SQLite

    char *zRet = sqlite3MallocZero(p->nCol * 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->nCol-1); 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);
  }

      char *zRet = sqlite3MallocZero(p->nCol * 25);
      if( zRet==0 ){
        sqlite3_result_error_nomem(context);
      }else{
        int i;
        char *z = zRet;
        for(i=0; i<p->nCol; i++){
          sqlite3_snprintf(24, z, "%llu ", (u64)aCnt[i]);
          z += sqlite3Strlen30(z);
        }
        assert( z[0]=='\0' && z>zRet );
        z[-1] = '\0';
        sqlite3_result_text(context, zRet, -1, sqlite3_free);
      }
    }

/*
** 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++;
  }
#ifndef SQLITE_ENABLE_STAT3_OR_STAT4
  assert( pIndex!=0 );
#else
  if( pIndex )
#endif
  {
    if( strcmp(z, "unordered")==0 ){
      pIndex->bUnordered = 1;
    }else if( sqlite3_strglob("sz=[0-9]*", z)==0 ){
      int v32 = 0;
      sqlite3GetInt32(z+3, &v32);
      pIndex->szIdxRow = sqlite3LogEst(v32);
    }
  }
}

/*
** This callback is invoked once for each index when reading the
** sqlite_stat1 table.  
**

    pIndex = sqlite3FindIndex(pInfo->db, argv[1], pInfo->zDatabase);
  }else{
    pIndex = 0;
  }
  z = argv[2];

  if( pIndex ){

    decodeIntArray((char*)z, pIndex->nColumn+1, pIndex->aiRowEst, pIndex);
    if( pIndex->pPartIdxWhere==0 ) pTable->nRowEst = pIndex->aiRowEst[0];

  }else{
    Index fakeIdx;
    fakeIdx.szIdxRow = pTable->szTabRow;
    decodeIntArray((char*)z, 1, &pTable->nRowEst, &fakeIdx);
    pTable->szTabRow = fakeIdx.szIdxRow;
  }

  return 0;
}

/*
** If the Index.aSample variable is not NULL, delete the aSample[] array

    pParse->nErr++;
    goto begin_table_error;
  }
  pTable->zName = zName;
  pTable->iPKey = -1;
  pTable->pSchema = db->aDb[iDb].pSchema;
  pTable->nRef = 1;
  pTable->nRowEst = 1048576;
  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.
  */

  pCol->zName = z;
 
  /* If there is no type specified, columns have the default affinity
  ** 'NONE'. If there is a type specified, then sqlite3AddColumnType() will
  ** be called next to set pCol->affinity correctly.
  */
  pCol->affinity = SQLITE_AFF_NONE;
  pCol->szEst = 1;
  p->nCol++;
}

/*
** This routine is called by the parser while in the middle of
** parsing a CREATE TABLE statement.  A "NOT NULL" constraint has
** been seen on a column.  This routine sets the notNull flag on

** 'REAL'        | SQLITE_AFF_REAL
** 'FLOA'        | SQLITE_AFF_REAL
** 'DOUB'        | SQLITE_AFF_REAL
**
** If none of the substrings in the above table are found,
** SQLITE_AFF_NUMERIC is returned.
*/
char sqlite3AffinityType(const char *zIn, u8 *pszEst){
  u32 h = 0;
  char aff = SQLITE_AFF_NUMERIC;
  const char *zChar = 0;

  if( zIn==0 ) return aff;
  while( zIn[0] ){
    h = (h<<8) + sqlite3UpperToLower[(*zIn)&0xff];
    zIn++;
    if( h==(('c'<<24)+('h'<<16)+('a'<<8)+'r') ){             /* CHAR */
      aff = SQLITE_AFF_TEXT;
      zChar = zIn;
    }else if( h==(('c'<<24)+('l'<<16)+('o'<<8)+'b') ){       /* CLOB */
      aff = SQLITE_AFF_TEXT;
    }else if( h==(('t'<<24)+('e'<<16)+('x'<<8)+'t') ){       /* TEXT */
      aff = SQLITE_AFF_TEXT;
    }else if( h==(('b'<<24)+('l'<<16)+('o'<<8)+'b')          /* BLOB */
        && (aff==SQLITE_AFF_NUMERIC || aff==SQLITE_AFF_REAL) ){
      aff = SQLITE_AFF_NONE;
      if( zIn[0]=='(' ) zChar = zIn;
#ifndef SQLITE_OMIT_FLOATING_POINT
    }else if( h==(('r'<<24)+('e'<<16)+('a'<<8)+'l')          /* REAL */
        && aff==SQLITE_AFF_NUMERIC ){
      aff = SQLITE_AFF_REAL;
    }else if( h==(('f'<<24)+('l'<<16)+('o'<<8)+'a')          /* FLOA */
        && aff==SQLITE_AFF_NUMERIC ){
      aff = SQLITE_AFF_REAL;
    }else if( h==(('d'<<24)+('o'<<16)+('u'<<8)+'b')          /* DOUB */
        && aff==SQLITE_AFF_NUMERIC ){
      aff = SQLITE_AFF_REAL;
#endif
    }else if( (h&0x00FFFFFF)==(('i'<<16)+('n'<<8)+'t') ){    /* INT */
      aff = SQLITE_AFF_INTEGER;
      break;
    }
  }

  /* If pszEst is not NULL, store an estimate of the field size.  The
  ** estimate is scaled so that the size of an integer is 1.  */
  if( pszEst ){
    *pszEst = 1;   /* default size is approx 4 bytes */
    if( aff<=SQLITE_AFF_NONE ){
      if( zChar ){
        while( zChar[0] ){
          if( sqlite3Isdigit(zChar[0]) ){
            int v;
            sqlite3GetInt32(zChar, &v);
            v = v/4 + 1;
            if( v>255 ) v = 255;
            *pszEst = v; /* BLOB(k), VARCHAR(k), CHAR(k) -> r=(k/4+1) */
            break;
          }
          zChar++;
        }
      }else{
        *pszEst = 5;   /* BLOB, TEXT, CLOB -> r=5  (approx 20 bytes)*/
      }
    }
  }
  return aff;
}

/*
** This routine is called by the parser while in the middle of
** parsing a CREATE TABLE statement.  The pFirst token is the first
** token in the sequence of tokens that describe the type of the

  Column *pCol;

  p = pParse->pNewTable;
  if( p==0 || NEVER(p->nCol<1) ) return;
  pCol = &p->aCol[p->nCol-1];
  assert( pCol->zType==0 );
  pCol->zType = sqlite3NameFromToken(pParse->db, pType);
  pCol->affinity = sqlite3AffinityType(pCol->zType, &pCol->szEst);
}

/*
** The expression is the default value for the most recently added column
** of the table currently under construction.
**
** Default value expressions must be constant.  Raise an exception if this

    testcase( pCol->affinity==SQLITE_AFF_NUMERIC );
    testcase( pCol->affinity==SQLITE_AFF_INTEGER );
    testcase( pCol->affinity==SQLITE_AFF_REAL );
    
    zType = azType[pCol->affinity - SQLITE_AFF_TEXT];
    len = sqlite3Strlen30(zType);
    assert( pCol->affinity==SQLITE_AFF_NONE 
            || pCol->affinity==sqlite3AffinityType(zType, 0) );
    memcpy(&zStmt[k], zType, len);
    k += len;
    assert( k<=n );
  }
  sqlite3_snprintf(n-k, &zStmt[k], "%s", zEnd);
  return zStmt;
}

/*
** Estimate the total row width for a table.
*/
static void estimateTableWidth(Table *pTab){
  unsigned wTable = 0;
  const Column *pTabCol;
  int i;
  for(i=pTab->nCol, pTabCol=pTab->aCol; i>0; i--, pTabCol++){
    wTable += pTabCol->szEst;
  }
  if( pTab->iPKey<0 ) wTable++;
  pTab->szTabRow = sqlite3LogEst(wTable*4);
}

/*
** Estimate the average size of a row for an index.
*/
static void estimateIndexWidth(Index *pIdx){
  unsigned wIndex = 1;
  int i;
  const Column *aCol = pIdx->pTable->aCol;
  for(i=0; i<pIdx->nColumn; i++){
    assert( pIdx->aiColumn[i]>=0 && pIdx->aiColumn[i]<pIdx->pTable->nCol );
    wIndex += aCol[pIdx->aiColumn[i]].szEst;
  }
  pIdx->szIdxRow = sqlite3LogEst(wIndex*4);
}

/*
** This routine is called to report the final ")" that terminates
** a CREATE TABLE statement.
**
** The table structure that other action routines have been building
** is added to the internal hash tables, assuming no errors have

*/
void sqlite3EndTable(
  Parse *pParse,          /* Parse context */
  Token *pCons,           /* The ',' token after the last column defn. */
  Token *pEnd,            /* The final ')' token in the CREATE TABLE */
  Select *pSelect         /* Select from a "CREATE ... AS SELECT" */
){
  Table *p;                 /* The new table */
  sqlite3 *db = pParse->db; /* The database connection */
  int iDb;                  /* Database in which the table lives */
  Index *pIdx;              /* An implied index of the table */

  if( (pEnd==0 && pSelect==0) || db->mallocFailed ){
    return;
  }
  p = pParse->pNewTable;
  if( p==0 ) return;

  assert( !db->init.busy || !pSelect );

  iDb = sqlite3SchemaToIndex(db, p->pSchema);

#ifndef SQLITE_OMIT_CHECK
  /* Resolve names in all CHECK constraint expressions.
  */
  if( p->pCheck ){
    sqlite3ResolveSelfReference(pParse, p, NC_IsCheck, 0, p->pCheck);
  }
#endif /* !defined(SQLITE_OMIT_CHECK) */

  /* Estimate the average row size for the table and for all implied indices */
  estimateTableWidth(p);
  for(pIdx=p->pIndex; pIdx; pIdx=pIdx->pNext){
    estimateIndexWidth(pIdx);
  }

  /* If the db->init.busy is 1 it means we are reading the SQL off the
  ** "sqlite_master" or "sqlite_temp_master" table on the disk.
  ** So do not write to the disk again.  Extract the root page number
  ** for the table from the db->init.newTnum field.  (The page number
  ** should have been put there by the sqliteOpenCb routine.)
  */

