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Overview
Comment:Try to remember statistics from ANALYZE using LogEst instead of u64.
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | log-stats
Files: files | file ages | folders
SHA1: 8e78557a40a6b97009852f5b72e68d6483fb00fc
User & Date: drh 2013-10-07 16:53:50
Context
2013-10-07
16:53
Try to remember statistics from ANALYZE using LogEst instead of u64. Leaf check-in: 8e78557a user: drh tags: log-stats
10:48
Merge bug fixes from trunk. check-in: 1d7b2dc0 user: drh tags: row-size-est
Changes
Hide Diffs Unified Diffs Show Whitespace Changes Patch

Changes to src/analyze.c.

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** The first argument points to a nul-terminated string containing a
** list of space separated integers. Read the first nOut of these into
** the array aOut[].
*/
static void decodeIntArray(
  char *zIntArray,       /* String containing int array to decode */
  int nOut,              /* Number of slots in aOut[] */
  tRowcnt *aOut,         /* Store integers here */
  Index *pIndex          /* Handle extra flags for this index, if not NULL */
){
  char *z = zIntArray;
  int c;
  int i;
  tRowcnt v;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  if( z==0 ) z = "";
#else
  if( NEVER(z==0) ) z = "";
#endif
  for(i=0; *z && i<nOut; i++){
    v = 0;
    while( (c=z[0])>='0' && c<='9' ){
      v = v*10 + c - '0';
      z++;
    }
    aOut[i] = v;
    if( *z==' ' ) z++;
  }
  if( pIndex ){
    if( strcmp(z, "unordered")==0 ){
      pIndex->bUnordered = 1;
    }else if( sqlite3_strglob("sz=[0-9]*", z)==0 ){
      int v32 = 0;
................................................................................
static void initAvgEq(Index *pIdx){
  if( pIdx ){
    IndexSample *aSample = pIdx->aSample;
    IndexSample *pFinal = &aSample[pIdx->nSample-1];
    int iCol;
    for(iCol=0; iCol<pIdx->nColumn; iCol++){
      int i;                    /* Used to iterate through samples */
      tRowcnt sumEq = 0;        /* Sum of the nEq values */
      tRowcnt nSum = 0;         /* Number of terms contributing to sumEq */
      tRowcnt avgEq = 0;
      tRowcnt nDLt = pFinal->anDLt[iCol];

      /* Set nSum to the number of distinct (iCol+1) field prefixes that
      ** occur in the stat4 table for this index before pFinal. Set
      ** sumEq to the sum of the nEq values for column iCol for the same
      ** set (adding the value only once where there exist dupicate 
      ** prefixes).  */
      for(i=0; i<(pIdx->nSample-1); i++){
        if( aSample[i].anDLt[iCol]!=aSample[i+1].anDLt[iCol] ){
          sumEq += aSample[i].anEq[iCol];
          nSum++;
        }
      }
      if( nDLt>nSum ){
        avgEq = (pFinal->anLt[iCol] - sumEq)/(nDLt - nSum);
      }
      if( avgEq==0 ) avgEq = 1;
      pIdx->aAvgEq[iCol] = avgEq;
      if( pIdx->nSampleCol==1 ) break;
    }
  }
}

/*
** Load the content from either the sqlite_stat4 or sqlite_stat3 table 
................................................................................
    int nAvgCol = 1;              /* Number of entries in Index.aAvgEq */

    char *zIndex;   /* Index name */
    Index *pIdx;    /* Pointer to the index object */
    int nSample;    /* Number of samples */
    int nByte;      /* Bytes of space required */
    int i;          /* Bytes of space required */
    tRowcnt *pSpace;

    zIndex = (char *)sqlite3_column_text(pStmt, 0);
    if( zIndex==0 ) continue;
    nSample = sqlite3_column_int(pStmt, 1);
    pIdx = sqlite3FindIndex(db, zIndex, zDb);
    assert( pIdx==0 || bStat3 || pIdx->nSample==0 );
    /* Index.nSample is non-zero at this point if data has already been
................................................................................
    if( pIdx==0 || pIdx->nSample ) continue;
    if( bStat3==0 ){
      nIdxCol = pIdx->nColumn+1;
      nAvgCol = pIdx->nColumn;
    }
    pIdx->nSampleCol = nIdxCol;
    nByte = sizeof(IndexSample) * nSample;
    nByte += sizeof(tRowcnt) * nIdxCol * 3 * nSample;
    nByte += nAvgCol * sizeof(tRowcnt);     /* Space for Index.aAvgEq[] */

    pIdx->aSample = sqlite3DbMallocZero(db, nByte);
    if( pIdx->aSample==0 ){
      sqlite3_finalize(pStmt);
      return SQLITE_NOMEM;
    }
    pSpace = (tRowcnt*)&pIdx->aSample[nSample];
    pIdx->aAvgEq = pSpace; pSpace += nAvgCol;
    for(i=0; i<nSample; i++){
      pIdx->aSample[i].anEq = pSpace; pSpace += nIdxCol;
      pIdx->aSample[i].anLt = pSpace; pSpace += nIdxCol;
      pIdx->aSample[i].anDLt = pSpace; pSpace += nIdxCol;
    }
    assert( ((u8*)pSpace)-nByte==(u8*)(pIdx->aSample) );







