regc_nfa.c 82.3 KB
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/*
 * 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.
 *
 * 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))
#define STACK_TOO_DEEP(x) (0)
#define CANCEL_REQUESTED(x) (0)
#define REG_CANCEL 777

/*
 - newnfa - set up an NFA
 ^ static struct nfa *newnfa(struct vars *, struct colormap *, struct 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;
    }

    nfa->states = NULL;
    nfa->slast = NULL;
    nfa->free = NULL;
    nfa->nstates = 0;
    nfa->cm = cm;
    nfa->v = v;
    nfa->bos[0] = nfa->bos[1] = COLORLESS;
    nfa->eos[0] = nfa->eos[1] = COLORLESS;
    nfa->parent = parent;	/* Precedes newfstate so parent is valid. */
    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 *);
 */
static void
freenfa(
    struct nfa *nfa)
{
    struct state *s;

    while ((s = nfa->states) != NULL) {
	s->nins = s->nouts = 0;	/* don't worry about arcs */
	freestate(nfa, s);
    }
    while ((s = nfa->free) != NULL) {
	nfa->free = s->next;
	destroystate(nfa, s);
    }

    nfa->slast = NULL;
    nfa->nstates = -1;
    nfa->pre = NULL;
    nfa->post = NULL;
    FREE(nfa);
}

/*
 - newstate - allocate an NFA state, with zero flag value
 ^ static struct state *newstate(struct nfa *);
 */
static struct state *		/* NULL on error */
newstate(
    struct nfa *nfa)
{
    struct state *s;

    if (nfa->free != NULL) {
	s = nfa->free;
	nfa->free = s->next;
    } else {
	if (nfa->v->spaceused >= REG_MAX_COMPILE_SPACE) {
	    NERR(REG_ETOOBIG);
	    return NULL;
	}
	s = (struct state *) MALLOC(sizeof(struct state));
	if (s == NULL) {
	    NERR(REG_ESPACE);
	    return NULL;
	}
	nfa->v->spaceused += sizeof(struct state);
	s->oas.next = NULL;
	s->free = NULL;
	s->noas = 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 *newfstate(struct nfa *, int flag);
 */
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 *, struct state *);
 */
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 *, struct state *);
 */
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->free;	/* don't delete it, put it on the free list */
    nfa->free = s;
}

/*
 - destroystate - really get rid of an already-freed state
 ^ static void destroystate(struct nfa *, struct state *);
 */
static void
destroystate(
    struct nfa *nfa,
    struct state *s)
{
    struct arcbatch *ab;
    struct arcbatch *abnext;

    assert(s->no == FREESTATE);
    for (ab=s->oas.next ; ab!=NULL ; ab=abnext) {
	abnext = ab->next;
	FREE(ab);
	nfa->v->spaceused -= sizeof(struct arcbatch);
    }
    s->ins = NULL;
    s->outs = NULL;
    s->next = NULL;
    FREE(s);
    nfa->v->spaceused -= sizeof(struct state);
}

/*
 - newarc - set up a new arc within an NFA
 ^ static void newarc(struct nfa *, int, pcolor, struct state *,
 ^	struct state *);
 */
/*
 * This function checks to make sure that no duplicate arcs are created.
 * In general we never want duplicates.
 */
static void
newarc(
    struct nfa *nfa,
    int t,
    pcolor co,
    struct state *from,
    struct state *to)
{
    struct arc *a;

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

    /* 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,
    pcolor co,
    struct state * from,
    struct state * to)
{
    struct arc *a;

    /* the arc is physically allocated within its from-state */
    a = allocarc(nfa, from);
    if (NISERR()) {
	return;
    }
    assert(a != NULL);

    a->type = t;
    a->co = (color) 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 out-arc within a state
 ^ static struct arc *allocarc(struct nfa *, struct state *);
 */
static struct arc *		/* NULL for failure */
allocarc(
    struct nfa *nfa,
    struct state *s)
{
    struct arc *a;

    /*
     * Shortcut
     */

    if (s->free == NULL && s->noas < ABSIZE) {
	a = &s->oas.a[s->noas];
	s->noas++;
	return a;
    }

