestates != NULL)
	{
		s = nfa->freestates;
		nfa->freestates = s->next;
	}
	/* otherwise, is there anything left in the last statebatch? */
	else if (nfa->lastsb != NULL && nfa->lastsbused < nfa->lastsb->nstates)
	{
		s = &nfa->lastsb->s[nfa->lastsbused++];
	}
	/* otherwise, need to allocate a new statebatch */
	else
	{
		struct statebatch *newSb;
		size_t		nstates;

		if (nfa->v->spaceused >= REG_MAX_COMPILE_SPACE)
		{
			NERR(REG_ETOOBIG);
			return NULL;
		}
		nstates = (nfa->lastsb != NULL) ? nfa->lastsb->nstates * 2 : FIRSTSBSIZE;
		if (nstates > MAXSBSIZE)
			nstates = MAXSBSIZE;
		newSb = (struct statebatch *) MALLOC(STATEBATCHSIZE(nstates));
		if (newSb == NULL)
		{
			NERR(REG_ESPACE);
			return NULL;
		}
		nfa->v->spaceused += STATEBATCHSIZE(nstates);
		newSb->nstates = nstates;
		newSb->next = nfa->lastsb;
		nfa->lastsb = newSb;
		nfa->lastsbused = 1;
		s = &newSb->s[0];
	}

	assert(nfa->nstates >= 0);
	s->no = nfa->nstates++;
	s->flag = 0;
	if (nfa->states == NULL)
		nfa->states = s;
	s->nins = 0;
	s->ins = NULL;
	s->nouts = 0;
	s->outs = NULL;
	s->tmp = NULL;
	s->next = NULL;
	if (nfa->slast != NULL)
	{
		assert(nfa->slast->next == NULL);
		nfa->slast->next = s;
	}
	s->prev = nfa->slast;
	nfa->slast = s;
	return s;
}

/*
 * newfstate - allocate an NFA state with a specified flag value
 */
static struct state *			/* NULL on error */
newfstate(struct nfa *nfa, int flag)
{
	struct state *s;

	s = newstate(nfa);
	if (s != NULL)
		s->flag = (char) flag;
	return s;
}

/*
 * dropstate - delete a state's inarcs and outarcs and free it
 */
static void
dropstate(struct nfa *nfa,
		  struct state *s)
{
	struct arc *a;

	while ((a = s->ins) != NULL)
		freearc(nfa, a);
	while ((a = s->outs) != NULL)
		freearc(nfa, a);
	freestate(nfa, s);
}

/*
 * freestate - free a state, which has no in-arcs or out-arcs
 */
static void
freestate(struct nfa *nfa,
		  struct state *s)
{
	assert(s != NULL);
	assert(s->nins == 0 && s->nouts == 0);

	s->no = FREESTATE;
	s->flag = 0;
	if (s->next != NULL)
		s->next->prev = s->prev;
	else
	{
		assert(s == nfa->slast);
		nfa->slast = s->prev;
	}
	if (s->prev != NULL)
		s->prev->next = s->next;
	else
	{
		assert(s == nfa->states);
		nfa->states = s->next;
	}
	s->prev = NULL;
	s->next = nfa->freestates;	/* don't delete it, put it on the free list */
	nfa->freestates = s;
}

/*
 * newarc - set up a new arc within an NFA
 *
 * This function checks to make sure that no duplicate arcs are created.
 * In general we never want duplicates.
 *
 * However: in principle, a RAINBOW arc is redundant with any plain arc
 * (unless that arc is for a pseudocolor).  But we don't try to recognize
 * that redundancy, either here or in allied operations such as moveins().
 * The pseudocolor consideration makes that more costly than it seems worth.
 */
static void
newarc(struct nfa *nfa,
	   int t,
	   color co,
	   struct state *from,
	   struct state *to)
{
	struct arc *a;

	assert(from != NULL && to != NULL);

	/*
	 * This is a handy place to check for operation cancel during regex
	 * compilation, since no code path will go very long without making a new
	 * state or arc.
	 */
	INTERRUPT(nfa->v->re);

	/* check for duplicate arc, using whichever chain is shorter */
	if (from->nouts <= to->nins)
	{
		for (a = from->outs; a != NULL; a = a->outchain)
			if (a->to == to && a->co == co && a->type == t)
				return;
	}
	else
	{
		for (a = to->ins; a != NULL; a = a->inchain)
			if (a->from == from && a->co == co && a->type == t)
				return;
	}

	/* no dup, so create the arc */
	createarc(nfa, t, co, from, to);
}

/*
 * createarc - create a new arc within an NFA
 *
 * This function must *only* be used after verifying that there is no existing
 * identical arc (same type/color/from/to).
 */
static void
createarc(struct nfa *nfa,
		  int t,
		  color co,
		  struct state *from,
		  struct state *to)
{
	struct arc *a;

	a = allocarc(nfa);
	if (NISERR())
		return;
	assert(a != NULL);

	a->type = t;
	a->co = co;
	a->to = to;
	a->from = from;

	/*
	 * Put the new arc on the beginning, not the end, of the chains; it's
	 * simpler here, and freearc() is the same cost either way.  See also the
	 * logic in moveins() and its cohorts, as well as fixempties().
	 */
	a->inchain = to->ins;
	a->inchainRev = NULL;
	if (to->ins)
		to->ins->inchainRev = a;
	to->ins = a;
	a->outchain = from->outs;
	a->outchainRev = NULL;
	if (from->outs)
		from->outs->outchainRev = a;
	from->outs = a;

	from->nouts++;
	to->nins++;

	if (COLORED(a) && nfa->parent == NULL)
		colorchain(nfa->cm, a);
}

/*
 * allocarc - allocate a new arc within an NFA
 */
static struct arc *				/* NULL for failure */
allocarc(struct nfa *nfa)
{
	struct arc *a;

	/* first, recycle anything that's on the freelist */
	if (nfa->freearcs != NULL)
	{
		a = nfa->freearcs;
		nfa->freearcs = a->freechain;
	}
	/* otherwise, is there anything left in the last arcbatch? */
	else if (nfa->lastab != NULL && nfa->lastabused < nfa->lastab->narcs)
	{
		a = &nfa->lastab->a[nfa->lastabused++];
	}
	/* otherwise, need to allocate a new arcbatch */
	else
	{
		struct arcbatch *newAb;
		size_t		narcs;

		if (nfa->v->spaceused >= REG_MAX_COMPILE_SPACE)
		{
			NERR(REG_ETOOBIG);
			return NULL;
		}
		narcs = (nfa->lastab != NULL) ? nfa->lastab->narcs * 2 : FIRSTABSIZE;
		if (narcs > MAXABSIZE)
			narcs = MAXABSIZE;
		newAb = (struct arcbatch *) MALLOC(ARCBATCHSIZE(narcs));
		if (newAb == NULL)
		{
			NERR(REG_ESPACE);
			return NULL;
		}
		nfa->v->spaceused += ARCBATCHSIZE(narcs);
		newAb->narcs = narcs;
		newAb->next = nfa->lastab;
		nfa->lastab = newAb;
		nfa->lastabused = 1;
		a = &newAb->a[0];
	}

	return a;
}

/*
 * freearc - free an arc
 */
static void
freearc(struct nfa *nfa,
		struct arc *victim)
{
	struct state *from = victim->from;
	struct state *to = victim->to;
	struct arc *predecessor;

	assert(victim->type != 0);

	/* take it off color chain if necessary */
	if (COLORED(victim) && nfa->parent == NULL)
		uncolorchain(nfa->cm, victim);

	/* take it off source's out-chain */
	assert(from != NULL);
	predecessor = victim->outchainRev;
	if (predecessor == NULL)
	{
		assert(from->outs == victim);
		from->outs = victim->outchain;
	}
	else
	{
		assert(predecessor->outchain == victim);
		predecessor->outchain = victim->outchain;
	}
	if (victim->outchain != NULL)
	{
		assert(victim->outchain->outchainRev == victim);
		victim->outchain->outchainRev = predecessor;
	}
	from->nouts--;

	/* take it off target's in-chain */
	assert(to != NULL);
	predecessor = victim->inchainRev;
	if (predecessor == NULL)
	{
		assert(to->ins == victim);
		to->ins = victim->inchain;
	}
	else
	{
		assert(predecessor->inchain == victim);
		predecessor->inchain = victim->inchain;
	}
	if (victim->inchain != NULL)
	{
		assert(victim->inchain->inchainRev == victim);
		victim->inchain->inchainRev = predecessor;
	}
	to->nins--;

	/* clean up and place on NFA's free list */
	victim->type = 0;
	victim->from = NULL;		/* precautions... */
	victim->to = NULL;
	victim->inchain = NULL;
	victim->inchainRev = NULL;
	victim->outchain = NULL;
	victim->outchainRev = NULL;
	victim->freechain = nfa->freearcs;
	nfa->freearcs = victim;
}

/*
 * changearcsource - flip an arc to have a different from state
 *
 * Caller must have verified that there is no pre-existing duplicate arc.
 */
static void
changearcsource(struct arc *a, struct state *newfrom)
{
	struct state *oldfrom = a->from;
	struct arc *predecessor;

	assert(oldfrom != newfrom);

	/* take it off old source's out-chain */
	assert(oldfrom != NULL);
	predecessor = a->outchainRev;
	if (predecessor == NULL)
	{
		assert(oldfrom->outs == a);
		oldfrom->outs = a->outchain;
	}
	else
	{
		assert(predecessor->outchain == a);
		predecessor->outchain = a->outchain;
	}
	if (a->outchain != NULL)
	{
		assert(a->outchain->outchainRev == a);
		a->outchain->outchainRev = predecessor;
	}
	oldfrom->nouts--;

	a->from = newfrom;

	/* prepend it to new source's out-chain */
	a->outchain = newfrom->outs;
	a->outchainRev = NULL;
	if (newfrom->outs)
		newfrom->outs->outchainRev = a;
	newfrom->outs = a;
	newfrom->nouts++;
}

/*
 * changearctarget - flip an arc to have a different to state
 *
 * Caller must have verified that there is no pre-existing duplicate arc.
 */
static void
changearctarget(struct arc *a, struct state *newto)
{
	struct state *oldto = a->to;
	struct arc *predecessor;

	assert(oldto != newto);

	/* take it off old target's in-chain */
	assert(oldto != NULL);
	predecessor = a->inchainRev;
	if (predecessor == NULL)
	{
		assert(oldto->ins == a);
		oldto->ins = a->inchain;
	}
	else
	{
		assert(predecessor->inchain == a);
		predecessor->inchain = a->inchain;
	}
	if (a->inchain != NULL)
	{
		assert(a->inchain->inchainRev == a);
		a->inchain->inchainRev = predecessor;
	}
	oldto->nins--;

	a->to = newto;

	/* prepend it to new target's in-chain */
	a->inchain = newto->ins;
	a->inchainRev = NULL;
	if (newto->ins)
		newto->ins->inchainRev = a;
	newto->ins = a;
	newto->nins++;
}

/*
 * hasnonemptyout - Does state have a non-EMPTY out arc?
 */
static int
hasnonemptyout(struct state *s)
{
	struct arc *a;

	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (a->type != EMPTY)
			return 1;
	}
	return 0;
}

/*
 * 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 *s,
		int type,
		color co)
{
	struct arc *a;

	for (a = s->outs; a != NULL; a = a->outchain)
		if (a->type == type && a->co == co)
			return a;
	return NULL;
}

/*
 * cparc - allocate a new arc within an NFA, copying details from old one
 */
static void
cparc(struct nfa *nfa,
	  struct arc *oa,
	  struct state *from,
	  struct state *to)
{
	newarc(nfa, oa->type, oa->co, from, to);
}

/*
 * sortins - sort the in arcs of a state by from/color/type
 */
static void
sortins(struct nfa *nfa,
		struct state *s)
{
	struct arc **sortarray;
	struct arc *a;
	int			n = s->nins;
	int			i;

	if (n <= 1)
		return;					/* nothing to do */
	/* make an array of arc pointers ... */
	sortarray = (struct arc **) MALLOC(n * sizeof(struct arc *));
	if (sortarray == NULL)
	{
		NERR(REG_ESPACE);
		return;
	}
	i = 0;
	for (a = s->ins; a != NULL; a = a->inchain)
		sortarray[i++] = a;
	assert(i == n);
	/* ... sort the array */
	qsort(sortarray, n, sizeof(struct arc *), sortins_cmp);
	/* ... and rebuild arc list in order */
	/* it seems worth special-casing first and last items to simplify loop */
	a = sortarray[0];
	s->ins = a;
	a->inchain = sortarray[1];
	a->inchainRev = NULL;
	for (i = 1; i < n - 1; i++)
	{
		a = sortarray[i];
		a->inchain = sortarray[i + 1];
		a->inchainRev = sortarray[i - 1];
	}
	a = sortarray[i];
	a->inchain = NULL;
	a->inchainRev = sortarray[i - 1];
	FREE(sortarray);
}

static int
sortins_cmp(const void *a, const void *b)
{
	const struct arc *aa = *((const struct arc *const *) a);
	const struct arc *bb = *((const struct arc *const *) b);

