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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.
 *
 * 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 *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) {
      return NULL;
    }

    nfa->states = NULL;
    nfa->slast = NULL;
    nfa->free = NULL;
    nfa->nstates = 0;
    nfa->cm = cm;
    nfa->v = v;
    nfa->size = 0;
    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;
}

/*
 - TooManyStates - checks if the max states exceeds the compile-time value
 ^ static int TooManyStates(struct nfa *);
 */
static int
TooManyStates(
    struct nfa *nfa)
{
    struct nfa *parent = nfa->parent;
    size_t sz = nfa->size;

    while (parent != NULL) {
      sz = parent->size;
      parent = parent->parent;
    }
    if (sz > REG_MAX_STATES) {
      return 1;
    }
    return 0;
}

/*
 - IncrementSize - increases the tracked size of the NFA and its parents.
 ^ static void IncrementSize(struct nfa *);
 */
static void
IncrementSize(
    struct nfa *nfa)
{
    struct nfa *parent = nfa->parent;

    nfa->size++;
    while (parent != NULL) {
      parent->size++;
      parent = parent->parent;
    }
}

/*
 - DecrementSize - increases the tracked size of the NFA and its parents.
 ^ static void DecrementSize(struct nfa *);
 */
static void
DecrementSize(
    struct nfa *nfa)
{
    struct nfa *parent = nfa->parent;

    nfa->size--;
    while (parent != NULL) {
      parent->size--;
      parent = parent->parent;
    }
}

/*
 - 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 (TooManyStates(nfa)) {
      /* XXX: add specific error for this */
      NERR(REG_ETOOBIG);
      return NULL;
    }
    if (nfa->free != NULL) {
      s = nfa->free;
      nfa->free = s->next;
    } else {
      s = (struct state *) MALLOC(sizeof(struct state));
      if (s == NULL) {
          NERR(REG_ESPACE);
          return NULL;
      }
      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;

    /*
     * Track the current size and the parent size.
     */

    IncrementSize(nfa);
    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;
    DecrementSize(nfa);
}

/*
 - 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);
    }
    s->ins = NULL;
    s->outs = NULL;
    s->next = NULL;
    FREE(s);
}

/*
 - newarc - set up a new arc within an NFA
 ^ static VOID newarc(struct nfa *, int, pcolor, struct state *,
 ^    struct state *);
 */
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 duplicates.
     */

    for (a=from->outs ; a!=NULL ; a=a->outchain) {
      if (a->to == to && a->co == co && a->type == t) {
          return;
      }
    }

    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. Not only
     * is this easier, it has the very useful side effect that deleting the
     * most-recently-added arc is the cheapest case rather than the most
     * expensive one.
     */

    a->inchain = to->ins;
    to->ins = a;
    a->outchain = from->outs;
    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 = (struct arcbatch *)
            MALLOC(sizeof(struct arcbatch));
      int i;

      if (newAb == NULL) {
          NERR(REG_ESPACE);
          return NULL;
      }
      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 *a;

    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);
    assert(from->outs != NULL);
    a = from->outs;
    if (a == victim) {        /* simple case: first in chain */
      from->outs = victim->outchain;
    } else {
      for (; a!=NULL && a->outchain!=victim ; a=a->outchain) {
          continue;
      }
      assert(a != NULL);
      a->outchain = victim->outchain;
    }
    from->nouts--;

    /*
     * Take it off target's in-chain.
     */

    assert(to != NULL);
    assert(to->ins != NULL);
    a = to->ins;
    if (a == victim) {        /* simple case: first in chain */
      to->ins = victim->inchain;
    } else {
      for (; a->inchain!=victim ; a=a->inchain) {
          assert(a->inchain != NULL);
          continue;
      }
      a->inchain = victim->inchain;
    }
    to->nins--;

    /*
     * Clean up and place on free list.
     */

    victim->type = 0;
    victim->from = NULL;      /* precautions... */
    victim->to = NULL;
    victim->inchain = NULL;
    victim->outchain = NULL;
    victim->freechain = from->free;
    from->free = victim;
}

/*
 - 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);
}

/*
 - 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 desire
 * for duplicate suppression, which makes it easier to just make new
 * ones to exploit the suppression built into newarc.
 ^ static VOID moveins(struct nfa *, struct state *, struct state *);
 */
static void
moveins(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    struct arc *a;

    assert(oldState != newState);

    while ((a = oldState->ins) != NULL) {
      cparc(nfa, a, a->from, newState);
      freearc(nfa, a);
    }
    assert(oldState->nins == 0);
    assert(oldState->ins == NULL);
}