  DbFixer sFix;        /* For assigning database names to pTable */
  int sortOrderMask;   /* 1 to honor DESC in index.  0 to ignore. */
  sqlite3 *db = pParse->db;
  Db *pDb;             /* The specific table containing the indexed database */
  int iDb;             /* Index of the database that is being written */
  Token *pName = 0;    /* Unqualified name of the index to create */
  struct ExprList_item *pListItem; /* For looping over pList */
  const Column *pTabCol;           /* A column in the table */
  int nCol;                        /* Number of columns */
  int nExtra = 0;                  /* Space allocated for zExtra[] */
  char *zExtra;                    /* Extra space after the Index object */

  assert( pParse->nErr==0 );      /* Never called with prior errors */
  if( db->mallocFailed || IN_DECLARE_VTAB ){
    goto exit_create_index;
  }
  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){
    goto exit_create_index;

  ** more than once within the same index.  Only the first instance of
  ** the column will ever be used by the optimizer.  Note that using the
  ** same column more than once cannot be an error because that would 
  ** break backwards compatibility - it needs to be a warning.
  */
  for(i=0, pListItem=pList->a; i<pList->nExpr; i++, pListItem++){
    const char *zColName = pListItem->zName;

    int requestedSortOrder;
    char *zColl;                   /* Collation sequence name */

    for(j=0, pTabCol=pTab->aCol; j<pTab->nCol; j++, pTabCol++){
      if( sqlite3StrICmp(zColName, pTabCol->zName)==0 ) break;
    }
    if( j>=pTab->nCol ){

    }
    pIndex->azColl[i] = zColl;
    requestedSortOrder = pListItem->sortOrder & sortOrderMask;
    pIndex->aSortOrder[i] = (u8)requestedSortOrder;
    if( pTab->aCol[j].notNull==0 ) pIndex->uniqNotNull = 0;
  }
  sqlite3DefaultRowEst(pIndex);
  if( pParse->pNewTable==0 ) estimateIndexWidth(pIndex);

  if( pTab==pParse->pNewTable ){
    /* This routine has been called to create an automatic index as a
    ** result of a PRIMARY KEY or UNIQUE clause on a column definition, or
    ** a PRIMARY KEY or UNIQUE clause following the column definitions.
    ** i.e. one of:
    **

  if( op==TK_SELECT ){
    assert( pExpr->flags&EP_xIsSelect );
    return sqlite3ExprAffinity(pExpr->x.pSelect->pEList->a[0].pExpr);
  }
#ifndef SQLITE_OMIT_CAST
  if( op==TK_CAST ){
    assert( !ExprHasProperty(pExpr, EP_IntValue) );
    return sqlite3AffinityType(pExpr->u.zToken, 0);
  }
#endif
  if( (op==TK_AGG_COLUMN || op==TK_COLUMN || op==TK_REGISTER) 
   && pExpr->pTab!=0
  ){
    /* op==TK_REGISTER && pExpr->pTab!=0 happens when pExpr was originally
    ** a TK_COLUMN but was previously evaluated and cached in a register */

    }
#ifndef SQLITE_OMIT_CAST
    case TK_CAST: {
      /* Expressions of the form:   CAST(pLeft AS token) */
      int aff, to_op;
      inReg = sqlite3ExprCodeTarget(pParse, pExpr->pLeft, target);
      assert( !ExprHasProperty(pExpr, EP_IntValue) );
      aff = sqlite3AffinityType(pExpr->u.zToken, 0);
      to_op = aff - SQLITE_AFF_TEXT + OP_ToText;
      assert( to_op==OP_ToText    || aff!=SQLITE_AFF_TEXT    );
      assert( to_op==OP_ToBlob    || aff!=SQLITE_AFF_NONE    );
      assert( to_op==OP_ToNumeric || aff!=SQLITE_AFF_NUMERIC );
      assert( to_op==OP_ToInt     || aff!=SQLITE_AFF_INTEGER );
      assert( to_op==OP_ToReal    || aff!=SQLITE_AFF_REAL    );
      testcase( to_op==OP_ToText );

      sqlite3ExplainExpr(pOut, pExpr->pLeft);
      break;
    }
#ifndef SQLITE_OMIT_CAST
    case TK_CAST: {
      /* Expressions of the form:   CAST(pLeft AS token) */
      const char *zAff = "unk";
      switch( sqlite3AffinityType(pExpr->u.zToken, 0) ){
        case SQLITE_AFF_TEXT:    zAff = "TEXT";     break;
        case SQLITE_AFF_NONE:    zAff = "NONE";     break;
        case SQLITE_AFF_NUMERIC: zAff = "NUMERIC";  break;
        case SQLITE_AFF_INTEGER: zAff = "INTEGER";  break;
        case SQLITE_AFF_REAL:    zAff = "REAL";     break;
      }
      sqlite3ExplainPrintf(pOut, "CAST-%s(", zAff);

    }
  }
  break;

  case PragTyp_INDEX_LIST: if( zRight ){
    Index *pIdx;
    Table *pTab;
    int i;
    pTab = sqlite3FindTable(db, zRight, zDb);
    if( pTab ){
      v = sqlite3GetVdbe(pParse);



      sqlite3VdbeSetNumCols(v, 4);
      pParse->nMem = 4;
      sqlite3CodeVerifySchema(pParse, iDb);
      sqlite3VdbeSetColName(v, 0, COLNAME_NAME, "seq", SQLITE_STATIC);
      sqlite3VdbeSetColName(v, 1, COLNAME_NAME, "name", SQLITE_STATIC);
      sqlite3VdbeSetColName(v, 2, COLNAME_NAME, "unique", SQLITE_STATIC);
      sqlite3VdbeSetColName(v, 3, COLNAME_NAME, "avgrowsize", SQLITE_STATIC);
      sqlite3VdbeAddOp2(v, OP_Integer, 0, 1);
      sqlite3VdbeAddOp2(v, OP_Null, 0, 2);
      sqlite3VdbeAddOp2(v, OP_Integer, 1, 3);
      sqlite3VdbeAddOp2(v, OP_Integer,
                           (int)sqlite3LogEstToInt(pTab->szTabRow), 4);
      sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 4);
      for(pIdx=pTab->pIndex, i=1; pIdx; pIdx=pIdx->pNext, i++){
        sqlite3VdbeAddOp2(v, OP_Integer, i, 1);
        sqlite3VdbeAddOp4(v, OP_String8, 0, 2, 0, pIdx->zName, 0);
        sqlite3VdbeAddOp2(v, OP_Integer, pIdx->onError!=OE_None, 3);
        sqlite3VdbeAddOp2(v, OP_Integer,

                             (int)sqlite3LogEstToInt(pIdx->szIdxRow), 4);

        sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 4);
      }
    }
  }
  break;

  case PragTyp_DATABASE_LIST: {
    int i;

    sqlite3VdbeAddOp2(v, OP_Close, pseudoTab, 0);
  }
}

/*
** Return a pointer to a string containing the 'declaration type' of the
** expression pExpr. The string may be treated as static by the caller.
**
** Also try to estimate the size of the returned value and return that
** result in *pEstWidth.
**
** The declaration type is the exact datatype definition extracted from the
** original CREATE TABLE statement if the expression is a column. The
** declaration type for a ROWID field is INTEGER. Exactly when an expression
** is considered a column can be complex in the presence of subqueries. The
** result-set expression in all of the following SELECT statements is 
** considered a column by this function.
**
**   SELECT col FROM tbl;
**   SELECT (SELECT col FROM tbl;
**   SELECT (SELECT col FROM tbl);
**   SELECT abc FROM (SELECT col AS abc FROM tbl);
** 
** The declaration type for any expression other than a column is NULL.
**
** This routine has either 3 or 6 parameters depending on whether or not
** the SQLITE_ENABLE_COLUMN_METADATA compile-time option is used.
*/
#ifdef SQLITE_ENABLE_COLUMN_METADATA
# define columnType(A,B,C,D,E,F) columnTypeImpl(A,B,C,D,E,F)
static const char *columnTypeImpl(
  NameContext *pNC, 
  Expr *pExpr,
  const char **pzOrigDb,
  const char **pzOrigTab,
  const char **pzOrigCol,
  u8 *pEstWidth
){
  char const *zOrigDb = 0;
  char const *zOrigTab = 0;
  char const *zOrigCol = 0;
#else /* if !defined(SQLITE_ENABLE_COLUMN_METADATA) */
# define columnType(A,B,C,D,E,F) columnTypeImpl(A,B,F)
static const char *columnTypeImpl(
  NameContext *pNC, 
  Expr *pExpr,
  u8 *pEstWidth
){
#endif /* !defined(SQLITE_ENABLE_COLUMN_METADATA) */
  char const *zType = 0;
  int j;

  u8 estWidth = 1;

  if( NEVER(pExpr==0) || pNC->pSrcList==0 ) return 0;
  switch( pExpr->op ){
    case TK_AGG_COLUMN:
    case TK_COLUMN: {
      /* The expression is a column. Locate the table the column is being
      ** extracted from in NameContext.pSrcList. This table may be real
      ** database table or a subquery.
      */

          ** test case misc2.2.2) - it always evaluates to NULL.
          */
          NameContext sNC;
          Expr *p = pS->pEList->a[iCol].pExpr;
          sNC.pSrcList = pS->pSrc;
          sNC.pNext = pNC;
          sNC.pParse = pNC->pParse;
          zType = columnType(&sNC, p,&zOrigDb,&zOrigTab,&zOrigCol, &estWidth); 
        }
      }else if( ALWAYS(pTab->pSchema) ){
        /* A real table */
        assert( !pS );
        if( iCol<0 ) iCol = pTab->iPKey;
        assert( iCol==-1 || (iCol>=0 && iCol<pTab->nCol) );
#ifdef SQLITE_ENABLE_COLUMN_METADATA
        if( iCol<0 ){
          zType = "INTEGER";
          zOrigCol = "rowid";
        }else{
          zType = pTab->aCol[iCol].zType;
          zOrigCol = pTab->aCol[iCol].zName;
          estWidth = pTab->aCol[iCol].szEst;
        }
        zOrigTab = pTab->zName;
        if( pNC->pParse ){
          int iDb = sqlite3SchemaToIndex(pNC->pParse->db, pTab->pSchema);
          zOrigDb = pNC->pParse->db->aDb[iDb].zName;
        }
#else
        if( iCol<0 ){
          zType = "INTEGER";
        }else{
          zType = pTab->aCol[iCol].zType;
          estWidth = pTab->aCol[iCol].szEst;
        }
#endif
      }
      break;
    }
#ifndef SQLITE_OMIT_SUBQUERY
    case TK_SELECT: {
      /* The expression is a sub-select. Return the declaration type and
      ** origin info for the single column in the result set of the SELECT
      ** statement.
      */
      NameContext sNC;
      Select *pS = pExpr->x.pSelect;
      Expr *p = pS->pEList->a[0].pExpr;
      assert( ExprHasProperty(pExpr, EP_xIsSelect) );
      sNC.pSrcList = pS->pSrc;
      sNC.pNext = pNC;
      sNC.pParse = pNC->pParse;
      zType = columnType(&sNC, p, &zOrigDb, &zOrigTab, &zOrigCol, &estWidth); 
      break;
    }
#endif
  }

