*************************************************************************
** This file contains the implementation of the sqlite3_backup_XXX() 
** API functions and the related features.
*/
#include "sqliteInt.h"
#include "btreeInt.h"

/* Macro to find the minimum of two numeric values.
*/
#ifndef MIN
# define MIN(x,y) ((x)<(y)?(x):(y))
#endif

/*
** Structure allocated for each backup operation.
*/
struct sqlite3_backup {
  sqlite3* pDestDb;        /* Destination database handle */
  Btree *pDest;            /* Destination b-tree file */
  u32 iDestSchema;         /* Original schema cookie in destination */

*************************************************************************
** This file contains the implementation of the sqlite3_backup_XXX() 
** API functions and the related features.
*/
#include "sqliteInt.h"
#include "btreeInt.h"







/*
** Structure allocated for each backup operation.
*/
struct sqlite3_backup {
  sqlite3* pDestDb;        /* Destination database handle */
  Btree *pDest;            /* Destination b-tree file */
  u32 iDestSchema;         /* Original schema cookie in destination */

** The size chosen is a little less than a power of two.  That way,
** the FileChunk object will have a size that almost exactly fills
** a power-of-two allocation.  This mimimizes wasted space in power-of-two
** memory allocators.
*/
#define JOURNAL_CHUNKSIZE ((int)(1024-sizeof(FileChunk*)))

/* Macro to find the minimum of two numeric values.
*/
#ifndef MIN
# define MIN(x,y) ((x)<(y)?(x):(y))
#endif

/*
** The rollback journal is composed of a linked list of these structures.
*/
struct FileChunk {
  FileChunk *pNext;               /* Next chunk in the journal */
  u8 zChunk[JOURNAL_CHUNKSIZE];   /* Content of this chunk */
};

** The size chosen is a little less than a power of two.  That way,
** the FileChunk object will have a size that almost exactly fills
** a power-of-two allocation.  This mimimizes wasted space in power-of-two
** memory allocators.
*/
#define JOURNAL_CHUNKSIZE ((int)(1024-sizeof(FileChunk*)))







/*
** The rollback journal is composed of a linked list of these structures.
*/
struct FileChunk {
  FileChunk *pNext;               /* Next chunk in the journal */
  u8 zChunk[JOURNAL_CHUNKSIZE];   /* Content of this chunk */
};

/*
** This file mapping API is common to both Win32 and WinRT.
*/
WINBASEAPI BOOL WINAPI UnmapViewOfFile(LPCVOID);
#endif /* SQLITE_WIN32_FILEMAPPING_API && !defined(SQLITE_OMIT_WAL) */

/*
** Macro to find the minimum of two numeric values.
*/
#ifndef MIN
# define MIN(x,y) ((x)<(y)?(x):(y))
#endif

/*
** Some Microsoft compilers lack this definition.
*/
#ifndef INVALID_FILE_ATTRIBUTES
# define INVALID_FILE_ATTRIBUTES ((DWORD)-1) 
#endif

/*
** This file mapping API is common to both Win32 and WinRT.
*/
WINBASEAPI BOOL WINAPI UnmapViewOfFile(LPCVOID);
#endif /* SQLITE_WIN32_FILEMAPPING_API && !defined(SQLITE_OMIT_WAL) */








/*
** Some Microsoft compilers lack this definition.
*/
#ifndef INVALID_FILE_ATTRIBUTES
# define INVALID_FILE_ATTRIBUTES ((DWORD)-1) 
#endif

** GCC does not define the offsetof() macro so we'll have to do it
** ourselves.
*/
#ifndef offsetof
#define offsetof(STRUCTURE,FIELD) ((int)((char*)&((STRUCTURE*)0)->FIELD))
#endif







/*
** Check to see if this machine uses EBCDIC.  (Yes, believe it or
** not, there are still machines out there that use EBCDIC.)
*/
#if 'A' == '\301'
# define SQLITE_EBCDIC 1
#else

