**      of 4-byte coordinates. For leaf nodes the integer is the rowid
**      of a record. For internal nodes it is the node number of a
**      child page.
*/

#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)

/*
** This file contains an implementation of a couple of different variants
** of the r-tree algorithm. See the README file for further details. The 
** same data-structure is used for all, but the algorithms for insert and
** delete operations vary. The variants used are selected at compile time 
** by defining the following symbols:
*/

/* Either, both or none of the following may be set to activate 
** r*tree variant algorithms.
*/
#define VARIANT_RSTARTREE_CHOOSESUBTREE 0
#define VARIANT_RSTARTREE_REINSERT      1

/* 
** Exactly one of the following must be set to 1.
*/
#define VARIANT_GUTTMAN_QUADRATIC_SPLIT 0
#define VARIANT_GUTTMAN_LINEAR_SPLIT    0
#define VARIANT_RSTARTREE_SPLIT         1

#define VARIANT_GUTTMAN_SPLIT \
        (VARIANT_GUTTMAN_LINEAR_SPLIT||VARIANT_GUTTMAN_QUADRATIC_SPLIT)

#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
  #define PickNext QuadraticPickNext
  #define PickSeeds QuadraticPickSeeds
  #define AssignCells splitNodeGuttman
#endif
#if VARIANT_GUTTMAN_LINEAR_SPLIT
  #define PickNext LinearPickNext
  #define PickSeeds LinearPickSeeds
  #define AssignCells splitNodeGuttman
#endif
#if VARIANT_RSTARTREE_SPLIT
  #define AssignCells splitNodeStartree
#endif

#if !defined(NDEBUG) && !defined(SQLITE_DEBUG) 
# define NDEBUG 1
#endif

#ifndef SQLITE_CORE
  #include "sqlite3ext.h"
  SQLITE_EXTENSION_INIT1
#else
  #include "sqlite3.h"
#endif

#include <string.h>
#include <assert.h>


#ifndef SQLITE_AMALGAMATION
#include "sqlite3rtree.h"
typedef sqlite3_int64 i64;
typedef unsigned char u8;

typedef unsigned int u32;
#endif

/*  The following macro is used to suppress compiler warnings.
*/
#ifndef UNUSED_PARAMETER
# define UNUSED_PARAMETER(x) (void)(x)
................................................................................
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef struct RtreeMatchArg RtreeMatchArg;
typedef struct RtreeGeomCallback RtreeGeomCallback;
typedef union RtreeCoord RtreeCoord;


/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5

/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is 
** used.
*/
#define HASHSIZE 128

/* The xBestIndex method of this virtual table requires an estimate of
** the number of rows in the virtual table to calculate the costs of
** various strategies. If possible, this estimate is loaded from the
** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
** Otherwise, if no sqlite_stat1 entry is available, use 
** RTREE_DEFAULT_ROWEST.
................................................................................
#define RTREE_DEFAULT_ROWEST 1048576
#define RTREE_MIN_ROWEST         100

/* 
** An rtree virtual-table object.
*/
struct Rtree {
  sqlite3_vtab base;
  sqlite3 *db;                /* Host database connection */
  int iNodeSize;              /* Size in bytes of each node in the node table */
  int nDim;                   /* Number of dimensions */

  int nBytesPerCell;          /* Bytes consumed per cell */
  int iDepth;                 /* Current depth of the r-tree structure */
  char *zDb;                  /* Name of database containing r-tree table */
  char *zName;                /* Name of r-tree table */ 
  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
  int nBusy;                  /* Current number of users of this structure */
  i64 nRowEst;                /* Estimated number of rows in this table */

  /* List of nodes removed during a CondenseTree operation. List is
  ** linked together via the pointer normally used for hash chains -
  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree 
  ** headed by the node (leaf nodes have RtreeNode.iNode==0).
................................................................................
  sqlite3_stmt *pDeleteRowid;

  /* Statements to read/write/delete a record from xxx_parent */
  sqlite3_stmt *pReadParent;
  sqlite3_stmt *pWriteParent;
  sqlite3_stmt *pDeleteParent;

  int eCoordType;
};

/* Possible values for eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32  1

/*
** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
** only deal with integer coordinates.  No floating point operations
** will be done.
*/
#ifdef SQLITE_RTREE_INT_ONLY
  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */
  typedef int RtreeValue;                  /* Low accuracy coordinate */

#else
  typedef double RtreeDValue;              /* High accuracy coordinate */
  typedef float RtreeValue;                /* Low accuracy coordinate */

#endif


















/*
** The minimum number of cells allowed for a node is a third of the 
** maximum. In Gutman's notation:
**
**     m = M/3
**
................................................................................
** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
** Therefore all non-root nodes must contain at least 3 entries. Since 
** 2^40 is greater than 2^64, an r-tree structure always has a depth of
** 40 or less.
*/
#define RTREE_MAX_DEPTH 40









/* 
** An rtree cursor object.
*/
struct RtreeCursor {
  sqlite3_vtab_cursor base;
  RtreeNode *pNode;                 /* Node cursor is currently pointing at */
  int iCell;                        /* Index of current cell in pNode */
  int iStrategy;                    /* Copy of idxNum search parameter */
  int nConstraint;                  /* Number of entries in aConstraint */
  RtreeConstraint *aConstraint;     /* Search constraints. */







};








union RtreeCoord {
  RtreeValue f;
  int i;


};

/*
** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
** formatted as a RtreeDValue (double or int64). This macro assumes that local
** variable pRtree points to the Rtree structure associated with the
** RtreeCoord.
................................................................................

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                     /* Index of constrained coordinate */
  int op;                         /* Constraining operation */

  RtreeDValue rValue;             /* Constraint value. */
  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
  sqlite3_rtree_geometry *pGeom;  /* Constraint callback argument for a MATCH */



};

/* Possible values for RtreeConstraint.op */
#define RTREE_EQ    0x41
#define RTREE_LE    0x42
#define RTREE_LT    0x43
#define RTREE_GE    0x44
#define RTREE_GT    0x45
#define RTREE_MATCH 0x46



/* 
** An rtree structure node.
*/
struct RtreeNode {
  RtreeNode *pParent;               /* Parent node */
  i64 iNode;
  int nRef;
  int isDirty;
  u8 *zData;
  RtreeNode *pNext;                 /* Next node in this hash chain */
};


#define NCELL(pNode) readInt16(&(pNode)->zData[2])

/* 
** Structure to store a deserialized rtree record.
*/
struct RtreeCell {
  i64 iRowid;
  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];






















};


/*
** Value for the first field of every RtreeMatchArg object. The MATCH
** operator tests that the first field of a blob operand matches this
** value to avoid operating on invalid blobs (which could cause a segfault).
*/
#define RTREE_GEOMETRY_MAGIC 0x891245AB

/*
** An instance of this structure must be supplied as a blob argument to
** the right-hand-side of an SQL MATCH operator used to constrain an
** r-tree query.

*/
struct RtreeMatchArg {
  u32 magic;                      /* Always RTREE_GEOMETRY_MAGIC */
  int (*xGeom)(sqlite3_rtree_geometry *, int, RtreeDValue*, int *);
  void *pContext;
  int nParam;
  RtreeDValue aParam[1];
};

/*
** When a geometry callback is created (see sqlite3_rtree_geometry_callback),
** a single instance of the following structure is allocated. It is used
** as the context for the user-function created by by s_r_g_c(). The object
** is eventually deleted by the destructor mechanism provided by
** sqlite3_create_function_v2() (which is called by s_r_g_c() to create
** the geometry callback function).
*/
struct RtreeGeomCallback {
  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
  void *pContext;
};

#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
................................................................................
}

/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){
  return (
    (iNode>>56) ^ (iNode>>48) ^ (iNode>>40) ^ (iNode>>32) ^ 
    (iNode>>24) ^ (iNode>>16) ^ (iNode>> 8) ^ (iNode>> 0)
  ) % HASHSIZE;
}

/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
................................................................................
  }
  return pNode;
}

/*
** Obtain a reference to an r-tree node.
*/
static int
nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;
  int rc2 = SQLITE_OK;
................................................................................
  return rc;
}

/*
** Overwrite cell iCell of node pNode with the contents of pCell.
*/
static void nodeOverwriteCell(
  Rtree *pRtree, 
  RtreeNode *pNode,  
  RtreeCell *pCell, 
  int iCell
){
  int ii;
  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  p += writeInt64(p, pCell->iRowid);
  for(ii=0; ii<(pRtree->nDim*2); ii++){
    p += writeCoord(p, &pCell->aCoord[ii]);
  }
  pNode->isDirty = 1;
}

/*
** Remove cell the cell with index iCell from node pNode.
*/
static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
  u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  u8 *pSrc = &pDst[pRtree->nBytesPerCell];
  int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
  memmove(pDst, pSrc, nByte);
  writeInt16(&pNode->zData[2], NCELL(pNode)-1);
................................................................................

/*
** Insert the contents of cell pCell into node pNode. If the insert
** is successful, return SQLITE_OK.
**
** If there is not enough free space in pNode, return SQLITE_FULL.
*/
static int
nodeInsertCell(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  RtreeCell *pCell 
){
  int nCell;                    /* Current number of cells in pNode */
  int nMaxCell;                 /* Maximum number of cells for pNode */

  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
  nCell = NCELL(pNode);

................................................................................

  return (nCell==nMaxCell);
}

/*
** If the node is dirty, write it out to the database.
*/
static int
nodeWrite(Rtree *pRtree, RtreeNode *pNode){
  int rc = SQLITE_OK;
  if( pNode->isDirty ){
    sqlite3_stmt *p = pRtree->pWriteNode;
    if( pNode->iNode ){
      sqlite3_bind_int64(p, 1, pNode->iNode);
    }else{
      sqlite3_bind_null(p, 1);
................................................................................
  return rc;
}

/*
** Release a reference to a node. If the node is dirty and the reference
** count drops to zero, the node data is written to the database.
*/
static int
nodeRelease(Rtree *pRtree, RtreeNode *pNode){
  int rc = SQLITE_OK;
  if( pNode ){
    assert( pNode->nRef>0 );
    pNode->nRef--;
    if( pNode->nRef==0 ){
      if( pNode->iNode==1 ){
        pRtree->iDepth = -1;
................................................................................

/*
** Return the 64-bit integer value associated with cell iCell of
** node pNode. If pNode is a leaf node, this is a rowid. If it is
** an internal node, then the 64-bit integer is a child page number.
*/
static i64 nodeGetRowid(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell
){
  assert( iCell<NCELL(pNode) );
  return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);
}

/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static void nodeGetCoord(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell,
  int iCoord,
  RtreeCoord *pCoord           /* Space to write result to */
){
  readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
}

/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell,
  RtreeCell *pCell
){
  int ii;


  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);

  for(ii=0; ii<pRtree->nDim*2; ii++){
    nodeGetCoord(pRtree, pNode, iCell, ii, &pCell->aCoord[ii]);



  }
}


/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
................................................................................
/*
** Free the RtreeCursor.aConstraint[] array and its contents.
*/
static void freeCursorConstraints(RtreeCursor *pCsr){
  if( pCsr->aConstraint ){
    int i;                        /* Used to iterate through constraint array */
    for(i=0; i<pCsr->nConstraint; i++){
      sqlite3_rtree_geometry *pGeom = pCsr->aConstraint[i].pGeom;
      if( pGeom ){
        if( pGeom->xDelUser ) pGeom->xDelUser(pGeom->pUser);
        sqlite3_free(pGeom);
      }
    }
    sqlite3_free(pCsr->aConstraint);
    pCsr->aConstraint = 0;
  }
}

/* 
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int rc;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  freeCursorConstraints(pCsr);

  rc = nodeRelease(pRtree, pCsr->pNode);
  sqlite3_free(pCsr);
  return rc;
}

/*
** Rtree virtual table module xEof method.
**
** Return non-zero if the cursor does not currently point to a valid 
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  return (pCsr->pNode==0);

}

/*
** The r-tree constraint passed as the second argument to this function is
** guaranteed to be a MATCH constraint.













*/
static int testRtreeGeom(
  Rtree *pRtree,                  /* R-Tree object */
  RtreeConstraint *pConstraint,   /* MATCH constraint to test */
  RtreeCell *pCell,               /* Cell to test */



  int *pbRes                      /* OUT: Test result */
){
  int i;
  RtreeDValue aCoord[RTREE_MAX_DIMENSIONS*2];
  int nCoord = pRtree->nDim*2;




  assert( pConstraint->op==RTREE_MATCH );
  assert( pConstraint->pGeom );






  for(i=0; i<nCoord; i++){
    aCoord[i] = DCOORD(pCell->aCoord[i]);






  }
  return pConstraint->xGeom(pConstraint->pGeom, nCoord, aCoord, pbRes);

}

/* 
** Cursor pCursor currently points to a cell in a non-leaf page.
** Set *pbEof to true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[] 
** array, or false otherwise.
**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.


*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  int bRes = 0;
  int rc = SQLITE_OK;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; bRes==0 && ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    RtreeDValue cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
    RtreeDValue cell_max = DCOORD(cell.aCoord[(p->iCoord>>1)*2+1]);

    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_MATCH





    );






    switch( p->op ){
      case RTREE_LE: case RTREE_LT: 
        bRes = p->rValue<cell_min; 
        break;



      case RTREE_GE: case RTREE_GT: 
        bRes = p->rValue>cell_max; 
        break;



      case RTREE_EQ:
        bRes = (p->rValue>cell_max || p->rValue<cell_min);
        break;




      default: {
        assert( p->op==RTREE_MATCH );
        rc = testRtreeGeom(pRtree, p, &cell, &bRes);
        bRes = !bRes;
        break;













      }
    }
  }

  *pbEof = bRes;
  return rc;
}

/* 
** Test if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the 
** pCursor->aConstraint[] array. If so, set *pbEof to true before
** returning. If the cell is not filtered (excluded) by the constraints,
** set pbEof to zero.



**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.
**
** This function assumes that the cell is part of a leaf node.










*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  *pbEof = 0;


  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    RtreeDValue coord = DCOORD(cell.aCoord[p->iCoord]);
    int res;
    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_MATCH
    );
    switch( p->op ){
      case RTREE_LE: res = (coord<=p->rValue); break;
      case RTREE_LT: res = (coord<p->rValue);  break;
      case RTREE_GE: res = (coord>=p->rValue); break;
      case RTREE_GT: res = (coord>p->rValue);  break;
      case RTREE_EQ: res = (coord==p->rValue); break;
      default: {
        int rc;
        assert( p->op==RTREE_MATCH );
        rc = testRtreeGeom(pRtree, p, &cell, &res);
        if( rc!=SQLITE_OK ){
          return rc;
        }

        break;



      }
    }

    if( !res ){
      *pbEof = 1;
      return SQLITE_OK;



    }

  }

  return SQLITE_OK;
}

/*
** Cursor pCursor currently points at a node that heads a sub-tree of
** height iHeight (if iHeight==0, then the node is a leaf). Descend
** to point to the left-most cell of the sub-tree that matches the 
** configured constraints.





*/
static int descendToCell(
  Rtree *pRtree, 
  RtreeCursor *pCursor, 
  int iHeight,
  int *pEof                 /* OUT: Set to true if cannot descend */





){
  int isEof;
  int rc;
  int ii;
  RtreeNode *pChild;
  sqlite3_int64 iRowid;


  RtreeNode *pSavedNode = pCursor->pNode;
  int iSavedCell = pCursor->iCell;


  assert( iHeight>=0 );


  if( iHeight==0 ){
    rc = testRtreeEntry(pRtree, pCursor, &isEof);
  }else{
    rc = testRtreeCell(pRtree, pCursor, &isEof);
  }

  if( rc!=SQLITE_OK || isEof || iHeight==0 ){
    goto descend_to_cell_out;
  }

  iRowid = nodeGetRowid(pRtree, pCursor->pNode, pCursor->iCell);
  rc = nodeAcquire(pRtree, iRowid, pCursor->pNode, &pChild);
  if( rc!=SQLITE_OK ){
    goto descend_to_cell_out;
  }

  nodeRelease(pRtree, pCursor->pNode);
  pCursor->pNode = pChild;
  isEof = 1;
  for(ii=0; isEof && ii<NCELL(pChild); ii++){
    pCursor->iCell = ii;
    rc = descendToCell(pRtree, pCursor, iHeight-1, &isEof);
    if( rc!=SQLITE_OK ){
      goto descend_to_cell_out;
    }
  }

  if( isEof ){
    assert( pCursor->pNode==pChild );
    nodeReference(pSavedNode);
    nodeRelease(pRtree, pChild);
    pCursor->pNode = pSavedNode;
    pCursor->iCell = iSavedCell;
  }

descend_to_cell_out:
  *pEof = isEof;
  return rc;

}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(
................................................................................
  Rtree *pRtree, 
  RtreeNode *pNode, 
  i64 iRowid,
  int *piIndex
){
  int ii;
  int nCell = NCELL(pNode);

  for(ii=0; ii<nCell; ii++){
    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
      *piIndex = ii;
      return SQLITE_OK;
    }
  }
  return SQLITE_CORRUPT_VTAB;
................................................................................
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
  }
  *piIndex = -1;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xNext method.







*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
  Rtree *pRtree = (Rtree *)(pVtabCursor->pVtab);
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  int rc = SQLITE_OK;










  /* RtreeCursor.pNode must not be NULL. If is is NULL, then this cursor is
  ** already at EOF. It is against the rules to call the xNext() method of
  ** a cursor that has already reached EOF.



  */


































  assert( pCsr->pNode );



  if( pCsr->iStrategy==1 ){
    /* This "scan" is a direct lookup by rowid. There is no next entry. */
    nodeRelease(pRtree, pCsr->pNode);
    pCsr->pNode = 0;





























































  }else{
    /* Move to the next entry that matches the configured constraints. */





























    int iHeight = 0;
    while( pCsr->pNode ){



































































      RtreeNode *pNode = pCsr->pNode;


      int nCell = NCELL(pNode);
      for(pCsr->iCell++; pCsr->iCell<nCell; pCsr->iCell++){

        int isEof;
        rc = descendToCell(pRtree, pCsr, iHeight, &isEof);
        if( rc!=SQLITE_OK || !isEof ){






          return rc;
















        }

      }
      pCsr->pNode = pNode->pParent;
      rc = nodeParentIndex(pRtree, pNode, &pCsr->iCell);
      if( rc!=SQLITE_OK ){
        return rc;









      }
      nodeReference(pCsr->pNode);
      nodeRelease(pRtree, pNode);
      iHeight++;



    }








  }




















  return rc;
}

/* 
** Rtree virtual table module xRowid method.
*/
static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){
  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;



  assert(pCsr->pNode);

  *pRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);

  return SQLITE_OK;
}

/* 
** Rtree virtual table module xColumn method.
*/
static int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
  Rtree *pRtree = (Rtree *)cur->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)cur;







  if( i==0 ){
    i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
    sqlite3_result_int64(ctx, iRowid);
  }else{
    RtreeCoord c;

    nodeGetCoord(pRtree, pCsr->pNode, pCsr->iCell, i-1, &c);
#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      sqlite3_result_double(ctx, c.f);
    }else
#endif
    {
      assert( pRtree->eCoordType==RTREE_COORD_INT32 );
      sqlite3_result_int(ctx, c.i);
    }
  }

  return SQLITE_OK;
}

/* 
** Use nodeAcquire() to obtain the leaf node containing the record with 
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(Rtree *pRtree, i64 iRowid, RtreeNode **ppLeaf){





  int rc;
  *ppLeaf = 0;
  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);

    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}
................................................................................
/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
  RtreeMatchArg *p;
  sqlite3_rtree_geometry *pGeom;
  int nBlob;


  /* Check that value is actually a blob. */
  if( sqlite3_value_type(pValue)!=SQLITE_BLOB ) return SQLITE_ERROR;

  /* Check that the blob is roughly the right size. */
  nBlob = sqlite3_value_bytes(pValue);
  if( nBlob<(int)sizeof(RtreeMatchArg) 
   || ((nBlob-sizeof(RtreeMatchArg))%sizeof(RtreeDValue))!=0
  ){
    return SQLITE_ERROR;
  }

  pGeom = (sqlite3_rtree_geometry *)sqlite3_malloc(
      sizeof(sqlite3_rtree_geometry) + nBlob
  );
  if( !pGeom ) return SQLITE_NOMEM;
  memset(pGeom, 0, sizeof(sqlite3_rtree_geometry));
  p = (RtreeMatchArg *)&pGeom[1];

  memcpy(p, sqlite3_value_blob(pValue), nBlob);
  if( p->magic!=RTREE_GEOMETRY_MAGIC 
   || nBlob!=(int)(sizeof(RtreeMatchArg) + (p->nParam-1)*sizeof(RtreeDValue))
  ){
    sqlite3_free(pGeom);
    return SQLITE_ERROR;
  }

  pGeom->pContext = p->pContext;
  pGeom->nParam = p->nParam;
  pGeom->aParam = p->aParam;

  pCons->xGeom = p->xGeom;
  pCons->pGeom = pGeom;


  return SQLITE_OK;
}

/* 
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
  sqlite3_vtab_cursor *pVtabCursor, 
  int idxNum, const char *idxStr,
  int argc, sqlite3_value **argv
){
  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;

  RtreeNode *pRoot = 0;
  int ii;
  int rc = SQLITE_OK;


  rtreeReference(pRtree);

  freeCursorConstraints(pCsr);
  pCsr->iStrategy = idxNum;

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */

    i64 iRowid = sqlite3_value_int64(argv[0]);

    rc = findLeafNode(pRtree, iRowid, &pLeaf);
    pCsr->pNode = pLeaf; 
    if( pLeaf ){
      assert( rc==SQLITE_OK );





      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &pCsr->iCell);




    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */

    if( argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);

        assert( (idxStr==0 && argc==0)
                || (idxStr && (int)strlen(idxStr)==argc*2) );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'a';
          if( p->op==RTREE_MATCH ){
            /* A MATCH operator. The right-hand-side must be a blob that
            ** can be cast into an RtreeMatchArg object. One created using
            ** an sqlite3_rtree_geometry_callback() SQL user function.
            */
            rc = deserializeGeometry(argv[ii], p);
            if( rc!=SQLITE_OK ){
              break;
            }



          }else{
#ifdef SQLITE_RTREE_INT_ONLY
            p->rValue = sqlite3_value_int64(argv[ii]);
#else
            p->rValue = sqlite3_value_double(argv[ii]);
#endif
          }
        }
      }
    }
  
    if( rc==SQLITE_OK ){
      pCsr->pNode = 0;
      rc = nodeAcquire(pRtree, 1, 0, &pRoot);
    }

    if( rc==SQLITE_OK ){

      int isEof = 1;
      int nCell = NCELL(pRoot);
      pCsr->pNode = pRoot;
      for(pCsr->iCell=0; rc==SQLITE_OK && pCsr->iCell<nCell; pCsr->iCell++){
        assert( pCsr->pNode==pRoot );
        rc = descendToCell(pRtree, pCsr, pRtree->iDepth, &isEof);
        if( !isEof ){
          break;
        }
      }
      if( rc==SQLITE_OK && isEof ){
        assert( pCsr->pNode==pRoot );
        nodeRelease(pRtree, pRoot);
        pCsr->pNode = 0;


      }
      assert( rc!=SQLITE_OK || !pCsr->pNode || pCsr->iCell<NCELL(pCsr->pNode) );
    }
  }


  rtreeRelease(pRtree);
  return rc;
}

/*
** Set the pIdxInfo->estimatedRows variable to nRow. Unless this
** extension is currently being used by a version of SQLite too old to
................................................................................
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
        default:
          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );
          op = RTREE_MATCH; 
          break;
      }
      zIdxStr[iIdx++] = op;
      zIdxStr[iIdx++] = p->iColumn - 1 + 'a';
      pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
      pIdxInfo->aConstraintUsage[ii].omit = 1;
    }
  }

  pIdxInfo->idxNum = 2;
  pIdxInfo->needToFreeIdxStr = 1;
................................................................................
  RtreeCell cell;
  memcpy(&cell, p, sizeof(RtreeCell));
  area = cellArea(pRtree, &cell);
  cellUnion(pRtree, &cell, pCell);
  return (cellArea(pRtree, &cell)-area);
}

#if VARIANT_RSTARTREE_CHOOSESUBTREE || VARIANT_RSTARTREE_SPLIT
static RtreeDValue cellOverlap(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  int ii;
  RtreeDValue overlap = 0.0;
  for(ii=0; ii<nCell; ii++){
#if VARIANT_RSTARTREE_CHOOSESUBTREE
    if( ii!=iExclude )
#else
    assert( iExclude==-1 );
    UNUSED_PARAMETER(iExclude);
#endif
    {
      int jj;
      RtreeDValue o = (RtreeDValue)1;
      for(jj=0; jj<(pRtree->nDim*2); jj+=2){
        RtreeDValue x1, x2;

        x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
        x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));

        if( x2<x1 ){
          o = 0.0;

          break;
        }else{
          o = o * (x2-x1);
        }
      }
      overlap += o;
    }
  }
  return overlap;
}
#endif

#if VARIANT_RSTARTREE_CHOOSESUBTREE
static RtreeDValue cellOverlapEnlargement(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *pInsert, 
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  RtreeDValue before, after;
  before = cellOverlap(pRtree, p, aCell, nCell, iExclude);
  cellUnion(pRtree, p, pInsert);
  after = cellOverlap(pRtree, p, aCell, nCell, iExclude);
  return (after-before);
}
#endif


/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
................................................................................
  RtreeNode *pNode;
  rc = nodeAcquire(pRtree, 1, 0, &pNode);

  for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
    int iCell;
    sqlite3_int64 iBest = 0;

    RtreeDValue fMinGrowth = 0.0;
    RtreeDValue fMinArea = 0.0;
#if VARIANT_RSTARTREE_CHOOSESUBTREE
    RtreeDValue fMinOverlap = 0.0;
    RtreeDValue overlap;
#endif

    int nCell = NCELL(pNode);
    RtreeCell cell;
    RtreeNode *pChild;

    RtreeCell *aCell = 0;

#if VARIANT_RSTARTREE_CHOOSESUBTREE
    if( ii==(pRtree->iDepth-1) ){
      int jj;
      aCell = sqlite3_malloc(sizeof(RtreeCell)*nCell);
      if( !aCell ){
        rc = SQLITE_NOMEM;
        nodeRelease(pRtree, pNode);
        pNode = 0;
        continue;
      }
      for(jj=0; jj<nCell; jj++){
        nodeGetCell(pRtree, pNode, jj, &aCell[jj]);
      }
    }
#endif

    /* Select the child node which will be enlarged the least if pCell
    ** is inserted into it. Resolve ties by choosing the entry with
    ** the smallest area.
    */
    for(iCell=0; iCell<nCell; iCell++){
      int bBest = 0;
      RtreeDValue growth;
      RtreeDValue area;
      nodeGetCell(pRtree, pNode, iCell, &cell);
      growth = cellGrowth(pRtree, &cell, pCell);
      area = cellArea(pRtree, &cell);

#if VARIANT_RSTARTREE_CHOOSESUBTREE
      if( ii==(pRtree->iDepth-1) ){
        overlap = cellOverlapEnlargement(pRtree,&cell,pCell,aCell,nCell,iCell);
      }else{
        overlap = 0.0;
      }
      if( (iCell==0) 
       || (overlap<fMinOverlap) 
       || (overlap==fMinOverlap && growth<fMinGrowth)
       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
      ){
        bBest = 1;
        fMinOverlap = overlap;
      }
#else
      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
        bBest = 1;
      }
#endif
      if( bBest ){
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

................................................................................
  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
  sqlite3_step(pRtree->pWriteParent);
  return sqlite3_reset(pRtree->pWriteParent);
}

static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);

#if VARIANT_GUTTMAN_LINEAR_SPLIT
/*
** Implementation of the linear variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *LinearPickNext(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  RtreeCell *pLeftBox, 
  RtreeCell *pRightBox,
  int *aiUsed
){
  int ii;
  for(ii=0; aiUsed[ii]; ii++);
  aiUsed[ii] = 1;
  return &aCell[ii];
}

/*
** Implementation of the linear variant of the PickSeeds() function from
** Guttman[84].
*/
static void LinearPickSeeds(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  int *piLeftSeed, 
  int *piRightSeed
){
  int i;
  int iLeftSeed = 0;
  int iRightSeed = 1;
  RtreeDValue maxNormalInnerWidth = (RtreeDValue)0;

  /* Pick two "seed" cells from the array of cells. The algorithm used
  ** here is the LinearPickSeeds algorithm from Gutman[1984]. The 
  ** indices of the two seed cells in the array are stored in local
  ** variables iLeftSeek and iRightSeed.
  */
  for(i=0; i<pRtree->nDim; i++){
    RtreeDValue x1 = DCOORD(aCell[0].aCoord[i*2]);
    RtreeDValue x2 = DCOORD(aCell[0].aCoord[i*2+1]);
    RtreeDValue x3 = x1;
    RtreeDValue x4 = x2;
    int jj;

    int iCellLeft = 0;
    int iCellRight = 0;

    for(jj=1; jj<nCell; jj++){
      RtreeDValue left = DCOORD(aCell[jj].aCoord[i*2]);
      RtreeDValue right = DCOORD(aCell[jj].aCoord[i*2+1]);

      if( left<x1 ) x1 = left;
      if( right>x4 ) x4 = right;
      if( left>x3 ){
        x3 = left;
        iCellRight = jj;
      }
      if( right<x2 ){
        x2 = right;
        iCellLeft = jj;
      }
    }

    if( x4!=x1 ){
      RtreeDValue normalwidth = (x3 - x2) / (x4 - x1);
      if( normalwidth>maxNormalInnerWidth ){
        iLeftSeed = iCellLeft;
        iRightSeed = iCellRight;
      }
    }
  }

  *piLeftSeed = iLeftSeed;
  *piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_LINEAR_SPLIT */

#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
/*
** Implementation of the quadratic variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *QuadraticPickNext(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  RtreeCell *pLeftBox, 
  RtreeCell *pRightBox,
  int *aiUsed
){
  #define FABS(a) ((a)<0.0?-1.0*(a):(a))

  int iSelect = -1;
  RtreeDValue fDiff;
  int ii;
  for(ii=0; ii<nCell; ii++){
    if( aiUsed[ii]==0 ){
      RtreeDValue left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
      RtreeDValue right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
      RtreeDValue diff = FABS(right-left);
      if( iSelect<0 || diff>fDiff ){
        fDiff = diff;
        iSelect = ii;
      }
    }
  }
  aiUsed[iSelect] = 1;
  return &aCell[iSelect];
}

/*
** Implementation of the quadratic variant of the PickSeeds() function from
** Guttman[84].
*/
static void QuadraticPickSeeds(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  int *piLeftSeed, 
  int *piRightSeed
){
  int ii;
  int jj;

  int iLeftSeed = 0;
  int iRightSeed = 1;
  RtreeDValue fWaste = 0.0;

  for(ii=0; ii<nCell; ii++){
    for(jj=ii+1; jj<nCell; jj++){
      RtreeDValue right = cellArea(pRtree, &aCell[jj]);
      RtreeDValue growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
      RtreeDValue waste = growth - right;

      if( waste>fWaste ){
        iLeftSeed = ii;
        iRightSeed = jj;
        fWaste = waste;
      }
    }
  }

  *piLeftSeed = iLeftSeed;
  *piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_QUADRATIC_SPLIT */

/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to 
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
................................................................................
        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
      }
    }
#endif
  }
}