#ifdef SQLITE_ENABLE_COLUMN_METADATA  
  if( pzOrigDb ){
    assert( pzOrigTab && pzOrigCol );
    *pzOrigDb = zOrigDb;
    *pzOrigTab = zOrigTab;
    *pzOrigCol = zOrigCol;
  }
#endif
  if( pEstWidth ) *pEstWidth = estWidth;
  return zType;
}

/*
** Generate code that will tell the VDBE the declaration types of columns
** in the result set.
*/

  for(i=0; i<pEList->nExpr; i++){
    Expr *p = pEList->a[i].pExpr;
    const char *zType;
#ifdef SQLITE_ENABLE_COLUMN_METADATA
    const char *zOrigDb = 0;
    const char *zOrigTab = 0;
    const char *zOrigCol = 0;
    zType = columnType(&sNC, p, &zOrigDb, &zOrigTab, &zOrigCol, 0);

    /* The vdbe must make its own copy of the column-type and other 
    ** column specific strings, in case the schema is reset before this
    ** virtual machine is deleted.
    */
    sqlite3VdbeSetColName(v, i, COLNAME_DATABASE, zOrigDb, SQLITE_TRANSIENT);
    sqlite3VdbeSetColName(v, i, COLNAME_TABLE, zOrigTab, SQLITE_TRANSIENT);
    sqlite3VdbeSetColName(v, i, COLNAME_COLUMN, zOrigCol, SQLITE_TRANSIENT);
#else
    zType = columnType(&sNC, p, 0, 0, 0, 0);
#endif
    sqlite3VdbeSetColName(v, i, COLNAME_DECLTYPE, zType, SQLITE_TRANSIENT);
  }
#endif /* !defined(SQLITE_OMIT_DECLTYPE) */
}

/*
** Generate code that will tell the VDBE the names of columns
** in the result set.  This information is used to provide the
** azCol[] values in the callback.
*/

** routine goes through and adds the types and collations.
**
** This routine requires that all identifiers in the SELECT
** statement be resolved.
*/
static void selectAddColumnTypeAndCollation(
  Parse *pParse,        /* Parsing contexts */
  Table *pTab,          /* Add column type information to this table */

  Select *pSelect       /* SELECT used to determine types and collations */
){
  sqlite3 *db = pParse->db;
  NameContext sNC;
  Column *pCol;
  CollSeq *pColl;
  int i;
  Expr *p;
  struct ExprList_item *a;
  u64 szAll = 0;

  assert( pSelect!=0 );
  assert( (pSelect->selFlags & SF_Resolved)!=0 );
  assert( pTab->nCol==pSelect->pEList->nExpr || db->mallocFailed );
  if( db->mallocFailed ) return;
  memset(&sNC, 0, sizeof(sNC));
  sNC.pSrcList = pSelect->pSrc;
  a = pSelect->pEList->a;
  for(i=0, pCol=pTab->aCol; i<pTab->nCol; i++, pCol++){
    p = a[i].pExpr;
    pCol->zType = sqlite3DbStrDup(db, columnType(&sNC, p,0,0,0, &pCol->szEst));
    szAll += pCol->szEst;
    pCol->affinity = sqlite3ExprAffinity(p);
    if( pCol->affinity==0 ) pCol->affinity = SQLITE_AFF_NONE;
    pColl = sqlite3ExprCollSeq(pParse, p);
    if( pColl ){
      pCol->zColl = sqlite3DbStrDup(db, pColl->zName);
    }
  }
  pTab->szTabRow = sqlite3LogEst(szAll*4);
}

/*
** Given a SELECT statement, generate a Table structure that describes
** the result set of that SELECT.
*/
Table *sqlite3ResultSetOfSelect(Parse *pParse, Select *pSelect){

    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 = 1048576;
  selectColumnsFromExprList(pParse, pSelect->pEList, &pTab->nCol, &pTab->aCol);
  selectAddColumnTypeAndCollation(pParse, pTab, pSelect);
  pTab->iPKey = -1;
  if( db->mallocFailed ){
    sqlite3DeleteTable(db, pTab);
    return 0;
  }
  return pTab;
}

      /* A sub-query in the FROM clause of a SELECT */
      assert( pSel!=0 );
      assert( pFrom->pTab==0 );
      sqlite3WalkSelect(pWalker, pSel);
      pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));
      if( pTab==0 ) return WRC_Abort;
      pTab->nRef = 1;
      pTab->zName = sqlite3MPrintf(db, "sqlite_sq_%p", (void*)pTab);
      while( pSel->pPrior ){ pSel = pSel->pPrior; }
      selectColumnsFromExprList(pParse, pSel->pEList, &pTab->nCol, &pTab->aCol);
      pTab->iPKey = -1;
      pTab->nRowEst = 1048576;
      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;

    for(i=0, pFrom=pTabList->a; i<pTabList->nSrc; i++, pFrom++){
      Table *pTab = pFrom->pTab;
      if( ALWAYS(pTab!=0) && (pTab->tabFlags & TF_Ephemeral)!=0 ){
        /* A sub-query in the FROM clause of a SELECT */
        Select *pSel = pFrom->pSelect;
        assert( pSel );
        while( pSel->pPrior ) pSel = pSel->pPrior;
        selectAddColumnTypeAndCollation(pParse, pTab, pSel);
      }
    }
  }
  return WRC_Continue;
}
#endif

        KeyInfo *pKeyInfo = 0;               /* Keyinfo for scanned index */
        Index *pBest = 0;                    /* Best index found so far */
        int iRoot = pTab->tnum;              /* Root page of scanned b-tree */

        sqlite3CodeVerifySchema(pParse, iDb);
        sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);

        /* Search for the index that has the lowest scan cost.






        **
        ** (2011-04-15) Do not do a full scan of an unordered index.
        **
        ** (2013-10-03) Do not count the entires in a partial index.
        **
        ** In practice the KeyInfo structure will not be used. It is only 
        ** passed to keep OP_OpenRead happy.
        */
        for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
          if( pIdx->bUnordered==0
           && pIdx->szIdxRow<pTab->szTabRow
           && pIdx->pPartIdxWhere==0
           && (!pBest || pIdx->szIdxRow<pBest->szIdxRow)
          ){
            pBest = pIdx;
          }
        }
        if( pBest ){
          iRoot = pBest->tnum;
          pKeyInfo = sqlite3IndexKeyinfo(pParse, pBest);
        }

        /* Open a read-only cursor, execute the OP_Count, close the cursor. */
        sqlite3VdbeAddOp3(v, OP_OpenRead, iCsr, iRoot, iDb);
        if( pKeyInfo ){

*/
#ifdef SQLITE_64BIT_STATS
 typedef u64 tRowcnt;    /* 64-bit only if requested at compile-time */
#else
 typedef u32 tRowcnt;    /* 32-bit is the default */
#endif

/*
** Estimated quantities used for query planning are stored as 16-bit
** logarithms.  For quantity X, the value stored is 10*log2(X).  This
** gives a possible range of values of approximately 1.0e986 to 1e-986.
** But the allowed values are "grainy".  Not every value is representable.
** For example, quantities 16 and 17 are both represented by a LogEst
** of 40.  However, since LogEst quantatites are suppose to be estimates,
** not exact values, this imprecision is not a problem.
**
** "LogEst" is short for "Logarithimic Estimate".
**
** Examples:
**      1 -> 0              20 -> 43          10000 -> 132
**      2 -> 10             25 -> 46          25000 -> 146
**      3 -> 16            100 -> 66        1000000 -> 199
**      4 -> 20           1000 -> 99        1048576 -> 200
**     10 -> 33           1024 -> 100    4294967296 -> 320
**
** The LogEst can be negative to indicate fractional values. 
** Examples:
**
**    0.5 -> -10           0.1 -> -33        0.0625 -> -40
*/
typedef INT16_TYPE LogEst;

/*
** Macros to determine whether the machine is big or little endian,
** evaluated at runtime.
*/
#ifdef SQLITE_AMALGAMATION
const int sqlite3one = 1;
#else

  char *zName;     /* Name of this column */
  Expr *pDflt;     /* Default value of this column */
  char *zDflt;     /* Original text of the default value */
  char *zType;     /* Data type for this column */
  char *zColl;     /* Collating sequence.  If NULL, use the default */
  u8 notNull;      /* An OE_ code for handling a NOT NULL constraint */
  char affinity;   /* One of the SQLITE_AFF_... values */
  u8 szEst;        /* Estimated size of this column.  INT==1 */
  u8 colFlags;     /* Boolean properties.  See COLFLAG_ defines below */
};

/* Allowed values for Column.colFlags:
*/
#define COLFLAG_PRIMKEY  0x0001    /* Column is part of the primary key */
#define COLFLAG_HIDDEN   0x0002    /* A hidden column in a virtual table */

  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
  int nModuleArg;      /* Number of arguments to the module */

#define OE_Replace  5   /* Delete existing record, then do INSERT or UPDATE */

#define OE_Restrict 6   /* OE_Abort for IMMEDIATE, OE_Rollback for DEFERRED */
#define OE_SetNull  7   /* Set the foreign key value to NULL */
#define OE_SetDflt  8   /* Set the foreign key value to its default */
#define OE_Cascade  9   /* Cascade the changes */

#define OE_Default  10  /* Do whatever the default action is */


/*
** An instance of the following structure is passed as the first
** argument to sqlite3VdbeKeyCompare and is used to control the 
** comparison of the two index keys.
**

  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 */
  int tnum;                /* DB Page containing root of this index */
  LogEst szIdxRow;         /* Estimated average row size in bytes */
  u16 nColumn;             /* Number of columns in table used by this index */
  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 sqlite3FixTriggerStep(DbFixer*, TriggerStep*);
int sqlite3AtoF(const char *z, double*, int, u8);
int sqlite3GetInt32(const char *, int*);
int sqlite3Atoi(const char*);
int sqlite3Utf16ByteLen(const void *pData, int nChar);
int sqlite3Utf8CharLen(const char *pData, int nByte);
u32 sqlite3Utf8Read(const u8**);
LogEst sqlite3LogEst(u64);
LogEst sqlite3LogEstAdd(LogEst,LogEst);
#ifndef SQLITE_OMIT_VIRTUALTABLE
LogEst sqlite3LogEstFromDouble(double);
#endif
u64 sqlite3LogEstToInt(LogEst);