/*
 - copyins - copy all in arcs of a state to another state
 ^ static VOID copyins(struct nfa *, struct state *, struct state *);
 */
static void
copyins(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    struct arc *a;

    assert(oldState != newState);

    for (a=oldState->ins ; a!=NULL ; a=a->inchain) {
      cparc(nfa, a, a->from, newState);
    }
}

/*
 - moveouts - move all out arcs of a state to another state
 ^ static VOID moveouts(struct nfa *, struct state *, struct state *);
 */
static void
moveouts(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    struct arc *a;

    assert(oldState != newState);

    while ((a = oldState->outs) != NULL) {
      cparc(nfa, a, newState, a->to);
      freearc(nfa, a);
    }
}

/*
 - copyouts - copy all out arcs of a state to another state
 ^ static VOID copyouts(struct nfa *, struct state *, struct state *);
 */
static void
copyouts(
    struct nfa *nfa,
    struct state *oldState,
    struct state *newState)
{
    struct arc *a;

    assert(oldState != newState);

    for (a=oldState->outs ; a!=NULL ; a=a->outchain) {
      cparc(nfa, a, 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);
    /* 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 */
{
    struct arc *a;

    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, NULL);
      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 *);
 */
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");
    }
    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 */
    return analyze(nfa);      /* and analysis */
}

/*
 - pullback - pull back constraints backward to (with luck) 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;
    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;
          for (a=s->outs ; a!=NULL && !NISERR() ; a=nexta) {
            nexta = a->outchain;
            if (a->type == '^' || a->type == BEHIND) {
                if (pull(nfa, a)) {
                  progress = 1;
                }
            }
            assert(nexta == NULL || s->no != FREESTATE);
          }
      }
      if (progress && f != NULL) {
          dumpnfa(nfa, f);
      }
    } while (progress && !NISERR());
    if (NISERR()) {
      return;
    }

    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
 * A significant property of this function is that it deletes at most
 * one state -- the constraint's from state -- and only if the constraint
 * was that state's last outarc.
 ^ static int pull(struct nfa *, struct arc *);
 */
static int              /* 0 couldn't, 1 could */
pull(
    struct nfa *nfa,
    struct arc *con)
{
    struct state *from = con->from;
    struct state *to = con->to;
    struct arc *a;
    struct arc *nexta;
    struct state *s;

    if (from == to) {         /* circular constraint is pointless */
      freearc(nfa, con);
      return 1;
    }
    if (from->flag) {         /* can't pull back beyond start */
      return 0;
    }
    if (from->nins == 0) {    /* unreachable */
      freearc(nfa, con);
      return 1;
    }

    /*
     * DGP 2007-11-15: Cloning a state with a circular constraint on its list
     * of outs can lead to trouble [Bug 1810038], so get rid of them first.
     */

    for (a = from->outs; a != NULL; a = nexta) {
      nexta = a->outchain;
      switch (a->type) {
      case '^':
      case '$':
      case BEHIND:
      case AHEAD:
          if (from == a->to) {
            freearc(nfa, a);
          }
          break;
      }
    }

    /*
     * First, clone from state if necessary to avoid other outarcs.
     */

    if (from->nouts > 1) {
      s = newstate(nfa);
      if (NISERR()) {
          return 0;
      }
      assert(to != from);     /* con is not an inarc */
      copyins(nfa, from, s);  /* duplicate inarcs */
      cparc(nfa, con, s, to); /* move constraint arc */
      freearc(nfa, con);
      from = s;
      con = from->outs;
    }
    assert(from->nouts == 1);

    /*
     * Propagate the constraint into the from state's inarcs.
     */

    for (a=from->ins ; a!=NULL ; 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 */
          s = newstate(nfa);
          if (NISERR()) {
            return 0;
          }
          cparc(nfa, a, s, to);     /* anticipate move */
          cparc(nfa, con, a->from, s);
          if (NISERR()) {
            return 0;
          }
          freearc(nfa, a);
          break;
      default:
          assert(NOTREACHED);
          break;
      }
    }

    /*
     * Remaining inarcs, if any, incorporate the constraint.
     */

    moveins(nfa, from, to);
    dropstate(nfa, from);     /* will free the constraint */
    return 1;
}