** GCC does not define the offsetof() macro so we'll have to do it
** ourselves.
*/
#ifndef offsetof
#define offsetof(STRUCTURE,FIELD) ((int)((char*)&((STRUCTURE*)0)->FIELD))
#endif

/*
** Macros to compute minimum and maximum of two numbers.
*/
#define MIN(A,B) ((A)<(B)?(A):(B))
#define MAX(A,B) ((A)>(B)?(A):(B))

/*
** Check to see if this machine uses EBCDIC.  (Yes, believe it or
** not, there are still machines out there that use EBCDIC.)
*/
#if 'A' == '\301'
# define SQLITE_EBCDIC 1
#else

** So all costs can be stored in a 16-bit unsigned integer without risk
** of overflow.
**
** Costs are estimates, so don't go to the computational trouble 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.
**




*/
typedef unsigned short int WhereCost;

/*
** This object contains information needed to implement a single nestd
** loop in WHERE clause.
**
................................................................................
  }
}

/*
** Convert an integer into a WhereCost.  In other words, compute a
** good approximatation for 10*log2(x).
*/
static WhereCost whereCostFromInt(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; }
................................................................................
** 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 whereCostFromInt((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 = whereCostFromInt(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
................................................................................
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      WhereCost iBase = whereCostFromInt(p->aiRowEst[0]);
      if( iUpper>iLower ){
        iBase -= whereCostFromInt(iUpper - iLower);
      }
      *pRangeDiv = iBase;
      WHERETRACE(0x100, ("range scan regions: %u..%u  div=%d\n",
                         (u32)iLower, (u32)iUpper, *pRangeDiv));
      return SQLITE_OK;
    }
  }
................................................................................
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = 0;


  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
    *pRangeDiv += 20;  assert( 20==whereCostFromInt(4) );
  }
  if( pUpper ){
    *pRangeDiv += 20;  assert( 20==whereCostFromInt(4) );
  }
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
................................................................................
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = whereCostFromInt(pProbe->aiRowEst[pNew->u.btree.nEq+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(whereCostFromInt(pProbe->aiRowEst[0]));
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
      pNew->wsFlags |= WHERE_COLUMN_IN;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
        nIn = 46;  assert( 46==whereCostFromInt(25) );
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = whereCostFromInt(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->wsFlags |= WHERE_ONEROW;
      }
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul;
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;

      nIn = 10;  assert( 10==whereCostFromInt(2) );
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else if( pTerm->eOperator & (WO_LT|WO_LE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
................................................................................
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight, &nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList, &nOut);
      }
      pNew->nOut = whereCostFromInt(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);
    }
................................................................................
    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 = whereCostFromInt(pSrc->pTab->nRowEst);
  rLogSize = estLog(rSize);

  /* Automatic indexes */
  if( !pBuilder->pBest
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
   && pSrc->pIndex==0
   && !pSrc->viaCoroutine
................................................................................
    for(pTerm=pWC->a; rc==SQLITE_OK && pTerm<pWCEnd; pTerm++){
      if( pTerm->prereqRight & pNew->maskSelf ) continue;
      if( termCanDriveIndex(pTerm, pSrc, 0) ){
        pNew->u.btree.nEq = 1;
        pNew->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        assert( 43==whereCostFromInt(20) );
        pNew->rSetup = 43 + rLogSize + rSize;



        pNew->nOut = 33;  assert( 33==whereCostFromInt(10) );
        pNew->rRun = whereCostAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_TEMP_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
................................................................................
    if( pProbe->tnum<=0 ){
      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      pNew->nOut = rSize;





      pNew->rRun = whereCostAdd(rSize,rLogSize) + 16 - b;
      rc = whereLoopInsert(pBuilder, pNew);
      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 */
................................................................................
       && pProbe->bUnordered==0
       && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
       && sqlite3GlobalConfig.bUseCis
       && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        pNew->nOut = rSize;









        pNew->rRun = whereCostAdd(rSize,rLogSize);
        pNew->rRun += ((m!=0) ? rLogSize : 10) - b;






        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);

