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Changes In Branch row-size-est Excluding Merge-Ins

This is equivalent to a diff from de78250ad2 to e97d7d3044

2013-10-10
12:38
Estimate row sizes for tables and indices and use those estimates during query planning. Enhance the index_info pragma to show the estimated row sizes and to show the estimated row size for the main table as well. Allow an alternative row size estimate to be specified in the sqlite_stat1 table. check-in: d27b88b8c2 user: drh tags: trunk
2013-10-09
19:07
Make sure the correct printf format is used for type tRowcnt regardless of whether 32-bit or 64-bit row counts are specified at compile-time. Closed-Leaf check-in: e97d7d3044 user: drh tags: row-size-est
2013-10-08
23:16
Move a conditional inside of an #ifdef in order to make all branches reachable regardless of compile-time options used. check-in: f7cc30d45b user: drh tags: row-size-est
2013-10-05
18:16
Begin an experimental refactoring to estimate the average number of bytes in table and index rows and to use that information in query planner. Begin by renaming WhereCost to LogEst and making that type and its conversion routines available outside of where.c. check-in: 66c4a251d6 user: drh tags: row-size-est
02:56
In the index_list pragma, make sure the "r" column is the same on output as it was on input in the sqlite_stat1 table. Closed-Leaf check-in: de78250ad2 user: drh tags: index-scan-rate
2013-10-04
20:39
Merge trunk changes. check-in: c6ac80ed8d user: drh tags: index-scan-rate

Changes to src/analyze.c.

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

    sqlite3_snprintf(24, zRet, "%lld", p->nRow);
    z = zRet + sqlite3Strlen30(zRet);
    for(i=0; i<(p->nCol-1); i++){
      i64 nDistinct = p->current.anDLt[i] + 1;
      i64 iVal = (p->nRow + nDistinct - 1) / nDistinct;
      sqlite3_snprintf(24, z, " %lld", 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, "%lld ", aCnt[i]);
          z += sqlite3Strlen30(z);
        }
        assert( z[0]=='\0' && z>zRet );
        z[-1] = '\0';
        sqlite3_result_text(context, zRet, -1, sqlite3_free);
      }
    }
................................................................................
    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("r=[0-9]*", z)==0 ){
      int v32 = 0;
      sqlite3GetInt32(z+2, &v32);
      if( v32>=200 ){
        v32 = 255;
      }else if( v32<=0 ){
        v32 = 1;
      }else{
        v32 = (128*v32)/100;
      }
      pIndex->iScanRatio = (u8)v32;
    }
  }
}

/*
** This callback is invoked once for each index when reading the
** sqlite_stat1 table.  
................................................................................
  }
  z = argv[2];

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


    decodeIntArray((char*)z, 1, &pTable->nRowEst, 0);

  }

  return 0;
}

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







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    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);
      }
    }
................................................................................
    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.  
................................................................................
  }
  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

Changes to src/btree.c.

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    pBt->max1bytePayload = 127;
  }else{
    pBt->max1bytePayload = (u8)pBt->maxLocal;
  }
  assert( pBt->maxLeaf + 23 <= MX_CELL_SIZE(pBt) );
  pBt->pPage1 = pPage1;
  pBt->nPage = nPage;
assert( pPage1->leaf==0 || pPage1->leaf==1 );
  return SQLITE_OK;

page1_init_failed:
  releasePage(pPage1);
  pBt->pPage1 = 0;
  return rc;
}







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    pBt->max1bytePayload = 127;
  }else{
    pBt->max1bytePayload = (u8)pBt->maxLocal;
  }
  assert( pBt->maxLeaf + 23 <= MX_CELL_SIZE(pBt) );
  pBt->pPage1 = pPage1;
  pBt->nPage = nPage;

  return SQLITE_OK;

page1_init_failed:
  releasePage(pPage1);
  pBt->pPage1 = 0;
  return rc;
}

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.
  */
................................................................................
  sqlite3_snprintf(n-k, &zStmt[k], "%s", zEnd);
  return zStmt;
}

/*
** Estimate the total row width for a table.
*/
static unsigned estimatedTableWidth(const 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++;
  return wTable;
}

