helgrind/hg_wordset.c

/*--------------------------------------------------------------------*/
/*--- Sets of words, with unique set identifiers.                  ---*/
/*---                                                 hg_wordset.c ---*/
/*--------------------------------------------------------------------*/

/*
   This file is part of Helgrind, a Valgrind tool for detecting errors
   in threaded programs.

   Copyright (C) 2007-2009 OpenWorks LLP
       info@open-works.co.uk

   This program is free software; you can redistribute it and/or
   modify it under the terms of the GNU General Public License as
   published by the Free Software Foundation; either version 2 of the
   License, or (at your option) any later version.

   This program is distributed in the hope that it will be useful, but
   WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307, USA.

   The GNU General Public License is contained in the file COPYING.

   Neither the names of the U.S. Department of Energy nor the
   University of California nor the names of its contributors may be
   used to endorse or promote products derived from this software
   without prior written permission.
*/

#include "pub_tool_basics.h"
#include "pub_tool_libcassert.h"
#include "pub_tool_libcbase.h"
#include "pub_tool_libcprint.h"
#include "pub_tool_threadstate.h"
#include "pub_tool_wordfm.h"

#include "hg_basics.h"
#include "hg_wordset.h"     /* self */

//------------------------------------------------------------------//
//--- Word Cache                                                 ---//
//------------------------------------------------------------------//

typedef
   struct { UWord arg1; UWord arg2; UWord res; }
   WCacheEnt;

/* Each cache is a fixed sized array of N_WCACHE_STAT_MAX entries.
   However only the first .dynMax are used.  This is because at some
   point, expanding the cache further overall gives a slowdown because
   searching more entries more than negates any performance advantage
   from caching those entries in the first place.  Hence use .dynMax
   to allow the size of the cache(s) to be set differently for each
   different WordSetU. */
#define N_WCACHE_STAT_MAX 32
typedef
   struct {
      WCacheEnt ent[N_WCACHE_STAT_MAX];
      UWord     dynMax; /* 1 .. N_WCACHE_STAT_MAX inclusive */
      UWord     inUse;  /* 0 .. dynMax inclusive */
   }
   WCache;

#define WCache_INIT(_zzcache,_zzdynmax)                              \
   do {                                                              \
      tl_assert((_zzdynmax) >= 1);                                   \
      tl_assert((_zzdynmax) <= N_WCACHE_STAT_MAX);                   \
      (_zzcache).dynMax = (_zzdynmax);                               \
      (_zzcache).inUse = 0;                                          \
   } while (0)

#define WCache_LOOKUP_AND_RETURN(_retty,_zzcache,_zzarg1,_zzarg2)    \
   do {                                                              \
      UWord   _i;                                                    \
      UWord   _arg1  = (UWord)(_zzarg1);                             \
      UWord   _arg2  = (UWord)(_zzarg2);                             \
      WCache* _cache = &(_zzcache);                                  \
      tl_assert(_cache->dynMax >= 1);                                \
      tl_assert(_cache->dynMax <= N_WCACHE_STAT_MAX);                \
      tl_assert(_cache->inUse >= 0);                                 \
      tl_assert(_cache->inUse <= _cache->dynMax);                    \
      if (_cache->inUse > 0) {                                       \
         if (_cache->ent[0].arg1 == _arg1                            \
             && _cache->ent[0].arg2 == _arg2)                        \
            return (_retty)_cache->ent[0].res;                       \
         for (_i = 1; _i < _cache->inUse; _i++) {                    \
            if (_cache->ent[_i].arg1 == _arg1                        \
                && _cache->ent[_i].arg2 == _arg2) {                  \
               WCacheEnt tmp     = _cache->ent[_i-1];                \
               _cache->ent[_i-1] = _cache->ent[_i];                  \
               _cache->ent[_i]   = tmp;                              \
               return (_retty)_cache->ent[_i-1].res;                 \
            }                                                        \
         }                                                           \
      }                                                              \
   } while (0)

