}

  /* Open the sqlite_stat[134] tables for writing. */
  for(i=0; aTable[i].zCols; i++){
    assert( i<ArraySize(aTable) );
    sqlite3VdbeAddOp4Int(v, OP_OpenWrite, iStatCur+i, aRoot[i], iDb, 3);
    sqlite3VdbeChangeP5(v, aCreateTbl[i]);
    VdbeComment((v, aTable[i].zName));
  }
}

/*
** Recommended number of samples for sqlite_stat4
*/
#ifndef SQLITE_STAT4_SAMPLES

  int iCol;                       /* If !isPSample, the reason for inclusion */
  u32 iHash;                      /* Tiebreaker hash */
#endif
};                                                    
struct Stat4Accum {
  tRowcnt nRow;             /* Number of rows in the entire table */
  tRowcnt nPSample;         /* How often to do a periodic sample */
  int nCol;                 /* Number of columns in index + pk/rowid */
  int nKeyCol;              /* Number of index columns w/o the pk/rowid */
  int mxSample;             /* Maximum number of samples to accumulate */
  Stat4Sample current;      /* Current row as a Stat4Sample */
  u32 iPrn;                 /* Pseudo-random number used for sampling */
  Stat4Sample *aBest;       /* Array of nCol best samples */
  int iMin;                 /* Index in a[] of entry with minimum score */
  int nSample;              /* Current number of samples */
  int iGet;                 /* Index of current sample accessed by stat_get() */

  for(i=0; i<p->mxSample; i++) sampleClear(p->db, p->a+i);
  sampleClear(p->db, &p->current);
#endif
  sqlite3DbFree(p->db, p);
}

/*
** Implementation of the stat_init(N,K,C) SQL function. The three parameters
** are:
**     N:    The number of columns in the index including the rowid/pk
**     K:    The number of columns in the index excluding the rowid/pk
**     C:    The number of rows in the index
**
** C is only used for STAT3 and STAT4.
**
** For ordinary rowid tables, N==K+1.  But for WITHOUT ROWID tables,
** N=K+P where P is the number of columns in the primary key.  For the
** covering index that implements the original WITHOUT ROWID table, N==K.
**
** This routine allocates the Stat4Accum object in heap memory. The return 
** value is a pointer to the the Stat4Accum object encoded as a blob (i.e. 
** the size of the blob is sizeof(void*) bytes). 
*/
static void statInit(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  Stat4Accum *p;
  int nCol;                       /* Number of columns in index being sampled */
  int nKeyCol;                    /* Number of key columns */
  int nColUp;                     /* nCol rounded up for alignment */
  int n;                          /* Bytes of space to allocate */
  sqlite3 *db;                    /* Database connection */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  int mxSample = SQLITE_STAT4_SAMPLES;
#endif

  /* Decode the three function arguments */
  UNUSED_PARAMETER(argc);
  nCol = sqlite3_value_int(argv[0]);
  assert( nCol>0 );
  nColUp = sizeof(tRowcnt)<8 ? (nCol+1)&~1 : nCol;
  nKeyCol = sqlite3_value_int(argv[1]);
  assert( nKeyCol<=nCol );
  assert( nKeyCol>0 );

  /* Allocate the space required for the Stat4Accum object */
  n = sizeof(*p) 
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anEq */
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anDLt */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anLt */

    sqlite3_result_error_nomem(context);
    return;
  }

  p->db = db;
  p->nRow = 0;
  p->nCol = nCol;
  p->nKeyCol = nKeyCol;
  p->current.anDLt = (tRowcnt*)&p[1];
  p->current.anEq = &p->current.anDLt[nColUp];

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  {
    u8 *pSpace;                     /* Allocated space not yet assigned */
    int i;                          /* Used to iterate through p->aSample[] */

    p->iGet = -1;
    p->mxSample = mxSample;
    p->nPSample = (tRowcnt)(sqlite3_value_int64(argv[2])/(mxSample/3+1) + 1);
    p->current.anLt = &p->current.anEq[nColUp];
    p->iPrn = nCol*0x689e962d ^ sqlite3_value_int(argv[2])*0xd0944565;
  