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** The first argument points to a nul-terminated string containing a
** list of space separated integers. Read the first nOut of these into
** the array aOut[].
*/
static void decodeIntArray(
  char *zIntArray,       /* String containing int array to decode */
  int nOut,              /* Number of slots in aOut[] */
  LogEst *aOut,          /* Convert values to 10*log2() and store here */
  Index *pIndex          /* Handle extra flags for this index, if not NULL */
){
  char *z = zIntArray;
  int c;
  int i;
  u64 v;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  if( z==0 ) z = "";
#else
  if( NEVER(z==0) ) z = "";
#endif
  for(i=0; *z && i<nOut; i++){
    v = 0;
    while( (c=z[0])>='0' && c<='9' ){
      v = v*10 + c - '0';
      z++;
    }
    aOut[i] = sqlite3LogEst(v);
    if( *z==' ' ) z++;
  }
  if( pIndex ){
    if( strcmp(z, "unordered")==0 ){
      pIndex->bUnordered = 1;
    }else if( sqlite3_strglob("sz=[0-9]*", z)==0 ){
      int v32 = 0;
................................................................................
static void initAvgEq(Index *pIdx){
  if( pIdx ){
    IndexSample *aSample = pIdx->aSample;
    IndexSample *pFinal = &aSample[pIdx->nSample-1];
    int iCol;
    for(iCol=0; iCol<pIdx->nColumn; iCol++){
      int i;                    /* Used to iterate through samples */
      u64 sumEq = 0;        /* Sum of the nEq values */
      u64 nSum = 0;         /* Number of terms contributing to sumEq */
      u64 avgEq = 0;
      u64 nDLt = sqlite3LogEstToInt(pFinal->anDLt[iCol]);

      /* Set nSum to the number of distinct (iCol+1) field prefixes that
      ** occur in the stat4 table for this index before pFinal. Set
      ** sumEq to the sum of the nEq values for column iCol for the same
      ** set (adding the value only once where there exist dupicate 
      ** prefixes).  */
      for(i=0; i<(pIdx->nSample-1); i++){
        if( aSample[i].anDLt[iCol]!=aSample[i+1].anDLt[iCol] ){
          sumEq += sqlite3LogEstToInt(aSample[i].anEq[iCol]);
          nSum++;
        }
      }
      if( nDLt>nSum ){
        avgEq = (sqlite3LogEstToInt(pFinal->anLt[iCol]) - sumEq)/(nDLt - nSum);
      }
      if( avgEq<=0 ) avgEq = 1;
      pIdx->aAvgEq[iCol] = sqlite3LogEst(avgEq);
      if( pIdx->nSampleCol==1 ) break;
    }
  }
}

/*
** Load the content from either the sqlite_stat4 or sqlite_stat3 table 
................................................................................
    int nAvgCol = 1;              /* Number of entries in Index.aAvgEq */

    char *zIndex;   /* Index name */
    Index *pIdx;    /* Pointer to the index object */
    int nSample;    /* Number of samples */
    int nByte;      /* Bytes of space required */
    int i;          /* Bytes of space required */
    LogEst *pSpace;

    zIndex = (char *)sqlite3_column_text(pStmt, 0);
    if( zIndex==0 ) continue;
    nSample = sqlite3_column_int(pStmt, 1);
    pIdx = sqlite3FindIndex(db, zIndex, zDb);
    assert( pIdx==0 || bStat3 || pIdx->nSample==0 );
    /* Index.nSample is non-zero at this point if data has already been
................................................................................
    if( pIdx==0 || pIdx->nSample ) continue;
    if( bStat3==0 ){
      nIdxCol = pIdx->nColumn+1;
      nAvgCol = pIdx->nColumn;
    }
    pIdx->nSampleCol = nIdxCol;
    nByte = sizeof(IndexSample) * nSample;
    nByte += sizeof(LogEst) * nIdxCol * 3 * nSample;
    nByte += nAvgCol * sizeof(LogEst);     /* Space for Index.aAvgEq[] */

    pIdx->aSample = sqlite3DbMallocZero(db, nByte);
    if( pIdx->aSample==0 ){
      sqlite3_finalize(pStmt);
      return SQLITE_NOMEM;
    }
    pSpace = (LogEst*)&pIdx->aSample[nSample];
    pIdx->aAvgEq = pSpace; pSpace += nAvgCol;
    for(i=0; i<nSample; i++){
      pIdx->aSample[i].anEq = pSpace; pSpace += nIdxCol;
      pIdx->aSample[i].anLt = pSpace; pSpace += nIdxCol;
      pIdx->aSample[i].anDLt = pSpace; pSpace += nIdxCol;
    }
    assert( ((u8*)pSpace)-nByte==(u8*)(pIdx->aSample) );

Changes to src/build.c.

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    pParse->nErr++;
    goto begin_table_error;
  }
  pTable->zName = zName;
  pTable->iPKey = -1;
  pTable->pSchema = db->aDb[iDb].pSchema;
  pTable->nRef = 1;
  pTable->nRowEst = 1000000;
  assert( pParse->pNewTable==0 );
  pParse->pNewTable = pTable;