#define WCache_UPDATE(_zzcache,_zzarg1,_zzarg2,_zzresult)            \
   do {                                                              \
      Word    _i;                                                    \
      UWord   _arg1  = (UWord)(_zzarg1);                             \
      UWord   _arg2  = (UWord)(_zzarg2);                             \
      UWord   _res   = (UWord)(_zzresult);                           \
      WCache* _cache = &(_zzcache);                                  \
      tl_assert(_cache->dynMax >= 1);                                \
      tl_assert(_cache->dynMax <= N_WCACHE_STAT_MAX);                \
      tl_assert(_cache->inUse >= 0);                                 \
      tl_assert(_cache->inUse <= _cache->dynMax);                    \
      if (_cache->inUse < _cache->dynMax)                            \
         _cache->inUse++;                                            \
      for (_i = _cache->inUse-1; _i >= 1; _i--)                      \
         _cache->ent[_i] = _cache->ent[_i-1];                        \
      _cache->ent[0].arg1 = _arg1;                                   \
      _cache->ent[0].arg2 = _arg2;                                   \
      _cache->ent[0].res  = _res;                                    \
   } while (0)


//------------------------------------------------------------------//
//---                          WordSet                           ---//
//---                       Implementation                       ---//
//------------------------------------------------------------------//

typedef
   struct {
      WordSetU* owner; /* for sanity checking */
      UWord*    words;
      UWord     size; /* Really this should be SizeT */
   }
   WordVec;

/* ix2vec[0 .. ix2vec_used-1] are pointers to the lock sets (WordVecs)
   really.  vec2ix is the inverse mapping, mapping WordVec* to the
   corresponding ix2vec entry number.  The two mappings are mutually
   redundant. */
struct _WordSetU {
      void*     (*alloc)(HChar*,SizeT);
      HChar*    cc;
      void      (*dealloc)(void*);
      WordFM*   vec2ix; /* WordVec-to-WordSet mapping tree */
      WordVec** ix2vec; /* WordSet-to-WordVec mapping array */
      UWord     ix2vec_size;
      UWord     ix2vec_used;
      WordSet   empty; /* cached, for speed */
      /* Caches for some operations */
      WCache    cache_addTo;
      WCache    cache_delFrom;
      WCache    cache_intersect;
      WCache    cache_minus;
      /* Stats */
      UWord     n_add;
      UWord     n_add_uncached;
      UWord     n_del;
      UWord     n_del_uncached;
      UWord     n_union;
      UWord     n_intersect;
      UWord     n_intersect_uncached;
      UWord     n_minus;
      UWord     n_minus_uncached;
      UWord     n_elem;
      UWord     n_doubleton;
      UWord     n_isEmpty;
      UWord     n_isSingleton;
      UWord     n_anyElementOf;
      UWord     n_isSubsetOf;
   };

/* Create a new WordVec of the given size. */

static WordVec* new_WV_of_size ( WordSetU* wsu, UWord sz )
{
   WordVec* wv;
   tl_assert(sz >= 0);
   wv = wsu->alloc( wsu->cc, sizeof(WordVec) );
   wv->owner = wsu;
   wv->words = NULL;
   wv->size = sz;
   if (sz > 0) {
     wv->words = wsu->alloc( wsu->cc, (SizeT)sz * sizeof(UWord) );
   }
   return wv;
}

static void delete_WV ( WordVec* wv )
{
   void (*dealloc)(void*) = wv->owner->dealloc;
   if (wv->words) {
      dealloc(wv->words);
   }
   dealloc(wv);
}
static void delete_WV_for_FM ( UWord wv ) {
   delete_WV( (WordVec*)wv );
}

static Word cmp_WordVecs_for_FM ( UWord wv1W, UWord wv2W )
{
   UWord    i;
   WordVec* wv1    = (WordVec*)wv1W;
   WordVec* wv2    = (WordVec*)wv2W;
   UWord    common = wv1->size < wv2->size ? wv1->size : wv2->size;
   for (i = 0; i < common; i++) {
      if (wv1->words[i] == wv2->words[i])
         continue;
      if (wv1->words[i] < wv2->words[i])
         return -1;
      if (wv1->words[i] > wv2->words[i])
         return 1;
      tl_assert(0);
   }
   /* Ok, the common sections are identical.  So now consider the
      tails.  Both sets are considered to finish in an implied
      sequence of -infinity. */
   if (wv1->size < wv2->size) {
      tl_assert(common == wv1->size);
      return -1; /* impliedly, wv1 contains some -infinitys in places
                    where wv2 doesn't. */
   }
   if (wv1->size > wv2->size) {
      tl_assert(common == wv2->size);
      return 1;
   }
   tl_assert(common == wv1->size);
   return 0; /* identical */
}

