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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.
 *
 * $PostgreSQL: pgsql/src/backend/regex/regc_nfa.c,v 1.7 2009/06/11 14:49:01 momjian Exp $
 *
 *
 * One or two things that technically ought to be in here
 * are actually in color.c, thanks to some incestuous relationships in
 * the color chains.
 */

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


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

      nfa = (struct nfa *) MALLOC(sizeof(struct nfa));
      if (nfa == NULL)
            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 * 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 * nfa)
{
      struct nfa *parent = nfa->parent;

      nfa->size++;
      while (parent != NULL)
      {
            parent->size++;
            parent = parent->parent;
      }
}

/*
 * DecrementSize - decreases the tracked size of the NFA and its parents.
 */
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 * 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 *               /* NULL on error */
newstate(struct nfa * nfa)
{
      struct state *s;

      if (TooManyStates(nfa))
      {
            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 *               /* NULL on error */
newfstate(struct nfa * nfa, int flag)
{
      struct state *s;

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

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

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

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

      s->no = FREESTATE;
      s->flag = 0;
      if (s->next != NULL)
            s->next->prev = s->prev;
      else
      {
            assert(s == nfa->slast);
            nfa->slast = s->prev;
      }
      if (s->prev != NULL)
            s->prev->next = s->next;
      else
      {
            assert(s == nfa->states);
            nfa->states = s->next;
      }
      s->prev = NULL;
      s->next = nfa->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 * 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 * 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 *                       /* 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;

            newAb = (struct arcbatch *) MALLOC(sizeof(struct arcbatch));
            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 * 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 != NULL && a->inchain != victim; a = a->inchain)
                  continue;
            assert(a != NULL);
            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 * 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 * 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 * 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 * 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 * 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 * 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 * 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 * 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 * 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 * nfa,
         struct state * start,      /* duplicate of subNFA starting here */
         struct state * stop,       /* and stopping here */
         struct state * from,       /* stringing duplicate from here */
         struct state * to)         /* to here */
{
      if (start == stop)
      {
            newarc(nfa, EMPTY, 0, from, to);
            return;
      }

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

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

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

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

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

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

/*
 * cleartraverse - recursive cleanup for algorithms that leave tmp ptrs set
 */
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 * 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                               /* re_info bits */
optimize(struct nfa * nfa,
             FILE *f)                     /* for debug output; NULL none */
{
#ifdef REG_DEBUG
      int               verbose = (f != NULL) ? 1 : 0;

      if (verbose)
            fprintf(f, "\ninitial cleanup:\n");
#endif
      cleanup(nfa);                       /* may simplify situation */
#ifdef REG_DEBUG
      if (verbose)
            dumpnfa(nfa, f);
      if (verbose)
            fprintf(f, "\nempties:\n");
#endif
      fixempties(nfa, f);                 /* get rid of EMPTY arcs */
#ifdef REG_DEBUG
      if (verbose)
            fprintf(f, "\nconstraints:\n");
#endif
      pullback(nfa, f);             /* pull back constraints backward */
      pushfwd(nfa, f);              /* push fwd constraints forward */
#ifdef REG_DEBUG
      if (verbose)
            fprintf(f, "\nfinal cleanup:\n");
#endif
      cleanup(nfa);                       /* final tidying */
      return analyze(nfa);          /* and analysis */
}

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

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

      fprintf(f, "%d%s%c", s->no, (s->tmp != NULL) ? "T" : "",
                  (s->flag) ? s->flag : '.');
      if (s->prev != NULL && s->prev->next != s)
            fprintf(f, "\tstate chain bad\n");
      if (s->nouts == 0)
            fprintf(f, "\tno out arcs\n");
      else
            dumparcs(s, f);
      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 * 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                                /* 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 * 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   /* REG_DEBUG */

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

      fprintf(f, "pre %d, post %d", cnfa->pre, cnfa->post);
      if (cnfa->bos[0] != COLORLESS)
            fprintf(f, ", bos [%ld]", (long) cnfa->bos[0]);
      if (cnfa->bos[1] != COLORLESS)
            fprintf(f, ", bol [%ld]", (long) cnfa->bos[1]);
      if (cnfa->eos[0] != COLORLESS)
            fprintf(f, ", eos [%ld]", (long) cnfa->eos[0]);
      if (cnfa->eos[1] != COLORLESS)
            fprintf(f, ", eol [%ld]", (long) cnfa->eos[1]);
      if (cnfa->flags & HASLACONS)
            fprintf(f, ", haslacons");
      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 */

/*
 * dumpcstate - dump a compacted-NFA state in human-readable form
 */
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   /* REG_DEBUG */

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