/*
** 2008 February 16
**
** The author disclaims copyright to this source code.  In place of
** a legal notice, here is a blessing:
**
**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This file implements an object that represents a fixed-length
** bitmap.  Bits are numbered starting with 1.
**
** A bitmap is used to record which pages of a database file have been
** journalled during a transaction, or which pages have the "dont-write"
** property.  Usually only a few pages are meet either condition.
** So the bitmap is usually sparse and has low cardinality.
** But sometimes (for example when during a DROP of a large table) most
** or all of the pages in a database can get journalled.  In those cases, 
** the bitmap becomes dense with high cardinality.  The algorithm needs 
** to handle both cases well.
**
** The size of the bitmap is fixed when the object is created.
**
** All bits are clear when the bitmap is created.  Individual bits
** may be set or cleared one at a time.
**
** Test operations are about 100 times more common that set operations.
** Clear operations are exceedingly rare.  There are usually between
** 5 and 500 set operations per Bitvec object, though the number of sets can
** sometimes grow into tens of thousands or larger.  The size of the
** Bitvec object is the number of pages in the database file at the
** start of a transaction, and is thus usually less than a few thousand,
** but can be as large as 2 billion for a really big database.
*/
#include "sqliteInt.h"

/* Size of the Bitvec structure in bytes. */
#define BITVEC_SZ        512

/* Round the union size down to the nearest pointer boundary, since that's how 
** it will be aligned within the Bitvec struct. */
#define BITVEC_USIZE     (((BITVEC_SZ-(3*sizeof(u32)))/sizeof(Bitvec*))*sizeof(Bitvec*))

/* Type of the array "element" for the bitmap representation. 
** Should be a power of 2, and ideally, evenly divide into BITVEC_USIZE. 
** Setting this to the "natural word" size of your CPU may improve
** performance. */
#define BITVEC_TELEM     u8
/* Size, in bits, of the bitmap element. */
#define BITVEC_SZELEM    8
/* Number of elements in a bitmap array. */
#define BITVEC_NELEM     (BITVEC_USIZE/sizeof(BITVEC_TELEM))
/* Number of bits in the bitmap array. */
#define BITVEC_NBIT      (BITVEC_NELEM*BITVEC_SZELEM)

/* Number of u32 values in hash table. */
#define BITVEC_NINT      (BITVEC_USIZE/sizeof(u32))
/* Maximum number of entries in hash table before 
** sub-dividing and re-hashing. */
#define BITVEC_MXHASH    (BITVEC_NINT/2)
/* Hashing function for the aHash representation.
** Empirical testing showed that the *37 multiplier 
** (an arbitrary prime)in the hash function provided 
** no fewer collisions than the no-op *1. */
#define BITVEC_HASH(X)   (((X)*1)%BITVEC_NINT)

#define BITVEC_NPTR      (BITVEC_USIZE/sizeof(Bitvec *))


/*
** A bitmap is an instance of the following structure.
**
** This bitmap records the existence of zero or more bits
** with values between 1 and iSize, inclusive.
**
** There are three possible representations of the bitmap.
** If iSizeBITVEC_NBIT and iDivisor==0 then Bitvec.u.aHash[] is
** a hash table that will hold up to BITVEC_MXHASH distinct values.
**
** Otherwise, the value i is redirected into one of BITVEC_NPTR
** sub-bitmaps pointed to by Bitvec.u.apSub[].  Each subbitmap
** handles up to iDivisor separate values of i.  apSub[0] holds
** values between 1 and iDivisor.  apSub[1] holds values between
** iDivisor+1 and 2*iDivisor.  apSub[N] holds values between
** N*iDivisor+1 and (N+1)*iDivisor.  Each subbitmap is normalized
** to hold deal with values between 1 and iDivisor.
*/
struct Bitvec {
  u32 iSize;      /* Maximum bit index.  Max iSize is 4,294,967,296. */
  u32 nSet;       /* Number of bits that are set - only valid for aHash
                  ** element.  Max is BITVEC_NINT.  For BITVEC_SZ of 512,
                  ** this would be 125. */
  u32 iDivisor;   /* Number of bits handled by each apSub[] entry. */
                  /* Should >=0 for apSub element. */
                  /* Max iDivisor is max(u32) / BITVEC_NPTR + 1.  */
                  /* For a BITVEC_SZ of 512, this would be 34,359,739. */
  union {
    BITVEC_TELEM aBitmap[BITVEC_NELEM];    /* Bitmap representation */
    u32 aHash[BITVEC_NINT];      /* Hash table representation */
    Bitvec *apSub[BITVEC_NPTR];  /* Recursive representation */
  } u;
};

/*
** Create a new bitmap object able to handle bits between 0 and iSize,
** inclusive.  Return a pointer to the new object.  Return NULL if 
** malloc fails.
*/
Bitvec *sqlite3BitvecCreate(u32 iSize){
  Bitvec *p;
  assert( sizeof(*p)==BITVEC_SZ );
  p = sqlite3MallocZero( sizeof(*p) );
  if( p ){
    p->iSize = iSize;
  }
  return p;
}

/*
** Check to see if the i-th bit is set.  Return true or false.
** If p is NULL (if the bitmap has not been created) or if
** i is out of range, then return false.
*/
int sqlite3BitvecTest(Bitvec *p, u32 i){
  if( p==0 ) return 0;
  if( i>p->iSize || i==0 ) return 0;
  i--;
  while( p->iDivisor ){
    u32 bin = i/p->iDivisor;
    i = i%p->iDivisor;
    p = p->u.apSub[bin];
    if (!p) {
      return 0;
    }
  }
  if( p->iSizeu.aBitmap[i/BITVEC_SZELEM] & (1u.aHash[h]==i ) return 1;
      h = (h+1) % BITVEC_NINT;
    }
    return 0;
  }
}

/*
** Set the i-th bit.  Return 0 on success and an error code if
** anything goes wrong.
**
** This routine might cause sub-bitmaps to be allocated.  Failing
** to get the memory needed to hold the sub-bitmap is the only
** that can go wrong with an insert, assuming p and i are valid.
**
** The calling function must ensure that p is a valid Bitvec object
** and that the value for "i" is within range of the Bitvec object.
** Otherwise the behavior is undefined.
*/
int sqlite3BitvecSet(Bitvec *p, u32 i){
  u32 h;
  if( p==0 ) return SQLITE_OK;
  assert( i>0 );
  assert( iiSize );
  i--;
  while((p->iSize > BITVEC_NBIT) && p->iDivisor) {
    u32 bin = i/p->iDivisor;
    i = i%p->iDivisor;
    if( p->u.apSub[bin]==0 ){
      p->u.apSub[bin] = sqlite3BitvecCreate( p->iDivisor );
      if( p->u.apSub[bin]==0 ) return SQLITE_NOMEM;
    }
    p = p->u.apSub[bin];
  }
  if( p->iSizeu.aBitmap[i/BITVEC_SZELEM] |= 1 u.aHash[h] ){
    if (p->nSetnSet>=BITVEC_MXHASH ){
    unsigned int j;
    int rc;
    u32 *aiValues = sqlite3StackAllocRaw(0, sizeof(p->u.aHash));
    if( aiValues==0 ){
      return SQLITE_NOMEM;
    }else{
      memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));
      memset(p->u.apSub, 0, sizeof(p->u.apSub));
      p->iDivisor = (p->iSize + BITVEC_NPTR - 1)/BITVEC_NPTR;
      rc = sqlite3BitvecSet(p, i);
      for(j=0; jnSet++;
  p->u.aHash[h] = i;
  return SQLITE_OK;
}

/*
** Clear the i-th bit.
**
** pBuf must be a pointer to at least BITVEC_SZ bytes of temporary storage
** that BitvecClear can use to rebuilt its hash table.
*/
void sqlite3BitvecClear(Bitvec *p, u32 i, void *pBuf){
  if( p==0 ) return;
  assert( i>0 );
  i--;
  while( p->iDivisor ){
    u32 bin = i/p->iDivisor;
    i = i%p->iDivisor;
    p = p->u.apSub[bin];
    if (!p) {
      return;
    }
  }
  if( p->iSizeu.aBitmap[i/BITVEC_SZELEM] &= ~(1 u.aHash, sizeof(p->u.aHash));
    memset(p->u.aHash, 0, sizeof(p->u.aHash));
    p->nSet = 0;
    for(j=0; jnSet++;
        while( p->u.aHash[h] ){
          h++;
          if( h>=BITVEC_NINT ) h = 0;
        }
        p->u.aHash[h] = aiValues[j];
      }
    }
  }
}

/*
** Destroy a bitmap object.  Reclaim all memory used.
*/
void sqlite3BitvecDestroy(Bitvec *p){
  if( p==0 ) return;
  if( p->iDivisor ){
    unsigned int i;
    for(i=0; iu.apSub[i]);
    }
  }
  sqlite3_free(p);
}

/*
** Return the value of the iSize parameter specified when Bitvec *p
** was created.
*/
u32 sqlite3BitvecSize(Bitvec *p){
  return p->iSize;
}

#ifndef SQLITE_OMIT_BUILTIN_TEST
/*
** Let V[] be an array of unsigned characters sufficient to hold
** up to N bits.  Let I be an integer between 0 and N.  03] |= (13] &= ~(13]&(1