	/* we check the fields in the order they are most likely to be different */
	if (aa->from->no < bb->from->no)
		return -1;
	if (aa->from->no > bb->from->no)
		return 1;
	if (aa->co < bb->co)
		return -1;
	if (aa->co > bb->co)
		return 1;
	if (aa->type < bb->type)
		return -1;
	if (aa->type > bb->type)
		return 1;
	return 0;
}

/*
 * sortouts - sort the out arcs of a state by to/color/type
 */
static void
sortouts(struct nfa *nfa,
		 struct state *s)
{
	struct arc **sortarray;
	struct arc *a;
	int			n = s->nouts;
	int			i;

	if (n <= 1)
		return;					/* nothing to do */
	/* make an array of arc pointers ... */
	sortarray = (struct arc **) MALLOC(n * sizeof(struct arc *));
	if (sortarray == NULL)
	{
		NERR(REG_ESPACE);
		return;
	}
	i = 0;
	for (a = s->outs; a != NULL; a = a->outchain)
		sortarray[i++] = a;
	assert(i == n);
	/* ... sort the array */
	qsort(sortarray, n, sizeof(struct arc *), sortouts_cmp);
	/* ... and rebuild arc list in order */
	/* it seems worth special-casing first and last items to simplify loop */
	a = sortarray[0];
	s->outs = a;
	a->outchain = sortarray[1];
	a->outchainRev = NULL;
	for (i = 1; i < n - 1; i++)
	{
		a = sortarray[i];
		a->outchain = sortarray[i + 1];
		a->outchainRev = sortarray[i - 1];
	}
	a = sortarray[i];
	a->outchain = NULL;
	a->outchainRev = sortarray[i - 1];
	FREE(sortarray);
}

static int
sortouts_cmp(const void *a, const void *b)
{
	const struct arc *aa = *((const struct arc *const *) a);
	const struct arc *bb = *((const struct arc *const *) b);

	/* we check the fields in the order they are most likely to be different */
	if (aa->to->no < bb->to->no)
		return -1;
	if (aa->to->no > bb->to->no)
		return 1;
	if (aa->co < bb->co)
		return -1;
	if (aa->co > bb->co)
		return 1;
	if (aa->type < bb->type)
		return -1;
	if (aa->type > bb->type)
		return 1;
	return 0;
}

/*
 * Common decision logic about whether to use arc-by-arc operations or
 * sort/merge.  If there's just a few source arcs we cannot recoup the
 * cost of sorting the destination arc list, no matter how large it is.
 * Otherwise, limit the number of arc-by-arc comparisons to about 1000
 * (a somewhat arbitrary choice, but the breakeven point would probably
 * be machine dependent anyway).
 */
#define BULK_ARC_OP_USE_SORT(nsrcarcs, ndestarcs) \
	((nsrcarcs) < 4 ? 0 : ((nsrcarcs) > 32 || (ndestarcs) > 32))

/*
 * moveins - move all in arcs of a state to another state
 *
 * You might think this could be done better by just updating the
 * existing arcs, and you would be right if it weren't for the need
 * for duplicate suppression, which makes it easier to just make new
 * ones to exploit the suppression built into newarc.
 *
 * However, if we have a whole lot of arcs to deal with, retail duplicate
 * checks become too slow.  In that case we proceed by sorting and merging
 * the arc lists, and then we can indeed just update the arcs in-place.
 *
 * On the other hand, it's also true that this is frequently called with
 * a brand-new newState that has no existing in-arcs.  In that case,
 * de-duplication is unnecessary, so we can just blindly move all the arcs.
 */
static void
moveins(struct nfa *nfa,
		struct state *oldState,
		struct state *newState)
{
	assert(oldState != newState);

	if (newState->nins == 0)
	{
		/* No need for de-duplication */
		struct arc *a;

		while ((a = oldState->ins) != NULL)
		{
			createarc(nfa, a->type, a->co, a->from, newState);
			freearc(nfa, a);
		}
	}
	else if (!BULK_ARC_OP_USE_SORT(oldState->nins, newState->nins))
	{
		/* With not too many arcs, just do them one at a time */
		struct arc *a;

		while ((a = oldState->ins) != NULL)
		{
			cparc(nfa, a, a->from, newState);
			freearc(nfa, a);
		}
	}
	else
	{
		/*
		 * With many arcs, use a sort-merge approach.  Note changearctarget()
		 * will put the arc onto the front of newState's chain, so it does not
		 * break our walk through the sorted part of the chain.
		 */
		struct arc *oa;
		struct arc *na;

		/*
		 * Because we bypass newarc() in this code path, we'd better include a
		 * cancel check.
		 */
		INTERRUPT(nfa->v->re);

		sortins(nfa, oldState);
		sortins(nfa, newState);
		if (NISERR())
			return;				/* might have failed to sort */
		oa = oldState->ins;
		na = newState->ins;
		while (oa != NULL && na != NULL)
		{
			struct arc *a = oa;

			switch (sortins_cmp(&oa, &na))
			{
				case -1:
					/* newState does not have anything matching oa */
					oa = oa->inchain;

					/*
					 * Rather than doing createarc+freearc, we can just unlink
					 * and relink the existing arc struct.
					 */
					changearctarget(a, newState);
					break;
				case 0:
					/* match, advance in both lists */
					oa = oa->inchain;
					na = na->inchain;
					/* ... and drop duplicate arc from oldState */
					freearc(nfa, a);
					break;
				case +1:
					/* advance only na; oa might have a match later */
					na = na->inchain;
					break;
				default:
					assert(NOTREACHED);
			}
		}
		while (oa != NULL)
		{
			/* newState does not have anything matching oa */
			struct arc *a = oa;

			oa = oa->inchain;
			changearctarget(a, newState);
		}
	}

	assert(oldState->nins == 0);
	assert(oldState->ins == NULL);
}

/*
 * copyins - copy in arcs of a state to another state
 *
 * The comments for moveins() apply here as well.  However, in current
 * usage, this is *only* called with brand-new target states, so that
 * only the "no need for de-duplication" code path is ever reached.
 * We keep the rest #ifdef'd out in case it's needed in the future.
 */
static void
copyins(struct nfa *nfa,
		struct state *oldState,
		struct state *newState)
{
	assert(oldState != newState);
	assert(newState->nins == 0);	/* see comment above */

	if (newState->nins == 0)
	{
		/* No need for de-duplication */
		struct arc *a;

		for (a = oldState->ins; a != NULL; a = a->inchain)
			createarc(nfa, a->type, a->co, a->from, newState);
	}
#ifdef NOT_USED					/* see comment above */
	else if (!BULK_ARC_OP_USE_SORT(oldState->nins, newState->nins))
	{
		/* With not too many arcs, just do them one at a time */
		struct arc *a;

		for (a = oldState->ins; a != NULL; a = a->inchain)
			cparc(nfa, a, a->from, newState);
	}
	else
	{
		/*
		 * With many arcs, use a sort-merge approach.  Note that createarc()
		 * will put new arcs onto the front of newState's chain, so it does
		 * not break our walk through the sorted part of the chain.
		 */
		struct arc *oa;
		struct arc *na;

		/*
		 * Because we bypass newarc() in this code path, we'd better include a
		 * cancel check.
		 */
		INTERRUPT(nfa->v->re);

		sortins(nfa, oldState);
		sortins(nfa, newState);
		if (NISERR())
			return;				/* might have failed to sort */
		oa = oldState->ins;
		na = newState->ins;
		while (oa != NULL && na != NULL)
		{
			struct arc *a = oa;

			switch (sortins_cmp(&oa, &na))
			{
				case -1:
					/* newState does not have anything matching oa */
					oa = oa->inchain;
					createarc(nfa, a->type, a->co, a->from, newState);
					break;
				case 0:
					/* match, advance in both lists */
					oa = oa->inchain;
					na = na->inchain;
					break;
				case +1:
					/* advance only na; oa might have a match later */
					na = na->inchain;
					break;
				default:
					assert(NOTREACHED);
			}
		}
		while (oa != NULL)
		{
			/* newState does not have anything matching oa */
			struct arc *a = oa;

			oa = oa->inchain;
			createarc(nfa, a->type, a->co, a->from, newState);
		}
	}
#endif							/* NOT_USED */
}

/*
 * mergeins - merge a list of inarcs into a state
 *
 * This is much like copyins, but the source arcs are listed in an array,
 * and are not guaranteed unique.  It's okay to clobber the array contents.
 */
static void
mergeins(struct nfa *nfa,
		 struct state *s,
		 struct arc **arcarray,
		 int arccount)
{
	struct arc *na;
	int			i;
	int			j;

	if (arccount <= 0)
		return;

	/*
	 * Because we bypass newarc() in this code path, we'd better include a
	 * cancel check.
	 */
	INTERRUPT(nfa->v->re);

	/* Sort existing inarcs as well as proposed new ones */
	sortins(nfa, s);
	if (NISERR())
		return;					/* might have failed to sort */

	qsort(arcarray, arccount, sizeof(struct arc *), sortins_cmp);

	/*
	 * arcarray very likely includes dups, so we must eliminate them.  (This
	 * could be folded into the next loop, but it's not worth the trouble.)
	 */
	j = 0;
	for (i = 1; i < arccount; i++)
	{
		switch (sortins_cmp(&arcarray[j], &arcarray[i]))
		{
			case -1:
				/* non-dup */
				arcarray[++j] = arcarray[i];
				break;
			case 0:
				/* dup */
				break;
			default:
				/* trouble */
				assert(NOTREACHED);
		}
	}
	arccount = j + 1;

	/*
	 * Now merge into s' inchain.  Note that createarc() will put new arcs
	 * onto the front of s's chain, so it does not break our walk through the
	 * sorted part of the chain.
	 */
	i = 0;
	na = s->ins;
	while (i < arccount && na != NULL)
	{
		struct arc *a = arcarray[i];

		switch (sortins_cmp(&a, &na))
		{
			case -1:
				/* s does not have anything matching a */
				createarc(nfa, a->type, a->co, a->from, s);
				i++;
				break;
			case 0:
				/* match, advance in both lists */
				i++;
				na = na->inchain;
				break;
			case +1:
				/* advance only na; array might have a match later */
				na = na->inchain;
				break;
			default:
				assert(NOTREACHED);
		}
	}
	while (i < arccount)
	{
		/* s does not have anything matching a */
		struct arc *a = arcarray[i];

		createarc(nfa, a->type, a->co, a->from, s);
		i++;
	}
}

/*
 * moveouts - move all out arcs of a state to another state
 *
 * See comments for moveins()
 */
static void
moveouts(struct nfa *nfa,
		 struct state *oldState,
		 struct state *newState)
{
	assert(oldState != newState);

	if (newState->nouts == 0)
	{
		/* No need for de-duplication */
		struct arc *a;

		while ((a = oldState->outs) != NULL)
		{
			createarc(nfa, a->type, a->co, newState, a->to);
			freearc(nfa, a);
		}
	}
	else if (!BULK_ARC_OP_USE_SORT(oldState->nouts, newState->nouts))
	{
		/* With not too many arcs, just do them one at a time */
		struct arc *a;

		while ((a = oldState->outs) != NULL)
		{
			cparc(nfa, a, newState, a->to);
			freearc(nfa, a);
		}
	}
	else
	{
		/*
		 * With many arcs, use a sort-merge approach.  Note changearcsource()
		 * will put the arc onto the front of newState's chain, so it does not
		 * break our walk through the sorted part of the chain.
		 */
		struct arc *oa;
		struct arc *na;

		/*
		 * Because we bypass newarc() in this code path, we'd better include a
		 * cancel check.
		 */
		INTERRUPT(nfa->v->re);

		sortouts(nfa, oldState);
		sortouts(nfa, newState);
		if (NISERR())
			return;				/* might have failed to sort */
		oa = oldState->outs;
		na = newState->outs;
		while (oa != NULL && na != NULL)
		{
			struct arc *a = oa;

			switch (sortouts_cmp(&oa, &na))
			{
				case -1:
					/* newState does not have anything matching oa */
					oa = oa->outchain;