    /* Set up the Stat4Accum.a[] and aBest[] arrays */
    p->a = (struct Stat4Sample*)&p->current.anLt[nColUp];
    p->aBest = &p->a[mxSample];
    pSpace = (u8*)(&p->a[mxSample+nCol]);
    for(i=0; i<(mxSample+nCol); i++){
      p->a[i].anEq = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);

  }
#endif

  /* Return a pointer to the allocated object to the caller */
  sqlite3_result_blob(context, p, sizeof(p), stat4Destructor);
}
static const FuncDef statInitFuncdef = {
  2+IsStat34,      /* nArg */
  SQLITE_UTF8,     /* funcFlags */
  0,               /* pUserData */
  0,               /* pNext */
  statInit,        /* xFunc */
  0,               /* xStep */
  0,               /* xFinalize */
  "stat_init",     /* zName */

  /* The three function arguments */
  Stat4Accum *p = (Stat4Accum*)sqlite3_value_blob(argv[0]);
  int iChng = sqlite3_value_int(argv[1]);

  UNUSED_PARAMETER( argc );
  UNUSED_PARAMETER( context );
  assert( p->nCol>0 );
  assert( iChng<p->nCol );

  if( p->nRow==0 ){
    /* This is the first call to this function. Do initialization. */
    for(i=0; i<p->nCol; i++) p->current.anEq[i] = 1;
  }else{
    /* Second and subsequent calls get processed here */

    ** rows, then each estimate is computed as:
    **
    **        I = (K+D-1)/D
    */
    char *z;
    int i;

    char *zRet = sqlite3MallocZero( (p->nKeyCol+1)*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->nKeyCol; 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 );

    int addrRewind;               /* Address of "OP_Rewind iIdxCur" */
    int addrGotoChng0;            /* Address of "Goto addr_chng_0" */
    int addrNextRow;              /* Address of "next_row:" */
    const char *zIdxName;         /* Name of the index */

    if( pOnlyIdx && pOnlyIdx!=pIdx ) continue;
    if( pIdx->pPartIdxWhere==0 ) needTableCnt = 0;
    if( !HasRowid(pTab) && IsPrimaryKeyIndex(pIdx) ){
      nCol = pIdx->nKeyCol;
      zIdxName = pTab->zName;
    }else{
      nCol = pIdx->nColumn;
      zIdxName = pIdx->zName;
    }
    aGotoChng = sqlite3DbMallocRaw(db, sizeof(int)*(nCol+1));
    if( aGotoChng==0 ) continue;

    /* Populate the register containing the index name. */





    sqlite3VdbeAddOp4(v, OP_String8, 0, regIdxname, 0, zIdxName, 0);
    VdbeComment((v, "Analysis for %s.%s", pTab->zName, zIdxName));

    /*
    ** Pseudo-code for loop that calls stat_push():
    **
    **   Rewind csr
    **   if eof(csr) goto end_of_scan;
    **   regChng = 0

    ** 
    **    (1) the number of columns in the index including the rowid,
    **    (2) the number of rows in the index,
    **
    ** The second argument is only used for STAT3 and STAT4
    */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regStat4+3);
#endif
    sqlite3VdbeAddOp2(v, OP_Integer, nCol, regStat4+1);
    sqlite3VdbeAddOp2(v, OP_Integer, pIdx->nKeyCol, regStat4+2);
    sqlite3VdbeAddOp3(v, OP_Function, 0, regStat4+1, regStat4);
    sqlite3VdbeChangeP4(v, -1, (char*)&statInitFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 2+IsStat34);