  /* If this is the magic sqlite_sequence table used by autoincrement,
  ** then record a pointer to this table in the main database structure
  ** so that INSERT can find the table easily.
  */
................................................................................
  /* 
  ** Allocate the index structure. 
  */
  nName = sqlite3Strlen30(zName);
  nCol = pList->nExpr;
  pIndex = sqlite3DbMallocZero(db, 
      ROUND8(sizeof(Index)) +              /* Index structure  */
      ROUND8(sizeof(tRowcnt)*(nCol+1)) +   /* Index.aiRowEst   */
      sizeof(char *)*nCol +                /* Index.azColl     */
      sizeof(int)*nCol +                   /* Index.aiColumn   */
      sizeof(u8)*nCol +                    /* Index.aSortOrder */
      nName + 1 +                          /* Index.zName      */
      nExtra                               /* Collation sequence names */
  );
  if( db->mallocFailed ){
    goto exit_create_index;
  }
  zExtra = (char*)pIndex;
  pIndex->aiRowEst = (tRowcnt*)&zExtra[ROUND8(sizeof(Index))];
  pIndex->azColl = (char**)
     ((char*)pIndex->aiRowEst + ROUND8(sizeof(tRowcnt)*nCol+1));
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->aiRowEst) );
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->azColl) );
  pIndex->aiColumn = (int *)(&pIndex->azColl[nCol]);
  pIndex->aSortOrder = (u8 *)(&pIndex->aiColumn[nCol]);
  pIndex->zName = (char *)(&pIndex->aSortOrder[nCol]);
  zExtra = (char *)(&pIndex->zName[nName+1]);
  memcpy(pIndex->zName, zName, nName+1);
................................................................................
**           aiRowEst[N]>=1
**
** Apart from that, we have little to go on besides intuition as to
** how aiRowEst[] should be initialized.  The numbers generated here
** are based on typical values found in actual indices.
*/
void sqlite3DefaultRowEst(Index *pIdx){
  tRowcnt *a = pIdx->aiRowEst;
  int i;
  tRowcnt n;
  assert( a!=0 );
  a[0] = pIdx->pTable->nRowEst;
  if( a[0]<10 ) a[0] = 10;

  n = 10;
  for(i=1; i<=pIdx->nColumn; i++){
    a[i] = n;
    if( n>5 ) n--;
  }
  if( pIdx->onError!=OE_None ){
    a[pIdx->nColumn] = 1;
  }
}

/*
** This routine will drop an existing named index.  This routine
** implements the DROP INDEX statement.
*/







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    pParse->nErr++;
    goto begin_table_error;
  }
  pTable->zName = zName;
  pTable->iPKey = -1;
  pTable->pSchema = db->aDb[iDb].pSchema;
  pTable->nRef = 1;
  pTable->nRowEst = 200;
  assert( pParse->pNewTable==0 );
  pParse->pNewTable = pTable;

  /* If this is the magic sqlite_sequence table used by autoincrement,
  ** then record a pointer to this table in the main database structure
  ** so that INSERT can find the table easily.
  */
................................................................................
  /* 
  ** Allocate the index structure. 
  */
  nName = sqlite3Strlen30(zName);
  nCol = pList->nExpr;
  pIndex = sqlite3DbMallocZero(db, 
      ROUND8(sizeof(Index)) +              /* Index structure  */
      ROUND8(sizeof(LogEst)*(nCol+1)) +    /* Index.aiRowEst   */
      sizeof(char *)*nCol +                /* Index.azColl     */
      sizeof(int)*nCol +                   /* Index.aiColumn   */
      sizeof(u8)*nCol +                    /* Index.aSortOrder */
      nName + 1 +                          /* Index.zName      */
      nExtra                               /* Collation sequence names */
  );
  if( db->mallocFailed ){
    goto exit_create_index;
  }
  zExtra = (char*)pIndex;
  pIndex->aiRowEst = (LogEst*)&zExtra[ROUND8(sizeof(Index))];
  pIndex->azColl = (char**)
     ((char*)pIndex->aiRowEst + ROUND8(sizeof(LogEst)*nCol+1));
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->aiRowEst) );
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->azColl) );
  pIndex->aiColumn = (int *)(&pIndex->azColl[nCol]);
  pIndex->aSortOrder = (u8 *)(&pIndex->aiColumn[nCol]);
  pIndex->zName = (char *)(&pIndex->aSortOrder[nCol]);
  zExtra = (char *)(&pIndex->zName[nName+1]);
  memcpy(pIndex->zName, zName, nName+1);
................................................................................
**           aiRowEst[N]>=1
**
** Apart from that, we have little to go on besides intuition as to
** how aiRowEst[] should be initialized.  The numbers generated here
** are based on typical values found in actual indices.
*/
void sqlite3DefaultRowEst(Index *pIdx){
  LogEst *a = pIdx->aiRowEst;
  int i;
  LogEst n;
  assert( a!=0 );
  a[0] = pIdx->pTable->nRowEst;
  assert( 33==sqlite3LogEst(10) );
  if( a[0]<34 ){ a[0] = 34; }
  n = 34;
  for(i=1; i<=pIdx->nColumn; i++){
    a[i] = n;
    if( n>24 ) n -= 2;
  }
  if( pIdx->onError!=OE_None ){
    a[pIdx->nColumn] = 0;
  }
}

/*
** This routine will drop an existing named index.  This routine
** implements the DROP INDEX statement.
*/

Changes to src/select.c.

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    return 0;
  }
  /* The sqlite3ResultSetOfSelect() is only used n contexts where lookaside
  ** is disabled */
  assert( db->lookaside.bEnabled==0 );
  pTab->nRef = 1;
  pTab->zName = 0;
  pTab->nRowEst = 1000000;
  selectColumnsFromExprList(pParse, pSelect->pEList, &pTab->nCol, &pTab->aCol);
  selectAddColumnTypeAndCollation(pParse, pTab->nCol, pTab->aCol, pSelect);
  pTab->iPKey = -1;
  if( db->mallocFailed ){
    sqlite3DeleteTable(db, pTab);
    return 0;
  }
................................................................................
      pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));
      if( pTab==0 ) return WRC_Abort;
      pTab->nRef = 1;
      pTab->zName = sqlite3MPrintf(db, "sqlite_subquery_%p_", (void*)pTab);
      while( pSel->pPrior ){ pSel = pSel->pPrior; }
      selectColumnsFromExprList(pParse, pSel->pEList, &pTab->nCol, &pTab->aCol);
      pTab->iPKey = -1;
      pTab->nRowEst = 1000000;
      pTab->tabFlags |= TF_Ephemeral;
#endif
    }else{
      /* An ordinary table or view name in the FROM clause */
      assert( pFrom->pTab==0 );
      pFrom->pTab = pTab = sqlite3LocateTableItem(pParse, 0, pFrom);
      if( pTab==0 ) return WRC_Abort;







