Adding upstream version 3.40.1.upstream/3.40.1upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

37 files changed, 15246 insertions, 0 deletions

diff --git a/ext/rtree/README b/ext/rtree/README
new file mode 100644
index 0000000..3736f45
--- /dev/null
+++ b/ext/rtree/README
@@ -0,0 +1,120 @@
+
+This directory contains an SQLite extension that implements a virtual 
+table type that allows users to create, query and manipulate r-tree[1] 
+data structures inside of SQLite databases. Users create, populate 
+and query r-tree structures using ordinary SQL statements.
+
+    1.  SQL Interface
+
+        1.1  Table Creation
+        1.2  Data Manipulation
+        1.3  Data Querying
+        1.4  Introspection and Analysis
+
+    2.  Compilation and Deployment
+
+    3.  References
+
+
+1. SQL INTERFACE
+
+  1.1 Table Creation.
+
+    All r-tree virtual tables have an odd number of columns between
+    3 and 11. Unlike regular SQLite tables, r-tree tables are strongly 
+    typed. 
+
+    The leftmost column is always the pimary key and contains 64-bit 
+    integer values. Each subsequent column contains a 32-bit real
+    value. For each pair of real values, the first (leftmost) must be 
+    less than or equal to the second. R-tree tables may be 
+    constructed using the following syntax:
+
+      CREATE VIRTUAL TABLE <name> USING rtree(<column-names>)
+
+    For example:
+
+      CREATE VIRTUAL TABLE boxes USING rtree(boxno, xmin, xmax, ymin, ymax);
+      INSERT INTO boxes VALUES(1, 1.0, 3.0, 2.0, 4.0);
+
+    Constructing a virtual r-tree table <name> creates the following three
+    real tables in the database to store the data structure:
+
+      <name>_node
+      <name>_rowid
+      <name>_parent
+
+    Dropping or modifying the contents of these tables directly will
+    corrupt the r-tree structure. To delete an r-tree from a database,
+    use a regular DROP TABLE statement:
+
+      DROP TABLE <name>;
+
+    Dropping the main r-tree table automatically drops the automatically
+    created tables. 
+
+  1.2 Data Manipulation (INSERT, UPDATE, DELETE).
+
+    The usual INSERT, UPDATE or DELETE syntax is used to manipulate data
+    stored in an r-tree table. Please note the following:
+
+      * Inserting a NULL value into the primary key column has the
+        same effect as inserting a NULL into an INTEGER PRIMARY KEY
+        column of a regular table. The system automatically assigns
+        an unused integer key value to the new record. Usually, this
+        is one greater than the largest primary key value currently
+        present in the table.
+
+      * Attempting to insert a duplicate primary key value fails with
+        an SQLITE_CONSTRAINT error.
+
+      * Attempting to insert or modify a record such that the value
+        stored in the (N*2)th column is greater than that stored in
+        the (N*2+1)th column fails with an SQLITE_CONSTRAINT error.
+
+      * When a record is inserted, values are always converted to 
+        the required type (64-bit integer or 32-bit real) as if they
+        were part of an SQL CAST expression. Non-numeric strings are
+        converted to zero.
+
+  1.3 Queries.
+
+    R-tree tables may be queried using all of the same SQL syntax supported
+    by regular tables. However, some query patterns are more efficient
+    than others.
+
+    R-trees support fast lookup by primary key value (O(logN), like 
+    regular tables).
+
+    Any combination of equality and range (<, <=, >, >=) constraints
+    on spatial data columns may be used to optimize other queries. This
+    is the key advantage to using r-tree tables instead of creating 
+    indices on regular tables.
+
+  1.4 Introspection and Analysis.
+
+    TODO: Describe rtreenode() and rtreedepth() functions.
+
+
+2. COMPILATION AND USAGE
+
+  The easiest way to compile and use the RTREE extension is to build
+  and use it as a dynamically loadable SQLite extension. To do this
+  using gcc on *nix:
+
+    gcc -shared rtree.c -o libSqliteRtree.so
+
+  You may need to add "-I" flags so that gcc can find sqlite3ext.h
+  and sqlite3.h. The resulting shared lib, libSqliteRtree.so, may be
+  loaded into sqlite in the same way as any other dynamicly loadable
+  extension.