/*
** Set the iScanRatio for an index based on estimates of the average
** table row width and average index row width.  Estimates are derived
** from the declared datatypes of the various columns.
*/
static void setIndexScanRatio(Index *pIdx, unsigned wTable){

  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;
  }
  assert( 100*wIndex/wTable <= 255 );
  pIdx->iScanRatio = (u8)(128*wIndex/wTable);
  /* printf("%s: wIndex=%d wTable=%d ratio=%d\n",
  ** pIdx->zName, wIndex, wTable, (100*pIdx->iScanRatio)/128); */
}

/*
** This routine is called to report the final ")" that terminates
** a CREATE TABLE statement.
**
** The table structure that other action routines have been building
................................................................................
  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 */
  unsigned wTable;          /* Estimated average width of a row in the table */

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

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

  /* Compute the iScanRatio of implied indices */
  wTable = estimatedTableWidth(p);
  for(pIdx=p->pIndex; pIdx; pIdx=pIdx->pNext){
    setIndexScanRatio(pIdx, wTable);
  }

  /* 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.)
................................................................................
    }
    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 ){
    setIndexScanRatio(pIndex, estimatedTableWidth(pTab));
  }

  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:
    **







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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 = 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.
  */
................................................................................
  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
................................................................................
  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;

................................................................................
  /* 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.)
................................................................................
    }
    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:
    **

Changes to src/pragma.c.

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    /* ePragFlag: */ 0,
    /* iArg:      */ SQLITE_FullFSync },
#if defined(SQLITE_HAS_CODEC)
  { /* zName:     */ "hexkey",
    /* ePragTyp:  */ PragTyp_HEXKEY,
    /* ePragFlag: */ 0,
    /* iArg:      */ 0 },




#endif
#if !defined(SQLITE_OMIT_CHECK)
  { /* zName:     */ "ignore_check_constraints",
    /* ePragTyp:  */ PragTyp_FLAG,
    /* ePragFlag: */ 0,
    /* iArg:      */ SQLITE_IgnoreChecks },
#endif
................................................................................
    /* iArg:      */ 0 },
#endif
  { /* zName:     */ "writable_schema",
    /* ePragTyp:  */ PragTyp_FLAG,
    /* ePragFlag: */ 0,
    /* iArg:      */ SQLITE_WriteSchema|SQLITE_RecoveryMode },
};
/* Number of pragmas: 55 on by default, 66 total. */
/* End of the automatically generated pragma table.
***************************************************************************/

/*
** Interpret the given string as a safety level.  Return 0 for OFF,
** 1 for ON or NORMAL and 2 for FULL.  Return 1 for an empty or 
** unrecognized string argument.  The FULL option is disallowed
................................................................................
    }
  }
  break;

  case PragTyp_INDEX_LIST: if( zRight ){
    Index *pIdx;
    Table *pTab;

    pTab = sqlite3FindTable(db, zRight, zDb);
    if( pTab ){
      v = sqlite3GetVdbe(pParse);
      pIdx = pTab->pIndex;
      if( pIdx ){
        int i = 0; 
        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, "r", SQLITE_STATIC);


        while(pIdx){




          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, (pIdx->iScanRatio*100+127)/128, 4);

          sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 4);
          ++i;
          pIdx = pIdx->pNext;
        }
      }
    }
  }
  break;

  case PragTyp_DATABASE_LIST: {
    int i;
................................................................................
  }
  case PragTyp_REKEY: {
    if( zRight ) sqlite3_rekey_v2(db, zDb, zRight, sqlite3Strlen30(zRight));
    break;
  }
  case PragTyp_HEXKEY: {
    if( zRight ){

      int i, h1, h2;
      char zKey[40];
      for(i=0; (h1 = zRight[i])!=0 && (h2 = zRight[i+1])!=0; i+=2){
        h1 += 9*(1&(h1>>6));
        h2 += 9*(1&(h2>>6));
        zKey[i/2] = (h2 & 0x0f) | ((h1 & 0xf)<<4);
      }
      if( (zLeft[3] & 0xf)==0xb ){
        sqlite3_key_v2(db, zDb, zKey, i/2);
      }else{
        sqlite3_rekey_v2(db, zDb, zKey, i/2);
      }
    }







