*pRes = -1;
      return SQLITE_OK;
    }
  }

  if( pIdxKey ){
    xRecordCompare = sqlite3VdbeFindCompare(pIdxKey);

    assert( pIdxKey->default_rc==1 
         || pIdxKey->default_rc==0 
         || pIdxKey->default_rc==-1
    );
  }else{
    xRecordCompare = 0; /* All keys are integers */
  }
................................................................................
          if( rc ){
            sqlite3_free(pCellKey);
            goto moveto_finish;
          }
          c = xRecordCompare(nCell, pCellKey, pIdxKey, 0);
          sqlite3_free(pCellKey);
        }

        if( c<0 ){
          lwr = idx+1;
        }else if( c>0 ){
          upr = idx-1;
        }else{
          assert( c==0 );
          *pRes = 0;
          rc = SQLITE_OK;
          pCur->aiIdx[pCur->iPage] = (u16)idx;

          goto moveto_finish;
        }
        if( lwr>upr ) break;
        assert( lwr+upr>=0 );
        idx = (lwr+upr)>>1;  /* idx = (lwr+upr)/2 */
      }
    }

      *pRes = -1;
      return SQLITE_OK;
    }
  }

  if( pIdxKey ){
    xRecordCompare = sqlite3VdbeFindCompare(pIdxKey);
    pIdxKey->isCorrupt = 0;
    assert( pIdxKey->default_rc==1 
         || pIdxKey->default_rc==0 
         || pIdxKey->default_rc==-1
    );
  }else{
    xRecordCompare = 0; /* All keys are integers */
  }
................................................................................
          if( rc ){
            sqlite3_free(pCellKey);
            goto moveto_finish;
          }
          c = xRecordCompare(nCell, pCellKey, pIdxKey, 0);
          sqlite3_free(pCellKey);
        }
        assert( pIdxKey->isCorrupt==0 || c==0 );
        if( c<0 ){
          lwr = idx+1;
        }else if( c>0 ){
          upr = idx-1;
        }else{
          assert( c==0 );
          *pRes = 0;
          rc = SQLITE_OK;
          pCur->aiIdx[pCur->iPage] = (u16)idx;
          if( pIdxKey->isCorrupt ) rc = SQLITE_CORRUPT;
          goto moveto_finish;
        }
        if( lwr>upr ) break;
        assert( lwr+upr>=0 );
        idx = (lwr+upr)>>1;  /* idx = (lwr+upr)/2 */
      }
    }

** The r1 and r2 member variables are only used by the optimized comparison
** functions vdbeRecordCompareInt() and vdbeRecordCompareString().
*/
struct UnpackedRecord {
  KeyInfo *pKeyInfo;  /* Collation and sort-order information */
  u16 nField;         /* Number of entries in apMem[] */
  i8 default_rc;      /* Comparison result if keys are equal */

  Mem *aMem;          /* Values */
  int r1;             /* Value to return if (lhs > rhs) */
  int r2;             /* Value to return if (rhs < lhs) */
};


/*

** The r1 and r2 member variables are only used by the optimized comparison
** functions vdbeRecordCompareInt() and vdbeRecordCompareString().
*/
struct UnpackedRecord {
  KeyInfo *pKeyInfo;  /* Collation and sort-order information */
  u16 nField;         /* Number of entries in apMem[] */
  i8 default_rc;      /* Comparison result if keys are equal */
  u8 isCorrupt;       /* Corruption detected by xRecordCompare() */
  Mem *aMem;          /* Values */
  int r1;             /* Value to return if (lhs > rhs) */
  int r2;             /* Value to return if (rhs < lhs) */
};