					/*
					 * Rather than doing createarc+freearc, we can just unlink
					 * and relink the existing arc struct.
					 */
					changearcsource(a, newState);
					break;
				case 0:
					/* match, advance in both lists */
					oa = oa->outchain;
					na = na->outchain;
					/* ... and drop duplicate arc from oldState */
					freearc(nfa, a);
					break;
				case +1:
					/* advance only na; oa might have a match later */
					na = na->outchain;
					break;
				default:
					assert(NOTREACHED);
			}
		}
		while (oa != NULL)
		{
			/* newState does not have anything matching oa */
			struct arc *a = oa;

			oa = oa->outchain;
			changearcsource(a, newState);
		}
	}

	assert(oldState->nouts == 0);
	assert(oldState->outs == NULL);
}

/*
 * copyouts - copy out arcs of a state to another state
 *
 * See comments for copyins()
 */
static void
copyouts(struct nfa *nfa,
		 struct state *oldState,
		 struct state *newState)
{
	assert(oldState != newState);
	assert(newState->nouts == 0);	/* see comment above */

	if (newState->nouts == 0)
	{
		/* No need for de-duplication */
		struct arc *a;

		for (a = oldState->outs; a != NULL; a = a->outchain)
			createarc(nfa, a->type, a->co, newState, a->to);
	}
#ifdef NOT_USED					/* see comment above */
	else if (!BULK_ARC_OP_USE_SORT(oldState->nouts, newState->nouts))
	{
		/* With not too many arcs, just do them one at a time */
		struct arc *a;

		for (a = oldState->outs; a != NULL; a = a->outchain)
			cparc(nfa, a, newState, a->to);
	}
	else
	{
		/*
		 * With many arcs, use a sort-merge approach.  Note that createarc()
		 * will put new arcs onto the front of newState's chain, so it does
		 * not break our walk through the sorted part of the chain.
		 */
		struct arc *oa;
		struct arc *na;

		/*
		 * Because we bypass newarc() in this code path, we'd better include a
		 * cancel check.
		 */
		INTERRUPT(nfa->v->re);

		sortouts(nfa, oldState);
		sortouts(nfa, newState);
		if (NISERR())
			return;				/* might have failed to sort */
		oa = oldState->outs;
		na = newState->outs;
		while (oa != NULL && na != NULL)
		{
			struct arc *a = oa;

			switch (sortouts_cmp(&oa, &na))
			{
				case -1:
					/* newState does not have anything matching oa */
					oa = oa->outchain;
					createarc(nfa, a->type, a->co, newState, a->to);
					break;
				case 0:
					/* match, advance in both lists */
					oa = oa->outchain;
					na = na->outchain;
					break;
				case +1:
					/* advance only na; oa might have a match later */
					na = na->outchain;
					break;
				default:
					assert(NOTREACHED);
			}
		}
		while (oa != NULL)
		{
			/* newState does not have anything matching oa */
			struct arc *a = oa;

			oa = oa->outchain;
			createarc(nfa, a->type, a->co, newState, a->to);
		}
	}
#endif							/* NOT_USED */
}

/*
 * cloneouts - copy out arcs of a state to another state pair, modifying type
 *
 * This is only used to convert PLAIN arcs to AHEAD/BEHIND arcs, which share
 * the same interpretation of "co".  It wouldn't be sensible with LACONs.
 */
static void
cloneouts(struct nfa *nfa,
		  struct state *old,
		  struct state *from,
		  struct state *to,
		  int type)
{
	struct arc *a;

	assert(old != from);
	assert(type == AHEAD || type == BEHIND);

	for (a = old->outs; a != NULL; a = a->outchain)
	{
		assert(a->type == PLAIN);
		newarc(nfa, type, a->co, from, to);
	}
}

/*
 * delsub - delete a sub-NFA, updating subre pointers if necessary
 *
 * This uses a recursive traversal of the sub-NFA, marking already-seen
 * states using their tmp pointer.
 */
static void
delsub(struct nfa *nfa,
	   struct state *lp,		/* the sub-NFA goes from here... */
	   struct state *rp)		/* ...to here, *not* inclusive */
{
	assert(lp != rp);

	rp->tmp = rp;				/* mark end */

	deltraverse(nfa, lp, lp);
	if (NISERR())
		return;					/* asserts might not hold after failure */
	assert(lp->nouts == 0 && rp->nins == 0);	/* did the job */
	assert(lp->no != FREESTATE && rp->no != FREESTATE); /* no more */

	rp->tmp = NULL;				/* unmark end */
	lp->tmp = NULL;				/* and begin, marked by deltraverse */
}

/*
 * deltraverse - the recursive heart of delsub
 * This routine's basic job is to destroy all out-arcs of the state.
 */
static void
deltraverse(struct nfa *nfa,
			struct state *leftend,
			struct state *s)
{
	struct arc *a;
	struct state *to;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	if (s->nouts == 0)
		return;					/* nothing to do */
	if (s->tmp != NULL)
		return;					/* already in progress */

	s->tmp = s;					/* mark as in progress */

	while ((a = s->outs) != NULL)
	{
		to = a->to;
		deltraverse(nfa, leftend, to);
		if (NISERR())
			return;				/* asserts might not hold after failure */
		assert(to->nouts == 0 || to->tmp != NULL);
		freearc(nfa, a);
		if (to->nins == 0 && to->tmp == NULL)
		{
			assert(to->nouts == 0);
			freestate(nfa, to);
		}
	}

	assert(s->no != FREESTATE); /* we're still here */
	assert(s == leftend || s->nins != 0);	/* and still reachable */
	assert(s->nouts == 0);		/* but have no outarcs */

	s->tmp = NULL;				/* we're done here */
}

/*
 * dupnfa - duplicate sub-NFA
 *
 * Another recursive traversal, this time using tmp to point to duplicates
 * as well as mark already-seen states.  (You knew there was a reason why
 * it's a state pointer, didn't you? :-))
 */
static void
dupnfa(struct nfa *nfa,
	   struct state *start,		/* duplicate of subNFA starting here */
	   struct state *stop,		/* and stopping here */
	   struct state *from,		/* stringing duplicate from here */
	   struct state *to)		/* to here */
{
	if (start == stop)
	{
		newarc(nfa, EMPTY, 0, from, to);
		return;
	}

	stop->tmp = to;
	duptraverse(nfa, start, from);
	/* done, except for clearing out the tmp pointers */

	stop->tmp = NULL;
	cleartraverse(nfa, start);
}

/*
 * duptraverse - recursive heart of dupnfa
 */
static void
duptraverse(struct nfa *nfa,
			struct state *s,
			struct state *stmp) /* s's duplicate, or NULL */
{
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	if (s->tmp != NULL)
		return;					/* already done */

	s->tmp = (stmp == NULL) ? newstate(nfa) : stmp;
	if (s->tmp == NULL)
	{
		assert(NISERR());
		return;
	}

	for (a = s->outs; a != NULL && !NISERR(); a = a->outchain)
	{
		duptraverse(nfa, a->to, (struct state *) NULL);
		if (NISERR())
			break;
		assert(a->to->tmp != NULL);
		cparc(nfa, a, s->tmp, a->to->tmp);
	}
}

/*
 * removeconstraints - remove any constraints in an NFA
 *
 * Constraint arcs are replaced by empty arcs, essentially treating all
 * constraints as automatically satisfied.
 */
static void
removeconstraints(struct nfa *nfa,
				  struct state *start,	/* process subNFA starting here */
				  struct state *stop)	/* and stopping here */
{
	if (start == stop)
		return;

	stop->tmp = stop;
	removetraverse(nfa, start);
	/* done, except for clearing out the tmp pointers */

	stop->tmp = NULL;
	cleartraverse(nfa, start);
}

/*
 * removetraverse - recursive heart of removeconstraints
 */
static void
removetraverse(struct nfa *nfa,
			   struct state *s)
{
	struct arc *a;
	struct arc *oa;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	if (s->tmp != NULL)
		return;					/* already done */

	s->tmp = s;
	for (a = s->outs; a != NULL && !NISERR(); a = oa)
	{
		removetraverse(nfa, a->to);
		if (NISERR())
			break;
		oa = a->outchain;
		switch (a->type)
		{
			case PLAIN:
			case EMPTY:
			case CANTMATCH:
				/* nothing to do */
				break;
			case AHEAD:
			case BEHIND:
			case '^':
			case '$':
			case LACON:
				/* replace it */
				newarc(nfa, EMPTY, 0, s, a->to);
				freearc(nfa, a);
				break;
			default:
				NERR(REG_ASSERT);
				break;
		}
	}
}

/*
 * cleartraverse - recursive cleanup for algorithms that leave tmp ptrs set
 */
static void
cleartraverse(struct nfa *nfa,
			  struct state *s)
{
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	if (s->tmp == NULL)
		return;
	s->tmp = NULL;

	for (a = s->outs; a != NULL; a = a->outchain)
		cleartraverse(nfa, a->to);
}

/*
 * single_color_transition - does getting from s1 to s2 cross one PLAIN arc?
 *
 * If traversing from s1 to s2 requires a single PLAIN match (possibly of any
 * of a set of colors), return a state whose outarc list contains only PLAIN
 * arcs of those color(s).  Otherwise return NULL.
 *
 * This is used before optimizing the NFA, so there may be EMPTY arcs, which
 * we should ignore; the possibility of an EMPTY is why the result state could
 * be different from s1.
 *
 * It's worth troubling to handle multiple parallel PLAIN arcs here because a
 * bracket construct such as [abc] might yield either one or several parallel
 * PLAIN arcs depending on earlier atoms in the expression.  We'd rather that
 * that implementation detail not create user-visible performance differences.
 */
static struct state *
single_color_transition(struct state *s1, struct state *s2)
{
	struct arc *a;

	/* Ignore leading EMPTY arc, if any */
	if (s1->nouts == 1 && s1->outs->type == EMPTY)
		s1 = s1->outs->to;
	/* Likewise for any trailing EMPTY arc */
	if (s2->nins == 1 && s2->ins->type == EMPTY)
		s2 = s2->ins->from;
	/* Perhaps we could have a single-state loop in between, if so reject */
	if (s1 == s2)
		return NULL;
	/* s1 must have at least one outarc... */
	if (s1->outs == NULL)
		return NULL;
	/* ... and they must all be PLAIN arcs to s2 */
	for (a = s1->outs; a != NULL; a = a->outchain)
	{
		if (a->type != PLAIN || a->to != s2)
			return NULL;
	}
	/* OK, return s1 as the possessor of the relevant outarcs */
	return s1;
}

/*
 * specialcolors - fill in special colors for an NFA
 */
static void
specialcolors(struct nfa *nfa)
{
	/* false colors for BOS, BOL, EOS, EOL */
	if (nfa->parent == NULL)
	{
		nfa->bos[0] = pseudocolor(nfa->cm);
		nfa->bos[1] = pseudocolor(nfa->cm);
		nfa->eos[0] = pseudocolor(nfa->cm);
		nfa->eos[1] = pseudocolor(nfa->cm);
	}
	else
	{
		assert(nfa->parent->bos[0] != COLORLESS);
		nfa->bos[0] = nfa->parent->bos[0];
		assert(nfa->parent->bos[1] != COLORLESS);
		nfa->bos[1] = nfa->parent->bos[1];
		assert(nfa->parent->eos[0] != COLORLESS);
		nfa->eos[0] = nfa->parent->eos[0];
		assert(nfa->parent->eos[1] != COLORLESS);
		nfa->eos[1] = nfa->parent->eos[1];
	}
}

/*
 * optimize - optimize an NFA
 *
 * The main goal of this function is not so much "optimization" (though it
 * does try to get rid of useless NFA states) as reducing the NFA to a form
 * the regex executor can handle.  The executor, and indeed the cNFA format
 * that is its input, can only handle PLAIN and LACON arcs.  The output of
 * the regex parser also includes EMPTY (do-nothing) arcs, as well as
 * ^, $, AHEAD, and BEHIND constraint arcs, which we must get rid of here.
 * We first get rid of EMPTY arcs and then deal with the constraint arcs.
 * The hardest part of either job is to get rid of circular loops of the
 * target arc type.  We would have to do that in any case, though, as such a
 * loop would otherwise allow the executor to cycle through the loop endlessly
 * without making any progress in the input string.
 */
static long						/* re_info bits */
optimize(struct nfa *nfa,
		 FILE *f)				/* for debug output; NULL none */
{
#ifdef REG_DEBUG
	int			verbose = (f != NULL) ? 1 : 0;

	if (verbose)
		fprintf(f, "\ninitial cleanup:\n");
#endif
	/* If we have any CANTMATCH arcs, drop them; but this is uncommon */
	if (nfa->flags & HASCANTMATCH)
	{
		removecantmatch(nfa);
		nfa->flags &= ~HASCANTMATCH;
	}
	cleanup(nfa);				/* may simplify situation */
#ifdef REG_DEBUG
	if (verbose)
		dumpnfa(nfa, f);
	if (verbose)
		fprintf(f, "\nempties:\n");
#endif
	fixempties(nfa, f);			/* get rid of EMPTY arcs */
#ifdef REG_DEBUG
	if (verbose)
		fprintf(f, "\nconstraints:\n");
#endif
	fixconstraintloops(nfa, f); /* get rid of constraint loops */
	pullback(nfa, f);			/* pull back constraints backward */
	pushfwd(nfa, f);			/* push fwd constraints forward */
#ifdef REG_DEBUG
	if (verbose)
		fprintf(f, "\nfinal cleanup:\n");
#endif
	cleanup(nfa);				/* final tidying */
#ifdef REG_DEBUG
	if (verbose)
		dumpnfa(nfa, f);
#endif
	return analyze(nfa);		/* and analysis */
}