/*
** Routines to read and write variable-length integers.  These used to
** be defined locally, but now we use the varint routines in the util.c
** file.  Code should use the MACRO forms below, as the Varint32 versions
** are coded to assume the single byte case is already handled (which 
** the MACRO form does).

void sqlite3ResolveSelectNames(Parse*, Select*, NameContext*);
void sqlite3ResolveSelfReference(Parse*,Table*,int,Expr*,ExprList*);
int sqlite3ResolveOrderGroupBy(Parse*, Select*, ExprList*, const char*);
void sqlite3ColumnDefault(Vdbe *, Table *, int, int);
void sqlite3AlterFinishAddColumn(Parse *, Token *);
void sqlite3AlterBeginAddColumn(Parse *, SrcList *);
CollSeq *sqlite3GetCollSeq(Parse*, u8, CollSeq *, const char*);
char sqlite3AffinityType(const char*, u8*);
void sqlite3Analyze(Parse*, Token*, Token*);
int sqlite3InvokeBusyHandler(BusyHandler*);
int sqlite3FindDb(sqlite3*, Token*);
int sqlite3FindDbName(sqlite3 *, const char *);
int sqlite3AnalysisLoad(sqlite3*,int iDB);
void sqlite3DeleteIndexSamples(sqlite3*,Index*);
void sqlite3DefaultRowEst(Index*);

  /* For each index, figure out the left-most column and set the 
  ** corresponding entry in aIndex[] to 1.
  */
  while( pStmt && sqlite3_step(pStmt)==SQLITE_ROW ){
    const char *zIdx = (const char *)sqlite3_column_text(pStmt, 1);
    sqlite3_stmt *pStmt2 = 0;
    if( zIdx==0 ) continue;
    zSql = sqlite3_mprintf("PRAGMA index_info(%s)", zIdx);
    if( !zSql ){
      rc = SQLITE_NOMEM;
      goto get_index_array_out;
    }
    rc = sqlite3_prepare(db, zSql, -1, &pStmt2, 0);
    sqlite3_free(zSql);

    int i, sz;
    sz = sqlite3Strlen30(z);
    for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}
    if( z[i]=='.' && ALWAYS(sz>i+4) ) memmove(&z[i+1], &z[sz-3], 4);
  }
}
#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 */
      6, 6, 6,                       /* 9,10,11 */
      5, 5, 5,                       /* 12-14 */
      4, 4, 4, 4,                    /* 15-18 */
      3, 3, 3, 3, 3, 3,              /* 19-24 */
      2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
  };
  if( a>=b ){
    if( a>b+49 ) return a;
    if( a>b+31 ) return a+1;
    return a+x[a-b];
  }else{
    if( b>a+49 ) return b;
    if( b>a+31 ) return b+1;
    return b+x[b-a];
  }
}

/*
** Convert an integer into a LogEst.  In other words, compute a
** good approximatation for 10*log2(x).
*/
LogEst sqlite3LogEst(u64 x){
  static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  LogEst y = 40;
  if( x<8 ){
    if( x<2 ) return 0;
    while( x<8 ){  y -= 10; x <<= 1; }
  }else{
    while( x>255 ){ y += 40; x >>= 4; }
    while( x>15 ){  y += 10; x >>= 1; }
  }
  return a[x&7] + y - 10;
}

#ifndef SQLITE_OMIT_VIRTUALTABLE
/*
** Convert a double into a LogEst
** In other words, compute an approximation for 10*log2(x).
*/
LogEst sqlite3LogEstFromDouble(double x){
  u64 a;
  LogEst e;
  assert( sizeof(x)==8 && sizeof(a)==8 );
  if( x<=1 ) return 0;
  if( x<=2000000000 ) return sqlite3LogEst((u64)x);
  memcpy(&a, &x, 8);
  e = (a>>52) - 1022;
  return e*10;
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** Convert a LogEst into an integer.
*/
u64 sqlite3LogEstToInt(LogEst x){
  u64 n;
  if( x<10 ) return 1;
  n = x%10;
  x /= 10;
  if( n>=5 ) n -= 2;
  else if( n>=1 ) n -= 1;
  if( x>=3 ) return (n+8)<<(x-3);
  return (n+8)>>(3-x);
}

typedef struct WherePath WherePath;
typedef struct WhereTerm WhereTerm;
typedef struct WhereLoopBuilder WhereLoopBuilder;
typedef struct WhereScan WhereScan;
typedef struct WhereOrCost WhereOrCost;
typedef struct WhereOrSet WhereOrSet;





















/*
** This object contains information needed to implement a single nested
** loop in WHERE clause.
**
** Contrast this object with WhereLoop.  This object describes the
** implementation of the loop.  WhereLoop describes the algorithm.
** This object contains a pointer to the WhereLoop algorithm as one of

  Bitmask prereq;       /* Bitmask of other loops that must run first */
  Bitmask maskSelf;     /* Bitmask identifying table iTab */
#ifdef SQLITE_DEBUG
  char cId;             /* Symbolic ID of this loop for debugging use */
#endif
  u8 iTab;              /* Position in FROM clause of table for this loop */
  u8 iSortIdx;          /* Sorting index number.  0==None */
  LogEst rSetup;        /* One-time setup cost (ex: create transient index) */
  LogEst rRun;          /* Cost of running each loop */
  LogEst nOut;          /* Estimated number of output rows */
  union {
    struct {               /* Information for internal btree tables */
      int nEq;               /* Number of equality constraints */
      Index *pIndex;         /* Index used, or NULL */
    } btree;
    struct {               /* Information for virtual tables */
      int idxNum;            /* Index number */

/* This object holds the prerequisites and the cost of running a
** subquery on one operand of an OR operator in the WHERE clause.
** See WhereOrSet for additional information 
*/
struct WhereOrCost {
  Bitmask prereq;     /* Prerequisites */
  LogEst rRun;        /* Cost of running this subquery */
  LogEst nOut;        /* Number of outputs for this subquery */
};

/* The WhereOrSet object holds a set of possible WhereOrCosts that
** correspond to the subquery(s) of OR-clause processing.  Only the
** best N_OR_COST elements are retained.
*/
#define N_OR_COST 3

** of length 2.  And so forth until the length of WherePaths equals the
** number of nodes in the FROM clause.  The best (lowest cost) WherePath
** at the end is the choosen query plan.
*/
struct WherePath {
  Bitmask maskLoop;     /* Bitmask of all WhereLoop objects in this path */
  Bitmask revLoop;      /* aLoop[]s that should be reversed for ORDER BY */
  LogEst nRow;          /* Estimated number of rows generated by this path */
  LogEst rCost;         /* Total cost of this path */
  u8 isOrdered;         /* True if this path satisfies ORDER BY */
  u8 isOrderedValid;    /* True if the isOrdered field is valid */
  WhereLoop **aLoop;    /* Array of WhereLoop objects implementing this path */
};

/*
** The query generator uses an array of instances of this structure to

  int iParent;            /* Disable pWC->a[iParent] when this term disabled */
  int leftCursor;         /* Cursor number of X in "X <op> <expr>" */
  union {
    int leftColumn;         /* Column number of X in "X <op> <expr>" */
    WhereOrInfo *pOrInfo;   /* Extra information if (eOperator & WO_OR)!=0 */
    WhereAndInfo *pAndInfo; /* Extra information if (eOperator& WO_AND)!=0 */
  } u;
  LogEst truthProb;       /* Probability of truth for this expression */
  u16 eOperator;          /* A WO_xx value describing <op> */
  u8 wtFlags;             /* TERM_xxx bit flags.  See below */
  u8 nChild;              /* Number of children that must disable us */
  WhereClause *pWC;       /* The clause this term is part of */
  Bitmask prereqRight;    /* Bitmask of tables used by pExpr->pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by pExpr */
};

struct WhereInfo {
  Parse *pParse;            /* Parsing and code generating context */
  SrcList *pTabList;        /* List of tables in the join */
  ExprList *pOrderBy;       /* The ORDER BY clause or NULL */
  ExprList *pResultSet;     /* Result set. DISTINCT operates on these */
  WhereLoop *pLoops;        /* List of all WhereLoop objects */
  Bitmask revMask;          /* Mask of ORDER BY terms that need reversing */
  LogEst nRowOut;           /* Estimated number of output rows */
  u16 wctrlFlags;           /* Flags originally passed to sqlite3WhereBegin() */
  u8 bOBSat;                /* ORDER BY satisfied by indices */
  u8 okOnePass;             /* Ok to use one-pass algorithm for UPDATE/DELETE */
  u8 untestedTerms;         /* Not all WHERE terms resolved by outer loop */
  u8 eDistinct;             /* One of the WHERE_DISTINCT_* values below */
  u8 nLevel;                /* Number of nested loop */
  int iTop;                 /* The very beginning of the WHERE loop */

#define WHERE_INDEXED      0x00000200  /* WhereLoop.u.btree.pIndex is valid */
#define WHERE_VIRTUALTABLE 0x00000400  /* WhereLoop.u.vtab is valid */
#define WHERE_IN_ABLE      0x00000800  /* Able to support an IN operator */
#define WHERE_ONEROW       0x00001000  /* Selects no more than one row */
#define WHERE_MULTI_OR     0x00002000  /* OR using multiple indices */
#define WHERE_AUTO_INDEX   0x00004000  /* Uses an ephemeral index */
















/*
** Return the estimated number of output rows from a WHERE clause
*/
u64 sqlite3WhereOutputRowCount(WhereInfo *pWInfo){
  return sqlite3LogEstToInt(pWInfo->nRowOut);
}

/*
** Return one of the WHERE_DISTINCT_xxxxx values to indicate how this
** WHERE clause returns outputs for DISTINCT processing.
*/
int sqlite3WhereIsDistinct(WhereInfo *pWInfo){

** The new entry might overwrite an existing entry, or it might be
** appended, or it might be discarded.  Do whatever is the right thing
** so that pSet keeps the N_OR_COST best entries seen so far.
*/
static int whereOrInsert(
  WhereOrSet *pSet,      /* The WhereOrSet to be updated */
  Bitmask prereq,        /* Prerequisites of the new entry */
  LogEst rRun,           /* Run-cost of the new entry */
  LogEst nOut            /* Number of outputs for the new entry */
){
  u16 i;
  WhereOrCost *p;
  for(i=pSet->n, p=pSet->a; i>0; i--, p++){
    if( rRun<=p->rRun && (prereq & p->prereq)==prereq ){
      goto whereOrInsert_done;
    }