static void ensure_ix2vec_space ( WordSetU* wsu )
{
   UInt      i, new_sz;
   WordVec** new_vec;
   tl_assert(wsu->ix2vec_used <= wsu->ix2vec_size);
   if (wsu->ix2vec_used < wsu->ix2vec_size)
      return;
   new_sz = 2 * wsu->ix2vec_size;
   if (new_sz == 0) new_sz = 2;
   new_vec = wsu->alloc( wsu->cc, new_sz * sizeof(WordVec*) );
   tl_assert(new_vec);
   for (i = 0; i < wsu->ix2vec_size; i++)
      new_vec[i] = wsu->ix2vec[i];
   if (wsu->ix2vec)
      wsu->dealloc(wsu->ix2vec);
   wsu->ix2vec = new_vec;
   wsu->ix2vec_size = new_sz;
}

/* Index into a WordSetU, doing the obvious range check.  Failure of
   the assertions marked XXX and YYY is an indication of passing the
   wrong WordSetU* in the public API of this module. */
static WordVec* do_ix2vec ( WordSetU* wsu, WordSet ws )
{
   WordVec* wv;
   tl_assert(wsu->ix2vec_used <= wsu->ix2vec_size);
   if (wsu->ix2vec_used > 0)
      tl_assert(wsu->ix2vec);
   /* If this assertion fails, it may mean you supplied a 'ws'
      that does not come from the 'wsu' universe. */
   tl_assert(ws < wsu->ix2vec_used); /* XXX */
   wv = wsu->ix2vec[ws];
   /* Make absolutely sure that 'ws' is a member of 'wsu'. */
   tl_assert(wv);
   tl_assert(wv->owner == wsu); /* YYY */
   return wv;
}

/* See if wv is contained within wsu.  If so, deallocate wv and return
   the index of the already-present copy.  If not, add wv to both the
   vec2ix and ix2vec mappings and return its index. 
*/
static WordSet add_or_dealloc_WordVec( WordSetU* wsu, WordVec* wv_new )
{
   Bool     have;
   WordVec* wv_old;
   UWord/*Set*/ ix_old = -1;
   /* Really WordSet, but need something that can safely be casted to
      a Word* in the lookupFM.  Making it WordSet (which is 32 bits)
      causes failures on a 64-bit platform. */
   tl_assert(wv_new->owner == wsu);
   have = VG_(lookupFM)( wsu->vec2ix, 
                         (Word*)&wv_old, (Word*)&ix_old,
                         (Word)wv_new );
   if (have) {
      tl_assert(wv_old != wv_new);
      tl_assert(wv_old);
      tl_assert(wv_old->owner == wsu);
      tl_assert(ix_old < wsu->ix2vec_used);
      tl_assert(wsu->ix2vec[ix_old] == wv_old);
      delete_WV( wv_new );
      return (WordSet)ix_old;
   } else {
      ensure_ix2vec_space( wsu );
      tl_assert(wsu->ix2vec);
      tl_assert(wsu->ix2vec_used < wsu->ix2vec_size);
      wsu->ix2vec[wsu->ix2vec_used] = wv_new;
      VG_(addToFM)( wsu->vec2ix, (Word)wv_new, (Word)wsu->ix2vec_used );
      if (0) VG_(printf)("aodW %d\n", (Int)wsu->ix2vec_used );
      wsu->ix2vec_used++;
      tl_assert(wsu->ix2vec_used <= wsu->ix2vec_size);
      return (WordSet)(wsu->ix2vec_used - 1);
   }
}


WordSetU* HG_(newWordSetU) ( void* (*alloc_nofail)( HChar*, SizeT ),
                             HChar* cc,
                             void  (*dealloc)(void*),
                             Word  cacheSize )
{
   WordSetU* wsu;
   WordVec*  empty;

   wsu          = alloc_nofail( cc, sizeof(WordSetU) );
   VG_(memset)( wsu, 0, sizeof(WordSetU) );
   wsu->alloc   = alloc_nofail;
   wsu->cc      = cc;
   wsu->dealloc = dealloc;
   wsu->vec2ix  = VG_(newFM)( alloc_nofail, cc,
                              dealloc, cmp_WordVecs_for_FM );
   wsu->ix2vec_used = 0;
   wsu->ix2vec_size = 0;
   wsu->ix2vec      = NULL;
   WCache_INIT(wsu->cache_addTo,     cacheSize);
   WCache_INIT(wsu->cache_delFrom,   cacheSize);
   WCache_INIT(wsu->cache_intersect, cacheSize);
   WCache_INIT(wsu->cache_minus,     cacheSize);
   empty = new_WV_of_size( wsu, 0 );
   wsu->empty = add_or_dealloc_WordVec( wsu, empty );

   return wsu;
}

void HG_(deleteWordSetU) ( WordSetU* wsu )
{
   void (*dealloc)(void*) = wsu->dealloc;
   tl_assert(wsu->vec2ix);
   VG_(deleteFM)( wsu->vec2ix, delete_WV_for_FM, NULL/*val-finalizer*/ );
   if (wsu->ix2vec)
      dealloc(wsu->ix2vec);
   dealloc(wsu);
}