+
+
+3. REFERENCES
+
+  [1]  Atonin Guttman, "R-trees - A Dynamic Index Structure For Spatial 
+       Searching", University of California Berkeley, 1984.
+
+  [2]  Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, Bernhard Seeger,
+       "The R*-tree: An Efficient and Robust Access Method for Points and
+       Rectangles", Universitaet Bremen, 1990.
diff --git a/ext/rtree/geopoly.c b/ext/rtree/geopoly.c
new file mode 100644
index 0000000..7b41e79
--- /dev/null
+++ b/ext/rtree/geopoly.c
@@ -0,0 +1,1814 @@
+/*
+** 2018-05-25
+**
+** The author disclaims copyright to this source code.  In place of
+** a legal notice, here is a blessing:
+**
+**    May you do good and not evil.
+**    May you find forgiveness for yourself and forgive others.
+**    May you share freely, never taking more than you give.
+**
+******************************************************************************
+**
+** This file implements an alternative R-Tree virtual table that
+** uses polygons to express the boundaries of 2-dimensional objects.
+**
+** This file is #include-ed onto the end of "rtree.c" so that it has
+** access to all of the R-Tree internals.
+*/
+#include <stdlib.h>
+
+/* Enable -DGEOPOLY_ENABLE_DEBUG for debugging facilities */
+#ifdef GEOPOLY_ENABLE_DEBUG
+  static int geo_debug = 0;
+# define GEODEBUG(X) if(geo_debug)printf X
+#else
+# define GEODEBUG(X)
+#endif
+
+/* Character class routines */
+#ifdef sqlite3Isdigit
+   /* Use the SQLite core versions if this routine is part of the
+   ** SQLite amalgamation */
+#  define safe_isdigit(x)  sqlite3Isdigit(x)
+#  define safe_isalnum(x)  sqlite3Isalnum(x)
+#  define safe_isxdigit(x) sqlite3Isxdigit(x)
+#else
+   /* Use the standard library for separate compilation */
+#include <ctype.h>  /* amalgamator: keep */
+#  define safe_isdigit(x)  isdigit((unsigned char)(x))
+#  define safe_isalnum(x)  isalnum((unsigned char)(x))
+#  define safe_isxdigit(x) isxdigit((unsigned char)(x))
+#endif
+
+#ifndef JSON_NULL   /* The following stuff repeats things found in json1 */
+/*
+** Growing our own isspace() routine this way is twice as fast as
+** the library isspace() function.
+*/
+static const char geopolyIsSpace[] = {
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 1, 1, 0, 0, 1, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  1, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+};
+#define fast_isspace(x) (geopolyIsSpace[(unsigned char)x])
+#endif /* JSON NULL - back to original code */
+
+/* Compiler and version */
+#ifndef GCC_VERSION
+#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)
+#else
+# define GCC_VERSION 0
+#endif
+#endif
+#ifndef MSVC_VERSION
+#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define MSVC_VERSION _MSC_VER
+#else
+# define MSVC_VERSION 0
+#endif
+#endif
+
+/* Datatype for coordinates
+*/
+typedef float GeoCoord;
+
+/*
+** Internal representation of a polygon.
+**
+** The polygon consists of a sequence of vertexes.  There is a line
+** segment between each pair of vertexes, and one final segment from
+** the last vertex back to the first.  (This differs from the GeoJSON
+** standard in which the final vertex is a repeat of the first.)
+**
+** The polygon follows the right-hand rule.  The area to the right of
+** each segment is "outside" and the area to the left is "inside".
+**
+** The on-disk representation consists of a 4-byte header followed by
+** the values.  The 4-byte header is:
+**
+**      encoding    (1 byte)   0=big-endian, 1=little-endian
+**      nvertex     (3 bytes)  Number of vertexes as a big-endian integer
+**
+** Enough space is allocated for 4 coordinates, to work around over-zealous
+** warnings coming from some compiler (notably, clang). In reality, the size
+** of each GeoPoly memory allocate is adjusted as necessary so that the
+** GeoPoly.a[] array at the end is the appropriate size.