/*

sqlite3_value *sqlite3VdbeGetBoundValue(Vdbe*, int, u8);
void sqlite3VdbeSetVarmask(Vdbe*, int);
#ifndef SQLITE_OMIT_TRACE
  char *sqlite3VdbeExpandSql(Vdbe*, const char*);
#endif

void sqlite3VdbeRecordUnpack(KeyInfo*,int,const void*,UnpackedRecord*);
int sqlite3VdbeRecordCompare(int,const void*,const UnpackedRecord*,int);
UnpackedRecord *sqlite3VdbeAllocUnpackedRecord(KeyInfo *, char *, int, char **);

typedef int (*RecordCompare)(int,const void*,const UnpackedRecord*,int);
RecordCompare sqlite3VdbeFindCompare(UnpackedRecord*);

#ifndef SQLITE_OMIT_TRIGGER
void sqlite3VdbeLinkSubProgram(Vdbe *, SubProgram *);
#endif

/* Use SQLITE_ENABLE_COMMENTS to enable generation of extra comments on

sqlite3_value *sqlite3VdbeGetBoundValue(Vdbe*, int, u8);
void sqlite3VdbeSetVarmask(Vdbe*, int);
#ifndef SQLITE_OMIT_TRACE
  char *sqlite3VdbeExpandSql(Vdbe*, const char*);
#endif

void sqlite3VdbeRecordUnpack(KeyInfo*,int,const void*,UnpackedRecord*);
int sqlite3VdbeRecordCompare(int,const void*,UnpackedRecord*,int);
UnpackedRecord *sqlite3VdbeAllocUnpackedRecord(KeyInfo *, char *, int, char **);

typedef int (*RecordCompare)(int,const void*,UnpackedRecord*,int);
RecordCompare sqlite3VdbeFindCompare(UnpackedRecord*);

#ifndef SQLITE_OMIT_TRIGGER
void sqlite3VdbeLinkSubProgram(Vdbe *, SubProgram *);
#endif

/* Use SQLITE_ENABLE_COMMENTS to enable generation of extra comments on

u32 sqlite3VdbeSerialTypeLen(u32);
u32 sqlite3VdbeSerialType(Mem*, int);
u32 sqlite3VdbeSerialPut(unsigned char*, Mem*, u32);
u32 sqlite3VdbeSerialGet(const unsigned char*, u32, Mem*);
void sqlite3VdbeDeleteAuxData(Vdbe*, int, int);

int sqlite2BtreeKeyCompare(BtCursor *, const void *, int, int, int *);
int sqlite3VdbeIdxKeyCompare(VdbeCursor*,const UnpackedRecord*,int*);
int sqlite3VdbeIdxRowid(sqlite3*, BtCursor *, i64 *);
int sqlite3MemCompare(const Mem*, const Mem*, const CollSeq*);
int sqlite3VdbeExec(Vdbe*);
int sqlite3VdbeList(Vdbe*);
int sqlite3VdbeHalt(Vdbe*);
int sqlite3VdbeChangeEncoding(Mem *, int);
int sqlite3VdbeMemTooBig(Mem*);

u32 sqlite3VdbeSerialTypeLen(u32);
u32 sqlite3VdbeSerialType(Mem*, int);
u32 sqlite3VdbeSerialPut(unsigned char*, Mem*, u32);
u32 sqlite3VdbeSerialGet(const unsigned char*, u32, Mem*);
void sqlite3VdbeDeleteAuxData(Vdbe*, int, int);

int sqlite2BtreeKeyCompare(BtCursor *, const void *, int, int, int *);
int sqlite3VdbeIdxKeyCompare(VdbeCursor*,UnpackedRecord*,int*);
int sqlite3VdbeIdxRowid(sqlite3*, BtCursor *, i64 *);
int sqlite3MemCompare(const Mem*, const Mem*, const CollSeq*);
int sqlite3VdbeExec(Vdbe*);
int sqlite3VdbeList(Vdbe*);
int sqlite3VdbeHalt(Vdbe*);
int sqlite3VdbeChangeEncoding(Mem *, int);
int sqlite3VdbeMemTooBig(Mem*);

**
** If argument bSkip is non-zero, it is assumed that the caller has already
** determined that the first fields of the keys are equal.
**
** Key1 and Key2 do not have to contain the same number of fields. If all 
** fields that appear in both keys are equal, then pPKey2->default_rc is 
** returned.