#if VARIANT_RSTARTREE_SPLIT
/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
  Rtree *pRtree,
  RtreeCell *aCell,
  int nCell,
................................................................................
){
  int **aaSorted;
  int *aSpare;
  int ii;

  int iBestDim = 0;
  int iBestSplit = 0;
  RtreeDValue fBestMargin = 0.0;

  int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));

  aaSorted = (int **)sqlite3_malloc(nByte);
  if( !aaSorted ){
    return SQLITE_NOMEM;
  }
................................................................................
    for(jj=0; jj<nCell; jj++){
      aaSorted[ii][jj] = jj;
    }
    SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
  }

  for(ii=0; ii<pRtree->nDim; ii++){
    RtreeDValue margin = 0.0;
    RtreeDValue fBestOverlap = 0.0;
    RtreeDValue fBestArea = 0.0;
    int iBestLeft = 0;
    int nLeft;

    for(
      nLeft=RTREE_MINCELLS(pRtree); 
      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); 
      nLeft++
................................................................................
          cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
        }else{
          cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
        }
      }
      margin += cellMargin(pRtree, &left);
      margin += cellMargin(pRtree, &right);
      overlap = cellOverlap(pRtree, &left, &right, 1, -1);
      area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
      if( (nLeft==RTREE_MINCELLS(pRtree))
       || (overlap<fBestOverlap)
       || (overlap==fBestOverlap && area<fBestArea)
      ){
        iBestLeft = nLeft;
        fBestOverlap = overlap;
................................................................................
    nodeInsertCell(pRtree, pTarget, pCell);
    cellUnion(pRtree, pBbox, pCell);
  }

  sqlite3_free(aaSorted);
  return SQLITE_OK;
}
#endif

#if VARIANT_GUTTMAN_SPLIT
/*
** Implementation of the regular R-tree SplitNode from Guttman[1984].
*/
static int splitNodeGuttman(
  Rtree *pRtree,
  RtreeCell *aCell,
  int nCell,
  RtreeNode *pLeft,
  RtreeNode *pRight,
  RtreeCell *pBboxLeft,
  RtreeCell *pBboxRight
){
  int iLeftSeed = 0;
  int iRightSeed = 1;
  int *aiUsed;
  int i;

  aiUsed = sqlite3_malloc(sizeof(int)*nCell);
  if( !aiUsed ){
    return SQLITE_NOMEM;
  }
  memset(aiUsed, 0, sizeof(int)*nCell);

  PickSeeds(pRtree, aCell, nCell, &iLeftSeed, &iRightSeed);

  memcpy(pBboxLeft, &aCell[iLeftSeed], sizeof(RtreeCell));
  memcpy(pBboxRight, &aCell[iRightSeed], sizeof(RtreeCell));
  nodeInsertCell(pRtree, pLeft, &aCell[iLeftSeed]);
  nodeInsertCell(pRtree, pRight, &aCell[iRightSeed]);
  aiUsed[iLeftSeed] = 1;
  aiUsed[iRightSeed] = 1;

  for(i=nCell-2; i>0; i--){
    RtreeCell *pNext;
    pNext = PickNext(pRtree, aCell, nCell, pBboxLeft, pBboxRight, aiUsed);
    RtreeDValue diff =  
      cellGrowth(pRtree, pBboxLeft, pNext) - 
      cellGrowth(pRtree, pBboxRight, pNext)
    ;
    if( (RTREE_MINCELLS(pRtree)-NCELL(pRight)==i)
     || (diff>0.0 && (RTREE_MINCELLS(pRtree)-NCELL(pLeft)!=i))
    ){
      nodeInsertCell(pRtree, pRight, pNext);
      cellUnion(pRtree, pBboxRight, pNext);
    }else{
      nodeInsertCell(pRtree, pLeft, pNext);
      cellUnion(pRtree, pBboxLeft, pNext);
    }
  }

  sqlite3_free(aiUsed);
  return SQLITE_OK;
}
#endif

static int updateMapping(
  Rtree *pRtree, 
  i64 iRowid, 
  RtreeNode *pNode, 
  int iHeight
){
................................................................................
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }

  memset(pLeft->zData, 0, pRtree->iNodeSize);
  memset(pRight->zData, 0, pRtree->iNodeSize);

  rc = AssignCells(pRtree, aCell, nCell, pLeft, pRight, &leftbbox, &rightbbox);

  if( rc!=SQLITE_OK ){
    goto splitnode_out;
  }

  /* Ensure both child nodes have node numbers assigned to them by calling
  ** nodeWrite(). Node pRight always needs a node number, as it was created
  ** by nodeNew() above. But node pLeft sometimes already has a node number.
................................................................................
    }
  }
  for(iDim=0; iDim<pRtree->nDim; iDim++){
    aCenterCoord[iDim] = (aCenterCoord[iDim]/(nCell*(RtreeDValue)2));
  }

  for(ii=0; ii<nCell; ii++){
    aDistance[ii] = 0.0;
    for(iDim=0; iDim<pRtree->nDim; iDim++){
      RtreeDValue coord = (DCOORD(aCell[ii].aCoord[iDim*2+1]) - 
                               DCOORD(aCell[ii].aCoord[iDim*2]));
      aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
    }
  }

................................................................................
    if( pChild ){
      nodeRelease(pRtree, pChild->pParent);
      nodeReference(pNode);
      pChild->pParent = pNode;
    }
  }
  if( nodeInsertCell(pRtree, pNode, pCell) ){
#if VARIANT_RSTARTREE_REINSERT
    if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
      rc = SplitNode(pRtree, pNode, pCell, iHeight);
    }else{
      pRtree->iReinsertHeight = iHeight;
      rc = Reinsert(pRtree, pNode, pCell, iHeight);
    }
#else
    rc = SplitNode(pRtree, pNode, pCell, iHeight);
#endif
  }else{
    rc = AdjustTree(pRtree, pNode, pCell);
    if( rc==SQLITE_OK ){
      if( iHeight==0 ){
        rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
................................................................................
  /* Obtain a reference to the root node to initialize Rtree.iDepth */
  rc = nodeAcquire(pRtree, 1, 0, &pRoot);

  /* Obtain a reference to the leaf node that contains the entry 
  ** about to be deleted. 
  */
  if( rc==SQLITE_OK ){
    rc = findLeafNode(pRtree, iDelete, &pLeaf);
  }

  /* Delete the cell in question from the leaf node. */
  if( rc==SQLITE_OK ){
    int rc2;
    rc = nodeRowidIndex(pRtree, pLeaf, iDelete, &iCell);
    if( rc==SQLITE_OK ){
................................................................................

  pRtree->db = db;

  if( isCreate ){
    char *zCreate = sqlite3_mprintf(
"CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY, data BLOB);"
"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"
"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY, parentnode INTEGER);"

"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",
      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
    );
    if( !zCreate ){
      return SQLITE_NOMEM;
    }
    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
................................................................................
}


/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.
**
** The scalar function takes two arguments, a blob of data containing
** an r-tree node, and the number of dimensions the r-tree indexes.
** For a two-dimensional r-tree structure called "rt", to deserialize
** all nodes, a statement like:
**
**   SELECT rtreenode(2, data) FROM rt_node;
**
** The human readable string takes the form of a Tcl list with one
** entry for each cell in the r-tree node. Each entry is itself a
** list, containing the 8-byte rowid/pageno followed by the 
** <num-dimension>*2 coordinates.
................................................................................
    int jj;

    nodeGetCell(&tree, &node, ii, &cell);
    sqlite3_snprintf(512-nCell,&zCell[nCell],"%lld", cell.iRowid);
    nCell = (int)strlen(zCell);
    for(jj=0; jj<tree.nDim*2; jj++){
#ifndef SQLITE_RTREE_INT_ONLY
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %f",
                       (double)cell.aCoord[jj].f);
#else
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %d",
                       cell.aCoord[jj].i);
#endif
      nCell = (int)strlen(zCell);
    }
................................................................................
      zText = sqlite3_mprintf("{%s}", zCell);
    }
  }
  
  sqlite3_result_text(ctx, zText, -1, sqlite3_free);
}










static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
  UNUSED_PARAMETER(nArg);
  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB 
   || sqlite3_value_bytes(apArg[0])<2
  ){
    sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1); 
  }else{
................................................................................
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

  return rc;
}

/*
** A version of sqlite3_free() that can be used as a callback. This is used
** in two places - as the destructor for the blob value returned by the
** invocation of a geometry function, and as the destructor for the geometry
** functions themselves.

*/
static void doSqlite3Free(void *p){



  sqlite3_free(p);
}

/*
** Each call to sqlite3_rtree_geometry_callback() creates an ordinary SQLite
** scalar user function. This C function is the callback used for all such
** registered SQL functions.
**
** The scalar user functions return a blob that is interpreted by r-tree
** table MATCH operators.






*/
static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
  RtreeMatchArg *pBlob;
  int nBlob;

  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue);
  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);
  if( !pBlob ){
    sqlite3_result_error_nomem(ctx);
  }else{
    int i;
    pBlob->magic = RTREE_GEOMETRY_MAGIC;
    pBlob->xGeom = pGeomCtx->xGeom;
    pBlob->pContext = pGeomCtx->pContext;
    pBlob->nParam = nArg;
    for(i=0; i<nArg; i++){
#ifdef SQLITE_RTREE_INT_ONLY
      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
#else
      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
#endif
    }
    sqlite3_result_blob(ctx, pBlob, nBlob, doSqlite3Free);
  }
}

/*
** Register a new geometry function for use with the r-tree MATCH operator.
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,
  int (*xGeom)(sqlite3_rtree_geometry *, int, RtreeDValue *, int *),
  void *pContext
){
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = xGeom;


  pGeomCtx->pContext = pContext;




  /* Create the new user-function. Register a destructor function to delete
  ** the context object when it is no longer required.  */





















  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, doSqlite3Free
  );
}

#if !SQLITE_CORE
#ifdef _WIN32
__declspec(dllexport)
#endif

**      of 4-byte coordinates. For leaf nodes the integer is the rowid
**      of a record. For internal nodes it is the node number of a
**      child page.
*/

#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)











































#ifndef SQLITE_CORE
  #include "sqlite3ext.h"
  SQLITE_EXTENSION_INIT1
#else
  #include "sqlite3.h"
#endif

#include <string.h>
#include <assert.h>
#include <stdio.h>

#ifndef SQLITE_AMALGAMATION
#include "sqlite3rtree.h"
typedef sqlite3_int64 i64;
typedef unsigned char u8;
typedef unsigned short u16;
typedef unsigned int u32;
#endif

/*  The following macro is used to suppress compiler warnings.
*/
#ifndef UNUSED_PARAMETER
# define UNUSED_PARAMETER(x) (void)(x)
................................................................................
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef struct RtreeMatchArg RtreeMatchArg;
typedef struct RtreeGeomCallback RtreeGeomCallback;
typedef union RtreeCoord RtreeCoord;
typedef struct RtreeSearchPoint RtreeSearchPoint;

/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5

/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is 
** used.
*/
#define HASHSIZE 97

/* The xBestIndex method of this virtual table requires an estimate of
** the number of rows in the virtual table to calculate the costs of
** various strategies. If possible, this estimate is loaded from the
** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
** Otherwise, if no sqlite_stat1 entry is available, use 
** RTREE_DEFAULT_ROWEST.
................................................................................
#define RTREE_DEFAULT_ROWEST 1048576
#define RTREE_MIN_ROWEST         100

/* 
** An rtree virtual-table object.
*/
struct Rtree {
  sqlite3_vtab base;          /* Base class.  Must be first */
  sqlite3 *db;                /* Host database connection */
  int iNodeSize;              /* Size in bytes of each node in the node table */
  u8 nDim;                    /* Number of dimensions */
  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
  u8 nBytesPerCell;           /* Bytes consumed per cell */
  int iDepth;                 /* Current depth of the r-tree structure */
  char *zDb;                  /* Name of database containing r-tree table */
  char *zName;                /* Name of r-tree table */ 

  int nBusy;                  /* Current number of users of this structure */
  i64 nRowEst;                /* Estimated number of rows in this table */

  /* List of nodes removed during a CondenseTree operation. List is
  ** linked together via the pointer normally used for hash chains -
  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree 
  ** headed by the node (leaf nodes have RtreeNode.iNode==0).
................................................................................
  sqlite3_stmt *pDeleteRowid;

  /* Statements to read/write/delete a record from xxx_parent */
  sqlite3_stmt *pReadParent;
  sqlite3_stmt *pWriteParent;
  sqlite3_stmt *pDeleteParent;

  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
};

/* Possible values for Rtree.eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32  1

/*
** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
** only deal with integer coordinates.  No floating point operations
** will be done.
*/
#ifdef SQLITE_RTREE_INT_ONLY
  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */
  typedef int RtreeValue;                  /* Low accuracy coordinate */
# define RTREE_ZERO 0
#else
  typedef double RtreeDValue;              /* High accuracy coordinate */
  typedef float RtreeValue;                /* Low accuracy coordinate */
# define RTREE_ZERO 0.0
#endif

/*
** When doing a search of an r-tree, instances of the following structure
** record intermediate results from the tree walk.
**
** The id is always a node-id.  For iLevel>=1 the id is the node-id of
** the node that the RtreeSearchPoint represents.  When iLevel==0, however,
** the id is of the parent node and the cell that RtreeSearchPoint
** represents is the iCell-th entry in the parent node.
*/
struct RtreeSearchPoint {
  RtreeDValue rScore;    /* The score for this node.  Smallest goes first. */
  sqlite3_int64 id;      /* Node ID */
  u8 iLevel;             /* 0=entries.  1=leaf node.  2+ for higher */
  u8 eWithin;            /* PARTLY_WITHIN or FULLY_WITHIN */
  u8 iCell;              /* Cell index within the node */
};

/*
** The minimum number of cells allowed for a node is a third of the 
** maximum. In Gutman's notation:
**
**     m = M/3
**
................................................................................
** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
** Therefore all non-root nodes must contain at least 3 entries. Since 
** 2^40 is greater than 2^64, an r-tree structure always has a depth of
** 40 or less.
*/
#define RTREE_MAX_DEPTH 40


/*
** Number of entries in the cursor RtreeNode cache.  The first entry is
** used to cache the RtreeNode for RtreeCursor.sPoint.  The remaining
** entries cache the RtreeNode for the first elements of the priority queue.
*/
#define RTREE_CACHE_SZ  5

/* 
** An rtree cursor object.
*/
struct RtreeCursor {
  sqlite3_vtab_cursor base;         /* Base class.  Must be first */
  u8 atEOF;                         /* True if at end of search */
  u8 bPoint;                        /* True if sPoint is valid */
  int iStrategy;                    /* Copy of idxNum search parameter */
  int nConstraint;                  /* Number of entries in aConstraint */
  RtreeConstraint *aConstraint;     /* Search constraints. */
  int nPointAlloc;                  /* Number of slots allocated for aPoint[] */
  int nPoint;                       /* Number of slots used in aPoint[] */
  int mxLevel;                      /* iLevel value for root of the tree */
  RtreeSearchPoint *aPoint;         /* Priority queue for search points */
  RtreeSearchPoint sPoint;          /* Cached next search point */
  RtreeNode *aNode[RTREE_CACHE_SZ]; /* Rtree node cache */
  u32 anQueue[RTREE_MAX_DEPTH+1];   /* Number of queued entries by iLevel */
};

/* Return the Rtree of a RtreeCursor */
#define RTREE_OF_CURSOR(X)   ((Rtree*)((X)->base.pVtab))

/*
** A coordinate can be either a floating point number or a integer.  All
** coordinates within a single R-Tree are always of the same time.
*/
union RtreeCoord {
  RtreeValue f;      /* Floating point value */

  int i;             /* Integer value */
  u32 u;             /* Unsigned for byte-order conversions */
};

/*
** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
** formatted as a RtreeDValue (double or int64). This macro assumes that local
** variable pRtree points to the Rtree structure associated with the
** RtreeCoord.
................................................................................

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                     /* Index of constrained coordinate */
  int op;                         /* Constraining operation */
  union {
    RtreeDValue rValue;             /* Constraint value. */
    int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*);

    int (*xQueryFunc)(sqlite3_rtree_query_info*);
  } u;
  sqlite3_rtree_query_info *pInfo;  /* xGeom and xQueryFunc argument */
};

/* Possible values for RtreeConstraint.op */
#define RTREE_EQ    0x41  /* A */
#define RTREE_LE    0x42  /* B */
#define RTREE_LT    0x43  /* C */
#define RTREE_GE    0x44  /* D */
#define RTREE_GT    0x45  /* E */
#define RTREE_MATCH 0x46  /* F: Old-style sqlite3_rtree_geometry_callback() */
#define RTREE_QUERY 0x47  /* G: New-style sqlite3_rtree_query_callback() */


/* 
** An rtree structure node.
*/
struct RtreeNode {
  RtreeNode *pParent;         /* Parent node */
  i64 iNode;                  /* The node number */
  int nRef;                   /* Number of references to this node */
  int isDirty;                /* True if the node needs to be written to disk */
  u8 *zData;                  /* Content of the node, as should be on disk */
  RtreeNode *pNext;           /* Next node in this hash collision chain */
};

/* Return the number of cells in a node  */
#define NCELL(pNode) readInt16(&(pNode)->zData[2])

/* 
** A single cell from a node, deserialized
*/
struct RtreeCell {
  i64 iRowid;                                 /* Node or entry ID */
  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];  /* Bounding box coordinates */
};


/*
** This object becomes the sqlite3_user_data() for the SQL functions
** that are created by sqlite3_rtree_geometry_callback() and
** sqlite3_rtree_query_callback() and which appear on the right of MATCH
** operators in order to constrain a search.
**
** xGeom and xQueryFunc are the callback functions.  Exactly one of 
** xGeom and xQueryFunc fields is non-NULL, depending on whether the
** SQL function was created using sqlite3_rtree_geometry_callback() or
** sqlite3_rtree_query_callback().
** 
** This object is deleted automatically by the destructor mechanism in
** sqlite3_create_function_v2().
*/
struct RtreeGeomCallback {
  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
  int (*xQueryFunc)(sqlite3_rtree_query_info*);
  void (*xDestructor)(void*);
  void *pContext;
};


/*
** Value for the first field of every RtreeMatchArg object. The MATCH
** operator tests that the first field of a blob operand matches this
** value to avoid operating on invalid blobs (which could cause a segfault).
*/
#define RTREE_GEOMETRY_MAGIC 0x891245AB

/*
** An instance of this structure (in the form of a BLOB) is returned by
** the SQL functions that sqlite3_rtree_geometry_callback() and
** sqlite3_rtree_query_callback() create, and is read as the right-hand
** operand to the MATCH operator of an R-Tree.
*/
struct RtreeMatchArg {
  u32 magic;                  /* Always RTREE_GEOMETRY_MAGIC */

  RtreeGeomCallback cb;       /* Info about the callback functions */
  int nParam;                 /* Number of parameters to the SQL function */
  RtreeDValue aParam[1];      /* Values for parameters to the SQL function */













};

#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
................................................................................
}

/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){



  return iNode % HASHSIZE;
}

/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
................................................................................
  }
  return pNode;
}

/*
** Obtain a reference to an r-tree node.
*/

static int nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;
  int rc2 = SQLITE_OK;
................................................................................
  return rc;
}

/*
** Overwrite cell iCell of node pNode with the contents of pCell.
*/
static void nodeOverwriteCell(
  Rtree *pRtree,             /* The overall R-Tree */
  RtreeNode *pNode,          /* The node into which the cell is to be written */
  RtreeCell *pCell,          /* The cell to write */
  int iCell                  /* Index into pNode into which pCell is written */
){
  int ii;
  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  p += writeInt64(p, pCell->iRowid);
  for(ii=0; ii<(pRtree->nDim*2); ii++){
    p += writeCoord(p, &pCell->aCoord[ii]);
  }
  pNode->isDirty = 1;
}

/*
** Remove the cell with index iCell from node pNode.
*/
static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
  u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  u8 *pSrc = &pDst[pRtree->nBytesPerCell];
  int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
  memmove(pDst, pSrc, nByte);
  writeInt16(&pNode->zData[2], NCELL(pNode)-1);
................................................................................

/*
** Insert the contents of cell pCell into node pNode. If the insert
** is successful, return SQLITE_OK.
**
** If there is not enough free space in pNode, return SQLITE_FULL.
*/

static int nodeInsertCell(
  Rtree *pRtree,                /* The overall R-Tree */
  RtreeNode *pNode,             /* Write new cell into this node */
  RtreeCell *pCell              /* The cell to be inserted */
){
  int nCell;                    /* Current number of cells in pNode */
  int nMaxCell;                 /* Maximum number of cells for pNode */

  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
  nCell = NCELL(pNode);

................................................................................

  return (nCell==nMaxCell);
}

/*
** If the node is dirty, write it out to the database.
*/

static int nodeWrite(Rtree *pRtree, RtreeNode *pNode){
  int rc = SQLITE_OK;
  if( pNode->isDirty ){
    sqlite3_stmt *p = pRtree->pWriteNode;
    if( pNode->iNode ){
      sqlite3_bind_int64(p, 1, pNode->iNode);
    }else{
      sqlite3_bind_null(p, 1);
................................................................................
  return rc;
}

/*
** Release a reference to a node. If the node is dirty and the reference
** count drops to zero, the node data is written to the database.
*/

static int nodeRelease(Rtree *pRtree, RtreeNode *pNode){
  int rc = SQLITE_OK;
  if( pNode ){
    assert( pNode->nRef>0 );
    pNode->nRef--;
    if( pNode->nRef==0 ){
      if( pNode->iNode==1 ){
        pRtree->iDepth = -1;
................................................................................

/*
** Return the 64-bit integer value associated with cell iCell of
** node pNode. If pNode is a leaf node, this is a rowid. If it is
** an internal node, then the 64-bit integer is a child page number.
*/
static i64 nodeGetRowid(
  Rtree *pRtree,       /* The overall R-Tree */
  RtreeNode *pNode,    /* The node from which to extract the ID */
  int iCell            /* The cell index from which to extract the ID */
){
  assert( iCell<NCELL(pNode) );
  return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);
}

/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static void nodeGetCoord(
  Rtree *pRtree,               /* The overall R-Tree */
  RtreeNode *pNode,            /* The node from which to extract a coordinate */
  int iCell,                   /* The index of the cell within the node */
  int iCoord,                  /* Which coordinate to extract */
  RtreeCoord *pCoord           /* OUT: Space to write result to */
){
  readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
}

/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
  Rtree *pRtree,               /* The overall R-Tree */
  RtreeNode *pNode,            /* The node containing the cell to be read */
  int iCell,                   /* Index of the cell within the node */
  RtreeCell *pCell             /* OUT: Write the cell contents here */
){
  u8 *pData;
  u8 *pEnd;
  RtreeCoord *pCoord;
  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
  pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);
  pEnd = pData + pRtree->nDim*8;

  pCoord = pCell->aCoord;
  for(; pData<pEnd; pData+=4, pCoord++){
    readCoord(pData, pCoord);
  }
}


/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
................................................................................
/*
** Free the RtreeCursor.aConstraint[] array and its contents.
*/
static void freeCursorConstraints(RtreeCursor *pCsr){
  if( pCsr->aConstraint ){
    int i;                        /* Used to iterate through constraint array */
    for(i=0; i<pCsr->nConstraint; i++){
      sqlite3_rtree_query_info *pInfo = pCsr->aConstraint[i].pInfo;
      if( pInfo ){
        if( pInfo->xDelUser ) pInfo->xDelUser(pInfo->pUser);
        sqlite3_free(pInfo);
      }
    }
    sqlite3_free(pCsr->aConstraint);
    pCsr->aConstraint = 0;
  }
}

/* 
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int ii;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  freeCursorConstraints(pCsr);
  sqlite3_free(pCsr->aPoint);
  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
  sqlite3_free(pCsr);
  return SQLITE_OK;
}

/*
** Rtree virtual table module xEof method.
**
** Return non-zero if the cursor does not currently point to a valid 
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
  RtreeCursor *pCsr = (RtreeCursor *)cur;

  return pCsr->atEOF;
}

/*

** Convert raw bits from the on-disk RTree record into a coordinate value.
** The on-disk format is big-endian and needs to be converted for little-
** endian platforms.  The on-disk record stores integer coordinates if
** eInt is true and it stores 32-bit floating point records if eInt is
** false.  a[] is the four bytes of the on-disk record to be decoded.
** Store the results in "r".
**
** There are three versions of this macro, one each for little-endian and
** big-endian processors and a third generic implementation.  The endian-
** specific implementations are much faster and are preferred if the
** processor endianness is known at compile-time.  The SQLITE_BYTEORDER
** macro is part of sqliteInt.h and hence the endian-specific
** implementation will only be used if this module is compiled as part
** of the amalgamation.
*/




#if defined(SQLITE_BYTEORDER) && SQLITE_BYTEORDER==1234
#define RTREE_DECODE_COORD(eInt, a, r) {                        \
    RtreeCoord c;    /* Coordinate decoded */                   \
    memcpy(&c.u,a,4);                                           \




    c.u = ((c.u>>24)&0xff)|((c.u>>8)&0xff00)|                   \
          ((c.u&0xff)<<24)|((c.u&0xff00)<<8);                   \
    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}


#elif defined(SQLITE_BYTEORDER) && SQLITE_BYTEORDER==4321
#define RTREE_DECODE_COORD(eInt, a, r) {                        \
    RtreeCoord c;    /* Coordinate decoded */                   \
    memcpy(&c.u,a,4);                                           \
    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}


#else
#define RTREE_DECODE_COORD(eInt, a, r) {                        \
    RtreeCoord c;    /* Coordinate decoded */                   \
    c.u = ((u32)a[0]<<24) + ((u32)a[1]<<16)                     \
           +((u32)a[2]<<8) + a[3];                              \
    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}

#endif


/*







** Check the RTree node or entry given by pCellData and p against the MATCH
** constraint pConstraint.  
*/












static int rtreeCallbackConstraint(
  RtreeConstraint *pConstraint,  /* The constraint to test */
  int eInt,                      /* True if RTree holding integer coordinates */
  u8 *pCellData,                 /* Raw cell content */
  RtreeSearchPoint *pSearch,     /* Container of this cell */
  sqlite3_rtree_dbl *prScore,    /* OUT: score for the cell */
  int *peWithin                  /* OUT: visibility of the cell */
){
  int i;                                                /* Loop counter */
  sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */
  int nCoord = pInfo->nCoord;                           /* No. of coordinates */
  int rc;                                             /* Callback return code */
  sqlite3_rtree_dbl aCoord[RTREE_MAX_DIMENSIONS*2];   /* Decoded coordinates */





  assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );
  assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );




  if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){
    pInfo->iRowid = readInt64(pCellData);
  }



  pCellData += 8;
  for(i=0; i<nCoord; i++, pCellData += 4){
    RTREE_DECODE_COORD(eInt, pCellData, aCoord[i]);
  }

  if( pConstraint->op==RTREE_MATCH ){



    rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,
                              nCoord, aCoord, &i);
    if( i==0 ) *peWithin = NOT_WITHIN;
    *prScore = RTREE_ZERO;
  }else{
    pInfo->aCoord = aCoord;
    pInfo->iLevel = pSearch->iLevel - 1;
    pInfo->rScore = pInfo->rParentScore = pSearch->rScore;
    pInfo->eWithin = pInfo->eParentWithin = pSearch->eWithin;
    rc = pConstraint->u.xQueryFunc(pInfo);
    if( pInfo->eWithin<*peWithin ) *peWithin = pInfo->eWithin;
    if( pInfo->rScore<*prScore || *prScore<RTREE_ZERO ){
      *prScore = pInfo->rScore;
    }
  }



  return rc;
}

/* 





** Check the internal RTree node given by pCellData against constraint p.
** If this constraint cannot be satisfied by any child within the node,
** set *peWithin to NOT_WITHIN.
*/




static void rtreeNonleafConstraint(
  RtreeConstraint *p,        /* The constraint to test */
  int eInt,                  /* True if RTree holds integer coordinates */
  u8 *pCellData,             /* Raw cell content as appears on disk */
  int *peWithin              /* Adjust downward, as appropriate */
){
  sqlite3_rtree_dbl val;     /* Coordinate value convert to a double */

  /* p->iCoord might point to either a lower or upper bound coordinate
  ** in a coordinate pair.  But make pCellData point to the lower bound.
  */




  pCellData += 8 + 4*(p->iCoord&0xfe);






  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
      || p->op==RTREE_GT || p->op==RTREE_EQ );

  switch( p->op ){
    case RTREE_LE:
    case RTREE_LT:


    case RTREE_EQ:







      RTREE_DECODE_COORD(eInt, pCellData, val);
      /* val now holds the lower bound of the coordinate pair */
      if( p->u.rValue>=val ) return;
      if( p->op!=RTREE_EQ ) break;  /* RTREE_LE and RTREE_LT end here */
      /* Fall through for the RTREE_EQ case */




    default: /* RTREE_GT or RTREE_GE,  or fallthrough of RTREE_EQ */
      pCellData += 4;
      RTREE_DECODE_COORD(eInt, pCellData, val);
      /* val now holds the upper bound of the coordinate pair */
      if( p->u.rValue<=val ) return;
  }
  *peWithin = NOT_WITHIN;
}




/*

** Check the leaf RTree cell given by pCellData against constraint p.
** If this constraint is not satisfied, set *peWithin to NOT_WITHIN.
** If the constraint is satisfied, leave *peWithin unchanged.
**
** The constraint is of the form:  xN op $val
**
** The op is given by p->op.  The xN is p->iCoord-th coordinate in
** pCellData.  $val is given by p->u.rValue.
*/





static void rtreeLeafConstraint(
  RtreeConstraint *p,        /* The constraint to test */
  int eInt,                  /* True if RTree holds integer coordinates */
  u8 *pCellData,             /* Raw cell content as appears on disk */
  int *peWithin              /* Adjust downward, as appropriate */
){





  RtreeDValue xN;      /* Coordinate value converted to a double */


  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 

      || p->op==RTREE_GT || p->op==RTREE_EQ );
  pCellData += 8 + p->iCoord*4;

  RTREE_DECODE_COORD(eInt, pCellData, xN);
  switch( p->op ){
    case RTREE_LE: if( xN <= p->u.rValue ) return;  break;
    case RTREE_LT: if( xN <  p->u.rValue ) return;  break;
    case RTREE_GE: if( xN >= p->u.rValue ) return;  break;

    case RTREE_GT: if( xN >  p->u.rValue ) return;  break;
    default:       if( xN == p->u.rValue ) return;  break;

  }





























  *peWithin = NOT_WITHIN;
}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(
................................................................................
  Rtree *pRtree, 
  RtreeNode *pNode, 
  i64 iRowid,
  int *piIndex
){
  int ii;
  int nCell = NCELL(pNode);
  assert( nCell<200 );
  for(ii=0; ii<nCell; ii++){
    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
      *piIndex = ii;
      return SQLITE_OK;
    }
  }
  return SQLITE_CORRUPT_VTAB;
................................................................................
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
  }
  *piIndex = -1;
  return SQLITE_OK;
}

/*
** Compare two search points.  Return negative, zero, or positive if the first
** is less than, equal to, or greater than the second.
**
** The rScore is the primary key.  Smaller rScore values come first.
** If the rScore is a tie, then use iLevel as the tie breaker with smaller
** iLevel values coming first.  In this way, if rScore is the same for all
** SearchPoints, then iLevel becomes the deciding factor and the result
** is a depth-first search, which is the desired default behavior.
*/




static int rtreeSearchPointCompare(
  const RtreeSearchPoint *pA,
  const RtreeSearchPoint *pB
){
  if( pA->rScore<pB->rScore ) return -1;
  if( pA->rScore>pB->rScore ) return +1;
  if( pA->iLevel<pB->iLevel ) return -1;
  if( pA->iLevel>pB->iLevel ) return +1;
  return 0;
}




/*
** Interchange to search points in a cursor.
*/
static void rtreeSearchPointSwap(RtreeCursor *p, int i, int j){
  RtreeSearchPoint t = p->aPoint[i];
  assert( i<j );
  p->aPoint[i] = p->aPoint[j];
  p->aPoint[j] = t;
  i++; j++;
  if( i<RTREE_CACHE_SZ ){
    if( j>=RTREE_CACHE_SZ ){
      nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
      p->aNode[i] = 0;
    }else{
      RtreeNode *pTemp = p->aNode[i];
      p->aNode[i] = p->aNode[j];
      p->aNode[j] = pTemp;
    }
  }
}

/*
** Return the search point with the lowest current score.
*/
static RtreeSearchPoint *rtreeSearchPointFirst(RtreeCursor *pCur){
  return pCur->bPoint ? &pCur->sPoint : pCur->nPoint ? pCur->aPoint : 0;
}