+*/
+typedef struct GeoPoly GeoPoly;
+struct GeoPoly {
+  int nVertex;          /* Number of vertexes */
+  unsigned char hdr[4]; /* Header for on-disk representation */
+  GeoCoord a[8];        /* 2*nVertex values. X (longitude) first, then Y */
+};
+
+/* The size of a memory allocation needed for a GeoPoly object sufficient
+** to hold N coordinate pairs.
+*/
+#define GEOPOLY_SZ(N)  (sizeof(GeoPoly) + sizeof(GeoCoord)*2*((N)-4))
+
+/* Macros to access coordinates of a GeoPoly.
+** We have to use these macros, rather than just say p->a[i] in order
+** to silence (incorrect) UBSAN warnings if the array index is too large.
+*/
+#define GeoX(P,I)  (((GeoCoord*)(P)->a)[(I)*2])
+#define GeoY(P,I)  (((GeoCoord*)(P)->a)[(I)*2+1])
+
+
+/*
+** State of a parse of a GeoJSON input.
+*/
+typedef struct GeoParse GeoParse;
+struct GeoParse {
+  const unsigned char *z;   /* Unparsed input */
+  int nVertex;              /* Number of vertexes in a[] */
+  int nAlloc;               /* Space allocated to a[] */
+  int nErr;                 /* Number of errors encountered */
+  GeoCoord *a;          /* Array of vertexes.  From sqlite3_malloc64() */
+};
+
+/* Do a 4-byte byte swap */
+static void geopolySwab32(unsigned char *a){
+  unsigned char t = a[0];
+  a[0] = a[3];
+  a[3] = t;
+  t = a[1];
+  a[1] = a[2];
+  a[2] = t;
+}
+
+/* Skip whitespace.  Return the next non-whitespace character. */
+static char geopolySkipSpace(GeoParse *p){
+  while( fast_isspace(p->z[0]) ) p->z++;
+  return p->z[0];
+}
+
+/* Parse out a number.  Write the value into *pVal if pVal!=0.
+** return non-zero on success and zero if the next token is not a number.
+*/
+static int geopolyParseNumber(GeoParse *p, GeoCoord *pVal){
+  char c = geopolySkipSpace(p);
+  const unsigned char *z = p->z;
+  int j = 0;
+  int seenDP = 0;
+  int seenE = 0;
+  if( c=='-' ){
+    j = 1;
+    c = z[j];
+  }
+  if( c=='0' && z[j+1]>='0' && z[j+1]<='9' ) return 0;
+  for(;; j++){
+    c = z[j];
+    if( safe_isdigit(c) ) continue;
+    if( c=='.' ){
+      if( z[j-1]=='-' ) return 0;
+      if( seenDP ) return 0;
+      seenDP = 1;
+      continue;
+    }
+    if( c=='e' || c=='E' ){
+      if( z[j-1]<'0' ) return 0;
+      if( seenE ) return -1;
+      seenDP = seenE = 1;
+      c = z[j+1];
+      if( c=='+' || c=='-' ){
+        j++;
+        c = z[j+1];
+      }
+      if( c<'0' || c>'9' ) return 0;
+      continue;
+    }
+    break;
+  }
+  if( z[j-1]<'0' ) return 0;
+  if( pVal ){
+#ifdef SQLITE_AMALGAMATION
+     /* The sqlite3AtoF() routine is much much faster than atof(), if it
+     ** is available */
+     double r;
+     (void)sqlite3AtoF((const char*)p->z, &r, j, SQLITE_UTF8);
+     *pVal = r;
+#else
+     *pVal = (GeoCoord)atof((const char*)p->z);
+#endif
+  }
+  p->z += j;
+  return 1;
+}
+
+/*
+** If the input is a well-formed JSON array of coordinates with at least
+** four coordinates and where each coordinate is itself a two-value array,
+** then convert the JSON into a GeoPoly object and return a pointer to
+** that object.