*/
int sqlite3VdbeRecordCompare(
  int nKey1, const void *pKey1,   /* Left key */
  const UnpackedRecord *pPKey2,   /* Right key */
  int bSkip                       /* If true, skip the first field */
){
  u32 d1;                         /* Offset into aKey[] of next data element */
  int i;                          /* Index of next field to compare */
  u32 szHdr1;                     /* Size of record header in bytes */
  u32 idx1;                       /* Offset of first type in header */
  int rc = 0;                     /* Return value */
................................................................................
    szHdr1 = aKey1[0];
    d1 = szHdr1 + sqlite3VdbeSerialTypeLen(s1);
    i = 1;
    pRhs++;
  }else{
    idx1 = getVarint32(aKey1, szHdr1);
    d1 = szHdr1;
    if( d1>(unsigned)nKey1 ) return 1;  /* Corruption */



    i = 0;
  }

  VVA_ONLY( mem1.zMalloc = 0; ) /* Only needed by assert() statements */
  assert( pPKey2->pKeyInfo->nField+pPKey2->pKeyInfo->nXField>=pPKey2->nField 
       || CORRUPT_DB );
  assert( pPKey2->pKeyInfo->aSortOrder!=0 );
................................................................................
      }else if( !(serial_type & 0x01) ){
        rc = +1;
      }else{
        mem1.n = (serial_type - 12) / 2;
        testcase( (d1+mem1.n)==(unsigned)nKey1 );
        testcase( (d1+mem1.n+1)==(unsigned)nKey1 );
        if( (d1+mem1.n) > (unsigned)nKey1 ){

          rc = 1;                /* Corruption */
        }else if( pKeyInfo->aColl[i] ){
          mem1.enc = pKeyInfo->enc;
          mem1.db = pKeyInfo->db;
          mem1.flags = MEM_Str;
          mem1.z = (char*)&aKey1[d1];
          rc = vdbeCompareMemString(&mem1, pRhs, pKeyInfo->aColl[i]);
        }else{
................................................................................
      if( serial_type<12 || (serial_type & 0x01) ){
        rc = -1;
      }else{
        int nStr = (serial_type - 12) / 2;
        testcase( (d1+nStr)==(unsigned)nKey1 );
        testcase( (d1+nStr+1)==(unsigned)nKey1 );
        if( (d1+nStr) > (unsigned)nKey1 ){

          rc = 1;                /* Corruption */
        }else{
          int nCmp = MIN(nStr, pRhs->n);
          rc = memcmp(&aKey1[d1], pRhs->z, nCmp);
          if( rc==0 ) rc = nStr - pRhs->n;
        }
      }
    }
................................................................................
** byte (i.e. is less than 128).
**
** To avoid concerns about buffer overreads, this routine is only used
** on schemas where the maximum valid header size is 63 bytes or less.
*/
static int vdbeRecordCompareInt(
  int nKey1, const void *pKey1, /* Left key */
  const UnpackedRecord *pPKey2, /* Right key */
  int bSkip                     /* Ignored */
){
  const u8 *aKey = &((const u8*)pKey1)[*(const u8*)pKey1 & 0x3F];
  int serial_type = ((const u8*)pKey1)[1];
  int res;
  u32 y;
  u64 x;
................................................................................
** This function is an optimized version of sqlite3VdbeRecordCompare() 
** that (a) the first field of pPKey2 is a string, that (b) the first field
** uses the collation sequence BINARY and (c) that the size-of-header varint 
** at the start of (pKey1/nKey1) fits in a single byte.
*/
static int vdbeRecordCompareString(
  int nKey1, const void *pKey1, /* Left key */
  const UnpackedRecord *pPKey2, /* Right key */
  int bSkip
){
  const u8 *aKey1 = (const u8*)pKey1;
  int serial_type;
  int res;
  UNUSED_PARAMETER(bSkip);