>
>
>
>







 







|







 







>



<
<
<
|
|
|
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|
|
>
>
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<







 







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|
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204
205
206
207
208
209
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211
212
213
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215
216
217
218
219
220
221
...
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418
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420
421
422
423
424
425
426
427
428
429
430
....
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459



1460
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1472
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1476
1477
1478
1479



1480
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1482
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....
2181
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2189
2190

2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
    /* ePragFlag: */ 0,
    /* iArg:      */ SQLITE_FullFSync },
#if defined(SQLITE_HAS_CODEC)
  { /* zName:     */ "hexkey",
    /* ePragTyp:  */ PragTyp_HEXKEY,
    /* ePragFlag: */ 0,
    /* iArg:      */ 0 },
  { /* zName:     */ "hexrekey",
    /* ePragTyp:  */ PragTyp_HEXKEY,
    /* ePragFlag: */ 0,
    /* iArg:      */ 0 },
#endif
#if !defined(SQLITE_OMIT_CHECK)
  { /* zName:     */ "ignore_check_constraints",
    /* ePragTyp:  */ PragTyp_FLAG,
    /* ePragFlag: */ 0,
    /* iArg:      */ SQLITE_IgnoreChecks },
#endif
................................................................................
    /* iArg:      */ 0 },
#endif
  { /* zName:     */ "writable_schema",
    /* ePragTyp:  */ PragTyp_FLAG,
    /* ePragFlag: */ 0,
    /* iArg:      */ SQLITE_WriteSchema|SQLITE_RecoveryMode },
};
/* Number of pragmas: 55 on by default, 67 total. */
/* End of the automatically generated pragma table.
***************************************************************************/

/*
** Interpret the given string as a safety level.  Return 0 for OFF,
** 1 for ON or NORMAL and 2 for FULL.  Return 1 for an empty or 
** unrecognized string argument.  The FULL option is disallowed
................................................................................
    }
  }
  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;
................................................................................
  }
  case PragTyp_REKEY: {
    if( zRight ) sqlite3_rekey_v2(db, zDb, zRight, sqlite3Strlen30(zRight));
    break;
  }
  case PragTyp_HEXKEY: {
    if( zRight ){
      u8 iByte;
      int i;
      char zKey[40];

      for(i=0, iByte=0; i<sizeof(zKey)*2 && sqlite3Isxdigit(zRight[i]); i++){
        iByte = (iByte<<4) + sqlite3HexToInt(zRight[i]);
        if( (i&1)!=0 ) zKey[i/2] = iByte;
      }
      if( (zLeft[3] & 0xf)==0xb ){
        sqlite3_key_v2(db, zDb, zKey, i/2);
      }else{
        sqlite3_rekey_v2(db, zDb, zKey, i/2);
      }
    }

Changes to src/select.c.

1056
1057
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1063
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1069
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1075
1076



1077


1078
1079
1080
1081
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1083

1084
1085
1086
1087








1088
1089
1090

1091

1092
1093
1094
1095
1096
1097
1098
....
1145
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1163
1164

1165
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1170








1171
1172
1173
1174
1175
1176
1177
....
1180
1181
1182
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1184
1185
1186
1187
1188
1189
1190
1191
1192

1193
1194
1195
1196
1197
1198


1199
1200
1201
1202
1203
1204
1205
....
1217
1218
1219
1220
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1222
1223
1224
1225
1226
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1228
1229
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1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
....
1420
1421
1422
1423
1424
1425
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1427
1428
1429
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1431
1432
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1437

1438
1439
1440
1441
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1446
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1448

1449
1450
1451
1452
1453
1454
1455

1456
1457
1458
1459
1460
1461
1462
....
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
....
3390
3391
3392
3393
3394
3395
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3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
....
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
....
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
    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.