/*
** Get the RtreeNode for the search point with the lowest score.
*/
static RtreeNode *rtreeNodeOfFirstSearchPoint(RtreeCursor *pCur, int *pRC){
  sqlite3_int64 id;
  int ii = 1 - pCur->bPoint;
  assert( ii==0 || ii==1 );
  assert( pCur->bPoint || pCur->nPoint );
  if( pCur->aNode[ii]==0 ){
    assert( pRC!=0 );
    id = ii ? pCur->aPoint[0].id : pCur->sPoint.id;
    *pRC = nodeAcquire(RTREE_OF_CURSOR(pCur), id, 0, &pCur->aNode[ii]);
  }




  return pCur->aNode[ii];
}

/*
** Push a new element onto the priority queue
*/
static RtreeSearchPoint *rtreeEnqueue(
  RtreeCursor *pCur,    /* The cursor */
  RtreeDValue rScore,   /* Score for the new search point */
  u8 iLevel             /* Level for the new search point */
){
  int i, j;
  RtreeSearchPoint *pNew;
  if( pCur->nPoint>=pCur->nPointAlloc ){
    int nNew = pCur->nPointAlloc*2 + 8;
    pNew = sqlite3_realloc(pCur->aPoint, nNew*sizeof(pCur->aPoint[0]));
    if( pNew==0 ) return 0;
    pCur->aPoint = pNew;
    pCur->nPointAlloc = nNew;
  }
  i = pCur->nPoint++;
  pNew = pCur->aPoint + i;
  pNew->rScore = rScore;
  pNew->iLevel = iLevel;
  assert( iLevel>=0 && iLevel<=RTREE_MAX_DEPTH );
  while( i>0 ){
    RtreeSearchPoint *pParent;
    j = (i-1)/2;
    pParent = pCur->aPoint + j;
    if( rtreeSearchPointCompare(pNew, pParent)>=0 ) break;
    rtreeSearchPointSwap(pCur, j, i);
    i = j;
    pNew = pParent;
  }
  return pNew;
}

/*
** Allocate a new RtreeSearchPoint and return a pointer to it.  Return
** NULL if malloc fails.
*/
static RtreeSearchPoint *rtreeSearchPointNew(
  RtreeCursor *pCur,    /* The cursor */
  RtreeDValue rScore,   /* Score for the new search point */
  u8 iLevel             /* Level for the new search point */
){
  RtreeSearchPoint *pNew, *pFirst;
  pFirst = rtreeSearchPointFirst(pCur);
  pCur->anQueue[iLevel]++;
  if( pFirst==0
   || pFirst->rScore>rScore 
   || (pFirst->rScore==rScore && pFirst->iLevel>iLevel)
  ){
    if( pCur->bPoint ){
      int ii;
      pNew = rtreeEnqueue(pCur, rScore, iLevel);
      if( pNew==0 ) return 0;
      ii = (int)(pNew - pCur->aPoint) + 1;
      if( ii<RTREE_CACHE_SZ ){
        assert( pCur->aNode[ii]==0 );
        pCur->aNode[ii] = pCur->aNode[0];
       }else{

        nodeRelease(RTREE_OF_CURSOR(pCur), pCur->aNode[0]);
      }
      pCur->aNode[0] = 0;
      *pNew = pCur->sPoint;
    }
    pCur->sPoint.rScore = rScore;
    pCur->sPoint.iLevel = iLevel;
    pCur->bPoint = 1;
    return &pCur->sPoint;
  }else{
    return rtreeEnqueue(pCur, rScore, iLevel);
  }
}

#if 0
/* Tracing routines for the RtreeSearchPoint queue */
static void tracePoint(RtreeSearchPoint *p, int idx, RtreeCursor *pCur){
  if( idx<0 ){ printf(" s"); }else{ printf("%2d", idx); }
  printf(" %d.%05lld.%02d %g %d",
    p->iLevel, p->id, p->iCell, p->rScore, p->eWithin
  );
  idx++;
  if( idx<RTREE_CACHE_SZ ){
    printf(" %p\n", pCur->aNode[idx]);
  }else{
    printf("\n");
  }
}
static void traceQueue(RtreeCursor *pCur, const char *zPrefix){
  int ii;

  printf("=== %9s ", zPrefix);
  if( pCur->bPoint ){
    tracePoint(&pCur->sPoint, -1, pCur);
  }
  for(ii=0; ii<pCur->nPoint; ii++){
    if( ii>0 || pCur->bPoint ) printf("              ");
    tracePoint(&pCur->aPoint[ii], ii, pCur);
  }
}
# define RTREE_QUEUE_TRACE(A,B) traceQueue(A,B)
#else
# define RTREE_QUEUE_TRACE(A,B)   /* no-op */
#endif

/* Remove the search point with the lowest current score.
*/
static void rtreeSearchPointPop(RtreeCursor *p){
  int i, j, k, n;
  i = 1 - p->bPoint;
  assert( i==0 || i==1 );
  if( p->aNode[i] ){
    nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
    p->aNode[i] = 0;
  }
  if( p->bPoint ){
    p->anQueue[p->sPoint.iLevel]--;
    p->bPoint = 0;
  }else if( p->nPoint ){
    p->anQueue[p->aPoint[0].iLevel]--;
    n = --p->nPoint;
    p->aPoint[0] = p->aPoint[n];
    if( n<RTREE_CACHE_SZ-1 ){
      p->aNode[1] = p->aNode[n+1];
      p->aNode[n+1] = 0;
    }
    i = 0;
    while( (j = i*2+1)<n ){
      k = j+1;
      if( k<n && rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[j])<0 ){
        if( rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[i])<0 ){
          rtreeSearchPointSwap(p, i, k);
          i = k;
        }else{
          break;
        }
      }else{
        if( rtreeSearchPointCompare(&p->aPoint[j], &p->aPoint[i])<0 ){
          rtreeSearchPointSwap(p, i, j);
          i = j;
        }else{
          break;
        }
      }
    }
  }
}


/*
** Continue the search on cursor pCur until the front of the queue
** contains an entry suitable for returning as a result-set row,
** or until the RtreeSearchPoint queue is empty, indicating that the
** query has completed.
*/
static int rtreeStepToLeaf(RtreeCursor *pCur){
  RtreeSearchPoint *p;
  Rtree *pRtree = RTREE_OF_CURSOR(pCur);
  RtreeNode *pNode;
  int eWithin;
  int rc = SQLITE_OK;
  int nCell;

  int nConstraint = pCur->nConstraint;
  int ii;


  int eInt;
  RtreeSearchPoint x;

  eInt = pRtree->eCoordType==RTREE_COORD_INT32;
  while( (p = rtreeSearchPointFirst(pCur))!=0 && p->iLevel>0 ){
    pNode = rtreeNodeOfFirstSearchPoint(pCur, &rc);
    if( rc ) return rc;
    nCell = NCELL(pNode);
    assert( nCell<200 );
    while( p->iCell<nCell ){
      sqlite3_rtree_dbl rScore = (sqlite3_rtree_dbl)-1;
      u8 *pCellData = pNode->zData + (4+pRtree->nBytesPerCell*p->iCell);
      eWithin = FULLY_WITHIN;
      for(ii=0; ii<nConstraint; ii++){
        RtreeConstraint *pConstraint = pCur->aConstraint + ii;
        if( pConstraint->op>=RTREE_MATCH ){
          rc = rtreeCallbackConstraint(pConstraint, eInt, pCellData, p,
                                       &rScore, &eWithin);
          if( rc ) return rc;
        }else if( p->iLevel==1 ){
          rtreeLeafConstraint(pConstraint, eInt, pCellData, &eWithin);
        }else{
          rtreeNonleafConstraint(pConstraint, eInt, pCellData, &eWithin);
        }
        if( eWithin==NOT_WITHIN ) break;
      }




      p->iCell++;
      if( eWithin==NOT_WITHIN ) continue;
      x.iLevel = p->iLevel - 1;
      if( x.iLevel ){
        x.id = readInt64(pCellData);
        x.iCell = 0;
      }else{
        x.id = p->id;
        x.iCell = p->iCell - 1;
      }



      if( p->iCell>=nCell ){
        RTREE_QUEUE_TRACE(pCur, "POP-S:");
        rtreeSearchPointPop(pCur);
      }
      if( rScore<RTREE_ZERO ) rScore = RTREE_ZERO;
      p = rtreeSearchPointNew(pCur, rScore, x.iLevel);
      if( p==0 ) return SQLITE_NOMEM;
      p->eWithin = eWithin;
      p->id = x.id;
      p->iCell = x.iCell;
      RTREE_QUEUE_TRACE(pCur, "PUSH-S:");
      break;
    }
    if( p->iCell>=nCell ){
      RTREE_QUEUE_TRACE(pCur, "POP-Se:");
      rtreeSearchPointPop(pCur);
    }
  }
  pCur->atEOF = p==0;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  int rc = SQLITE_OK;

  /* Move to the next entry that matches the configured constraints. */
  RTREE_QUEUE_TRACE(pCsr, "POP-Nx:");
  rtreeSearchPointPop(pCsr);
  rc = rtreeStepToLeaf(pCsr);
  return rc;
}

/* 
** Rtree virtual table module xRowid method.
*/
static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){

  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;

  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
  int rc = SQLITE_OK;
  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
  if( rc==SQLITE_OK && p ){
    *pRowid = nodeGetRowid(RTREE_OF_CURSOR(pCsr), pNode, p->iCell);
  }
  return rc;
}

/* 
** Rtree virtual table module xColumn method.
*/
static int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
  Rtree *pRtree = (Rtree *)cur->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
  RtreeCoord c;
  int rc = SQLITE_OK;
  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);

  if( rc ) return rc;
  if( p==0 ) return SQLITE_OK;
  if( i==0 ){

    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
  }else{

    if( rc ) return rc;
    nodeGetCoord(pRtree, pNode, p->iCell, i-1, &c);
#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      sqlite3_result_double(ctx, c.f);
    }else
#endif
    {
      assert( pRtree->eCoordType==RTREE_COORD_INT32 );
      sqlite3_result_int(ctx, c.i);
    }
  }

  return SQLITE_OK;
}

/* 
** Use nodeAcquire() to obtain the leaf node containing the record with 
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(
  Rtree *pRtree,              /* RTree to search */
  i64 iRowid,                 /* The rowid searching for */
  RtreeNode **ppLeaf,         /* Write the node here */
  sqlite3_int64 *piNode       /* Write the node-id here */
){
  int rc;
  *ppLeaf = 0;
  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);
    if( piNode ) *piNode = iNode;
    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}
................................................................................
/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
  RtreeMatchArg *pBlob;              /* BLOB returned by geometry function */
  sqlite3_rtree_query_info *pInfo;   /* Callback information */
  int nBlob;                         /* Size of the geometry function blob */
  int nExpected;                     /* Expected size of the BLOB */

  /* Check that value is actually a blob. */
  if( sqlite3_value_type(pValue)!=SQLITE_BLOB ) return SQLITE_ERROR;

  /* Check that the blob is roughly the right size. */
  nBlob = sqlite3_value_bytes(pValue);
  if( nBlob<(int)sizeof(RtreeMatchArg) 
   || ((nBlob-sizeof(RtreeMatchArg))%sizeof(RtreeDValue))!=0
  ){
    return SQLITE_ERROR;
  }

  pInfo = (sqlite3_rtree_query_info*)sqlite3_malloc( sizeof(*pInfo)+nBlob );
  if( !pInfo ) return SQLITE_NOMEM;
  memset(pInfo, 0, sizeof(*pInfo));
  pBlob = (RtreeMatchArg*)&pInfo[1];

  memcpy(pBlob, sqlite3_value_blob(pValue), nBlob);
  nExpected = (int)(sizeof(RtreeMatchArg) +
                    (pBlob->nParam-1)*sizeof(RtreeDValue));
  if( pBlob->magic!=RTREE_GEOMETRY_MAGIC || nBlob!=nExpected ){
    sqlite3_free(pInfo);
    return SQLITE_ERROR;
  }
  pInfo->pContext = pBlob->cb.pContext;
  pInfo->nParam = pBlob->nParam;
  pInfo->aParam = pBlob->aParam;

  if( pBlob->cb.xGeom ){
    pCons->u.xGeom = pBlob->cb.xGeom;
  }else{
    pCons->op = RTREE_QUERY;
    pCons->u.xQueryFunc = pBlob->cb.xQueryFunc;
  }
  pCons->pInfo = pInfo;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
  sqlite3_vtab_cursor *pVtabCursor, 
  int idxNum, const char *idxStr,
  int argc, sqlite3_value **argv
){
  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;

  RtreeNode *pRoot = 0;
  int ii;
  int rc = SQLITE_OK;
  int iCell = 0;

  rtreeReference(pRtree);

  freeCursorConstraints(pCsr);
  pCsr->iStrategy = idxNum;

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
    RtreeSearchPoint *p;     /* Search point for the the leaf */
    i64 iRowid = sqlite3_value_int64(argv[0]);
    i64 iNode = 0;
    rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);


    if( rc==SQLITE_OK && pLeaf!=0 ){
      p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);
      assert( p!=0 );  /* Always returns pCsr->sPoint */
      pCsr->aNode[0] = pLeaf;
      p->id = iNode;
      p->eWithin = PARTLY_WITHIN;
      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);
      p->iCell = iCell;
      RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
    }else{
      pCsr->atEOF = 1;
    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */
    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
    if( rc==SQLITE_OK && argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);
        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
        assert( (idxStr==0 && argc==0)
                || (idxStr && (int)strlen(idxStr)==argc*2) );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'0';
          if( p->op>=RTREE_MATCH ){
            /* A MATCH operator. The right-hand-side must be a blob that
            ** can be cast into an RtreeMatchArg object. One created using
            ** an sqlite3_rtree_geometry_callback() SQL user function.
            */
            rc = deserializeGeometry(argv[ii], p);
            if( rc!=SQLITE_OK ){
              break;
            }
            p->pInfo->nCoord = pRtree->nDim*2;
            p->pInfo->anQueue = pCsr->anQueue;
            p->pInfo->mxLevel = pRtree->iDepth + 1;
          }else{
#ifdef SQLITE_RTREE_INT_ONLY
            p->u.rValue = sqlite3_value_int64(argv[ii]);
#else
            p->u.rValue = sqlite3_value_double(argv[ii]);
#endif
          }
        }
      }
    }

    if( rc==SQLITE_OK ){



      RtreeSearchPoint *pNew;
      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, pRtree->iDepth+1);
      if( pNew==0 ) return SQLITE_NOMEM;
      pNew->id = 1;

      pNew->iCell = 0;
      pNew->eWithin = PARTLY_WITHIN;
      assert( pCsr->bPoint==1 );
      pCsr->aNode[0] = pRoot;







      pRoot = 0;
      RTREE_QUEUE_TRACE(pCsr, "PUSH-Fm:");
      rc = rtreeStepToLeaf(pCsr);
    }

  }


  nodeRelease(pRtree, pRoot);
  rtreeRelease(pRtree);
  return rc;
}

/*
** Set the pIdxInfo->estimatedRows variable to nRow. Unless this
** extension is currently being used by a version of SQLite too old to
................................................................................
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
        default:
          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );
          op = RTREE_MATCH; 
          break;
      }
      zIdxStr[iIdx++] = op;
      zIdxStr[iIdx++] = p->iColumn - 1 + '0';
      pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
      pIdxInfo->aConstraintUsage[ii].omit = 1;
    }
  }

  pIdxInfo->idxNum = 2;
  pIdxInfo->needToFreeIdxStr = 1;
................................................................................
  RtreeCell cell;
  memcpy(&cell, p, sizeof(RtreeCell));
  area = cellArea(pRtree, &cell);
  cellUnion(pRtree, &cell, pCell);
  return (cellArea(pRtree, &cell)-area);
}


static RtreeDValue cellOverlap(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *aCell, 
  int nCell

){
  int ii;
  RtreeDValue overlap = RTREE_ZERO;
  for(ii=0; ii<nCell; ii++){







    int jj;
    RtreeDValue o = (RtreeDValue)1;
    for(jj=0; jj<(pRtree->nDim*2); jj+=2){
      RtreeDValue x1, x2;

      x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
      x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));

      if( x2<x1 ){

        o = (RtreeDValue)0;
        break;
      }else{
        o = o * (x2-x1);
      }
    }
    overlap += o;

  }
  return overlap;
}




















/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
................................................................................
  RtreeNode *pNode;
  rc = nodeAcquire(pRtree, 1, 0, &pNode);

  for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
    int iCell;
    sqlite3_int64 iBest = 0;

    RtreeDValue fMinGrowth = RTREE_ZERO;
    RtreeDValue fMinArea = RTREE_ZERO;





    int nCell = NCELL(pNode);
    RtreeCell cell;
    RtreeNode *pChild;

    RtreeCell *aCell = 0;

















    /* Select the child node which will be enlarged the least if pCell
    ** is inserted into it. Resolve ties by choosing the entry with
    ** the smallest area.
    */
    for(iCell=0; iCell<nCell; iCell++){
      int bBest = 0;
      RtreeDValue growth;
      RtreeDValue area;
      nodeGetCell(pRtree, pNode, iCell, &cell);
      growth = cellGrowth(pRtree, &cell, pCell);
      area = cellArea(pRtree, &cell);
















      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
        bBest = 1;
      }

      if( bBest ){
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

................................................................................
  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
  sqlite3_step(pRtree->pWriteParent);
  return sqlite3_reset(pRtree->pWriteParent);
}

static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);























































































































































/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to 
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
................................................................................
        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
      }
    }
#endif
  }
}


/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
  Rtree *pRtree,
  RtreeCell *aCell,
  int nCell,
................................................................................
){
  int **aaSorted;
  int *aSpare;
  int ii;

  int iBestDim = 0;
  int iBestSplit = 0;
  RtreeDValue fBestMargin = RTREE_ZERO;

  int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));

  aaSorted = (int **)sqlite3_malloc(nByte);
  if( !aaSorted ){
    return SQLITE_NOMEM;
  }
................................................................................
    for(jj=0; jj<nCell; jj++){
      aaSorted[ii][jj] = jj;
    }
    SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
  }

  for(ii=0; ii<pRtree->nDim; ii++){
    RtreeDValue margin = RTREE_ZERO;
    RtreeDValue fBestOverlap = RTREE_ZERO;
    RtreeDValue fBestArea = RTREE_ZERO;
    int iBestLeft = 0;
    int nLeft;

    for(
      nLeft=RTREE_MINCELLS(pRtree); 
      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); 
      nLeft++
................................................................................
          cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
        }else{
          cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
        }
      }
      margin += cellMargin(pRtree, &left);
      margin += cellMargin(pRtree, &right);
      overlap = cellOverlap(pRtree, &left, &right, 1);
      area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
      if( (nLeft==RTREE_MINCELLS(pRtree))
       || (overlap<fBestOverlap)
       || (overlap==fBestOverlap && area<fBestArea)
      ){
        iBestLeft = nLeft;
        fBestOverlap = overlap;
................................................................................
    nodeInsertCell(pRtree, pTarget, pCell);
    cellUnion(pRtree, pBbox, pCell);
  }

  sqlite3_free(aaSorted);
  return SQLITE_OK;
}


























































static int updateMapping(
  Rtree *pRtree, 
  i64 iRowid, 
  RtreeNode *pNode, 
  int iHeight
){
................................................................................
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }

  memset(pLeft->zData, 0, pRtree->iNodeSize);
  memset(pRight->zData, 0, pRtree->iNodeSize);

  rc = splitNodeStartree(pRtree, aCell, nCell, pLeft, pRight,
                         &leftbbox, &rightbbox);
  if( rc!=SQLITE_OK ){
    goto splitnode_out;
  }

  /* Ensure both child nodes have node numbers assigned to them by calling
  ** nodeWrite(). Node pRight always needs a node number, as it was created
  ** by nodeNew() above. But node pLeft sometimes already has a node number.
................................................................................
    }
  }
  for(iDim=0; iDim<pRtree->nDim; iDim++){
    aCenterCoord[iDim] = (aCenterCoord[iDim]/(nCell*(RtreeDValue)2));
  }

  for(ii=0; ii<nCell; ii++){
    aDistance[ii] = RTREE_ZERO;
    for(iDim=0; iDim<pRtree->nDim; iDim++){
      RtreeDValue coord = (DCOORD(aCell[ii].aCoord[iDim*2+1]) - 
                               DCOORD(aCell[ii].aCoord[iDim*2]));
      aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
    }
  }

................................................................................
    if( pChild ){
      nodeRelease(pRtree, pChild->pParent);
      nodeReference(pNode);
      pChild->pParent = pNode;
    }
  }
  if( nodeInsertCell(pRtree, pNode, pCell) ){

    if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
      rc = SplitNode(pRtree, pNode, pCell, iHeight);
    }else{
      pRtree->iReinsertHeight = iHeight;
      rc = Reinsert(pRtree, pNode, pCell, iHeight);
    }



  }else{
    rc = AdjustTree(pRtree, pNode, pCell);
    if( rc==SQLITE_OK ){
      if( iHeight==0 ){
        rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
................................................................................
  /* Obtain a reference to the root node to initialize Rtree.iDepth */
  rc = nodeAcquire(pRtree, 1, 0, &pRoot);

  /* Obtain a reference to the leaf node that contains the entry 
  ** about to be deleted. 
  */
  if( rc==SQLITE_OK ){
    rc = findLeafNode(pRtree, iDelete, &pLeaf, 0);
  }

  /* Delete the cell in question from the leaf node. */
  if( rc==SQLITE_OK ){
    int rc2;
    rc = nodeRowidIndex(pRtree, pLeaf, iDelete, &iCell);
    if( rc==SQLITE_OK ){
................................................................................

  pRtree->db = db;

  if( isCreate ){
    char *zCreate = sqlite3_mprintf(
"CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY, data BLOB);"
"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"
"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY,"
                                  " parentnode INTEGER);"
"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",
      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
    );
    if( !zCreate ){
      return SQLITE_NOMEM;
    }
    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
................................................................................
}


/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.
**
** The scalar function takes two arguments: (1) the number of dimensions
** to the rtree (between 1 and 5, inclusive) and (2) a blob of data containing
** an r-tree node.  For a two-dimensional r-tree structure called "rt", to
** deserialize all nodes, a statement like:
**
**   SELECT rtreenode(2, data) FROM rt_node;
**
** The human readable string takes the form of a Tcl list with one
** entry for each cell in the r-tree node. Each entry is itself a
** list, containing the 8-byte rowid/pageno followed by the 
** <num-dimension>*2 coordinates.
................................................................................
    int jj;

    nodeGetCell(&tree, &node, ii, &cell);
    sqlite3_snprintf(512-nCell,&zCell[nCell],"%lld", cell.iRowid);
    nCell = (int)strlen(zCell);
    for(jj=0; jj<tree.nDim*2; jj++){
#ifndef SQLITE_RTREE_INT_ONLY
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %g",
                       (double)cell.aCoord[jj].f);
#else
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %d",
                       cell.aCoord[jj].i);
#endif
      nCell = (int)strlen(zCell);
    }
................................................................................
      zText = sqlite3_mprintf("{%s}", zCell);
    }
  }
  
  sqlite3_result_text(ctx, zText, -1, sqlite3_free);
}

/* This routine implements an SQL function that returns the "depth" parameter
** from the front of a blob that is an r-tree node.  For example:
**
**     SELECT rtreedepth(data) FROM rt_node WHERE nodeno=1;
**
** The depth value is 0 for all nodes other than the root node, and the root
** node always has nodeno=1, so the example above is the primary use for this
** routine.  This routine is intended for testing and analysis only.
*/
static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
  UNUSED_PARAMETER(nArg);
  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB 
   || sqlite3_value_bytes(apArg[0])<2
  ){
    sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1); 
  }else{
................................................................................
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

  return rc;
}

/*
** This routine deletes the RtreeGeomCallback object that was attached
** one of the SQL functions create by sqlite3_rtree_geometry_callback()
** or sqlite3_rtree_query_callback().  In other words, this routine is the
** destructor for an RtreeGeomCallback objecct.  This routine is called when
** the corresponding SQL function is deleted.
*/

static void rtreeFreeCallback(void *p){
  RtreeGeomCallback *pInfo = (RtreeGeomCallback*)p;
  if( pInfo->xDestructor ) pInfo->xDestructor(pInfo->pContext);
  sqlite3_free(p);
}

/*
** Each call to sqlite3_rtree_geometry_callback() or
** sqlite3_rtree_query_callback() creates an ordinary SQLite
** scalar function that is implemented by this routine.
**
** All this function does is construct an RtreeMatchArg object that
** contains the geometry-checking callback routines and a list of
** parameters to this function, then return that RtreeMatchArg object
** as a BLOB.
**
** The R-Tree MATCH operator will read the returned BLOB, deserialize
** the RtreeMatchArg object, and use the RtreeMatchArg object to figure
** out which elements of the R-Tree should be returned by the query.
*/
static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
  RtreeMatchArg *pBlob;
  int nBlob;

  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue);
  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);
  if( !pBlob ){
    sqlite3_result_error_nomem(ctx);
  }else{
    int i;
    pBlob->magic = RTREE_GEOMETRY_MAGIC;
    pBlob->cb = pGeomCtx[0];

    pBlob->nParam = nArg;
    for(i=0; i<nArg; i++){
#ifdef SQLITE_RTREE_INT_ONLY
      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
#else
      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
#endif
    }
    sqlite3_result_blob(ctx, pBlob, nBlob, sqlite3_free);
  }
}

/*
** Register a new geometry function for use with the r-tree MATCH operator.
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,                  /* Register SQL function on this connection */
  const char *zGeom,            /* Name of the new SQL function */
  int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*), /* Callback */
  void *pContext                /* Extra data associated with the callback */
){
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = xGeom;
  pGeomCtx->xQueryFunc = 0;
  pGeomCtx->xDestructor = 0;
  pGeomCtx->pContext = pContext;
  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
  );
}



/*
** Register a new 2nd-generation geometry function for use with the
** r-tree MATCH operator.
*/
int sqlite3_rtree_query_callback(
  sqlite3 *db,                 /* Register SQL function on this connection */
  const char *zQueryFunc,      /* Name of new SQL function */
  int (*xQueryFunc)(sqlite3_rtree_query_info*), /* Callback */
  void *pContext,              /* Extra data passed into the callback */
  void (*xDestructor)(void*)   /* Destructor for the extra data */
){
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = 0;
  pGeomCtx->xQueryFunc = xQueryFunc;
  pGeomCtx->xDestructor = xDestructor;
  pGeomCtx->pContext = pContext;
  return sqlite3_create_function_v2(db, zQueryFunc, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
  );
}

#if !SQLITE_CORE
#ifdef _WIN32
__declspec(dllexport)
#endif

  }
  return $out
}

# Test that it is possible to open an existing database that contains
# r-tree tables.
#
do_test rtree-1.4.1 {
  execsql {
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2);
    INSERT INTO t1 VALUES(1, 5.0, 10.0);



    INSERT INTO t1 VALUES(2, 15.0, 20.0);
  }
} {}
do_test rtree-1.4.2 {
  db close
  sqlite3 db test.db
  execsql_intout { SELECT * FROM t1 ORDER BY ii }
} {1 5 10 2 15 20}
do_test rtree-1.4.3 {
................................................................................
  }
} {2}

#-------------------------------------------------------------------------
# Test on-conflict clause handling.
#
db_delete_and_reopen
do_execsql_test 12.0 {
  CREATE VIRTUAL TABLE t1 USING rtree_i32(idx, x1, x2, y1, y2);
  INSERT INTO t1 VALUES(1,   1, 2, 3, 4);



  INSERT INTO t1 VALUES(2,   2, 3, 4, 5);
  INSERT INTO t1 VALUES(3,   3, 4, 5, 6);

  CREATE TABLE source(idx, x1, x2, y1, y2);
  INSERT INTO source VALUES(5, 8, 8, 8, 8);
  INSERT INTO source VALUES(2, 7, 7, 7, 7);
  
}
db_save_and_close
foreach {tn sql_template testdata} {
  1    "INSERT %CONF% INTO t1 VALUES(2, 7, 7, 7, 7)" {
    ROLLBACK 0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
    ABORT    0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}

  }
  return $out
}

# Test that it is possible to open an existing database that contains
# r-tree tables.
#
do_execsql_test rtree-1.4.1a {

  CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2);
  INSERT INTO t1 VALUES(1, 5.0, 10.0);
  SELECT substr(hex(data),1,40) FROM t1_node;
} {00000001000000000000000140A0000041200000}
do_execsql_test rtree-1.4.1b {
  INSERT INTO t1 VALUES(2, 15.0, 20.0);

} {}
do_test rtree-1.4.2 {
  db close
  sqlite3 db test.db
  execsql_intout { SELECT * FROM t1 ORDER BY ii }
} {1 5 10 2 15 20}
do_test rtree-1.4.3 {
................................................................................
  }
} {2}

#-------------------------------------------------------------------------
# Test on-conflict clause handling.
#
db_delete_and_reopen
do_execsql_test 12.0.1 {
  CREATE VIRTUAL TABLE t1 USING rtree_i32(idx, x1, x2, y1, y2);
  INSERT INTO t1 VALUES(1,   1, 2, 3, 4);
  SELECT substr(hex(data),1,56) FROM t1_node;
} {00000001000000000000000100000001000000020000000300000004}
do_execsql_test 12.0.2 {
  INSERT INTO t1 VALUES(2,   2, 3, 4, 5);
  INSERT INTO t1 VALUES(3,   3, 4, 5, 6);

  CREATE TABLE source(idx, x1, x2, y1, y2);
  INSERT INTO source VALUES(5, 8, 8, 8, 8);
  INSERT INTO source VALUES(2, 7, 7, 7, 7);

}
db_save_and_close
foreach {tn sql_template testdata} {
  1    "INSERT %CONF% INTO t1 VALUES(2, 7, 7, 7, 7)" {
    ROLLBACK 0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
    ABORT    0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}

    CREATE TABLE t2(k INTEGER PRIMARY KEY, v);
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
  }
} {}

do_test rtree6-1.2 {
  rtree_strategy {SELECT * FROM t1 WHERE x1>10}
} {Ea}

do_test rtree6-1.3 {
  rtree_strategy {SELECT * FROM t1 WHERE x1<10}
} {Ca}

do_test rtree6-1.4 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=ii AND x1<10}
} {Ca}

do_test rtree6-1.5 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=+ii AND x1<10}
} {Ca}

do_eqp_test rtree6.2.1 {
  SELECT * FROM t1,t2 WHERE k=+ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:Ca} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.2 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:Ca} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.3 {
  SELECT * FROM t1,t2 WHERE k=ii
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.4 {
  SELECT * FROM t1,t2 WHERE v=10 and x1<10 and x2>10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:CaEb} 
  0 1 1 {SEARCH TABLE t2 USING AUTOMATIC COVERING INDEX (v=?)}
}

do_eqp_test rtree6.2.5 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<v
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
................................................................................
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 
  }
} {EaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEa}
do_test rtree6.3.3 {
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5
  }
} {EaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEa}

do_execsql_test rtree6-3.4 {
  SELECT * FROM t3 WHERE x1>0.5 AND x1>0.8 AND x1>1.1
} {}
do_execsql_test rtree6-3.5 {
  SELECT * FROM t3 WHERE 
    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 

    CREATE TABLE t2(k INTEGER PRIMARY KEY, v);
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
  }
} {}

do_test rtree6-1.2 {
  rtree_strategy {SELECT * FROM t1 WHERE x1>10}
} {E0}

do_test rtree6-1.3 {
  rtree_strategy {SELECT * FROM t1 WHERE x1<10}
} {C0}

do_test rtree6-1.4 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=ii AND x1<10}
} {C0}

do_test rtree6-1.5 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=+ii AND x1<10}
} {C0}

do_eqp_test rtree6.2.1 {
  SELECT * FROM t1,t2 WHERE k=+ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:C0} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.2 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:C0} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.3 {
  SELECT * FROM t1,t2 WHERE k=ii
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.4 {
  SELECT * FROM t1,t2 WHERE v=10 and x1<10 and x2>10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:C0E1} 
  0 1 1 {SEARCH TABLE t2 USING AUTOMATIC COVERING INDEX (v=?)}
}

do_eqp_test rtree6.2.5 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<v
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
................................................................................
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 
  }
} {E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0}
do_test rtree6.3.3 {
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5
  }
} {E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0}

do_execsql_test rtree6-3.4 {
  SELECT * FROM t3 WHERE x1>0.5 AND x1>0.8 AND x1>1.1
} {}
do_execsql_test rtree6-3.5 {
  SELECT * FROM t3 WHERE 
    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 