................................................................................
    res = pPKey2->r2;      /* (pKey1/nKey1) is a blob */
  }else{
    int nCmp;
    int nStr;
    int szHdr = aKey1[0];

    nStr = (serial_type-12) / 2;


    if( (szHdr + nStr) > nKey1 ) return 0;    /* Corruption */

    nCmp = MIN( pPKey2->aMem[0].n, nStr );
    res = memcmp(&aKey1[szHdr], pPKey2->aMem[0].z, nCmp);

    if( res==0 ){
      res = nStr - pPKey2->aMem[0].n;
      if( res==0 ){
        if( pPKey2->nField>1 ){
................................................................................
** pUnpacked is either created without a rowid or is truncated so that it
** omits the rowid at the end.  The rowid at the end of the index entry
** is ignored as well.  Hence, this routine only compares the prefixes 
** of the keys prior to the final rowid, not the entire key.
*/
int sqlite3VdbeIdxKeyCompare(
  VdbeCursor *pC,                  /* The cursor to compare against */
  const UnpackedRecord *pUnpacked, /* Unpacked version of key */
  int *res                         /* Write the comparison result here */
){
  i64 nCellKey = 0;
  int rc;
  BtCursor *pCur = pC->pCursor;
  Mem m;

**
** If argument bSkip is non-zero, it is assumed that the caller has already
** determined that the first fields of the keys are equal.
**
** Key1 and Key2 do not have to contain the same number of fields. If all 
** fields that appear in both keys are equal, then pPKey2->default_rc is 
** returned.
**
** If database corruption is discovered, set pPKey2->isCorrupt to non-zero
** and return 0.
*/
int sqlite3VdbeRecordCompare(
  int nKey1, const void *pKey1,   /* Left key */
  UnpackedRecord *pPKey2,         /* Right key */
  int bSkip                       /* If true, skip the first field */
){
  u32 d1;                         /* Offset into aKey[] of next data element */
  int i;                          /* Index of next field to compare */
  u32 szHdr1;                     /* Size of record header in bytes */
  u32 idx1;                       /* Offset of first type in header */
  int rc = 0;                     /* Return value */
................................................................................
    szHdr1 = aKey1[0];
    d1 = szHdr1 + sqlite3VdbeSerialTypeLen(s1);
    i = 1;
    pRhs++;
  }else{
    idx1 = getVarint32(aKey1, szHdr1);
    d1 = szHdr1;
    if( d1>(unsigned)nKey1 ){ 
      pPKey2->isCorrupt = (u8)SQLITE_CORRUPT_BKPT;
      return 0;  /* Corruption */
    }
    i = 0;
  }