+**
+** If any error occurs, return NULL.
+*/
+static GeoPoly *geopolyParseJson(const unsigned char *z, int *pRc){
+  GeoParse s;
+  int rc = SQLITE_OK;
+  memset(&s, 0, sizeof(s));
+  s.z = z;
+  if( geopolySkipSpace(&s)=='[' ){
+    s.z++;
+    while( geopolySkipSpace(&s)=='[' ){
+      int ii = 0;
+      char c;
+      s.z++;
+      if( s.nVertex>=s.nAlloc ){
+        GeoCoord *aNew;
+        s.nAlloc = s.nAlloc*2 + 16;
+        aNew = sqlite3_realloc64(s.a, s.nAlloc*sizeof(GeoCoord)*2 );
+        if( aNew==0 ){
+          rc = SQLITE_NOMEM;
+          s.nErr++;
+          break;
+        }
+        s.a = aNew;
+      }
+      while( geopolyParseNumber(&s, ii<=1 ? &s.a[s.nVertex*2+ii] : 0) ){
+        ii++;
+        if( ii==2 ) s.nVertex++;
+        c = geopolySkipSpace(&s);
+        s.z++;
+        if( c==',' ) continue;
+        if( c==']' && ii>=2 ) break;
+        s.nErr++;
+        rc = SQLITE_ERROR;
+        goto parse_json_err;
+      }
+      if( geopolySkipSpace(&s)==',' ){
+        s.z++;
+        continue;
+      }
+      break;
+    }
+    if( geopolySkipSpace(&s)==']'
+     && s.nVertex>=4
+     && s.a[0]==s.a[s.nVertex*2-2]
+     && s.a[1]==s.a[s.nVertex*2-1]
+     && (s.z++, geopolySkipSpace(&s)==0)
+    ){
+      GeoPoly *pOut;
+      int x = 1;
+      s.nVertex--;  /* Remove the redundant vertex at the end */
+      pOut = sqlite3_malloc64( GEOPOLY_SZ((sqlite3_int64)s.nVertex) );
+      x = 1;
+      if( pOut==0 ) goto parse_json_err;
+      pOut->nVertex = s.nVertex;
+      memcpy(pOut->a, s.a, s.nVertex*2*sizeof(GeoCoord));
+      pOut->hdr[0] = *(unsigned char*)&x;
+      pOut->hdr[1] = (s.nVertex>>16)&0xff;
+      pOut->hdr[2] = (s.nVertex>>8)&0xff;
+      pOut->hdr[3] = s.nVertex&0xff;
+      sqlite3_free(s.a);
+      if( pRc ) *pRc = SQLITE_OK;
+      return pOut;
+    }else{
+      s.nErr++;
+      rc = SQLITE_ERROR;
+    }
+  }
+parse_json_err:
+  if( pRc ) *pRc = rc;
+  sqlite3_free(s.a);
+  return 0;
+}
+
+/*
+** Given a function parameter, try to interpret it as a polygon, either
+** in the binary format or JSON text.  Compute a GeoPoly object and
+** return a pointer to that object.  Or if the input is not a well-formed
+** polygon, put an error message in sqlite3_context and return NULL.