      INSERT INTO t1 VALUES(1073741824, 0.0, 0.0, 100.0, 100.0);
      INSERT INTO t1 VALUES(2147483646, 0.0, 0.0, 200.0, 200.0);
      INSERT INTO t1 VALUES(4294967296, 0.0, 0.0, 300.0, 300.0);
      INSERT INTO t1 VALUES(8589934592, 20.0, 20.0, 150.0, 150.0);
      INSERT INTO t1 VALUES(9223372036854775807, 150, 150, 400, 400);
      SELECT rtreenode(2, data) FROM t1_node;
    }
  } {{{1073741824 0.000000 0.000000 100.000000 100.000000} {2147483646 0.000000 0.000000 200.000000 200.000000} {4294967296 0.000000 0.000000 300.000000 300.000000} {8589934592 20.000000 20.000000 150.000000 150.000000} {9223372036854775807 150.000000 150.000000 400.000000 400.000000}}}
}

finish_test

      INSERT INTO t1 VALUES(1073741824, 0.0, 0.0, 100.0, 100.0);
      INSERT INTO t1 VALUES(2147483646, 0.0, 0.0, 200.0, 200.0);
      INSERT INTO t1 VALUES(4294967296, 0.0, 0.0, 300.0, 300.0);
      INSERT INTO t1 VALUES(8589934592, 20.0, 20.0, 150.0, 150.0);
      INSERT INTO t1 VALUES(9223372036854775807, 150, 150, 400, 400);
      SELECT rtreenode(2, data) FROM t1_node;
    }
  } {{{1073741824 0 0 100 100} {2147483646 0 0 200 200} {4294967296 0 0 300 300} {8589934592 20 20 150 150} {9223372036854775807 150 150 400 400}}}
}

finish_test

}

do_eqp_test 1.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 1.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 1.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 1.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
sqlite3 db test.db

do_eqp_test 2.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 2.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 2.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 2.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
    execsql { SELECT * FROM rt }
  } {1 2.0 3.0}
  db close
}


finish_test

}

do_eqp_test 1.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 1.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 1.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 1.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
sqlite3 db test.db

do_eqp_test 2.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 2.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 2.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 2.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
    execsql { SELECT * FROM rt }
  } {1 2.0 3.0}
  db close
}


finish_test

# 2010 August 28
#
# 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 tests for the r-tree module. Specifically, it tests
# that new-style custom r-tree queries (geometry callbacks) work.
# 

if {![info exists testdir]} {
  set testdir [file join [file dirname [info script]] .. .. test]
} 
source $testdir/tester.tcl
ifcapable !rtree { finish_test ; return }
ifcapable rtree_int_only { finish_test; return }


#-------------------------------------------------------------------------
# Test the example 2d "circle" geometry callback.
#
register_circle_geom db

do_execsql_test rtreeE-1.1 {
  PRAGMA page_size=512;
  CREATE VIRTUAL TABLE rt1 USING rtree(id,x0,x1,y0,y1);
  
  /* A tight pattern of small boxes near 0,0 */
  WITH RECURSIVE
    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
  INSERT INTO rt1 SELECT x+5*y, x, x+2, y, y+2 FROM x, y;

  /* A looser pattern of small boxes near 100, 0 */
  WITH RECURSIVE
    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
  INSERT INTO rt1 SELECT 100+x+5*y, x*3+100, x*3+102, y*3, y*3+2 FROM x, y;

  /* A looser pattern of larger boxes near 0, 200 */
  WITH RECURSIVE
    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
  INSERT INTO rt1 SELECT 200+x+5*y, x*7, x*7+15, y*7+200, y*7+215 FROM x, y;
} {}

# Queries against each of the three clusters */
do_execsql_test rtreeE-1.1 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0.0, 0.0, 50.0, 3) ORDER BY id;
} {0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24}
do_execsql_test rtreeE-1.2 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(100.0, 0.0, 50.0, 3) ORDER BY id;
} {100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124}
do_execsql_test rtreeE-1.3 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0.0, 200.0, 50.0, 3) ORDER BY id;
} {200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224}

# The Qcircle geometry function gives a lower score to larger leaf-nodes.
# This causes the 200s to sort before the 100s and the 0s to sort before
# last.
#
do_execsql_test rtreeE-1.4 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,3) AND id%100==0
} {200 100 0}

# Exclude odd rowids on a depth-first search
do_execsql_test rtreeE-1.5 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,4) ORDER BY +id
} {0 2 4 6 8 10 12 14 16 18 20 22 24 100 102 104 106 108 110 112 114 116 118 120 122 124 200 202 204 206 208 210 212 214 216 218 220 222 224}

# Exclude odd rowids on a breadth-first search.
do_execsql_test rtreeE-1.6 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,5) ORDER BY +id
} {0 2 4 6 8 10 12 14 16 18 20 22 24 100 102 104 106 108 110 112 114 116 118 120 122 124 200 202 204 206 208 210 212 214 216 218 220 222 224}

# Construct a large 2-D RTree with thousands of random entries.
#
do_test rtreeE-2.1 {
  db eval {
    CREATE TABLE t2(id,x0,x1,y0,y1);
    CREATE VIRTUAL TABLE rt2 USING rtree(id,x0,x1,y0,y1);
    BEGIN;
  }
  expr srand(0)
  for {set i 1} {$i<=10000} {incr i} {
    set dx [expr {int(rand()*40)+1}]
    set dy [expr {int(rand()*40)+1}]
    set x0 [expr {int(rand()*(10000 - $dx))}]
    set x1 [expr {$x0+$dx}]
    set y0 [expr {int(rand()*(10000 - $dy))}]
    set y1 [expr {$y0+$dy}]
    set id [expr {$i+10000}]
    db eval {INSERT INTO t2 VALUES($id,$x0,$x1,$y0,$y1)}
  }
  db eval {
    INSERT INTO rt2 SELECT * FROM t2;
    COMMIT;
  }
} {}

for {set i 1} {$i<=200} {incr i} {
  set dx [expr {int(rand()*100)}]
  set dy [expr {int(rand()*100)}]
  set x0 [expr {int(rand()*(10000 - $dx))}]
  set x1 [expr {$x0+$dx}]
  set y0 [expr {int(rand()*(10000 - $dy))}]
  set y1 [expr {$y0+$dy}]
  set ans [db eval {SELECT id FROM t2 WHERE x1>=$x0 AND x0<=$x1 AND y1>=$y0 AND y0<=$y1 ORDER BY id}]
  do_execsql_test rtreeE-2.2.$i {
    SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch($x0,$x1,$y0,$y1) ORDER BY id
  } $ans
}

# Run query that have very deep priority queues
#
set ans [db eval {SELECT id FROM t2 WHERE x1>=0 AND x0<=5000 AND y1>=0 AND y0<=5000 ORDER BY id}]
do_execsql_test rtreeE-2.3 {
  SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch(0,5000,0,5000) ORDER BY id
} $ans
set ans [db eval {SELECT id FROM t2 WHERE x1>=0 AND x0<=10000 AND y1>=0 AND y0<=10000 ORDER BY id}]
do_execsql_test rtreeE-2.4 {
  SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch(0,10000,0,10000) ORDER BY id
} $ans

finish_test

#include <sqlite3.h>

#ifdef __cplusplus
extern "C" {
#endif

typedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;











/*
** Register a geometry callback named zGeom that can be used as part of an
** R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,
#ifdef SQLITE_RTREE_INT_ONLY
  int (*xGeom)(sqlite3_rtree_geometry*, int n, sqlite3_int64 *a, int *pRes),
#else
  int (*xGeom)(sqlite3_rtree_geometry*, int n, double *a, int *pRes),
#endif
  void *pContext
);


/*
** A pointer to a structure of the following type is passed as the first
** argument to callbacks registered using rtree_geometry_callback().
*/
struct sqlite3_rtree_geometry {
  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */
  int nParam;                     /* Size of array aParam[] */
  double *aParam;                 /* Parameters passed to SQL geom function */
  void *pUser;                    /* Callback implementation user data */
  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */
};



















































#ifdef __cplusplus
}  /* end of the 'extern "C"' block */
#endif

#endif  /* ifndef _SQLITE3RTREE_H_ */

#include <sqlite3.h>

#ifdef __cplusplus
extern "C" {
#endif

typedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;
typedef struct sqlite3_rtree_query_info sqlite3_rtree_query_info;

/* The double-precision datatype used by RTree depends on the
** SQLITE_RTREE_INT_ONLY compile-time option.
*/
#ifdef SQLITE_RTREE_INT_ONLY
  typedef sqlite3_int64 sqlite3_rtree_dbl;
#else
  typedef double sqlite3_rtree_dbl;
#endif

/*
** Register a geometry callback named zGeom that can be used as part of an
** R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,



  int (*xGeom)(sqlite3_rtree_geometry*, int, sqlite3_rtree_dbl*,int*),

  void *pContext
);


/*
** A pointer to a structure of the following type is passed as the first
** argument to callbacks registered using rtree_geometry_callback().
*/
struct sqlite3_rtree_geometry {
  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */
  int nParam;                     /* Size of array aParam[] */
  sqlite3_rtree_dbl *aParam;      /* Parameters passed to SQL geom function */
  void *pUser;                    /* Callback implementation user data */
  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */
};

/*
** Register a 2nd-generation geometry callback named zScore that can be 
** used as part of an R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zQueryFunc(... params ...)
*/
int sqlite3_rtree_query_callback(
  sqlite3 *db,
  const char *zQueryFunc,
  int (*xQueryFunc)(sqlite3_rtree_query_info*),
  void *pContext,
  void (*xDestructor)(void*)
);


/*
** A pointer to a structure of the following type is passed as the 
** argument to scored geometry callback registered using
** sqlite3_rtree_query_callback().
**
** Note that the first 5 fields of this structure are identical to
** sqlite3_rtree_geometry.  This structure is a subclass of
** sqlite3_rtree_geometry.
*/
struct sqlite3_rtree_query_info {
  void *pContext;                   /* pContext from when function registered */
  int nParam;                       /* Number of function parameters */
  sqlite3_rtree_dbl *aParam;        /* value of function parameters */
  void *pUser;                      /* callback can use this, if desired */
  void (*xDelUser)(void*);          /* function to free pUser */
  sqlite3_rtree_dbl *aCoord;        /* Coordinates of node or entry to check */
  unsigned int *anQueue;            /* Number of pending entries in the queue */
  int nCoord;                       /* Number of coordinates */
  int iLevel;                       /* Level of current node or entry */
  int mxLevel;                      /* The largest iLevel value in the tree */
  sqlite3_int64 iRowid;             /* Rowid for current entry */
  sqlite3_rtree_dbl rParentScore;   /* Score of parent node */
  int eParentWithin;                /* Visibility of parent node */
  int eWithin;                      /* OUT: Visiblity */
  sqlite3_rtree_dbl rScore;         /* OUT: Write the score here */
};

/*
** Allowed values for sqlite3_rtree_query.eWithin and .eParentWithin.
*/
#define NOT_WITHIN       0   /* Object completely outside of query region */
#define PARTLY_WITHIN    1   /* Object partially overlaps query region */
#define FULLY_WITHIN     2   /* Object fully contained within query region */


#ifdef __cplusplus
}  /* end of the 'extern "C"' block */
#endif

#endif  /* ifndef _SQLITE3RTREE_H_ */

parse.c:	$(TOP)/src/parse.y lemon $(TOP)/addopcodes.awk
	cp $(TOP)/src/parse.y .
	rm -f parse.h
	./lemon $(OPTS) parse.y
	mv parse.h parse.h.temp
	$(NAWK) -f $(TOP)/addopcodes.awk parse.h.temp >parse.h

sqlite3.h:	$(TOP)/src/sqlite.h.in $(TOP)/manifest.uuid $(TOP)/VERSION
	tclsh $(TOP)/tool/mksqlite3h.tcl $(TOP) >sqlite3.h

keywordhash.h:	$(TOP)/tool/mkkeywordhash.c
	$(BCC) -o mkkeywordhash $(OPTS) $(TOP)/tool/mkkeywordhash.c
	./mkkeywordhash >keywordhash.h

parse.c:	$(TOP)/src/parse.y lemon $(TOP)/addopcodes.awk
	cp $(TOP)/src/parse.y .
	rm -f parse.h
	./lemon $(OPTS) parse.y
	mv parse.h parse.h.temp
	$(NAWK) -f $(TOP)/addopcodes.awk parse.h.temp >parse.h

sqlite3.h:	$(TOP)/src/sqlite.h.in $(TOP)/manifest.uuid $(TOP)/VERSION $(TOP)/ext/rtree/sqlite3rtree.h
	tclsh $(TOP)/tool/mksqlite3h.tcl $(TOP) >sqlite3.h

keywordhash.h:	$(TOP)/tool/mkkeywordhash.c
	$(BCC) -o mkkeywordhash $(OPTS) $(TOP)/tool/mkkeywordhash.c
	./mkkeywordhash >keywordhash.h

** list of space separated integers. Read the first nOut of these into
** the array aOut[].
*/
static void decodeIntArray(
  char *zIntArray,       /* String containing int array to decode */
  int nOut,              /* Number of slots in aOut[] */
  tRowcnt *aOut,         /* Store integers here */

  Index *pIndex          /* Handle extra flags for this index, if not NULL */
){
  char *z = zIntArray;
  int c;
  int i;
  tRowcnt v;

................................................................................
#endif
  for(i=0; *z && i<nOut; i++){
    v = 0;
    while( (c=z[0])>='0' && c<='9' ){
      v = v*10 + c - '0';
      z++;
    }


    aOut[i] = v;








    if( *z==' ' ) z++;
  }
#ifndef SQLITE_ENABLE_STAT3_OR_STAT4
  assert( pIndex!=0 );
#else
  if( pIndex )
#endif
................................................................................
    pIndex = sqlite3PrimaryKeyIndex(pTable);
  }else{
    pIndex = sqlite3FindIndex(pInfo->db, argv[1], pInfo->zDatabase);
  }
  z = argv[2];

  if( pIndex ){
    decodeIntArray((char*)z, pIndex->nKeyCol+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;
}

/*
................................................................................
    nCol = pIdx->nSampleCol;
    if( bStat3 && nCol>1 ) continue;
    if( pIdx!=pPrevIdx ){
      initAvgEq(pPrevIdx);
      pPrevIdx = pIdx;
    }
    pSample = &pIdx->aSample[pIdx->nSample];
    decodeIntArray((char*)sqlite3_column_text(pStmt,1), nCol, pSample->anEq, 0);
    decodeIntArray((char*)sqlite3_column_text(pStmt,2), nCol, pSample->anLt, 0);
    decodeIntArray((char*)sqlite3_column_text(pStmt,3), nCol, pSample->anDLt,0);

    /* Take a copy of the sample. Add two 0x00 bytes the end of the buffer.
    ** This is in case the sample record is corrupted. In that case, the
    ** sqlite3VdbeRecordCompare() may read up to two varints past the
    ** end of the allocated buffer before it realizes it is dealing with
    ** a corrupt record. Adding the two 0x00 bytes prevents this from causing
    ** a buffer overread.  */

** list of space separated integers. Read the first nOut of these into
** the array aOut[].
*/
static void decodeIntArray(
  char *zIntArray,       /* String containing int array to decode */
  int nOut,              /* Number of slots in aOut[] */
  tRowcnt *aOut,         /* Store integers here */
  LogEst *aLog,          /* Or, if aOut==0, here */
  Index *pIndex          /* Handle extra flags for this index, if not NULL */
){
  char *z = zIntArray;
  int c;
  int i;
  tRowcnt v;

................................................................................
#endif
  for(i=0; *z && i<nOut; i++){
    v = 0;
    while( (c=z[0])>='0' && c<='9' ){
      v = v*10 + c - '0';
      z++;
    }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    if( aOut ){
      aOut[i] = v;
    }else
#else
    assert( aOut==0 );
    UNUSED_PARAMETER(aOut);
#endif
    {
      aLog[i] = sqlite3LogEst(v);
    }
    if( *z==' ' ) z++;
  }
#ifndef SQLITE_ENABLE_STAT3_OR_STAT4
  assert( pIndex!=0 );
#else
  if( pIndex )
#endif
................................................................................
    pIndex = sqlite3PrimaryKeyIndex(pTable);
  }else{
    pIndex = sqlite3FindIndex(pInfo->db, argv[1], pInfo->zDatabase);
  }
  z = argv[2];

  if( pIndex ){
    decodeIntArray((char*)z, pIndex->nKeyCol+1, 0, pIndex->aiRowLogEst, pIndex);
    if( pIndex->pPartIdxWhere==0 ) pTable->nRowLogEst = pIndex->aiRowLogEst[0];
  }else{
    Index fakeIdx;
    fakeIdx.szIdxRow = pTable->szTabRow;
    decodeIntArray((char*)z, 1, 0, &pTable->nRowLogEst, &fakeIdx);
    pTable->szTabRow = fakeIdx.szIdxRow;
  }

  return 0;
}

/*
................................................................................
    nCol = pIdx->nSampleCol;
    if( bStat3 && nCol>1 ) continue;
    if( pIdx!=pPrevIdx ){
      initAvgEq(pPrevIdx);
      pPrevIdx = pIdx;
    }
    pSample = &pIdx->aSample[pIdx->nSample];
    decodeIntArray((char*)sqlite3_column_text(pStmt,1),nCol,pSample->anEq,0,0);
    decodeIntArray((char*)sqlite3_column_text(pStmt,2),nCol,pSample->anLt,0,0);
    decodeIntArray((char*)sqlite3_column_text(pStmt,3),nCol,pSample->anDLt,0,0);

    /* Take a copy of the sample. Add two 0x00 bytes the end of the buffer.
    ** This is in case the sample record is corrupted. In that case, the
    ** sqlite3VdbeRecordCompare() may read up to two varints past the
    ** end of the allocated buffer before it realizes it is dealing with
    ** a corrupt record. Adding the two 0x00 bytes prevents this from causing
    ** a buffer overread.  */

    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.
  */
................................................................................
  char **ppExtra       /* Pointer to the "extra" space */
){
  Index *p;            /* Allocated index object */
  int nByte;           /* Bytes of space for Index object + arrays */

  nByte = ROUND8(sizeof(Index)) +              /* Index structure  */
          ROUND8(sizeof(char*)*nCol) +         /* Index.azColl     */
          ROUND8(sizeof(tRowcnt)*(nCol+1) +    /* Index.aiRowEst   */
                 sizeof(i16)*nCol +            /* Index.aiColumn   */
                 sizeof(u8)*nCol);             /* Index.aSortOrder */
  p = sqlite3DbMallocZero(db, nByte + nExtra);
  if( p ){
    char *pExtra = ((char*)p)+ROUND8(sizeof(Index));
    p->azColl = (char**)pExtra;      pExtra += ROUND8(sizeof(char*)*nCol);
    p->aiRowEst = (tRowcnt*)pExtra;  pExtra += sizeof(tRowcnt)*(nCol+1);
    p->aiColumn = (i16*)pExtra;      pExtra += sizeof(i16)*nCol;
    p->aSortOrder = (u8*)pExtra;
    p->nColumn = nCol;
    p->nKeyCol = nCol - 1;
    *ppExtra = ((char*)p) + nByte;
  }
  return p;
}
................................................................................
  nName = sqlite3Strlen30(zName);
  nExtraCol = pPk ? pPk->nKeyCol : 1;
  pIndex = sqlite3AllocateIndexObject(db, pList->nExpr + nExtraCol,
                                      nName + nExtra + 1, &zExtra);
  if( db->mallocFailed ){
    goto exit_create_index;
  }
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->aiRowEst) );
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->azColl) );
  pIndex->zName = zExtra;
  zExtra += nName + 1;
  memcpy(pIndex->zName, zName, nName+1);
  pIndex->pTable = pTab;
  pIndex->onError = (u8)onError;
  pIndex->uniqNotNull = onError!=OE_None;
................................................................................
** Fill the Index.aiRowEst[] array with default information - information
** to be used when we have not run the ANALYZE command.
**
** aiRowEst[0] is suppose to contain the number of elements in the index.
** Since we do not know, guess 1 million.  aiRowEst[1] is an estimate of the
** number of rows in the table that match any particular value of the
** first column of the index.  aiRowEst[2] is an estimate of the number
** of rows that match any particular combiniation of the first 2 columns
** of the index.  And so forth.  It must always be the case that
*
**           aiRowEst[N]<=aiRowEst[N-1]
**           aiRowEst[N]>=1
**
** Apart from that, we have little to go on besides intuition as to
** how aiRowEst[] should be initialized.  The numbers generated here
** are based on typical values found in actual indices.
*/
void sqlite3DefaultRowEst(Index *pIdx){


  tRowcnt *a = pIdx->aiRowEst;

  int i;
  tRowcnt n;
  assert( a!=0 );




  a[0] = pIdx->pTable->nRowEst;
  if( a[0]<10 ) a[0] = 10;
  n = 10;





  for(i=1; i<=pIdx->nKeyCol; i++){
    a[i] = n;
    if( n>5 ) n--;

  }
  if( pIdx->onError!=OE_None ){
    a[pIdx->nKeyCol] = 1;
  }


}

/*
** This routine will drop an existing named index.  This routine
** implements the DROP INDEX statement.
*/
void sqlite3DropIndex(Parse *pParse, SrcList *pName, int ifExists){

    pParse->nErr++;
    goto begin_table_error;
  }
  pTable->zName = zName;
  pTable->iPKey = -1;
  pTable->pSchema = db->aDb[iDb].pSchema;
  pTable->nRef = 1;
  pTable->nRowLogEst = 200; assert( 200==sqlite3LogEst(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.
  */
................................................................................
  char **ppExtra       /* Pointer to the "extra" space */
){
  Index *p;            /* Allocated index object */
  int nByte;           /* Bytes of space for Index object + arrays */

  nByte = ROUND8(sizeof(Index)) +              /* Index structure  */
          ROUND8(sizeof(char*)*nCol) +         /* Index.azColl     */
          ROUND8(sizeof(LogEst)*(nCol+1) +     /* Index.aiRowLogEst   */
                 sizeof(i16)*nCol +            /* Index.aiColumn   */
                 sizeof(u8)*nCol);             /* Index.aSortOrder */
  p = sqlite3DbMallocZero(db, nByte + nExtra);
  if( p ){
    char *pExtra = ((char*)p)+ROUND8(sizeof(Index));
    p->azColl = (char**)pExtra;       pExtra += ROUND8(sizeof(char*)*nCol);
    p->aiRowLogEst = (LogEst*)pExtra; pExtra += sizeof(LogEst)*(nCol+1);
    p->aiColumn = (i16*)pExtra;       pExtra += sizeof(i16)*nCol;
    p->aSortOrder = (u8*)pExtra;
    p->nColumn = nCol;
    p->nKeyCol = nCol - 1;
    *ppExtra = ((char*)p) + nByte;
  }
  return p;
}
................................................................................
  nName = sqlite3Strlen30(zName);
  nExtraCol = pPk ? pPk->nKeyCol : 1;
  pIndex = sqlite3AllocateIndexObject(db, pList->nExpr + nExtraCol,
                                      nName + nExtra + 1, &zExtra);
  if( db->mallocFailed ){
    goto exit_create_index;
  }
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->aiRowLogEst) );
  assert( EIGHT_BYTE_ALIGNMENT(pIndex->azColl) );
  pIndex->zName = zExtra;
  zExtra += nName + 1;
  memcpy(pIndex->zName, zName, nName+1);
  pIndex->pTable = pTab;
  pIndex->onError = (u8)onError;
  pIndex->uniqNotNull = onError!=OE_None;
................................................................................
** Fill the Index.aiRowEst[] array with default information - information
** to be used when we have not run the ANALYZE command.
**
** aiRowEst[0] is suppose to contain the number of elements in the index.
** Since we do not know, guess 1 million.  aiRowEst[1] is an estimate of the
** number of rows in the table that match any particular value of the
** first column of the index.  aiRowEst[2] is an estimate of the number
** of rows that match any particular combination of the first 2 columns
** of the index.  And so forth.  It must always be the case that
*
**           aiRowEst[N]<=aiRowEst[N-1]
**           aiRowEst[N]>=1
**
** Apart from that, we have little to go on besides intuition as to
** how aiRowEst[] should be initialized.  The numbers generated here
** are based on typical values found in actual indices.
*/
void sqlite3DefaultRowEst(Index *pIdx){
  /*                10,  9,  8,  7,  6 */
  LogEst aVal[] = { 33, 32, 30, 28, 26 };
  LogEst *a = pIdx->aiRowLogEst;
  int nCopy = MIN(ArraySize(aVal), pIdx->nKeyCol);
  int i;



  /* Set the first entry (number of rows in the index) to the estimated 
  ** number of rows in the table. Or 10, if the estimated number of rows 
  ** in the table is less than that.  */
  a[0] = pIdx->pTable->nRowLogEst;


  if( a[0]<33 ) a[0] = 33;        assert( 33==sqlite3LogEst(10) );

  /* Estimate that a[1] is 10, a[2] is 9, a[3] is 8, a[4] is 7, a[5] is
  ** 6 and each subsequent value (if any) is 5.  */
  memcpy(&a[1], aVal, nCopy*sizeof(LogEst));
  for(i=nCopy+1; i<=pIdx->nKeyCol; i++){


    a[i] = 23;                    assert( 23==sqlite3LogEst(5) );
  }



  assert( 0==sqlite3LogEst(1) );
  if( pIdx->onError!=OE_None ) a[pIdx->nKeyCol] = 0;
}

/*
** This routine will drop an existing named index.  This routine
** implements the DROP INDEX statement.
*/
void sqlite3DropIndex(Parse *pParse, SrcList *pName, int ifExists){

  if( pDest->nCol!=pSrc->nCol ){
    return 0;   /* Number of columns must be the same in tab1 and tab2 */
  }
  if( pDest->iPKey!=pSrc->iPKey ){
    return 0;   /* Both tables must have the same INTEGER PRIMARY KEY */
  }
  for(i=0; i<pDest->nCol; i++){
    if( pDest->aCol[i].affinity!=pSrc->aCol[i].affinity ){


      return 0;    /* Affinity must be the same on all columns */
    }
    if( !xferCompatibleCollation(pDest->aCol[i].zColl, pSrc->aCol[i].zColl) ){
      return 0;    /* Collating sequence must be the same on all columns */
    }
    if( pDest->aCol[i].notNull && !pSrc->aCol[i].notNull ){

      return 0;    /* tab2 must be NOT NULL if tab1 is */







    }
  }
  for(pDestIdx=pDest->pIndex; pDestIdx; pDestIdx=pDestIdx->pNext){
    if( pDestIdx->onError!=OE_None ){
      destHasUniqueIdx = 1;
    }
    for(pSrcIdx=pSrc->pIndex; pSrcIdx; pSrcIdx=pSrcIdx->pNext){

  if( pDest->nCol!=pSrc->nCol ){
    return 0;   /* Number of columns must be the same in tab1 and tab2 */
  }
  if( pDest->iPKey!=pSrc->iPKey ){
    return 0;   /* Both tables must have the same INTEGER PRIMARY KEY */
  }
  for(i=0; i<pDest->nCol; i++){
    Column *pDestCol = &pDest->aCol[i];
    Column *pSrcCol = &pSrc->aCol[i];
    if( pDestCol->affinity!=pSrcCol->affinity ){
      return 0;    /* Affinity must be the same on all columns */
    }
    if( !xferCompatibleCollation(pDestCol->zColl, pSrcCol->zColl) ){
      return 0;    /* Collating sequence must be the same on all columns */
    }

    if( pDestCol->notNull && !pSrcCol->notNull ){
      return 0;    /* tab2 must be NOT NULL if tab1 is */
    }
    /* Default values for second and subsequent columns need to match. */
    if( i>0
     && ((pDestCol->zDflt==0)!=(pSrcCol->zDflt==0) 
         || (pDestCol->zDflt && strcmp(pDestCol->zDflt, pSrcCol->zDflt)!=0))
    ){
      return 0;    /* Default values must be the same for all columns */
    }
  }
  for(pDestIdx=pDest->pIndex; pDestIdx; pDestIdx=pDestIdx->pNext){
    if( pDestIdx->onError!=OE_None ){
      destHasUniqueIdx = 1;
    }
    for(pSrcIdx=pSrc->pIndex; pSrcIdx; pSrcIdx=pSrcIdx->pNext){

    sqlite3VdbeSetColName(v, 3, COLNAME_NAME, "height", SQLITE_STATIC);
    for(i=sqliteHashFirst(&pDb->pSchema->tblHash); i; i=sqliteHashNext(i)){
      Table *pTab = sqliteHashData(i);
      sqlite3VdbeAddOp4(v, OP_String8, 0, 1, 0, pTab->zName, 0);
      sqlite3VdbeAddOp2(v, OP_Null, 0, 2);
      sqlite3VdbeAddOp2(v, OP_Integer,
                           (int)sqlite3LogEstToInt(pTab->szTabRow), 3);
      sqlite3VdbeAddOp2(v, OP_Integer, (int)pTab->nRowEst, 4);

      sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 4);
      for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
        sqlite3VdbeAddOp4(v, OP_String8, 0, 2, 0, pIdx->zName, 0);
        sqlite3VdbeAddOp2(v, OP_Integer,
                             (int)sqlite3LogEstToInt(pIdx->szIdxRow), 3);
        sqlite3VdbeAddOp2(v, OP_Integer, (int)pIdx->aiRowEst[0], 4);

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

  case PragTyp_INDEX_INFO: if( zRight ){

    sqlite3VdbeSetColName(v, 3, COLNAME_NAME, "height", SQLITE_STATIC);
    for(i=sqliteHashFirst(&pDb->pSchema->tblHash); i; i=sqliteHashNext(i)){
      Table *pTab = sqliteHashData(i);
      sqlite3VdbeAddOp4(v, OP_String8, 0, 1, 0, pTab->zName, 0);
      sqlite3VdbeAddOp2(v, OP_Null, 0, 2);
      sqlite3VdbeAddOp2(v, OP_Integer,
                           (int)sqlite3LogEstToInt(pTab->szTabRow), 3);
      sqlite3VdbeAddOp2(v, OP_Integer, 
          (int)sqlite3LogEstToInt(pTab->nRowLogEst), 4);
      sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 4);
      for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
        sqlite3VdbeAddOp4(v, OP_String8, 0, 2, 0, pIdx->zName, 0);
        sqlite3VdbeAddOp2(v, OP_Integer,
                             (int)sqlite3LogEstToInt(pIdx->szIdxRow), 3);
        sqlite3VdbeAddOp2(v, OP_Integer, 
            (int)sqlite3LogEstToInt(pIdx->aiRowLogEst[0]), 4);
        sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 4);
      }
    }
  }
  break;

  case PragTyp_INDEX_INFO: if( zRight ){

  int nPrefixReg         /* No. of reg prior to regData available for use */
){
  Vdbe *v = pParse->pVdbe;                         /* Stmt under construction */
  int bSeq = ((pSort->sortFlags & SORTFLAG_UseSorter)==0);
  int nExpr = pSort->pOrderBy->nExpr;              /* No. of ORDER BY terms */
  int nBase = nExpr + bSeq + nData;                /* Fields in sorter record */
  int regBase;                                     /* Regs for sorter record */
  int regRecord = sqlite3GetTempReg(pParse);       /* Assembled sorter record */
  int nOBSat = pSort->nOBSat;                      /* ORDER BY terms to skip */
  int op;                            /* Opcode to add sorter record to sorter */

  assert( bSeq==0 || bSeq==1 );
  if( nPrefixReg ){
    assert( nPrefixReg==nExpr+bSeq );
    regBase = regData - nExpr - bSeq;
  }else{
    regBase = sqlite3GetTempRange(pParse, nBase);