/*
 - pushfwd - push forward constraints forward to (with luck) 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;
    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;
          for (a = s->ins; a != NULL && !NISERR(); a = nexta) {
            nexta = a->inchain;
            if (a->type == '$' || a->type == AHEAD) {
                if (push(nfa, a)) {
                  progress = 1;
                }
            }
            assert(nexta == NULL || s->no != FREESTATE);
          }
      }
      if (progress && f != NULL) {
          dumpnfa(nfa, f);
      }
    } while (progress && !NISERR());
    if (NISERR()) {
      return;
    }

    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
 * A significant property of this function is that it deletes at most
 * one state -- the constraint's to state -- and only if the constraint
 * was that state's last inarc.
 ^ static int push(struct nfa *, struct arc *);
 */
static int              /* 0 couldn't, 1 could */
push(
    struct nfa *nfa,
    struct arc *con)
{
    struct state *from = con->from;
    struct state *to = con->to;
    struct arc *a;
    struct arc *nexta;
    struct state *s;

    if (to == from) {         /* circular constraint is pointless */
      freearc(nfa, con);
      return 1;
    }
    if (to->flag) {           /* can't push forward beyond end */
      return 0;
    }
    if (to->nouts == 0) {     /* dead end */
      freearc(nfa, con);
      return 1;
    }

    /*
     * DGP 2007-11-15: Here we duplicate the same protections as appear
     * in pull() above to avoid troubles with cloning a state with a
     * circular constraint on its list of ins.  It is not clear whether
     * this is necessary, or is protecting against a "can't happen".
     * Any test case that actually leads to a freearc() call here would
     * be a welcome addition to the test suite.
     */

    for (a = to->ins; a != NULL; a = nexta) {
      nexta = a->inchain;
      switch (a->type) {
      case '^':
      case '$':
      case BEHIND:
      case AHEAD:
          if (a->from == to) {
            freearc(nfa, a);
          }
          break;
      }
    }
    /*
     * First, clone to state if necessary to avoid other inarcs.
     */

    if (to->nins > 1) {
      s = newstate(nfa);
      if (NISERR()) {
          return 0;
      }
      copyouts(nfa, to, s);   /* duplicate outarcs */
      cparc(nfa, con, from, s);     /* move constraint */
      freearc(nfa, con);
      to = s;
      con = to->ins;
    }
    assert(to->nins == 1);

    /*
     * Propagate the constraint into the to state's outarcs.
     */

    for (a = to->outs; a != NULL; 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 */
          s = newstate(nfa);
          if (NISERR()) {
            return 0;
          }
          cparc(nfa, con, s, a->to);      /* anticipate move */
          cparc(nfa, a, from, s);
          if (NISERR()) {
            return 0;
          }
          freearc(nfa, a);
          break;
      default:
          assert(NOTREACHED);
          break;
      }
    }

    /*
     * Remaining outarcs, if any, incorporate the constraint.
     */

    moveouts(nfa, to, from);
    dropstate(nfa, to);       /* will free the constraint */
    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 *nexts;
    struct arc *a;
    struct arc *nexta;
    int progress;

    /*
     * Find and eliminate empties until there are no more.
     */

    do {
      progress = 0;
      for (s = nfa->states; s != NULL && !NISERR()
            && s->no != FREESTATE; s = nexts) {
          nexts = s->next;
          for (a = s->outs; a != NULL && !NISERR(); a = nexta) {
            nexta = a->outchain;
            if (a->type == EMPTY && unempty(nfa, a)) {
                progress = 1;
            }
            assert(nexta == NULL || s->no != FREESTATE);
          }
      }
      if (progress && f != NULL) {
          dumpnfa(nfa, f);
      }
    } while (progress && !NISERR());
}

/*
 - unempty - optimize out an EMPTY arc, if possible
 * Actually, as it stands this function always succeeds, but the return value
 * is kept with an eye on possible future changes.
 ^ static int unempty(struct nfa *, struct arc *);
 */
static int              /* 0 couldn't, 1 could */
unempty(
    struct nfa *nfa,
    struct arc *a)
{
    struct state *from = a->from;
    struct state *to = a->to;
    int usefrom;        /* work on from, as opposed to to? */

    assert(a->type == EMPTY);
    assert(from != nfa->pre && to != nfa->post);

    if (from == to) {         /* vacuous loop */
      freearc(nfa, a);
      return 1;
    }