    }
  }
  if( pWC->a!=pWC->aStatic ){
    sqlite3DbFree(db, pWC->a);
  }
}




/*
** Add a single new WhereTerm entry to the WhereClause object pWC.
** The new WhereTerm object is constructed from Expr p and with wtFlags.
** The index in pWC->a[] of the new WhereTerm is returned on success.
** 0 is returned if the new WhereTerm could not be added due to a memory
** allocation error.  The memory allocation failure will be recorded in
** the db->mallocFailed flag so that higher-level functions can detect it.

    if( pOld!=pWC->aStatic ){
      sqlite3DbFree(db, pOld);
    }
    pWC->nSlot = sqlite3DbMallocSize(db, pWC->a)/sizeof(pWC->a[0]);
  }
  pTerm = &pWC->a[idx = pWC->nTerm++];
  if( p && ExprHasProperty(p, EP_Unlikely) ){
    pTerm->truthProb = sqlite3LogEst(p->iTable) - 99;
  }else{
    pTerm->truthProb = -1;
  }
  pTerm->pExpr = sqlite3ExprSkipCollate(p);
  pTerm->wtFlags = wtFlags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;

      return 1;
    }
  }

  return 0;
}






























/*



































** Estimate the logarithm of the input value to base 2.
*/
static LogEst estLog(LogEst N){
  LogEst x = sqlite3LogEst(N);
  return x>33 ? x - 33 : 0;
}

/*
** Two routines for printing the content of an sqlite3_index_info
** structure.  Used for testing and debugging only.  If neither
** SQLITE_TEST or SQLITE_DEBUG are defined, then these routines

** then nEq is set to 1 (as the range restricted column, b, is the second 
** left-most column of the index). Or, if the query is:
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**
** then nEq is set to 0.
**
** When this function is called, *pnOut is set to the sqlite3LogEst() of the
** number of rows that the index scan is expected to visit without 
** considering the range constraints. If nEq is 0, this is the number of 
** rows in the index. Assuming no error occurs, *pnOut is adjusted (reduced)
** to account for the range contraints pLower and pUpper.
** 
** In the absence of sqlite_stat4 ANALYZE data, or if such data cannot be
** used, each range inequality reduces the search space by a factor of 4. 
** Hence a pair of constraints (x>? AND x<?) reduces the expected number of
** rows visited by a factor of 16.
*/
static int whereRangeScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
  WhereLoop *pLoop     /* Modify the .nOut and maybe .rRun fields */
){
  int rc = SQLITE_OK;
  int nOut = pLoop->nOut;
  int nEq = pLoop->u.btree.nEq;
  LogEst nNew;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  Index *p = pLoop->u.btree.pIndex;


  if( p->nSample>0
   && nEq==pBuilder->nRecValid
   && nEq<p->nSampleCol
   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 
  ){
    UnpackedRecord *pRec = pBuilder->pRec;

        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;
      }
      pLoop->nOut = (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
  assert( pLower || pUpper );
  /* TUNING:  Each inequality constraint reduces the search space 4-fold.
  ** A BETWEEN operator, therefore, reduces the search space 16-fold */
  nNew = nOut;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
    nNew -= 20;        assert( 20==sqlite3LogEst(4) );
    nOut--;
  }
  if( pUpper ){
    nNew -= 20;        assert( 20==sqlite3LogEst(4) );
    nOut--;
  }
  if( nNew<10 ) nNew = 10;
  if( nNew<nOut ) nOut = nNew;
  pLoop->nOut = (LogEst)nOut;
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in

** If pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
*/
static int whereLoopAddBtreeIndex(
  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */
  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */
  Index *pProbe,                  /* An index on pSrc */
  LogEst nInMul                   /* log(Number of iterations due to IN) */
){
  WhereInfo *pWInfo = pBuilder->pWInfo;  /* WHERE analyse context */
  Parse *pParse = pWInfo->pParse;        /* Parsing context */
  sqlite3 *db = pParse->db;       /* Database connection malloc context */
  WhereLoop *pNew;                /* Template WhereLoop under construction */
  WhereTerm *pTerm;               /* A WhereTerm under consideration */
  int opMask;                     /* Valid operators for constraints */
  WhereScan scan;                 /* Iterator for WHERE terms */
  Bitmask saved_prereq;           /* Original value of pNew->prereq */
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  int saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
  LogEst saved_nOut;              /* Original value of pNew->nOut */
  int iCol;                       /* Index of the column in the table */
  int rc = SQLITE_OK;             /* Return code */
  LogEst nRowEst;                 /* Estimated index selectivity */
  LogEst rLogSize;                /* Logarithm of table size */
  WhereTerm *pTop = 0, *pBtm = 0; /* Top and bottom range constraints */

  pNew = pBuilder->pNew;
  if( db->mallocFailed ) return SQLITE_NOMEM;

  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );
  assert( (pNew->wsFlags & WHERE_TOP_LIMIT)==0 );
  if( pNew->wsFlags & WHERE_BTM_LIMIT ){
    opMask = WO_LT|WO_LE;
  }else if( pProbe->tnum<=0 || (pSrc->jointype & JT_LEFT)!=0 ){
    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE;
  }else{
    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)

    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize; /* Baseline cost is log2(N).  Adjustments below */
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
      pNew->wsFlags |= WHERE_COLUMN_IN;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  TUNING: the SELECT returns 25 rows */
        nIn = 46;  assert( 46==sqlite3LogEst(25) );
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = sqlite3LogEst(pExpr->x.pList->nExpr);
      }
      pNew->rRun += nIn;
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_EQ) ){
      assert( (pNew->wsFlags & (WHERE_COLUMN_NULL|WHERE_COLUMN_IN))!=0
                  || nInMul==0 );

      }
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul;
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      /* TUNING: IS NULL selects 2 rows */
      nIn = 10;  assert( 10==sqlite3LogEst(2) );
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){
      testcase( pTerm->eOperator & WO_GT );
      testcase( pTerm->eOperator & WO_GE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else{
      assert( pTerm->eOperator & (WO_LT|WO_LE) );
      testcase( pTerm->eOperator & WO_LT );
      testcase( pTerm->eOperator & WO_LE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      assert( pNew->nOut==saved_nOut );
      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);
    }
#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);
    }
    /* Step cost for each output row */
    pNew->rRun = sqlite3LogEstAdd(pNew->rRun, pNew->nOut);
    whereLoopOutputAdjust(pBuilder->pWC, pNew, pSrc->iCursor);
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<(pProbe->nColumn + (pProbe->zName!=0))
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }

  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 */
  LogEst rSize;               /* number of rows in the table */
  LogEst rLogSize;            /* Logarithm of the number of rows in the table */
  WhereClause *pWC;           /* The parsed WHERE clause */
  Table *pTab;                /* Table being queried */
  
  pNew = pBuilder->pNew;
  pWInfo = pBuilder->pWInfo;
  pTabList = pWInfo->pTabList;
  pSrc = pTabList->a + pNew->iTab;
  pTab = pSrc->pTab;
  pWC = pBuilder->pWC;
  assert( !IsVirtual(pSrc->pTab) );

  if( pSrc->pIndex ){
    /* An INDEXED BY clause specifies a particular index to use */
    pProbe = pSrc->pIndex;
  }else{
    /* There is no INDEXED BY clause.  Create a fake Index object in local
    ** variable sPk to represent the rowid primary key index.  Make this
    ** fake index the first in a chain of Index objects with all of the real
    ** indices to follow */
    Index *pFirst;                  /* First of real indices on the table */
    memset(&sPk, 0, sizeof(Index));
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pTab;
    aiRowEstPk[0] = 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(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

        pNew->u.btree.nEq = 1;
        pNew->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        /* TUNING: One-time cost for computing the automatic index is
        ** approximately 7*N*log2(N) where N is the number of rows in
        ** the table being indexed. */
        pNew->rSetup = rLogSize + rSize + 28;  assert( 28==sqlite3LogEst(7) );
        /* TUNING: Each index lookup yields 20 rows in the table.  This
        ** is more than the usual guess of 10 rows, since we have no way
        ** of knowning how selective the index will ultimately be.  It would
        ** not be unreasonable to make this value much larger. */
        pNew->nOut = 43;  assert( 43==sqlite3LogEst(20) );
        pNew->rRun = sqlite3LogEstAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_AUTO_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */

      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      /* TUNING: Cost of full table scan is 3*(N + log2(N)).
      **  +  The extra 3 factor is to encourage the use of indexed lookups
      **     over full scans.  FIXME */


      pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 16;
      whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
      rc = whereLoopInsert(pBuilder, pNew);
      pNew->nOut = rSize;
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsInIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
      if( b
       || ( m==0
         && pProbe->bUnordered==0
         && pProbe->szIdxRow<pTab->szTabRow
         && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
         && sqlite3GlobalConfig.bUseCis
         && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
          )
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        if( m==0 ){
          /* TUNING: Cost of a covering index scan is K*(N + log2(N)).
          **  +  The extra factor K of between 1.1 and 3.0 that depends
          **     on the relative sizes of the table and the index.  K
          **     is smaller for smaller indices, thus favoring them.
          */



          pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 1 +
                        (15*pProbe->szIdxRow)/pTab->szTabRow;
        }else{
          assert( b!=0 ); 
          /* TUNING: Cost of scanning a non-covering index is (N+1)*log2(N)
          ** which we will simplify to just N*log2(N) */
          pNew->rRun = rSize + rLogSize;
        }
        whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);

      pNew->u.vtab.idxNum = pIdxInfo->idxNum;
      pNew->u.vtab.needFree = pIdxInfo->needToFreeIdxStr;
      pIdxInfo->needToFreeIdxStr = 0;
      pNew->u.vtab.idxStr = pIdxInfo->idxStr;
      pNew->u.vtab.isOrdered = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = 0;
      pNew->rRun = sqlite3LogEstFromDouble(pIdxInfo->estimatedCost);
      /* TUNING: Every virtual table query returns 25 rows */
      pNew->nOut = 46;  assert( 46==sqlite3LogEst(25) );
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
    }
  }  

  struct SrcList_item *pItem;
  
  pWC = pBuilder->pWC;
  if( pWInfo->wctrlFlags & WHERE_AND_ONLY ) return SQLITE_OK;
  pWCEnd = pWC->a + pWC->nTerm;
  pNew = pBuilder->pNew;
  memset(&sSum, 0, sizeof(sSum));
  pItem = pWInfo->pTabList->a + pNew->iTab;
  iCur = pItem->iCursor;

  for(pTerm=pWC->a; pTerm<pWCEnd && rc==SQLITE_OK; pTerm++){
    if( (pTerm->eOperator & WO_OR)!=0
     && (pTerm->u.pOrInfo->indexable & pNew->maskSelf)!=0 
    ){
      WhereClause * const pOrWC = &pTerm->u.pOrInfo->wc;
      WhereTerm * const pOrWCEnd = &pOrWC->a[pOrWC->nTerm];
      WhereTerm *pOrTerm;
      int once = 1;
      int i, j;
    


      sSubBuild = *pBuilder;
      sSubBuild.pOrderBy = 0;
      sSubBuild.pOrSet = &sCur;

      for(pOrTerm=pOrWC->a; pOrTerm<pOrWCEnd; pOrTerm++){
        if( (pOrTerm->eOperator & WO_AND)!=0 ){
          sSubBuild.pWC = &pOrTerm->u.pAndInfo->wc;

          once = 0;
        }else{
          whereOrMove(&sPrev, &sSum);
          sSum.n = 0;
          for(i=0; i<sPrev.n; i++){
            for(j=0; j<sCur.n; j++){
              whereOrInsert(&sSum, sPrev.a[i].prereq | sCur.a[j].prereq,
                            sqlite3LogEstAdd(sPrev.a[i].rRun, sCur.a[j].rRun),
                            sqlite3LogEstAdd(sPrev.a[i].nOut, sCur.a[j].nOut));
            }
          }
        }
      }
      pNew->nLTerm = 1;
      pNew->aLTerm[0] = pTerm;
      pNew->wsFlags = WHERE_MULTI_OR;