  VVA_ONLY( mem1.zMalloc = 0; ) /* Only needed by assert() statements */
  assert( pPKey2->pKeyInfo->nField+pPKey2->pKeyInfo->nXField>=pPKey2->nField 
       || CORRUPT_DB );
  assert( pPKey2->pKeyInfo->aSortOrder!=0 );
................................................................................
      }else if( !(serial_type & 0x01) ){
        rc = +1;
      }else{
        mem1.n = (serial_type - 12) / 2;
        testcase( (d1+mem1.n)==(unsigned)nKey1 );
        testcase( (d1+mem1.n+1)==(unsigned)nKey1 );
        if( (d1+mem1.n) > (unsigned)nKey1 ){
          pPKey2->isCorrupt = (u8)SQLITE_CORRUPT_BKPT;
          return 0;                /* Corruption */
        }else if( pKeyInfo->aColl[i] ){
          mem1.enc = pKeyInfo->enc;
          mem1.db = pKeyInfo->db;
          mem1.flags = MEM_Str;
          mem1.z = (char*)&aKey1[d1];
          rc = vdbeCompareMemString(&mem1, pRhs, pKeyInfo->aColl[i]);
        }else{
................................................................................
      if( serial_type<12 || (serial_type & 0x01) ){
        rc = -1;
      }else{
        int nStr = (serial_type - 12) / 2;
        testcase( (d1+nStr)==(unsigned)nKey1 );
        testcase( (d1+nStr+1)==(unsigned)nKey1 );
        if( (d1+nStr) > (unsigned)nKey1 ){
          pPKey2->isCorrupt = (u8)SQLITE_CORRUPT_BKPT;
          return 0;                /* Corruption */
        }else{
          int nCmp = MIN(nStr, pRhs->n);
          rc = memcmp(&aKey1[d1], pRhs->z, nCmp);
          if( rc==0 ) rc = nStr - pRhs->n;
        }
      }
    }
................................................................................
** byte (i.e. is less than 128).
**
** To avoid concerns about buffer overreads, this routine is only used
** on schemas where the maximum valid header size is 63 bytes or less.
*/
static int vdbeRecordCompareInt(
  int nKey1, const void *pKey1, /* Left key */
  UnpackedRecord *pPKey2,       /* Right key */
  int bSkip                     /* Ignored */
){
  const u8 *aKey = &((const u8*)pKey1)[*(const u8*)pKey1 & 0x3F];
  int serial_type = ((const u8*)pKey1)[1];
  int res;
  u32 y;
  u64 x;
................................................................................
** This function is an optimized version of sqlite3VdbeRecordCompare() 
** that (a) the first field of pPKey2 is a string, that (b) the first field
** uses the collation sequence BINARY and (c) that the size-of-header varint 
** at the start of (pKey1/nKey1) fits in a single byte.
*/
static int vdbeRecordCompareString(
  int nKey1, const void *pKey1, /* Left key */
  UnpackedRecord *pPKey2,       /* Right key */
  int bSkip
){
  const u8 *aKey1 = (const u8*)pKey1;
  int serial_type;
  int res;
  UNUSED_PARAMETER(bSkip);

................................................................................
    res = pPKey2->r2;      /* (pKey1/nKey1) is a blob */
  }else{
    int nCmp;
    int nStr;
    int szHdr = aKey1[0];

    nStr = (serial_type-12) / 2;
    if( (szHdr + nStr) > nKey1 ){
      pPKey2->isCorrupt = (u8)SQLITE_CORRUPT_BKPT;
      return 0;    /* Corruption */
    }
    nCmp = MIN( pPKey2->aMem[0].n, nStr );
    res = memcmp(&aKey1[szHdr], pPKey2->aMem[0].z, nCmp);

    if( res==0 ){
      res = nStr - pPKey2->aMem[0].n;
      if( res==0 ){
        if( pPKey2->nField>1 ){
................................................................................
** pUnpacked is either created without a rowid or is truncated so that it
** omits the rowid at the end.  The rowid at the end of the index entry
** is ignored as well.  Hence, this routine only compares the prefixes 
** of the keys prior to the final rowid, not the entire key.
*/
int sqlite3VdbeIdxKeyCompare(
  VdbeCursor *pC,                  /* The cursor to compare against */
  UnpackedRecord *pUnpacked,       /* Unpacked version of key */
  int *res                         /* Write the comparison result here */
){
  i64 nCellKey = 0;
  int rc;
  BtCursor *pCur = pC->pCursor;
  Mem m;