**
** 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.



*/


static const char *columnType(
  NameContext *pNC, 
  Expr *pExpr,
  const char **pzOriginDb,
  const char **pzOriginTab,
  const char **pzOriginCol

){
  char const *zType = 0;
  char const *zOriginDb = 0;
  char const *zOriginTab = 0;








  char const *zOriginCol = 0;
  int j;
  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, &zOriginDb, &zOriginTab, &zOriginCol); 
        }
      }else if( ALWAYS(pTab->pSchema) ){
        /* A real table */
        assert( !pS );
        if( iCol<0 ) iCol = pTab->iPKey;
        assert( iCol==-1 || (iCol>=0 && iCol<pTab->nCol) );

        if( iCol<0 ){
          zType = "INTEGER";
          zOriginCol = "rowid";
        }else{
          zType = pTab->aCol[iCol].zType;
          zOriginCol = pTab->aCol[iCol].zName;

        }
        zOriginTab = pTab->zName;
        if( pNC->pParse ){
          int iDb = sqlite3SchemaToIndex(pNC->pParse->db, pTab->pSchema);
          zOriginDb = pNC->pParse->db->aDb[iDb].zName;
        }








      }
      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
................................................................................
      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, &zOriginDb, &zOriginTab, &zOriginCol); 
      break;
    }
#endif
  }
  

  if( pzOriginDb ){
    assert( pzOriginTab && pzOriginCol );
    *pzOriginDb = zOriginDb;
    *pzOriginTab = zOriginTab;
    *pzOriginCol = zOriginCol;
  }


  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);

    /* 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);
#endif
    sqlite3VdbeSetColName(v, i, COLNAME_DECLTYPE, zType, SQLITE_TRANSIENT);
  }
#endif /* 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 */
  int nCol,             /* Number of columns */
  Column *aCol,         /* List of columns */
  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;


  assert( pSelect!=0 );
  assert( (pSelect->selFlags & SF_Resolved)!=0 );
  assert( 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=aCol; i<nCol; i++, pCol++){
    p = a[i].pExpr;
    pCol->zType = sqlite3DbStrDup(db, columnType(&sNC, p, 0, 0, 0));

    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);
    }
  }

}

/*
** 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 = 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;
  }
  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_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;
................................................................................
    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->nCol, pTab->aCol, pSel);
      }
    }
  }
  return WRC_Continue;
}
#endif

................................................................................
        ** (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->iScanRatio<128
           && pIdx->pPartIdxWhere==0
           && (!pBest || pIdx->iScanRatio<pBest->iScanRatio)
          ){
            pBest = pIdx;
          }
        }
        if( pBest ){
          iRoot = pBest->tnum;
          pKeyInfo = sqlite3IndexKeyinfo(pParse, pBest);







>
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>







 







>
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>

>
>
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>

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1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
....
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106

1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
....
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
....
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
....
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
....
1451
1452
1453
1454
1455
1456
1457
1458

1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
....
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
....
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
....
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
....
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
    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
................................................................................
      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

................................................................................
        ** (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);

Changes to src/sqliteInt.h.

466
467
468
469
470
471
472

























473
474
475
476
477
478
479
....
1358
1359
1360
1361
1362
1363
1364

1365
1366
1367
1368
1369
1370
1371
....
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
....
2963
2964
2965
2966
2967
2968
2969






2970
2971
2972
2973
2974
2975
2976
*/
#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


























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

  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 */
................................................................................
  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 */
  u16 nColumn;             /* Number of columns in table used by this index */
  u8 iScanRatio;           /* Scan rate relative to the main table */
  unsigned onError:4;      /* 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 */
................................................................................
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**);







/*
** 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).







>
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>







 







>







 







|
|
|







 







>
>
>
>
>
>







466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
....
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
....
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
....
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
*/
#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
................................................................................
  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 */
................................................................................
  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 nSampleCol;          /* Size of IndexSample.anEq[] and so on */
  tRowcnt *aAvgEq;         /* Average nEq values for keys not 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).

Changes to src/test8.c.

261
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263
264
265
266
267

268
269
270
271
272
273
274

  /* 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;

    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);







>







261
262
263
264
265
266
267
268
269
270
271
272
273
274
275

  /* 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);

Changes to src/util.c.