** Assume that the total number of output rows that will need to be sorted
** will be nRowEst (in the 10*log2 representation).  Or, ignore sorting
** costs if nRowEst==0.
**
** Return SQLITE_OK on success or SQLITE_NOMEM of a memory allocation
** error occurs.
*/
static int wherePathSolver(WhereInfo *pWInfo, LogEst nRowEst){
  int mxChoice;             /* Maximum number of simultaneous paths tracked */
  int nLoop;                /* Number of terms in the join */
  Parse *pParse;            /* Parsing context */
  sqlite3 *db;              /* The database connection */
  int iLoop;                /* Loop counter over the terms of the join */
  int ii, jj;               /* Loop counters */
  int mxI = 0;              /* Index of next entry to replace */
  LogEst rCost;             /* Cost of a path */
  LogEst nOut;              /* Number of outputs */
  LogEst mxCost = 0;        /* Maximum cost of a set of paths */
  LogEst mxOut = 0;         /* Maximum nOut value on the set of paths */
  LogEst rSortCost;         /* Cost to do a sort */
  int nTo, nFrom;           /* Number of valid entries in aTo[] and aFrom[] */
  WherePath *aFrom;         /* All nFrom paths at the previous level */
  WherePath *aTo;           /* The nTo best paths at the current level */
  WherePath *pFrom;         /* An element of aFrom[] that we are working on */
  WherePath *pTo;           /* An element of aTo[] that we are working on */
  WhereLoop *pWLoop;        /* One of the WhereLoop objects */
  WhereLoop **pX;           /* Used to divy up the pSpace memory */

  }

  /* Seed the search with a single WherePath containing zero WhereLoops.
  **
  ** TUNING: Do not let the number of iterations go above 25.  If the cost
  ** of computing an automatic index is not paid back within the first 25
  ** rows, then do not use the automatic index. */
  aFrom[0].nRow = MIN(pParse->nQueryLoop, 46);  assert( 46==sqlite3LogEst(25) );
  nFrom = 1;

  /* Precompute the cost of sorting the final result set, if the caller
  ** to sqlite3WhereBegin() was concerned about sorting */
  rSortCost = 0;
  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* TUNING: Estimated cost of sorting is 48*N*log2(N) where N is the
    ** number of output rows. The 48 is the expected size of a row to sort. 
    ** FIXME:  compute a better estimate of the 48 multiplier based on the
    ** result set expressions. */
    rSortCost = nRowEst + estLog(nRowEst);
    WHERETRACE(0x002,("---- sort cost=%-3d\n", rSortCost));
  }

  /* Compute successively longer WherePaths using the previous generation
  ** of WherePaths as the basis for the next.  Keep track of the mxChoice
  ** best paths at each generation */
  for(iLoop=0; iLoop<nLoop; iLoop++){
    nTo = 0;
    for(ii=0, pFrom=aFrom; ii<nFrom; ii++, pFrom++){
      for(pWLoop=pWInfo->pLoops; pWLoop; pWLoop=pWLoop->pNextLoop){
        Bitmask maskNew;
        Bitmask revMask = 0;
        u8 isOrderedValid = pFrom->isOrderedValid;
        u8 isOrdered = pFrom->isOrdered;
        if( (pWLoop->prereq & ~pFrom->maskLoop)!=0 ) continue;
        if( (pWLoop->maskSelf & pFrom->maskLoop)!=0 ) continue;
        /* At this point, pWLoop is a candidate to be the next loop. 
        ** Compute its cost */
        rCost = sqlite3LogEstAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);
        rCost = sqlite3LogEstAdd(rCost, pFrom->rCost);
        nOut = pFrom->nRow + pWLoop->nOut;
        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( !isOrderedValid ){
          switch( wherePathSatisfiesOrderBy(pWInfo,
                       pWInfo->pOrderBy, pFrom, pWInfo->wctrlFlags,
                       iLoop, pWLoop, &revMask) ){
            case 1:  /* Yes.  pFrom+pWLoop does satisfy the ORDER BY clause */
              isOrdered = 1;
              isOrderedValid = 1;
              break;
            case 0:  /* No.  pFrom+pWLoop will require a separate sort */
              isOrdered = 0;
              isOrderedValid = 1;
              rCost = sqlite3LogEstAdd(rCost, rSortCost);
              break;
            default: /* Cannot tell yet.  Try again on the next iteration */
              break;
          }
        }else{
          revMask = pFrom->revLoop;
        }

  pTerm = findTerm(pWC, iCur, -1, 0, WO_EQ, 0);
  if( pTerm ){
    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;
    pLoop->aLTerm[0] = pTerm;
    pLoop->nLTerm = 1;
    pLoop->u.btree.nEq = 1;
    /* TUNING: Cost of a rowid lookup is 10 */
    pLoop->rRun = 33;  /* 33==sqlite3LogEst(10) */
  }else{
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      assert( pLoop->aLTermSpace==pLoop->aLTerm );
      assert( ArraySize(pLoop->aLTermSpace)==4 );
      if( pIdx->onError==OE_None 
       || pIdx->pPartIdxWhere!=0 
       || pIdx->nColumn>ArraySize(pLoop->aLTermSpace) 

      if( (pItem->colUsed & ~columnsInIndex(pIdx))==0 ){
        pLoop->wsFlags |= WHERE_IDX_ONLY;
      }
      pLoop->nLTerm = j;
      pLoop->u.btree.nEq = j;
      pLoop->u.btree.pIndex = pIdx;
      /* TUNING: Cost of a unique index lookup is 15 */
      pLoop->rRun = 39;  /* 39==sqlite3LogEst(15) */
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (LogEst)1;
    pWInfo->a[0].pWLoop = pLoop;
    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);
    pWInfo->a[0].iTabCur = iCur;
    pWInfo->nRowOut = 1;
    if( pWInfo->pOrderBy ) pWInfo->bOBSat =  1;
    if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;

proc eqp {sql {db db}} {
  uplevel execsql [list "EXPLAIN QUERY PLAN $sql"] $db
}

do_test analyze6-1.0 {
  db eval {
    CREATE TABLE cat(x INT, yz TEXT);
    CREATE UNIQUE INDEX catx ON cat(x);
    /* Give cat 16 unique integers */
    INSERT INTO cat(x) VALUES(1);
    INSERT INTO cat(x) VALUES(2);
    INSERT INTO cat(x) SELECT x+2 FROM cat;
    INSERT INTO cat(x) SELECT x+4 FROM cat;
    INSERT INTO cat(x) SELECT x+8 FROM cat;

    CREATE TABLE ev(y INT);
    CREATE INDEX evy ON ev(y);
    /* ev will hold 32 copies of 16 integers found in cat */
    INSERT INTO ev SELECT x FROM cat;
    INSERT INTO ev SELECT x FROM cat;
    INSERT INTO ev SELECT y FROM ev;

} [concat {-60.06 {} {}} {-39.24 {} encompass -1}]

# EVIDENCE-OF: R-44414-54710 There is a row in the cartesian product
# dataset formed by combining each unique combination of a row from the
# left-hand and right-hand datasets.
#
do_join_test e_select-1.4.2.1 {
  SELECT * FROM x2 %JOIN% x3 ORDER BY +c, +f
} [list -60.06 {} {}      -39.24 {} encompass -1                 \
        -60.06 {} {}      alerting {} -93.79 {}                  \

        -60.06 {} {}      coldest -96 dramatists 82.3            \
        -60.06 {} {}      conducting -87.24 37.56 {}             \
        -60.06 {} {}      presenting 51 reformation dignified    \
        -58 {} 1.21       -39.24 {} encompass -1                 \
        -58 {} 1.21       alerting {} -93.79 {}                  \

        -58 {} 1.21       coldest -96 dramatists 82.3            \
        -58 {} 1.21       conducting -87.24 37.56 {}             \
        -58 {} 1.21       presenting 51 reformation dignified    \
]
# TODO: Come back and add a few more like the above.

# EVIDENCE-OF: R-20659-43267 In other words, if the left-hand dataset
# consists of Nlhs rows of Mlhs columns, and the right-hand dataset of
# Nrhs rows of Mrhs columns, then the cartesian product is a dataset of
# Nlhs.Nrhs rows, each containing Mlhs+Mrhs columns.