  }
  sqlite3ExprCodeExprList(pParse, pSort->pOrderBy, regBase, SQLITE_ECEL_DUP);
  if( bSeq ){
    sqlite3VdbeAddOp2(v, OP_Sequence, pSort->iECursor, regBase+nExpr);
  }
  if( nPrefixReg==0 ){
    sqlite3VdbeAddOp3(v, OP_Move, regData, regBase+nExpr+bSeq, nData);
................................................................................
    }else{
      addrFirst = sqlite3VdbeAddOp1(v, OP_SequenceTest, pSort->iECursor);
    }
    VdbeCoverage(v);
    sqlite3VdbeAddOp3(v, OP_Compare, regPrevKey, regBase, pSort->nOBSat);
    pOp = sqlite3VdbeGetOp(v, pSort->addrSortIndex);
    if( pParse->db->mallocFailed ) return;
    pOp->p2 = nKey + 1;
    pKI = pOp->p4.pKeyInfo;
    memset(pKI->aSortOrder, 0, pKI->nField); /* Makes OP_Jump below testable */
    sqlite3VdbeChangeP4(v, -1, (char*)pKI, P4_KEYINFO);
    pOp->p4.pKeyInfo = keyInfoFromExprList(pParse, pSort->pOrderBy, nOBSat, 1);
    addrJmp = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp3(v, OP_Jump, addrJmp+1, 0, addrJmp+1); VdbeCoverage(v);
    pSort->labelBkOut = sqlite3VdbeMakeLabel(v);
................................................................................
  }
  if( pSort->sortFlags & SORTFLAG_UseSorter ){
    op = OP_SorterInsert;
  }else{
    op = OP_IdxInsert;
  }
  sqlite3VdbeAddOp2(v, op, pSort->iECursor, regRecord);
  if( nOBSat==0 ){
    sqlite3ReleaseTempReg(pParse, regRecord);
    if( nPrefixReg==0 ){
      sqlite3ReleaseTempRange(pParse, regBase, nBase);
    }
  }
  if( pSelect->iLimit ){
    int addr1, addr2;
    int iLimit;
    if( pSelect->iOffset ){
      iLimit = pSelect->iOffset+1;
    }else{
      iLimit = pSelect->iLimit;
................................................................................
    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;
  }
................................................................................

    assert( pFrom->pTab==0 );
    pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));
    if( pTab==0 ) return WRC_Abort;
    pTab->nRef = 1;
    pTab->zName = sqlite3DbStrDup(db, pCte->zName);
    pTab->iPKey = -1;
    pTab->nRowEst = 1048576;
    pTab->tabFlags |= TF_Ephemeral;
    pFrom->pSelect = sqlite3SelectDup(db, pCte->pSelect, 0);
    if( db->mallocFailed ) return SQLITE_NOMEM;
    assert( pFrom->pSelect );

    /* Check if this is a recursive CTE. */
    pSel = pFrom->pSelect;
................................................................................
      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;
................................................................................
      pItem->regReturn = ++pParse->nMem;
      sqlite3VdbeAddOp3(v, OP_InitCoroutine, pItem->regReturn, 0, addrTop);
      VdbeComment((v, "%s", pItem->pTab->zName));
      pItem->addrFillSub = addrTop;
      sqlite3SelectDestInit(&dest, SRT_Coroutine, pItem->regReturn);
      explainSetInteger(pItem->iSelectId, (u8)pParse->iNextSelectId);
      sqlite3Select(pParse, pSub, &dest);
      pItem->pTab->nRowEst = (unsigned)pSub->nSelectRow;
      pItem->viaCoroutine = 1;
      pItem->regResult = dest.iSdst;
      sqlite3VdbeAddOp1(v, OP_EndCoroutine, pItem->regReturn);
      sqlite3VdbeJumpHere(v, addrTop-1);
      sqlite3ClearTempRegCache(pParse);
    }else{
      /* Generate a subroutine that will fill an ephemeral table with
................................................................................
        VdbeComment((v, "materialize \"%s\"", pItem->pTab->zName));
      }else{
        VdbeNoopComment((v, "materialize \"%s\"", pItem->pTab->zName));
      }
      sqlite3SelectDestInit(&dest, SRT_EphemTab, pItem->iCursor);
      explainSetInteger(pItem->iSelectId, (u8)pParse->iNextSelectId);
      sqlite3Select(pParse, pSub, &dest);
      pItem->pTab->nRowEst = (unsigned)pSub->nSelectRow;
      if( onceAddr ) sqlite3VdbeJumpHere(v, onceAddr);
      retAddr = sqlite3VdbeAddOp1(v, OP_Return, pItem->regReturn);
      VdbeComment((v, "end %s", pItem->pTab->zName));
      sqlite3VdbeChangeP1(v, topAddr, retAddr);
      sqlite3ClearTempRegCache(pParse);
    }
    if( /*pParse->nErr ||*/ db->mallocFailed ){

  int nPrefixReg         /* No. of reg prior to regData available for use */
){
  Vdbe *v = pParse->pVdbe;                         /* Stmt under construction */
  int bSeq = ((pSort->sortFlags & SORTFLAG_UseSorter)==0);
  int nExpr = pSort->pOrderBy->nExpr;              /* No. of ORDER BY terms */
  int nBase = nExpr + bSeq + nData;                /* Fields in sorter record */
  int regBase;                                     /* Regs for sorter record */
  int regRecord = ++pParse->nMem;                  /* Assembled sorter record */
  int nOBSat = pSort->nOBSat;                      /* ORDER BY terms to skip */
  int op;                            /* Opcode to add sorter record to sorter */

  assert( bSeq==0 || bSeq==1 );
  if( nPrefixReg ){
    assert( nPrefixReg==nExpr+bSeq );
    regBase = regData - nExpr - bSeq;
  }else{
    regBase = pParse->nMem + 1;
    pParse->nMem += nBase;
  }
  sqlite3ExprCodeExprList(pParse, pSort->pOrderBy, regBase, SQLITE_ECEL_DUP);
  if( bSeq ){
    sqlite3VdbeAddOp2(v, OP_Sequence, pSort->iECursor, regBase+nExpr);
  }
  if( nPrefixReg==0 ){
    sqlite3VdbeAddOp3(v, OP_Move, regData, regBase+nExpr+bSeq, nData);
................................................................................
    }else{
      addrFirst = sqlite3VdbeAddOp1(v, OP_SequenceTest, pSort->iECursor);
    }
    VdbeCoverage(v);
    sqlite3VdbeAddOp3(v, OP_Compare, regPrevKey, regBase, pSort->nOBSat);
    pOp = sqlite3VdbeGetOp(v, pSort->addrSortIndex);
    if( pParse->db->mallocFailed ) return;
    pOp->p2 = nKey + nData;
    pKI = pOp->p4.pKeyInfo;
    memset(pKI->aSortOrder, 0, pKI->nField); /* Makes OP_Jump below testable */
    sqlite3VdbeChangeP4(v, -1, (char*)pKI, P4_KEYINFO);
    pOp->p4.pKeyInfo = keyInfoFromExprList(pParse, pSort->pOrderBy, nOBSat, 1);
    addrJmp = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp3(v, OP_Jump, addrJmp+1, 0, addrJmp+1); VdbeCoverage(v);
    pSort->labelBkOut = sqlite3VdbeMakeLabel(v);
................................................................................
  }
  if( pSort->sortFlags & SORTFLAG_UseSorter ){
    op = OP_SorterInsert;
  }else{
    op = OP_IdxInsert;
  }
  sqlite3VdbeAddOp2(v, op, pSort->iECursor, regRecord);






  if( pSelect->iLimit ){
    int addr1, addr2;
    int iLimit;
    if( pSelect->iOffset ){
      iLimit = pSelect->iOffset+1;
    }else{
      iLimit = pSelect->iLimit;
................................................................................
    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->nRowLogEst = 200; assert( 200==sqlite3LogEst(1048576) );
  selectColumnsFromExprList(pParse, pSelect->pEList, &pTab->nCol, &pTab->aCol);
  selectAddColumnTypeAndCollation(pParse, pTab, pSelect);
  pTab->iPKey = -1;
  if( db->mallocFailed ){
    sqlite3DeleteTable(db, pTab);
    return 0;
  }
................................................................................

    assert( pFrom->pTab==0 );
    pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));
    if( pTab==0 ) return WRC_Abort;
    pTab->nRef = 1;
    pTab->zName = sqlite3DbStrDup(db, pCte->zName);
    pTab->iPKey = -1;
    pTab->nRowLogEst = 200; assert( 200==sqlite3LogEst(1048576) );
    pTab->tabFlags |= TF_Ephemeral;
    pFrom->pSelect = sqlite3SelectDup(db, pCte->pSelect, 0);
    if( db->mallocFailed ) return SQLITE_NOMEM;
    assert( pFrom->pSelect );

    /* Check if this is a recursive CTE. */
    pSel = pFrom->pSelect;
................................................................................
      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->nRowLogEst = 200; assert( 200==sqlite3LogEst(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;
................................................................................
      pItem->regReturn = ++pParse->nMem;
      sqlite3VdbeAddOp3(v, OP_InitCoroutine, pItem->regReturn, 0, addrTop);
      VdbeComment((v, "%s", pItem->pTab->zName));
      pItem->addrFillSub = addrTop;
      sqlite3SelectDestInit(&dest, SRT_Coroutine, pItem->regReturn);
      explainSetInteger(pItem->iSelectId, (u8)pParse->iNextSelectId);
      sqlite3Select(pParse, pSub, &dest);
      pItem->pTab->nRowLogEst = sqlite3LogEst(pSub->nSelectRow);
      pItem->viaCoroutine = 1;
      pItem->regResult = dest.iSdst;
      sqlite3VdbeAddOp1(v, OP_EndCoroutine, pItem->regReturn);
      sqlite3VdbeJumpHere(v, addrTop-1);
      sqlite3ClearTempRegCache(pParse);
    }else{
      /* Generate a subroutine that will fill an ephemeral table with
................................................................................
        VdbeComment((v, "materialize \"%s\"", pItem->pTab->zName));
      }else{
        VdbeNoopComment((v, "materialize \"%s\"", pItem->pTab->zName));
      }
      sqlite3SelectDestInit(&dest, SRT_EphemTab, pItem->iCursor);
      explainSetInteger(pItem->iSelectId, (u8)pParse->iNextSelectId);
      sqlite3Select(pParse, pSub, &dest);
      pItem->pTab->nRowLogEst = sqlite3LogEst(pSub->nSelectRow);
      if( onceAddr ) sqlite3VdbeJumpHere(v, onceAddr);
      retAddr = sqlite3VdbeAddOp1(v, OP_Return, pItem->regReturn);
      VdbeComment((v, "end %s", pItem->pTab->zName));
      sqlite3VdbeChangeP1(v, topAddr, retAddr);
      sqlite3ClearTempRegCache(pParse);
    }
    if( /*pParse->nErr ||*/ db->mallocFailed ){

/*
** 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
................................................................................
  Index *pIndex;       /* List of SQL indexes on this table. */
  Select *pSelect;     /* NULL for tables.  Points to definition if a view. */
  FKey *pFKey;         /* Linked list of all foreign keys in this table */
  char *zColAff;       /* String defining the affinity of each column */
#ifndef SQLITE_OMIT_CHECK
  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 */
................................................................................
** and the value of Index.onError indicate the which conflict resolution 
** algorithm to employ whenever an attempt is made to insert a non-unique
** element.
*/
struct Index {
  char *zName;             /* Name of this index */
  i16 *aiColumn;           /* Which columns are used by this index.  1st is 0 */
  tRowcnt *aiRowEst;       /* From ANALYZE: Est. rows selected by each column */
  Table *pTable;           /* The SQL table being indexed */
  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 */

/*
** 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 quantaties are suppose to be estimates,
** not exact values, this imprecision is not a problem.
**
** "LogEst" is short for "Logarithmic 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
................................................................................
  Index *pIndex;       /* List of SQL indexes on this table. */
  Select *pSelect;     /* NULL for tables.  Points to definition if a view. */
  FKey *pFKey;         /* Linked list of all foreign keys in this table */
  char *zColAff;       /* String defining the affinity of each column */
#ifndef SQLITE_OMIT_CHECK
  ExprList *pCheck;    /* All CHECK constraints */
#endif
  LogEst nRowLogEst;   /* 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 */
................................................................................
** and the value of Index.onError indicate the which conflict resolution 
** algorithm to employ whenever an attempt is made to insert a non-unique
** element.
*/
struct Index {
  char *zName;             /* Name of this index */
  i16 *aiColumn;           /* Which columns are used by this index.  1st is 0 */
  LogEst *aiRowLogEst;     /* From ANALYZE: Est. rows selected by each column */
  Table *pTable;           /* The SQL table being indexed */
  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 */

    double xmax;
    double ymin;
    double ymax;
  } aBox[2];
  double centerx;
  double centery;
  double radius;


};

/*
** Destructor function for Circle objects allocated by circle_geom().
*/
static void circle_del(void *p){
  sqlite3_free(p);
................................................................................

/*
** Implementation of "circle" r-tree geometry callback.
*/
static int circle_geom(
  sqlite3_rtree_geometry *p,
  int nCoord, 
#ifdef SQLITE_RTREE_INT_ONLY
  sqlite3_int64 *aCoord,
#else
  double *aCoord, 
#endif
  int *pRes
){
  int i;                          /* Iterator variable */
  Circle *pCircle;                /* Structure defining circular region */
  double xmin, xmax;              /* X dimensions of box being tested */
  double ymin, ymax;              /* X dimensions of box being tested */

  if( p->pUser==0 ){





    /* If pUser is still 0, then the parameter values have not been tested
    ** for correctness or stored into a Circle structure yet. Do this now. */

    /* This geometry callback is for use with a 2-dimensional r-tree table.
    ** Return an error if the table does not have exactly 2 dimensions. */
    if( nCoord!=4 ) return SQLITE_ERROR;

................................................................................
    pCircle->aBox[0].xmax = pCircle->centerx;
    pCircle->aBox[0].ymin = pCircle->centery + pCircle->radius;
    pCircle->aBox[0].ymax = pCircle->centery - pCircle->radius;
    pCircle->aBox[1].xmin = pCircle->centerx + pCircle->radius;
    pCircle->aBox[1].xmax = pCircle->centerx - pCircle->radius;
    pCircle->aBox[1].ymin = pCircle->centery;
    pCircle->aBox[1].ymax = pCircle->centery;

  }

  pCircle = (Circle *)p->pUser;
  xmin = aCoord[0];
  xmax = aCoord[1];
  ymin = aCoord[2];
  ymax = aCoord[3];

  /* Check if any of the 4 corners of the bounding-box being tested lie 
  ** inside the circular region. If they do, then the bounding-box does
  ** intersect the region of interest. Set the output variable to true and
  ** return SQLITE_OK in this case. */
  for(i=0; i<4; i++){
    double x = (i&0x01) ? xmax : xmin;
    double y = (i&0x02) ? ymax : ymin;
................................................................................
  }

  /* The specified bounding box does not intersect the circular region. Set
  ** the output variable to zero and return SQLITE_OK. */
  *pRes = 0;
  return SQLITE_OK;
}





































































































































































/* END of implementation of "circle" geometry callback.
**************************************************************************
*************************************************************************/

#include <assert.h>
#include "tcl.h"
................................................................................
**   cube(x, y, z, width, height, depth)
**
** The width, height and depth parameters must all be greater than zero.
*/
static int cube_geom(
  sqlite3_rtree_geometry *p,
  int nCoord,
#ifdef SQLITE_RTREE_INT_ONLY
  sqlite3_int64 *aCoord, 
#else
  double *aCoord, 
#endif
  int *piRes
){
  Cube *pCube = (Cube *)p->pUser;

  assert( p->pContext==(void *)&gHere );

  if( pCube==0 ){
................................................................................

  if( objc!=2 ){
    Tcl_WrongNumArgs(interp, 1, objv, "DB");
    return TCL_ERROR;
  }
  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;
  rc = sqlite3_rtree_geometry_callback(db, "circle", circle_geom, 0);








  Tcl_SetResult(interp, (char *)sqlite3ErrName(rc), TCL_STATIC);
#endif
  return TCL_OK;
}

int Sqlitetestrtree_Init(Tcl_Interp *interp){
  Tcl_CreateObjCommand(interp, "register_cube_geom", register_cube_geom, 0, 0);
  Tcl_CreateObjCommand(interp, "register_circle_geom",register_circle_geom,0,0);
  return TCL_OK;
}

    double xmax;
    double ymin;
    double ymax;
  } aBox[2];
  double centerx;
  double centery;
  double radius;
  double mxArea;
  int eScoreType;
};

/*
** Destructor function for Circle objects allocated by circle_geom().
*/
static void circle_del(void *p){
  sqlite3_free(p);
................................................................................

/*
** Implementation of "circle" r-tree geometry callback.
*/
static int circle_geom(
  sqlite3_rtree_geometry *p,
  int nCoord, 



  sqlite3_rtree_dbl *aCoord,

  int *pRes
){
  int i;                          /* Iterator variable */
  Circle *pCircle;                /* Structure defining circular region */
  double xmin, xmax;              /* X dimensions of box being tested */
  double ymin, ymax;              /* X dimensions of box being tested */

  xmin = aCoord[0];
  xmax = aCoord[1];
  ymin = aCoord[2];
  ymax = aCoord[3];
  pCircle = (Circle *)p->pUser;
  if( pCircle==0 ){
    /* If pUser is still 0, then the parameter values have not been tested
    ** for correctness or stored into a Circle structure yet. Do this now. */

    /* This geometry callback is for use with a 2-dimensional r-tree table.
    ** Return an error if the table does not have exactly 2 dimensions. */
    if( nCoord!=4 ) return SQLITE_ERROR;

................................................................................
    pCircle->aBox[0].xmax = pCircle->centerx;
    pCircle->aBox[0].ymin = pCircle->centery + pCircle->radius;
    pCircle->aBox[0].ymax = pCircle->centery - pCircle->radius;
    pCircle->aBox[1].xmin = pCircle->centerx + pCircle->radius;
    pCircle->aBox[1].xmax = pCircle->centerx - pCircle->radius;
    pCircle->aBox[1].ymin = pCircle->centery;
    pCircle->aBox[1].ymax = pCircle->centery;
    pCircle->mxArea = (xmax - xmin)*(ymax - ymin) + 1.0;
  }







  /* Check if any of the 4 corners of the bounding-box being tested lie 
  ** inside the circular region. If they do, then the bounding-box does
  ** intersect the region of interest. Set the output variable to true and
  ** return SQLITE_OK in this case. */
  for(i=0; i<4; i++){
    double x = (i&0x01) ? xmax : xmin;
    double y = (i&0x02) ? ymax : ymin;
................................................................................
  }

  /* The specified bounding box does not intersect the circular region. Set
  ** the output variable to zero and return SQLITE_OK. */
  *pRes = 0;
  return SQLITE_OK;
}

/*
** Implementation of "circle" r-tree geometry callback using the 
** 2nd-generation interface that allows scoring.
*/
static int circle_query_func(sqlite3_rtree_query_info *p){
  int i;                          /* Iterator variable */
  Circle *pCircle;                /* Structure defining circular region */
  double xmin, xmax;              /* X dimensions of box being tested */
  double ymin, ymax;              /* X dimensions of box being tested */
  int nWithin = 0;                /* Number of corners inside the circle */

  xmin = p->aCoord[0];
  xmax = p->aCoord[1];
  ymin = p->aCoord[2];
  ymax = p->aCoord[3];
  pCircle = (Circle *)p->pUser;
  if( pCircle==0 ){
    /* If pUser is still 0, then the parameter values have not been tested
    ** for correctness or stored into a Circle structure yet. Do this now. */

    /* This geometry callback is for use with a 2-dimensional r-tree table.
    ** Return an error if the table does not have exactly 2 dimensions. */
    if( p->nCoord!=4 ) return SQLITE_ERROR;

    /* Test that the correct number of parameters (4) have been supplied,
    ** and that the parameters are in range (that the radius of the circle 
    ** radius is greater than zero). */
    if( p->nParam!=4 || p->aParam[2]<0.0 ) return SQLITE_ERROR;

    /* Allocate a structure to cache parameter data in. Return SQLITE_NOMEM
    ** if the allocation fails. */
    pCircle = (Circle *)(p->pUser = sqlite3_malloc(sizeof(Circle)));
    if( !pCircle ) return SQLITE_NOMEM;
    p->xDelUser = circle_del;

    /* Record the center and radius of the circular region. One way that
    ** tested bounding boxes that intersect the circular region are detected
    ** is by testing if each corner of the bounding box lies within radius
    ** units of the center of the circle. */
    pCircle->centerx = p->aParam[0];
    pCircle->centery = p->aParam[1];
    pCircle->radius = p->aParam[2];
    pCircle->eScoreType = (int)p->aParam[3];

    /* Define two bounding box regions. The first, aBox[0], extends to
    ** infinity in the X dimension. It covers the same range of the Y dimension
    ** as the circular region. The second, aBox[1], extends to infinity in
    ** the Y dimension and is constrained to the range of the circle in the
    ** X dimension.
    **
    ** Then imagine each box is split in half along its short axis by a line
    ** that intersects the center of the circular region. A bounding box
    ** being tested can be said to intersect the circular region if it contains
    ** points from each half of either of the two infinite bounding boxes.
    */
    pCircle->aBox[0].xmin = pCircle->centerx;
    pCircle->aBox[0].xmax = pCircle->centerx;
    pCircle->aBox[0].ymin = pCircle->centery + pCircle->radius;
    pCircle->aBox[0].ymax = pCircle->centery - pCircle->radius;
    pCircle->aBox[1].xmin = pCircle->centerx + pCircle->radius;
    pCircle->aBox[1].xmax = pCircle->centerx - pCircle->radius;
    pCircle->aBox[1].ymin = pCircle->centery;
    pCircle->aBox[1].ymax = pCircle->centery;
    pCircle->mxArea = 200.0*200.0;
  }

  /* Check if any of the 4 corners of the bounding-box being tested lie 
  ** inside the circular region. If they do, then the bounding-box does
  ** intersect the region of interest. Set the output variable to true and
  ** return SQLITE_OK in this case. */
  for(i=0; i<4; i++){
    double x = (i&0x01) ? xmax : xmin;
    double y = (i&0x02) ? ymax : ymin;
    double d2;
    
    d2  = (x-pCircle->centerx)*(x-pCircle->centerx);
    d2 += (y-pCircle->centery)*(y-pCircle->centery);
    if( d2<(pCircle->radius*pCircle->radius) ) nWithin++;
  }

  /* Check if the bounding box covers any other part of the circular region.
  ** See comments above for a description of how this test works. If it does
  ** cover part of the circular region, set the output variable to true
  ** and return SQLITE_OK. */
  if( nWithin==0 ){
    for(i=0; i<2; i++){
      if( xmin<=pCircle->aBox[i].xmin 
       && xmax>=pCircle->aBox[i].xmax 
       && ymin<=pCircle->aBox[i].ymin 
       && ymax>=pCircle->aBox[i].ymax 
      ){
        nWithin = 1;
        break;
      }
    }
  }

  if( pCircle->eScoreType==1 ){
    /* Depth first search */
    p->rScore = p->iLevel;
  }else if( pCircle->eScoreType==2 ){
    /* Breadth first search */
    p->rScore = 100 - p->iLevel;
  }else if( pCircle->eScoreType==3 ){
    /* Depth-first search, except sort the leaf nodes by area with
    ** the largest area first */
    if( p->iLevel==1 ){
      p->rScore = 1.0 - (xmax-xmin)*(ymax-ymin)/pCircle->mxArea;
      if( p->rScore<0.01 ) p->rScore = 0.01;
    }else{
      p->rScore = 0.0;
    }
  }else if( pCircle->eScoreType==4 ){
    /* Depth-first search, except exclude odd rowids */
    p->rScore = p->iLevel;
    if( p->iRowid&1 ) nWithin = 0;
  }else{
    /* Breadth-first search, except exclude odd rowids */
    p->rScore = 100 - p->iLevel;
    if( p->iRowid&1 ) nWithin = 0;
  }
  if( nWithin==0 ){
    p->eWithin = NOT_WITHIN;
  }else if( nWithin>=4 ){
    p->eWithin = FULLY_WITHIN;
  }else{
    p->eWithin = PARTLY_WITHIN;
  }
  return SQLITE_OK;
}
/*
** Implementation of "breadthfirstsearch" r-tree geometry callback using the 
** 2nd-generation interface that allows scoring.
**
**     ... WHERE id MATCH breadthfirstsearch($x0,$x1,$y0,$y1) ...
**
** It returns all entries whose bounding boxes overlap with $x0,$x1,$y0,$y1.
*/
static int bfs_query_func(sqlite3_rtree_query_info *p){
  double x0,x1,y0,y1;        /* Dimensions of box being tested */
  double bx0,bx1,by0,by1;    /* Boundary of the query function */

  if( p->nParam!=4 ) return SQLITE_ERROR;
  x0 = p->aCoord[0];
  x1 = p->aCoord[1];
  y0 = p->aCoord[2];
  y1 = p->aCoord[3];
  bx0 = p->aParam[0];
  bx1 = p->aParam[1];
  by0 = p->aParam[2];
  by1 = p->aParam[3];
  p->rScore = 100 - p->iLevel;
  if( p->eParentWithin==FULLY_WITHIN ){
    p->eWithin = FULLY_WITHIN;
  }else if( x0>=bx0 && x1<=bx1 && y0>=by0 && y1<=by1 ){
    p->eWithin = FULLY_WITHIN;
  }else if( x1>=bx0 && x0<=bx1 && y1>=by0 && y0<=by1 ){
    p->eWithin = PARTLY_WITHIN;
  }else{
    p->eWithin = NOT_WITHIN;
  }
  return SQLITE_OK;
}

/* END of implementation of "circle" geometry callback.
**************************************************************************
*************************************************************************/

#include <assert.h>
#include "tcl.h"
................................................................................
**   cube(x, y, z, width, height, depth)
**
** The width, height and depth parameters must all be greater than zero.
*/
static int cube_geom(
  sqlite3_rtree_geometry *p,
  int nCoord,



  sqlite3_rtree_dbl *aCoord,

  int *piRes
){
  Cube *pCube = (Cube *)p->pUser;

  assert( p->pContext==(void *)&gHere );

  if( pCube==0 ){
................................................................................

  if( objc!=2 ){
    Tcl_WrongNumArgs(interp, 1, objv, "DB");
    return TCL_ERROR;
  }
  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;
  rc = sqlite3_rtree_geometry_callback(db, "circle", circle_geom, 0);
  if( rc==SQLITE_OK ){
    rc = sqlite3_rtree_query_callback(db, "Qcircle",
                                      circle_query_func, 0, 0);
  }
  if( rc==SQLITE_OK ){
    rc = sqlite3_rtree_query_callback(db, "breadthfirstsearch",
                                      bfs_query_func, 0, 0);
  }
  Tcl_SetResult(interp, (char *)sqlite3ErrName(rc), TCL_STATIC);
#endif
  return TCL_OK;
}

int Sqlitetestrtree_Init(Tcl_Interp *interp){
  Tcl_CreateObjCommand(interp, "register_cube_geom", register_cube_geom, 0, 0);
  Tcl_CreateObjCommand(interp, "register_circle_geom",register_circle_geom,0,0);
  return TCL_OK;
}

  const char *zPath, 
  int flags, 
  int *pResOut
){
  vfstrace_info *pInfo = (vfstrace_info*)pVfs->pAppData;
  sqlite3_vfs *pRoot = pInfo->pRootVfs;
  int rc;
  vfstrace_printf(pInfo, "%s.xDelete(\"%s\",%d)",
                  pInfo->zVfsName, zPath, flags);
  rc = pRoot->xAccess(pRoot, zPath, flags, pResOut);
  vfstrace_print_errcode(pInfo, " -> %s", rc);
  vfstrace_printf(pInfo, ", out=%d\n", *pResOut);
  return rc;
}

  const char *zPath, 
  int flags, 
  int *pResOut
){
  vfstrace_info *pInfo = (vfstrace_info*)pVfs->pAppData;
  sqlite3_vfs *pRoot = pInfo->pRootVfs;
  int rc;
  vfstrace_printf(pInfo, "%s.xAccess(\"%s\",%d)",
                  pInfo->zVfsName, zPath, flags);
  rc = pRoot->xAccess(pRoot, zPath, flags, pResOut);
  vfstrace_print_errcode(pInfo, " -> %s", rc);
  vfstrace_printf(pInfo, ", out=%d\n", *pResOut);
  return rc;
}

    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; }

    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 an
** approximation 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; }

case OP_SorterData: {
  VdbeCursor *pC;

  pOut = &aMem[pOp->p2];
  pC = p->apCsr[pOp->p1];
  assert( isSorter(pC) );
  rc = sqlite3VdbeSorterRowkey(pC, pOut);

  break;
}

/* Opcode: RowData P1 P2 * * *
** Synopsis: r[P2]=data
**
** Write into register P2 the complete row data for cursor P1.
................................................................................
** readability.  From this point on down, the normal indentation rules are
** restored.
*****************************************************************************/
    }

#ifdef VDBE_PROFILE
    {
      u64 elapsed = sqlite3Hwtime() - start;
      pOp->cycles += elapsed;
      pOp->cnt++;
    }
#endif

    /* The following code adds nothing to the actual functionality
    ** of the program.  It is only here for testing and debugging.
    ** On the other hand, it does burn CPU cycles every time through

case OP_SorterData: {
  VdbeCursor *pC;

  pOut = &aMem[pOp->p2];
  pC = p->apCsr[pOp->p1];
  assert( isSorter(pC) );
  rc = sqlite3VdbeSorterRowkey(pC, pOut);
  assert( rc!=SQLITE_OK || (pOut->flags & MEM_Blob) );
  break;
}

/* Opcode: RowData P1 P2 * * *
** Synopsis: r[P2]=data
**
** Write into register P2 the complete row data for cursor P1.
................................................................................
** readability.  From this point on down, the normal indentation rules are
** restored.
*****************************************************************************/
    }

#ifdef VDBE_PROFILE
    {
      u64 endTime = sqlite3Hwtime();
      if( endTime>start ) pOp->cycles += endTime - start;
      pOp->cnt++;
    }
#endif

    /* The following code adds nothing to the actual functionality
    ** of the program.  It is only here for testing and debugging.
    ** On the other hand, it does burn CPU cycles every time through

    }
    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 idx;
}
................................................................................
    aStat[1] = aSample[i].anEq[iCol];
  }else{
    tRowcnt iLower, iUpper, iGap;
    if( i==0 ){
      iLower = 0;
      iUpper = aSample[0].anLt[iCol];
    }else{

      iUpper = i>=pIdx->nSample ? pIdx->aiRowEst[0] : aSample[i].anLt[iCol];
      iLower = aSample[i-1].anEq[iCol] + aSample[i-1].anLt[iCol];
    }
    aStat[1] = (pIdx->nKeyCol>iCol ? pIdx->aAvgEq[iCol] : 1);
    if( iLower>=iUpper ){
      iGap = 0;
    }else{
      iGap = iUpper - iLower;
................................................................................
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
























/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
** and lower bounds are represented by pLower and pUpper respectively. For
** example, assuming that index p is on t1(a):
................................................................................
      aff = SQLITE_AFF_INTEGER;
    }else{
      aff = p->pTable->aCol[p->aiColumn[nEq]].affinity;
    }
    /* Determine iLower and iUpper using ($P) only. */
    if( nEq==0 ){
      iLower = 0;
      iUpper = p->aiRowEst[0];
    }else{
      /* Note: this call could be optimized away - since the same values must 
      ** have been requested when testing key $P in whereEqualScanEst().  */
      whereKeyStats(pParse, p, pRec, 0, a);
      iLower = a[0];
      iUpper = a[0] + a[1];
    }
................................................................................
    }
  }
#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
................................................................................
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;

  int nRecValid = pBuilder->nRecValid;
  int rc = SQLITE_OK;     /* Subfunction return code */
  tRowcnt nEst;           /* Number of rows for a single term */
  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
    pBuilder->nRecValid = nRecValid;
  }

  if( rc==SQLITE_OK ){
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    *pnRow = nRowEst;
    WHERETRACE(0x10,("IN row estimate: est=%g\n", nRowEst));
  }
  assert( pBuilder->nRecValid==nRecValid );
  return rc;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
................................................................................
**
**   (2) pTemplate costs more than any other WhereLoops for which pTemplate
**       is a proper subset.
**
** To say "WhereLoop X is a proper subset of Y" means that X uses fewer
** WHERE clause terms than Y and that every WHERE clause term used by X is
** also used by Y.