WordSet HG_(emptyWS) ( WordSetU* wsu )
{
   return wsu->empty;
}

Bool HG_(isEmptyWS) ( WordSetU* wsu, WordSet ws )
{
   WordVec* wv = do_ix2vec( wsu, ws );
   wsu->n_isEmpty++;
   if (wv->size == 0) {
      tl_assert(ws == wsu->empty);
      return True;
   } else {
      tl_assert(ws != wsu->empty);
      return False;
   }
}

Bool HG_(isSingletonWS) ( WordSetU* wsu, WordSet ws, UWord w )
{
   WordVec* wv;
   tl_assert(wsu);
   wsu->n_isSingleton++;
   wv = do_ix2vec( wsu, ws );
   return (Bool)(wv->size == 1 && wv->words[0] == w);
}

UWord HG_(cardinalityWS) ( WordSetU* wsu, WordSet ws )
{
   WordVec* wv;
   tl_assert(wsu);
   wv = do_ix2vec( wsu, ws );
   tl_assert(wv->size >= 0);
   return wv->size;
}

UWord HG_(anyElementOfWS) ( WordSetU* wsu, WordSet ws )
{
   WordVec* wv;
   tl_assert(wsu);
   wsu->n_anyElementOf++;
   wv = do_ix2vec( wsu, ws );
   tl_assert(wv->size >= 1);
   return wv->words[0];
}

UWord HG_(cardinalityWSU) ( WordSetU* wsu )
{
   tl_assert(wsu);
   return wsu->ix2vec_used;
}

void HG_(getPayloadWS) ( /*OUT*/UWord** words, /*OUT*/UWord* nWords, 
                         WordSetU* wsu, WordSet ws )
{
   WordVec* wv;
   tl_assert(wsu);
   wv = do_ix2vec( wsu, ws );
   tl_assert(wv->size >= 0);
   *nWords = wv->size;
   *words  = wv->words;
}

Bool HG_(plausibleWS) ( WordSetU* wsu, WordSet ws )
{
   if (wsu == NULL) return False;
   if (ws < 0 || ws >= wsu->ix2vec_used)
      return False;
   return True;
}

Bool HG_(saneWS_SLOW) ( WordSetU* wsu, WordSet ws )
{
   WordVec* wv;
   UWord    i;
   if (wsu == NULL) return False;
   if (ws < 0 || ws >= wsu->ix2vec_used)
      return False;
   wv = do_ix2vec( wsu, ws );
   /* can never happen .. do_ix2vec will assert instead.  Oh well. */
   if (wv->owner != wsu) return False;
   if (wv->size < 0) return False;
   if (wv->size > 0) {
      for (i = 0; i < wv->size-1; i++) {
         if (wv->words[i] >= wv->words[i+1])
            return False;
      }
   }
   return True;
}

Bool HG_(elemWS) ( WordSetU* wsu, WordSet ws, UWord w )
{
   UWord    i;
   WordVec* wv = do_ix2vec( wsu, ws );
   wsu->n_elem++;
   for (i = 0; i < wv->size; i++) {
      if (wv->words[i] == w)
         return True;
   }
   return False;
}

WordSet HG_(doubletonWS) ( WordSetU* wsu, UWord w1, UWord w2 )
{
   WordVec* wv;
   wsu->n_doubleton++;
   if (w1 == w2) {
      wv = new_WV_of_size(wsu, 1);
      wv->words[0] = w1;
   }
   else if (w1 < w2) {
      wv = new_WV_of_size(wsu, 2);
      wv->words[0] = w1;
      wv->words[1] = w2;
   }
   else {
      tl_assert(w1 > w2);
      wv = new_WV_of_size(wsu, 2);
      wv->words[0] = w2;
      wv->words[1] = w1;
   }
   return add_or_dealloc_WordVec( wsu, wv );
}

