Import SQLite 3.8.7.4.

third_party/sqlite/src/ext/rtree/rtree.c

 /*
 ** 2001 September 15
 **
 ** 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.
 **
@@ skipping 36 matching lines @@
 **
 **   3. The remainder of the node contains the node entries. Each entry
 **      consists of a single 8-byte integer followed by an even number
 **      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>
+#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)
 #endif
 
 typedef struct Rtree Rtree;
 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 128
+#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;
+  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 */
-  int nDim;                   /* Number of dimensions */
-  int nBytesPerCell;          /* Bytes consumed per cell */
+  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 */ 
-  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).
   */
   RtreeNode *pDeleted;
   int iReinsertHeight;        /* Height of sub-trees Reinsert() has run on */
 
   /* Statements to read/write/delete a record from xxx_node */
   sqlite3_stmt *pReadNode;
   sqlite3_stmt *pWriteNode;
   sqlite3_stmt *pDeleteNode;
 
   /* Statements to read/write/delete a record from xxx_rowid */
   sqlite3_stmt *pReadRowid;
   sqlite3_stmt *pWriteRowid;
   sqlite3_stmt *pDeleteRowid;
 
   /* Statements to read/write/delete a record from xxx_parent */
   sqlite3_stmt *pReadParent;
   sqlite3_stmt *pWriteParent;
   sqlite3_stmt *pDeleteParent;
 
-  int eCoordType;
+  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
 };
 
-/* Possible values for eCoordType: */
+/* 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
 **
 ** If an R*-tree "Reinsert" operation is required, the same number of
 ** cells are removed from the overfull node and reinserted into the tree.
 */
 #define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
 #define RTREE_REINSERT(p) RTREE_MINCELLS(p)
 #define RTREE_MAXCELLS 51
 
 /*
 ** The smallest possible node-size is (512-64)==448 bytes. And the largest
 ** 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;
-  RtreeNode *pNode;                 /* Node cursor is currently pointing at */
-  int iCell;                        /* Index of current cell in pNode */
+  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 {
-  float f;
-  int i;
+  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 double. This macro assumes that local variable pRtree points
-** to the Rtree structure associated with 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.
 */
-#define DCOORD(coord) (                           \
-  (pRtree->eCoordType==RTREE_COORD_REAL32) ?      \
-    ((double)coord.f) :                           \
-    ((double)coord.i)                             \
-)
+#ifdef SQLITE_RTREE_INT_ONLY
+# define DCOORD(coord) ((RtreeDValue)coord.i)
+#else
+# define DCOORD(coord) (                           \
+    (pRtree->eCoordType==RTREE_COORD_REAL32) ?      \
+      ((double)coord.f) :                           \
+      ((double)coord.i)                             \
+  )
+#endif
 
 /*
 ** A search constraint.
 */
 struct RtreeConstraint {
   int iCoord;                     /* Index of constrained coordinate */
   int op;                         /* Constraining operation */
-  double rValue;                  /* Constraint value. */
-  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *);
-  sqlite3_rtree_geometry *pGeom;  /* Constraint callback argument for a MATCH */
+  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
-#define RTREE_LE    0x42
-#define RTREE_LT    0x43
-#define RTREE_GE    0x44
-#define RTREE_GT    0x45
-#define RTREE_MATCH 0x46
+#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;
-  int nRef;
-  int isDirty;
-  u8 *zData;
-  RtreeNode *pNext;                 /* Next node in this hash chain */
+  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])
 
 /* 
-** Structure to store a deserialized rtree record.
+** A single cell from a node, deserialized
 */
 struct RtreeCell {
-  i64 iRowid;
-  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];
+  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 must be supplied as a blob argument to
-** the right-hand-side of an SQL MATCH operator used to constrain an
-** r-tree query.
+** 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 */
-  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *);
-  void *pContext;
-  int nParam;
-  double 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, double *, int *);
-  void *pContext;
+  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))
 #endif
 
 /*
@@ skipping 73 matching lines @@
 static void nodeZero(Rtree *pRtree, RtreeNode *p){
   memset(&p->zData[2], 0, pRtree->iNodeSize-2);
   p->isDirty = 1;
 }
 
 /*
 ** 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;
+  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){
   RtreeNode *p;
   for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
   return p;
@@ skipping 39 matching lines @@
     pNode->pParent = pParent;
     pNode->isDirty = 1;
     nodeReference(pParent);
   }
   return pNode;
 }
 
 /*
 ** Obtain a reference to an r-tree node.
 */
-static int
-nodeAcquire(
+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;
   RtreeNode *pNode;
 
   /* Check if the requested node is already in the hash table. If so,
@@ skipping 35 matching lines @@
 
   /* If the root node was just loaded, set pRtree->iDepth to the height
   ** of the r-tree structure. A height of zero means all data is stored on
   ** the root node. A height of one means the children of the root node
   ** are the leaves, and so on. If the depth as specified on the root node
   ** is greater than RTREE_MAX_DEPTH, the r-tree structure must be corrupt.
   */
   if( pNode && iNode==1 ){
     pRtree->iDepth = readInt16(pNode->zData);
     if( pRtree->iDepth>RTREE_MAX_DEPTH ){
-      rc = SQLITE_CORRUPT;
+      rc = SQLITE_CORRUPT_VTAB;
     }
   }
 
   /* If no error has occurred so far, check if the "number of entries"
   ** field on the node is too large. If so, set the return code to 
-  ** SQLITE_CORRUPT.
+  ** SQLITE_CORRUPT_VTAB.
   */
   if( pNode && rc==SQLITE_OK ){
     if( NCELL(pNode)>((pRtree->iNodeSize-4)/pRtree->nBytesPerCell) ){
-      rc = SQLITE_CORRUPT;
+      rc = SQLITE_CORRUPT_VTAB;
     }
   }
 
   if( rc==SQLITE_OK ){
     if( pNode!=0 ){
       nodeHashInsert(pRtree, pNode);
     }else{
-      rc = SQLITE_CORRUPT;
+      rc = SQLITE_CORRUPT_VTAB;
     }
     *ppNode = pNode;
   }else{
     sqlite3_free(pNode);
     *ppNode = 0;
   }
 
   return rc;
 }
 
 /*
 ** Overwrite cell iCell of node pNode with the contents of pCell.
 */
 static void nodeOverwriteCell(
-  Rtree *pRtree, 
-  RtreeNode *pNode,  
-  RtreeCell *pCell, 
-  int iCell
+  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 cell the cell with index iCell from node pNode.
+** 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);
   pNode->isDirty = 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 
+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);
 
   assert( nCell<=nMaxCell );
   if( nCell<nMaxCell ){
     nodeOverwriteCell(pRtree, pNode, pCell, nCell);
     writeInt16(&pNode->zData[2], nCell+1);
     pNode->isDirty = 1;
   }
 
   return (nCell==nMaxCell);
 }
 
 /*
 ** If the node is dirty, write it out to the database.
 */
-static int
-nodeWrite(Rtree *pRtree, RtreeNode *pNode){
+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);
     }
     sqlite3_bind_blob(p, 2, pNode->zData, pRtree->iNodeSize, SQLITE_STATIC);
     sqlite3_step(p);
     pNode->isDirty = 0;
     rc = sqlite3_reset(p);
     if( pNode->iNode==0 && rc==SQLITE_OK ){
       pNode->iNode = sqlite3_last_insert_rowid(pRtree->db);
       nodeHashInsert(pRtree, pNode);
     }
   }
   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){
+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;
       }
       if( pNode->pParent ){
         rc = nodeRelease(pRtree, pNode->pParent);
       }
       if( rc==SQLITE_OK ){
         rc = nodeWrite(pRtree, pNode);
       }
       nodeHashDelete(pRtree, pNode);
       sqlite3_free(pNode);
     }
   }
   return rc;
 }
 