# ...
# eqp-7.*:        "SELECT count(*) FROM tbl" statements (VDBE code OP_Count).
#

proc det {args} { uplevel do_eqp_test $args }

do_execsql_test 1.1 {
  CREATE TABLE t1(a INT, b INT, ex TEXT);
  CREATE INDEX i1 ON t1(a);
  CREATE INDEX i2 ON t1(b);
  CREATE TABLE t2(a INT, b INT, ex TEXT);
  CREATE TABLE t3(a INT, b INT, ex TEXT);
}

do_eqp_test 1.2 {
  SELECT * FROM t2, t1 WHERE t1.a=1 OR t1.b=2;
} {
  0 0 1 {SEARCH TABLE t1 USING INDEX i1 (a=?)} 
  0 0 1 {SEARCH TABLE t1 USING INDEX i2 (b=?)} 

}

#-------------------------------------------------------------------------
# Test cases eqp-2.* - tests for single select statements.
#
drop_all_tables
do_execsql_test 2.1 {
  CREATE TABLE t1(x INT, y INT, ex TEXT);

  CREATE TABLE t2(x INT, y INT, ex TEXT);
  CREATE INDEX t2i1 ON t2(x);
}

det 2.2.1 "SELECT DISTINCT min(x), max(x) FROM t1 GROUP BY x ORDER BY 1" {
  0 0 0 {SCAN TABLE t1}
  0 0 0 {USE TEMP B-TREE FOR GROUP BY}
  0 0 0 {USE TEMP B-TREE FOR DISTINCT}

#
drop_all_tables

# EVIDENCE-OF: R-47779-47605 sqlite> EXPLAIN QUERY PLAN SELECT a, b
# FROM t1 WHERE a=1;
# 0|0|0|SCAN TABLE t1
#
do_execsql_test 5.1.0 { CREATE TABLE t1(a INT, b INT, ex TEXT) }
det 5.1.1 "SELECT a, b FROM t1 WHERE a=1" {
  0 0 0 {SCAN TABLE t1}
}

# EVIDENCE-OF: R-55852-17599 sqlite> CREATE INDEX i1 ON t1(a);
# sqlite> EXPLAIN QUERY PLAN SELECT a, b FROM t1 WHERE a=1;
# 0|0|0|SEARCH TABLE t1 USING INDEX i1

}

# EVIDENCE-OF: R-09991-48941 sqlite> EXPLAIN QUERY PLAN
# SELECT t1.*, t2.* FROM t1, t2 WHERE t1.a=1 AND t1.b>2;
# 0|0|0|SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?)
# 0|1|1|SCAN TABLE t2
#
do_execsql_test 5.4.0 {CREATE TABLE t2(c INT, d INT, ex TEXT)}
det 5.4.1 "SELECT t1.a, t2.c FROM t1, t2 WHERE t1.a=1 AND t1.b>2" {
  0 0 0 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?)}
  0 1 1 {SCAN TABLE t2}
}

# EVIDENCE-OF: R-33626-61085 sqlite> EXPLAIN QUERY PLAN
# SELECT t1.*, t2.* FROM t2, t1 WHERE t1.a=1 AND t1.b>2;
# 0|0|1|SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?)
# 0|1|0|SCAN TABLE t2
#
det 5.5 "SELECT t1.a, t2.c FROM t2, t1 WHERE t1.a=1 AND t1.b>2" {
  0 0 1 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?)}
  0 1 0 {SCAN TABLE t2}
}

# EVIDENCE-OF: R-04002-25654 sqlite> CREATE INDEX i3 ON t1(b);
# sqlite> EXPLAIN QUERY PLAN SELECT * FROM t1 WHERE a=1 OR b=2;
# 0|0|0|SEARCH TABLE t1 USING COVERING INDEX i2 (a=?)
# 0|0|0|SEARCH TABLE t1 USING INDEX i3 (b=?)
#
do_execsql_test 5.5.0 {CREATE INDEX i3 ON t1(b)}
det 5.6.1 "SELECT a, b FROM t1 WHERE a=1 OR b=2" {
  0 0 0 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=?)}
  0 0 0 {SEARCH TABLE t1 USING INDEX i3 (b=?)}
}

# EVIDENCE-OF: R-24577-38891 sqlite> EXPLAIN QUERY PLAN
# SELECT c, d FROM t2 ORDER BY c;
# 0|0|0|SCAN TABLE t2

}

# EVIDENCE-OF: R-46219-33846 sqlite> EXPLAIN QUERY PLAN
# SELECT * FROM (SELECT * FROM t2 WHERE c=1), t1;
# 0|0|0|SEARCH TABLE t2 USING INDEX i4 (c=?)
# 0|1|1|SCAN TABLE t1
#
det 5.11 "SELECT a, b FROM (SELECT * FROM t2 WHERE c=1), t1" {
  0 0 0 {SEARCH TABLE t2 USING INDEX i4 (c=?)}
  0 1 1 {SCAN TABLE t1 USING COVERING INDEX i2}
}

# EVIDENCE-OF: R-37879-39987 sqlite> EXPLAIN QUERY PLAN
# SELECT a FROM t1 UNION SELECT c FROM t2;
# 1|0|0|SCAN TABLE t1
# 2|0|0|SCAN TABLE t2
# 0|0|0|COMPOUND SUBQUERIES 1 AND 2 USING TEMP B-TREE (UNION)
#
det 5.12 "SELECT a,b FROM t1 UNION SELECT c, 99 FROM t2" {
  1 0 0 {SCAN TABLE t1 USING COVERING INDEX i2}
  2 0 0 {SCAN TABLE t2 USING COVERING INDEX i4}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 USING TEMP B-TREE (UNION)}
}

# EVIDENCE-OF: R-44864-63011 sqlite> EXPLAIN QUERY PLAN
# SELECT a FROM t1 EXCEPT SELECT d FROM t2 ORDER BY 1;
# 1|0|0|SCAN TABLE t1 USING COVERING INDEX i2
# 2|0|0|SCAN TABLE t2 2|0|0|USE TEMP B-TREE FOR ORDER BY
# 0|0|0|COMPOUND SUBQUERIES 1 AND 2 (EXCEPT)
#
det 5.13 "SELECT a FROM t1 EXCEPT SELECT d FROM t2 ORDER BY 1" {
  1 0 0 {SCAN TABLE t1 USING COVERING INDEX i1}
  2 0 0 {SCAN TABLE t2}
  2 0 0 {USE TEMP B-TREE FOR ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (EXCEPT)}
}


#-------------------------------------------------------------------------

    set data [read $fd]
    close $fd
    set data
  }] [list $res]
}

do_peqp_test 6.1 {
  SELECT a, b FROM t1 EXCEPT SELECT d, 99 FROM t2 ORDER BY 1
} [string trimleft {
1 0 0 SCAN TABLE t1 USING COVERING INDEX i2
2 0 0 SCAN TABLE t2
2 0 0 USE TEMP B-TREE FOR ORDER BY
0 0 0 COMPOUND SUBQUERIES 1 AND 2 (EXCEPT)
}]

#-------------------------------------------------------------------------
# The following tests - eqp-7.* - test that queries that use the OP_Count
# optimization return something sensible with EQP.
#
drop_all_tables

do_execsql_test 7.0 {
  CREATE TABLE t1(a INT, b INT, ex CHAR(100));
  CREATE TABLE t2(a INT, b INT, ex CHAR(100));
  CREATE INDEX i1 ON t2(a);
}

det 7.1 "SELECT count(*) FROM t1" {
  0 0 0 {SCAN TABLE t1}
}

det 7.2 "SELECT count(*) FROM t2" {
  0 0 0 {SCAN TABLE t2 USING COVERING INDEX i1}
}

do_execsql_test 7.3 {
  INSERT INTO t1(a,b) VALUES(1, 2);
  INSERT INTO t1(a,b) VALUES(3, 4);

  INSERT INTO t2(a,b) VALUES(1, 2);
  INSERT INTO t2(a,b) VALUES(3, 4);
  INSERT INTO t2(a,b) VALUES(5, 6);
 
  ANALYZE;
}

db close
sqlite3 db test.db

      pragma foreign_key_list(t5);
    }
  } {}
  do_test pragma-6.4 {
    execsql {
      pragma index_list(t3);
    }
  } {/0 {} 1 \d+ 1 sqlite_autoindex_t3_1 1 \d+/}
}
ifcapable {!foreignkey} {
  execsql {CREATE TABLE t3(a,b UNIQUE)}
}
do_test pragma-6.5.1 {
  execsql {
    CREATE INDEX t3i1 ON t3(a,b);

do_test pragma-7.1.1 {
  # Make sure a pragma knows to read the schema if it needs to
  db close
  sqlite3 db test.db
  execsql {
    pragma index_list(t3);
  }
} {/0 {} 1 \d+ 1 t3i1 0 \d+ 2 sqlite_autoindex_t3_1 1 \d+/}
do_test pragma-7.1.2 {
  execsql {
    pragma index_list(t3_bogus);
  }
} {}
} ;# ifcapable schema_pragmas
ifcapable {utf16} {

  db2 eval {PRAGMA index_info(i2)}
} {0 2 c 1 3 d 2 1 b}
do_test 23.3 {
  db eval {
    CREATE INDEX i3 ON t1(d,b,c);
  }
  db2 eval {PRAGMA index_list(t1)}
} {/0 {} 1 \d+ 1 i3 0 \d+ 2 i2 0 \d+ 3 i1 0 \d+/}
do_test 23.4 {
  db eval {
    ALTER TABLE t1 ADD COLUMN e;
  }
  db2 eval {
    PRAGMA table_info(t1);
  }

     SELECT * FROM test1 a, test1 b LIMIT 1
  }
} {a.f1 11 a.f2 22 b.f1 11 b.f2 22}
do_test select1-6.9.7 {
  set x [execsql2 {
     SELECT * FROM test1 a, (select 5, 6) LIMIT 1
  }]
  regsub -all {sq_[0-9a-fA-F_]+} $x {subquery} x
  set x
} {a.f1 11 a.f2 22 sqlite_subquery.5 5 sqlite_subquery.6 6}
do_test select1-6.9.8 {
  set x [execsql2 {
     SELECT * FROM test1 a, (select 5 AS x, 6 AS y) AS b LIMIT 1
  }]
  regsub -all {subquery_[0-9a-fA-F]+_} $x {subquery} x

} {10.0}
do_test subquery-2.5.3.2 {
  # Verify that the t4i index was not used in the previous query
  execsql {
    EXPLAIN QUERY PLAN
    SELECT * FROM t4 WHERE x IN (SELECT a FROM t3);
  }
} {~/t4i/}
do_test subquery-2.5.4 {
  execsql {
    DROP TABLE t3;
    DROP TABLE t4;
  }
} {}

#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

do_test tkt-78e04-1.0 {
  execsql {
    CREATE TABLE ""("" UNIQUE, x CHAR(100));
    CREATE TABLE t2(x);
    INSERT INTO ""("") VALUES(1);
    INSERT INTO t2 VALUES(2);
    SELECT * FROM "", t2;
  }
} {1 {} 2}
do_test tkt-78e04-1.1 {
  catchsql {
    INSERT INTO ""("") VALUES(1);
  }
} {1 {column  is not unique}}
do_test tkt-78e04-1.2 {
  execsql {
    PRAGMA table_info("");
  }
} {0 {} {} 0 {} 0 1 x CHAR(100) 0 {} 0}
do_test tkt-78e04-1.3 {
  execsql {
    CREATE INDEX i1 ON ""("" COLLATE nocase);
  }
} {}
do_test tkt-78e04-1.4 {
  execsql {
    EXPLAIN QUERY PLAN SELECT "" FROM "" WHERE "" LIKE 'abc%';
  }
} {0 0 0 {SCAN TABLE  USING COVERING INDEX i1}}
do_test tkt-78e04-1.5 {
  execsql {
    DROP TABLE "";
    SELECT name FROM sqlite_master;
  }