+*/
+static GeoPoly *geopolyFuncParam(
+  sqlite3_context *pCtx,      /* Context for error messages */
+  sqlite3_value *pVal,        /* The value to decode */
+  int *pRc                    /* Write error here */
+){
+  GeoPoly *p = 0;
+  int nByte;
+  testcase( pCtx==0 );
+  if( sqlite3_value_type(pVal)==SQLITE_BLOB
+   && (nByte = sqlite3_value_bytes(pVal))>=(4+6*sizeof(GeoCoord))
+  ){
+    const unsigned char *a = sqlite3_value_blob(pVal);
+    int nVertex;
+    if( a==0 ){
+      if( pCtx ) sqlite3_result_error_nomem(pCtx);
+      return 0;
+    }
+    nVertex = (a[1]<<16) + (a[2]<<8) + a[3];
+    if( (a[0]==0 || a[0]==1)
+     && (nVertex*2*sizeof(GeoCoord) + 4)==(unsigned int)nByte
+    ){
+      p = sqlite3_malloc64( sizeof(*p) + (nVertex-1)*2*sizeof(GeoCoord) );
+      if( p==0 ){
+        if( pRc ) *pRc = SQLITE_NOMEM;
+        if( pCtx ) sqlite3_result_error_nomem(pCtx);
+      }else{
+        int x = 1;
+        p->nVertex = nVertex;
+        memcpy(p->hdr, a, nByte);
+        if( a[0] != *(unsigned char*)&x ){
+          int ii;
+          for(ii=0; ii<nVertex; ii++){
+            geopolySwab32((unsigned char*)&GeoX(p,ii));
+            geopolySwab32((unsigned char*)&GeoY(p,ii));
+          }
+          p->hdr[0] ^= 1;
+        }
+      }
+    }
+    if( pRc ) *pRc = SQLITE_OK;
+    return p;
+  }else if( sqlite3_value_type(pVal)==SQLITE_TEXT ){
+    const unsigned char *zJson = sqlite3_value_text(pVal);
+    if( zJson==0 ){
+      if( pRc ) *pRc = SQLITE_NOMEM;
+      return 0;
+    }
+    return geopolyParseJson(zJson, pRc);
+  }else{
+    if( pRc ) *pRc = SQLITE_ERROR;
+    return 0;
+  }
+}
+
+/*
+** Implementation of the geopoly_blob(X) function.
+**
+** If the input is a well-formed Geopoly BLOB or JSON string
+** then return the BLOB representation of the polygon.  Otherwise
+** return NULL.
+*/
+static void geopolyBlobFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** SQL function:     geopoly_json(X)
+**
+** Interpret X as a polygon and render it as a JSON array
+** of coordinates.  Or, if X is not a valid polygon, return NULL.
+*/
+static void geopolyJsonFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3 *db = sqlite3_context_db_handle(context);
+    sqlite3_str *x = sqlite3_str_new(db);
+    int i;
+    sqlite3_str_append(x, "[", 1);
+    for(i=0; i<p->nVertex; i++){
+      sqlite3_str_appendf(x, "[%!g,%!g],", GeoX(p,i), GeoY(p,i));
+    }
+    sqlite3_str_appendf(x, "[%!g,%!g]]", GeoX(p,0), GeoY(p,0));
+    sqlite3_result_text(context, sqlite3_str_finish(x), -1, sqlite3_free);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** SQL function:     geopoly_svg(X, ....)
+**
+** Interpret X as a polygon and render it as a SVG <polyline>.
+** Additional arguments are added as attributes to the <polyline>.
+*/
+static void geopolySvgFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p;
+  if( argc<1 ) return;
+  p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3 *db = sqlite3_context_db_handle(context);
+    sqlite3_str *x = sqlite3_str_new(db);
+    int i;
+    char cSep = '\'';
+    sqlite3_str_appendf(x, "<polyline points=");
+    for(i=0; i<p->nVertex; i++){
+      sqlite3_str_appendf(x, "%c%g,%g", cSep, GeoX(p,i), GeoY(p,i));
+      cSep = ' ';
+    }
+    sqlite3_str_appendf(x, " %g,%g'", GeoX(p,0), GeoY(p,0));
+    for(i=1; i<argc; i++){
+      const char *z = (const char*)sqlite3_value_text(argv[i]);
+      if( z && z[0] ){
+        sqlite3_str_appendf(x, " %s", z);
+      }
+    }
+    sqlite3_str_appendf(x, "></polyline>");
+    sqlite3_result_text(context, sqlite3_str_finish(x), -1, sqlite3_free);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** SQL Function:      geopoly_xform(poly, A, B, C, D, E, F)
+**
+** Transform and/or translate a polygon as follows:
+**
+**      x1 = A*x0 + B*y0 + E
+**      y1 = C*x0 + D*y0 + F
+**
+** For a translation:
+**
+**      geopoly_xform(poly, 1, 0, 0, 1, x-offset, y-offset)
+**
+** Rotate by R around the point (0,0):
+**
+**      geopoly_xform(poly, cos(R), sin(R), -sin(R), cos(R), 0, 0)
+*/
+static void geopolyXformFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  double A = sqlite3_value_double(argv[1]);
+  double B = sqlite3_value_double(argv[2]);
+  double C = sqlite3_value_double(argv[3]);
+  double D = sqlite3_value_double(argv[4]);
+  double E = sqlite3_value_double(argv[5]);
+  double F = sqlite3_value_double(argv[6]);
+  GeoCoord x1, y1, x0, y0;
+  int ii;
+  if( p ){
+    for(ii=0; ii<p->nVertex; ii++){
+      x0 = GeoX(p,ii);
+      y0 = GeoY(p,ii);
+      x1 = (GeoCoord)(A*x0 + B*y0 + E);
+      y1 = (GeoCoord)(C*x0 + D*y0 + F);
+      GeoX(p,ii) = x1;
+      GeoY(p,ii) = y1;
+    }
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** Compute the area enclosed by the polygon.