 /*
 ** 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
+  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, 
-  RtreeNode *pNode, 
-  int iCell,
-  int iCoord,
-  RtreeCoord *pCoord           /* Space to write result to */
+  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, 
-  RtreeNode *pNode, 
-  int iCell,
-  RtreeCell *pCell
+  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 */
 ){
-  int ii;
+  u8 *pData;
+  u8 *pEnd;
+  RtreeCoord *pCoord;
   pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
-  for(ii=0; ii<pRtree->nDim*2; ii++){
-    nodeGetCoord(pRtree, pNode, iCell, ii, &pCell->aCoord[ii]);
+  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.
 */
 static int rtreeInit(
   sqlite3 *, void *, int, const char *const*, sqlite3_vtab **, char **, int
 );
@@ skipping 105 matching lines @@
 }
 
 
 /*
 ** 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_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 rc;
+  int ii;
   RtreeCursor *pCsr = (RtreeCursor *)cur;
   freeCursorConstraints(pCsr);
-  rc = nodeRelease(pRtree, pCsr->pNode);
+  sqlite3_free(pCsr->aPoint);
+  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
   sqlite3_free(pCsr);
-  return rc;
+  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->pNode==0);
+  return pCsr->atEOF;
 }
 
 /*
-** The r-tree constraint passed as the second argument to this function is
-** guaranteed to be a MATCH constraint.
+** 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.
 */
-static int testRtreeGeom(
-  Rtree *pRtree,                  /* R-Tree object */
-  RtreeConstraint *pConstraint,   /* MATCH constraint to test */
-  RtreeCell *pCell,               /* Cell to test */
-  int *pbRes                      /* OUT: Test result */
+#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;
-  double aCoord[RTREE_MAX_DIMENSIONS*2];
-  int nCoord = pRtree->nDim*2;
+  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 );
-  assert( pConstraint->pGeom );
+  assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );
+  assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );
 
-  for(i=0; i<nCoord; i++){
-    aCoord[i] = DCOORD(pCell->aCoord[i]);
+  if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){
+    pInfo->iRowid = readInt64(pCellData);
   }
-  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];
-    double cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
-    double 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;
-      }
+  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;
     }
   }
-
-  *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.
+** 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 int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
-  RtreeCell cell;
-  int ii;
-  *pbEof = 0;
+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 */
 
-  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
-  for(ii=0; ii<pCursor->nConstraint; ii++){
-    RtreeConstraint *p = &pCursor->aConstraint[ii];
-    double 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;
-      }
-    }
+  /* 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);
 
-    if( !res ){
-      *pbEof = 1;
-      return SQLITE_OK;
-    }
+  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;
   }
-
-  return SQLITE_OK;
+  *peWithin = NOT_WITHIN;
 }
 
 /*
-** 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.
+** 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 int descendToCell(
-  Rtree *pRtree, 
-  RtreeCursor *pCursor, 
-  int iHeight,
-  int *pEof                 /* OUT: Set to true if cannot descend */
+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 */
 ){
-  int isEof;
-  int rc;
-  int ii;
-  RtreeNode *pChild;
-  sqlite3_int64 iRowid;
+  RtreeDValue xN;      /* Coordinate value converted to a double */
 
-  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);
+  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;
   }
-  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;
+  *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;
+  return SQLITE_CORRUPT_VTAB;
 }
 
 /*
 ** Return the index of the cell containing a pointer to node pNode
 ** in its parent. If pNode is the root node, return -1.
 */
 static int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode, int *piIndex){
   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){
-  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++;
-    }
-  }
-
+  /* 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){
-  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
   RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
-
-  assert(pCsr->pNode);
-  *pRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
-
-  return SQLITE_OK;
+  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 ){
-    i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
-    sqlite3_result_int64(ctx, iRowid);
+    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
   }else{
-    RtreeCoord c;
-    nodeGetCoord(pRtree, pCsr->pNode, pCsr->iCell, i-1, &c);
+    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{
+    }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){
+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 *p;
-  sqlite3_rtree_geometry *pGeom;
-  int nBlob;
+  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;
+  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(double))!=0
+   || ((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];
+  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(p, sqlite3_value_blob(pValue), nBlob);
-  if( p->magic!=RTREE_GEOMETRY_MAGIC 
-   || nBlob!=(int)(sizeof(RtreeMatchArg) + (p->nParam-1)*sizeof(double))
-  ){
-    sqlite3_free(pGeom);
+  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;
 
-  pGeom->pContext = p->pContext;
-  pGeom->nParam = p->nParam;
-  pGeom->aParam = p->aParam;
-
-  pCons->xGeom = p->xGeom;
-  pCons->pGeom = pGeom;
+  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);
 
+  /* Reset the cursor to the same state as rtreeOpen() leaves it in. */
   freeCursorConstraints(pCsr);
+  sqlite3_free(pCsr->aPoint);
+  memset(pCsr, 0, sizeof(RtreeCursor));
+  pCsr->base.pVtab = (sqlite3_vtab*)pRtree;
+
   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]);
-    rc = findLeafNode(pRtree, iRowid, &pLeaf);
-    pCsr->pNode = pLeaf; 
-    if( pLeaf ){
-      assert( rc==SQLITE_OK );
-      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &pCsr->iCell);
+    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. 
     */
-    if( argc>0 ){
+    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);
-        assert( (idxStr==0 && argc==0) || (int)strlen(idxStr)==argc*2 );
+        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]-'a';
-          if( p->op==RTREE_MATCH ){
+          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{
-            p->rValue = sqlite3_value_double(argv[ii]);
+#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 ){
-      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) );
+      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
+** support estimatedRows. In that case this function is a no-op.
+*/
+static void setEstimatedRows(sqlite3_index_info *pIdxInfo, i64 nRow){
+#if SQLITE_VERSION_NUMBER>=3008002
+  if( sqlite3_libversion_number()>=3008002 ){
+    pIdxInfo->estimatedRows = nRow;
+  }
+#endif
+}
+
+/*
 ** Rtree virtual table module xBestIndex method. There are three
 ** table scan strategies to choose from (in order from most to 
 ** least desirable):
 **
 **   idxNum     idxStr        Strategy
 **   ------------------------------------------------
 **     1        Unused        Direct lookup by rowid.
 **     2        See below     R-tree query or full-table scan.
 **   ------------------------------------------------
 **
@@ skipping 14 matching lines @@
 **     >=        0x44 ('D')
 **      >        0x45 ('E')
 **   MATCH       0x46 ('F')
 **   ----------------------
 **
 ** The second of each pair of bytes identifies the coordinate column
 ** to which the constraint applies. The leftmost coordinate column
 ** is 'a', the second from the left 'b' etc.
 */
 static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
+  Rtree *pRtree = (Rtree*)tab;
   int rc = SQLITE_OK;
   int ii;
+  i64 nRow;                       /* Estimated rows returned by this scan */
 
   int iIdx = 0;
   char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
   memset(zIdxStr, 0, sizeof(zIdxStr));
-  UNUSED_PARAMETER(tab);
 
   assert( pIdxInfo->idxStr==0 );
   for(ii=0; ii<pIdxInfo->nConstraint && iIdx<(int)(sizeof(zIdxStr)-1); ii++){
     struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];
 
     if( p->usable && p->iColumn==0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ ){
       /* We have an equality constraint on the rowid. Use strategy 1. */
       int jj;
       for(jj=0; jj<ii; jj++){
         pIdxInfo->aConstraintUsage[jj].argvIndex = 0;
         pIdxInfo->aConstraintUsage[jj].omit = 0;
       }
       pIdxInfo->idxNum = 1;
       pIdxInfo->aConstraintUsage[ii].argvIndex = 1;
       pIdxInfo->aConstraintUsage[jj].omit = 1;
 