         && (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{
          /* 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);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }
................................................................................
        if( mTerm==0 && !sqlite3ExprIsConstant(p) ) continue;
        if( (mTerm&~orderDistinctMask)==0 ){
          obSat |= MASKBIT(i);
        }
      }
    }
  } /* End the loop over all WhereLoops from outer-most down to inner-most */
  if( obSat==obDone ) return nOrderBy;
  if( !isOrderDistinct ){
    for(i=nOrderBy-1; i>0; i--){
      Bitmask m = MASKBIT(i) - 1;
      if( (obSat&m)==m ) return i;
    }
    return 0;
  }
................................................................................
        nOut = pFrom->nRow + pWLoop->nOut;
        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( isOrdered<0 ){
          isOrdered = wherePathSatisfiesOrderBy(pWInfo,
                       pWInfo->pOrderBy, pFrom, pWInfo->wctrlFlags,
                       iLoop, pWLoop, &revMask);
          if( isOrdered>=0 && isOrdered<nOrderBy ){
            /* TUNING: Estimated cost of sorting cost as roughly N*log(N).
            ** If some but not all of the columns are in sorted order, then
            ** scale down the log(N) term. */








            LogEst rScale = sqlite3LogEst((nOrderBy-isOrdered)*100/nOrderBy);
            LogEst rSortCost = nRowEst + estLog(nRowEst) + rScale - 66;
            /* TUNING: The cost of implementing DISTINCT using a B-TREE is
            ** also N*log(N) but it has a larger constant of proportionality.
            ** Multiply by 3.0. */
            if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
              rSortCost += 16;
            }
            WHERETRACE(0x002,

         && (pProbe->szIdxRow<pTab->szTabRow)
         && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
         && sqlite3GlobalConfig.bUseCis
         && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
          )
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        /* TUNING:  The base cost of an index scan is N + log2(N).
        ** The log2(N) is for the initial seek to the beginning and the N
        ** is for the scan itself. */
        pNew->rRun = sqlite3LogEstAdd(rSize, rLogSize);
        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.
          **     The upper bound on K (3.0) matches the penalty factor
          **     on a full table scan that tries to encourage the use of
          **     indexed lookups over full scans.
          */

          pNew->rRun +=  1 + (15*pProbe->szIdxRow)/pTab->szTabRow;
        }else{
          /* TUNING: The cost of scanning a non-covering index is multiplied

          ** by log2(N) to account for the binary search of the main table
          ** that must happen for each row of the index.
          ** TODO: Should there be a multiplier here, analogous to the 3x
          ** multiplier for a fulltable scan or covering index scan, to
          ** further discourage the use of an index scan?  Or is the log2(N)
          ** term sufficient discouragement?
          ** TODO: What if some or all of the WHERE clause terms can be
          ** computed without reference to the original table.  Then the
          ** penality should reduce to logK where K is the number of output
          ** rows.
          */
          pNew->rRun += rLogSize;
        }
        whereLoopOutputAdjust(pWC, pNew);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }
................................................................................
        if( mTerm==0 && !sqlite3ExprIsConstant(p) ) continue;
        if( (mTerm&~orderDistinctMask)==0 ){
          obSat |= MASKBIT(i);
        }
      }
    }
  } /* End the loop over all WhereLoops from outer-most down to inner-most */
  if( obSat==obDone ) return (i8)nOrderBy;
  if( !isOrderDistinct ){
    for(i=nOrderBy-1; i>0; i--){
      Bitmask m = MASKBIT(i) - 1;
      if( (obSat&m)==m ) return i;
    }
    return 0;
  }
................................................................................
        nOut = pFrom->nRow + pWLoop->nOut;
        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( isOrdered<0 ){
          isOrdered = wherePathSatisfiesOrderBy(pWInfo,
                       pWInfo->pOrderBy, pFrom, pWInfo->wctrlFlags,
                       iLoop, pWLoop, &revMask);
          if( isOrdered>=0 && isOrdered<nOrderBy ){
            /* TUNING: Estimated cost of sorting is N*log(N).
            ** If the order-by clause has X terms but only the last Y terms
            ** are out of order, then block-sorting will reduce the sorting
            ** cost to N*log(N)*log(Y/X).  The log(Y/X) term is computed
            ** by rScale.
            ** TODO: Should the sorting cost get a small multiplier to help
            ** discourage the use of sorting and encourage the use of index
            ** scans instead?
            */
            LogEst rScale, rSortCost;
            assert( nOrderBy>0 );
            rScale = sqlite3LogEst((nOrderBy-isOrdered)*100/nOrderBy) - 66;
            rSortCost = nRowEst + estLog(nRowEst) + rScale;
            /* TUNING: The cost of implementing DISTINCT using a B-TREE is
            ** also N*log(N) but it has a larger constant of proportionality.
            ** Multiply by 3.0. */
            if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
              rSortCost += 16;
            }
            WHERETRACE(0x002,