    /*
     * if none at hand, get more
     */

    if (s->free == NULL) {
	struct arcbatch *newAb;
	int i;

	if (nfa->v->spaceused >= REG_MAX_COMPILE_SPACE) {
	    NERR(REG_ETOOBIG);
	    return NULL;
	}
	newAb = (struct arcbatch *) MALLOC(sizeof(struct arcbatch));
	if (newAb == NULL) {
	    NERR(REG_ESPACE);
	    return NULL;
	}
	nfa->v->spaceused += sizeof(struct arcbatch);
	newAb->next = s->oas.next;
	s->oas.next = newAb;

	for (i=0 ; i<ABSIZE ; i++) {
	    newAb->a[i].type = 0;
	    newAb->a[i].freechain = &newAb->a[i+1];
	}
	newAb->a[ABSIZE-1].freechain = NULL;
	s->free = &newAb->a[0];
    }
    assert(s->free != NULL);

    a = s->free;
    s->free = a->freechain;
    return a;
}

/*
 - freearc - free an arc
 ^ static void freearc(struct nfa *, struct 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 from-state'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 = from->free;
    from->free = victim;
}

/*
 * changearctarget - flip an arc to have a different to state
 *
 * Caller must have verified that there is no pre-existing duplicate arc.
 *
 * Note that because we store arcs in their from state, we can't easily have
 * a similar changearcsource function.
 */
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 *);
 */
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 *, int, pcolor);
 */
static struct arc *
findarc(
    struct state *s,
    int type,
    pcolor 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 *, struct arc *, struct state *,
 ^ 	struct state *);
 */
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.
 *
 ^ static void moveins(struct nfa *, struct state *, struct state *);
 */
static void
moveins(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    assert(oldState != newState);

    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.
	 */
	if (CANCEL_REQUESTED(nfa->v->re)) {
	    NERR(REG_CANCEL);
	    return;
	}

	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
846
 ^ static void copyins(struct nfa *, struct state *, struct state *, int);
847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102
 */
static void
copyins(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    assert(oldState != newState);

    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.
	 */
	if (CANCEL_REQUESTED(nfa->v->re)) {
	    NERR(REG_CANCEL);
	    return;
	}

	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);
	}
    }
}

/*
 * 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.
     */
    if (CANCEL_REQUESTED(nfa->v->re)) {
	NERR(REG_CANCEL);
	return;
    }

    /* 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
 ^ static void moveouts(struct nfa *, struct state *, struct state *);
 */
static void
moveouts(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    assert(oldState != newState);

    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 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.
	 */
	if (CANCEL_REQUESTED(nfa->v->re)) {
	    NERR(REG_CANCEL);
	    return;
	}

	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);
		    freearc(nfa, a);
		    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;
	    createarc(nfa, a->type, a->co, newState, a->to);
	    freearc(nfa, a);
	}
    }

    assert(oldState->nouts == 0);
    assert(oldState->outs == NULL);
}

/*
 - copyouts - copy out arcs of a state to another state
1103
 ^ static void copyouts(struct nfa *, struct state *, struct state *, int);
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 */
static void
copyouts(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    assert(oldState != newState);

    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.
	 */
	if (CANCEL_REQUESTED(nfa->v->re)) {
	    NERR(REG_CANCEL);
	    return;
	}

	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);
	}
    }
}

/*
 - cloneouts - copy out arcs of a state to another state pair, modifying type
 ^ static void cloneouts(struct nfa *, struct state *, struct state *,
 ^ 	struct state *, int);
 */
static void
cloneouts(
    struct nfa *nfa,
    struct state *old,
    struct state *from,
    struct state *to,
    int type)
{
    struct arc *a;

    assert(old != from);

    for (a=old->outs ; a!=NULL ; a=a->outchain) {
	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 *, struct state *, struct state *);
 */
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);
    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 *, struct state *, struct state *);
 */
static void
deltraverse(
    struct nfa *nfa,
    struct state *leftend,
    struct state *s)
{
    struct arc *a;
    struct state *to;

    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);
	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 *, struct state *, struct state *,
 ^ 	struct state *, struct state *);
 */
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, 0);
    /* done, except for clearing out the tmp pointers */

    stop->tmp = NULL;
    cleartraverse(nfa, start);
}

/*
 - duptraverse - recursive heart of dupnfa
 ^ static void duptraverse(struct nfa *, struct state *, struct state *);
 */
static void
duptraverse(
    struct nfa *nfa,
    struct state *s,
    struct state *stmp,		/* s's duplicate, or NULL */
    int depth)
{
    struct arc *a;