       /* This strategy involves a two rowid lookups on an B-Tree structures
       ** and then a linear search of an R-Tree node. This should be 
       ** considered almost as quick as a direct rowid lookup (for which 
-      ** sqlite uses an internal cost of 0.0).
+      ** sqlite uses an internal cost of 0.0). It is expected to return
+      ** a single row.
       */ 
-      pIdxInfo->estimatedCost = 10.0;
+      pIdxInfo->estimatedCost = 30.0;
+      setEstimatedRows(pIdxInfo, 1);
       return SQLITE_OK;
     }
 
     if( p->usable && (p->iColumn>0 || p->op==SQLITE_INDEX_CONSTRAINT_MATCH) ){
       u8 op;
       switch( p->op ){
         case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;
         case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;
         case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
         case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;
         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';
+      zIdxStr[iIdx++] = p->iColumn - 1 + '0';
       pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
       pIdxInfo->aConstraintUsage[ii].omit = 1;
     }
   }
 
   pIdxInfo->idxNum = 2;
   pIdxInfo->needToFreeIdxStr = 1;
   if( iIdx>0 && 0==(pIdxInfo->idxStr = sqlite3_mprintf("%s", zIdxStr)) ){
     return SQLITE_NOMEM;
   }
-  assert( iIdx>=0 );
-  pIdxInfo->estimatedCost = (2000000.0 / (double)(iIdx + 1));
+
+  nRow = pRtree->nRowEst / (iIdx + 1);
+  pIdxInfo->estimatedCost = (double)6.0 * (double)nRow;
+  setEstimatedRows(pIdxInfo, nRow);
+
   return rc;
 }
 
 /*
 ** Return the N-dimensional volumn of the cell stored in *p.
 */
-static float cellArea(Rtree *pRtree, RtreeCell *p){
-  float area = 1.0;
+static RtreeDValue cellArea(Rtree *pRtree, RtreeCell *p){
+  RtreeDValue area = (RtreeDValue)1;
   int ii;
   for(ii=0; ii<(pRtree->nDim*2); ii+=2){
-    area = area * (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
+    area = (area * (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii])));
   }
   return area;
 }
 
 /*
 ** Return the margin length of cell p. The margin length is the sum
 ** of the objects size in each dimension.
 */
-static float cellMargin(Rtree *pRtree, RtreeCell *p){
-  float margin = 0.0;
+static RtreeDValue cellMargin(Rtree *pRtree, RtreeCell *p){
+  RtreeDValue margin = (RtreeDValue)0;
   int ii;
   for(ii=0; ii<(pRtree->nDim*2); ii+=2){
     margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
   }
   return margin;
 }
 
 /*
 ** Store the union of cells p1 and p2 in p1.
 */
@@ skipping 27 matching lines @@
     ){
       return 0;
     }
   }
   return 1;
 }
 
 /*
 ** Return the amount cell p would grow by if it were unioned with pCell.
 */
-static float cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell *pCell){
-  float area;
+static RtreeDValue cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell *pCell){
+  RtreeDValue area;
   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 float cellOverlap(
+static RtreeDValue cellOverlap(
   Rtree *pRtree, 
   RtreeCell *p, 
   RtreeCell *aCell, 
-  int nCell, 
-  int iExclude
+  int nCell
 ){
   int ii;
-  float overlap = 0.0;
+  RtreeDValue overlap = RTREE_ZERO;
   for(ii=0; ii<nCell; ii++){
-#if VARIANT_RSTARTREE_CHOOSESUBTREE
-    if( ii!=iExclude )
-#else
-    assert( iExclude==-1 );
-    UNUSED_PARAMETER(iExclude);
-#endif
-    {
-      int jj;
-      float o = 1.0;
-      for(jj=0; jj<(pRtree->nDim*2); jj+=2){
-        double x1;
-        double 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);
-        }
+    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;
     }
+    overlap += o;
   }
   return overlap;
 }
-#endif
-
-#if VARIANT_RSTARTREE_CHOOSESUBTREE
-static float cellOverlapEnlargement(
-  Rtree *pRtree, 
-  RtreeCell *p, 
-  RtreeCell *pInsert, 
-  RtreeCell *aCell, 
-  int nCell, 
-  int iExclude
-){
-  float before;
-  float 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(
   Rtree *pRtree,               /* Rtree table */
   RtreeCell *pCell,            /* Cell to insert into rtree */
   int iHeight,                 /* Height of sub-tree rooted at pCell */
   RtreeNode **ppLeaf           /* OUT: Selected leaf page */
 ){
   int rc;
   int ii;
   RtreeNode *pNode;
   rc = nodeAcquire(pRtree, 1, 0, &pNode);
 
   for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
     int iCell;
-    sqlite3_int64 iBest;
+    sqlite3_int64 iBest = 0;
 
-    float fMinGrowth;
-    float fMinArea;
-    float fMinOverlap;
+    RtreeDValue fMinGrowth = RTREE_ZERO;
+    RtreeDValue fMinArea = RTREE_ZERO;
 
     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;
-      float growth;
-      float area;
-      float overlap = 0.0;
+      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);
-      }
-      if( (iCell==0) 
-       || (overlap<fMinOverlap) 
-       || (overlap==fMinOverlap && growth<fMinGrowth)
-       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
-      ){
-        bBest = 1;
-      }
-#else
       if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
         bBest = 1;
       }
-#endif
       if( bBest ){
-        fMinOverlap = overlap;
         fMinGrowth = growth;
         fMinArea = area;
         iBest = cell.iRowid;
       }
     }
 
     sqlite3_free(aCell);
     rc = nodeAcquire(pRtree, iBest, pNode, &pChild);
     nodeRelease(pRtree, pNode);
     pNode = pChild;
@@ skipping 13 matching lines @@
   RtreeNode *pNode,                 /* Adjust ancestry of this node. */
   RtreeCell *pCell                  /* This cell was just inserted */
 ){
   RtreeNode *p = pNode;
   while( p->pParent ){
     RtreeNode *pParent = p->pParent;
     RtreeCell cell;
     int iCell;
 
     if( nodeParentIndex(pRtree, p, &iCell) ){
-      return SQLITE_CORRUPT;
+      return SQLITE_CORRUPT_VTAB;
     }
 
     nodeGetCell(pRtree, pParent, iCell, &cell);
     if( !cellContains(pRtree, &cell, pCell) ){
       cellUnion(pRtree, &cell, pCell);
       nodeOverwriteCell(pRtree, pParent, &cell, iCell);
     }
  