    /* If there was an INDEXED BY clause, then only that one index is
................................................................................
      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);

      pNew->nOut = 46;  assert( 46 == whereCostFromInt(25) );
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 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 */

  sqlite3 *db;              /* The database connection */
  int iLoop;                /* Loop counter over the terms of the join */
  int ii, jj;               /* Loop counters */
  WhereCost rCost;             /* Cost of a path */
  WhereCost mxCost;            /* Maximum cost of a set of paths */
  WhereCost rSortCost;         /* Cost to do a sort */
  int nTo, nFrom;           /* Number of valid entries in aTo[] and aFrom[] */
................................................................................
  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 */
  char *pSpace;             /* Temporary memory used by this routine */

  db = pWInfo->pParse->db;

  nLoop = pWInfo->nLevel;



  mxChoice = (nLoop==1) ? 1 : (nLoop==2 ? 5 : 10);
  assert( nLoop<=pWInfo->pTabList->nSrc );
  WHERETRACE(0x002, ("---- begin solver\n"));

  /* Allocate and initialize space for aTo and aFrom */
  ii = (sizeof(WherePath)+sizeof(WhereLoop*)*nLoop)*mxChoice*2;
  pSpace = sqlite3DbMallocRaw(db, ii);
................................................................................
  aFrom = aTo+mxChoice;
  memset(aFrom, 0, sizeof(aFrom[0]));
  pX = (WhereLoop**)(aFrom+mxChoice);
  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){
    pFrom->aLoop = pX;
  }

  /* Seed the search with a single WherePath containing zero WhereLoops */
  aFrom[0].nRow = pWInfo->pParse->nQueryLoop;





  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{
    /* Compute an estimate on the cost to sort the entire result set */

    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 */
................................................................................
    pFrom = aTo;
    aTo = aFrom;
    aFrom = pFrom;
    nFrom = nTo;
  }

  if( nFrom==0 ){
    sqlite3ErrorMsg(pWInfo->pParse, "no query solution");
    sqlite3DbFree(db, pSpace);
    return SQLITE_ERROR;
  }
  
  /* Find the lowest cost path.  pFrom will be left pointing to that path */
  pFrom = aFrom;
  for(ii=1; ii<nFrom; ii++){
................................................................................
  pLoop->wsFlags = 0;
  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;

    pLoop->rRun = 33;  /* 33 == whereCostFromInt(10) */
  }else{
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      if( pIdx->onError==OE_None ) continue;
      for(j=0; j<pIdx->nColumn; j++){
        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
        if( pTerm==0 ) break;
        whereLoopResize(pWInfo->pParse->db, pLoop, j);
................................................................................
      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
      if( (pItem->colUsed & ~columnsInIndex(pIdx))==0 ){
        pLoop->wsFlags |= WHERE_IDX_ONLY;
      }
      pLoop->nLTerm = j;
      pLoop->u.btree.nEq = j;
      pLoop->u.btree.pIndex = pIdx;

      pLoop->rRun = 39;  /* 39 == whereCostFromInt(15) */
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (WhereCost)1;
    pWInfo->a[0].pWLoop = pLoop;
    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);

** So all costs can be stored in a 16-bit unsigned integer without risk
** of overflow.
**
** Costs are estimates, so don't go to the computational trouble 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.
**
** The tool/wherecosttest.c source file implements a command-line program
** that will convert between WhereCost to integers and do addition and
** multiplication on WhereCost values.  That command-line program is a
** useful utility to have around when working with this module.
*/
typedef unsigned short int WhereCost;

/*
** This object contains information needed to implement a single nestd
** loop in WHERE clause.
**
................................................................................
  }
}