*/
static void whereLoopAdjustCost(const WhereLoop *p, WhereLoop *pTemplate){
  if( (pTemplate->wsFlags & WHERE_INDEXED)==0 ) return;

  for(; p; p=p->pNextLoop){
    if( p->iTab!=pTemplate->iTab ) continue;
    if( (p->wsFlags & WHERE_INDEXED)==0 ) continue;

    if( whereLoopCheaperProperSubset(p, pTemplate) ){
      /* Adjust pTemplate cost downward so that it is cheaper than its 
      ** subset p */
      pTemplate->rRun = p->rRun;
      pTemplate->nOut = p->nOut - 1;
    }else if( whereLoopCheaperProperSubset(pTemplate, p) ){
      /* Adjust pTemplate cost upward so that it is costlier than p since
................................................................................
    if( (pTerm->prereqAll & notAllowed)!=0 ) continue;
    for(j=pLoop->nLTerm-1; j>=0; j--){
      pX = pLoop->aLTerm[j];
      if( pX==0 ) continue;
      if( pX==pTerm ) break;
      if( pX->iParent>=0 && (&pWC->a[pX->iParent])==pTerm ) break;
    }
    if( j<0 ) pLoop->nOut += pTerm->truthProb;


  }
}

/*
** We have so far matched pBuilder->pNew->u.btree.nEq terms of the index pIndex.
** Try to match one more.





**
** 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 */
................................................................................
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  u16 saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u16 saved_nSkip;                /* Original value of pNew->u.btree.nSkip */
  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 );
................................................................................
    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->nKeyCol );
  if( pNew->u.btree.nEq < pProbe->nKeyCol ){
    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_nSkip = pNew->u.btree.nSkip;
  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]));

  /* Consider using a skip-scan if there are no WHERE clause constraints
  ** available for the left-most terms of the index, and if the average
  ** number of repeats in the left-most terms is at least 18.  The magic
  ** number 18 was found by experimentation to be the payoff point where
  ** skip-scan become faster than a full-scan.
  */







  if( pTerm==0
   && saved_nEq==saved_nSkip
   && saved_nEq+1<pProbe->nKeyCol
   && pProbe->aiRowEst[saved_nEq+1]>=18  /* TUNING: Minimum for skip-scan */
   && (rc = whereLoopResize(db, pNew, pNew->nLTerm+1))==SQLITE_OK
  ){
    LogEst nIter;
    pNew->u.btree.nEq++;
    pNew->u.btree.nSkip++;
    pNew->aLTerm[pNew->nLTerm++] = 0;
    pNew->wsFlags |= WHERE_SKIPSCAN;
    nIter = sqlite3LogEst(pProbe->aiRowEst[0]/pProbe->aiRowEst[saved_nEq+1]);
    pNew->rRun = rLogSize + nIter;
    pNew->nOut += nIter;
    whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nIter);
    pNew->nOut = saved_nOut;
  }
  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)
    ){
      continue; /* ignore IS [NOT] NULL constraints on NOT NULL columns */
    }
    if( pTerm->prereqRight & pNew->maskSelf ) continue;

    assert( pNew->nOut==saved_nOut );

    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==sqlite3LogEst(25) );
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = sqlite3LogEst(pExpr->x.pList->nExpr);
      }
      assert( nIn>0 );  /* RHS always has 2 or more terms...  The parser
                        ** changes "x IN (?)" into "x=?". */
      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|WHERE_SKIPSCAN))!=0
        || nInMul==0
      );
      pNew->wsFlags |= WHERE_COLUMN_EQ;
      if( iCol<0 || (nInMul==0 && pNew->u.btree.nEq==pProbe->nKeyCol-1)){
        assert( (pNew->wsFlags & WHERE_COLUMN_IN)==0 || iCol<0 );
        if( iCol>=0 && pProbe->onError==OE_None ){
          pNew->wsFlags |= WHERE_UNQ_WANTED;
        }else{
          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==sqlite3LogEst(2) );
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){
      testcase( pTerm->eOperator & WO_GT );
      testcase( pTerm->eOperator & WO_GE );


      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else{
      assert( pTerm->eOperator & (WO_LT|WO_LE) );
      testcase( pTerm->eOperator & WO_LT );
      testcase( pTerm->eOperator & WO_LE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){

      /* Adjust nOut and rRun for STAT3 range values */




      assert( pNew->nOut==saved_nOut );



      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);



    }








#ifdef SQLITE_ENABLE_STAT3_OR_STAT4

    if( nInMul==0 
     && pProbe->nSample 
     && pNew->u.btree.nEq<=pProbe->nSampleCol
     && OptimizationEnabled(db, SQLITE_Stat3) 


    ){
      Expr *pExpr = pTerm->pExpr;
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        testcase( pTerm->eOperator & WO_EQ );

        testcase( pTerm->eOperator & WO_ISNULL );
        rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pExpr, EP_xIsSelect)  ){

        rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);
      }
      assert( nOut==0 || rc==SQLITE_OK );



      if( nOut ){
        pNew->nOut = sqlite3LogEst(nOut);
        if( pNew->nOut>saved_nOut ) pNew->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);
    rc = whereLoopInsert(pBuilder, pNew);







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

/*
** Add all WhereLoop objects for a single table of the join where the table
** is idenfied by pBuilder->pNew->iTab.  That table is guaranteed to be
** a b-tree table, not a virtual table.























*/
static int whereLoopAddBtree(
  WhereLoopBuilder *pBuilder, /* WHERE clause information */
  Bitmask mExtra              /* Extra prerequesites for using this table */
){
  WhereInfo *pWInfo;          /* WHERE analysis context */
  Index *pProbe;              /* An index we are evaluating */
  Index sPk;                  /* A fake index object for the primary key */
  tRowcnt aiRowEstPk[2];      /* The aiRowEst[] value for the sPk index */
  i16 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 */
................................................................................
    ** 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.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
................................................................................
  /* Loop over all indices
  */
  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
    if( pProbe->pPartIdxWhere!=0
     && !whereUsablePartialIndex(pNew->iTab, pWC, pProbe->pPartIdxWhere) ){
      continue;  /* Partial index inappropriate for this query */
    }

    pNew->u.btree.nEq = 0;
    pNew->u.btree.nSkip = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = 0;
    pNew->prereq = mExtra;
    pNew->nOut = rSize;
................................................................................
    assert( (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || b==0 );
    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);
      rc = whereLoopInsert(pBuilder, pNew);
      pNew->nOut = rSize;
      if( rc ) break;
    }else{
      Bitmask m;
      if( pProbe->isCovering ){
................................................................................
         && (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;
      }
    }

................................................................................
  WhereClause *pWC;
  WhereLoop *pNew;
  WhereTerm *pTerm, *pWCEnd;
  int rc = SQLITE_OK;
  int iCur;
  WhereClause tempWC;
  WhereLoopBuilder sSubBuild;
  WhereOrSet sSum, sCur, sPrev;
  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));
................................................................................
        if( sCur.n==0 ){
          sSum.n = 0;
          break;
        }else if( once ){
          whereOrMove(&sSum, &sCur);
          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;
      pNew->rSetup = 0;
      pNew->iSortIdx = 0;
      memset(&pNew->u, 0, sizeof(pNew->u));
      for(i=0; rc==SQLITE_OK && i<sSum.n; i++){
        /* TUNING: Multiple by 3.5 for the secondary table lookup */











        pNew->rRun = sSum.a[i].rRun + 18;
        pNew->nOut = sSum.a[i].nOut;
        pNew->prereq = sSum.a[i].prereq;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
  return rc;
................................................................................
  **
  ** The rowid for a table is always UNIQUE and NOT NULL so whenever the
  ** rowid appears in the ORDER BY clause, the corresponding WhereLoop is
  ** automatically order-distinct.
  */

  assert( pOrderBy!=0 );

  /* Sortability of virtual tables is determined by the xBestIndex method
  ** of the virtual table itself */
  if( pLast->wsFlags & WHERE_VIRTUALTABLE ){
    testcase( nLoop>0 );  /* True when outer loops are one-row and match 
                          ** no ORDER BY terms */
    return pLast->u.vtab.isOrdered;
  }
  if( nLoop && OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return 0;

  nOrderBy = pOrderBy->nExpr;
  testcase( nOrderBy==BMS-1 );
  if( nOrderBy>BMS-1 ) return 0;  /* Cannot optimize overly large ORDER BYs */
  isOrderDistinct = 1;
  obDone = MASKBIT(nOrderBy)-1;
  orderDistinctMask = 0;
  ready = 0;
  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){
    if( iLoop>0 ) ready |= pLoop->maskSelf;
    pLoop = iLoop<nLoop ? pPath->aLoop[iLoop] : pLast;
    assert( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0 );



    iCur = pWInfo->pTabList->a[pLoop->iTab].iCursor;

    /* Mark off any ORDER BY term X that is a column in the table of
    ** the current loop for which there is term in the WHERE
    ** clause of the form X IS NULL or X=? that reference only outer
    ** loops.
    */
................................................................................
        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,
               ("---- sort cost=%-3d (%d/%d) increases cost %3d to %-3d\n",
                rSortCost, (nOrderBy-isOrdered), nOrderBy, rCost,
                sqlite3LogEstAdd(rCost,rSortCost)));

    }
    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 idx;
}
................................................................................
    aStat[1] = aSample[i].anEq[iCol];
  }else{
    tRowcnt iLower, iUpper, iGap;
    if( i==0 ){
      iLower = 0;
      iUpper = aSample[0].anLt[iCol];
    }else{
      i64 nRow0 = sqlite3LogEstToInt(pIdx->aiRowLogEst[0]);
      iUpper = i>=pIdx->nSample ? nRow0 : aSample[i].anLt[iCol];
      iLower = aSample[i-1].anEq[iCol] + aSample[i-1].anLt[iCol];
    }
    aStat[1] = (pIdx->nKeyCol>iCol ? pIdx->aAvgEq[iCol] : 1);
    if( iLower>=iUpper ){
      iGap = 0;
    }else{
      iGap = iUpper - iLower;
................................................................................
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

/*
** If it is not NULL, pTerm is a term that provides an upper or lower
** bound on a range scan. Without considering pTerm, it is estimated 
** that the scan will visit nNew rows. This function returns the number
** estimated to be visited after taking pTerm into account.
**
** If the user explicitly specified a likelihood() value for this term,
** then the return value is the likelihood multiplied by the number of
** input rows. Otherwise, this function assumes that an "IS NOT NULL" term
** has a likelihood of 0.50, and any other term a likelihood of 0.25.
*/
static LogEst whereRangeAdjust(WhereTerm *pTerm, LogEst nNew){
  LogEst nRet = nNew;
  if( pTerm ){
    if( pTerm->truthProb<=0 ){
      nRet += pTerm->truthProb;
    }else if( (pTerm->wtFlags & TERM_VNULL)==0 ){
      nRet -= 20;        assert( 20==sqlite3LogEst(4) );
    }
  }
  return nRet;
}

/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
** and lower bounds are represented by pLower and pUpper respectively. For
** example, assuming that index p is on t1(a):
................................................................................
      aff = SQLITE_AFF_INTEGER;
    }else{
      aff = p->pTable->aCol[p->aiColumn[nEq]].affinity;
    }
    /* Determine iLower and iUpper using ($P) only. */
    if( nEq==0 ){
      iLower = 0;
      iUpper = sqlite3LogEstToInt(p->aiRowLogEst[0]);
    }else{
      /* Note: this call could be optimized away - since the same values must 
      ** have been requested when testing key $P in whereEqualScanEst().  */
      whereKeyStats(pParse, p, pRec, 0, a);
      iLower = a[0];
      iUpper = a[0] + a[1];
    }
................................................................................
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(pBuilder);
#endif
  assert( pLower || pUpper );
  assert( pUpper==0 || (pUpper->wtFlags & TERM_VNULL)==0 );
  nNew = whereRangeAdjust(pLower, nOut);
  nNew = whereRangeAdjust(pUpper, nNew);

  /* TUNING: If there is both an upper and lower limit, assume the range is
  ** reduced by an additional 75%. This means that, by default, an open-ended
  ** range query (e.g. col > ?) is assumed to match 1/4 of the rows in the
  ** index. While a closed range (e.g. col BETWEEN ? AND ?) is estimated to
  ** match 1/64 of the index. */ 
  if( pLower && pUpper ) nNew -= 20;

  nOut -= (pLower!=0) + (pUpper!=0);
  if( nNew<10 ) nNew = 10;
  if( nNew<nOut ) nOut = nNew;
  pLoop->nOut = (LogEst)nOut;
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  i64 nRow0 = sqlite3LogEstToInt(p->aiRowLogEst[0]);
  int nRecValid = pBuilder->nRecValid;
  int rc = SQLITE_OK;     /* Subfunction return code */
  tRowcnt nEst;           /* Number of rows for a single term */
  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = nRow0;
    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
    pBuilder->nRecValid = nRecValid;
  }

  if( rc==SQLITE_OK ){
    if( nRowEst > nRow0 ) nRowEst = nRow0;
    *pnRow = nRowEst;
    WHERETRACE(0x10,("IN row estimate: est=%g\n", nRowEst));
  }
  assert( pBuilder->nRecValid==nRecValid );
  return rc;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
................................................................................
**
**   (2) pTemplate costs more than any other WhereLoops for which pTemplate
**       is a proper subset.
**
** To say "WhereLoop X is a proper subset of Y" means that X uses fewer
** WHERE clause terms than Y and that every WHERE clause term used by X is
** also used by Y.
**
** This adjustment is omitted for SKIPSCAN loops.  In a SKIPSCAN loop, the
** WhereLoop.nLTerm field is not an accurate measure of the number of WHERE
** clause terms covered, since some of the first nLTerm entries in aLTerm[]
** will be NULL (because they are skipped).  That makes it more difficult
** to compare the loops.  We could add extra code to do the comparison, and
** perhaps we will someday.  But SKIPSCAN is sufficiently uncommon, and this
** adjustment is sufficient minor, that it is very difficult to construct
** a test case where the extra code would improve the query plan.  Better
** to avoid the added complexity and just omit cost adjustments to SKIPSCAN
** loops.
*/
static void whereLoopAdjustCost(const WhereLoop *p, WhereLoop *pTemplate){
  if( (pTemplate->wsFlags & WHERE_INDEXED)==0 ) return;
  if( (pTemplate->wsFlags & WHERE_SKIPSCAN)!=0 ) return;
  for(; p; p=p->pNextLoop){
    if( p->iTab!=pTemplate->iTab ) continue;
    if( (p->wsFlags & WHERE_INDEXED)==0 ) continue;
    if( (p->wsFlags & WHERE_SKIPSCAN)!=0 ) continue;
    if( whereLoopCheaperProperSubset(p, pTemplate) ){
      /* Adjust pTemplate cost downward so that it is cheaper than its 
      ** subset p */
      pTemplate->rRun = p->rRun;
      pTemplate->nOut = p->nOut - 1;
    }else if( whereLoopCheaperProperSubset(pTemplate, p) ){
      /* Adjust pTemplate cost upward so that it is costlier than p since
................................................................................
    if( (pTerm->prereqAll & notAllowed)!=0 ) continue;
    for(j=pLoop->nLTerm-1; j>=0; j--){
      pX = pLoop->aLTerm[j];
      if( pX==0 ) continue;
      if( pX==pTerm ) break;
      if( pX->iParent>=0 && (&pWC->a[pX->iParent])==pTerm ) break;
    }
    if( j<0 ){
      pLoop->nOut += (pTerm->truthProb<=0 ? pTerm->truthProb : -1);
    }
  }
}

/*
** We have so far matched pBuilder->pNew->u.btree.nEq terms of the 
** index pIndex. Try to match one more.
**
** When this function is called, pBuilder->pNew->nOut contains the 
** number of rows expected to be visited by filtering using the nEq 
** terms only. If it is modified, this value is restored before this 
** function returns.
**
** 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 */
................................................................................
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  u16 saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u16 saved_nSkip;                /* Original value of pNew->u.btree.nSkip */
  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 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 );
................................................................................
    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->nKeyCol );
  if( pNew->u.btree.nEq < pProbe->nKeyCol ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];


  }else{
    iCol = -1;

  }
  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;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(pProbe->aiRowLogEst[0]);

  /* Consider using a skip-scan if there are no WHERE clause constraints
  ** available for the left-most terms of the index, and if the average
  ** number of repeats in the left-most terms is at least 18. 


  **
  ** The magic number 18 is selected on the basis that scanning 17 rows
  ** is almost always quicker than an index seek (even though if the index
  ** contains fewer than 2^17 rows we assume otherwise in other parts of
  ** the code). And, even if it is not, it should not be too much slower. 
  ** On the other hand, the extra seeks could end up being significantly
  ** more expensive.  */
  assert( 42==sqlite3LogEst(18) );
  if( pTerm==0
   && saved_nEq==saved_nSkip
   && saved_nEq+1<pProbe->nKeyCol
   && pProbe->aiRowLogEst[saved_nEq+1]>=42  /* TUNING: Minimum for skip-scan */
   && (rc = whereLoopResize(db, pNew, pNew->nLTerm+1))==SQLITE_OK
  ){
    LogEst nIter;
    pNew->u.btree.nEq++;
    pNew->u.btree.nSkip++;
    pNew->aLTerm[pNew->nLTerm++] = 0;
    pNew->wsFlags |= WHERE_SKIPSCAN;
    nIter = pProbe->aiRowLogEst[saved_nEq] - pProbe->aiRowLogEst[saved_nEq+1];

    pNew->nOut -= nIter;
    whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nIter + nInMul);
    pNew->nOut = saved_nOut;
  }
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    u16 eOp = pTerm->eOperator;   /* Shorthand for pTerm->eOperator */
    LogEst rCostIdx;
    LogEst nOutUnadjusted;        /* nOut before IN() and WHERE adjustments */
    int nIn = 0;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    int nRecValid = pBuilder->nRecValid;
#endif
    if( (eOp==WO_ISNULL || (pTerm->wtFlags&TERM_VNULL)!=0)
     && (iCol<0 || pSrc->pTab->aCol[iCol].notNull)
    ){
      continue; /* ignore IS [NOT] NULL constraints on NOT NULL columns */
    }
    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;


    assert( nInMul==0
        || (pNew->wsFlags & WHERE_COLUMN_NULL)!=0 
        || (pNew->wsFlags & WHERE_COLUMN_IN)!=0 
        || (pNew->wsFlags & WHERE_SKIPSCAN)!=0 
    );

    if( eOp & 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);
      }
      assert( nIn>0 );  /* RHS always has 2 or more terms...  The parser
                        ** changes "x IN (?)" into "x=?". */




    }else if( eOp & (WO_EQ) ){




      pNew->wsFlags |= WHERE_COLUMN_EQ;
      if( iCol<0 || (nInMul==0 && pNew->u.btree.nEq==pProbe->nKeyCol-1) ){

        if( iCol>=0 && pProbe->onError==OE_None ){
          pNew->wsFlags |= WHERE_UNQ_WANTED;
        }else{
          pNew->wsFlags |= WHERE_ONEROW;
        }
      }
    }else if( eOp & WO_ISNULL ){


      pNew->wsFlags |= WHERE_COLUMN_NULL;




    }else if( eOp & (WO_GT|WO_GE) ){


      testcase( eOp & WO_GT );
      testcase( eOp & WO_GE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else{
      assert( eOp & (WO_LT|WO_LE) );
      testcase( eOp & WO_LT );
      testcase( eOp & WO_LE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }


    /* At this point pNew->nOut is set to the number of rows expected to
    ** be visited by the index scan before considering term pTerm, or the
    ** values of nIn and nInMul. In other words, assuming that all 
    ** "x IN(...)" terms are replaced with "x = ?". This block updates
    ** the value of pNew->nOut to account for pTerm (but not nIn/nInMul).  */
    assert( pNew->nOut==saved_nOut );
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut using stat3/stat4 data. Or, if there is no stat3/stat4
      ** data, using some other estimate.  */
      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);
    }else{
      int nEq = ++pNew->u.btree.nEq;
      assert( eOp & (WO_ISNULL|WO_EQ|WO_IN) );

      assert( pNew->nOut==saved_nOut );
      if( pTerm->truthProb<=0 && iCol>=0 ){
        assert( (eOp & WO_IN) || nIn==0 );
        testcase( eOp & WO_IN );
        pNew->nOut += pTerm->truthProb;
        pNew->nOut -= nIn;
        pNew->wsFlags |= WHERE_LIKELIHOOD;
      }else{
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
        tRowcnt nOut = 0;
        if( nInMul==0 
         && pProbe->nSample 
         && pNew->u.btree.nEq<=pProbe->nSampleCol
         && OptimizationEnabled(db, SQLITE_Stat3) 
         && ((eOp & WO_IN)==0 || !ExprHasProperty(pTerm->pExpr, EP_xIsSelect))
         && (pNew->wsFlags & WHERE_LIKELIHOOD)==0
        ){
          Expr *pExpr = pTerm->pExpr;

          if( (eOp & (WO_EQ|WO_ISNULL))!=0 ){

            testcase( eOp & WO_EQ );
            testcase( eOp & WO_ISNULL );
            rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);


          }else{
            rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);
          }

          assert( rc!=SQLITE_OK || nOut>0 );
          if( rc==SQLITE_NOTFOUND ) rc = SQLITE_OK;
          if( rc!=SQLITE_OK ) break;          /* Jump out of the pTerm loop */
          if( nOut ){
            pNew->nOut = sqlite3LogEst(nOut);
            if( pNew->nOut>saved_nOut ) pNew->nOut = saved_nOut;
            pNew->nOut -= nIn;
          }
        }
        if( nOut==0 )
#endif
        {
          pNew->nOut += (pProbe->aiRowLogEst[nEq] - pProbe->aiRowLogEst[nEq-1]);
          if( eOp & WO_ISNULL ){
            /* TUNING: If there is no likelihood() value, assume that a 
            ** "col IS NULL" expression matches twice as many rows 
            ** as (col=?). */
            pNew->nOut += 10;
          }
        }
      }
    }

    /* Set rCostIdx to the cost of visiting selected rows in index. Add
    ** it to pNew->rRun, which is currently set to the cost of the index
    ** seek only. Then, if this is a non-covering index, add the cost of
    ** visiting the rows in the main table.  */
    rCostIdx = pNew->nOut + 1 + (15*pProbe->szIdxRow)/pSrc->pTab->szTabRow;
    pNew->rRun = sqlite3LogEstAdd(rLogSize, rCostIdx);
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){


      pNew->rRun = sqlite3LogEstAdd(pNew->rRun, pNew->nOut + 16);
    }



    nOutUnadjusted = pNew->nOut;
    pNew->rRun += nInMul + nIn;
    pNew->nOut += nInMul + nIn;
    whereLoopOutputAdjust(pBuilder->pWC, pNew);
    rc = whereLoopInsert(pBuilder, pNew);

    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->nKeyCol + (pProbe->zName!=0))
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }
    pNew->nOut = saved_nOut;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
  return 0;
}

/*
** Add all WhereLoop objects for a single table of the join where the table
** is idenfied by pBuilder->pNew->iTab.  That table is guaranteed to be
** a b-tree table, not a virtual table.
**
** The costs (WhereLoop.rRun) of the b-tree loops added by this function
** are calculated as follows:
**
** For a full scan, assuming the table (or index) contains nRow rows:
**
**     cost = nRow * 3.0                    // full-table scan
**     cost = nRow * K                      // scan of covering index
**     cost = nRow * (K+3.0)                // scan of non-covering index
**
** where K is a value between 1.1 and 3.0 set based on the relative 
** estimated average size of the index and table records.
**
** For an index scan, where nVisit is the number of index rows visited
** by the scan, and nSeek is the number of seek operations required on 
** the index b-tree:
**
**     cost = nSeek * (log(nRow) + K * nVisit)          // covering index
**     cost = nSeek * (log(nRow) + (K+3.0) * nVisit)    // non-covering index
**
** Normally, nSeek is 1. nSeek values greater than 1 come about if the 
** WHERE clause includes "x IN (....)" terms used in place of "x=?". Or when 
** implicit "x IN (SELECT x FROM tbl)" terms are added for skip-scans.
*/
static int whereLoopAddBtree(
  WhereLoopBuilder *pBuilder, /* WHERE clause information */
  Bitmask mExtra              /* Extra prerequesites for using this table */
){
  WhereInfo *pWInfo;          /* WHERE analysis context */
  Index *pProbe;              /* An index we are evaluating */
  Index sPk;                  /* A fake index object for the primary key */
  LogEst aiRowEstPk[2];       /* The aiRowLogEst[] value for the sPk index */
  i16 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 */
................................................................................
    ** 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.aiColumn = &aiColumnPk;
    sPk.aiRowLogEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pTab;
    sPk.szIdxRow = pTab->szTabRow;
    aiRowEstPk[0] = pTab->nRowLogEst;
    aiRowEstPk[1] = 0;
    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 = pTab->nRowLogEst;
  rLogSize = estLog(rSize);

#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
  /* Automatic indexes */
  if( !pBuilder->pOrSet
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
   && pSrc->pIndex==0
................................................................................
  /* Loop over all indices
  */
  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
    if( pProbe->pPartIdxWhere!=0
     && !whereUsablePartialIndex(pNew->iTab, pWC, pProbe->pPartIdxWhere) ){
      continue;  /* Partial index inappropriate for this query */
    }
    rSize = pProbe->aiRowLogEst[0];
    pNew->u.btree.nEq = 0;
    pNew->u.btree.nSkip = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = 0;
    pNew->prereq = mExtra;
    pNew->nOut = rSize;
................................................................................
    assert( (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || b==0 );
    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 (N*3.0). */
      pNew->rRun = rSize + 16;


      whereLoopOutputAdjust(pWC, pNew);
      rc = whereLoopInsert(pBuilder, pNew);
      pNew->nOut = rSize;
      if( rc ) break;
    }else{
      Bitmask m;
      if( pProbe->isCovering ){
................................................................................
         && (pProbe->szIdxRow<pTab->szTabRow)
         && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
         && sqlite3GlobalConfig.bUseCis
         && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
          )
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;


        /* The cost of visiting the index rows is N*K, where K is





        ** between 1.1 and 3.0, depending on the relative sizes of the





        ** index and table rows. If this is a non-covering index scan,
        ** also add the cost of visiting table rows (N*3.0).  */
        pNew->rRun = rSize + 1 + (15*pProbe->szIdxRow)/pTab->szTabRow;














        if( m!=0 ){
          pNew->rRun = sqlite3LogEstAdd(pNew->rRun, rSize+16);
        }

        whereLoopOutputAdjust(pWC, pNew);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }

................................................................................
  WhereClause *pWC;
  WhereLoop *pNew;
  WhereTerm *pTerm, *pWCEnd;
  int rc = SQLITE_OK;
  int iCur;
  WhereClause tempWC;
  WhereLoopBuilder sSubBuild;
  WhereOrSet sSum, sCur;
  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));
................................................................................
        if( sCur.n==0 ){
          sSum.n = 0;
          break;
        }else if( once ){
          whereOrMove(&sSum, &sCur);
          once = 0;
        }else{
          WhereOrSet sPrev;
          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;
      pNew->rSetup = 0;
      pNew->iSortIdx = 0;
      memset(&pNew->u, 0, sizeof(pNew->u));
      for(i=0; rc==SQLITE_OK && i<sSum.n; i++){
        /* TUNING: Currently sSum.a[i].rRun is set to the sum of the costs
        ** of all sub-scans required by the OR-scan. However, due to rounding
        ** errors, it may be that the cost of the OR-scan is equal to its
        ** most expensive sub-scan. Add the smallest possible penalty 
        ** (equivalent to multiplying the cost by 1.07) to ensure that 
        ** this does not happen. Otherwise, for WHERE clauses such as the
        ** following where there is an index on "y":
        **
        **     WHERE likelihood(x=?, 0.99) OR y=?
        **
        ** the planner may elect to "OR" together a full-table scan and an
        ** index lookup. And other similarly odd results.  */
        pNew->rRun = sSum.a[i].rRun + 1;
        pNew->nOut = sSum.a[i].nOut;
        pNew->prereq = sSum.a[i].prereq;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
  return rc;
................................................................................
  **
  ** The rowid for a table is always UNIQUE and NOT NULL so whenever the
  ** rowid appears in the ORDER BY clause, the corresponding WhereLoop is
  ** automatically order-distinct.
  */

  assert( pOrderBy!=0 );








  if( nLoop && OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return 0;

  nOrderBy = pOrderBy->nExpr;
  testcase( nOrderBy==BMS-1 );
  if( nOrderBy>BMS-1 ) return 0;  /* Cannot optimize overly large ORDER BYs */
  isOrderDistinct = 1;
  obDone = MASKBIT(nOrderBy)-1;
  orderDistinctMask = 0;
  ready = 0;
  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){
    if( iLoop>0 ) ready |= pLoop->maskSelf;
    pLoop = iLoop<nLoop ? pPath->aLoop[iLoop] : pLast;
    if( pLoop->wsFlags & WHERE_VIRTUALTABLE ){
      if( pLoop->u.vtab.isOrdered ) obSat = obDone;
      break;
    }
    iCur = pWInfo->pTabList->a[pLoop->iTab].iCursor;

    /* Mark off any ORDER BY term X that is a column in the table of
    ** the current loop for which there is term in the WHERE
    ** clause of the form X IS NULL or X=? that reference only outer
    ** loops.
    */
................................................................................
        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 a full external sort, where N is 
            ** the number of rows to sort is:
            **
            **   cost = (3.0 * N * log(N)).
            ** 
            ** Or, 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:
            **
            **   cost = (3.0 * N * log(N)) * (Y/X)
            **
            ** The (Y/X) term is implemented using stack variable rScale
            ** below.  */
            LogEst rScale, rSortCost;
            assert( nOrderBy>0 && 66==sqlite3LogEst(100) );
            rScale = sqlite3LogEst((nOrderBy-isOrdered)*100/nOrderBy) - 66;
            rSortCost = nRowEst + estLog(nRowEst) + rScale + 16;

            /* TUNING: The cost of implementing DISTINCT using a B-TREE is
            ** similar but with a larger constant of proportionality. 
            ** Multiply by an additional factor of 3.0.  */
            if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
              rSortCost += 16;
            }
            WHERETRACE(0x002,
               ("---- sort cost=%-3d (%d/%d) increases cost %3d to %-3d\n",
                rSortCost, (nOrderBy-isOrdered), nOrderBy, rCost,
                sqlite3LogEstAdd(rCost,rSortCost)));

#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 */
#define WHERE_SKIPSCAN     0x00008000  /* Uses the skip-scan algorithm */
#define WHERE_UNQ_WANTED   0x00010000  /* WHERE_ONEROW would have been helpful*/

#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 */
#define WHERE_SKIPSCAN     0x00008000  /* Uses the skip-scan algorithm */
#define WHERE_UNQ_WANTED   0x00010000  /* WHERE_ONEROW would have been helpful*/
#define WHERE_LIKELIHOOD   0x00020000  /* A likelihood() is affecting nOut */

  ifcapable stat4 {
    execsql { SELECT count(*)>0 FROM sqlite_stat4; }
  } else {
    execsql { SELECT count(*)>0 FROM sqlite_stat3; }
  }
} {1}










do_eqp_test analyze3-1.1.2 {
  SELECT sum(y) FROM t1 WHERE x>200 AND x<300
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (x>? AND x<?)}}
do_eqp_test analyze3-1.1.3 {
  SELECT sum(y) FROM t1 WHERE x>0 AND x<1100 
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (x>? AND x<?)}}

do_test analyze3-1.1.4 {
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>200 AND x<300 }
} {199 0 14850}
do_test analyze3-1.1.5 {
  set l [string range "200" 0 end]
  set u [string range "300" 0 end]
................................................................................
do_test analyze3-1.1.6 {
  set l [expr int(200)]
  set u [expr int(300)]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.1.7 {
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>0 AND x<1100 }
} {2000 0 499500}
do_test analyze3-1.1.8 {
  set l [string range "0" 0 end]
  set u [string range "1100" 0 end]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {2000 0 499500}
do_test analyze3-1.1.9 {
  set l [expr int(0)]
  set u [expr int(1100)]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {2000 0 499500}