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    return 0;
  }
  /* The sqlite3ResultSetOfSelect() is only used n contexts where lookaside
  ** is disabled */
  assert( db->lookaside.bEnabled==0 );
  pTab->nRef = 1;
  pTab->zName = 0;
  pTab->nRowEst = 200;
  selectColumnsFromExprList(pParse, pSelect->pEList, &pTab->nCol, &pTab->aCol);
  selectAddColumnTypeAndCollation(pParse, pTab->nCol, pTab->aCol, pSelect);
  pTab->iPKey = -1;
  if( db->mallocFailed ){
    sqlite3DeleteTable(db, pTab);
    return 0;
  }
................................................................................
      pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));
      if( pTab==0 ) return WRC_Abort;
      pTab->nRef = 1;
      pTab->zName = sqlite3MPrintf(db, "sqlite_subquery_%p_", (void*)pTab);
      while( pSel->pPrior ){ pSel = pSel->pPrior; }
      selectColumnsFromExprList(pParse, pSel->pEList, &pTab->nCol, &pTab->aCol);
      pTab->iPKey = -1;
      pTab->nRowEst = 200;
      pTab->tabFlags |= TF_Ephemeral;
#endif
    }else{
      /* An ordinary table or view name in the FROM clause */
      assert( pFrom->pTab==0 );
      pFrom->pTab = pTab = sqlite3LocateTableItem(pParse, 0, pFrom);
      if( pTab==0 ) return WRC_Abort;

Changes to src/sqliteInt.h.

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  Index *pIndex;       /* List of SQL indexes on this table. */
  Select *pSelect;     /* NULL for tables.  Points to definition if a view. */
  FKey *pFKey;         /* Linked list of all foreign keys in this table */
  char *zColAff;       /* String defining the affinity of each column */
#ifndef SQLITE_OMIT_CHECK
  ExprList *pCheck;    /* All CHECK constraints */
#endif
  tRowcnt nRowEst;     /* Estimated rows in table - from sqlite_stat1 table */
  int tnum;            /* Root BTree node for this table (see note above) */
  i16 iPKey;           /* If not negative, use aCol[iPKey] as the primary key */
  i16 nCol;            /* Number of columns in this table */
  u16 nRef;            /* Number of pointers to this Table */

  LogEst szTabRow;     /* Estimated size of each table row in bytes */
  u8 tabFlags;         /* Mask of TF_* values */
  u8 keyConf;          /* What to do in case of uniqueness conflict on iPKey */
#ifndef SQLITE_OMIT_ALTERTABLE
  int addColOffset;    /* Offset in CREATE TABLE stmt to add a new column */
#endif
#ifndef SQLITE_OMIT_VIRTUALTABLE
................................................................................
** and the value of Index.onError indicate the which conflict resolution 
** algorithm to employ whenever an attempt is made to insert a non-unique
** element.
*/
struct Index {
  char *zName;             /* Name of this index */
  int *aiColumn;           /* Which columns are used by this index.  1st is 0 */
  tRowcnt *aiRowEst;       /* From ANALYZE: Est. rows selected by each column */
  Table *pTable;           /* The SQL table being indexed */
  char *zColAff;           /* String defining the affinity of each column */
  Index *pNext;            /* The next index associated with the same table */
  Schema *pSchema;         /* Schema containing this index */
  u8 *aSortOrder;          /* for each column: True==DESC, False==ASC */
  char **azColl;           /* Array of collation sequence names for index */
  Expr *pPartIdxWhere;     /* WHERE clause for partial indices */
................................................................................
  u8 onError;              /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */
  unsigned autoIndex:2;    /* 1==UNIQUE, 2==PRIMARY KEY, 0==CREATE INDEX */
  unsigned bUnordered:1;   /* Use this index for == or IN queries only */
  unsigned uniqNotNull:1;  /* True if UNIQUE and NOT NULL for all columns */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  int nSample;             /* Number of elements in aSample[] */
  int nSampleCol;          /* Size of IndexSample.anEq[] and so on */
  tRowcnt *aAvgEq;         /* Average nEq values for keys not in aSample */
  IndexSample *aSample;    /* Samples of the left-most key */
#endif
};

/*
** Each sample stored in the sqlite_stat3 table is represented in memory 
** using a structure of this type.  See documentation at the top of the
** analyze.c source file for additional information.
*/
struct IndexSample {
  void *p;          /* Pointer to sampled record */
  int n;            /* Size of record in bytes */
  tRowcnt *anEq;    /* Est. number of rows where the key equals this sample */
  tRowcnt *anLt;    /* Est. number of rows where key is less than this sample */
  tRowcnt *anDLt;   /* Est. number of distinct keys less than this sample */
};

/*
** Each token coming out of the lexer is an instance of
** this structure.  Tokens are also used as part of an expression.
**
** Note if Token.z==0 then Token.dyn and Token.n are undefined and