/*
** 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; }
................................................................................
** 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
................................................................................
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      WhereCost iBase = whereCost(p->aiRowEst[0]);
      if( iUpper>iLower ){
        iBase -= whereCost(iUpper - iLower);
      }
      *pRangeDiv = iBase;
      WHERETRACE(0x100, ("range scan regions: %u..%u  div=%d\n",
                         (u32)iLower, (u32)iUpper, *pRangeDiv));
      return SQLITE_OK;
    }
  }
................................................................................
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = 0;
  /* TUNING:  Each inequality constraint reduces the search space 4-fold.
  ** A BETWEEN operator, therefore, reduces the search space 16-fold */
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
    *pRangeDiv += 20;  assert( 20==whereCost(4) );
  }
  if( pUpper ){
    *pRangeDiv += 20;  assert( 20==whereCost(4) );
  }
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
................................................................................
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = whereCost(pProbe->aiRowEst[pNew->u.btree.nEq+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;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    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->wsFlags |= WHERE_ONEROW;
      }
      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) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else if( pTerm->eOperator & (WO_LT|WO_LE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
................................................................................
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight, &nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList, &nOut);
      }
      pNew->nOut = whereCost(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);
    }
................................................................................
    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);

  /* Automatic indexes */
  if( !pBuilder->pBest
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
   && pSrc->pIndex==0
   && !pSrc->viaCoroutine
................................................................................
    for(pTerm=pWC->a; rc==SQLITE_OK && pTerm<pWCEnd; pTerm++){
      if( pTerm->prereqRight & pNew->maskSelf ) continue;
      if( termCanDriveIndex(pTerm, pSrc, 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 6*N*log2(N) where N is the number of rows in
        ** the table being indexed. */
        pNew->rSetup = rLogSize + rSize + 26;  assert( 26==whereCost(6) );
        /* TUNING: Each index lookup yields 10 rows in the table */
        pNew->nOut = 33;  assert( 33==whereCost(10) );
        pNew->rRun = whereCostAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_TEMP_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
................................................................................
    if( pProbe->tnum<=0 ){
      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      pNew->nOut = rSize;
      /* 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.  A smaller constant 2 is used for covering
      **     index scans so that a covering index scan will be favored over
      **     a table scan. */
      pNew->rRun = whereCostAdd(rSize,rLogSize) + 16;
      rc = whereLoopInsert(pBuilder, pNew);
      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 */
................................................................................
       && pProbe->bUnordered==0
       && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
       && sqlite3GlobalConfig.bUseCis
       && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        pNew->nOut = rSize;
        if( m==0 ){
          /* TUNING: Cost of a covering index scan is 2*(N + log2(N)).
          **  +  The extra 2 factor is to encourage the use of indexed lookups
          **     over index scans.  A table scan uses a factor of 3 so that
          **     index scans are favored over table scans.
          **  +  If this covering index might also help satisfy the ORDER BY
          **     clause, then the cost is fudged down slightly so that this
          **     index is favored above other indices that have no hope of
          **     helping with the ORDER BY. */
          pNew->rRun = 10 + whereCostAdd(rSize,rLogSize) - b;

        }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;
        }
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);

    /* If there was an INDEXED BY clause, then only that one index is
................................................................................
      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;
      }
    }
  }  
................................................................................
**
** 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 */
  WhereCost rCost;             /* Cost of a path */
  WhereCost mxCost;            /* Maximum cost of a set of paths */
  WhereCost rSortCost;         /* Cost to do a sort */
  int nTo, nFrom;           /* Number of valid entries in aTo[] and aFrom[] */
................................................................................
  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 */
  char *pSpace;             /* Temporary memory used by this routine */

  pParse = pWInfo->pParse;
  db = pParse->db;
  nLoop = pWInfo->nLevel;
  /* TUNING: For simple queries, only the best path is tracked.
  ** For 2-way joins, the 5 best paths are followed.
  ** For joins of 3 or more tables, track the 10 best paths */
  mxChoice = (nLoop==1) ? 1 : (nLoop==2 ? 5 : 10);
  assert( nLoop<=pWInfo->pTabList->nSrc );
  WHERETRACE(0x002, ("---- begin solver\n"));