# The following tests are similar to the block above. The difference is
# that the indexed column has TEXT affinity in this case. In the tests
# above the affinity is INTEGER.
#
do_test analyze3-1.2.1 {
................................................................................
      CREATE TABLE t2(x TEXT, y);
      INSERT INTO t2 SELECT * FROM t1;
      CREATE INDEX i2 ON t2(x);
    COMMIT;
    ANALYZE;
  }
} {}




do_eqp_test analyze3-1.2.2 {
  SELECT sum(y) FROM t2 WHERE x>1 AND x<2
} {0 0 0 {SEARCH TABLE t2 USING INDEX i2 (x>? AND x<?)}}
do_eqp_test analyze3-1.2.3 {
  SELECT sum(y) FROM t2 WHERE x>0 AND x<99
} {0 0 0 {SEARCH TABLE t2 USING INDEX i2 (x>? AND x<?)}}

do_test analyze3-1.2.4 {
  sf_execsql { SELECT sum(y) FROM t2 WHERE x>12 AND x<20 }
} {161 0 4760}
do_test analyze3-1.2.5 {
  set l [string range "12" 0 end]
  set u [string range "20" 0 end]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
................................................................................
do_test analyze3-1.2.6 {
  set l [expr int(12)]
  set u [expr int(20)]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {161 0 integer integer 4760}
do_test analyze3-1.2.7 {
  sf_execsql { SELECT sum(y) FROM t2 WHERE x>0 AND x<99 }
} {1981 0 490555}
do_test analyze3-1.2.8 {
  set l [string range "0" 0 end]
  set u [string range "99" 0 end]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {1981 0 text text 490555}
do_test analyze3-1.2.9 {
  set l [expr int(0)]
  set u [expr int(99)]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {1981 0 integer integer 490555}

# Same tests a third time. This time, column x has INTEGER affinity and
# is not the leftmost column of the table. This triggered a bug causing
# SQLite to use sub-optimal query plans in 3.6.18 and earlier.
#
do_test analyze3-1.3.1 {
  execsql {
................................................................................
      CREATE TABLE t3(y TEXT, x INTEGER);
      INSERT INTO t3 SELECT y, x FROM t1;
      CREATE INDEX i3 ON t3(x);
    COMMIT;
    ANALYZE;
  }
} {}




do_eqp_test analyze3-1.3.2 {
  SELECT sum(y) FROM t3 WHERE x>200 AND x<300
} {0 0 0 {SEARCH TABLE t3 USING INDEX i3 (x>? AND x<?)}}
do_eqp_test analyze3-1.3.3 {
  SELECT sum(y) FROM t3 WHERE x>0 AND x<1100
} {0 0 0 {SEARCH TABLE t3 USING INDEX i3 (x>? AND x<?)}}

do_test analyze3-1.3.4 {
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>200 AND x<300 }
} {199 0 14850}
do_test analyze3-1.3.5 {
  set l [string range "200" 0 end]
  set u [string range "300" 0 end]
................................................................................
do_test analyze3-1.3.6 {
  set l [expr int(200)]
  set u [expr int(300)]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.3.7 {
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>0 AND x<1100 }
} {2000 0 499500}
do_test analyze3-1.3.8 {
  set l [string range "0" 0 end]
  set u [string range "1100" 0 end]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {2000 0 499500}
do_test analyze3-1.3.9 {
  set l [expr int(0)]
  set u [expr int(1100)]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {2000 0 499500}

#-------------------------------------------------------------------------
# Test that the values of bound SQL variables may be used for the LIKE
# optimization.
#
drop_all_tables
do_test analyze3-2.1 {

  ifcapable stat4 {
    execsql { SELECT count(*)>0 FROM sqlite_stat4; }
  } else {
    execsql { SELECT count(*)>0 FROM sqlite_stat3; }
  }
} {1}

do_execsql_test analyze3-1.1.x {
  SELECT count(*) FROM t1 WHERE x>200 AND x<300;
  SELECT count(*) FROM t1 WHERE x>0 AND x<1100;
} {99 1000}

# The first of the following two SELECT statements visits 99 rows. So
# it is better to use the index. But the second visits every row in 
# the table (1000 in total) so it is better to do a full-table scan.
#
do_eqp_test analyze3-1.1.2 {
  SELECT sum(y) FROM t1 WHERE x>200 AND x<300
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (x>? AND x<?)}}
do_eqp_test analyze3-1.1.3 {
  SELECT sum(y) FROM t1 WHERE x>0 AND x<1100 
} {0 0 0 {SCAN TABLE t1}}

do_test analyze3-1.1.4 {
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>200 AND x<300 }
} {199 0 14850}
do_test analyze3-1.1.5 {
  set l [string range "200" 0 end]
  set u [string range "300" 0 end]
................................................................................
do_test analyze3-1.1.6 {
  set l [expr int(200)]
  set u [expr int(300)]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.1.7 {
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>0 AND x<1100 }
} {999 999 499500}
do_test analyze3-1.1.8 {
  set l [string range "0" 0 end]
  set u [string range "1100" 0 end]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {999 999 499500}
do_test analyze3-1.1.9 {
  set l [expr int(0)]
  set u [expr int(1100)]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {999 999 499500}


# The following tests are similar to the block above. The difference is
# that the indexed column has TEXT affinity in this case. In the tests
# above the affinity is INTEGER.
#
do_test analyze3-1.2.1 {
................................................................................
      CREATE TABLE t2(x TEXT, y);
      INSERT INTO t2 SELECT * FROM t1;
      CREATE INDEX i2 ON t2(x);
    COMMIT;
    ANALYZE;
  }
} {}
do_execsql_test analyze3-2.1.x {
  SELECT count(*) FROM t2 WHERE x>1 AND x<2;
  SELECT count(*) FROM t2 WHERE x>0 AND x<99;
} {200 990}
do_eqp_test analyze3-1.2.2 {
  SELECT sum(y) FROM t2 WHERE x>1 AND x<2
} {0 0 0 {SEARCH TABLE t2 USING INDEX i2 (x>? AND x<?)}}
do_eqp_test analyze3-1.2.3 {
  SELECT sum(y) FROM t2 WHERE x>0 AND x<99
} {0 0 0 {SCAN TABLE t2}}

do_test analyze3-1.2.4 {
  sf_execsql { SELECT sum(y) FROM t2 WHERE x>12 AND x<20 }
} {161 0 4760}
do_test analyze3-1.2.5 {
  set l [string range "12" 0 end]
  set u [string range "20" 0 end]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
................................................................................
do_test analyze3-1.2.6 {
  set l [expr int(12)]
  set u [expr int(20)]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {161 0 integer integer 4760}
do_test analyze3-1.2.7 {
  sf_execsql { SELECT sum(y) FROM t2 WHERE x>0 AND x<99 }
} {999 999 490555}
do_test analyze3-1.2.8 {
  set l [string range "0" 0 end]
  set u [string range "99" 0 end]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {999 999 text text 490555}
do_test analyze3-1.2.9 {
  set l [expr int(0)]
  set u [expr int(99)]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {999 999 integer integer 490555}

# Same tests a third time. This time, column x has INTEGER affinity and
# is not the leftmost column of the table. This triggered a bug causing
# SQLite to use sub-optimal query plans in 3.6.18 and earlier.
#
do_test analyze3-1.3.1 {
  execsql {
................................................................................
      CREATE TABLE t3(y TEXT, x INTEGER);
      INSERT INTO t3 SELECT y, x FROM t1;
      CREATE INDEX i3 ON t3(x);
    COMMIT;
    ANALYZE;
  }
} {}
do_execsql_test analyze3-1.3.x {
  SELECT count(*) FROM t3 WHERE x>200 AND x<300;
  SELECT count(*) FROM t3 WHERE x>0 AND x<1100
} {99 1000}
do_eqp_test analyze3-1.3.2 {
  SELECT sum(y) FROM t3 WHERE x>200 AND x<300
} {0 0 0 {SEARCH TABLE t3 USING INDEX i3 (x>? AND x<?)}}
do_eqp_test analyze3-1.3.3 {
  SELECT sum(y) FROM t3 WHERE x>0 AND x<1100
} {0 0 0 {SCAN TABLE t3}}

do_test analyze3-1.3.4 {
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>200 AND x<300 }
} {199 0 14850}
do_test analyze3-1.3.5 {
  set l [string range "200" 0 end]
  set u [string range "300" 0 end]
................................................................................
do_test analyze3-1.3.6 {
  set l [expr int(200)]
  set u [expr int(300)]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.3.7 {
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>0 AND x<1100 }
} {999 999 499500}
do_test analyze3-1.3.8 {
  set l [string range "0" 0 end]
  set u [string range "1100" 0 end]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {999 999 499500}
do_test analyze3-1.3.9 {
  set l [expr int(0)]
  set u [expr int(1100)]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {999 999 499500}

#-------------------------------------------------------------------------
# Test that the values of bound SQL variables may be used for the LIKE
# optimization.
#
drop_all_tables
do_test analyze3-2.1 {

#-------------------------------------------------------------------------
# Check that affinities are taken into account when using stat4 data to
# estimate the number of rows scanned by a rowid constraint.
#
drop_all_tables
do_test 13.1 {
  execsql {
    CREATE TABLE t1(a, b, c);
    CREATE INDEX i1 ON t1(a);
    CREATE INDEX i2 ON t1(b, c);
  }
  for {set i 0} {$i<100} {incr i} {
    if {$i %2} {set a abc} else {set a def}
    execsql { INSERT INTO t1(rowid, a, b, c) VALUES($i, $a, $i, $i) }
  }
  execsql ANALYZE
} {}
do_eqp_test 13.2.1 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<15 AND b<20
} {/SEARCH TABLE t1 USING INDEX i1/}
do_eqp_test 13.2.2 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<'15' AND b<20
} {/SEARCH TABLE t1 USING INDEX i1/}
do_eqp_test 13.3.1 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<100 AND b<20
} {/SEARCH TABLE t1 USING INDEX i2/}
do_eqp_test 13.3.2 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<'100' AND b<20
} {/SEARCH TABLE t1 USING INDEX i2/}

#-------------------------------------------------------------------------
# Check also that affinities are taken into account when using stat4 data 
# to estimate the number of rows scanned by any other constraint on a 
# column other than the leftmost.
#

#-------------------------------------------------------------------------
# Check that affinities are taken into account when using stat4 data to
# estimate the number of rows scanned by a rowid constraint.
#
drop_all_tables
do_test 13.1 {
  execsql {
    CREATE TABLE t1(a, b, c, d);
    CREATE INDEX i1 ON t1(a);
    CREATE INDEX i2 ON t1(b, c);
  }
  for {set i 0} {$i<100} {incr i} {
    if {$i %2} {set a abc} else {set a def}
    execsql { INSERT INTO t1(rowid, a, b, c) VALUES($i, $a, $i, $i) }
  }
  execsql ANALYZE
} {}
do_eqp_test 13.2.1 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<15 AND b<12
} {/SEARCH TABLE t1 USING INDEX i1/}
do_eqp_test 13.2.2 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<'15' AND b<12
} {/SEARCH TABLE t1 USING INDEX i1/}
do_eqp_test 13.3.1 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<100 AND b<12
} {/SEARCH TABLE t1 USING INDEX i2/}
do_eqp_test 13.3.2 {
  SELECT * FROM t1 WHERE a='abc' AND rowid<'100' AND b<12
} {/SEARCH TABLE t1 USING INDEX i2/}

#-------------------------------------------------------------------------
# Check also that affinities are taken into account when using stat4 data 
# to estimate the number of rows scanned by any other constraint on a 
# column other than the leftmost.
#

  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}

  db status autoindex
} {0}
do_test autoindex1-210 {
  db eval {
    PRAGMA automatic_index=ON;
    ANALYZE;
    UPDATE sqlite_stat1 SET stat='10000' WHERE tbl='t1';
    -- Table t2 actually contains 8 rows.
    UPDATE sqlite_stat1 SET stat='16' WHERE tbl='t2';
    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}

# 2014-04-26
#
# 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.
#
#***********************************************************************
# 

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


do_execsql_test 1.1 {
  CREATE TABLE t3(id INTEGER PRIMARY KEY, b NOT NULL);
  CREATE TABLE t4(c, d, e);
  CREATE UNIQUE INDEX i3 ON t3(b);
  CREATE UNIQUE INDEX i4 ON t4(c, d);
}
do_eqp_test 1.2 {
  SELECT e FROM t3, t4 WHERE b=c ORDER BY b, d;
} {
  0 0 0 {SCAN TABLE t3 USING COVERING INDEX i3} 
  0 1 1 {SEARCH TABLE t4 USING INDEX i4 (c=?)}
}


do_execsql_test 2.1 {
  CREATE TABLE t1(a, b);
  CREATE INDEX i1 ON t1(a);
}

# It is better to use an index for ORDER BY than sort externally, even 
# if the index is a non-covering index.
do_eqp_test 2.2 {
  SELECT * FROM t1 ORDER BY a;
} {
  0 0 0 {SCAN TABLE t1 USING INDEX i1}
}

do_execsql_test 3.1 {
  CREATE TABLE t5(a INTEGER PRIMARY KEY,b,c,d,e,f,g);
  CREATE INDEX t5b ON t5(b);
  CREATE INDEX t5c ON t5(c);
  CREATE INDEX t5d ON t5(d);
  CREATE INDEX t5e ON t5(e);
  CREATE INDEX t5f ON t5(f);
  CREATE INDEX t5g ON t5(g);
}

do_eqp_test 3.2 {
  SELECT a FROM t5 
  WHERE b IS NULL OR c IS NULL OR d IS NULL 
  ORDER BY a;
} {
  0 0 0 {SEARCH TABLE t5 USING INDEX t5b (b=?)} 
  0 0 0 {SEARCH TABLE t5 USING INDEX t5c (c=?)} 
  0 0 0 {SEARCH TABLE t5 USING INDEX t5d (d=?)} 
  0 0 0 {USE TEMP B-TREE FOR ORDER BY}
}

#-------------------------------------------------------------------------
# If there is no likelihood() or stat3 data, SQLite assumes that a closed
# range scan (e.g. one constrained by "col BETWEEN ? AND ?" constraint)
# visits 1/64 of the rows in a table.
#
# Note: 1/63 =~ 0.016
# Note: 1/65 =~ 0.015
#
reset_db
do_execsql_test 4.1 {
  CREATE TABLE t1(a, b);
  CREATE INDEX i1 ON t1(a);
  CREATE INDEX i2 ON t1(b);
}
do_eqp_test 4.2 {
  SELECT * FROM t1 WHERE likelihood(a=?, 0.014) AND b BETWEEN ? AND ?;
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a=?)}
}
do_eqp_test 4.3 {
  SELECT * FROM t1 WHERE likelihood(a=?, 0.016) AND b BETWEEN ? AND ?;
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX i2 (b>? AND b<?)}
}


#-------------------------------------------------------------------------
#
reset_db
do_execsql_test 5.1 {
  CREATE TABLE t2(x, y);
  CREATE INDEX t2i1 ON t2(x);
}

do_eqp_test 5.2 {
  SELECT * FROM t2 ORDER BY x, y;
} {
  0 0 0 {SCAN TABLE t2 USING INDEX t2i1} 
  0 0 0 {USE TEMP B-TREE FOR RIGHT PART OF ORDER BY}
}

do_eqp_test 5.3 {
  SELECT * FROM t2 WHERE x BETWEEN ? AND ? ORDER BY rowid;
} {
  0 0 0 {SEARCH TABLE t2 USING INDEX t2i1 (x>? AND x<?)} 
  0 0 0 {USE TEMP B-TREE FOR ORDER BY}
}

# where7.test, where8.test:
#
do_execsql_test 6.1 {
  CREATE TABLE t3(a INTEGER PRIMARY KEY, b, c);
  CREATE INDEX t3i1 ON t3(b);
  CREATE INDEX t3i2 ON t3(c);
}

do_eqp_test 6.2 {
  SELECT a FROM t3 WHERE (b BETWEEN 2 AND 4) OR c=100 ORDER BY a
} {
  0 0 0 {SEARCH TABLE t3 USING INDEX t3i1 (b>? AND b<?)} 
  0 0 0 {SEARCH TABLE t3 USING INDEX t3i2 (c=?)}
  0 0 0 {USE TEMP B-TREE FOR ORDER BY}
}

#-------------------------------------------------------------------------
#
reset_db
do_execsql_test 7.1 {
  CREATE TABLE t1(a INTEGER PRIMARY KEY,b,c,d,e,f,g);
  CREATE INDEX t1b ON t1(b);
  CREATE INDEX t1c ON t1(c);
  CREATE INDEX t1d ON t1(d);
  CREATE INDEX t1e ON t1(e);
  CREATE INDEX t1f ON t1(f);
  CREATE INDEX t1g ON t1(g);
}

do_eqp_test 7.2 {
  SELECT a FROM t1
     WHERE (b>=950 AND b<=1010) OR (b IS NULL AND c NOT NULL)
  ORDER BY a
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>? AND b<?)} 
  0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b=?)} 
  0 0 0 {USE TEMP B-TREE FOR ORDER BY}
}

do_eqp_test 7.3 {
  SELECT rowid FROM t1
  WHERE (+b IS NULL AND c NOT NULL AND d NOT NULL)
        OR (b NOT NULL AND c IS NULL AND d NOT NULL)
        OR (b NOT NULL AND c NOT NULL AND d IS NULL)
} {
  0 0 0 {SCAN TABLE t1}
}

do_eqp_test 7.4 {
  SELECT rowid FROM t1 WHERE (+b IS NULL AND c NOT NULL) OR c IS NULL
} {
  0 0 0 {SCAN TABLE t1}
}

#-------------------------------------------------------------------------
#
reset_db
do_execsql_test 8.1 {
  CREATE TABLE composer(
    cid INTEGER PRIMARY KEY,
    cname TEXT
  );
  CREATE TABLE album(
    aid INTEGER PRIMARY KEY,
    aname TEXT
  );
  CREATE TABLE track(
    tid INTEGER PRIMARY KEY,
    cid INTEGER REFERENCES composer,
    aid INTEGER REFERENCES album,
    title TEXT
  );
  CREATE INDEX track_i1 ON track(cid);
  CREATE INDEX track_i2 ON track(aid);
}

do_eqp_test 8.2 {
  SELECT DISTINCT aname
    FROM album, composer, track
   WHERE cname LIKE '%bach%'
     AND unlikely(composer.cid=track.cid)
     AND unlikely(album.aid=track.aid);
} {
  0 0 2 {SCAN TABLE track} 
  0 1 0 {SEARCH TABLE album USING INTEGER PRIMARY KEY (rowid=?)}
  0 2 1 {SEARCH TABLE composer USING INTEGER PRIMARY KEY (rowid=?)}
  0 0 0 {USE TEMP B-TREE FOR DISTINCT}
}

#-------------------------------------------------------------------------
#
do_execsql_test 9.1 {
  CREATE TABLE t1(
    a,b,c,d,e, f,g,h,i,j,
    k,l,m,n,o, p,q,r,s,t
  );
  CREATE INDEX i1 ON t1(k,l,m,n,o,p,q,r,s,t);
}
do_test 9.2 {
  for {set i 0} {$i < 100} {incr i} {
    execsql { INSERT INTO t1 DEFAULT VALUES }
  }
  execsql {
    ANALYZE;
    CREATE INDEX i2 ON t1(a,b,c,d,e,f,g,h,i,j);
  }
} {}

set L [list a=? b=? c=? d=? e=? f=? g=? h=? i=? j=?]
foreach {tn nTerm nRow} {
  1   1 10
  2   2  9
  3   3  8
  4   4  7
  5   5  6
  6   6  5
  7   7  5
  8   8  5
  9   9  5
  10 10  5
} {
  set w [join [lrange $L 0 [expr $nTerm-1]] " AND "]
  set p1 [expr ($nRow-1) / 100.0]
  set p2 [expr ($nRow+1) / 100.0]

  set sql1 "SELECT * FROM t1 WHERE likelihood(k=?, $p1) AND $w"
  set sql2 "SELECT * FROM t1 WHERE likelihood(k=?, $p2) AND $w"

  do_eqp_test 9.3.$tn.1 $sql1 {/INDEX i1/}
  do_eqp_test 9.3.$tn.2 $sql2 {/INDEX i2/}
}



finish_test

    h DEFAULT ( substr('abcd', 0, 2) || 'cd' ),
    i DEFAULT CURRENT_TIME,
    j DEFAULT CURRENT_DATE,
    k DEFAULT CURRENT_TIMESTAMP
  );
} {}

# EVIDENCE-OF: R-10288-43169 For the purposes of the DEFAULT clause, an
# expression is considered constant provided that it does not contain
# any sub-queries or string constants enclosed in double quotes.

#
do_createtable_tests 3.4.1 -error {
  default value of column [x] is not constant
} {
  1   {CREATE TABLE t5(x DEFAULT ( (SELECT 1) ))}  {}
  2   {CREATE TABLE t5(x DEFAULT ( "abc" ))}  {}
  3   {CREATE TABLE t5(x DEFAULT ( 1 IN (SELECT 1) ))}  {}

    h DEFAULT ( substr('abcd', 0, 2) || 'cd' ),
    i DEFAULT CURRENT_TIME,
    j DEFAULT CURRENT_DATE,
    k DEFAULT CURRENT_TIMESTAMP
  );
} {}

# EVIDENCE-OF: R-36381-62919 For the purposes of the DEFAULT clause, an
# expression is considered constant provided that it does not contain
# any sub-queries, column or table references, or string literals
# enclosed in double-quotes instead of single-quotes.
#
do_createtable_tests 3.4.1 -error {
  default value of column [x] is not constant
} {
  1   {CREATE TABLE t5(x DEFAULT ( (SELECT 1) ))}  {}
  2   {CREATE TABLE t5(x DEFAULT ( "abc" ))}  {}
  3   {CREATE TABLE t5(x DEFAULT ( 1 IN (SELECT 1) ))}  {}

#-------------------------------------------------------------------------
# EVIDENCE-OF: R-07280-60510 Assuming the library is compiled with
# foreign key constraints enabled, it must still be enabled by the
# application at runtime, using the PRAGMA foreign_keys command.
#
# This also tests that foreign key constraints are disabled by default.
#
# EVIDENCE-OF: R-59578-04990 Foreign key constraints are disabled by
# default (for backwards compatibility), so must be enabled separately
# for each database connection separately.
#
drop_all_tables
do_test e_fkey-4.1 {
  execsql {
    CREATE TABLE p(i PRIMARY KEY);
    CREATE TABLE c(j REFERENCES p ON UPDATE CASCADE);
    INSERT INTO p VALUES('hello');
................................................................................
    INSERT INTO c VALUES('hello');
    UPDATE p SET i = 'world';
    SELECT * FROM c;
  } 
} {world}

#-------------------------------------------------------------------------
# EVIDENCE-OF: R-15278-54456 The application can can also use a PRAGMA
# foreign_keys statement to determine if foreign keys are currently
# enabled.

#
# This also tests the example code in section 2 of foreignkeys.in.
#
# EVIDENCE-OF: R-11255-19907
# 
reset_db
do_test e_fkey-5.1 {
................................................................................
  } {5}
}

#-------------------------------------------------------------------------
# The setting of the recursive_triggers pragma does not affect foreign
# key actions.
#
# EVIDENCE-OF: R-51769-32730 The PRAGMA recursive_triggers setting does
# not not affect the operation of foreign key actions.
#
foreach recursive_triggers_setting [list 0 1 ON OFF] {
  drop_all_tables
  execsql "PRAGMA recursive_triggers = $recursive_triggers_setting"

  do_test e_fkey-64.$recursive_triggers_setting.1 {
    execsql {

#-------------------------------------------------------------------------
# EVIDENCE-OF: R-07280-60510 Assuming the library is compiled with
# foreign key constraints enabled, it must still be enabled by the
# application at runtime, using the PRAGMA foreign_keys command.
#
# This also tests that foreign key constraints are disabled by default.
#
# EVIDENCE-OF: R-44261-39702 Foreign key constraints are disabled by
# default (for backwards compatibility), so must be enabled separately
# for each database connection.
#
drop_all_tables
do_test e_fkey-4.1 {
  execsql {
    CREATE TABLE p(i PRIMARY KEY);
    CREATE TABLE c(j REFERENCES p ON UPDATE CASCADE);
    INSERT INTO p VALUES('hello');
................................................................................
    INSERT INTO c VALUES('hello');
    UPDATE p SET i = 'world';
    SELECT * FROM c;
  } 
} {world}

#-------------------------------------------------------------------------
# EVIDENCE-OF: R-08013-37737 The application can also use a PRAGMA
# foreign_keys statement to determine if foreign keys are currently
# enabled.

#
# This also tests the example code in section 2 of foreignkeys.in.
#
# EVIDENCE-OF: R-11255-19907
# 
reset_db
do_test e_fkey-5.1 {
................................................................................
  } {5}
}

#-------------------------------------------------------------------------
# The setting of the recursive_triggers pragma does not affect foreign
# key actions.
#
# EVIDENCE-OF: R-44355-00270 The PRAGMA recursive_triggers setting does
# not affect the operation of foreign key actions.
#
foreach recursive_triggers_setting [list 0 1 ON OFF] {
  drop_all_tables
  execsql "PRAGMA recursive_triggers = $recursive_triggers_setting"

  do_test e_fkey-64.$recursive_triggers_setting.1 {
    execsql {

  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (UNION ALL)} 
}
do_eqp_test 4.2.3 {
  SELECT * FROM t1 UNION SELECT * FROM t2 ORDER BY 1
} {
  1 0 0 {SCAN TABLE t1} 
  1 0 0 {USE TEMP B-TREE FOR ORDER BY}
  2 0 0 {SCAN TABLE t2} 
  2 0 0 {USE TEMP B-TREE FOR ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (UNION)} 
}
do_eqp_test 4.2.4 {
  SELECT * FROM t1 INTERSECT SELECT * FROM t2 ORDER BY 1
} {
  1 0 0 {SCAN TABLE t1} 
  1 0 0 {USE TEMP B-TREE FOR ORDER BY}
  2 0 0 {SCAN TABLE t2} 
  2 0 0 {USE TEMP B-TREE FOR ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (INTERSECT)} 
}
do_eqp_test 4.2.5 {
  SELECT * FROM t1 EXCEPT SELECT * FROM t2 ORDER BY 1
} {
  1 0 0 {SCAN TABLE t1} 
  1 0 0 {USE TEMP B-TREE FOR ORDER BY}
  2 0 0 {SCAN TABLE t2} 
  2 0 0 {USE TEMP B-TREE FOR ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (EXCEPT)} 
}

do_eqp_test 4.3.1 {
  SELECT x FROM t1 UNION SELECT x FROM t2
} {
  1 0 0 {SCAN TABLE t1} 

  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (UNION ALL)} 
}
do_eqp_test 4.2.3 {
  SELECT * FROM t1 UNION SELECT * FROM t2 ORDER BY 1
} {
  1 0 0 {SCAN TABLE t1} 
  1 0 0 {USE TEMP B-TREE FOR ORDER BY}
  2 0 0 {SCAN TABLE t2 USING INDEX t2i1} 
  2 0 0 {USE TEMP B-TREE FOR RIGHT PART OF ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (UNION)} 
}
do_eqp_test 4.2.4 {
  SELECT * FROM t1 INTERSECT SELECT * FROM t2 ORDER BY 1
} {
  1 0 0 {SCAN TABLE t1} 
  1 0 0 {USE TEMP B-TREE FOR ORDER BY}
  2 0 0 {SCAN TABLE t2 USING INDEX t2i1} 
  2 0 0 {USE TEMP B-TREE FOR RIGHT PART OF ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (INTERSECT)} 
}
do_eqp_test 4.2.5 {
  SELECT * FROM t1 EXCEPT SELECT * FROM t2 ORDER BY 1
} {
  1 0 0 {SCAN TABLE t1} 
  1 0 0 {USE TEMP B-TREE FOR ORDER BY}
  2 0 0 {SCAN TABLE t2 USING INDEX t2i1} 
  2 0 0 {USE TEMP B-TREE FOR RIGHT PART OF ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (EXCEPT)} 
}

do_eqp_test 4.3.1 {
  SELECT x FROM t1 UNION SELECT x FROM t2
} {
  1 0 0 {SCAN TABLE t1} 

# Queries use partial indices as appropriate times.
#
do_test index6-2.1 {
  execsql {
    CREATE TABLE t2(a,b);
    INSERT INTO t2(a,b) SELECT value, value FROM nums WHERE value<1000;
    UPDATE t2 SET a=NULL WHERE b%5==0;
    CREATE INDEX t2a1 ON t2(a) WHERE a IS NOT NULL;
    SELECT count(*) FROM t2 WHERE a IS NOT NULL;
  }
} {800}
do_test index6-2.2 {
  execsql {
    EXPLAIN QUERY PLAN
    SELECT * FROM t2 WHERE a=5;
  }
} {/.* TABLE t2 USING INDEX t2a1 .*/}
ifcapable stat4||stat3 {

  do_test index6-2.3stat4 {
    execsql {
      EXPLAIN QUERY PLAN
      SELECT * FROM t2 WHERE a IS NOT NULL;
    }
  } {/.* TABLE t2 USING INDEX t2a1 .*/}
} else {

# Queries use partial indices as appropriate times.
#
do_test index6-2.1 {
  execsql {
    CREATE TABLE t2(a,b);
    INSERT INTO t2(a,b) SELECT value, value FROM nums WHERE value<1000;
    UPDATE t2 SET a=NULL WHERE b%2==0;
    CREATE INDEX t2a1 ON t2(a) WHERE a IS NOT NULL;
    SELECT count(*) FROM t2 WHERE a IS NOT NULL;
  }
} {500}
do_test index6-2.2 {
  execsql {
    EXPLAIN QUERY PLAN
    SELECT * FROM t2 WHERE a=5;
  }
} {/.* TABLE t2 USING INDEX t2a1 .*/}
ifcapable stat4||stat3 {
  execsql ANALYZE
  do_test index6-2.3stat4 {
    execsql {
      EXPLAIN QUERY PLAN
      SELECT * FROM t2 WHERE a IS NOT NULL;
    }
  } {/.* TABLE t2 USING INDEX t2a1 .*/}
} else {

  INSERT INTO sqlite_stat1 VALUES('t1','t1bc','1000000 10 9');
  INSERT INTO sqlite_stat1 VALUES('t2','t2bc','100 10 5');
  ANALYZE sqlite_master;

  EXPLAIN QUERY PLAN
  SELECT * FROM t2 WHERE a=0 ORDER BY a, b, c;
} {~/B-TREE/}

do_execsql_test 2.1b {
  EXPLAIN QUERY PLAN
  SELECT * FROM t1 WHERE a=0 ORDER BY a, b, c;
} {/B-TREE/}


do_execsql_test 2.2 {
  EXPLAIN QUERY PLAN
  SELECT * FROM t1 WHERE +a=0 ORDER BY a, b, c;
} {/B-TREE/}
do_execsql_test 2.3 {
  EXPLAIN QUERY PLAN

  INSERT INTO sqlite_stat1 VALUES('t1','t1bc','1000000 10 9');
  INSERT INTO sqlite_stat1 VALUES('t2','t2bc','100 10 5');
  ANALYZE sqlite_master;

  EXPLAIN QUERY PLAN
  SELECT * FROM t2 WHERE a=0 ORDER BY a, b, c;
} {~/B-TREE/}

do_execsql_test 2.1b {
  EXPLAIN QUERY PLAN
  SELECT * FROM t1 WHERE likelihood(a=0, 0.05) ORDER BY a, b, c;
} {/B-TREE/}


do_execsql_test 2.2 {
  EXPLAIN QUERY PLAN
  SELECT * FROM t1 WHERE +a=0 ORDER BY a, b, c;
} {/B-TREE/}
do_execsql_test 2.3 {
  EXPLAIN QUERY PLAN