sqlite3 db test.db

# Try to use the file.
do_test 1.2 {
  catchsql {
    SELECT c FROM t1 WHERE a>'abc';
  }
} {0 {}}
do_test 1.3 {
  catchsql {
     PRAGMA integrity_check
  }
} {0 ok}
do_test 1.4 {
  catchsql {
    SELECT c FROM t1 ORDER BY a;
  }
} {1 {database disk image is malformed}}

# Corrupt the same file in a slightly different way.  Make the record header
................................................................................
hexio_write test.db [expr {$idxroot*512-15}] 0513ff7f01
sqlite3 db test.db

do_test 2.1 {
  catchsql {
    SELECT rowid FROM t1 WHERE a='abc' and b='xyz123456789XYZ';
  }
  # The following test result is brittle.  The point above is to try to
  # force a buffer overread by a corrupt database file.  If we get an
  # incorrect answer from a corrupt database file, that is OK.  If the
  # result below changes, that just means that "undefined behavior" has
  # changed.
} {/0 .*/}

finish_test

sqlite3 db test.db

# Try to use the file.
do_test 1.2 {
  catchsql {
    SELECT c FROM t1 WHERE a>'abc';
  }
} {1 {database disk image is malformed}}
do_test 1.3 {
  catchsql {
     PRAGMA integrity_check
  }
} {1 {database disk image is malformed}}
do_test 1.4 {
  catchsql {
    SELECT c FROM t1 ORDER BY a;
  }
} {1 {database disk image is malformed}}

# Corrupt the same file in a slightly different way.  Make the record header
................................................................................
hexio_write test.db [expr {$idxroot*512-15}] 0513ff7f01
sqlite3 db test.db

do_test 2.1 {
  catchsql {
    SELECT rowid FROM t1 WHERE a='abc' and b='xyz123456789XYZ';
  }
} {1 {database disk image is malformed}}






finish_test

do_test 1.3 {
  db close
  set offset [hexio_get_int [hexio_read test.db [expr 2*1024 + 8] 2]]
  set off [expr 2*1024 + $offset + 1]
  hexio_write test.db $off FFFF7f02
  sqlite3 db test.db
  catchsql { SELECT * FROM t1 WHERE a = 10 }
} {0 {}}

do_test 2.0 {
  execsql {
    CREATE TABLE r(x);
    INSERT INTO r VALUES('ABCDEFGHIJK');
    CREATE INDEX r1 ON r(x);
  }

do_test 1.3 {
  db close
  set offset [hexio_get_int [hexio_read test.db [expr 2*1024 + 8] 2]]
  set off [expr 2*1024 + $offset + 1]
  hexio_write test.db $off FFFF7f02
  sqlite3 db test.db
  catchsql { SELECT * FROM t1 WHERE a = 10 }
} {1 {database disk image is malformed}}

do_test 2.0 {
  execsql {
    CREATE TABLE r(x);
    INSERT INTO r VALUES('ABCDEFGHIJK');
    CREATE INDEX r1 ON r(x);
  }