/*
 * pullback - pull back constraints backward to eliminate them
 */
static void
pullback(struct nfa *nfa,
		 FILE *f)				/* for debug output; NULL none */
{
	struct state *s;
	struct state *nexts;
	struct arc *a;
	struct arc *nexta;
	struct state *intermediates;
	int			progress;

	/* find and pull until there are no more */
	do
	{
		progress = 0;
		for (s = nfa->states; s != NULL && !NISERR(); s = nexts)
		{
			nexts = s->next;
			intermediates = NULL;
			for (a = s->outs; a != NULL && !NISERR(); a = nexta)
			{
				nexta = a->outchain;
				if (a->type == '^' || a->type == BEHIND)
					if (pull(nfa, a, &intermediates))
						progress = 1;
			}
			/* clear tmp fields of intermediate states created here */
			while (intermediates != NULL)
			{
				struct state *ns = intermediates->tmp;

				intermediates->tmp = NULL;
				intermediates = ns;
			}
			/* if s is now useless, get rid of it */
			if ((s->nins == 0 || s->nouts == 0) && !s->flag)
				dropstate(nfa, s);
		}
		if (progress && f != NULL)
			dumpnfa(nfa, f);
	} while (progress && !NISERR());
	if (NISERR())
		return;

	/*
	 * Any ^ constraints we were able to pull to the start state can now be
	 * replaced by PLAIN arcs referencing the BOS or BOL colors.  There should
	 * be no other ^ or BEHIND arcs left in the NFA, though we do not check
	 * that here (compact() will fail if so).
	 */
	for (a = nfa->pre->outs; a != NULL; a = nexta)
	{
		nexta = a->outchain;
		if (a->type == '^')
		{
			assert(a->co == 0 || a->co == 1);
			newarc(nfa, PLAIN, nfa->bos[a->co], a->from, a->to);
			freearc(nfa, a);
		}
	}
}

/*
 * pull - pull a back constraint backward past its source state
 *
 * Returns 1 if successful (which it always is unless the source is the
 * start state or we have an internal error), 0 if nothing happened.
 *
 * A significant property of this function is that it deletes no pre-existing
 * states, and no outarcs of the constraint's from state other than the given
 * constraint arc.  This makes the loops in pullback() safe, at the cost that
 * we may leave useless states behind.  Therefore, we leave it to pullback()
 * to delete such states.
 *
 * If the from state has multiple back-constraint outarcs, and/or multiple
 * compatible constraint inarcs, we only need to create one new intermediate
 * state per combination of predecessor and successor states.  *intermediates
 * points to a list of such intermediate states for this from state (chained
 * through their tmp fields).
 */
static int
pull(struct nfa *nfa,
	 struct arc *con,
	 struct state **intermediates)
{
	struct state *from = con->from;
	struct state *to = con->to;
	struct arc *a;
	struct arc *nexta;
	struct state *s;

	assert(from != to);			/* should have gotten rid of this earlier */
	if (from->flag)				/* can't pull back beyond start */
		return 0;
	if (from->nins == 0)
	{							/* unreachable */
		freearc(nfa, con);
		return 1;
	}

	/*
	 * First, clone from state if necessary to avoid other outarcs.  This may
	 * seem wasteful, but it simplifies the logic, and we'll get rid of the
	 * clone state again at the bottom.
	 */
	if (from->nouts > 1)
	{
		s = newstate(nfa);
		if (NISERR())
			return 0;
		copyins(nfa, from, s);	/* duplicate inarcs */
		cparc(nfa, con, s, to); /* move constraint arc */
		freearc(nfa, con);
		if (NISERR())
			return 0;
		from = s;
		con = from->outs;
	}
	assert(from->nouts == 1);

	/* propagate the constraint into the from state's inarcs */
	for (a = from->ins; a != NULL && !NISERR(); a = nexta)
	{
		nexta = a->inchain;
		switch (combine(nfa, con, a))
		{
			case INCOMPATIBLE:	/* destroy the arc */
				freearc(nfa, a);
				break;
			case SATISFIED:		/* no action needed */
				break;
			case COMPATIBLE:	/* swap the two arcs, more or less */
				/* need an intermediate state, but might have one already */
				for (s = *intermediates; s != NULL; s = s->tmp)
				{
					assert(s->nins > 0 && s->nouts > 0);
					if (s->ins->from == a->from && s->outs->to == to)
						break;
				}
				if (s == NULL)
				{
					s = newstate(nfa);
					if (NISERR())
						return 0;
					s->tmp = *intermediates;
					*intermediates = s;
				}
				cparc(nfa, con, a->from, s);
				cparc(nfa, a, s, to);
				freearc(nfa, a);
				break;
			case REPLACEARC:	/* replace arc's color */
				newarc(nfa, a->type, con->co, a->from, to);
				freearc(nfa, a);
				break;
			default:
				assert(NOTREACHED);
				break;
		}
	}

	/* remaining inarcs, if any, incorporate the constraint */
	moveins(nfa, from, to);
	freearc(nfa, con);
	/* from state is now useless, but we leave it to pullback() to clean up */
	return 1;
}

/*
 * pushfwd - push forward constraints forward to eliminate them
 */
static void
pushfwd(struct nfa *nfa,
		FILE *f)				/* for debug output; NULL none */
{
	struct state *s;
	struct state *nexts;
	struct arc *a;
	struct arc *nexta;
	struct state *intermediates;
	int			progress;

	/* find and push until there are no more */
	do
	{
		progress = 0;
		for (s = nfa->states; s != NULL && !NISERR(); s = nexts)
		{
			nexts = s->next;
			intermediates = NULL;
			for (a = s->ins; a != NULL && !NISERR(); a = nexta)
			{
				nexta = a->inchain;
				if (a->type == '$' || a->type == AHEAD)
					if (push(nfa, a, &intermediates))
						progress = 1;
			}
			/* clear tmp fields of intermediate states created here */
			while (intermediates != NULL)
			{
				struct state *ns = intermediates->tmp;

				intermediates->tmp = NULL;
				intermediates = ns;
			}
			/* if s is now useless, get rid of it */
			if ((s->nins == 0 || s->nouts == 0) && !s->flag)
				dropstate(nfa, s);
		}
		if (progress && f != NULL)
			dumpnfa(nfa, f);
	} while (progress && !NISERR());
	if (NISERR())
		return;

	/*
	 * Any $ constraints we were able to push to the post state can now be
	 * replaced by PLAIN arcs referencing the EOS or EOL colors.  There should
	 * be no other $ or AHEAD arcs left in the NFA, though we do not check
	 * that here (compact() will fail if so).
	 */
	for (a = nfa->post->ins; a != NULL; a = nexta)
	{
		nexta = a->inchain;
		if (a->type == '$')
		{
			assert(a->co == 0 || a->co == 1);
			newarc(nfa, PLAIN, nfa->eos[a->co], a->from, a->to);
			freearc(nfa, a);
		}
	}
}

/*
 * push - push a forward constraint forward past its destination state
 *
 * Returns 1 if successful (which it always is unless the destination is the
 * post state or we have an internal error), 0 if nothing happened.
 *
 * A significant property of this function is that it deletes no pre-existing
 * states, and no inarcs of the constraint's to state other than the given
 * constraint arc.  This makes the loops in pushfwd() safe, at the cost that
 * we may leave useless states behind.  Therefore, we leave it to pushfwd()
 * to delete such states.
 *
 * If the to state has multiple forward-constraint inarcs, and/or multiple
 * compatible constraint outarcs, we only need to create one new intermediate
 * state per combination of predecessor and successor states.  *intermediates
 * points to a list of such intermediate states for this to state (chained
 * through their tmp fields).
 */
static int
push(struct nfa *nfa,
	 struct arc *con,
	 struct state **intermediates)
{
	struct state *from = con->from;
	struct state *to = con->to;
	struct arc *a;
	struct arc *nexta;
	struct state *s;

	assert(to != from);			/* should have gotten rid of this earlier */
	if (to->flag)				/* can't push forward beyond end */
		return 0;
	if (to->nouts == 0)
	{							/* dead end */
		freearc(nfa, con);
		return 1;
	}

	/*
	 * First, clone to state if necessary to avoid other inarcs.  This may
	 * seem wasteful, but it simplifies the logic, and we'll get rid of the
	 * clone state again at the bottom.
	 */
	if (to->nins > 1)
	{
		s = newstate(nfa);
		if (NISERR())
			return 0;
		copyouts(nfa, to, s);	/* duplicate outarcs */
		cparc(nfa, con, from, s);	/* move constraint arc */
		freearc(nfa, con);
		if (NISERR())
			return 0;
		to = s;
		con = to->ins;
	}
	assert(to->nins == 1);

	/* propagate the constraint into the to state's outarcs */
	for (a = to->outs; a != NULL && !NISERR(); a = nexta)
	{
		nexta = a->outchain;
		switch (combine(nfa, con, a))
		{
			case INCOMPATIBLE:	/* destroy the arc */
				freearc(nfa, a);
				break;
			case SATISFIED:		/* no action needed */
				break;
			case COMPATIBLE:	/* swap the two arcs, more or less */
				/* need an intermediate state, but might have one already */
				for (s = *intermediates; s != NULL; s = s->tmp)
				{
					assert(s->nins > 0 && s->nouts > 0);
					if (s->ins->from == from && s->outs->to == a->to)
						break;
				}
				if (s == NULL)
				{
					s = newstate(nfa);
					if (NISERR())
						return 0;
					s->tmp = *intermediates;
					*intermediates = s;
				}
				cparc(nfa, con, s, a->to);
				cparc(nfa, a, from, s);
				freearc(nfa, a);
				break;
			case REPLACEARC:	/* replace arc's color */
				newarc(nfa, a->type, con->co, from, a->to);
				freearc(nfa, a);
				break;
			default:
				assert(NOTREACHED);
				break;
		}
	}

	/* remaining outarcs, if any, incorporate the constraint */
	moveouts(nfa, to, from);
	freearc(nfa, con);
	/* to state is now useless, but we leave it to pushfwd() to clean up */
	return 1;
}

/*
 * combine - constraint lands on an arc, what happens?
 *
 * #def INCOMPATIBLE	1	// destroys arc
 * #def SATISFIED		2	// constraint satisfied
 * #def COMPATIBLE		3	// compatible but not satisfied yet
 * #def REPLACEARC		4	// replace arc's color with constraint color
 */
static int
combine(struct nfa *nfa,
		struct arc *con,
		struct arc *a)
{
#define  CA(ct,at)	 (((ct)<<CHAR_BIT) | (at))

	switch (CA(con->type, a->type))
	{
		case CA('^', PLAIN):	/* newlines are handled separately */
		case CA('$', PLAIN):
			return INCOMPATIBLE;
			break;
		case CA(AHEAD, PLAIN):	/* color constraints meet colors */
		case CA(BEHIND, PLAIN):
			if (con->co == a->co)
				return SATISFIED;
			if (con->co == RAINBOW)
			{
				/* con is satisfied unless arc's color is a pseudocolor */
				if (!(nfa->cm->cd[a->co].flags & PSEUDO))
					return SATISFIED;
			}
			else if (a->co == RAINBOW)
			{
				/* con is incompatible if it's for a pseudocolor */
				/* (this is hypothetical; we make no such constraints today) */
				if (nfa->cm->cd[con->co].flags & PSEUDO)
					return INCOMPATIBLE;
				/* otherwise, constraint constrains arc to be only its color */
				return REPLACEARC;
			}
			return INCOMPATIBLE;
			break;
		case CA('^', '^'):		/* collision, similar constraints */
		case CA('$', '$'):
			if (con->co == a->co)	/* true duplication */
				return SATISFIED;
			return INCOMPATIBLE;
			break;
		case CA(AHEAD, AHEAD):	/* collision, similar constraints */
		case CA(BEHIND, BEHIND):
			if (con->co == a->co)	/* true duplication */
				return SATISFIED;
			if (con->co == RAINBOW)
			{
				/* con is satisfied unless arc's color is a pseudocolor */
				if (!(nfa->cm->cd[a->co].flags & PSEUDO))
					return SATISFIED;
			}
			else if (a->co == RAINBOW)
			{
				/* con is incompatible if it's for a pseudocolor */
				/* (this is hypothetical; we make no such constraints today) */
				if (nfa->cm->cd[con->co].flags & PSEUDO)
					return INCOMPATIBLE;
				/* otherwise, constraint constrains arc to be only its color */
				return REPLACEARC;
			}
			return INCOMPATIBLE;
			break;
		case CA('^', BEHIND):	/* collision, dissimilar constraints */
		case CA(BEHIND, '^'):
		case CA('$', AHEAD):
		case CA(AHEAD, '$'):
			return INCOMPATIBLE;
			break;
		case CA('^', '$'):		/* constraints passing each other */
		case CA('^', AHEAD):
		case CA(BEHIND, '$'):
		case CA(BEHIND, AHEAD):
		case CA('$', '^'):
		case CA('$', BEHIND):
		case CA(AHEAD, '^'):
		case CA(AHEAD, BEHIND):
		case CA('^', LACON):
		case CA(BEHIND, LACON):
		case CA('$', LACON):
		case CA(AHEAD, LACON):
			return COMPATIBLE;
			break;
	}
	assert(NOTREACHED);
	return INCOMPATIBLE;		/* for benefit of blind compilers */
}