WordSet HG_(singletonWS) ( WordSetU* wsu, UWord w )
{
   return HG_(doubletonWS)( wsu, w, w );
}

WordSet HG_(isSubsetOf) ( WordSetU* wsu, WordSet small, WordSet big )
{
   wsu->n_isSubsetOf++;
   return small == HG_(intersectWS)( wsu, small, big );
}

void HG_(ppWS) ( WordSetU* wsu, WordSet ws )
{
   UWord    i;
   WordVec* wv;
   tl_assert(wsu);
   wv = do_ix2vec( wsu, ws );
   VG_(printf)("{");
   for (i = 0; i < wv->size; i++) {
      VG_(printf)("%p", (void*)wv->words[i]);
      if (i < wv->size-1)
         VG_(printf)(",");
   }
   VG_(printf)("}");
}

void HG_(ppWSUstats) ( WordSetU* wsu, HChar* name )
{
   VG_(printf)("   WordSet \"%s\":\n", name);
   VG_(printf)("      addTo        %10lu (%lu uncached)\n",
               wsu->n_add, wsu->n_add_uncached);
   VG_(printf)("      delFrom      %10lu (%lu uncached)\n", 
               wsu->n_del, wsu->n_del_uncached);
   VG_(printf)("      union        %10lu\n", wsu->n_union);
   VG_(printf)("      intersect    %10lu (%lu uncached) "
               "[nb. incl isSubsetOf]\n", 
               wsu->n_intersect, wsu->n_intersect_uncached);
   VG_(printf)("      minus        %10lu (%lu uncached)\n",
               wsu->n_minus, wsu->n_minus_uncached);
   VG_(printf)("      elem         %10lu\n",   wsu->n_elem);
   VG_(printf)("      doubleton    %10lu\n",   wsu->n_doubleton);
   VG_(printf)("      isEmpty      %10lu\n",   wsu->n_isEmpty);
   VG_(printf)("      isSingleton  %10lu\n",   wsu->n_isSingleton);
   VG_(printf)("      anyElementOf %10lu\n",   wsu->n_anyElementOf);
   VG_(printf)("      isSubsetOf   %10lu\n",   wsu->n_isSubsetOf);
}

WordSet HG_(addToWS) ( WordSetU* wsu, WordSet ws, UWord w )
{
   UWord    k, j;
   WordVec* wv_new;
   WordVec* wv;
   WordSet  result = (WordSet)(-1); /* bogus */

   wsu->n_add++;
   WCache_LOOKUP_AND_RETURN(WordSet, wsu->cache_addTo, ws, w);
   wsu->n_add_uncached++;

   /* If already present, this is a no-op. */
   wv = do_ix2vec( wsu, ws );
   for (k = 0; k < wv->size; k++) {
      if (wv->words[k] == w) {
         result = ws;
         goto out;
      }
   }
   /* Ok, not present.  Build a new one ... */
   wv_new = new_WV_of_size( wsu, wv->size + 1 );
   k = j = 0;
   for (; k < wv->size && wv->words[k] < w; k++) {
      wv_new->words[j++] = wv->words[k];
   }
   wv_new->words[j++] = w;
   for (; k < wv->size; k++) {
      tl_assert(wv->words[k] > w);
      wv_new->words[j++] = wv->words[k];
   }
   tl_assert(j == wv_new->size);

   /* Find any existing copy, or add the new one. */
   result = add_or_dealloc_WordVec( wsu, wv_new );
   tl_assert(result != (WordSet)(-1));

  out:
   WCache_UPDATE(wsu->cache_addTo, ws, w, result);
   return result;
}

WordSet HG_(delFromWS) ( WordSetU* wsu, WordSet ws, UWord w )
{
   UWord    i, j, k;
   WordVec* wv_new;
   WordSet  result = (WordSet)(-1); /* bogus */
   WordVec* wv = do_ix2vec( wsu, ws );

   wsu->n_del++;

   /* special case empty set */
   if (wv->size == 0) {
      tl_assert(ws == wsu->empty);
      return ws;
   }

   WCache_LOOKUP_AND_RETURN(WordSet, wsu->cache_delFrom, ws, w);
   wsu->n_del_uncached++;