+**
+** This routine can also be used to detect polygons that rotate in
+** the wrong direction.  Polygons are suppose to be counter-clockwise (CCW).
+** This routine returns a negative value for clockwise (CW) polygons.
+*/
+static double geopolyArea(GeoPoly *p){
+  double rArea = 0.0;
+  int ii;
+  for(ii=0; ii<p->nVertex-1; ii++){
+    rArea += (GeoX(p,ii) - GeoX(p,ii+1))           /* (x0 - x1) */
+              * (GeoY(p,ii) + GeoY(p,ii+1))        /* (y0 + y1) */
+              * 0.5;
+  }
+  rArea += (GeoX(p,ii) - GeoX(p,0))                /* (xN - x0) */
+           * (GeoY(p,ii) + GeoY(p,0))              /* (yN + y0) */
+           * 0.5;
+  return rArea;
+}
+
+/*
+** Implementation of the geopoly_area(X) function.
+**
+** If the input is a well-formed Geopoly BLOB then return the area
+** enclosed by the polygon.  If the polygon circulates clockwise instead
+** of counterclockwise (as it should) then return the negative of the
+** enclosed area.  Otherwise return NULL.
+*/
+static void geopolyAreaFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3_result_double(context, geopolyArea(p));
+    sqlite3_free(p);
+  }            
+}
+
+/*
+** Implementation of the geopoly_ccw(X) function.
+**
+** If the rotation of polygon X is clockwise (incorrect) instead of
+** counter-clockwise (the correct winding order according to RFC7946)
+** then reverse the order of the vertexes in polygon X.  
+**
+** In other words, this routine returns a CCW polygon regardless of the
+** winding order of its input.
+**
+** Use this routine to sanitize historical inputs that that sometimes
+** contain polygons that wind in the wrong direction.
+*/
+static void geopolyCcwFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    if( geopolyArea(p)<0.0 ){
+      int ii, jj;
+      for(ii=1, jj=p->nVertex-1; ii<jj; ii++, jj--){
+        GeoCoord t = GeoX(p,ii);
+        GeoX(p,ii) = GeoX(p,jj);
+        GeoX(p,jj) = t;
+        t = GeoY(p,ii);
+        GeoY(p,ii) = GeoY(p,jj);
+        GeoY(p,jj) = t;
+      }
+    }
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }            
+}
+
+#define GEOPOLY_PI 3.1415926535897932385
+
+/* Fast approximation for sine(X) for X between -0.5*pi and 2*pi
+*/
+static double geopolySine(double r){
+  assert( r>=-0.5*GEOPOLY_PI && r<=2.0*GEOPOLY_PI );
+  if( r>=1.5*GEOPOLY_PI ){
+    r -= 2.0*GEOPOLY_PI;
+  }
+  if( r>=0.5*GEOPOLY_PI ){
+    return -geopolySine(r-GEOPOLY_PI);
+  }else{
+    double r2 = r*r;
+    double r3 = r2*r;
+    double r5 = r3*r2;
+    return 0.9996949*r - 0.1656700*r3 + 0.0075134*r5;
+  }
+}
+
+/*
+** Function:   geopoly_regular(X,Y,R,N)
+**
+** Construct a simple, convex, regular polygon centered at X, Y
+** with circumradius R and with N sides.
