/src/postgres/src/backend/regex/regc_nfa.c

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  return a;
}

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

  assert(victim->type != 0);

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

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

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

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

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

  assert(oldfrom != newfrom);

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

  a->from = newfrom;

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

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

  assert(oldto != newto);

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

  a->to = newto;

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

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

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

/*
 * findarc - find arc, if any, from given source with given type and color
 * If there is more than one such arc, the result is random.
 */
static struct arc *
findarc(struct state *s,
    int type,
    color co)
{
  struct arc *a;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  if (arccount <= 0)
    return;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/*
 * fixempties - get rid of EMPTY arcs
 */
static void
fixempties(struct nfa *nfa,
       FILE *f)       /* for debug output; NULL none */
{
  struct state *s;
  struct state *s2;
  struct state *nexts;
  struct arc *a;
  struct arc *nexta;
  int     totalinarcs;
  struct arc **inarcsorig;
  struct arc **arcarray;
  int     arccount;
  int     prevnins;
  int     nskip;

  /*
   * First, get rid of any states whose sole out-arc is an EMPTY, since
   * they're basically just aliases for their successor.  The parsing
   * algorithm creates enough of these that it's worth special-casing this.
   */
  for (s = nfa->states; s != NULL && !NISERR(); s = nexts)
  {
    nexts = s->next;
    if (s->flag || s->nouts != 1)
      continue;
    a = s->outs;
    assert(a != NULL && a->outchain == NULL);
    if (a->type != EMPTY)
      continue;
    if (s != a->to)
      moveins(nfa, s, a->to);
    dropstate(nfa, s);
  }

  /*
   * Similarly, get rid of any state with a single EMPTY in-arc, by folding
   * it into its predecessor.
   */
  for (s = nfa->states; s != NULL && !NISERR(); s = nexts)
  {
    nexts = s->next;
    /* while we're at it, ensure tmp fields are clear for next step */
    assert(s->tmp == NULL);
    if (s->flag || s->nins != 1)
      continue;
    a = s->ins;
    assert(a != NULL && a->inchain == NULL);
    if (a->type != EMPTY)
      continue;
    if (s != a->from)
      moveouts(nfa, s, a->from);
    dropstate(nfa, s);
  }

  if (NISERR())
    return;

  /*
   * For each remaining NFA state, find all other states from which it is
   * reachable by a chain of one or more EMPTY arcs.  Then generate new arcs
   * that eliminate the need for each such chain.
   *
   * We could replace a chain of EMPTY arcs that leads from a "from" state
   * to a "to" state either by pushing non-EMPTY arcs forward (linking
   * directly from "from"'s predecessors to "to") or by pulling them back
   * (linking directly from "from" to "to"'s successors).  We choose to
   * always do the former; this choice is somewhat arbitrary, but the
   * approach below requires that we uniformly do one or the other.
   *
   * Suppose we have a chain of N successive EMPTY arcs (where N can easily
   * approach the size of the NFA).  All of the intermediate states must
   * have additional inarcs and outarcs, else they'd have been removed by
   * the steps above.  Assuming their inarcs are mostly not empties, we will
   * add O(N^2) arcs to the NFA, since a non-EMPTY inarc leading to any one
   * state in the chain must be duplicated to lead to all its successor
   * states as well.  So there is no hope of doing less than O(N^2) work;
   * however, we should endeavor to keep the big-O cost from being even
   * worse than that, which it can easily become without care.  In
   * particular, suppose we were to copy all S1's inarcs forward to S2, and
   * then also to S3, and then later we consider pushing S2's inarcs forward
   * to S3.  If we include the arcs already copied from S1 in that, we'd be
   * doing O(N^3) work.  (The duplicate-arc elimination built into newarc()
   * and its cohorts would get rid of the extra arcs, but not without cost.)
   *
   * We can avoid this cost by treating only arcs that existed at the start
   * of this phase as candidates to be pushed forward.  To identify those,
   * we remember the first inarc each state had to start with.  We rely on
   * the fact that newarc() and friends put new arcs on the front of their
   * to-states' inchains, and that this phase never deletes arcs, so that
   * the original arcs must be the last arcs in their to-states' inchains.
   *
   * So the process here is that, for each state in the NFA, we gather up
   * all non-EMPTY inarcs of states that can reach the target state via
   * EMPTY arcs.  We then sort, de-duplicate, and merge these arcs into the
   * target state's inchain.  (We can safely use sort-merge for this as long
   * as we update each state's original-arcs pointer after we add arcs to
   * it; the sort step of mergeins probably changed the order of the old
   * arcs.)
   *
   * Another refinement worth making is that, because we only add non-EMPTY
   * arcs during this phase, and all added arcs have the same from-state as
   * the non-EMPTY arc they were cloned from, we know ahead of time that any
   * states having only EMPTY outarcs will be useless for lack of outarcs
   * after we drop the EMPTY arcs.  (They cannot gain non-EMPTY outarcs if
   * they had none to start with.)  So we need not bother to update the
   * inchains of such states at all.
   */

  /* Remember the states' first original inarcs */
  /* ... and while at it, count how many old inarcs there are altogether */
  inarcsorig = (struct arc **) MALLOC(nfa->nstates * sizeof(struct arc *));
  if (inarcsorig == NULL)
  {
    NERR(REG_ESPACE);
    return;
  }
  totalinarcs = 0;
  for (s = nfa->states; s != NULL; s = s->next)
  {
    inarcsorig[s->no] = s->ins;
    totalinarcs += s->nins;
  }