<




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  Index *pIndex;       /* List of SQL indexes on this table. */
  Select *pSelect;     /* NULL for tables.  Points to definition if a view. */
  FKey *pFKey;         /* Linked list of all foreign keys in this table */
  char *zColAff;       /* String defining the affinity of each column */
#ifndef SQLITE_OMIT_CHECK
  ExprList *pCheck;    /* All CHECK constraints */
#endif

  int tnum;            /* Root BTree node for this table (see note above) */
  i16 iPKey;           /* If not negative, use aCol[iPKey] as the primary key */
  i16 nCol;            /* Number of columns in this table */
  u16 nRef;            /* Number of pointers to this Table */
  LogEst nRowEst;      /* Estimated number of rows in the table */
  LogEst szTabRow;     /* Estimated size of each table row in bytes */
  u8 tabFlags;         /* Mask of TF_* values */
  u8 keyConf;          /* What to do in case of uniqueness conflict on iPKey */
#ifndef SQLITE_OMIT_ALTERTABLE
  int addColOffset;    /* Offset in CREATE TABLE stmt to add a new column */
#endif
#ifndef SQLITE_OMIT_VIRTUALTABLE
................................................................................
** and the value of Index.onError indicate the which conflict resolution 
** algorithm to employ whenever an attempt is made to insert a non-unique
** element.
*/
struct Index {
  char *zName;             /* Name of this index */
  int *aiColumn;           /* Which columns are used by this index.  1st is 0 */
  LogEst *aiRowEst;        /* From ANALYZE: Est. rows selected by each column */
  Table *pTable;           /* The SQL table being indexed */
  char *zColAff;           /* String defining the affinity of each column */
  Index *pNext;            /* The next index associated with the same table */
  Schema *pSchema;         /* Schema containing this index */
  u8 *aSortOrder;          /* for each column: True==DESC, False==ASC */
  char **azColl;           /* Array of collation sequence names for index */
  Expr *pPartIdxWhere;     /* WHERE clause for partial indices */
................................................................................
  u8 onError;              /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */
  unsigned autoIndex:2;    /* 1==UNIQUE, 2==PRIMARY KEY, 0==CREATE INDEX */
  unsigned bUnordered:1;   /* Use this index for == or IN queries only */
  unsigned uniqNotNull:1;  /* True if UNIQUE and NOT NULL for all columns */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  int nSample;             /* Number of elements in aSample[] */
  int nSampleCol;          /* Size of IndexSample.anEq[] and so on */
  LogEst *aAvgEq;          /* Average nEq values for keys not in aSample */
  IndexSample *aSample;    /* Samples of the left-most key */
#endif
};

/*
** Each sample stored in the sqlite_stat3 table is represented in memory 
** using a structure of this type.  See documentation at the top of the
** analyze.c source file for additional information.
*/
struct IndexSample {
  void *p;          /* Pointer to sampled record */
  int n;            /* Size of record in bytes */
  LogEst *anEq;     /* Est. number of rows where the key equals this sample */
  LogEst *anLt;     /* Est. number of rows where key is less than this sample */
  LogEst *anDLt;    /* Est. number of distinct keys less than this sample */
};

/*
** Each token coming out of the lexer is an instance of
** this structure.  Tokens are also used as part of an expression.
**
** Note if Token.z==0 then Token.dyn and Token.n are undefined and

Changes to src/util.c.

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}
#endif

/* 
** Find (an approximate) sum of two LogEst values.  This computation is
** not a simple "+" operator because LogEst is stored as a logarithmic
** value.
** 
*/
LogEst sqlite3LogEstAdd(LogEst a, LogEst b){
  static const unsigned char x[] = {
     10, 10,                         /* 0,1 */
      9, 9,                          /* 2,3 */
      8, 8,                          /* 4,5 */
      7, 7, 7,                       /* 6,7,8 */







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}
#endif

/* 
** Find (an approximate) sum of two LogEst values.  This computation is
** not a simple "+" operator because LogEst is stored as a logarithmic
** value.

*/
LogEst sqlite3LogEstAdd(LogEst a, LogEst b){
  static const unsigned char x[] = {
     10, 10,                         /* 0,1 */
      9, 9,                          /* 2,3 */
      8, 8,                          /* 4,5 */
      7, 7, 7,                       /* 6,7,8 */

Changes to src/where.c.

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** Return SQLITE_OK on success.
*/
static void whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  UnpackedRecord *pRec,       /* Vector of values to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
  int iCol;                   /* Index of required stats in anEq[] etc. */
  int iMin = 0;               /* Smallest sample not yet tested */
  int i = pIdx->nSample;      /* Smallest sample larger than or equal to pRec */
  int iTest;                  /* Next sample to test */
  int res;                    /* Result of comparison operation */
................................................................................
  ** or equal to pVal.  Or if i==pIdx->nSample, then all samples are less
  ** than pVal.  If aSample[i]==pVal, then res==0.
  */
  if( res==0 ){
    aStat[0] = aSample[i].anLt[iCol];
    aStat[1] = aSample[i].anEq[iCol];
  }else{
    tRowcnt iLower, iUpper, iGap;
    if( i==0 ){
      iLower = 0;
      iUpper = aSample[0].anLt[iCol];
    }else{
      iUpper = i>=pIdx->nSample ? pIdx->aiRowEst[0] : aSample[i].anLt[iCol];

      iLower = aSample[i-1].anEq[iCol] + aSample[i-1].anLt[iCol];
    }
    aStat[1] = (pIdx->nColumn>iCol ? pIdx->aAvgEq[iCol] : 1);
    if( iLower>=iUpper ){
      iGap = 0;
    }else{
      iGap = iUpper - iLower;
    }
    if( roundUp ){
      iGap = (iGap*2)/3;
................................................................................