     p = pParent;
   }
@@ skipping 15 matching lines @@
 */
 static int parentWrite(Rtree *pRtree, sqlite3_int64 iNode, sqlite3_int64 iPar){
   sqlite3_bind_int64(pRtree->pWriteParent, 1, iNode);
   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;
-  float maxNormalInnerWidth = 0.0;
-
-  /* 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++){
-    float x1 = DCOORD(aCell[0].aCoord[i*2]);
-    float x2 = DCOORD(aCell[0].aCoord[i*2+1]);
-    float x3 = x1;
-    float x4 = x2;
-    int jj;
-
-    int iCellLeft = 0;
-    int iCellRight = 0;
-
-    for(jj=1; jj<nCell; jj++){
-      float left = DCOORD(aCell[jj].aCoord[i*2]);
-      float 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 ){
-      float 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;
-  float fDiff;
-  int ii;
-  for(ii=0; ii<nCell; ii++){
-    if( aiUsed[ii]==0 ){
-      float left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
-      float right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
-      float 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;
-  float fWaste = 0.0;
-
-  for(ii=0; ii<nCell; ii++){
-    for(jj=ii+1; jj<nCell; jj++){
-      float right = cellArea(pRtree, &aCell[jj]);
-      float growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
-      float 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:
 **
 **   aIdx      = { 0,   1,   2,   3 }
 **   aDistance = { 5.0, 2.0, 7.0, 6.0 }
 **
 ** this function sets the aIdx array to contain:
 **
 **   aIdx      = { 0,   1,   2,   3 }
 **
 ** The aSpare array is used as temporary working space by the
 ** sorting algorithm.
 */
 static void SortByDistance(
   int *aIdx, 
   int nIdx, 
-  float *aDistance, 
+  RtreeDValue *aDistance, 
   int *aSpare
 ){
   if( nIdx>1 ){
     int iLeft = 0;
     int iRight = 0;
 
     int nLeft = nIdx/2;
     int nRight = nIdx-nLeft;
     int *aLeft = aIdx;
     int *aRight = &aIdx[nLeft];
 
     SortByDistance(aLeft, nLeft, aDistance, aSpare);
     SortByDistance(aRight, nRight, aDistance, aSpare);
 
     memcpy(aSpare, aLeft, sizeof(int)*nLeft);
     aLeft = aSpare;
 
     while( iLeft<nLeft || iRight<nRight ){
       if( iLeft==nLeft ){
         aIdx[iLeft+iRight] = aRight[iRight];
         iRight++;
       }else if( iRight==nRight ){
         aIdx[iLeft+iRight] = aLeft[iLeft];
         iLeft++;
       }else{
-        float fLeft = aDistance[aLeft[iLeft]];
-        float fRight = aDistance[aRight[iRight]];
+        RtreeDValue fLeft = aDistance[aLeft[iLeft]];
+        RtreeDValue fRight = aDistance[aRight[iRight]];
         if( fLeft<fRight ){
           aIdx[iLeft+iRight] = aLeft[iLeft];
           iLeft++;
         }else{
           aIdx[iLeft+iRight] = aRight[iRight];
           iRight++;
         }
       }
     }
 
 #if 0
     /* Check that the sort worked */
     {
       int jj;
       for(jj=1; jj<nIdx; jj++){
-        float left = aDistance[aIdx[jj-1]];
-        float right = aDistance[aIdx[jj]];
+        RtreeDValue left = aDistance[aIdx[jj-1]];
+        RtreeDValue right = aDistance[aIdx[jj]];
         assert( left<=right );
       }
     }
 #endif
   }
 }
 
 /*
 ** Arguments aIdx, aCell and aSpare all point to arrays of size
 ** nIdx. The aIdx array contains the set of integers from 0 to 
@@ skipping 22 matching lines @@
     int nRight = nIdx-nLeft;
     int *aLeft = aIdx;
     int *aRight = &aIdx[nLeft];
 
     SortByDimension(pRtree, aLeft, nLeft, iDim, aCell, aSpare);
     SortByDimension(pRtree, aRight, nRight, iDim, aCell, aSpare);
 
     memcpy(aSpare, aLeft, sizeof(int)*nLeft);
     aLeft = aSpare;
     while( iLeft<nLeft || iRight<nRight ){
-      double xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
-      double xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
-      double xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
-      double xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);
+      RtreeDValue xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
+      RtreeDValue xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
+      RtreeDValue xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
+      RtreeDValue xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);
       if( (iLeft!=nLeft) && ((iRight==nRight)
        || (xleft1<xright1)
        || (xleft1==xright1 && xleft2<xright2)
       )){
         aIdx[iLeft+iRight] = aLeft[iLeft];
         iLeft++;
       }else{
         aIdx[iLeft+iRight] = aRight[iRight];
         iRight++;
       }
     }
 
 #if 0
     /* Check that the sort worked */
     {
       int jj;
       for(jj=1; jj<nIdx; jj++){
-        float xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
-        float xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
-        float xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
-        float xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
+        RtreeDValue xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
+        RtreeDValue xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
+        RtreeDValue xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
+        RtreeDValue xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
         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,
   RtreeNode *pLeft,
   RtreeNode *pRight,
   RtreeCell *pBboxLeft,
   RtreeCell *pBboxRight
 ){
   int **aaSorted;
   int *aSpare;
   int ii;
 
-  int iBestDim;
-  int iBestSplit;
-  float fBestMargin;
+  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;
   }
 
   aSpare = &((int *)&aaSorted[pRtree->nDim])[pRtree->nDim*nCell];
   memset(aaSorted, 0, nByte);
   for(ii=0; ii<pRtree->nDim; ii++){
     int jj;
     aaSorted[ii] = &((int *)&aaSorted[pRtree->nDim])[ii*nCell];
     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++){
-    float margin = 0.0;
-    float fBestOverlap;
-    float fBestArea;
-    int iBestLeft;
+    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++
     ){
       RtreeCell left;
       RtreeCell right;
       int kk;
-      float overlap;
-      float area;
+      RtreeDValue overlap;
+      RtreeDValue area;
 
       memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
       memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));
       for(kk=1; kk<(nCell-1); kk++){
         if( kk<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);
+      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;
         fBestArea = area;
       }
     }
@@ skipping 11 matching lines @@
     RtreeNode *pTarget = (ii<iBestSplit)?pLeft:pRight;
     RtreeCell *pBbox = (ii<iBestSplit)?pBboxLeft:pBboxRight;
     RtreeCell *pCell = &aCell[aaSorted[iBestDim][ii]];
     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);
-    float 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
 ){
   int (*xSetMapping)(Rtree *, sqlite3_int64, sqlite3_int64);
   xSetMapping = ((iHeight==0)?rowidWrite:parentWrite);
   if( iHeight>0 ){
@@ skipping 57 matching lines @@
   }
 
   if( !pLeft || !pRight ){
     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);
+  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.
   ** In this case avoid the all to nodeWrite().
   */
   if( SQLITE_OK!=(rc = nodeWrite(pRtree, pRight))
@@ skipping 92 matching lines @@
       ** the referenced counted node structures.
       */
       iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
       for(pTest=pLeaf; pTest && pTest->iNode!=iNode; pTest=pTest->pParent);
       if( !pTest ){
         rc2 = nodeAcquire(pRtree, iNode, 0, &pChild->pParent);
       }
     }
     rc = sqlite3_reset(pRtree->pReadParent);
     if( rc==SQLITE_OK ) rc = rc2;
-    if( rc==SQLITE_OK && !pChild->pParent ) rc = SQLITE_CORRUPT;
+    if( rc==SQLITE_OK && !pChild->pParent ) rc = SQLITE_CORRUPT_VTAB;
     pChild = pChild->pParent;
   }
   return rc;
 }
 
 static int deleteCell(Rtree *, RtreeNode *, int, int);
 
 static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
   int rc;
   int rc2;
-  RtreeNode *pParent;
+  RtreeNode *pParent = 0;
   int iCell;
 
   assert( pNode->nRef==1 );
 