/*
 * fixempties - get rid of EMPTY arcs
 */
static void
fixempties(struct nfa *nfa,
		   FILE *f)				/* for debug output; NULL none */
{
	struct state *s;
	struct state *s2;
	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, 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->flag || s->nouts != 1)
			continue;
		a = s->outs;
		assert(a != NULL && a->outchain == NULL);
		if (a->type != EMPTY)
			continue;
		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 */
		assert(s->tmp == NULL);
		if (s->flag || s->nins != 1)
			continue;
		a = s->ins;
		assert(a != NULL && a->inchain == NULL);
		if (a->type != EMPTY)
			continue;
		if (s != a->from)
			moveouts(nfa, s, a->from);
		dropstate(nfa, s);
	}

	if (NISERR())
		return;

	/*
	 * 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.)
	 *
	 * 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)
	{
		/* 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);

		/* 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;
		inarcsorig[s->no] = a;
	}

	FREE(arcarray);
	FREE(inarcsorig);

	if (NISERR())
		return;

	/*
	 * Now remove all the EMPTY arcs, since we don't need them anymore.
	 */
	for (s = nfa->states; s != NULL; 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; s = nexts)
	{
		nexts = s->next;
		if ((s->nins == 0 || s->nouts == 0) && !s->flag)
			dropstate(nfa, s);
	}

	if (f != NULL)
		dumpnfa(nfa, f);
}

/*
 * 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 ... but that could still be enough to cause trouble.
 */
static struct state *
emptyreachable(struct nfa *nfa,
			   struct state *s,
			   struct state *lastfound,
			   struct arc **inarcsorig)
{
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return lastfound;
	}

	s->tmp = lastfound;
	lastfound = s;
	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;
}

/*
 * isconstraintarc - detect whether an arc is of a constraint type
 */
static inline int
isconstraintarc(struct arc *a)
{
	switch (a->type)
	{
		case '^':
		case '$':
		case BEHIND:
		case AHEAD:
		case LACON:
			return 1;
	}
	return 0;
}

/*
 * hasconstraintout - does state have a constraint out arc?
 */
static int
hasconstraintout(struct state *s)
{
	struct arc *a;

	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (isconstraintarc(a))
			return 1;
	}
	return 0;
}

/*
 * fixconstraintloops - get rid of loops containing only constraint arcs
 *
 * A loop of states that contains only constraint arcs is useless, since
 * passing around the loop represents no forward progress.  Moreover, it
 * would cause infinite looping in pullback/pushfwd, so we need to get rid
 * of such loops before doing that.
 */
static void
fixconstraintloops(struct nfa *nfa,
				   FILE *f)		/* for debug output; NULL none */
{
	struct state *s;
	struct state *nexts;
	struct arc *a;
	struct arc *nexta;
	int			hasconstraints;

	/*
	 * In the trivial case of a state that loops to itself, we can just drop
	 * the constraint arc altogether.  This is worth special-casing because
	 * such loops are far more common than loops containing multiple states.
	 * While we're at it, note whether any constraint arcs survive.
	 */
	hasconstraints = 0;
	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 */
		assert(s->tmp == NULL);
		for (a = s->outs; a != NULL && !NISERR(); a = nexta)
		{
			nexta = a->outchain;
			if (isconstraintarc(a))
			{
				if (a->to == s)
					freearc(nfa, a);
				else
					hasconstraints = 1;
			}
		}
		/* If we removed all the outarcs, the state is useless. */
		if (s->nouts == 0 && !s->flag)
			dropstate(nfa, s);
	}

	/* Nothing to do if no remaining constraint arcs */
	if (NISERR() || !hasconstraints)
		return;

	/*
	 * Starting from each remaining NFA state, search outwards for a
	 * constraint loop.  If we find a loop, break the loop, then start the
	 * search over.  (We could possibly retain some state from the first scan,
	 * but it would complicate things greatly, and multi-state constraint
	 * loops are rare enough that it's not worth optimizing the case.)
	 */
restart:
	for (s = nfa->states; s != NULL && !NISERR(); s = s->next)
	{
		if (findconstraintloop(nfa, s))
			goto restart;
	}

	if (NISERR())
		return;

	/*
	 * Now 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.)
	 *
	 * Because findconstraintloop intentionally doesn't reset all tmp fields,
	 * we have to clear them after it's done.  This is a convenient place to
	 * do that, too.
	 */
	for (s = nfa->states; s != NULL; s = nexts)
	{
		nexts = s->next;
		s->tmp = NULL;
		if ((s->nins == 0 || s->nouts == 0) && !s->flag)
			dropstate(nfa, s);
	}

	if (f != NULL)
		dumpnfa(nfa, f);
}

/*
 * findconstraintloop - recursively find a loop of constraint arcs
 *
 * If we find a loop, break it by calling breakconstraintloop(), then
 * return 1; otherwise return 0.
 *
 * State tmp fields are guaranteed all NULL on a success return, because
 * breakconstraintloop does that.  After a failure return, any state that
 * is known not to be part of a loop is marked with s->tmp == s; this allows
 * us not to have to re-prove that fact on later calls.  (This convention is
 * workable because we already eliminated single-state loops.)
 *
 * Note that the found loop doesn't necessarily include the first state we
 * are called on.  Any loop reachable from that state will do.
 *
 * The maximum recursion depth here is one more than the length of the longest
 * loop-free chain of constraint arcs, which is surely no more than the size
 * of the NFA ... but that could still be enough to cause trouble.
 */
static int
findconstraintloop(struct nfa *nfa, struct state *s)
{
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return 1;				/* to exit as quickly as possible */
	}

	if (s->tmp != NULL)
	{
		/* Already proven uninteresting? */
		if (s->tmp == s)
			return 0;
		/* Found a loop involving s */
		breakconstraintloop(nfa, s);
		/* The tmp fields have been cleaned up by breakconstraintloop */
		return 1;
	}
	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (isconstraintarc(a))
		{
			struct state *sto = a->to;

			assert(sto != s);
			s->tmp = sto;
			if (findconstraintloop(nfa, sto))
				return 1;
		}
	}

	/*
	 * If we get here, no constraint loop exists leading out from s.  Mark it
	 * with s->tmp == s so we need not rediscover that fact again later.
	 */
	s->tmp = s;
	return 0;
}

/*
 * breakconstraintloop - break a loop of constraint arcs
 *
 * sinitial is any one member state of the loop.  Each loop member's tmp
 * field links to its successor within the loop.  (Note that this function
 * will reset all the tmp fields to NULL.)
 *
 * We can break the loop by, for any one state S1 in the loop, cloning its
 * loop successor state S2 (and possibly following states), and then moving
 * all S1->S2 constraint arcs to point to the cloned S2.  The cloned S2 should
 * copy any non-constraint outarcs of S2.  Constraint outarcs should be
 * dropped if they point back to S1, else they need to be copied as arcs to
 * similarly cloned states S3, S4, etc.  In general, each cloned state copies
 * non-constraint outarcs, drops constraint outarcs that would lead to itself
 * or any earlier cloned state, and sends other constraint outarcs to newly
 * cloned states.  No cloned state will have any inarcs that aren't constraint
 * arcs or do not lead from S1 or earlier-cloned states.  It's okay to drop
 * constraint back-arcs since they would not take us to any state we've not
 * already been in; therefore, no new constraint loop is created.  In this way
 * we generate a modified NFA that can still represent every useful state
 * sequence, but not sequences that represent state loops with no consumption
 * of input data.  Note that the set of cloned states will certainly include
 * all of the loop member states other than S1, and it may also include
 * non-loop states that are reachable from S2 via constraint arcs.  This is
 * important because there is no guarantee that findconstraintloop found a
 * maximal loop (and searching for one would be NP-hard, so don't try).
 * Frequently the "non-loop states" are actually part of a larger loop that
 * we didn't notice, and indeed there may be several overlapping loops.
 * This technique ensures convergence in such cases, while considering only
 * the originally-found loop does not.
 *
 * If there is only one S1->S2 constraint arc, then that constraint is
 * certainly satisfied when we enter any of the clone states.  This means that
 * in the common case where many of the constraint arcs are identically
 * labeled, we can merge together clone states linked by a similarly-labeled
 * constraint: if we can get to the first one we can certainly get to the
 * second, so there's no need to distinguish.  This greatly reduces the number
 * of new states needed, so we preferentially break the given loop at a state
 * pair where this is true.
 *
 * Furthermore, it's fairly common to find that a cloned successor state has
 * no outarcs, especially if we're a bit aggressive about removing unnecessary
 * outarcs.  If that happens, then there is simply not any interesting state
 * that can be reached through the predecessor's loop arcs, which means we can
 * break the loop just by removing those loop arcs, with no new states added.
 */
static void
breakconstraintloop(struct nfa *nfa, struct state *sinitial)
{
	struct state *s;
	struct state *shead;
	struct state *stail;
	struct state *sclone;
	struct state *nexts;
	struct arc *refarc;
	struct arc *a;
	struct arc *nexta;

	/*
	 * Start by identifying which loop step we want to break at.
	 * Preferentially this is one with only one constraint arc.  (XXX are
	 * there any other secondary heuristics we want to use here?)  Set refarc
	 * to point to the selected lone constraint arc, if there is one.
	 */
	refarc = NULL;
	s = sinitial;
	do
	{
		nexts = s->tmp;
		assert(nexts != s);		/* should not see any one-element loops */
		if (refarc == NULL)
		{
			int			narcs = 0;

			for (a = s->outs; a != NULL; a = a->outchain)
			{
				if (a->to == nexts && isconstraintarc(a))
				{
					refarc = a;
					narcs++;
				}
			}
			assert(narcs > 0);
			if (narcs > 1)
				refarc = NULL;	/* multiple constraint arcs here, no good */
		}
		s = nexts;
	} while (s != sinitial);

	if (refarc)
	{
		/* break at the refarc */
		shead = refarc->from;
		stail = refarc->to;
		assert(stail == shead->tmp);
	}
	else
	{
		/* for lack of a better idea, break after sinitial */
		shead = sinitial;
		stail = sinitial->tmp;
	}

	/*
	 * Reset the tmp fields so that we can use them for local storage in
	 * clonesuccessorstates.  (findconstraintloop won't mind, since it's just
	 * going to abandon its search anyway.)
	 */
	for (s = nfa->states; s != NULL; s = s->next)
		s->tmp = NULL;

	/*
	 * Recursively build clone state(s) as needed.
	 */
	sclone = newstate(nfa);
	if (sclone == NULL)
	{
		assert(NISERR());
		return;
	}

	clonesuccessorstates(nfa, stail, sclone, shead, refarc,
						 NULL, NULL, nfa->nstates);

	if (NISERR())
		return;

	/*
	 * It's possible that sclone has no outarcs at all, in which case it's
	 * useless.  (We don't try extremely hard to get rid of useless states
	 * here, but this is an easy and fairly common case.)
	 */
	if (sclone->nouts == 0)
	{
		freestate(nfa, sclone);
		sclone = NULL;
	}