#
# When optimizing out ORDER BY clauses, make sure that trailing terms
# of the ORDER BY clause do not reference other tables in a join.
#
if {[permutation] != "no_optimization"} {
do_test where-14.1 {
  execsql {
    CREATE TABLE t8(a INTEGER PRIMARY KEY, b TEXT UNIQUE, c CHAR(100));
    INSERT INTO t8(a,b) VALUES(1,'one');
    INSERT INTO t8(a,b) VALUES(4,'four');
  }
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.a, y.b
  } 
} {1/4 1/1 4/4 4/1 nosort}
do_test where-14.2 {
  cksort {

if {[permutation] != "no_optimization"} {

# Ticket #2249.  Make sure the OR optimization is not attempted if
# comparisons between columns of different affinities are needed.
#
do_test where2-6.7 {
  execsql {
    CREATE TABLE t2249a(a TEXT UNIQUE, x CHAR(100));
    CREATE TABLE t2249b(b INTEGER);
    INSERT INTO t2249a(a) VALUES('0123');
    INSERT INTO t2249b VALUES(123);
  }
  queryplan {
    -- Because a is type TEXT and b is type INTEGER, both a and b
    -- will attempt to convert to NUMERIC before the comparison.
    -- They will thus compare equal.
    --
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a=b;
  }
} {123 0123 nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.9 {
  queryplan {
    -- The + operator removes affinity from the rhs.  No conversions
    -- occur and the comparison is false.  The result is an empty set.
    --
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a=+b;
  }
} {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.9.2 {
  # The same thing but with the expression flipped around.
  queryplan {
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE +b=a
  }
} {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.10 {
  queryplan {
    -- Use + on both sides of the comparison to disable indices
    -- completely.  Make sure we get the same result.
    --
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE +a=+b;
  }
} {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.11 {
  # This will not attempt the OR optimization because of the a=b
  # comparison.
  queryplan {
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a=b OR a='hello';
  }
} {123 0123 nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.11.2 {
  # Permutations of the expression terms.
  queryplan {
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE b=a OR a='hello';
  }
} {123 0123 nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.11.3 {
  # Permutations of the expression terms.
  queryplan {
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE 'hello'=a OR b=a;
  }
} {123 0123 nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
do_test where2-6.11.4 {
  # Permutations of the expression terms.
  queryplan {
    SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a='hello' OR b=a;
  }
} {123 0123 nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
ifcapable explain&&subquery {
  # These tests are not run if subquery support is not included in the
  # build. This is because these tests test the "a = 1 OR a = 2" to
  # "a IN (1, 2)" optimisation transformation, which is not enabled if
  # subqueries and the IN operator is not available.
  #
  do_test where2-6.12 {
    # In this case, the +b disables the affinity conflict and allows
    # the OR optimization to be used again.  The result is now an empty
    # set, the same as in where2-6.9.
    queryplan {
      SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a=+b OR a='hello';
    }
  } {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
  do_test where2-6.12.2 {
    # In this case, the +b disables the affinity conflict and allows
    # the OR optimization to be used again.  The result is now an empty
    # set, the same as in where2-6.9.
    queryplan {
      SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a='hello' OR +b=a;
    }
  } {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
  do_test where2-6.12.3 {
    # In this case, the +b disables the affinity conflict and allows
    # the OR optimization to be used again.  The result is now an empty
    # set, the same as in where2-6.9.
    queryplan {
      SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE +b=a OR a='hello';
    }
  } {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
  do_test where2-6.13 {
    # The addition of +a on the second term disabled the OR optimization.
    # But we should still get the same empty-set result as in where2-6.9.
    queryplan {
      SELECT b,a FROM t2249b CROSS JOIN t2249a WHERE a=+b OR +a='hello';
    }
  } {nosort t2249b * t2249a sqlite_autoindex_t2249a_1}
}

# Variations on the order of terms in a WHERE clause in order
# to make sure the OR optimizer can recognize them all.
do_test where2-6.20 {
  queryplan {
    SELECT x.a, y.a FROM t2249a x CROSS JOIN t2249a y WHERE x.a=y.a
  }
} {0123 0123 nosort x sqlite_autoindex_t2249a_1 y sqlite_autoindex_t2249a_1}
ifcapable explain&&subquery {
  # These tests are not run if subquery support is not included in the
  # build. This is because these tests test the "a = 1 OR a = 2" to
  # "a IN (1, 2)" optimisation transformation, which is not enabled if
  # subqueries and the IN operator is not available.
  #
  do_test where2-6.21 {
    queryplan {
      SELECT x.a,y.a FROM t2249a x CROSS JOIN t2249a y
       WHERE x.a=y.a OR y.a='hello'
    }
  } {0123 0123 nosort x sqlite_autoindex_t2249a_1 y sqlite_autoindex_t2249a_1}
  do_test where2-6.22 {
    queryplan {
      SELECT x.a,y.a FROM t2249a x CROSS JOIN t2249a y
       WHERE y.a=x.a OR y.a='hello'
    }
  } {0123 0123 nosort x sqlite_autoindex_t2249a_1 y sqlite_autoindex_t2249a_1}
  do_test where2-6.23 {
    queryplan {
      SELECT x.a,y.a FROM t2249a x CROSS JOIN t2249a y
       WHERE y.a='hello' OR x.a=y.a
    }
  } {0123 0123 nosort x sqlite_autoindex_t2249a_1 y sqlite_autoindex_t2249a_1}
}

# Unique queries (queries that are guaranteed to return only a single
# row of result) do not call the sorter.  But all tables must give
# a unique result.  If any one table in the join does not give a unique

  }
} {4 8 10}

# Verify that the OR clause is used in an outer loop even when
# the OR clause scores slightly better on an inner loop.
if {[permutation] != "no_optimization"} {
do_execsql_test where2-12.1 {
  CREATE TABLE t12(x INTEGER PRIMARY KEY, y INT, z CHAR(100));
  CREATE INDEX t12y ON t12(y);
  EXPLAIN QUERY PLAN
    SELECT a.x, b.x
      FROM t12 AS a JOIN t12 AS b ON a.y=b.x
     WHERE (b.x=$abc OR b.y=$abc);
} {/.*SEARCH TABLE t12 AS b .*SEARCH TABLE t12 AS b .*/}
}


finish_test

/*
** 2013-06-10
**
** 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 contains a simple command-line utility for converting from
** integers and LogEst values and back again and for doing simple
** arithmetic operations (multiple and add) on LogEst values.
**
** Usage:
**
**      ./LogEst ARGS
**
** Arguments:
**
**    'x'    Multiple the top two elements of the stack
**    '+'    Add the top two elements of the stack
**    NUM    Convert NUM from integer to LogEst and push onto the stack
**   ^NUM    Interpret NUM as a LogEst and push onto stack.
**
** Examples:
**
** To convert 123 from LogEst to integer:
** 
**         ./LogEst ^123
**
** To convert 123456 from integer to LogEst:
**
**         ./LogEst 123456
**
*/
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <assert.h>
#include <string.h>
#include "sqlite3.h"

typedef short int LogEst;  /* 10 times log2() */

LogEst logEstMultiply(LogEst a, LogEst b){ return a+b; }
LogEst logEstAdd(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 */
      6, 6, 6,                       /* 9,10,11 */
      5, 5, 5,                       /* 12-14 */
      4, 4, 4, 4,                    /* 15-18 */
      3, 3, 3, 3, 3, 3,              /* 19-24 */
      2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
  };
  if( a<b ){ LogEst t = a; a = b; b = t; }
  if( a>b+49 ) return a;
  if( a>b+31 ) return a+1;
  return a+x[a-b];
}
LogEst logEstFromInteger(sqlite3_uint64 x){
  static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  LogEst y = 40;
  if( x<8 ){
    if( x<2 ) return 0;
    while( x<8 ){  y -= 10; x <<= 1; }
  }else{
    while( x>255 ){ y += 40; x >>= 4; }
    while( x>15 ){  y += 10; x >>= 1; }
  }
  return a[x&7] + y - 10;
}
static sqlite3_uint64 logEstToInt(LogEst x){
  sqlite3_uint64 n;
  if( x<10 ) return 1;
  n = x%10;
  x /= 10;
  if( n>=5 ) n -= 2;
  else if( n>=1 ) n -= 1;
  if( x>=3 ) return (n+8)<<(x-3);
  return (n+8)>>(3-x);
}
static LogEst logEstFromDouble(double x){
  sqlite3_uint64 a;
  LogEst e;
  assert( sizeof(x)==8 && sizeof(a)==8 );
  if( x<=0.0 ) return -32768;
  if( x<1.0 ) return -logEstFromDouble(1/x);
  if( x<1024.0 ) return logEstFromInteger((sqlite3_uint64)(1024.0*x)) - 100;
  if( x<=2000000000.0 ) return logEstFromInteger((sqlite3_uint64)x);
  memcpy(&a, &x, 8);
  e = (a>>52) - 1022;
  return e*10;
}

int isFloat(const char *z){
  while( z[0] ){
    if( z[0]=='.' || z[0]=='E' || z[0]=='e' ) return 1;
    z++;
  }
  return 0;
}

int main(int argc, char **argv){
  int i;
  int n = 0;
  LogEst a[100];
  for(i=1; i<argc; i++){
    const char *z = argv[i];
    if( z[0]=='+' ){
      if( n>=2 ){
        a[n-2] = logEstAdd(a[n-2],a[n-1]);
        n--;
      }
    }else if( z[0]=='x' ){
      if( n>=2 ){
        a[n-2] = logEstMultiply(a[n-2],a[n-1]);
        n--;
      }
    }else if( z[0]=='^' ){
      a[n++] = atoi(z+1);
    }else if( isFloat(z) ){
      a[n++] = logEstFromDouble(atof(z));
    }else{
      a[n++] = logEstFromInteger(atoi(z));
    }
  }
  for(i=n-1; i>=0; i--){
    if( a[i]<0 ){
      printf("%d (%f)\n", a[i], 1.0/(double)logEstToInt(-a[i]));
    }else{
      sqlite3_uint64 x = logEstToInt(a[i]+100)*100/1024;
      printf("%d (%lld.%02lld)\n", a[i], x/100, x%100);
    }
  }
  return 0;
}