   /* Remove the entry in the parent cell. */
   rc = nodeParentIndex(pRtree, pNode, &iCell);
   if( rc==SQLITE_OK ){
     pParent = pNode->pParent;
     pNode->pParent = 0;
     rc = deleteCell(pRtree, pParent, iCell, iHeight+1);
@@ skipping 92 matching lines @@
 
 static int Reinsert(
   Rtree *pRtree, 
   RtreeNode *pNode, 
   RtreeCell *pCell, 
   int iHeight
 ){
   int *aOrder;
   int *aSpare;
   RtreeCell *aCell;
-  float *aDistance;
+  RtreeDValue *aDistance;
   int nCell;
-  float aCenterCoord[RTREE_MAX_DIMENSIONS];
+  RtreeDValue aCenterCoord[RTREE_MAX_DIMENSIONS];
   int iDim;
   int ii;
   int rc = SQLITE_OK;
+  int n;
 
-  memset(aCenterCoord, 0, sizeof(float)*RTREE_MAX_DIMENSIONS);
+  memset(aCenterCoord, 0, sizeof(RtreeDValue)*RTREE_MAX_DIMENSIONS);
 
   nCell = NCELL(pNode)+1;
+  n = (nCell+1)&(~1);
 
   /* Allocate the buffers used by this operation. The allocation is
   ** relinquished before this function returns.
   */
-  aCell = (RtreeCell *)sqlite3_malloc(nCell * (
-    sizeof(RtreeCell) +         /* aCell array */
-    sizeof(int)       +         /* aOrder array */
-    sizeof(int)       +         /* aSpare array */
-    sizeof(float)               /* aDistance array */
+  aCell = (RtreeCell *)sqlite3_malloc(n * (
+    sizeof(RtreeCell)     +         /* aCell array */
+    sizeof(int)           +         /* aOrder array */
+    sizeof(int)           +         /* aSpare array */
+    sizeof(RtreeDValue)             /* aDistance array */
   ));
   if( !aCell ){
     return SQLITE_NOMEM;
   }
-  aOrder    = (int *)&aCell[nCell];
-  aSpare    = (int *)&aOrder[nCell];
-  aDistance = (float *)&aSpare[nCell];
+  aOrder    = (int *)&aCell[n];
+  aSpare    = (int *)&aOrder[n];
+  aDistance = (RtreeDValue *)&aSpare[n];
 
   for(ii=0; ii<nCell; ii++){
     if( ii==(nCell-1) ){
       memcpy(&aCell[ii], pCell, sizeof(RtreeCell));
     }else{
       nodeGetCell(pRtree, pNode, ii, &aCell[ii]);
     }
     aOrder[ii] = ii;
     for(iDim=0; iDim<pRtree->nDim; iDim++){
       aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2]);
       aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2+1]);
     }
   }
   for(iDim=0; iDim<pRtree->nDim; iDim++){
-    aCenterCoord[iDim] = aCenterCoord[iDim]/((float)nCell*2.0);
+    aCenterCoord[iDim] = (aCenterCoord[iDim]/(nCell*(RtreeDValue)2));
   }
 
   for(ii=0; ii<nCell; ii++){
-    aDistance[ii] = 0.0;
+    aDistance[ii] = RTREE_ZERO;
     for(iDim=0; iDim<pRtree->nDim; iDim++){
-      float coord = DCOORD(aCell[ii].aCoord[iDim*2+1]) - 
-          DCOORD(aCell[ii].aCoord[iDim*2]);
+      RtreeDValue coord = (DCOORD(aCell[ii].aCoord[iDim*2+1]) - 
+                               DCOORD(aCell[ii].aCoord[iDim*2]));
       aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
     }
   }
 
   SortByDistance(aOrder, nCell, aDistance, aSpare);
   nodeZero(pRtree, pNode);
 
   for(ii=0; rc==SQLITE_OK && ii<(nCell-(RTREE_MINCELLS(pRtree)+1)); ii++){
     RtreeCell *p = &aCell[aOrder[ii]];
     nodeInsertCell(pRtree, pNode, p);
@@ skipping 42 matching lines @@
   int rc = SQLITE_OK;
   if( iHeight>0 ){
     RtreeNode *pChild = nodeHashLookup(pRtree, pCell->iRowid);
     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);
       }
     }
   }
   return rc;
 }
 
 static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
   int ii;
   int rc = SQLITE_OK;
   int nCell = NCELL(pNode);
 
   for(ii=0; rc==SQLITE_OK && ii<nCell; ii++){
     RtreeNode *pInsert;
     RtreeCell cell;
     nodeGetCell(pRtree, pNode, ii, &cell);
 
     /* Find a node to store this cell in. pNode->iNode currently contains
     ** the height of the sub-tree headed by the cell.
     */
-    rc = ChooseLeaf(pRtree, &cell, pNode->iNode, &pInsert);
+    rc = ChooseLeaf(pRtree, &cell, (int)pNode->iNode, &pInsert);
     if( rc==SQLITE_OK ){
       int rc2;
-      rc = rtreeInsertCell(pRtree, pInsert, &cell, pNode->iNode);
+      rc = rtreeInsertCell(pRtree, pInsert, &cell, (int)pNode->iNode);
       rc2 = nodeRelease(pRtree, pInsert);
       if( rc==SQLITE_OK ){
         rc = rc2;
       }
     }
   }
   return rc;
 }
 
 /*
 ** Select a currently unused rowid for a new r-tree record.
 */
 static int newRowid(Rtree *pRtree, i64 *piRowid){
   int rc;
   sqlite3_bind_null(pRtree->pWriteRowid, 1);
   sqlite3_bind_null(pRtree->pWriteRowid, 2);
   sqlite3_step(pRtree->pWriteRowid);
   rc = sqlite3_reset(pRtree->pWriteRowid);
   *piRowid = sqlite3_last_insert_rowid(pRtree->db);
   return rc;
 }
 