	/*
	 * Move shead's constraint-loop arcs to point to sclone, or just drop them
	 * if we discovered we don't need sclone.
	 */
	for (a = shead->outs; a != NULL; a = nexta)
	{
		nexta = a->outchain;
		if (a->to == stail && isconstraintarc(a))
		{
			if (sclone)
				cparc(nfa, a, shead, sclone);
			freearc(nfa, a);
			if (NISERR())
				break;
		}
	}
}

/*
 * clonesuccessorstates - create a tree of constraint-arc successor states
 *
 * ssource is the state to be cloned, and sclone is the state to copy its
 * outarcs into.  sclone's inarcs, if any, should already be set up.
 *
 * spredecessor is the original predecessor state that we are trying to build
 * successors for (it may not be the immediate predecessor of ssource).
 * refarc, if not NULL, is the original constraint arc that is known to have
 * been traversed out of spredecessor to reach the successor(s).
 *
 * For each cloned successor state, we transiently create a "donemap" that is
 * a boolean array showing which source states we've already visited for this
 * clone state.  This prevents infinite recursion as well as useless repeat
 * visits to the same state subtree (which can add up fast, since typical NFAs
 * have multiple redundant arc pathways).  Each donemap is a char array
 * indexed by state number.  The donemaps are all of the same size "nstates",
 * which is nfa->nstates as of the start of the recursion.  This is enough to
 * have entries for all pre-existing states, but *not* entries for clone
 * states created during the recursion.  That's okay since we have no need to
 * mark those.
 *
 * curdonemap is NULL when recursing to a new sclone state, or sclone's
 * donemap when we are recursing without having created a new state (which we
 * do when we decide we can merge a successor state into the current clone
 * state).  outerdonemap is NULL at the top level and otherwise the parent
 * clone state's donemap.
 *
 * The successor states we create and fill here form a strict tree structure,
 * with each state having exactly one predecessor, except that the toplevel
 * state has no inarcs as yet (breakconstraintloop will add its inarcs from
 * spredecessor after we're done).  Thus, we can examine sclone's inarcs back
 * to the root, plus refarc if any, to identify the set of constraints already
 * known valid at the current point.  This allows us to avoid generating extra
 * successor states.
 */
static void
clonesuccessorstates(struct nfa *nfa,
					 struct state *ssource,
					 struct state *sclone,
					 struct state *spredecessor,
					 struct arc *refarc,
					 char *curdonemap,
					 char *outerdonemap,
					 int nstates)
{
	char	   *donemap;
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	/* If this state hasn't already got a donemap, create one */
	donemap = curdonemap;
	if (donemap == NULL)
	{
		donemap = (char *) MALLOC(nstates * sizeof(char));
		if (donemap == NULL)
		{
			NERR(REG_ESPACE);
			return;
		}

		if (outerdonemap != NULL)
		{
			/*
			 * Not at outermost recursion level, so copy the outer level's
			 * donemap; this ensures that we see states in process of being
			 * visited at outer levels, or already merged into predecessor
			 * states, as ones we shouldn't traverse back to.
			 */
			memcpy(donemap, outerdonemap, nstates * sizeof(char));
		}
		else
		{
			/* At outermost level, only spredecessor is off-limits */
			memset(donemap, 0, nstates * sizeof(char));
			assert(spredecessor->no < nstates);
			donemap[spredecessor->no] = 1;
		}
	}

	/* Mark ssource as visited in the donemap */
	assert(ssource->no < nstates);
	assert(donemap[ssource->no] == 0);
	donemap[ssource->no] = 1;

	/*
	 * We proceed by first cloning all of ssource's outarcs, creating new
	 * clone states as needed but not doing more with them than that.  Then in
	 * a second pass, recurse to process the child clone states.  This allows
	 * us to have only one child clone state per reachable source state, even
	 * when there are multiple outarcs leading to the same state.  Also, when
	 * we do visit a child state, its set of inarcs is known exactly, which
	 * makes it safe to apply the constraint-is-already-checked optimization.
	 * Also, this ensures that we've merged all the states we can into the
	 * current clone before we recurse to any children, thus possibly saving
	 * them from making extra images of those states.
	 *
	 * While this function runs, child clone states of the current state are
	 * marked by setting their tmp fields to point to the original state they
	 * were cloned from.  This makes it possible to detect multiple outarcs
	 * leading to the same state, and also makes it easy to distinguish clone
	 * states from original states (which will have tmp == NULL).
	 */
	for (a = ssource->outs; a != NULL && !NISERR(); a = a->outchain)
	{
		struct state *sto = a->to;

		/*
		 * We do not consider cloning successor states that have no constraint
		 * outarcs; just link to them as-is.  They cannot be part of a
		 * constraint loop so there is no need to make copies.  In particular,
		 * this rule keeps us from trying to clone the post state, which would
		 * be a bad idea.
		 */
		if (isconstraintarc(a) && hasconstraintout(sto))
		{
			struct state *prevclone;
			int			canmerge;
			struct arc *a2;

			/*
			 * Back-link constraint arcs must not be followed.  Nor is there a
			 * need to revisit states previously merged into this clone.
			 */
			assert(sto->no < nstates);
			if (donemap[sto->no] != 0)
				continue;

			/*
			 * Check whether we already have a child clone state for this
			 * source state.
			 */
			prevclone = NULL;
			for (a2 = sclone->outs; a2 != NULL; a2 = a2->outchain)
			{
				if (a2->to->tmp == sto)
				{
					prevclone = a2->to;
					break;
				}
			}

			/*
			 * If this arc is labeled the same as refarc, or the same as any
			 * arc we must have traversed to get to sclone, then no additional
			 * constraints need to be met to get to sto, so we should just
			 * merge its outarcs into sclone.
			 */
			if (refarc && a->type == refarc->type && a->co == refarc->co)
				canmerge = 1;
			else
			{
				struct state *s;

				canmerge = 0;
				for (s = sclone; s->ins; s = s->ins->from)
				{
					if (s->nins == 1 &&
						a->type == s->ins->type && a->co == s->ins->co)
					{
						canmerge = 1;
						break;
					}
				}
			}

			if (canmerge)
			{
				/*
				 * We can merge into sclone.  If we previously made a child
				 * clone state, drop it; there's no need to visit it.  (This
				 * can happen if ssource has multiple pathways to sto, and we
				 * only just now found one that is provably a no-op.)
				 */
				if (prevclone)
					dropstate(nfa, prevclone);	/* kills our outarc, too */

				/* Recurse to merge sto's outarcs into sclone */
				clonesuccessorstates(nfa,
									 sto,
									 sclone,
									 spredecessor,
									 refarc,
									 donemap,
									 outerdonemap,
									 nstates);
				/* sto should now be marked as previously visited */
				assert(NISERR() || donemap[sto->no] == 1);
			}
			else if (prevclone)
			{
				/*
				 * We already have a clone state for this successor, so just
				 * make another arc to it.
				 */
				cparc(nfa, a, sclone, prevclone);
			}
			else
			{
				/*
				 * We need to create a new successor clone state.
				 */
				struct state *stoclone;

				stoclone = newstate(nfa);
				if (stoclone == NULL)
				{
					assert(NISERR());
					break;
				}
				/* Mark it as to what it's a clone of */
				stoclone->tmp = sto;
				/* ... and add the outarc leading to it */
				cparc(nfa, a, sclone, stoclone);
			}
		}
		else
		{
			/*
			 * Non-constraint outarcs just get copied to sclone, as do outarcs
			 * leading to states with no constraint outarc.
			 */
			cparc(nfa, a, sclone, sto);
		}
	}

	/*
	 * If we are at outer level for this clone state, recurse to all its child
	 * clone states, clearing their tmp fields as we go.  (If we're not
	 * outermost for sclone, leave this to be done by the outer call level.)
	 * Note that if we have multiple outarcs leading to the same clone state,
	 * it will only be recursed-to once.
	 */
	if (curdonemap == NULL)
	{
		for (a = sclone->outs; a != NULL && !NISERR(); a = a->outchain)
		{
			struct state *stoclone = a->to;
			struct state *sto = stoclone->tmp;

			if (sto != NULL)
			{
				stoclone->tmp = NULL;
				clonesuccessorstates(nfa,
									 sto,
									 stoclone,
									 spredecessor,
									 refarc,
									 NULL,
									 donemap,
									 nstates);
			}
		}

		/* Don't forget to free sclone's donemap when done with it */
		FREE(donemap);
	}
}

/*
 * removecantmatch - remove CANTMATCH arcs, which are no longer useful
 * once we are done with the parsing phase.  (We need them only to
 * preserve connectedness of NFA subgraphs during parsing.)
 */
static void
removecantmatch(struct nfa *nfa)
{
	struct state *s;

	for (s = nfa->states; s != NULL; s = s->next)
	{
		struct arc *a;
		struct arc *nexta;

		for (a = s->outs; a != NULL; a = nexta)
		{
			nexta = a->outchain;
			if (a->type == CANTMATCH)
			{
				freearc(nfa, a);
				if (NISERR())
					return;
			}
		}
	}
}

/*
 * cleanup - clean up NFA after optimizations
 */
static void
cleanup(struct nfa *nfa)
{
	struct state *s;
	struct state *nexts;
	int			n;

	if (NISERR())
		return;

	/* clear out unreachable or dead-end states */
	/* use pre to mark reachable, then post to mark can-reach-post */
	markreachable(nfa, nfa->pre, (struct state *) NULL, nfa->pre);
	markcanreach(nfa, nfa->post, nfa->pre, nfa->post);
	for (s = nfa->states; s != NULL && !NISERR(); s = nexts)
	{
		nexts = s->next;
		if (s->tmp != nfa->post && !s->flag)
			dropstate(nfa, s);
	}
	assert(NISERR() || nfa->post->nins == 0 || nfa->post->tmp == nfa->post);
	cleartraverse(nfa, nfa->pre);
	assert(NISERR() || nfa->post->nins == 0 || nfa->post->tmp == NULL);
	/* the nins==0 (final unreachable) case will be caught later */

	/* renumber surviving states */
	n = 0;
	for (s = nfa->states; s != NULL; s = s->next)
		s->no = n++;
	nfa->nstates = n;
}

/*
 * markreachable - recursive marking of reachable states
 */
static void
markreachable(struct nfa *nfa,
			  struct state *s,
			  struct state *okay,	/* consider only states with this mark */
			  struct state *mark)	/* the value to mark with */
{
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	if (s->tmp != okay)
		return;
	s->tmp = mark;

	for (a = s->outs; a != NULL; a = a->outchain)
		markreachable(nfa, a->to, okay, mark);
}

/*
 * markcanreach - recursive marking of states which can reach here
 */
static void
markcanreach(struct nfa *nfa,
			 struct state *s,
			 struct state *okay,	/* consider only states with this mark */
			 struct state *mark)	/* the value to mark with */
{
	struct arc *a;

	/* Since this is recursive, it could be driven to stack overflow */
	if (STACK_TOO_DEEP(nfa->v->re))
	{
		NERR(REG_ETOOBIG);
		return;
	}

	if (s->tmp != okay)
		return;
	s->tmp = mark;

	for (a = s->ins; a != NULL; a = a->inchain)
		markcanreach(nfa, a->from, okay, mark);
}

/*
 * analyze - ascertain potentially-useful facts about an optimized NFA
 */
static long						/* re_info bits to be ORed in */
analyze(struct nfa *nfa)
{
	struct arc *a;
	struct arc *aa;

	if (NISERR())
		return 0;

	/* Detect whether NFA can't match anything */
	if (nfa->pre->outs == NULL)
		return REG_UIMPOSSIBLE;

	/* Detect whether NFA matches all strings (possibly with length bounds) */
	checkmatchall(nfa);

	/* Detect whether NFA can possibly match a zero-length string */
	for (a = nfa->pre->outs; a != NULL; a = a->outchain)
		for (aa = a->to->outs; aa != NULL; aa = aa->outchain)
			if (aa->to == nfa->post)
				return REG_UEMPTYMATCH;
	return 0;
}

/*
 * checkmatchall - does the NFA represent no more than a string length test?
 *
 * If so, set nfa->minmatchall and nfa->maxmatchall correctly (they are -1
 * to begin with) and set the MATCHALL bit in nfa->flags.
 *
 * To succeed, we require all arcs to be PLAIN RAINBOW arcs, except for those
 * for pseudocolors (i.e., BOS/BOL/EOS/EOL).  We must be able to reach the
 * post state via RAINBOW arcs, and if there are any loops in the graph, they
 * must be loop-to-self arcs, ensuring that each loop iteration consumes
 * exactly one character.  (Longer loops are problematic because they create
 * non-consecutive possible match lengths; we have no good way to represent
 * that situation for lengths beyond the DUPINF limit.)
 *
 * Pseudocolor arcs complicate things a little.  We know that they can only
 * appear as pre-state outarcs (for BOS/BOL) or post-state inarcs (for
 * EOS/EOL).  There, they must exactly replicate the parallel RAINBOW arcs,
 * e.g. if the pre state has one RAINBOW outarc to state 2, it must have BOS
 * and BOL outarcs to state 2, and no others.  Missing or extra pseudocolor
 * arcs can occur, meaning that the NFA involves some constraint on the
 * adjacent characters, which makes it not a matchall NFA.
 */
static void
checkmatchall(struct nfa *nfa)
{
	bool	  **haspaths;
	struct state *s;
	int			i;