    /* Implementation of the following:
    **
    **   Rewind csr
    **   if eof(csr) goto end_of_scan;
    **   regChng = 0
    **   goto next_push_0;

      int regSample = regStat1+3;
      int regCol = regStat1+4;
      int regSampleRowid = regCol + nCol;
      int addrNext;
      int addrIsNull;
      u8 seekOp = HasRowid(pTab) ? OP_NotExists : OP_NotFound;

      pParse->nMem = MAX(pParse->nMem, regCol+nCol);

      addrNext = sqlite3VdbeCurrentAddr(v);
      callStatGet(v, regStat4, STAT_GET_ROWID, regSampleRowid);
      addrIsNull = sqlite3VdbeAddOp1(v, OP_IsNull, regSampleRowid);
      VdbeCoverage(v);
      callStatGet(v, regStat4, STAT_GET_NEQ, regEq);
      callStatGet(v, regStat4, STAT_GET_NLT, regLt);

      sqlite3ExprCodeGetColumnOfTable(v, pTab, iTabCur, 
                                      pIdx->aiColumn[0], regSample);
#else
      for(i=0; i<nCol; i++){
        i16 iCol = pIdx->aiColumn[i];
        sqlite3ExprCodeGetColumnOfTable(v, pTab, iTabCur, iCol, regCol+i);
      }
      sqlite3VdbeAddOp3(v, OP_MakeRecord, regCol, nCol, regSample);
#endif
      sqlite3VdbeAddOp3(v, OP_MakeRecord, regTabname, 6, regTemp);
      sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur+1, regNewRowid);
      sqlite3VdbeAddOp3(v, OP_Insert, iStatCur+1, regTemp, regNewRowid);
      sqlite3VdbeAddOp2(v, OP_Goto, 1, addrNext); /* P1==1 for end-of-loop */
      sqlite3VdbeJumpHere(v, addrIsNull);
    }

  /* memset(pScan, 0, sizeof(*pScan)); */
  pScan->pOrigWC = pWC;
  pScan->pWC = pWC;
  if( pIdx && iColumn>=0 ){
    pScan->idxaff = pIdx->pTable->aCol[iColumn].affinity;
    for(j=0; pIdx->aiColumn[j]!=iColumn; j++){
      if( NEVER(j>pIdx->nColumn) ) return 0;
    }
    pScan->zCollName = pIdx->azColl[j];
  }else{
    pScan->idxaff = 0;
    pScan->zCollName = 0;
  }
  pScan->opMask = opMask;

  UnpackedRecord *pRec = pBuilder->pRec;
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */
  int bOk;

  assert( nEq>=1 );
  assert( nEq<=p->nColumn );
  assert( p->aSample!=0 );
  assert( p->nSample>0 );
  assert( pBuilder->nRecValid<nEq );

  /* If values are not available for all fields of the index to the left
  ** of this one, no estimate can be made. Return SQLITE_NOTFOUND. */
  if( pBuilder->nRecValid<(nEq-1) ){
    return SQLITE_NOTFOUND;
  }

  /* This is an optimization only. The call to sqlite3Stat4ProbeSetValue()
  ** below would return the same value.  */
  if( nEq>=p->nColumn ){
    *pnRow = 1;
    return SQLITE_OK;
  }

  aff = p->pTable->aCol[p->aiColumn[nEq-1]].affinity;
  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq-1, &bOk);
  pBuilder->pRec = pRec;

  if( nEq==0 && (pLoop->wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))==0 ){
    return 0;
  }
  sqlite3StrAccumInit(&txt, 0, 0, SQLITE_MAX_LENGTH);
  txt.db = db;
  sqlite3StrAccumAppend(&txt, " (", 2);
  for(i=0; i<nEq; i++){
    char *z = aiColumn[i] < 0 ? "rowid" : aCol[aiColumn[i]].zName;
    if( i>=nSkip ){
      explainAppendTerm(&txt, i, z, "=");
    }else{
      if( i ) sqlite3StrAccumAppend(&txt, " AND ", 5);
      sqlite3StrAccumAppend(&txt, "ANY(", 4);
      sqlite3StrAccumAppendAll(&txt, z);
      sqlite3StrAccumAppend(&txt, ")", 1);
    }
  }