 /*
+** Remove the entry with rowid=iDelete from the r-tree structure.
+*/
+static int rtreeDeleteRowid(Rtree *pRtree, sqlite3_int64 iDelete){
+  int rc;                         /* Return code */
+  RtreeNode *pLeaf = 0;           /* Leaf node containing record iDelete */
+  int iCell;                      /* Index of iDelete cell in pLeaf */
+  RtreeNode *pRoot;               /* Root node of rtree structure */
+
+
+  /* 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 ){
+      rc = deleteCell(pRtree, pLeaf, iCell, 0);
+    }
+    rc2 = nodeRelease(pRtree, pLeaf);
+    if( rc==SQLITE_OK ){
+      rc = rc2;
+    }
+  }
+
+  /* Delete the corresponding entry in the <rtree>_rowid table. */
+  if( rc==SQLITE_OK ){
+    sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);
+    sqlite3_step(pRtree->pDeleteRowid);
+    rc = sqlite3_reset(pRtree->pDeleteRowid);
+  }
+
+  /* Check if the root node now has exactly one child. If so, remove
+  ** it, schedule the contents of the child for reinsertion and 
+  ** reduce the tree height by one.
+  **
+  ** This is equivalent to copying the contents of the child into
+  ** the root node (the operation that Gutman's paper says to perform 
+  ** in this scenario).
+  */
+  if( rc==SQLITE_OK && pRtree->iDepth>0 && NCELL(pRoot)==1 ){
+    int rc2;
+    RtreeNode *pChild;
+    i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
+    rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
+    if( rc==SQLITE_OK ){
+      rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
+    }
+    rc2 = nodeRelease(pRtree, pChild);
+    if( rc==SQLITE_OK ) rc = rc2;
+    if( rc==SQLITE_OK ){
+      pRtree->iDepth--;
+      writeInt16(pRoot->zData, pRtree->iDepth);
+      pRoot->isDirty = 1;
+    }
+  }
+
+  /* Re-insert the contents of any underfull nodes removed from the tree. */
+  for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
+    if( rc==SQLITE_OK ){
+      rc = reinsertNodeContent(pRtree, pLeaf);
+    }
+    pRtree->pDeleted = pLeaf->pNext;
+    sqlite3_free(pLeaf);
+  }
+
+  /* Release the reference to the root node. */
+  if( rc==SQLITE_OK ){
+    rc = nodeRelease(pRtree, pRoot);
+  }else{
+    nodeRelease(pRtree, pRoot);
+  }
+
+  return rc;
+}
+
+/*
+** Rounding constants for float->double conversion.
+*/
+#define RNDTOWARDS  (1.0 - 1.0/8388608.0)  /* Round towards zero */
+#define RNDAWAY     (1.0 + 1.0/8388608.0)  /* Round away from zero */
+
+#if !defined(SQLITE_RTREE_INT_ONLY)
+/*
+** Convert an sqlite3_value into an RtreeValue (presumably a float)
+** while taking care to round toward negative or positive, respectively.
+*/
+static RtreeValue rtreeValueDown(sqlite3_value *v){
+  double d = sqlite3_value_double(v);
+  float f = (float)d;
+  if( f>d ){
+    f = (float)(d*(d<0 ? RNDAWAY : RNDTOWARDS));
+  }
+  return f;
+}
+static RtreeValue rtreeValueUp(sqlite3_value *v){
+  double d = sqlite3_value_double(v);
+  float f = (float)d;
+  if( f<d ){
+    f = (float)(d*(d<0 ? RNDTOWARDS : RNDAWAY));
+  }
+  return f;
+}
+#endif /* !defined(SQLITE_RTREE_INT_ONLY) */
+
+
+/*
 ** The xUpdate method for rtree module virtual tables.
 */
 static int rtreeUpdate(
   sqlite3_vtab *pVtab, 
   int nData, 
   sqlite3_value **azData, 
   sqlite_int64 *pRowid
 ){
   Rtree *pRtree = (Rtree *)pVtab;
   int rc = SQLITE_OK;
+  RtreeCell cell;                 /* New cell to insert if nData>1 */
+  int bHaveRowid = 0;             /* Set to 1 after new rowid is determined */
 
   rtreeReference(pRtree);
-
   assert(nData>=1);
 
-  /* If azData[0] is not an SQL NULL value, it is the rowid of a
-  ** record to delete from the r-tree table. The following block does
-  ** just that.
+  /* Constraint handling. A write operation on an r-tree table may return
+  ** SQLITE_CONSTRAINT for two reasons:
+  **
+  **   1. A duplicate rowid value, or
+  **   2. The supplied data violates the "x2>=x1" constraint.
+  **
+  ** In the first case, if the conflict-handling mode is REPLACE, then
+  ** the conflicting row can be removed before proceeding. In the second
+  ** case, SQLITE_CONSTRAINT must be returned regardless of the
+  ** conflict-handling mode specified by the user.
   */
-  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
-    i64 iDelete;                /* The rowid to delete */
-    RtreeNode *pLeaf;           /* Leaf node containing record iDelete */
-    int iCell;                  /* Index of iDelete cell in pLeaf */
-    RtreeNode *pRoot;
-
-    /* Obtain a reference to the root node to initialise 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 ){
-      iDelete = sqlite3_value_int64(azData[0]);
-      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 ){
-        rc = deleteCell(pRtree, pLeaf, iCell, 0);
-      }
-      rc2 = nodeRelease(pRtree, pLeaf);
-      if( rc==SQLITE_OK ){
-        rc = rc2;
-      }
-    }
-
-    /* Delete the corresponding entry in the <rtree>_rowid table. */
-    if( rc==SQLITE_OK ){
-      sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);
-      sqlite3_step(pRtree->pDeleteRowid);
-      rc = sqlite3_reset(pRtree->pDeleteRowid);
-    }
-
-    /* Check if the root node now has exactly one child. If so, remove
-    ** it, schedule the contents of the child for reinsertion and 
-    ** reduce the tree height by one.
-    **
-    ** This is equivalent to copying the contents of the child into
-    ** the root node (the operation that Gutman's paper says to perform 
-    ** in this scenario).
-    */
-    if( rc==SQLITE_OK && pRtree->iDepth>0 && NCELL(pRoot)==1 ){
-      int rc2;
-      RtreeNode *pChild;
-      i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
-      rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
-      if( rc==SQLITE_OK ){
-        rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
-      }
-      rc2 = nodeRelease(pRtree, pChild);
-      if( rc==SQLITE_OK ) rc = rc2;
-      if( rc==SQLITE_OK ){
-        pRtree->iDepth--;
-        writeInt16(pRoot->zData, pRtree->iDepth);
-        pRoot->isDirty = 1;
-      }
-    }
-
-    /* Re-insert the contents of any underfull nodes removed from the tree. */
-    for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
-      if( rc==SQLITE_OK ){
-        rc = reinsertNodeContent(pRtree, pLeaf);
-      }
-      pRtree->pDeleted = pLeaf->pNext;
-      sqlite3_free(pLeaf);
-    }
-
-    /* Release the reference to the root node. */
-    if( rc==SQLITE_OK ){
-      rc = nodeRelease(pRtree, pRoot);
-    }else{
-      nodeRelease(pRtree, pRoot);
-    }
-  }
-
-  /* If the azData[] array contains more than one element, elements
-  ** (azData[2]..azData[argc-1]) contain a new record to insert into
-  ** the r-tree structure.
-  */
-  if( rc==SQLITE_OK && nData>1 ){
-    /* Insert a new record into the r-tree */
-    RtreeCell cell;
+  if( nData>1 ){
     int ii;
-    RtreeNode *pLeaf;
 
     /* Populate the cell.aCoord[] array. The first coordinate is azData[3]. */
     assert( nData==(pRtree->nDim*2 + 3) );
+#ifndef SQLITE_RTREE_INT_ONLY
     if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
       for(ii=0; ii<(pRtree->nDim*2); ii+=2){
-        cell.aCoord[ii].f = (float)sqlite3_value_double(azData[ii+3]);
-        cell.aCoord[ii+1].f = (float)sqlite3_value_double(azData[ii+4]);
+        cell.aCoord[ii].f = rtreeValueDown(azData[ii+3]);
+        cell.aCoord[ii+1].f = rtreeValueUp(azData[ii+4]);
         if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
           rc = SQLITE_CONSTRAINT;
           goto constraint;
         }
       }
-    }else{
+    }else
+#endif
+    {
       for(ii=0; ii<(pRtree->nDim*2); ii+=2){
         cell.aCoord[ii].i = sqlite3_value_int(azData[ii+3]);
         cell.aCoord[ii+1].i = sqlite3_value_int(azData[ii+4]);
         if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
           rc = SQLITE_CONSTRAINT;
           goto constraint;
         }
       }
     }
 