  /* Allocate and initialize space for aTo and aFrom */
  ii = (sizeof(WherePath)+sizeof(WhereLoop*)*nLoop)*mxChoice*2;
  pSpace = sqlite3DbMallocRaw(db, ii);
................................................................................
  aFrom = aTo+mxChoice;
  memset(aFrom, 0, sizeof(aFrom[0]));
  pX = (WhereLoop**)(aFrom+mxChoice);
  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){
    pFrom->aLoop = pX;
  }

  /* 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 */
................................................................................
    pFrom = aTo;
    aTo = aFrom;
    aFrom = pFrom;
    nFrom = nTo;
  }

  if( nFrom==0 ){
    sqlite3ErrorMsg(pParse, "no query solution");
    sqlite3DbFree(db, pSpace);
    return SQLITE_ERROR;
  }
  
  /* Find the lowest cost path.  pFrom will be left pointing to that path */
  pFrom = aFrom;
  for(ii=1; ii<nFrom; ii++){
................................................................................
  pLoop->wsFlags = 0;
  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){
      if( pIdx->onError==OE_None ) continue;
      for(j=0; j<pIdx->nColumn; j++){
        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
        if( pTerm==0 ) break;
        whereLoopResize(pWInfo->pParse->db, pLoop, j);
................................................................................
      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
      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);

} {35}
do_test autoindex1-202 {
  db status autoindex
} {0}
do_test autoindex1-210 {
  db eval {
    PRAGMA automatic_index=ON;



    SELECT b, (SELECT d FROM t2 WHERE c=a) FROM t1;
  }
} {11 911 22 922 33 933 44 944 55 955 66 966 77 977 88 988}
do_test autoindex1-211 {
  db status step
} {7}
do_test autoindex1-212 {
................................................................................
# Ticket [8011086c85c6c404014c947fcf3eb9f42b184a0d] from 2010-07-08
# Make sure automatic indices are not created for the RHS of an IN expression
# that is not a correlated subquery.
#
do_execsql_test autoindex1-500 {
  CREATE TABLE t501(a INTEGER PRIMARY KEY, b);
  CREATE TABLE t502(x INTEGER PRIMARY KEY, y);



  EXPLAIN QUERY PLAN
  SELECT b FROM t501
   WHERE t501.a IN (SELECT x FROM t502 WHERE y=?);
} {
  0 0 0 {SEARCH TABLE t501 USING INTEGER PRIMARY KEY (rowid=?)} 
  0 0 0 {EXECUTE LIST SUBQUERY 1} 
  1 0 0 {SCAN TABLE t502}

} {35}
do_test autoindex1-202 {
  db status autoindex
} {0}
do_test autoindex1-210 {
  db eval {
    PRAGMA automatic_index=ON;
    ANALYZE;
    UPDATE sqlite_stat1 SET stat='10000' WHERE tbl='t1';
    ANALYZE sqlite_master;
    SELECT b, (SELECT d FROM t2 WHERE c=a) FROM t1;
  }
} {11 911 22 922 33 933 44 944 55 955 66 966 77 977 88 988}
do_test autoindex1-211 {
  db status step
} {7}
do_test autoindex1-212 {
................................................................................
# Ticket [8011086c85c6c404014c947fcf3eb9f42b184a0d] from 2010-07-08
# Make sure automatic indices are not created for the RHS of an IN expression
# that is not a correlated subquery.
#
do_execsql_test autoindex1-500 {
  CREATE TABLE t501(a INTEGER PRIMARY KEY, b);
  CREATE TABLE t502(x INTEGER PRIMARY KEY, y);
  INSERT INTO sqlite_stat1(tbl,idx,stat) VALUES('t501',null,'1000000');
  INSERT INTO sqlite_stat1(tbl,idx,stat) VALUES('t502',null,'1000');
  ANALYZE sqlite_master;
  EXPLAIN QUERY PLAN
  SELECT b FROM t501
   WHERE t501.a IN (SELECT x FROM t502 WHERE y=?);
} {
  0 0 0 {SEARCH TABLE t501 USING INTEGER PRIMARY KEY (rowid=?)} 
  0 0 0 {EXECUTE LIST SUBQUERY 1} 
  1 0 0 {SCAN TABLE t502}