# 2014-04-25
#
# 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 implements regression tests for SQLite library.  The
# focus of this file is testing ORDER BY optimizations on joins
# that involve virtual tables.
#


set testdir [file dirname $argv0]
source $testdir/tester.tcl
set ::testprefix orderby7

ifcapable !fts3 {
  finish_test
  return
}

do_execsql_test 1.0 {
  CREATE VIRTUAL TABLE fts USING fts3(content TEXT);
  INSERT INTO fts(rowid,content)
     VALUES(1,'this is a test of the fts3 virtual'),
           (2,'table used as part of a join together'),
           (3,'with the DISTINCT keyword.  There was'),
           (4,'a bug at one time (2013-06 through 2014-04)'),
           (5,'that prevented this from working correctly.'),
           (11,'a row that occurs twice'),
           (12,'a row that occurs twice');
 
  CREATE TABLE t1(x TEXT PRIMARY KEY, y);
  INSERT OR IGNORE INTO t1 SELECT content, rowid+100 FROM fts;
} {}
do_execsql_test 1.1 {
  SELECT DISTINCT fts.rowid, t1.y
    FROM fts, t1
   WHERE fts MATCH 'that twice'
     AND content=x
   ORDER BY y;
} {11 111 12 111}
do_execsql_test 1.2 {
  SELECT DISTINCT fts.rowid, t1.x
    FROM fts, t1
   WHERE fts MATCH 'that twice'
     AND content=x
   ORDER BY 1;
} {11 {a row that occurs twice} 12 {a row that occurs twice}}
do_execsql_test 1.3 {
  SELECT DISTINCT t1.x
    FROM fts, t1
   WHERE fts MATCH 'that twice'
     AND content=x
   ORDER BY 1;
} {{a row that occurs twice}}
do_execsql_test 1.4 {
  SELECT t1.x
    FROM fts, t1
   WHERE fts MATCH 'that twice'
     AND content=x
   ORDER BY 1;
} {{a row that occurs twice} {a row that occurs twice}}
do_execsql_test 1.5 {
  SELECT DISTINCT t1.x
    FROM fts, t1
   WHERE fts MATCH 'that twice'
     AND content=x;
} {{a row that occurs twice}}
do_execsql_test 1.6 {
  SELECT t1.x
    FROM fts, t1
   WHERE fts MATCH 'that twice'
     AND content=x;
} {{a row that occurs twice} {a row that occurs twice}}

do_execsql_test 2.1 {
  SELECT DISTINCT t1.x
    FROM fts, t1
   WHERE fts.rowid=11
     AND content=x
   ORDER BY fts.rowid;
} {{a row that occurs twice}}
do_execsql_test 2.2 {
  SELECT DISTINCT t1.*
    FROM fts, t1
   WHERE fts.rowid=11
     AND content=x
   ORDER BY fts.rowid;
} {{a row that occurs twice} 111}
do_execsql_test 2.3 {
  SELECT DISTINCT t1.*
    FROM fts, t1
   WHERE fts.rowid=11
     AND content=x
   ORDER BY t1.y
} {{a row that occurs twice} 111}




finish_test

# explicit sort order and explicit collating secquites) and
# with and without optional LIMIT and OFFSET clauses.
#
# $Id: selectA.test,v 1.6 2008/08/21 14:24:29 drh Exp $

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


ifcapable !compound {
  finish_test
  return
}

do_test selectA-1.0 {
................................................................................
        UNION SELECT a,b,c FROM t3
        ORDER BY y COLLATE NOCASE DESC,x,z)))
      UNION ALL
      SELECT n || '+' FROM xyz WHERE length(n)<5
    )
  SELECT n FROM xyz ORDER BY +n;
} {MAD MAD+ MAD++}

































































finish_test

# explicit sort order and explicit collating secquites) and
# with and without optional LIMIT and OFFSET clauses.
#
# $Id: selectA.test,v 1.6 2008/08/21 14:24:29 drh Exp $

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

ifcapable !compound {
  finish_test
  return
}

do_test selectA-1.0 {
................................................................................
        UNION SELECT a,b,c FROM t3
        ORDER BY y COLLATE NOCASE DESC,x,z)))
      UNION ALL
      SELECT n || '+' FROM xyz WHERE length(n)<5
    )
  SELECT n FROM xyz ORDER BY +n;
} {MAD MAD+ MAD++}

#-------------------------------------------------------------------------
# At one point the following code exposed a temp register reuse problem.
#
proc f {args} { return 1 }
db func f f

do_execsql_test 4.1.1 {
  CREATE TABLE t4(a, b);
  CREATE TABLE t5(c, d);

  INSERT INTO t5 VALUES(1, 'x');
  INSERT INTO t5 VALUES(2, 'x');
  INSERT INTO t4 VALUES(3, 'x');
  INSERT INTO t4 VALUES(4, 'x');

  CREATE INDEX i1 ON t4(a);
  CREATE INDEX i2 ON t5(c);
}

do_eqp_test 4.1.2 {
  SELECT c, d FROM t5 
  UNION ALL
  SELECT a, b FROM t4 WHERE f()==f()
  ORDER BY 1,2
} {
  1 0 0 {SCAN TABLE t5 USING INDEX i2} 
  1 0 0 {USE TEMP B-TREE FOR RIGHT PART OF ORDER BY}
  2 0 0 {SCAN TABLE t4 USING INDEX i1} 
  2 0 0 {USE TEMP B-TREE FOR RIGHT PART OF ORDER BY}
  0 0 0 {COMPOUND SUBQUERIES 1 AND 2 (UNION ALL)}
}

do_execsql_test 4.1.3 {
  SELECT c, d FROM t5 
  UNION ALL
  SELECT a, b FROM t4 WHERE f()==f()
  ORDER BY 1,2
} {
  1 x 2 x 3 x 4 x
}

do_execsql_test 4.2.1 {
  CREATE TABLE t6(a, b);
  CREATE TABLE t7(c, d);

  INSERT INTO t7 VALUES(2, 9);
  INSERT INTO t6 VALUES(3, 0);
  INSERT INTO t6 VALUES(4, 1);
  INSERT INTO t7 VALUES(5, 6);
  INSERT INTO t6 VALUES(6, 0);
  INSERT INTO t7 VALUES(7, 6);

  CREATE INDEX i6 ON t6(a);
  CREATE INDEX i7 ON t7(c);
}

do_execsql_test 4.2.2 {
  SELECT c, f(d,c,d,c,d) FROM t7
  UNION ALL
  SELECT a, b FROM t6 
  ORDER BY 1,2
} {/2 . 3 . 4 . 5 . 6 . 7 ./}


finish_test

#!/usr/bin/tclsh
#
# This script displays the field of rectangles used by --testset rtree
# of speedtest1.  Run this script as follows:
#
#      rm test.db
#      ./speedtest1 --testset rtree --size 25 test.db
#      sqlite3 --separator ' ' test.db 'SELECT * FROM rt1' >data.txt
#      wish show_speedtest1_rtree.tcl
#
# The filename "data.txt" is hard coded into this script and so that name
# must be used on lines 3 and 4 above.  Elsewhere, different filenames can
# be used.  The --size N parameter can be adjusted as desired.
#
package require Tk
set f [open data.txt rb]
set data [read $f]
close $f
canvas .c
frame .b
button .b.b1 -text X-Y -command refill-xy
button .b.b2 -text X-Z -command refill-xz
button .b.b3 -text Y-Z -command refill-yz
pack .b.b1 .b.b2 .b.b3 -side left
pack .c -side top -fill both -expand 1
pack .b -side top
proc resize_canvas_to_fit {} {
  foreach {x0 y0 x1 y1} [.c bbox all] break
  set w [expr {$x1-$x0}]
  set h [expr {$y1-$y0}]
  .c config -width $w -height $h
}
proc refill-xy {} {
  .c delete all
  foreach {id x0 x1 y0 y1 z0 z1} $::data {
    .c create rectangle $x0 $y0 $x1 $y1
  }
  .c scale all 0 0 0.05 0.05
  resize_canvas_to_fit
}
proc refill-xz {} {
  .c delete all
  foreach {id x0 x1 y0 y1 z0 z1} $::data {
    .c create rectangle $x0 $z0 $x1 $z1
  }
  .c scale all 0 0 0.05 0.05
  resize_canvas_to_fit
}
proc refill-yz {} {
  .c delete all
  foreach {id x0 x1 y0 y1 z0 z1} $::data {
    .c create rectangle $y0 $z0 $y1 $z1
  }
  .c scale all 0 0 0.05 0.05
  resize_canvas_to_fit
}
refill-xy

#
do_execsql_test skipscan2-1.4 {
  ANALYZE;
  -- We do not have enough people above to actually force the use
  -- of a skip-scan.  So make a manual adjustment to the stat1 table
  -- to make it seem like there are many more.
  UPDATE sqlite_stat1 SET stat='10000 5000 20' WHERE idx='people_idx1';

  ANALYZE sqlite_master;
}
db cache flush
do_execsql_test skipscan2-1.5 {
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-1.5eqp {

#
do_execsql_test skipscan2-1.4 {
  ANALYZE;
  -- We do not have enough people above to actually force the use
  -- of a skip-scan.  So make a manual adjustment to the stat1 table
  -- to make it seem like there are many more.
  UPDATE sqlite_stat1 SET stat='10000 5000 20' WHERE idx='people_idx1';
  UPDATE sqlite_stat1 SET stat='10000 1' WHERE idx='sqlite_autoindex_people_1';
  ANALYZE sqlite_master;
}
db cache flush
do_execsql_test skipscan2-1.5 {
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-1.5eqp {

  "  --sqlonly           No-op.  Only show the SQL that would have been run.\n"
  "  --size N            Relative test size.  Default=100\n"
  "  --stats             Show statistics at the end\n"
  "  --testset T         Run test-set T\n"
  "  --trace             Turn on SQL tracing\n"
  "  --utf16be           Set text encoding to UTF-16BE\n"
  "  --utf16le           Set text encoding to UTF-16LE\n"

  "  --without-rowid     Use WITHOUT ROWID where appropriate\n"
;


#include "sqlite3.h"
#include <assert.h>
#include <stdio.h>
................................................................................
  sqlite3_stmt *pStmt;       /* Current SQL statement */
  sqlite3_int64 iStart;      /* Start-time for the current test */
  sqlite3_int64 iTotal;      /* Total time */
  int bWithoutRowid;         /* True for --without-rowid */
  int bReprepare;            /* True to reprepare the SQL on each rerun */
  int bSqlOnly;              /* True to print the SQL once only */
  int bExplain;              /* Print SQL with EXPLAIN prefix */

  int szTest;                /* Scale factor for test iterations */
  const char *zWR;           /* Might be WITHOUT ROWID */
  const char *zNN;           /* Might be NOT NULL */
  const char *zPK;           /* Might be UNIQUE or PRIMARY KEY */
  unsigned int x, y;         /* Pseudo-random number generator state */
  int nResult;               /* Size of the current result */
  char zResult[3000];        /* Text of the current result */
................................................................................
    ");",
    nElem, nElem
  );
  speedtest1_run();
  speedtest1_end_test();

}


















































































































































































/*
** A testset used for debugging speedtest1 itself.
*/
void testset_debug1(void){
  unsigned i, n;
  unsigned x1, x2;
................................................................................
        zTSet = argv[++i];
      }else if( strcmp(z,"trace")==0 ){
        doTrace = 1;
      }else if( strcmp(z,"utf16le")==0 ){
        zEncoding = "utf16le";
      }else if( strcmp(z,"utf16be")==0 ){
        zEncoding = "utf16be";


      }else if( strcmp(z,"without-rowid")==0 ){
        g.zWR = "WITHOUT ROWID";
        g.zPK = "PRIMARY KEY";
      }else if( strcmp(z, "help")==0 || strcmp(z,"?")==0 ){
        printf(zHelp, argv[0]);
        exit(0);
      }else{
................................................................................
  if( g.bExplain ) printf(".explain\n.echo on\n");
  if( strcmp(zTSet,"main")==0 ){
    testset_main();
  }else if( strcmp(zTSet,"debug1")==0 ){
    testset_debug1();
  }else if( strcmp(zTSet,"cte")==0 ){
    testset_cte();


  }else{
    fatal_error("unknown testset: \"%s\"\n", zTSet);

  }
  speedtest1_final();

  /* Database connection statistics printed after both prepared statements
  ** have been finalized */
#if SQLITE_VERSION_NUMBER>=3007009
  if( showStats ){

  "  --sqlonly           No-op.  Only show the SQL that would have been run.\n"
  "  --size N            Relative test size.  Default=100\n"
  "  --stats             Show statistics at the end\n"
  "  --testset T         Run test-set T\n"
  "  --trace             Turn on SQL tracing\n"
  "  --utf16be           Set text encoding to UTF-16BE\n"
  "  --utf16le           Set text encoding to UTF-16LE\n"
  "  --verify            Run additional verification steps.\n"
  "  --without-rowid     Use WITHOUT ROWID where appropriate\n"
;


#include "sqlite3.h"
#include <assert.h>
#include <stdio.h>
................................................................................
  sqlite3_stmt *pStmt;       /* Current SQL statement */
  sqlite3_int64 iStart;      /* Start-time for the current test */
  sqlite3_int64 iTotal;      /* Total time */
  int bWithoutRowid;         /* True for --without-rowid */
  int bReprepare;            /* True to reprepare the SQL on each rerun */
  int bSqlOnly;              /* True to print the SQL once only */
  int bExplain;              /* Print SQL with EXPLAIN prefix */
  int bVerify;               /* Try to verify that results are correct */
  int szTest;                /* Scale factor for test iterations */
  const char *zWR;           /* Might be WITHOUT ROWID */
  const char *zNN;           /* Might be NOT NULL */
  const char *zPK;           /* Might be UNIQUE or PRIMARY KEY */
  unsigned int x, y;         /* Pseudo-random number generator state */
  int nResult;               /* Size of the current result */
  char zResult[3000];        /* Text of the current result */
................................................................................
    ");",
    nElem, nElem
  );
  speedtest1_run();
  speedtest1_end_test();

}

/* Generate two numbers between 1 and mx.  The first number is less than
** the second.  Usually the numbers are near each other but can sometimes
** be far apart.
*/
static void twoCoords(
  int p1, int p2,                   /* Parameters adjusting sizes */
  unsigned mx,                      /* Range of 1..mx */
  unsigned *pX0, unsigned *pX1      /* OUT: write results here */
){
  unsigned d, x0, x1, span;

  span = mx/100 + 1;
  if( speedtest1_random()%3==0 ) span *= p1;
  if( speedtest1_random()%p2==0 ) span = mx/2;
  d = speedtest1_random()%span + 1;
  x0 = speedtest1_random()%(mx-d) + 1;
  x1 = x0 + d;
  *pX0 = x0;
  *pX1 = x1;
}

/* The following routine is an R-Tree geometry callback.  It returns
** true if the object overlaps a slice on the Y coordinate between the
** two values given as arguments.  In other words
**
**     SELECT count(*) FROM rt1 WHERE id MATCH xslice(10,20);
**
** Is the same as saying:
**
**     SELECT count(*) FROM rt1 WHERE y1>=10 AND y0<=20;
*/
static int xsliceGeometryCallback(
  sqlite3_rtree_geometry *p,
  int nCoord,
  double *aCoord,
  int *pRes
){
  *pRes = aCoord[3]>=p->aParam[0] && aCoord[2]<=p->aParam[1];
  return SQLITE_OK;
}

/*
** A testset for the R-Tree virtual table
*/
void testset_rtree(int p1, int p2){
  unsigned i, n;
  unsigned mxCoord;
  unsigned x0, x1, y0, y1, z0, z1;
  unsigned iStep;
  int *aCheck = sqlite3_malloc( sizeof(int)*g.szTest*100 );

  mxCoord = 15000;
  n = g.szTest*100;
  speedtest1_begin_test(100, "%d INSERTs into an r-tree", n);
  speedtest1_exec("BEGIN");
  speedtest1_exec("CREATE VIRTUAL TABLE rt1 USING rtree(id,x0,x1,y0,y1,z0,z1)");
  speedtest1_prepare("INSERT INTO rt1(id,x0,x1,y0,y1,z0,z1)"
                     "VALUES(?1,?2,?3,?4,?5,?6,?7)");
  for(i=1; i<=n; i++){
    twoCoords(p1, p2, mxCoord, &x0, &x1);
    twoCoords(p1, p2, mxCoord, &y0, &y1);
    twoCoords(p1, p2, mxCoord, &z0, &z1);
    sqlite3_bind_int(g.pStmt, 1, i);
    sqlite3_bind_int(g.pStmt, 2, x0);
    sqlite3_bind_int(g.pStmt, 3, x1);
    sqlite3_bind_int(g.pStmt, 4, y0);
    sqlite3_bind_int(g.pStmt, 5, y1);
    sqlite3_bind_int(g.pStmt, 6, z0);
    sqlite3_bind_int(g.pStmt, 7, z1);
    speedtest1_run();
  }
  speedtest1_exec("COMMIT");
  speedtest1_end_test();

  speedtest1_begin_test(101, "Copy from rtree to a regular table");
  speedtest1_exec("CREATE TABLE t1(id INTEGER PRIMARY KEY,x0,x1,y0,y1,z0,z1)");
  speedtest1_exec("INSERT INTO t1 SELECT * FROM rt1");
  speedtest1_end_test();

  n = g.szTest*20;
  speedtest1_begin_test(110, "%d one-dimensional intersect slice queries", n);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE x0>=?1 AND x1<=?2");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    aCheck[i] = atoi(g.zResult);
  }
  speedtest1_end_test();

  if( g.bVerify ){
    n = g.szTest*20;
    speedtest1_begin_test(111, "Verify result from 1-D intersect slice queries");
    speedtest1_prepare("SELECT count(*) FROM t1 WHERE x0>=?1 AND x1<=?2");
    iStep = mxCoord/n;
    for(i=0; i<n; i++){
      sqlite3_bind_int(g.pStmt, 1, i*iStep);
      sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
      speedtest1_run();
      if( aCheck[i]!=atoi(g.zResult) ){
        fatal_error("Count disagree step %d: %d..%d.  %d vs %d",
                    i, i*iStep, (i+1)*iStep, aCheck[i], atoi(g.zResult));
      }
    }
    speedtest1_end_test();
  }
  
  n = g.szTest*20;
  speedtest1_begin_test(120, "%d one-dimensional overlap slice queries", n);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE y1>=?1 AND y0<=?2");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    aCheck[i] = atoi(g.zResult);
  }
  speedtest1_end_test();

  if( g.bVerify ){
    n = g.szTest*20;
    speedtest1_begin_test(121, "Verify result from 1-D overlap slice queries");
    speedtest1_prepare("SELECT count(*) FROM t1 WHERE y1>=?1 AND y0<=?2");
    iStep = mxCoord/n;
    for(i=0; i<n; i++){
      sqlite3_bind_int(g.pStmt, 1, i*iStep);
      sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
      speedtest1_run();
      if( aCheck[i]!=atoi(g.zResult) ){
        fatal_error("Count disagree step %d: %d..%d.  %d vs %d",
                    i, i*iStep, (i+1)*iStep, aCheck[i], atoi(g.zResult));
      }
    }
    speedtest1_end_test();
  }
  

  n = g.szTest*20;
  speedtest1_begin_test(125, "%d custom geometry callback queries", n);
  sqlite3_rtree_geometry_callback(g.db, "xslice", xsliceGeometryCallback, 0);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE id MATCH xslice(?1,?2)");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    if( aCheck[i]!=atoi(g.zResult) ){
      fatal_error("Count disagree step %d: %d..%d.  %d vs %d",
                  i, i*iStep, (i+1)*iStep, aCheck[i], atoi(g.zResult));
    }
  }
  speedtest1_end_test();

  n = g.szTest*80;
  speedtest1_begin_test(130, "%d three-dimensional intersect box queries", n);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE x1>=?1 AND x0<=?2"
                     " AND y1>=?1 AND y0<=?2 AND z1>=?1 AND z0<=?2");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    aCheck[i] = atoi(g.zResult);
  }
  speedtest1_end_test();

  n = g.szTest*100;
  speedtest1_begin_test(140, "%d rowid queries", n);
  speedtest1_prepare("SELECT * FROM rt1 WHERE id=?1");
  for(i=1; i<=n; i++){
    sqlite3_bind_int(g.pStmt, 1, i);
    speedtest1_run();
  }
  speedtest1_end_test();
}

/*
** A testset used for debugging speedtest1 itself.
*/
void testset_debug1(void){
  unsigned i, n;
  unsigned x1, x2;
................................................................................
        zTSet = argv[++i];
      }else if( strcmp(z,"trace")==0 ){
        doTrace = 1;
      }else if( strcmp(z,"utf16le")==0 ){
        zEncoding = "utf16le";
      }else if( strcmp(z,"utf16be")==0 ){
        zEncoding = "utf16be";
      }else if( strcmp(z,"verify")==0 ){
        g.bVerify = 1;
      }else if( strcmp(z,"without-rowid")==0 ){
        g.zWR = "WITHOUT ROWID";
        g.zPK = "PRIMARY KEY";
      }else if( strcmp(z, "help")==0 || strcmp(z,"?")==0 ){
        printf(zHelp, argv[0]);
        exit(0);
      }else{
................................................................................
  if( g.bExplain ) printf(".explain\n.echo on\n");
  if( strcmp(zTSet,"main")==0 ){
    testset_main();
  }else if( strcmp(zTSet,"debug1")==0 ){
    testset_debug1();
  }else if( strcmp(zTSet,"cte")==0 ){
    testset_cte();
  }else if( strcmp(zTSet,"rtree")==0 ){
    testset_rtree(6, 147);
  }else{
    fatal_error("unknown testset: \"%s\"\nChoices: main debug1 cte rtree\n",
                 zTSet);
  }
  speedtest1_final();

  /* Database connection statistics printed after both prepared statements
  ** have been finalized */
#if SQLITE_VERSION_NUMBER>=3007009
  if( showStats ){

# 2014 April 26
#
# 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.
#
#***********************************************************************
# Test that ticket f67b41381a has been resolved.
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl
set testprefix tkt-f67b41381a

do_execsql_test 1.0 {
  CREATE TABLE t1(a);
  INSERT INTO t1 VALUES(1);
  ALTER TABLE t1 ADD COLUMN b DEFAULT 2;
  CREATE TABLE t2(a, b);
  INSERT INTO t2 SELECT * FROM t1;
  SELECT * FROM t2;
} {1 2}

db cache size 0
foreach {tn tbls xfer} {
  1 { CREATE TABLE t1(a, b); CREATE TABLE t2(a, b)             }             1
  2 { CREATE TABLE t1(a, b DEFAULT 'x'); CREATE TABLE t2(a, b) }             0
  3 { CREATE TABLE t1(a, b DEFAULT 'x'); CREATE TABLE t2(a, b DEFAULT 'x') } 1
  4 { CREATE TABLE t1(a, b DEFAULT NULL); CREATE TABLE t2(a, b) }            0
  5 { CREATE TABLE t1(a DEFAULT 2, b); CREATE TABLE t2(a DEFAULT 1, b) }     1
  6 { CREATE TABLE t1(a DEFAULT 1, b); CREATE TABLE t2(a DEFAULT 1, b) }     1
  7 { CREATE TABLE t1(a DEFAULT 1, b DEFAULT 1);
      CREATE TABLE t2(a DEFAULT 3, b DEFAULT 1) }                            1
  8 { CREATE TABLE t1(a DEFAULT 1, b DEFAULT 1);
      CREATE TABLE t2(a DEFAULT 3, b DEFAULT 3) }                            0

} {

  execsql { DROP TABLE t1; DROP TABLE t2 }
  execsql $tbls

  set res 1
  db eval { EXPLAIN INSERT INTO t1 SELECT * FROM t2 } {
    if {$opcode == "Column"} { set res 0 }
  }

  do_test 2.$tn [list set res] $xfer
}

finish_test

  }
  db close
  sqlite3 db test.db
  foreach {tn sql r(ordered) r(unordered)} {
    1   "SELECT * FROM t1 ORDER BY a"
        {0 0 0 {SCAN TABLE t1 USING INDEX i1}}
        {0 0 0 {SCAN TABLE t1} 0 0 0 {USE TEMP B-TREE FOR ORDER BY}}
    2   "SELECT * FROM t1 WHERE a >?"
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?)}}
        {0 0 0 {SCAN TABLE t1}}
    3   "SELECT * FROM t1 WHERE a = ? ORDER BY rowid"
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a=?)}}
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a=?)} 
         0 0 0 {USE TEMP B-TREE FOR ORDER BY}}
    4   "SELECT max(a) FROM t1"

  }
  db close
  sqlite3 db test.db
  foreach {tn sql r(ordered) r(unordered)} {
    1   "SELECT * FROM t1 ORDER BY a"
        {0 0 0 {SCAN TABLE t1 USING INDEX i1}}
        {0 0 0 {SCAN TABLE t1} 0 0 0 {USE TEMP B-TREE FOR ORDER BY}}
    2   "SELECT * FROM t1 WHERE a > 100"
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?)}}
        {0 0 0 {SCAN TABLE t1}}
    3   "SELECT * FROM t1 WHERE a = ? ORDER BY rowid"
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a=?)}}
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a=?)} 
         0 0 0 {USE TEMP B-TREE FOR ORDER BY}}
    4   "SELECT max(a) FROM t1"

    CREATE TABLE t1(a, b);
  }
  file size test.db
} {4096}
do_test wal2-7.1.2 {
  forcecopy test.db test2.db
  forcecopy test.db-wal test2.db-wal






  hexio_write test2.db-wal 48 FF
} {1}
do_test wal2-7.1.3 {
  sqlite3 db2 test2.db
  execsql { PRAGMA wal_checkpoint } db2
  execsql { SELECT * FROM sqlite_master } db2
} {}
db close

    CREATE TABLE t1(a, b);
  }
  file size test.db
} {4096}
do_test wal2-7.1.2 {
  forcecopy test.db test2.db
  forcecopy test.db-wal test2.db-wal
  # The first 32 bytes of the WAL file contain the WAL header. Offset 48
  # is the first byte of the checksum for the first frame in the WAL. 
  # The following three lines replaces the contents of that byte with 
  # a different value.
  set newval FF
  if {$newval == [hexio_read test2.db-wal 48 1]} { set newval 00 }
  hexio_write test2.db-wal 48 $newval
} {1}
do_test wal2-7.1.3 {
  sqlite3 db2 test2.db
  execsql { PRAGMA wal_checkpoint } db2
  execsql { SELECT * FROM sqlite_master } db2
} {}
db close

# the planner into use a table for the outer loop that might be indexable
# if held until an inner loop.
# 
do_execsql_test where3-3.0 {
  CREATE TABLE t301(a INTEGER PRIMARY KEY,b,c);
  CREATE INDEX t301c ON t301(c);
  INSERT INTO t301 VALUES(1,2,3);

  CREATE TABLE t302(x, y);
  INSERT INTO t302 VALUES(4,5);
  ANALYZE;
  explain query plan SELECT * FROM t302, t301 WHERE t302.x=5 AND t301.a=t302.y;
} {
  0 0 0 {SCAN TABLE t302} 
  0 1 1 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?)}
................................................................................
  0 1 0 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?)}
}
do_execsql_test where3-3.2 {
  SELECT * FROM t301 WHERE c=3 AND a IS NULL;
} {}
do_execsql_test where3-3.3 {
  SELECT * FROM t301 WHERE c=3 AND a IS NOT NULL;
} {1 2 3}

if 0 {  # Query planner no longer does this
# Verify that when there are multiple tables in a join which must be
# full table scans that the query planner attempts put the table with
# the fewest number of output rows as the outer loop.
#
do_execsql_test where3-4.0 {

# the planner into use a table for the outer loop that might be indexable
# if held until an inner loop.
# 
do_execsql_test where3-3.0 {
  CREATE TABLE t301(a INTEGER PRIMARY KEY,b,c);
  CREATE INDEX t301c ON t301(c);
  INSERT INTO t301 VALUES(1,2,3);
  INSERT INTO t301 VALUES(2,2,3);
  CREATE TABLE t302(x, y);
  INSERT INTO t302 VALUES(4,5);
  ANALYZE;
  explain query plan SELECT * FROM t302, t301 WHERE t302.x=5 AND t301.a=t302.y;
} {
  0 0 0 {SCAN TABLE t302} 
  0 1 1 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?)}
................................................................................
  0 1 0 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?)}
}
do_execsql_test where3-3.2 {
  SELECT * FROM t301 WHERE c=3 AND a IS NULL;
} {}
do_execsql_test where3-3.3 {
  SELECT * FROM t301 WHERE c=3 AND a IS NOT NULL;
} {1 2 3 2 2 3}

if 0 {  # Query planner no longer does this
# Verify that when there are multiple tables in a join which must be
# full table scans that the query planner attempts put the table with
# the fewest number of output rows as the outer loop.
#
do_execsql_test where3-4.0 {

#***********************************************************************
# 
# Test cases for query planning decisions and the unlikely() and
# likelihood() functions.

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


do_execsql_test whereG-1.0 {
  CREATE TABLE composer(
    cid INTEGER PRIMARY KEY,
    cname TEXT
  );
  CREATE TABLE album(
................................................................................
  INSERT INTO t4 VALUES('right'),('wrong');
  SELECT DISTINCT x
   FROM (SELECT x FROM t4 GROUP BY x)
   WHERE x='right'
   ORDER BY x;
} {right}










































finish_test

#***********************************************************************
# 
# Test cases for query planning decisions and the unlikely() and
# likelihood() functions.

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

do_execsql_test whereG-1.0 {
  CREATE TABLE composer(
    cid INTEGER PRIMARY KEY,
    cname TEXT
  );
  CREATE TABLE album(
................................................................................
  INSERT INTO t4 VALUES('right'),('wrong');
  SELECT DISTINCT x
   FROM (SELECT x FROM t4 GROUP BY x)
   WHERE x='right'
   ORDER BY x;
} {right}

#-------------------------------------------------------------------------
# Test that likelihood() specifications on indexed terms are taken into 
# account by various forms of loops.
#
#   5.1.*: open ended range scans
#   5.2.*: skip-scans
#
reset_db

do_execsql_test 5.1 {
  CREATE TABLE t1(a, b, c);
  CREATE INDEX i1 ON t1(a, b);
}
do_eqp_test 5.1.2 {
  SELECT * FROM t1 WHERE a>?
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?)}}
do_eqp_test 5.1.3 {
  SELECT * FROM t1 WHERE likelihood(a>?, 0.9)
} {0 0 0 {SCAN TABLE t1}}

do_test 5.2 {
  for {set i 0} {$i < 100} {incr i} {
    execsql { INSERT INTO t1 VALUES('abc', $i, $i); }
  }
  execsql { INSERT INTO t1 SELECT 'def', b, c FROM t1; }
  execsql { ANALYZE }
} {}
do_eqp_test 5.2.2 {
  SELECT * FROM t1 WHERE likelihood(b>?, 0.01)
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (ANY(a) AND b>?)}}
do_eqp_test 5.2.3 {
  SELECT * FROM t1 WHERE likelihood(b>?, 0.9)
} {0 0 0 {SCAN TABLE t1}}

do_eqp_test 5.3.1 {
  SELECT * FROM t1 WHERE a=?
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a=?)}}
do_eqp_test 5.3.2 {
  SELECT * FROM t1 WHERE likelihood(a=?, 0.9)
} {0 0 0 {SCAN TABLE t1}}

finish_test

  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;
}

................................................................................
    }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;
}

  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<0.01 ) return -logEstFromDouble(1.0/x);
  if( x<1.0 ) return logEstFromDouble(100.0*x) - 66;
  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;
}

................................................................................
    }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]<-40 ){
      printf("%5d (%f)\n", a[i], 1.0/(double)logEstToInt(-a[i]));
    }else if( a[i]<10 ){
      printf("%5d (%f)\n", a[i], logEstToInt(a[i]+100)/1024.0);
    }else{
      sqlite3_uint64 x = logEstToInt(a[i]+100)*100/1024;
      printf("%5d (%lld.%02lld)\n", a[i], x/100, x%100);
    }
  }
  return 0;
}