   /* If not already present, this is a no-op. */
   for (i = 0; i < wv->size; i++) {
      if (wv->words[i] == w)
         break;
   }
   if (i == wv->size) {
      result = ws;
      goto out;
   }
   /* So w is present in ws, and the new set will be one element
      smaller. */
   tl_assert(i >= 0 && i < wv->size);
   tl_assert(wv->size > 0);

   wv_new = new_WV_of_size( wsu, wv->size - 1 );
   j = k = 0;
   for (; j < wv->size; j++) {
      if (j == i)
         continue;
      wv_new->words[k++] = wv->words[j];
   }
   tl_assert(k == wv_new->size);

   result = add_or_dealloc_WordVec( wsu, wv_new );
   if (wv->size == 1) {
      tl_assert(result == wsu->empty);
   }

  out:
   WCache_UPDATE(wsu->cache_delFrom, ws, w, result);
   return result;
}

WordSet HG_(unionWS) ( WordSetU* wsu, WordSet ws1, WordSet ws2 )
{
   UWord    i1, i2, k, sz;
   WordVec* wv_new;
   WordVec* wv1 = do_ix2vec( wsu, ws1 );
   WordVec* wv2 = do_ix2vec( wsu, ws2 );
   wsu->n_union++;
   sz = 0;
   i1 = i2 = 0;
   while (1) {
      if (i1 >= wv1->size || i2 >= wv2->size)
         break;
      sz++;
      if (wv1->words[i1] < wv2->words[i2]) {
         i1++;
      } else 
      if (wv1->words[i1] > wv2->words[i2]) {
         i2++;
      } else {
         i1++;
         i2++;
      }
   }
   tl_assert(i1 <= wv1->size);
   tl_assert(i2 <= wv2->size);
   tl_assert(i1 == wv1->size || i2 == wv2->size);
   if (i1 == wv1->size && i2 < wv2->size) {
      sz += (wv2->size - i2);
   }
   if (i2 == wv2->size && i1 < wv1->size) {
      sz += (wv1->size - i1);
   }

   wv_new = new_WV_of_size( wsu, sz );
   k = 0;

   i1 = i2 = 0;
   while (1) {
      if (i1 >= wv1->size || i2 >= wv2->size)
         break;
      if (wv1->words[i1] < wv2->words[i2]) {
         wv_new->words[k++] = wv1->words[i1];
         i1++;
      } else 
      if (wv1->words[i1] > wv2->words[i2]) {
         wv_new->words[k++] = wv2->words[i2];
         i2++;
      } else {
         wv_new->words[k++] = wv1->words[i1];
         i1++;
         i2++;
      }
   }
   tl_assert(i1 <= wv1->size);
   tl_assert(i2 <= wv2->size);
   tl_assert(i1 == wv1->size || i2 == wv2->size);
   if (i1 == wv1->size && i2 < wv2->size) {
      while (i2 < wv2->size)
         wv_new->words[k++] = wv2->words[i2++];
   }
   if (i2 == wv2->size && i1 < wv1->size) {
      while (i1 < wv1->size)
         wv_new->words[k++] = wv1->words[i1++];
   }

   tl_assert(k == sz);

   return add_or_dealloc_WordVec( wsu, wv_new );
}

WordSet HG_(intersectWS) ( WordSetU* wsu, WordSet ws1, WordSet ws2 )
{
   UWord    i1, i2, k, sz;
   WordSet  ws_new = (WordSet)(-1); /* bogus */
   WordVec* wv_new;
   WordVec* wv1; 
   WordVec* wv2; 

   wsu->n_intersect++;

   /* Deal with an obvious case fast. */
   if (ws1 == ws2)
      return ws1;

   /* Since intersect(x,y) == intersect(y,x), convert both variants to
      the same query.  This reduces the number of variants the cache
      has to deal with. */
   if (ws1 > ws2) {
      WordSet wst = ws1; ws1 = ws2; ws2 = wst;
   }