1204
1205
1206
1207
1208
1209
1210













































































    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




















































































>
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1204
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1214
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1216
1217
1218
1219
1220
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1223
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1225
1226
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1228
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1230
1231
1232
1233
1234
1235
1236
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1238
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1241
1242
1243
1244
1245
1246
1247
1248
1249
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1251
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1255
1256
1257
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1260
1261
1262
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1265
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1267
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1278
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1281
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1287
    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);
}

Changes to src/where.c.

44
45
46
47
48
49
50
51
52
53
54
55
56
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58
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62
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typedef struct WherePath WherePath;
typedef struct WhereTerm WhereTerm;
typedef struct WhereLoopBuilder WhereLoopBuilder;
typedef struct WhereScan WhereScan;
typedef struct WhereOrCost WhereOrCost;
typedef struct WhereOrSet WhereOrSet;

/*
** Cost X is tracked as 10*log2(X) stored in a 16-bit integer.  The
** maximum cost for ordinary tables is 64*(2**63) which becomes 6900.
** (Virtual tables can return a larger cost, but let's assume they do not.)
** So all costs can be stored in a 16-bit integer without risk
** of overflow.
**
** Costs are estimates, so no effort is made to compute 10*log2(X) exactly.
** Instead, a close estimate is used.  Any value of X=1 is stored as 0.
** X=2 is 10.  X=3 is 16.  X=1000 is 99. etc.  Negative values are allowed.
** A WhereCost of -10 means 0.5.  WhereCost of -20 means 0.25.  And so forth.
**
** The tool/wherecosttest.c source file implements a command-line program
** that will convert WhereCosts to integers, convert integers to WhereCosts
** and do addition and multiplication on WhereCost values.  The wherecosttest
** command-line program is a useful utility to have around when working with
** this module.
*/
typedef short int WhereCost;

/*
** 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 */
  WhereCost rSetup;     /* One-time setup cost (ex: create transient index) */
  WhereCost rRun;       /* Cost of running each loop */
  WhereCost 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 */
  WhereCost rRun;     /* Cost of running this subquery */
  WhereCost 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 */
  WhereCost nRow;       /* Estimated number of rows generated by this path */
  WhereCost 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;
  WhereCost 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 */
  WhereCost 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 */


/* Convert a WhereCost value (10 times log2(X)) into its integer value X.
** A rough approximation is used.  The value returned is not exact.
*/
static u64 whereCostToInt(WhereCost 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);
}

/*
** Return the estimated number of output rows from a WHERE clause
*/
u64 sqlite3WhereOutputRowCount(WhereInfo *pWInfo){
  return whereCostToInt(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 */
  WhereCost rRun,        /* Run-cost of the new entry */
  WhereCost 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);
  }
}

/* Forward declaration */
static WhereCost whereCost(tRowcnt x);

/*
** 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 = whereCost(p->iTable) - 99;
  }else{
    pTerm->truthProb = -1;
  }
  pTerm->pExpr = sqlite3ExprSkipCollate(p);
  pTerm->wtFlags = wtFlags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;
................................................................................
      return 1;
    }
  }

  return 0;
}

/* 
** Find (an approximate) sum of two WhereCosts.  This computation is
** not a simple "+" operator because WhereCost is stored as a logarithmic
** value.
** 
*/
static WhereCost whereCostAdd(WhereCost a, WhereCost 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 WhereCost.  In other words, compute a
** good approximatation for 10*log2(x).
*/
static WhereCost whereCost(tRowcnt x){
  static WhereCost a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  WhereCost 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 (as received from xBestIndex of a virtual table)
** into a WhereCost.  In other words, compute an approximation for
** 10*log2(x).
*/
static WhereCost whereCostFromDouble(double x){
  u64 a;
  WhereCost e;
  assert( sizeof(x)==8 && sizeof(a)==8 );
  if( x<=1 ) return 0;
  if( x<=2000000000 ) return whereCost((tRowcnt)x);
  memcpy(&a, &x, 8);
  e = (a>>52) - 1022;
  return e*10;
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** Estimate the logarithm of the input value to base 2.
*/
static WhereCost estLog(WhereCost N){
  WhereCost x = whereCost(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 whereCost() 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. 
................................................................................
** 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 */
  WhereCost *pnOut     /* IN/OUT: Number of rows visited */
){
  int rc = SQLITE_OK;
  int nOut = (int)*pnOut;