+    /* If a rowid value was supplied, check if it is already present in 
+    ** the table. If so, the constraint has failed. */
+    if( sqlite3_value_type(azData[2])!=SQLITE_NULL ){
+      cell.iRowid = sqlite3_value_int64(azData[2]);
+      if( sqlite3_value_type(azData[0])==SQLITE_NULL
+       || sqlite3_value_int64(azData[0])!=cell.iRowid
+      ){
+        int steprc;
+        sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
+        steprc = sqlite3_step(pRtree->pReadRowid);
+        rc = sqlite3_reset(pRtree->pReadRowid);
+        if( SQLITE_ROW==steprc ){
+          if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){
+            rc = rtreeDeleteRowid(pRtree, cell.iRowid);
+          }else{
+            rc = SQLITE_CONSTRAINT;
+            goto constraint;
+          }
+        }
+      }
+      bHaveRowid = 1;
+    }
+  }
+
+  /* If azData[0] is not an SQL NULL value, it is the rowid of a
+  ** record to delete from the r-tree table. The following block does
+  ** just that.
+  */
+  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
+    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(azData[0]));
+  }
+
+  /* If the azData[] array contains more than one element, elements
+  ** (azData[2]..azData[argc-1]) contain a new record to insert into
+  ** the r-tree structure.
+  */
+  if( rc==SQLITE_OK && nData>1 ){
+    /* Insert the new record into the r-tree */
+    RtreeNode *pLeaf = 0;
+
     /* Figure out the rowid of the new row. */
-    if( sqlite3_value_type(azData[2])==SQLITE_NULL ){
+    if( bHaveRowid==0 ){
       rc = newRowid(pRtree, &cell.iRowid);
-    }else{
-      cell.iRowid = sqlite3_value_int64(azData[2]);
-      sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
-      if( SQLITE_ROW==sqlite3_step(pRtree->pReadRowid) ){
-        sqlite3_reset(pRtree->pReadRowid);
-        rc = SQLITE_CONSTRAINT;
-        goto constraint;
-      }
-      rc = sqlite3_reset(pRtree->pReadRowid);
     }
     *pRowid = cell.iRowid;
 
     if( rc==SQLITE_OK ){
       rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
     }
     if( rc==SQLITE_OK ){
       int rc2;
       pRtree->iReinsertHeight = -1;
       rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
@@ skipping 23 matching lines @@
     , pRtree->zDb, pRtree->zName, zNewName 
     , pRtree->zDb, pRtree->zName, zNewName
   );
   if( zSql ){
     rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);
     sqlite3_free(zSql);
   }
   return rc;
 }
 
+/*
+** This function populates the pRtree->nRowEst variable with an estimate
+** of the number of rows in the virtual table. If possible, this is based
+** on sqlite_stat1 data. Otherwise, use RTREE_DEFAULT_ROWEST.
+*/
+static int rtreeQueryStat1(sqlite3 *db, Rtree *pRtree){
+  const char *zFmt = "SELECT stat FROM %Q.sqlite_stat1 WHERE tbl = '%q_rowid'";
+  char *zSql;
+  sqlite3_stmt *p;
+  int rc;
+  i64 nRow = 0;
+
+  zSql = sqlite3_mprintf(zFmt, pRtree->zDb, pRtree->zName);
+  if( zSql==0 ){
+    rc = SQLITE_NOMEM;
+  }else{
+    rc = sqlite3_prepare_v2(db, zSql, -1, &p, 0);
+    if( rc==SQLITE_OK ){
+      if( sqlite3_step(p)==SQLITE_ROW ) nRow = sqlite3_column_int64(p, 0);
+      rc = sqlite3_finalize(p);
+    }else if( rc!=SQLITE_NOMEM ){
+      rc = SQLITE_OK;
+    }
+
+    if( rc==SQLITE_OK ){
+      if( nRow==0 ){
+        pRtree->nRowEst = RTREE_DEFAULT_ROWEST;
+      }else{
+        pRtree->nRowEst = MAX(nRow, RTREE_MIN_ROWEST);
+      }
+    }
+    sqlite3_free(zSql);
+  }
+
+  return rc;
+}
+
 static sqlite3_module rtreeModule = {
-  0,                         /* iVersion */
+  0,                          /* iVersion */
   rtreeCreate,                /* xCreate - create a table */
   rtreeConnect,               /* xConnect - connect to an existing table */
   rtreeBestIndex,             /* xBestIndex - Determine search strategy */
   rtreeDisconnect,            /* xDisconnect - Disconnect from a table */
   rtreeDestroy,               /* xDestroy - Drop a table */
   rtreeOpen,                  /* xOpen - open a cursor */
   rtreeClose,                 /* xClose - close a cursor */
   rtreeFilter,                /* xFilter - configure scan constraints */
   rtreeNext,                  /* xNext - advance a cursor */
   rtreeEof,                   /* xEof */
   rtreeColumn,                /* xColumn - read data */
   rtreeRowid,                 /* xRowid - read data */
   rtreeUpdate,                /* xUpdate - write data */
   0,                          /* xBegin - begin transaction */
   0,                          /* xSync - sync transaction */
   0,                          /* xCommit - commit transaction */
   0,                          /* xRollback - rollback transaction */
   0,                          /* xFindFunction - function overloading */
-  rtreeRename                 /* xRename - rename the table */
+  rtreeRename,                /* xRename - rename the table */
+  0,                          /* xSavepoint */
+  0,                          /* xRelease */
+  0                           /* xRollbackTo */
 };
 
 static int rtreeSqlInit(
   Rtree *pRtree, 
   sqlite3 *db, 
   const char *zDb, 
   const char *zPrefix, 
   int isCreate
 ){
   int rc = SQLITE_OK;
@@ skipping 17 matching lines @@
   };
   sqlite3_stmt **appStmt[N_STATEMENT];
   int i;
 
   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);"
+"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);
     sqlite3_free(zCreate);
     if( rc!=SQLITE_OK ){
       return rc;
     }
   }
 
   appStmt[0] = &pRtree->pReadNode;
   appStmt[1] = &pRtree->pWriteNode;
   appStmt[2] = &pRtree->pDeleteNode;
   appStmt[3] = &pRtree->pReadRowid;
   appStmt[4] = &pRtree->pWriteRowid;
   appStmt[5] = &pRtree->pDeleteRowid;
   appStmt[6] = &pRtree->pReadParent;
   appStmt[7] = &pRtree->pWriteParent;
   appStmt[8] = &pRtree->pDeleteParent;
 
+  rc = rtreeQueryStat1(db, pRtree);
   for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
     char *zSql = sqlite3_mprintf(azSql[i], zDb, zPrefix);
     if( zSql ){
       rc = sqlite3_prepare_v2(db, zSql, -1, appStmt[i], 0); 
     }else{
       rc = SQLITE_NOMEM;
     }
     sqlite3_free(zSql);
   }
 