	/*
	 * If there are too many states, don't bother trying to detect matchall.
	 * This limit serves to bound the time and memory we could consume below.
	 * Note that even if the graph is all-RAINBOW, if there are significantly
	 * more than DUPINF states then it's likely that there are paths of length
	 * more than DUPINF, which would force us to fail anyhow.  In practice,
	 * plausible ways of writing a matchall regex with maximum finite path
	 * length K tend not to have very many more than K states.
	 */
	if (nfa->nstates > DUPINF * 2)
		return;

	/*
	 * First, scan all the states to verify that only RAINBOW arcs appear,
	 * plus pseudocolor arcs adjacent to the pre and post states.  This lets
	 * us quickly eliminate most cases that aren't matchall NFAs.
	 */
	for (s = nfa->states; s != NULL; s = s->next)
	{
		struct arc *a;

		for (a = s->outs; a != NULL; a = a->outchain)
		{
			if (a->type != PLAIN)
				return;			/* any LACONs make it non-matchall */
			if (a->co != RAINBOW)
			{
				if (nfa->cm->cd[a->co].flags & PSEUDO)
				{
					/*
					 * Pseudocolor arc: verify it's in a valid place (this
					 * seems quite unlikely to fail, but let's be sure).
					 */
					if (s == nfa->pre &&
						(a->co == nfa->bos[0] || a->co == nfa->bos[1]))
						 /* okay BOS/BOL arc */ ;
					else if (a->to == nfa->post &&
							 (a->co == nfa->eos[0] || a->co == nfa->eos[1]))
						 /* okay EOS/EOL arc */ ;
					else
						return; /* unexpected pseudocolor arc */
					/* We'll check these arcs some more below. */
				}
				else
					return;		/* any other color makes it non-matchall */
			}
		}
		/* Also, assert that the tmp fields are available for use. */
		assert(s->tmp == NULL);
	}

	/*
	 * The next cheapest check we can make is to verify that the BOS/BOL
	 * outarcs of the pre state reach the same states as its RAINBOW outarcs.
	 * If they don't, the NFA expresses some constraints on the character
	 * before the matched string, making it non-matchall.  Likewise, the
	 * EOS/EOL inarcs of the post state must match its RAINBOW inarcs.
	 */
	if (!check_out_colors_match(nfa->pre, RAINBOW, nfa->bos[0]) ||
		!check_out_colors_match(nfa->pre, RAINBOW, nfa->bos[1]) ||
		!check_in_colors_match(nfa->post, RAINBOW, nfa->eos[0]) ||
		!check_in_colors_match(nfa->post, RAINBOW, nfa->eos[1]))
		return;

	/*
	 * Initialize an array of path-length arrays, in which
	 * checkmatchall_recurse will return per-state results.  This lets us
	 * memo-ize the recursive search and avoid exponential time consumption.
	 */
	haspaths = (bool **) MALLOC(nfa->nstates * sizeof(bool *));
	if (haspaths == NULL)
		return;					/* fail quietly */
	memset(haspaths, 0, nfa->nstates * sizeof(bool *));

	/*
	 * Recursively search the graph for all-RAINBOW paths to the "post" state,
	 * starting at the "pre" state, and computing the lengths of the paths.
	 * (Given the preceding checks, there should be at least one such path.
	 * However we could get back a false result anyway, in case there are
	 * multi-state loops, paths exceeding DUPINF+1 length, or non-algorithmic
	 * failures such as ENOMEM.)
	 */
	if (checkmatchall_recurse(nfa, nfa->pre, haspaths))
	{
		/* The useful result is the path length array for the pre state */
		bool	   *haspath = haspaths[nfa->pre->no];
		int			minmatch,
					maxmatch,
					morematch;

		assert(haspath != NULL);

		/*
		 * haspath[] now represents the set of possible path lengths; but we
		 * want to reduce that to a min and max value, because it doesn't seem
		 * worth complicating regexec.c to deal with nonconsecutive possible
		 * match lengths.  Find min and max of first run of lengths, then
		 * verify there are no nonconsecutive lengths.
		 */
		for (minmatch = 0; minmatch <= DUPINF + 1; minmatch++)
		{
			if (haspath[minmatch])
				break;
		}
		assert(minmatch <= DUPINF + 1); /* else checkmatchall_recurse lied */
		for (maxmatch = minmatch; maxmatch < DUPINF + 1; maxmatch++)
		{
			if (!haspath[maxmatch + 1])
				break;
		}
		for (morematch = maxmatch + 1; morematch <= DUPINF + 1; morematch++)
		{
			if (haspath[morematch])
			{
				haspath = NULL; /* fail, there are nonconsecutive lengths */
				break;
			}
		}

		if (haspath != NULL)
		{
			/*
			 * Success, so record the info.  Here we have a fine point: the
			 * path length from the pre state includes the pre-to-initial
			 * transition, so it's one more than the actually matched string
			 * length.  (We avoided counting the final-to-post transition
			 * within checkmatchall_recurse, but not this one.)  This is why
			 * checkmatchall_recurse allows one more level of path length than
			 * might seem necessary.  This decrement also takes care of
			 * converting checkmatchall_recurse's definition of "infinity" as
			 * "DUPINF+1" to our normal representation as "DUPINF".
			 */
			assert(minmatch > 0);	/* else pre and post states were adjacent */
			nfa->minmatchall = minmatch - 1;
			nfa->maxmatchall = maxmatch - 1;
			nfa->flags |= MATCHALL;
		}
	}

	/* Clean up */
	for (i = 0; i < nfa->nstates; i++)
	{
		if (haspaths[i] != NULL)
			FREE(haspaths[i]);
	}
	FREE(haspaths);
}

/*
 * checkmatchall_recurse - recursive search for checkmatchall
 *
 * s is the state to be examined in this recursion level.
 * haspaths[] is an array of per-state exit path length arrays.
 *
 * We return true if the search was performed successfully, false if
 * we had to fail because of multi-state loops or other internal reasons.
 * (Because "dead" states that can't reach the post state have been
 * eliminated, and we already verified that only RAINBOW and matching
 * pseudocolor arcs exist, every state should have RAINBOW path(s) to
 * the post state.  Hence we take a false result from recursive calls
 * as meaning that we'd better fail altogether, not just that that
 * particular state can't reach the post state.)
 *
 * On success, we store a malloc'd result array in haspaths[s->no],
 * showing the possible path lengths from s to the post state.
 * Each state's haspath[] array is of length DUPINF+2.  The entries from
 * k = 0 to DUPINF are true if there is an all-RAINBOW path of length k
 * from this state to the string end.  haspath[DUPINF+1] is true if all
 * path lengths >= DUPINF+1 are possible.  (Situations that cannot be
 * represented under these rules cause failure.)
 *
 * checkmatchall is responsible for eventually freeing the haspath[] arrays.
 */
static bool
checkmatchall_recurse(struct nfa *nfa, struct state *s, bool **haspaths)
{
	bool		result = false;
	bool		foundloop = false;
	bool	   *haspath;
	struct arc *a;

	/*
	 * Since this is recursive, it could be driven to stack overflow.  But we
	 * need not treat that as a hard failure; just deem the NFA non-matchall.
	 */
	if (STACK_TOO_DEEP(nfa->v->re))
		return false;

	/* In case the search takes a long time, check for cancel */
	INTERRUPT(nfa->v->re);

	/* Create a haspath array for this state */
	haspath = (bool *) MALLOC((DUPINF + 2) * sizeof(bool));
	if (haspath == NULL)
		return false;			/* again, treat as non-matchall */
	memset(haspath, 0, (DUPINF + 2) * sizeof(bool));

	/* Mark this state as being visited */
	assert(s->tmp == NULL);
	s->tmp = s;

	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (a->co != RAINBOW)
			continue;			/* ignore pseudocolor arcs */
		if (a->to == nfa->post)
		{
			/* We found an all-RAINBOW path to the post state */
			result = true;

			/*
			 * Mark this state as being zero steps away from the string end
			 * (the transition to the post state isn't counted).
			 */
			haspath[0] = true;
		}
		else if (a->to == s)
		{
			/* We found a cycle of length 1, which we'll deal with below. */
			foundloop = true;
		}
		else if (a->to->tmp != NULL)
		{
			/* It's busy, so we found a cycle of length > 1, so fail. */
			result = false;
			break;
		}
		else
		{
			/* Consider paths forward through this to-state. */
			bool	   *nexthaspath;
			int			i;

			/* If to-state was not already visited, recurse */
			if (haspaths[a->to->no] == NULL)
			{
				result = checkmatchall_recurse(nfa, a->to, haspaths);
				/* Fail if any recursive path fails */
				if (!result)
					break;
			}
			else
			{
				/* The previous visit must have found path(s) to the end */
				result = true;
			}
			assert(a->to->tmp == NULL);
			nexthaspath = haspaths[a->to->no];
			assert(nexthaspath != NULL);

			/*
			 * Now, for every path of length i from a->to to the string end,
			 * there is a path of length i + 1 from s to the string end.
			 */
			if (nexthaspath[DUPINF] != nexthaspath[DUPINF + 1])
			{
				/*
				 * a->to has a path of length exactly DUPINF, but not longer;
				 * or it has paths of all lengths > DUPINF but not one of
				 * exactly that length.  In either case, we cannot represent
				 * the possible path lengths from s correctly, so fail.
				 */
				result = false;
				break;
			}
			/* Merge knowledge of these path lengths into what we have */
			for (i = 0; i < DUPINF; i++)
				haspath[i + 1] |= nexthaspath[i];
			/* Infinity + 1 is still infinity */
			haspath[DUPINF + 1] |= nexthaspath[DUPINF + 1];
		}
	}

	if (result && foundloop)
	{
		/*
		 * If there is a length-1 loop at this state, then find the shortest
		 * known path length to the end.  The loop means that every larger
		 * path length is possible, too.  (It doesn't matter whether any of
		 * the longer lengths were already known possible.)
		 */
		int			i;

		for (i = 0; i <= DUPINF; i++)
		{
			if (haspath[i])
				break;
		}
		for (i++; i <= DUPINF + 1; i++)
			haspath[i] = true;
	}

	/* Report out the completed path length map */
	assert(s->no < nfa->nstates);
	assert(haspaths[s->no] == NULL);
	haspaths[s->no] = haspath;

	/* Mark state no longer busy */
	s->tmp = NULL;

	return result;
}

/*
 * check_out_colors_match - subroutine for checkmatchall
 *
 * Check whether the set of states reachable from s by arcs of color co1
 * is equivalent to the set reachable by arcs of color co2.
 * checkmatchall already verified that all of the NFA's arcs are PLAIN,
 * so we need not examine arc types here.
 */
static bool
check_out_colors_match(struct state *s, color co1, color co2)
{
	bool		result = true;
	struct arc *a;

	/*
	 * To do this in linear time, we assume that the NFA contains no duplicate
	 * arcs.  Run through the out-arcs, marking states reachable by arcs of
	 * color co1.  Run through again, un-marking states reachable by arcs of
	 * color co2; if we see a not-marked state, we know this co2 arc is
	 * unmatched.  Then run through again, checking for still-marked states,
	 * and in any case leaving all the tmp fields reset to NULL.
	 */
	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (a->co == co1)
		{
			assert(a->to->tmp == NULL);
			a->to->tmp = a->to;
		}
	}
	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (a->co == co2)
		{
			if (a->to->tmp != NULL)
				a->to->tmp = NULL;
			else
				result = false; /* unmatched co2 arc */
		}
	}
	for (a = s->outs; a != NULL; a = a->outchain)
	{
		if (a->co == co1)
		{
			if (a->to->tmp != NULL)
			{
				result = false; /* unmatched co1 arc */
				a->to->tmp = NULL;
			}
		}
	}
	return result;
}

/*
 * check_in_colors_match - subroutine for checkmatchall
 *
 * Check whether the set of states that can reach s by arcs of color co1
 * is equivalent to the set that can reach s by arcs of color co2.
 * checkmatchall already verified that all of the NFA's arcs are PLAIN,
 * so we need not examine arc types here.
 */
static bool
check_in_colors_match(struct state *s, color co1, color co2)
{
	bool		result = true;
	struct arc *a;