  /*
   * Create a workspace for accumulating the inarcs to be added to the
   * current target state.  totalinarcs is probably a considerable
   * overestimate of the space needed, but the NFA is unlikely to be large
   * enough at this point to make it worth being smarter.
   */
  arcarray = (struct arc **) MALLOC(totalinarcs * sizeof(struct arc *));
  if (arcarray == NULL)
  {
    NERR(REG_ESPACE);
    FREE(inarcsorig);
    return;
  }

  /* And iterate over the target states */
  for (s = nfa->states; s != NULL && !NISERR(); s = s->next)
  {
    /* Ignore target states without non-EMPTY outarcs, per note above */
    if (!s->flag && !hasnonemptyout(s))
      continue;

    /* Find predecessor states and accumulate their original inarcs */
    arccount = 0;
    for (s2 = emptyreachable(nfa, s, s, inarcsorig); s2 != s; s2 = nexts)
    {
      /* Add s2's original inarcs to arcarray[], but ignore empties */
      for (a = inarcsorig[s2->no]; a != NULL; a = a->inchain)
      {
        if (a->type != EMPTY)
          arcarray[arccount++] = a;
      }

      /* Reset the tmp fields as we walk back */
      nexts = s2->tmp;
      s2->tmp = NULL;
    }
    s->tmp = NULL;
    assert(arccount <= totalinarcs);

    /* Remember how many original inarcs this state has */
    prevnins = s->nins;

    /* Add non-duplicate inarcs to target state */
    mergeins(nfa, s, arcarray, arccount);

    /* Now we must update the state's inarcsorig pointer */
    nskip = s->nins - prevnins;
    a = s->ins;
    while (nskip-- > 0)
      a = a->inchain;
    inarcsorig[s->no] = a;
  }

  FREE(arcarray);
  FREE(inarcsorig);

  if (NISERR())
    return;

  /*
   * Now remove all the EMPTY arcs, since we don't need them anymore.
   */
  for (s = nfa->states; s != NULL; s = s->next)
  {
    for (a = s->outs; a != NULL; a = nexta)
    {
      nexta = a->outchain;
      if (a->type == EMPTY)
        freearc(nfa, a);
    }
  }

  /*
   * And remove any states that have become useless.  (This cleanup is not
   * very thorough, and would be even less so if we tried to combine it with
   * the previous step; but cleanup() will take care of anything we miss.)
   */
  for (s = nfa->states; s != NULL; s = nexts)
  {
    nexts = s->next;
    if ((s->nins == 0 || s->nouts == 0) && !s->flag)
      dropstate(nfa, s);
  }

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

/*
 * emptyreachable - recursively find all states that can reach s by EMPTY arcs
 *
 * The return value is the last such state found.  Its tmp field links back
 * to the next-to-last such state, and so on back to s, so that all these
 * states can be located without searching the whole NFA.
 *
 * Since this is only used in fixempties(), we pass in the inarcsorig[] array
 * maintained by that function.  This lets us skip over all new inarcs, which
 * are certainly not EMPTY arcs.
 *
 * The maximum recursion depth here is equal to the length of the longest
 * loop-free chain of EMPTY arcs, which is surely no more than the size of
 * the NFA ... but that could still be enough to cause trouble.
 */
static struct state *
emptyreachable(struct nfa *nfa,
         struct state *s,
         struct state *lastfound,
         struct arc **inarcsorig)
{
  struct arc *a;

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

  s->tmp = lastfound;
  lastfound = s;
  for (a = inarcsorig[s->no]; a != NULL; a = a->inchain)
  {
    if (a->type == EMPTY && a->from->tmp == NULL)
      lastfound = emptyreachable(nfa, a->from, lastfound, inarcsorig);
  }
  return lastfound;
}

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

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

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

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

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

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

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

  if (NISERR())
    return;

  /*
   * Now remove any states that have become useless.  (This cleanup is not
   * very thorough, and would be even less so if we tried to combine it with
   * the previous step; but cleanup() will take care of anything we miss.)
   *
   * Because findconstraintloop intentionally doesn't reset all tmp fields,
   * we have to clear them after it's done.  This is a convenient place to
   * do that, too.
   */
  for (s = nfa->states; s != NULL; s = nexts)
  {
    nexts = s->next;
    s->tmp = NULL;
    if ((s->nins == 0 || s->nouts == 0) && !s->flag)
      dropstate(nfa, s);
  }

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

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

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

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

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

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

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

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

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

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

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

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

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

  if (NISERR())
    return;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  if (NISERR())
    return;

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

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

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

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

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

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

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

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

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

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

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

  if (NISERR())
    return 0;

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

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

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

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

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

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

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

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

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

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

    assert(haspath != NULL);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  return result;
}

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

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

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

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

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

  assert(!NISERR());

  /*
   * The REG_MAX_COMPILE_SPACE restriction ensures that integer overflow
   * can't occur in this loop nor in the allocation requests below.
   */
  nstates = 0;
  narcs = 0;
  for (s = nfa->states; s != NULL; s = s->next)
  {
    nstates++;
    narcs += s->nouts + 1;  /* need one extra for endmarker */
  }

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

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

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

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

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

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

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

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

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

#ifdef REG_DEBUG        /* subordinates of dumpnfa */

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

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

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

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

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

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

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

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

#ifdef REG_DEBUG        /* subordinates of dumpcnfa */

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

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

#endif              /* REG_DEBUG */

Coverage Report

Created: 2026-10-16 06:48