   WCache_LOOKUP_AND_RETURN(WordSet, wsu->cache_intersect, ws1, ws2);
   wsu->n_intersect_uncached++;

   wv1 = do_ix2vec( wsu, ws1 );
   wv2 = do_ix2vec( wsu, ws2 );
   sz = 0;
   i1 = i2 = 0;
   while (1) {
      if (i1 >= wv1->size || i2 >= wv2->size)
         break;
      if (wv1->words[i1] < wv2->words[i2]) {
         i1++;
      } else 
      if (wv1->words[i1] > wv2->words[i2]) {
         i2++;
      } else {
         sz++;
         i1++;
         i2++;
      }
   }
   tl_assert(i1 <= wv1->size);
   tl_assert(i2 <= wv2->size);
   tl_assert(i1 == wv1->size || i2 == wv2->size);

   wv_new = new_WV_of_size( wsu, sz );
   k = 0;

   i1 = i2 = 0;
   while (1) {
      if (i1 >= wv1->size || i2 >= wv2->size)
         break;
      if (wv1->words[i1] < wv2->words[i2]) {
         i1++;
      } else 
      if (wv1->words[i1] > wv2->words[i2]) {
         i2++;
      } else {
         wv_new->words[k++] = wv1->words[i1];
         i1++;
         i2++;
      }
   }
   tl_assert(i1 <= wv1->size);
   tl_assert(i2 <= wv2->size);
   tl_assert(i1 == wv1->size || i2 == wv2->size);

   tl_assert(k == sz);

   ws_new = add_or_dealloc_WordVec( wsu, wv_new );
   if (sz == 0) {
      tl_assert(ws_new == wsu->empty);
   }

   tl_assert(ws_new != (WordSet)(-1));
   WCache_UPDATE(wsu->cache_intersect, ws1, ws2, ws_new);

   return ws_new;
}

WordSet HG_(minusWS) ( WordSetU* wsu, WordSet ws1, WordSet ws2 )
{
   UWord    i1, i2, k, sz;
   WordSet  ws_new = (WordSet)(-1); /* bogus */
   WordVec* wv_new;
   WordVec* wv1;
   WordVec* wv2;
   
   wsu->n_minus++;
   WCache_LOOKUP_AND_RETURN(WordSet, wsu->cache_minus, ws1, ws2);
   wsu->n_minus_uncached++;

   wv1 = do_ix2vec( wsu, ws1 );
   wv2 = do_ix2vec( wsu, ws2 );
   sz = 0;
   i1 = i2 = 0;
   while (1) {
      if (i1 >= wv1->size || i2 >= wv2->size)
         break;
      if (wv1->words[i1] < wv2->words[i2]) {
         sz++;
         i1++;
      } else 
      if (wv1->words[i1] > wv2->words[i2]) {
         i2++;
      } else {
         i1++;
         i2++;
      }
   }
   tl_assert(i1 <= wv1->size);
   tl_assert(i2 <= wv2->size);
   tl_assert(i1 == wv1->size || i2 == wv2->size);
   if (i2 == wv2->size && i1 < wv1->size) {
      sz += (wv1->size - i1);
   }

   wv_new = new_WV_of_size( wsu, sz );
   k = 0;

   i1 = i2 = 0;
   while (1) {
      if (i1 >= wv1->size || i2 >= wv2->size)
         break;
      if (wv1->words[i1] < wv2->words[i2]) {
         wv_new->words[k++] = wv1->words[i1];
         i1++;
      } else 
      if (wv1->words[i1] > wv2->words[i2]) {
         i2++;
      } else {
         i1++;
         i2++;
      }
   }
   tl_assert(i1 <= wv1->size);
   tl_assert(i2 <= wv2->size);
   tl_assert(i1 == wv1->size || i2 == wv2->size);
   if (i2 == wv2->size && i1 < wv1->size) {
      while (i1 < wv1->size)
         wv_new->words[k++] = wv1->words[i1++];
   }

   tl_assert(k == sz);

   ws_new = add_or_dealloc_WordVec( wsu, wv_new );
   if (sz == 0) {
      tl_assert(ws_new == wsu->empty);
   }

   tl_assert(ws_new != (WordSet)(-1));
   WCache_UPDATE(wsu->cache_minus, ws1, ws2, ws_new);

   return ws_new;
}

static __attribute__((unused))
void show_WS ( WordSetU* wsu, WordSet ws )
{
   UWord i;
   WordVec* wv = do_ix2vec( wsu, ws );
   VG_(printf)("#%u{", ws);
   for (i = 0; i < wv->size; i++) {
      VG_(printf)("%lu", wv->words[i]);
      if (i < wv->size-1)
         VG_(printf)(",");
   }
   VG_(printf)("}\n");
}

//------------------------------------------------------------------//
//---                        end WordSet                         ---//
//---                       Implementation                       ---//
//------------------------------------------------------------------//

/*--------------------------------------------------------------------*/
/*--- end                                             hg_wordset.c ---*/
/*--------------------------------------------------------------------*/