  WhereCost nNew;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nEq = pBuilder->pNew->u.btree.nEq;

  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 = whereCost(iUpper - iLower);
      }else{
        nNew = 10;        assert( 10==whereCost(2) );
      }
      if( nNew<nOut ){
        nOut = nNew;
      }
      *pnOut = (WhereCost)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==whereCost(4) );
    nOut--;
  }
  if( pUpper ){
    nNew -= 20;        assert( 20==whereCost(4) );
    nOut--;
  }
  if( nNew<10 ) nNew = 10;
  if( nNew<nOut ) nOut = nNew;
  *pnOut = (WhereCost)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 */
  WhereCost 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 */
  WhereCost saved_nOut;           /* Original value of pNew->nOut */
  int iCol;                       /* Index of the column in the table */
  int rc = SQLITE_OK;             /* Return code */
  WhereCost nRowEst;              /* Estimated index selectivity */
  WhereCost 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 );
................................................................................
    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 = whereCost(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(whereCost(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==whereCost(25) );
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = whereCost(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==whereCost(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;
................................................................................
      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->nOut);
    }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    if( nInMul==0 
     && pProbe->nSample 
     && pNew->u.btree.nEq<=pProbe->nSampleCol
     && OptimizationEnabled(db, SQLITE_Stat3) 
    ){
................................................................................
        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 = whereCost(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 =  whereCostAdd(pNew->rRun, rLogSize>27 ? rLogSize-17 : 10);
    }
    /* Step cost for each output row */
    pNew->rRun = whereCostAdd(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 */
  WhereCost rSize;            /* number of rows in the table */
  WhereCost rLogSize;         /* Logarithm of the number of rows in the table */
  WhereClause *pWC;           /* The parsed WHERE clause */

  
  pNew = pBuilder->pNew;
  pWInfo = pBuilder->pWInfo;
  pTabList = pWInfo->pTabList;
  pSrc = pTabList->a + pNew->iTab;

  pWC = pBuilder->pWC;
  assert( !IsVirtual(pSrc->pTab) );

  if( pSrc->pIndex ){
    /* An INDEXED BY clause specifies a particular index to use */
    pProbe = pSrc->pIndex;
  }else{
................................................................................
    ** 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 = 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 = whereCost(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
................................................................................
        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==whereCost(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==whereCost(20) );
        pNew->rRun = whereCostAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_AUTO_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */
................................................................................
    if( pProbe->tnum<=0 ){
      /* 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 4 factor is to encourage the use of indexed lookups
      **     over full scans. */
      pNew->rRun = whereCostAdd(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->iScanRatio<128
         && (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 1.0 and 3.0 is added to
          **     encourage the use of indexed lookups.  The value of K
          **     depends on the iScanRatio value for the index.
          */
          pNew->rRun = whereCostAdd(rSize,rLogSize) + pProbe->iScanRatio/9 + 1;

        }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 = whereCostFromDouble(pIdxInfo->estimatedCost);
      /* TUNING: Every virtual table query returns 25 rows */
      pNew->nOut = 46;  assert( 46==whereCost(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));



  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;
    
      pItem = pWInfo->pTabList->a + pNew->iTab;
      iCur = pItem->iCursor;
      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,
                            whereCostAdd(sPrev.a[i].rRun, sCur.a[j].rRun),
                            whereCostAdd(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, WhereCost 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 */
  WhereCost rCost;          /* Cost of a path */
  WhereCost nOut;           /* Number of outputs */
  WhereCost mxCost = 0;     /* Maximum cost of a set of paths */
  WhereCost mxOut = 0;      /* Maximum nOut value on the set of paths */
  WhereCost 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==whereCost(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 N*log2(N) where N is the
    ** number of output rows. */


    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 */
................................................................................
        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 = whereCostAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);
        rCost = whereCostAdd(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 = whereCostAdd(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==whereCost(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==whereCost(15) */
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (WhereCost)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;







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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. 
................................................................................
** 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 );
................................................................................
    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;
................................................................................
      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) 
    ){
................................................................................
        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{
................................................................................
    ** 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 */
................................................................................
    if( pProbe->tnum<=0 ){
      /* 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 */
................................................................................
        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;

Changes to test/e_select.test.