+*/
+static void geopolyRegularFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  double x = sqlite3_value_double(argv[0]);
+  double y = sqlite3_value_double(argv[1]);
+  double r = sqlite3_value_double(argv[2]);
+  int n = sqlite3_value_int(argv[3]);
+  int i;
+  GeoPoly *p;
+
+  if( n<3 || r<=0.0 ) return;
+  if( n>1000 ) n = 1000;
+  p = sqlite3_malloc64( sizeof(*p) + (n-1)*2*sizeof(GeoCoord) );
+  if( p==0 ){
+    sqlite3_result_error_nomem(context);
+    return;
+  }
+  i = 1;
+  p->hdr[0] = *(unsigned char*)&i;
+  p->hdr[1] = 0;
+  p->hdr[2] = (n>>8)&0xff;
+  p->hdr[3] = n&0xff;
+  for(i=0; i<n; i++){
+    double rAngle = 2.0*GEOPOLY_PI*i/n;
+    GeoX(p,i) = x - r*geopolySine(rAngle-0.5*GEOPOLY_PI);
+    GeoY(p,i) = y + r*geopolySine(rAngle);
+  }
+  sqlite3_result_blob(context, p->hdr, 4+8*n, SQLITE_TRANSIENT);
+  sqlite3_free(p);
+}
+
+/*
+** If pPoly is a polygon, compute its bounding box. Then:
+**
+**    (1) if aCoord!=0 store the bounding box in aCoord, returning NULL
+**    (2) otherwise, compute a GeoPoly for the bounding box and return the
+**        new GeoPoly
+**
+** If pPoly is NULL but aCoord is not NULL, then compute a new GeoPoly from
+** the bounding box in aCoord and return a pointer to that GeoPoly.
+*/
+static GeoPoly *geopolyBBox(
+  sqlite3_context *context,   /* For recording the error */
+  sqlite3_value *pPoly,       /* The polygon */
+  RtreeCoord *aCoord,         /* Results here */
+  int *pRc                    /* Error code here */
+){
+  GeoPoly *pOut = 0;
+  GeoPoly *p;
+  float mnX, mxX, mnY, mxY;
+  if( pPoly==0 && aCoord!=0 ){
+    p = 0;
+    mnX = aCoord[0].f;
+    mxX = aCoord[1].f;
+    mnY = aCoord[2].f;
+    mxY = aCoord[3].f;
+    goto geopolyBboxFill;
+  }else{
+    p = geopolyFuncParam(context, pPoly, pRc);
+  }
+  if( p ){
+    int ii;
+    mnX = mxX = GeoX(p,0);
+    mnY = mxY = GeoY(p,0);
+    for(ii=1; ii<p->nVertex; ii++){
+      double r = GeoX(p,ii);
+      if( r<mnX ) mnX = (float)r;
+      else if( r>mxX ) mxX = (float)r;
+      r = GeoY(p,ii);
+      if( r<mnY ) mnY = (float)r;
+      else if( r>mxY ) mxY = (float)r;
+    }
+    if( pRc ) *pRc = SQLITE_OK;
+    if( aCoord==0 ){
+      geopolyBboxFill:
+      pOut = sqlite3_realloc64(p, GEOPOLY_SZ(4));
+      if( pOut==0 ){
+        sqlite3_free(p);
+        if( context ) sqlite3_result_error_nomem(context);
+        if( pRc ) *pRc = SQLITE_NOMEM;
+        return 0;
+      }
+      pOut->nVertex = 4;
+      ii = 1;
+      pOut->hdr[0] = *(unsigned char*)&ii;
+      pOut->hdr[1] = 0;
+      pOut->hdr[2] = 0;
+      pOut->hdr[3] = 4;
+      GeoX(pOut,0) = mnX;
+      GeoY(pOut,0) = mnY;
+      GeoX(pOut,1) = mxX;
+      GeoY(pOut,1) = mnY;
+      GeoX(pOut,2) = mxX;
+      GeoY(pOut,2) = mxY;
+      GeoX(pOut,3) = mnX;
+      GeoY(pOut,3) = mxY;
+    }else{
+      sqlite3_free(p);
+      aCoord[0].f = mnX;
+      aCoord[1].f = mxX;
+      aCoord[2].f = mnY;
+      aCoord[3].f = mxY;
+    }
+  }else if( aCoord ){
+    memset(aCoord, 0, sizeof(RtreeCoord)*4);
+  }
+  return pOut;
+}
+
+/*
+** Implementation of the geopoly_bbox(X) SQL function.