#

set testdir [file dirname $argv0]
source $testdir/tester.tcl
set testprefix wal64k

ifcapable !wal {finish_test ; return }






db close
test_syscall pagesize 65536
sqlite3 db test.db

do_execsql_test 1.0 { 
  PRAGMA journal_mode = WAL;
................................................................................
} {131072}

integrity_check 1.3

db close
test_syscall pagesize -1
finish_test

#

set testdir [file dirname $argv0]
source $testdir/tester.tcl
set testprefix wal64k

ifcapable !wal {finish_test ; return }

if {$tcl_platform(platform) != "unix"} {
  finish_test
  return
}

db close
test_syscall pagesize 65536
sqlite3 db test.db

do_execsql_test 1.0 { 
  PRAGMA journal_mode = WAL;
................................................................................
} {131072}

integrity_check 1.3

db close
test_syscall pagesize -1
finish_test

** 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:
................................................................................
  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;
}

** integers and LogEst values and back again and for doing simple
** arithmetic operations (multiple and add) on LogEst values.
**
** Usage:
**
**      ./LogEst ARGS
**
** See the showHelp() routine for a description of valid arguments.






** Examples:
**
** To convert 123 from LogEst to integer:
** 
**         ./LogEst ^123
**
** To convert 123456 from integer to LogEst:
................................................................................
  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 isInteger(const char *z){
  while( z[0]>='0' && z[0]<='9' ) z++;
  return z[0]==0;

}

int isFloat(const char *z){
  char c;
  while( ((c=z[0])>='0' && c<='9') || c=='.' || c=='E' || c=='e'
          || c=='+' || c=='-'  ) z++;
  return z[0]==0;
}

static void showHelp(const char *zArgv0){
  printf("Usage: %s ARGS...\n", zArgv0);
  printf("Arguments:\n"
    "  NUM    Convert NUM from integer to LogEst and push onto the stack\n"
    " ^NUM    Interpret NUM as a LogEst and push onto stack\n"
    "  x      Multiple the top two elements of the stack\n"
    "  +      Add the top two elements of the stack\n"
    "  dup    Dupliate the top element on the stack\n"
    "  inv    Take the reciprocal of the top of stack.  N = 1/N.\n"
    "  log    Find the LogEst of the number on top of stack\n"
    "  nlogn  Compute NlogN where N is the top of stack\n"
  );
  exit(1);
}

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( strcmp(z,"+")==0 ){
      if( n>=2 ){
        a[n-2] = logEstAdd(a[n-2],a[n-1]);
        n--;
      }
    }else if( strcmp(z,"x")==0 ){
      if( n>=2 ){
        a[n-2] = logEstMultiply(a[n-2],a[n-1]);
        n--;
      }
    }else if( strcmp(z,"dup")==0 ){
      if( n>0 ){
        a[n] = a[n-1];
        n++;
      }
    }else if( strcmp(z,"log")==0 ){
      if( n>0 ) a[n-1] = logEstFromInteger(a[n-1]) - 33;
    }else if( strcmp(z,"nlogn")==0 ){
      if( n>0 ) a[n-1] += logEstFromInteger(a[n-1]) - 33;
    }else if( strcmp(z,"inv")==0 ){
      if( n>0 ) a[n-1] = -a[n-1];
    }else if( z[0]=='^' ){
      a[n++] = atoi(z+1);
    }else if( isInteger(z) ){
      a[n++] = logEstFromInteger(atoi(z));
    }else if( isFloat(z) && z[0]!='-' ){
      a[n++] = logEstFromDouble(atof(z));
    }else{

      showHelp(argv[0]);
    }
  }
  for(i=n-1; i>=0; i--){
    if( a[i]<0 ){
      printf("%5d (%f)\n", a[i], 1.0/(double)logEstToInt(-a[i]));
    }else{
      sqlite3_uint64 x = logEstToInt(a[i]+100)*100/1024;
      printf("%5d (%lld.%02lld)\n", a[i], x/100, x%100);
    }
  }
  return 0;
}