  j = i;
  if( pLoop->wsFlags&WHERE_BTM_LIMIT ){
    char *z = aiColumn[j] < 0 ? "rowid" : aCol[aiColumn[j]].zName;
    explainAppendTerm(&txt, i++, z, ">");
  }
  if( pLoop->wsFlags&WHERE_TOP_LIMIT ){
    char *z = aiColumn[j] < 0 ? "rowid" : aCol[aiColumn[j]].zName;
    explainAppendTerm(&txt, i, z, "<");
  }
  sqlite3StrAccumAppend(&txt, ")", 1);
  return sqlite3StrAccumFinish(&txt);
}

/*

  }else if( pProbe->tnum<=0 || (pSrc->jointype & JT_LEFT)!=0 ){
    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE;
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  assert( pNew->u.btree.nEq<pProbe->nColumn );

  iCol = pProbe->aiColumn[pNew->u.btree.nEq];



  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nSkip = pNew->u.btree.nSkip;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;

    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      pNew->nOut = saved_nOut;
    }else{
      pNew->nOut = nOutUnadjusted;
    }

    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<pProbe->nColumn
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }
    pNew->nOut = saved_nOut;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    pBuilder->nRecValid = nRecValid;
#endif

    /* There is no INDEXED BY clause.  Create a fake Index object in local
    ** variable sPk to represent the rowid primary key index.  Make this
    ** fake index the first in a chain of Index objects with all of the real
    ** indices to follow */
    Index *pFirst;                  /* First of real indices on the table */
    memset(&sPk, 0, sizeof(Index));
    sPk.nKeyCol = 1;
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowLogEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pTab;
    sPk.szIdxRow = pTab->szTabRow;
    aiRowEstPk[0] = pTab->nRowLogEst;
    aiRowEstPk[1] = 0;

for {set i 0} {$i<16} {incr i} {
    set val "$i $i $i $i"
    do_execsql_test 20.3.$i {
      SELECT count(*) FROM sqlite_stat4 
      WHERE lrange(test_decode(sample), 0, 3)=$val
    } {1}
}

#-------------------------------------------------------------------------
#
reset_db

do_execsql_test 21.0 {
  CREATE TABLE t2(a, b);
  CREATE INDEX i2 ON t2(a);
}

do_test 21.1 {
  for {set i 1} {$i < 100} {incr i} {
    execsql { 
      INSERT INTO t2 VALUES(CASE WHEN $i < 80 THEN 'one' ELSE 'two' END, $i) 
    }
  }
  execsql ANALYZE
} {}

# Condition (a='one') matches 80% of the table. (rowid<10) reduces this to
# 10%, but (rowid<50) only reduces it to 50%. So in the first case below
# the index is used. In the second, it is not. 
#
do_eqp_test 21.2 {
  SELECT * FROM t2 WHERE a='one' AND rowid < 10
} {/*USING INDEX i2 (a=? AND rowid<?)*/}
do_eqp_test 21.3 {
  SELECT * FROM t2 WHERE a='one' AND rowid < 50
} {/*USING INTEGER PRIMARY KEY*/}

#-------------------------------------------------------------------------
#
reset_db
do_execsql_test 22.0 {
  CREATE TABLE t3(a, b, c, d, PRIMARY KEY(a, b)) WITHOUT ROWID;
}
do_execsql_test 22.1 {
  WITH r(x) AS (
    SELECT 1
    UNION ALL
    SELECT x+1 FROM r WHERE x<=100
  )

  INSERT INTO t3 SELECT
    CASE WHEN (x>45 AND x<96) THEN 'B' ELSE 'A' END,  /* Column "a" */
    x,                                                /* Column "b" */
    CASE WHEN (x<51) THEN 'one' ELSE 'two' END,       /* Column "c" */
    x                                                 /* Column "d" */
  FROM r;