	/*
	 * Identical algorithm to check_out_colors_match, except examine the
	 * from-states of s' inarcs.
	 */
	for (a = s->ins; a != NULL; a = a->inchain)
	{
		if (a->co == co1)
		{
			assert(a->from->tmp == NULL);
			a->from->tmp = a->from;
		}
	}
	for (a = s->ins; a != NULL; a = a->inchain)
	{
		if (a->co == co2)
		{
			if (a->from->tmp != NULL)
				a->from->tmp = NULL;
			else
				result = false; /* unmatched co2 arc */
		}
	}
	for (a = s->ins; a != NULL; a = a->inchain)
	{
		if (a->co == co1)
		{
			if (a->from->tmp != NULL)
			{
				result = false; /* unmatched co1 arc */
				a->from->tmp = NULL;
			}
		}
	}
	return result;
}

/*
 * compact - construct the compact representation of an NFA
 */
static void
compact(struct nfa *nfa,
		struct cnfa *cnfa)
{
	struct state *s;
	struct arc *a;
	size_t		nstates;
	size_t		narcs;
	struct carc *ca;
	struct carc *first;

	assert(!NISERR());

	nstates = 0;
	narcs = 0;
	for (s = nfa->states; s != NULL; s = s->next)
	{
		nstates++;
		narcs += s->nouts + 1;	/* need one extra for endmarker */
	}

	cnfa->stflags = (char *) MALLOC(nstates * sizeof(char));
	cnfa->states = (struct carc **) MALLOC(nstates * sizeof(struct carc *));
	cnfa->arcs = (struct carc *) MALLOC(narcs * sizeof(struct carc));
	if (cnfa->stflags == NULL || cnfa->states == NULL || cnfa->arcs == NULL)
	{
		if (cnfa->stflags != NULL)
			FREE(cnfa->stflags);
		if (cnfa->states != NULL)
			FREE(cnfa->states);
		if (cnfa->arcs != NULL)
			FREE(cnfa->arcs);
		NERR(REG_ESPACE);
		return;
	}
	cnfa->nstates = nstates;
	cnfa->pre = nfa->pre->no;
	cnfa->post = nfa->post->no;
	cnfa->bos[0] = nfa->bos[0];
	cnfa->bos[1] = nfa->bos[1];
	cnfa->eos[0] = nfa->eos[0];
	cnfa->eos[1] = nfa->eos[1];
	cnfa->ncolors = maxcolor(nfa->cm) + 1;
	cnfa->flags = nfa->flags;
	cnfa->minmatchall = nfa->minmatchall;
	cnfa->maxmatchall = nfa->maxmatchall;

	ca = cnfa->arcs;
	for (s = nfa->states; s != NULL; s = s->next)
	{
		assert((size_t) s->no < nstates);
		cnfa->stflags[s->no] = 0;
		cnfa->states[s->no] = ca;
		first = ca;
		for (a = s->outs; a != NULL; a = a->outchain)
			switch (a->type)
			{
				case PLAIN:
					ca->co = a->co;
					ca->to = a->to->no;
					ca++;
					break;
				case LACON:
					assert(s->no != cnfa->pre);
					assert(a->co >= 0);
					ca->co = (color) (cnfa->ncolors + a->co);
					ca->to = a->to->no;
					ca++;
					cnfa->flags |= HASLACONS;
					break;
				default:
					NERR(REG_ASSERT);
					return;
			}
		carcsort(first, ca - first);
		ca->co = COLORLESS;
		ca->to = 0;
		ca++;
	}
	assert(ca == &cnfa->arcs[narcs]);
	assert(cnfa->nstates != 0);

	/* mark no-progress states */
	for (a = nfa->pre->outs; a != NULL; a = a->outchain)
		cnfa->stflags[a->to->no] = CNFA_NOPROGRESS;
	cnfa->stflags[nfa->pre->no] = CNFA_NOPROGRESS;
}

/*
 * carcsort - sort compacted-NFA arcs by color
 */
static void
carcsort(struct carc *first, size_t n)
{
	if (n > 1)
		qsort(first, n, sizeof(struct carc), carc_cmp);
}

static int
carc_cmp(const void *a, const void *b)
{
	const struct carc *aa = (const struct carc *) a;
	const struct carc *bb = (const struct carc *) b;

	if (aa->co < bb->co)
		return -1;
	if (aa->co > bb->co)
		return +1;
	if (aa->to < bb->to)
		return -1;
	if (aa->to > bb->to)
		return +1;
	/* This is unreached, since there should be no duplicate arcs now: */
	return 0;
}

/*
 * freecnfa - free a compacted NFA
 */
static void
freecnfa(struct cnfa *cnfa)
{
	assert(!NULLCNFA(*cnfa));	/* not empty already */
	FREE(cnfa->stflags);
	FREE(cnfa->states);
	FREE(cnfa->arcs);
	ZAPCNFA(*cnfa);
}

/*
 * dumpnfa - dump an NFA in human-readable form
 */
static void
dumpnfa(struct nfa *nfa,
		FILE *f)
{
#ifdef REG_DEBUG
	struct state *s;
	int			nstates = 0;
	int			narcs = 0;

	fprintf(f, "pre %d, post %d", nfa->pre->no, nfa->post->no);
	if (nfa->bos[0] != COLORLESS)
		fprintf(f, ", bos [%ld]", (long) nfa->bos[0]);
	if (nfa->bos[1] != COLORLESS)
		fprintf(f, ", bol [%ld]", (long) nfa->bos[1]);
	if (nfa->eos[0] != COLORLESS)
		fprintf(f, ", eos [%ld]", (long) nfa->eos[0]);
	if (nfa->eos[1] != COLORLESS)
		fprintf(f, ", eol [%ld]", (long) nfa->eos[1]);
	if (nfa->flags & HASLACONS)
		fprintf(f, ", haslacons");
	if (nfa->flags & HASCANTMATCH)
		fprintf(f, ", hascantmatch");
	if (nfa->flags & MATCHALL)
	{
		fprintf(f, ", minmatchall %d", nfa->minmatchall);
		if (nfa->maxmatchall == DUPINF)
			fprintf(f, ", maxmatchall inf");
		else
			fprintf(f, ", maxmatchall %d", nfa->maxmatchall);
	}
	fprintf(f, "\n");
	for (s = nfa->states; s != NULL; s = s->next)
	{
		dumpstate(s, f);
		nstates++;
		narcs += s->nouts;
	}
	fprintf(f, "total of %d states, %d arcs\n", nstates, narcs);
	if (nfa->parent == NULL)
		dumpcolors(nfa->cm, f);
	fflush(f);
#endif
}

#ifdef REG_DEBUG				/* subordinates of dumpnfa */

/*
 * dumpstate - dump an NFA state in human-readable form
 */
static void
dumpstate(struct state *s,
		  FILE *f)
{
	struct arc *a;

	fprintf(f, "%d%s%c", s->no, (s->tmp != NULL) ? "T" : "",
			(s->flag) ? s->flag : '.');
	if (s->prev != NULL && s->prev->next != s)
		fprintf(f, "\tstate chain bad\n");
	if (s->nouts == 0)
		fprintf(f, "\tno out arcs\n");
	else
		dumparcs(s, f);
	for (a = s->ins; a != NULL; a = a->inchain)
	{
		if (a->to != s)
			fprintf(f, "\tlink from %d to %d on %d's in-chain\n",
					a->from->no, a->to->no, s->no);
	}
	fflush(f);
}

/*
 * dumparcs - dump out-arcs in human-readable form
 */
static void
dumparcs(struct state *s,
		 FILE *f)
{
	int			pos;
	struct arc *a;

	/* printing oldest arcs first is usually clearer */
	a = s->outs;
	assert(a != NULL);
	while (a->outchain != NULL)
		a = a->outchain;
	pos = 1;
	do
	{
		dumparc(a, s, f);
		if (pos == 5)
		{
			fprintf(f, "\n");
			pos = 1;
		}
		else
			pos++;
		a = a->outchainRev;
	} while (a != NULL);
	if (pos != 1)
		fprintf(f, "\n");
}

/*
 * dumparc - dump one outarc in readable form, including prefixing tab
 */
static void
dumparc(struct arc *a,
		struct state *s,
		FILE *f)
{
	struct arc *aa;

	fprintf(f, "\t");
	switch (a->type)
	{
		case PLAIN:
			if (a->co == RAINBOW)
				fprintf(f, "[*]");
			else
				fprintf(f, "[%ld]", (long) a->co);
			break;
		case AHEAD:
			if (a->co == RAINBOW)
				fprintf(f, ">*>");
			else
				fprintf(f, ">%ld>", (long) a->co);
			break;
		case BEHIND:
			if (a->co == RAINBOW)
				fprintf(f, "<*<");
			else
				fprintf(f, "<%ld<", (long) a->co);
			break;
		case LACON:
			fprintf(f, ":%ld:", (long) a->co);
			break;
		case '^':
		case '$':
			fprintf(f, "%c%d", a->type, (int) a->co);
			break;
		case EMPTY:
			break;
		case CANTMATCH:
			fprintf(f, "X");
			break;
		default:
			fprintf(f, "0x%x/0%lo", a->type, (long) a->co);
			break;
	}
	if (a->from != s)
		fprintf(f, "?%d?", a->from->no);
	for (aa = a->from->outs; aa != NULL; aa = aa->outchain)
		if (aa == a)
			break;				/* NOTE BREAK OUT */
	if (aa == NULL)
		fprintf(f, "?!?");		/* missing from out-chain */
	fprintf(f, "->");
	if (a->to == NULL)
	{
		fprintf(f, "NULL");
		return;
	}
	fprintf(f, "%d", a->to->no);
	for (aa = a->to->ins; aa != NULL; aa = aa->inchain)
		if (aa == a)
			break;				/* NOTE BREAK OUT */
	if (aa == NULL)
		fprintf(f, "?!?");		/* missing from in-chain */
}
#endif							/* REG_DEBUG */

/*
 * dumpcnfa - dump a compacted NFA in human-readable form
 */
#ifdef REG_DEBUG
static void
dumpcnfa(struct cnfa *cnfa,
		 FILE *f)
{
	int			st;

	fprintf(f, "pre %d, post %d", cnfa->pre, cnfa->post);
	if (cnfa->bos[0] != COLORLESS)
		fprintf(f, ", bos [%ld]", (long) cnfa->bos[0]);
	if (cnfa->bos[1] != COLORLESS)
		fprintf(f, ", bol [%ld]", (long) cnfa->bos[1]);
	if (cnfa->eos[0] != COLORLESS)
		fprintf(f, ", eos [%ld]", (long) cnfa->eos[0]);
	if (cnfa->eos[1] != COLORLESS)
		fprintf(f, ", eol [%ld]", (long) cnfa->eos[1]);
	if (cnfa->flags & HASLACONS)
		fprintf(f, ", haslacons");
	if (cnfa->flags & MATCHALL)
	{
		fprintf(f, ", minmatchall %d", cnfa->minmatchall);
		if (cnfa->maxmatchall == DUPINF)
			fprintf(f, ", maxmatchall inf");
		else
			fprintf(f, ", maxmatchall %d", cnfa->maxmatchall);
	}
	fprintf(f, "\n");
	for (st = 0; st < cnfa->nstates; st++)
		dumpcstate(st, cnfa, f);
	fflush(f);
}
#endif

#ifdef REG_DEBUG				/* subordinates of dumpcnfa */

/*
 * dumpcstate - dump a compacted-NFA state in human-readable form
 */
static void
dumpcstate(int st,
		   struct cnfa *cnfa,
		   FILE *f)
{
	struct carc *ca;
	int			pos;

	fprintf(f, "%d%s", st, (cnfa->stflags[st] & CNFA_NOPROGRESS) ? ":" : ".");
	pos = 1;
	for (ca = cnfa->states[st]; ca->co != COLORLESS; ca++)
	{
		if (ca->co == RAINBOW)
			fprintf(f, "\t[*]->%d", ca->to);
		else if (ca->co < cnfa->ncolors)
			fprintf(f, "\t[%ld]->%d", (long) ca->co, ca->to);
		else
			fprintf(f, "\t:%ld:->%d", (long) (ca->co - cnfa->ncolors), ca->to);
		if (pos == 5)
		{
			fprintf(f, "\n");
			pos = 1;
		}
		else
			pos++;
	}
	if (ca == cnfa->states[st] || pos != 1)
		fprintf(f, "\n");
	fflush(f);
}

#endif							/* REG_DEBUG */