@@ skipping 33 matching lines @@
 ** the root node of the tree.
 **
 ** Otherwise, for an xCreate(), use 64 bytes less than the database page-size. 
 ** This ensures that each node is stored on a single database page. If the 
 ** database page-size is so large that more than RTREE_MAXCELLS entries 
 ** would fit in a single node, use a smaller node-size.
 */
 static int getNodeSize(
   sqlite3 *db,                    /* Database handle */
   Rtree *pRtree,                  /* Rtree handle */
-  int isCreate                    /* True for xCreate, false for xConnect */
+  int isCreate,                   /* True for xCreate, false for xConnect */
+  char **pzErr                    /* OUT: Error message, if any */
 ){
   int rc;
   char *zSql;
   if( isCreate ){
-    int iPageSize;
+    int iPageSize = 0;
     zSql = sqlite3_mprintf("PRAGMA %Q.page_size", pRtree->zDb);
     rc = getIntFromStmt(db, zSql, &iPageSize);
     if( rc==SQLITE_OK ){
       pRtree->iNodeSize = iPageSize-64;
       if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){
         pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;
       }
+    }else{
+      *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
     }
   }else{
     zSql = sqlite3_mprintf(
         "SELECT length(data) FROM '%q'.'%q_node' WHERE nodeno = 1",
         pRtree->zDb, pRtree->zName
     );
     rc = getIntFromStmt(db, zSql, &pRtree->iNodeSize);
+    if( rc!=SQLITE_OK ){
+      *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
+    }
   }
 
   sqlite3_free(zSql);
   return rc;
 }
 
 /* 
 ** This function is the implementation of both the xConnect and xCreate
 ** methods of the r-tree virtual table.
 **
@@ skipping 22 matching lines @@
     "Too few columns for an rtree table",                 /* 2 */
     "Too many columns for an rtree table"                 /* 3 */
   };
 
   int iErr = (argc<6) ? 2 : argc>(RTREE_MAX_DIMENSIONS*2+4) ? 3 : argc%2;
   if( aErrMsg[iErr] ){
     *pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
     return SQLITE_ERROR;
   }
 
+  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);
+
   /* Allocate the sqlite3_vtab structure */
-  nDb = strlen(argv[1]);
-  nName = strlen(argv[2]);
+  nDb = (int)strlen(argv[1]);
+  nName = (int)strlen(argv[2]);
   pRtree = (Rtree *)sqlite3_malloc(sizeof(Rtree)+nDb+nName+2);
   if( !pRtree ){
     return SQLITE_NOMEM;
   }
   memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
   pRtree->nBusy = 1;
   pRtree->base.pModule = &rtreeModule;
   pRtree->zDb = (char *)&pRtree[1];
   pRtree->zName = &pRtree->zDb[nDb+1];
   pRtree->nDim = (argc-4)/2;
   pRtree->nBytesPerCell = 8 + pRtree->nDim*4*2;
   pRtree->eCoordType = eCoordType;
   memcpy(pRtree->zDb, argv[1], nDb);
   memcpy(pRtree->zName, argv[2], nName);
 
   /* Figure out the node size to use. */
-  rc = getNodeSize(db, pRtree, isCreate);
+  rc = getNodeSize(db, pRtree, isCreate, pzErr);
 
   /* Create/Connect to the underlying relational database schema. If
   ** that is successful, call sqlite3_declare_vtab() to configure
   ** the r-tree table schema.
   */
   if( rc==SQLITE_OK ){
     if( (rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate)) ){
       *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
     }else{
       char *zSql = sqlite3_mprintf("CREATE TABLE x(%s", argv[3]);
@@ skipping 14 matching lines @@
       }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
         *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
       }
       sqlite3_free(zSql);
     }
   }
 
   if( rc==SQLITE_OK ){
     *ppVtab = (sqlite3_vtab *)pRtree;
   }else{
+    assert( *ppVtab==0 );
+    assert( pRtree->nBusy==1 );
     rtreeRelease(pRtree);
   }
   return rc;
 }
 
 
 /*
 ** 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:
+** 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.
 */
 static void rtreenode(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
   char *zText = 0;
   RtreeNode node;
   Rtree tree;
   int ii;
 
   UNUSED_PARAMETER(nArg);
   memset(&node, 0, sizeof(RtreeNode));
   memset(&tree, 0, sizeof(Rtree));
   tree.nDim = sqlite3_value_int(apArg[0]);
   tree.nBytesPerCell = 8 + 8 * tree.nDim;
   node.zData = (u8 *)sqlite3_value_blob(apArg[1]);
 
   for(ii=0; ii<NCELL(&node); ii++){
     char zCell[512];
     int nCell = 0;
     RtreeCell cell;
     int jj;
 
     nodeGetCell(&tree, &node, ii, &cell);
     sqlite3_snprintf(512-nCell,&zCell[nCell],"%lld", cell.iRowid);
-    nCell = strlen(zCell);
+    nCell = (int)strlen(zCell);
     for(jj=0; jj<tree.nDim*2; jj++){
-      sqlite3_snprintf(512-nCell,&zCell[nCell]," %f",(double)cell.aCoord[jj].f);
-      nCell = strlen(zCell);
+#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);
     }
 
     if( zText ){
       char *zTextNew = sqlite3_mprintf("%s {%s}", zText, zCell);
       sqlite3_free(zText);
       zText = zTextNew;
     }else{
       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{
     u8 *zBlob = (u8 *)sqlite3_value_blob(apArg[0]);
     sqlite3_result_int(ctx, readInt16(zBlob));
   }
 }
 
 /*
 ** Register the r-tree module with database handle db. This creates the
 ** virtual table module "rtree" and the debugging/analysis scalar 
 ** function "rtreenode".
 */
 int sqlite3RtreeInit(sqlite3 *db){
   const int utf8 = SQLITE_UTF8;
   int rc;
 
   rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
   if( rc==SQLITE_OK ){
     rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
   }
   if( rc==SQLITE_OK ){
+#ifdef SQLITE_RTREE_INT_ONLY
+    void *c = (void *)RTREE_COORD_INT32;
+#else
     void *c = (void *)RTREE_COORD_REAL32;
+#endif
     rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
   }
   if( rc==SQLITE_OK ){
     void *c = (void *)RTREE_COORD_INT32;
     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.
+** 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 doSqlite3Free(void *p){
+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() creates an ordinary SQLite
-** scalar user function. This C function is the callback used for all such
-** registered SQL functions.
+** Each call to sqlite3_rtree_geometry_callback() or
+** sqlite3_rtree_query_callback() creates an ordinary SQLite
+** scalar function that is implemented by this routine.
 **
-** The scalar user functions return a blob that is interpreted by r-tree
-** table MATCH operators.
+** 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(double);
+  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->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, doSqlite3Free);
+    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,
-  const char *zGeom,
-  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *),
-  void *pContext
+  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
+  );
+}
 
-  /* 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
+/*
+** 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
-int sqlite3_extension_init(
+#ifdef _WIN32
+__declspec(dllexport)
+#endif
+int sqlite3_rtree_init(
   sqlite3 *db,
   char **pzErrMsg,
   const sqlite3_api_routines *pApi
 ){
   SQLITE_EXTENSION_INIT2(pApi)
   return sqlite3RtreeInit(db);
 }
 #endif
 
 #endif