  if( p->nSample>0
   && nEq==pBuilder->nRecValid
   && nEq<p->nSampleCol
   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 
  ){
    UnpackedRecord *pRec = pBuilder->pRec;
    tRowcnt a[2];
    u8 aff;

    /* Variable iLower will be set to the estimate of the number of rows in 
    ** the index that are less than the lower bound of the range query. The
    ** lower bound being the concatenation of $P and $L, where $P is the
    ** key-prefix formed by the nEq values matched against the nEq left-most
    ** columns of the index, and $L is the value in pLower.
................................................................................
    ** ($P:$L) and the larger of the two returned values used.
    **
    ** Similarly, iUpper is to be set to the estimate of the number of rows
    ** less than the upper bound of the range query. Where the upper bound
    ** is either ($P) or ($P:$U). Again, even if $U is available, both values
    ** of iUpper are requested of whereKeyStats() and the smaller used.
    */
    tRowcnt iLower;
    tRowcnt iUpper;

    if( nEq==p->nColumn ){
      aff = SQLITE_AFF_INTEGER;
    }else{
      aff = p->pTable->aCol[p->aiColumn[nEq]].affinity;
    }
    /* Determine iLower and iUpper using ($P) only. */
................................................................................
      iLower = 0;
      iUpper = p->aiRowEst[0];
    }else{
      /* Note: this call could be optimized away - since the same values must 
      ** have been requested when testing key $P in whereEqualScanEst().  */
      whereKeyStats(pParse, p, pRec, 0, a);
      iLower = a[0];
      iUpper = a[0] + a[1];
    }

    /* If possible, improve on the iLower estimate using ($P:$L). */
    if( pLower ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pLower->pExpr->pRight;
      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        tRowcnt iNew;
        whereKeyStats(pParse, p, pRec, 0, a);
        iNew = a[0] + ((pLower->eOperator & WO_GT) ? a[1] : 0);
        if( iNew>iLower ) iLower = iNew;
        nOut--;
      }
    }

    /* If possible, improve on the iUpper estimate using ($P:$U). */
    if( pUpper ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pUpper->pExpr->pRight;
      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        tRowcnt iNew;
        whereKeyStats(pParse, p, pRec, 1, a);
        iNew = a[0] + ((pUpper->eOperator & WO_LE) ? a[1] : 0);
        if( iNew<iUpper ) iUpper = iNew;
        nOut--;
      }
    }

    pBuilder->pRec = pRec;
    if( rc==SQLITE_OK ){
      if( iUpper>iLower ){
        nNew = sqlite3LogEst(iUpper - iLower);
      }else{
        nNew = 10;        assert( 10==sqlite3LogEst(2) );
      }
      if( nNew<nOut ){
        nOut = nNew;
      }
      *pnOut = (LogEst)nOut;
      WHERETRACE(0x100, ("range scan regions: %u..%u  est=%d\n",
                         (u32)iLower, (u32)iUpper, nOut));


      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(pBuilder);
#endif
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nEq = pBuilder->pNew->u.btree.nEq;
  UnpackedRecord *pRec = pBuilder->pRec;
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */
  int bOk;

  assert( nEq>=1 );
  assert( nEq<=(p->nColumn+1) );
  assert( p->aSample!=0 );
  assert( p->nSample>0 );
  assert( pBuilder->nRecValid<nEq );
................................................................................
  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq-1, &bOk);
  pBuilder->pRec = pRec;
  if( rc!=SQLITE_OK ) return rc;
  if( bOk==0 ) return SQLITE_NOTFOUND;
  pBuilder->nRecValid = nEq;

  whereKeyStats(pParse, p, pRec, 0, a);
  WHERETRACE(0x100,("equality scan regions: %d\n", (int)a[1]));

  *pnRow = a[1];
  
  return rc;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nRecValid = pBuilder->nRecValid;
  int rc = SQLITE_OK;     /* Subfunction return code */
  tRowcnt nEst;           /* Number of rows for a single term */
  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
    pBuilder->nRecValid = nRecValid;
  }

  if( rc==SQLITE_OK ){

    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    *pnRow = nRowEst;
    WHERETRACE(0x100,("IN row estimate: est=%g\n", nRowEst));
  }
  assert( pBuilder->nRecValid==nRecValid );
  return rc;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