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} [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
} [list -60.06 {} {}      -39.24 {} encompass -1                 \
        -60.06 {} {}      presenting 51 reformation dignified    \
        -60.06 {} {}      conducting -87.24 37.56 {}             \
        -60.06 {} {}      coldest -96 dramatists 82.3            \

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

        -58 {} 1.21       alerting {} -93.79 {}                  \
]
# 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.







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} [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.

Changes to test/pragma.test.

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      pragma foreign_key_list(t5);
    }
  } {}
  do_test pragma-6.4 {
    execsql {
      pragma index_list(t3);
    }
  } {/0 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 t3i1 0 \d+ 1 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 i3 0 \d+ 1 i2 0 \d+ 2 i1 0 \d+/}
do_test 23.4 {
  db eval {
    ALTER TABLE t1 ADD COLUMN e;
  }
  db2 eval {
    PRAGMA table_info(t1);
  }







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      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);
  }

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     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 {subquery_[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







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     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

Added tool/logest.c.



























































































































































































































































































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/*
** 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;
}

Changes to tool/mkpragmatab.tcl.

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  NAME: rekey
  IF:   defined(SQLITE_HAS_CODEC)

  NAME: hexkey
  IF:   defined(SQLITE_HAS_CODEC)





  NAME: activate_extensions
  IF:   defined(SQLITE_HAS_CODEC) || defined(SQLITE_ENABLE_CEROD)

  NAME: soft_heap_limit
}
set name {}
set type {}







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  NAME: rekey
  IF:   defined(SQLITE_HAS_CODEC)

  NAME: hexkey
  IF:   defined(SQLITE_HAS_CODEC)

  NAME: hexrekey
  TYPE: HEXKEY
  IF:   defined(SQLITE_HAS_CODEC)

  NAME: activate_extensions
  IF:   defined(SQLITE_HAS_CODEC) || defined(SQLITE_ENABLE_CEROD)

  NAME: soft_heap_limit
}
set name {}
set type {}

Deleted tool/wherecosttest.c.

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/*
** 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 WhereCost values and back again and for doing simple
** arithmetic operations (multiple and add) on WhereCost values.
**
** Usage:
**
**      ./wherecosttest 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 WhereCost and push onto the stack
**   ^NUM    Interpret NUM as a WhereCost and push onto stack.
**
** Examples:
**
** To convert 123 from WhereCost to integer:
** 
**         ./wherecosttest ^123
**
** To convert 123456 from integer to WhereCost:
**
**         ./wherecosttest 123456
**
*/
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>

typedef unsigned short int WhereCost;  /* 10 times log2() */

WhereCost whereCostMultiply(WhereCost a, WhereCost b){ return a+b; }
WhereCost whereCostAdd(WhereCost a, WhereCost 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 ){ WhereCost t = a; a = b; b = t; }
  if( a>b+49 ) return a;
  if( a>b+31 ) return a+1;
  return a+x[a-b];
}
WhereCost whereCostFromInteger(int x){
  static WhereCost a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  WhereCost 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 unsigned long int whereCostToInt(WhereCost x){
  unsigned long int 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);
}

int main(int argc, char **argv){
  int i;
  int n = 0;
  WhereCost a[100];
  for(i=1; i<argc; i++){
    const char *z = argv[i];
    if( z[0]=='+' ){
      if( n>=2 ){
        a[n-2] = whereCostAdd(a[n-2],a[n-1]);
        n--;
      }
    }else if( z[0]=='x' ){
      if( n>=2 ){
        a[n-2] = whereCostMultiply(a[n-2],a[n-1]);
        n--;
      }
    }else if( z[0]=='^' ){
      a[n++] = atoi(z+1);
    }else{
      a[n++] = whereCostFromInteger(atoi(z));
    }
  }
  for(i=n-1; i>=0; i--){
    printf("%d (%lu)\n", a[i], whereCostToInt(a[i]));
  }
  return 0;
}
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