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

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

    /*
     * Arbitrary depth limit. Needs tuning, but this value is sufficient to
     * make all normal tests (not reg-33.14) pass.
     */
#ifndef DUPTRAVERSE_MAX_DEPTH
#define DUPTRAVERSE_MAX_DEPTH 15000
#endif

    if (depth++ > DUPTRAVERSE_MAX_DEPTH) {
	NERR(REG_ESPACE);
    }

    for (a=s->outs ; a!=NULL && !NISERR() ; a=a->outchain) {
	duptraverse(nfa, a->to, NULL, depth);
	if (NISERR()) {
	    break;
	}
	assert(a->to->tmp != NULL);
	cparc(nfa, a, s->tmp, a->to->tmp);
    }
}

/*
 - cleartraverse - recursive cleanup for algorithms that leave tmp ptrs set
 ^ static void cleartraverse(struct nfa *, struct state *);
 */
static void
cleartraverse(
    struct nfa *nfa,
    struct state *s)
{
    struct arc *a;

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

    for (a=s->outs ; a!=NULL ; a=a->outchain) {
	cleartraverse(nfa, a->to);
    }
}

/*
 - specialcolors - fill in special colors for an NFA
 ^ static void specialcolors(struct 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
 ^ static long optimize(struct nfa *, FILE *);
 */

 /*
  * 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 */
{
    int verbose = (f != NULL) ? 1 : 0;

    if (verbose) {
	fprintf(f, "\ninitial cleanup:\n");
    }
    cleanup(nfa);		/* may simplify situation */
    if (verbose) {
	dumpnfa(nfa, f);
    }
    if (verbose) {
	fprintf(f, "\nempties:\n");
    }
    fixempties(nfa, f);		/* get rid of EMPTY arcs */
    if (verbose) {
	fprintf(f, "\nconstraints:\n");
    }
    fixconstraintloops(nfa, f);	/* get rid of constraint loops */
    pullback(nfa, f);		/* pull back constraints backward */
    pushfwd(nfa, f);		/* push fwd constraints forward */
    if (verbose) {
	fprintf(f, "\nfinal cleanup:\n");
    }
    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 *, FILE *);
 */
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;
		    }
		}
		assert(nexta == NULL || s->no != FREESTATE);
	    }
	    /* 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 *, struct arc *);
 */
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(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;
	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 *, FILE *);
 */
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 *, struct arc *);
 */
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(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;
	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
 ^ static int combine(struct arc *, struct arc *);
 */
static int
combine(
    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('$', PLAIN):
	return INCOMPATIBLE;
	break;
    case CA(AHEAD, PLAIN):	/* color constraints meet colors */
    case CA(BEHIND, PLAIN):
	if (con->co == a->co) {
	    return SATISFIED;
	}
	return INCOMPATIBLE;
	break;
    case CA('^', '^'):		/* collision, similar constraints */
    case CA('$', '$'):
    case CA(AHEAD, AHEAD):
    case CA(BEHIND, BEHIND):
	if (con->co == a->co) {	/* true duplication */
	    return SATISFIED;
	}
	return INCOMPATIBLE;
	break;
    case CA('^', BEHIND):	/* collision, dissimilar constraints */
    case CA(BEHIND, '^'):
    case CA('$', 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 *, FILE *);
 */
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;
	/* 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;
    }

    /*
     * 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, and in practice will be less than that.
 ^ static struct state *emptyreachable(struct state *, struct state *);
 */
static struct state *
emptyreachable(
    struct nfa *nfa,
    struct state *s,
    struct state *lastfound,
    struct arc **inarcsorig)
{
    struct arc *a;

    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, and in practice will be a lot less than that.
 */
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);
    }
}

/*
 - cleanup - clean up NFA after optimizations
 ^ static void cleanup(struct nfa *);
 */
static void
cleanup(
    struct nfa *nfa)
{
    struct state *s;
    struct state *nexts;
    int n;