/*
................................................................................
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  assert( pNew->u.btree.nEq<=pProbe->nColumn );
  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = sqlite3LogEst(pProbe->aiRowEst[pNew->u.btree.nEq+1]);
    if( nRowEst==0 && pProbe->onError==OE_None ) nRowEst = 1;
  }else{
    iCol = -1;
    nRowEst = 0;
  }
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(sqlite3LogEst(pProbe->aiRowEst[0]));
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    int nRecValid = pBuilder->nRecValid;
#endif
    if( (pTerm->eOperator==WO_ISNULL || (pTerm->wtFlags&TERM_VNULL)!=0)
     && (iCol<0 || pSrc->pTab->aCol[iCol].notNull)
................................................................................
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    if( nInMul==0 
     && pProbe->nSample 
     && pNew->u.btree.nEq<=pProbe->nSampleCol
     && OptimizationEnabled(db, SQLITE_Stat3) 
    ){
      Expr *pExpr = pTerm->pExpr;
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        testcase( pTerm->eOperator & WO_EQ );
        testcase( pTerm->eOperator & WO_ISNULL );
        rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);
      }
      assert( nOut==0 || rc==SQLITE_OK );
      if( nOut ){
        nOut = sqlite3LogEst(nOut);
        pNew->nOut = MIN(nOut, saved_nOut);
      }
    }
#endif
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun =  sqlite3LogEstAdd(pNew->rRun,rLogSize>27 ? rLogSize-17 : 10);
    }
................................................................................
static int whereLoopAddBtree(
  WhereLoopBuilder *pBuilder, /* WHERE clause information */
  Bitmask mExtra              /* Extra prerequesites for using this table */
){
  WhereInfo *pWInfo;          /* WHERE analysis context */
  Index *pProbe;              /* An index we are evaluating */
  Index sPk;                  /* A fake index object for the primary key */
  tRowcnt aiRowEstPk[2];      /* The aiRowEst[] value for the sPk index */
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  SrcList *pTabList;          /* The FROM clause */
  struct SrcList_item *pSrc;  /* The FROM clause btree term to add */
  WhereLoop *pNew;            /* Template WhereLoop object */
  int rc = SQLITE_OK;         /* Return code */
  int iSortIdx = 1;           /* Index number */
  int b;                      /* A boolean value */
................................................................................
    memset(&sPk, 0, sizeof(Index));
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pSrc->pTab;
    aiRowEstPk[0] = pSrc->pTab->nRowEst;
    aiRowEstPk[1] = 1;
    pFirst = pSrc->pTab->pIndex;
    if( pSrc->notIndexed==0 ){
      /* The real indices of the table are only considered if the
      ** NOT INDEXED qualifier is omitted from the FROM clause */
      sPk.pNext = pFirst;
    }
    pProbe = &sPk;
  }
  rSize = sqlite3LogEst(pSrc->pTab->nRowEst);
  rLogSize = estLog(rSize);

#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
  /* Automatic indexes */
  if( !pBuilder->pOrSet
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
   && pSrc->pIndex==0







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** Return SQLITE_OK on success.
*/
static void whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  UnpackedRecord *pRec,       /* Vector of values to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  LogEst *aStat               /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
  int iCol;                   /* Index of required stats in anEq[] etc. */
  int iMin = 0;               /* Smallest sample not yet tested */
  int i = pIdx->nSample;      /* Smallest sample larger than or equal to pRec */
  int iTest;                  /* Next sample to test */
  int res;                    /* Result of comparison operation */
................................................................................
  ** or equal to pVal.  Or if i==pIdx->nSample, then all samples are less
  ** than pVal.  If aSample[i]==pVal, then res==0.
  */
  if( res==0 ){
    aStat[0] = aSample[i].anLt[iCol];
    aStat[1] = aSample[i].anEq[iCol];
  }else{
    LogEst iLower, iUpper, iGap;
    if( i==0 ){
      iLower = 0;
      iUpper = aSample[0].anLt[iCol];
    }else{
      iUpper = i>=pIdx->nSample ? pIdx->aiRowEst[0] : aSample[i].anLt[iCol];
      iLower = sqlite3LogEstAdd(aSample[i-1].anEq[iCol],
                                aSample[i-1].anLt[iCol]);
    }
    aStat[1] = (pIdx->nColumn>iCol ? pIdx->aAvgEq[iCol] : 0);
    if( iLower>=iUpper ){
      iGap = 0;
    }else{
      iGap = iUpper - iLower;
    }
    if( roundUp ){
      iGap = (iGap*2)/3;
................................................................................

  if( p->nSample>0
   && nEq==pBuilder->nRecValid
   && nEq<p->nSampleCol
   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 
  ){
    UnpackedRecord *pRec = pBuilder->pRec;
    LogEst a[2];
    u8 aff;

    /* Variable iLower will be set to the estimate of the number of rows in 
    ** the index that are less than the lower bound of the range query. The
    ** lower bound being the concatenation of $P and $L, where $P is the
    ** key-prefix formed by the nEq values matched against the nEq left-most
    ** columns of the index, and $L is the value in pLower.
................................................................................
    ** ($P:$L) and the larger of the two returned values used.
    **
    ** Similarly, iUpper is to be set to the estimate of the number of rows
    ** less than the upper bound of the range query. Where the upper bound
    ** is either ($P) or ($P:$U). Again, even if $U is available, both values
    ** of iUpper are requested of whereKeyStats() and the smaller used.
    */
    LogEst iLower;
    LogEst iUpper;

    if( nEq==p->nColumn ){
      aff = SQLITE_AFF_INTEGER;
    }else{
      aff = p->pTable->aCol[p->aiColumn[nEq]].affinity;
    }
    /* Determine iLower and iUpper using ($P) only. */
................................................................................
      iLower = 0;
      iUpper = p->aiRowEst[0];
    }else{
      /* Note: this call could be optimized away - since the same values must 
      ** have been requested when testing key $P in whereEqualScanEst().  */
      whereKeyStats(pParse, p, pRec, 0, a);
      iLower = a[0];
      iUpper = sqlite3LogEstAdd(a[0],a[1]);
    }

    /* If possible, improve on the iLower estimate using ($P:$L). */
    if( pLower ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pLower->pExpr->pRight;
      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        LogEst iNew;
        whereKeyStats(pParse, p, pRec, 0, a);
        iNew = sqlite3LogEstAdd(a[0],((pLower->eOperator & WO_GT) ? a[1] : 0));
        if( iNew>iLower ) iLower = iNew;
        nOut--;
      }
    }