    /*
     * Decide which end to work on.
     */

    usefrom = 1;        /* default: attack from */
    if (from->nouts > to->nins) {
      usefrom = 0;
    } else if (from->nouts == to->nins) {
      /*
       * Decide on secondary issue: move/copy fewest arcs.
       */

      if (from->nins > to->nouts) {
          usefrom = 0;
      }
    }

    freearc(nfa, a);
    if (usefrom) {
      if (from->nouts == 0) {
          /*
           * Was the state's only outarc.
           */

          moveins(nfa, from, to);
          freestate(nfa, from);
      } else {
          copyins(nfa, from, to);
      }
    } else {
      if (to->nins == 0) {
          /*
           * Was the state's only inarc.
           */

          moveouts(nfa, to, from);
          freestate(nfa, to);
      } else {
          copyouts(nfa, to, from);
      }
    }

    return 1;
}

/*
 - 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 - compact 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 += 1 + s->nouts + 1;
      /* 1 as a fake for flags, nouts for arcs, 1 as endmarker */
    }

    cnfa->states = (struct carc **) MALLOC(nstates * sizeof(struct carc *));
    cnfa->arcs = (struct carc *) MALLOC(narcs * sizeof(struct carc));
    if (cnfa->states == NULL || cnfa->arcs == NULL) {
      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->states[s->no] = ca;
      ca->co = 0;       /* clear and skip flags "arc" */
      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:
            assert(NOTREACHED);
            break;
          }
      }
      carcsort(first, ca-1);
      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->states[a->to->no]->co = 1;
    }
    cnfa->states[nfa->pre->no]->co = 1;
}

/*
 - carcsort - sort compacted-NFA arcs by color
 * Really dumb algorithm, but if the list is long enough for that to matter,
 * you're in real trouble anyway.
 ^ static VOID carcsort(struct carc *, struct carc *);
 */
static void
carcsort(
    struct carc *first,
    struct carc *last)
{
    struct carc *p;
    struct carc *q;
    struct carc tmp;

    if (last - first <= 1) {
      return;
    }

    for (p = first; p <= last; p++) {
      for (q = p; q <= last; q++) {
          if (p->co > q->co || (p->co == q->co && p->to > q->to)) {
            assert(p != q);
            tmp = *p;
            *p = *q;
            *q = tmp;
          }
      }
    }
}

/*
 - 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->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;

    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);
    }
    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;

    assert(s->nouts > 0);
    /* printing arcs in reverse order is usually clearer */
    pos = dumprarcs(s->outs, s, f, 1);
    if (pos != 1) {
      fprintf(f, "\n");
    }
}

/*
 - dumprarcs - dump remaining outarcs, recursively, in reverse order
 ^ static int dumprarcs(struct arc *, struct state *, FILE *, int);
 */
static int              /* resulting print position */
dumprarcs(
    struct arc *a,
    struct state *s,
    FILE *f,
    int pos)                  /* initial print position */
{
    if (a->outchain != NULL) {
      pos = dumprarcs(a->outchain, s, f, pos);
    }
    dumparc(a, s, f);
    if (pos == 5) {
      fprintf(f, "\n");
      pos = 1;
    } else {
      pos++;
    }
    return pos;
}

/*
 - 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->states[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 carc *, struct cnfa *, FILE *);
 */
static void
dumpcstate(
    int st,
    struct carc *ca,
    struct cnfa *cnfa,
    FILE *f)
{
    int i;
    int pos;

    fprintf(f, "%d%s", st, (ca[0].co) ? ":" : ".");
    pos = 1;
    for (i = 1; ca[i].co != COLORLESS; i++) {
      if (ca[i].co < cnfa->ncolors) {
          fprintf(f, "\t[%ld]->%d", (long) ca[i].co, ca[i].to);
      } else {
          fprintf(f, "\t:%ld:->%d", (long) ca[i].co-cnfa->ncolors,ca[i].to);
      }
      if (pos == 5) {
          fprintf(f, "\n");
          pos = 1;
      } else {
          pos++;
      }
    }
    if (i == 1 || pos != 1) {
      fprintf(f, "\n");
    }
    fflush(f);
}

/*
 ^ #endif
 */
#endif                        /* ifdef REG_DEBUG */

/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */

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