    /*
     * Clear out unreachable or dead-end states. Use pre to mark reachable,
     * then post to mark can-reach-post.
     */

    markreachable(nfa, nfa->pre, NULL, nfa->pre);
    markcanreach(nfa, nfa->post, nfa->pre, nfa->post);
    for (s = nfa->states; s != NULL; s = nexts) {
	nexts = s->next;
	if (s->tmp != nfa->post && !s->flag) {
	    dropstate(nfa, s);
	}
    }
    assert(nfa->post->nins == 0 || nfa->post->tmp == nfa->post);
    cleartraverse(nfa, nfa->pre);
    assert(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 *, struct state *, struct state *,
 ^ 	struct state *);
 */
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;

    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 *, struct state *, struct state *,
 ^ 	struct state *);
 */
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;

    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 analyze(struct nfa *);
 */
static long			/* re_info bits to be ORed in */
analyze(
    struct nfa *nfa)
{
    struct arc *a;
    struct arc *aa;

    if (nfa->pre->outs == NULL) {
	return REG_UIMPOSSIBLE;
    }
    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;
}

/*
 - compact - construct the compact representation of an NFA
 ^ static void compact(struct nfa *, struct cnfa *);
 */
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 = 0;

    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);
		ca->co = (color) (cnfa->ncolors + a->co);
		ca->to = a->to->no;
		ca++;
		cnfa->flags |= HASLACONS;
		break;
	    default:
		NERR(REG_ASSERT);
		break;
	    }
	}
	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 *, struct carc *);
 */
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;
    }
    return 0;
}

/*
 - freecnfa - free a compacted NFA
 ^ static void freecnfa(struct cnfa *);
 */
static void
freecnfa(
    struct cnfa *cnfa)
{
    assert(cnfa->nstates != 0);	/* not empty already */
    cnfa->nstates = 0;
    FREE(cnfa->stflags);
    FREE(cnfa->states);
    FREE(cnfa->arcs);
}

/*
 - dumpnfa - dump an NFA in human-readable form
 ^ static void dumpnfa(struct nfa *, FILE *);
 */
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]);
    }
    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 */
/*
 ^ #ifdef REG_DEBUG
 */

/*
 - dumpstate - dump an NFA state in human-readable form
 ^ static void dumpstate(struct state *, FILE *);
 */
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);
    }
    fflush(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);
	}
    }
}

/*
 - dumparcs - dump out-arcs in human-readable form
 ^ static void dumparcs(struct state *, FILE *);
 */
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 *, struct state *, FILE *);
 */
static void
dumparc(
    struct arc *a,
    struct state *s,
    FILE *f)
{
    struct arc *aa;
    struct arcbatch *ab;

    fprintf(f, "\t");
    switch (a->type) {
    case PLAIN:
	fprintf(f, "[%ld]", (long) a->co);
	break;
    case AHEAD:
	fprintf(f, ">%ld>", (long) a->co);
	break;
    case BEHIND:
	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;
    default:
	fprintf(f, "0x%x/0%lo", a->type, (long) a->co);
	break;
    }
    if (a->from != s) {
	fprintf(f, "?%d?", a->from->no);
    }
    for (ab = &a->from->oas; ab != NULL; ab = ab->next) {
	for (aa = &ab->a[0]; aa < &ab->a[ABSIZE]; aa++) {
	    if (aa == a) {
		break;		/* NOTE BREAK OUT */
	    }
	}
	if (aa < &ab->a[ABSIZE]) {	/* propagate break */
	    break;		/* NOTE BREAK OUT */
	}
    }
    if (ab == NULL) {
	fprintf(f, "?!?");	/* not in allocated space */
    }
    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
 */
#endif				/* ifdef REG_DEBUG */

/*
 - dumpcnfa - dump a compacted NFA in human-readable form
 ^ static void dumpcnfa(struct cnfa *, FILE *);
 */
static void
dumpcnfa(
    struct cnfa *cnfa,
    FILE *f)
{
#ifdef REG_DEBUG
    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");
    }
    fprintf(f, "\n");
    for (st = 0; st < cnfa->nstates; st++) {
	dumpcstate(st, cnfa, f);
    }
    fflush(f);
#endif
}

#ifdef REG_DEBUG		/* subordinates of dumpcnfa */
/*
 ^ #ifdef REG_DEBUG
 */

/*
 - dumpcstate - dump a compacted-NFA state in human-readable form
 ^ static void dumpcstate(int, struct cnfa *, FILE *);
 */
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 < 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
 */
#endif				/* ifdef REG_DEBUG */

/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */