** information.
*/
typedef struct Stat4Accum Stat4Accum;
typedef struct Stat4Sample Stat4Sample;
struct Stat4Sample {
  tRowcnt *anEq;                  /* sqlite_stat4.nEq */
  tRowcnt *anDLt;                 /* sqlite_stat4.nDLt */

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  tRowcnt *anLt;                  /* sqlite_stat4.nLt */
  union {
    i64 iRowid;                     /* Rowid in main table of the key */
    u8 *aRowid;                     /* Key for WITHOUT ROWID tables */
  } u;
  u32 nRowid;                     /* Sizeof aRowid[] */
................................................................................
  nKeyCol = sqlite3_value_int(argv[1]);
  assert( nKeyCol<=nCol );
  assert( nKeyCol>0 );

  /* Allocate the space required for the Stat4Accum object */
  n = sizeof(*p) 
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anEq */
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anDLt */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4

    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anLt */
    + sizeof(Stat4Sample)*(nCol+mxSample)     /* Stat4Accum.aBest[], a[] */
    + sizeof(tRowcnt)*3*nColUp*(nCol+mxSample)
#endif
  ;
  db = sqlite3_context_db_handle(context);
  p = sqlite3DbMallocZero(db, n);
................................................................................
    return;
  }

  p->db = db;
  p->nRow = 0;
  p->nCol = nCol;
  p->nKeyCol = nKeyCol;
  p->current.anDLt = (tRowcnt*)&p[1];
  p->current.anEq = &p->current.anDLt[nColUp];

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  {
    u8 *pSpace;                     /* Allocated space not yet assigned */
    int i;                          /* Used to iterate through p->aSample[] */

    p->iGet = -1;
    p->mxSample = mxSample;
    p->nPSample = (tRowcnt)(sqlite3_value_int64(argv[2])/(mxSample/3+1) + 1);

    p->current.anLt = &p->current.anEq[nColUp];
    p->iPrn = 0x689e962d*(u32)nCol ^ 0xd0944565*(u32)sqlite3_value_int(argv[2]);
  
    /* Set up the Stat4Accum.a[] and aBest[] arrays */
    p->a = (struct Stat4Sample*)&p->current.anLt[nColUp];
    p->aBest = &p->a[mxSample];
    pSpace = (u8*)(&p->a[mxSample+nCol]);
    for(i=0; i<(mxSample+nCol); i++){
................................................................................
  UNUSED_PARAMETER( argc );
  UNUSED_PARAMETER( context );
  assert( p->nCol>0 );
  assert( iChng<p->nCol );

  if( p->nRow==0 ){
    /* This is the first call to this function. Do initialization. */
    for(i=0; i<p->nCol; i++) p->current.anEq[i] = 1;



  }else{
    /* Second and subsequent calls get processed here */
    samplePushPrevious(p, iChng);

    /* Update anDLt[], anLt[] and anEq[] to reflect the values that apply
    ** to the current row of the index. */
    for(i=0; i<iChng; i++){

      p->current.anEq[i]++;
    }
    for(i=iChng; i<p->nCol; i++){
      p->current.anDLt[i]++;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4

      p->current.anLt[i] += p->current.anEq[i];
#endif
      p->current.anEq[i] = 1;
    }
  }
  p->nRow++;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
    /* Return the value to store in the "stat" column of the sqlite_stat1
    ** table for this index.
    **
    ** The value is a string composed of a list of integers describing 
    ** the index. The first integer in the list is the total number of 
    ** entries in the index. There is one additional integer in the list 
    ** for each indexed column. This additional integer is an estimate of
    ** the number of rows matched by a stabbing query on the index using
    ** a key with the corresponding number of fields. In other words,
    ** if the index is on columns (a,b) and the sqlite_stat1 value is 
    ** "100 10 2", then SQLite estimates that:
    **
    **   * the index contains 100 rows,
    **   * "WHERE a=?" matches 10 rows, and
    **   * "WHERE a=? AND b=?" matches 2 rows.
    **
    ** If D is the count of distinct values and K is the total number of 
    ** rows, then each estimate is computed as:
    **
    **        I = (K+D-1)/D
    */
    char *z;
    int i;

    char *zRet = sqlite3MallocZero( (p->nKeyCol+1)*25 );
    if( zRet==0 ){
      sqlite3_result_error_nomem(context);
      return;
    }

    sqlite3_snprintf(24, zRet, "%llu", (u64)p->nRow);
    z = zRet + sqlite3Strlen30(zRet);
    for(i=0; i<p->nKeyCol; i++){
      u64 nDistinct = p->current.anDLt[i] + 1;
      u64 iVal = (p->nRow + nDistinct - 1) / nDistinct;
      sqlite3_snprintf(24, z, " %llu", iVal);
      z += sqlite3Strlen30(z);
      assert( p->current.anEq[i] );
    }
    assert( z[0]=='\0' && z>zRet );

    sqlite3_result_text(context, zRet, -1, sqlite3_free);

** information.
*/
typedef struct Stat4Accum Stat4Accum;
typedef struct Stat4Sample Stat4Sample;
struct Stat4Sample {
  tRowcnt *anEq;                  /* sqlite_stat4.nEq */
  tRowcnt *anDLt;                 /* sqlite_stat4.nDLt */
  tRowcnt *amxEq;                 /* Maximum length run of equal values */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  tRowcnt *anLt;                  /* sqlite_stat4.nLt */
  union {
    i64 iRowid;                     /* Rowid in main table of the key */
    u8 *aRowid;                     /* Key for WITHOUT ROWID tables */
  } u;
  u32 nRowid;                     /* Sizeof aRowid[] */
................................................................................
  nKeyCol = sqlite3_value_int(argv[1]);
  assert( nKeyCol<=nCol );
  assert( nKeyCol>0 );

  /* Allocate the space required for the Stat4Accum object */
  n = sizeof(*p) 
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anEq */
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.amxEq */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anDLt */
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anLt */
    + sizeof(Stat4Sample)*(nCol+mxSample)     /* Stat4Accum.aBest[], a[] */
    + sizeof(tRowcnt)*3*nColUp*(nCol+mxSample)
#endif
  ;
  db = sqlite3_context_db_handle(context);
  p = sqlite3DbMallocZero(db, n);
................................................................................
    return;
  }

  p->db = db;
  p->nRow = 0;
  p->nCol = nCol;
  p->nKeyCol = nKeyCol;
  p->current.anEq = (tRowcnt*)&p[1];
  p->current.amxEq = &p->current.anEq[nColUp];

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  {
    u8 *pSpace;                     /* Allocated space not yet assigned */
    int i;                          /* Loop counter */

    p->iGet = -1;
    p->mxSample = mxSample;
    p->nPSample = (tRowcnt)(sqlite3_value_int64(argv[2])/(mxSample/3+1) + 1);
    p->current.anDLt = &p->current.amxEq[nColUp];
    p->current.anLt = &p->current.anDLt[nColUp];
    p->iPrn = 0x689e962d*(u32)nCol ^ 0xd0944565*(u32)sqlite3_value_int(argv[2]);
  
    /* Set up the Stat4Accum.a[] and aBest[] arrays */
    p->a = (struct Stat4Sample*)&p->current.anLt[nColUp];
    p->aBest = &p->a[mxSample];
    pSpace = (u8*)(&p->a[mxSample+nCol]);
    for(i=0; i<(mxSample+nCol); i++){
................................................................................
  UNUSED_PARAMETER( argc );
  UNUSED_PARAMETER( context );
  assert( p->nCol>0 );
  assert( iChng<p->nCol );

  if( p->nRow==0 ){
    /* This is the first call to this function. Do initialization. */
    for(i=0; i<p->nCol; i++){
      p->current.anEq[i] = 1;
      p->current.amxEq[i] = 1;
    }
  }else{
    /* Second and subsequent calls get processed here */
    samplePushPrevious(p, iChng);

    /* Update anDLt[], anLt[] and anEq[] to reflect the values that apply
    ** to the current row of the index. */
    for(i=0; i<iChng; i++){
      if( p->current.amxEq[i]==p->current.anEq[i] ) p->current.amxEq[i]++;
      p->current.anEq[i]++;
    }
    for(i=iChng; i<p->nCol; i++){

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
      p->current.anDLt[i]++;
      p->current.anLt[i] += p->current.anEq[i];
#endif
      p->current.anEq[i] = 1;
    }
  }
  p->nRow++;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
    /* Return the value to store in the "stat" column of the sqlite_stat1
    ** table for this index.
    **
    ** The value is a string composed of a list of integers describing 
    ** the index. The first integer in the list is the total number of 
    ** entries in the index. There is one additional integer in the list 
    ** for each indexed column. This additional integer is an estimate of
    ** the number of rows matched by a query on the index using
    ** a key with the corresponding number of fields. In other words,
    ** if the index is on columns (a,b) and the sqlite_stat1 value is 
    ** "100 10 2", then SQLite estimates that:
    **
    **   * the index contains 100 rows,
    **   * "WHERE a=?" matches 10 rows, and
    **   * "WHERE a=? AND b=?" matches 2 rows.
    **
    ** Use the worst-case estimate: the maximum number of repeated entries
    ** in the index.


    */
    char *z;
    int i;

    char *zRet = sqlite3MallocZero( (p->nKeyCol+1)*25 );
    if( zRet==0 ){
      sqlite3_result_error_nomem(context);
      return;
    }

    sqlite3_snprintf(24, zRet, "%llu", (u64)p->nRow);
    z = zRet + sqlite3Strlen30(zRet);
    for(i=0; i<p->nKeyCol; i++){
      u64 iVal = p->current.amxEq[i];

      sqlite3_snprintf(24, z, " %llu", iVal);
      z += sqlite3Strlen30(z);
      assert( p->current.anEq[i] );
    }
    assert( z[0]=='\0' && z>zRet );

    sqlite3_result_text(context, zRet, -1, sqlite3_free);