  CREATE INDEX i3 ON t3(c);
  CREATE INDEX i4 ON t3(d);
  ANALYZE;
}

# Expression (c='one' AND a='B') matches 5 table rows. But (c='one' AND a=A')
# matches 45. Expression (d<?) matches 20. Neither index is a covering index.
#
# Therefore, with stat4 data, SQLite prefers (c='one' AND a='B') over (d<20),
# and (d<20) over (c='one' AND a='A').
foreach {tn where res} {
  1 "c='one' AND a='B' AND d < 20"   {/*INDEX i3 (c=? AND a=?)*/}
  2 "c='one' AND a='A' AND d < 20"   {/*INDEX i4 (d<?)*/}
} {
  do_eqp_test 22.2.$tn "SELECT * FROM t3 WHERE $where" $res
}

finish_test

  CREATE TABLE t42(x);
  INSERT INTO t42 VALUES('xyz');
  SELECT t42.rowid FROM t41, t42;
} {1}
do_execsql_test 4.2 {
  SELECT t42.rowid FROM t42, t41;
} {1}


#--------------------------------------------------------------------------
# The following tests verify that the trailing PK fields added to each
# entry in an index on a WITHOUT ROWID table are used correctly.
#
do_execsql_test 5.0 {
  CREATE TABLE t45(a PRIMARY KEY, b, c) WITHOUT ROWID;
  CREATE INDEX i45 ON t45(b);

  INSERT INTO t45 VALUES(2, 'one', 'x');
  INSERT INTO t45 VALUES(4, 'one', 'x');
  INSERT INTO t45 VALUES(6, 'one', 'x');
  INSERT INTO t45 VALUES(8, 'one', 'x');
  INSERT INTO t45 VALUES(10, 'one', 'x');

  INSERT INTO t45 VALUES(1, 'two', 'x');
  INSERT INTO t45 VALUES(3, 'two', 'x');
  INSERT INTO t45 VALUES(5, 'two', 'x');
  INSERT INTO t45 VALUES(7, 'two', 'x');
  INSERT INTO t45 VALUES(9, 'two', 'x');
}

do_eqp_test 5.1 {
  SELECT * FROM t45 WHERE b=? AND a>?
} {/*USING INDEX i45 (b=? AND a>?)*/}

do_execsql_test 5.2 {
  SELECT * FROM t45 WHERE b='two' AND a>4
} {5 two x 7 two x 9 two x}

do_execsql_test 5.3 {
  SELECT * FROM t45 WHERE b='one' AND a<8
} { 2 one x 4 one x 6 one x }

do_execsql_test 5.4 {
  CREATE TABLE t46(a, b, c, d, PRIMARY KEY(a, b)) WITHOUT ROWID;
  WITH r(x) AS (
    SELECT 1 UNION ALL SELECT x+1 FROM r WHERE x<100
  )
  INSERT INTO t46 SELECT x / 20, x % 20, x % 10, x FROM r;
}

set queries {
  1    2    "c = 5 AND a = 1"          {/*i46 (c=? AND a=?)*/}
  2    6    "c = 4 AND a < 3"          {/*i46 (c=? AND a<?)*/}
  3    4    "c = 2 AND a >= 3"         {/*i46 (c=? AND a>?)*/}
  4    1    "c = 2 AND a = 1 AND b<10" {/*i46 (c=? AND a=? AND b<?)*/}
  5    1    "c = 0 AND a = 0 AND b>5"  {/*i46 (c=? AND a=? AND b>?)*/}
}

foreach {tn cnt where eqp} $queries {
  do_execsql_test 5.5.$tn.1 "SELECT count(*) FROM t46 WHERE $where" $cnt
}

do_execsql_test 5.6 {
  CREATE INDEX i46 ON t46(c);
}

foreach {tn cnt where eqp} $queries {
  do_execsql_test 5.7.$tn.1 "SELECT count(*) FROM t46 WHERE $where" $cnt
  do_eqp_test 5.7.$tn.2  "SELECT count(*) FROM t46 WHERE $where" $eqp
}

  
finish_test