    /* If possible, improve on the iUpper estimate using ($P:$U). */
    if( pUpper ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pUpper->pExpr->pRight;
      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        LogEst iNew;
        whereKeyStats(pParse, p, pRec, 1, a);
        iNew = sqlite3LogEstAdd(a[0],((pUpper->eOperator & WO_LE) ? a[1] : 0));
        if( iNew<iUpper ) iUpper = iNew;
        nOut--;
      }
    }

    pBuilder->pRec = pRec;
    if( rc==SQLITE_OK ){
      if( iUpper<=iLower ) iUpper = iLower+1;
      nNew = sqlite3LogEst(sqlite3LogEstToInt(iUpper)
                             - sqlite3LogEstToInt(iLower));


      if( nNew<nOut ){
        nOut = nNew;
      }
      *pnOut = (LogEst)nOut;
      WHERETRACE(0x100, ("range scan regions: %llu..%llu  est=%d\n",
                         sqlite3LogEstToInt(iLower),
                         sqlite3LogEstToInt(iUpper),
                         nOut));
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(pBuilder);
#endif
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  LogEst *pnRow        /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nEq = pBuilder->pNew->u.btree.nEq;
  UnpackedRecord *pRec = pBuilder->pRec;
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  LogEst a[2];              /* Statistics */
  int bOk;

  assert( nEq>=1 );
  assert( nEq<=(p->nColumn+1) );
  assert( p->aSample!=0 );
  assert( p->nSample>0 );
  assert( pBuilder->nRecValid<nEq );
................................................................................
  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq-1, &bOk);
  pBuilder->pRec = pRec;
  if( rc!=SQLITE_OK ) return rc;
  if( bOk==0 ) return SQLITE_NOTFOUND;
  pBuilder->nRecValid = nEq;

  whereKeyStats(pParse, p, pRec, 0, a);
  WHERETRACE(0x100,("equality scan regions: %d (%llu)\n", a[1],
                    sqlite3LogEstToInt(a[1])));
  *pnRow = a[1];
  
  return rc;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  LogEst *pnRow        /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nRecValid = pBuilder->nRecValid;
  int rc = SQLITE_OK;     /* Subfunction return code */
  LogEst nEst;            /* Number of rows for a single term */
  u64 nRowEst = 0;        /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);
    nRowEst += sqlite3LogEstToInt(nEst);
    pBuilder->nRecValid = nRecValid;
  }

  if( rc==SQLITE_OK ){
    nEst = sqlite3LogEst(nRowEst);
    if( nEst > p->aiRowEst[0] ) nEst = p->aiRowEst[0];
    *pnRow = nEst;
    WHERETRACE(0x100,("IN row estimate: est=%d (%llu)\n", nEst, nRowEst));
  }
  assert( pBuilder->nRecValid==nRecValid );
  return rc;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

/*
................................................................................
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  assert( pNew->u.btree.nEq<=pProbe->nColumn );
  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = pProbe->aiRowEst[pNew->u.btree.nEq+1];
    if( nRowEst<10 && pProbe->onError==OE_None ) nRowEst = 10;
  }else{
    iCol = -1;
    nRowEst = 0;
  }
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(pProbe->aiRowEst[0]);
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    int nRecValid = pBuilder->nRecValid;
#endif
    if( (pTerm->eOperator==WO_ISNULL || (pTerm->wtFlags&TERM_VNULL)!=0)
     && (iCol<0 || pSrc->pTab->aCol[iCol].notNull)
................................................................................
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    if( nInMul==0 
     && pProbe->nSample 
     && pNew->u.btree.nEq<=pProbe->nSampleCol
     && OptimizationEnabled(db, SQLITE_Stat3) 
    ){
      Expr *pExpr = pTerm->pExpr;
      LogEst nOut = pNew->nOut;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        testcase( pTerm->eOperator & WO_EQ );
        testcase( pTerm->eOperator & WO_ISNULL );
        rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);
      }
      assert( nOut==pNew->nOut || rc==SQLITE_OK );
      if( nOut<pNew->nOut ) pNew->nOut = nOut;



    }
#endif
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun =  sqlite3LogEstAdd(pNew->rRun,rLogSize>27 ? rLogSize-17 : 10);
    }
................................................................................
static int whereLoopAddBtree(
  WhereLoopBuilder *pBuilder, /* WHERE clause information */
  Bitmask mExtra              /* Extra prerequesites for using this table */
){
  WhereInfo *pWInfo;          /* WHERE analysis context */
  Index *pProbe;              /* An index we are evaluating */
  Index sPk;                  /* A fake index object for the primary key */
  LogEst aiRowEstPk[2];       /* The aiRowEst[] value for the sPk index */
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  SrcList *pTabList;          /* The FROM clause */
  struct SrcList_item *pSrc;  /* The FROM clause btree term to add */
  WhereLoop *pNew;            /* Template WhereLoop object */
  int rc = SQLITE_OK;         /* Return code */
  int iSortIdx = 1;           /* Index number */
  int b;                      /* A boolean value */
................................................................................
    memset(&sPk, 0, sizeof(Index));
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pSrc->pTab;
    aiRowEstPk[0] = pSrc->pTab->nRowEst;
    aiRowEstPk[1] = 0;
    pFirst = pSrc->pTab->pIndex;
    if( pSrc->notIndexed==0 ){
      /* The real indices of the table are only considered if the
      ** NOT INDEXED qualifier is omitted from the FROM clause */
      sPk.pNext = pFirst;
    }
    pProbe = &sPk;
  }
  rSize = pSrc->pTab->nRowEst;
  rLogSize = estLog(rSize);

#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
  /* Automatic indexes */
  if( !pBuilder->pOrSet
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
   && pSrc->pIndex==0