+*/
+static void geopolyBBoxFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyBBox(context, argv[0], 0, 0);
+  if( p ){
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** State vector for the geopoly_group_bbox() aggregate function.
+*/
+typedef struct GeoBBox GeoBBox;
+struct GeoBBox {
+  int isInit;
+  RtreeCoord a[4];
+};
+
+
+/*
+** Implementation of the geopoly_group_bbox(X) aggregate SQL function.
+*/
+static void geopolyBBoxStep(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  RtreeCoord a[4];
+  int rc = SQLITE_OK;
+  (void)geopolyBBox(context, argv[0], a, &rc);
+  if( rc==SQLITE_OK ){
+    GeoBBox *pBBox;
+    pBBox = (GeoBBox*)sqlite3_aggregate_context(context, sizeof(*pBBox));
+    if( pBBox==0 ) return;
+    if( pBBox->isInit==0 ){
+      pBBox->isInit = 1;
+      memcpy(pBBox->a, a, sizeof(RtreeCoord)*4);
+    }else{
+      if( a[0].f < pBBox->a[0].f ) pBBox->a[0] = a[0];
+      if( a[1].f > pBBox->a[1].f ) pBBox->a[1] = a[1];
+      if( a[2].f < pBBox->a[2].f ) pBBox->a[2] = a[2];
+      if( a[3].f > pBBox->a[3].f ) pBBox->a[3] = a[3];
+    }
+  }
+}
+static void geopolyBBoxFinal(
+  sqlite3_context *context
+){
+  GeoPoly *p;
+  GeoBBox *pBBox;
+  pBBox = (GeoBBox*)sqlite3_aggregate_context(context, 0);
+  if( pBBox==0 ) return;
+  p = geopolyBBox(context, 0, pBBox->a, 0);
+  if( p ){
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }
+}
+
+
+/*
+** Determine if point (x0,y0) is beneath line segment (x1,y1)->(x2,y2).
+** Returns:
+**
+**    +2  x0,y0 is on the line segement
+**
+**    +1  x0,y0 is beneath line segment
+**
+**    0   x0,y0 is not on or beneath the line segment or the line segment
+**        is vertical and x0,y0 is not on the line segment
+**
+** The left-most coordinate min(x1,x2) is not considered to be part of
+** the line segment for the purposes of this analysis.
+*/
+static int pointBeneathLine(
+  double x0, double y0,
+  double x1, double y1,
+  double x2, double y2
+){
+  double y;
+  if( x0==x1 && y0==y1 ) return 2;
+  if( x1<x2 ){
+    if( x0<=x1 || x0>x2 ) return 0;
+  }else if( x1>x2 ){
+    if( x0<=x2 || x0>x1 ) return 0;
+  }else{
+    /* Vertical line segment */
+    if( x0!=x1 ) return 0;
+    if( y0<y1 && y0<y2 ) return 0;
+    if( y0>y1 && y0>y2 ) return 0;
+    return 2;
+  }
+  y = y1 + (y2-y1)*(x0-x1)/(x2-x1);
+  if( y0==y ) return 2;
+  if( y0<y ) return 1;
+  return 0;
+}
+
+/*
+** SQL function:    geopoly_contains_point(P,X,Y)
+**
+** Return +2 if point X,Y is within polygon P.
+** Return +1 if point X,Y is on the polygon boundary.
+** Return 0 if point X,Y is outside the polygon
+*/
+static void geopolyContainsPointFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p1 = geopolyFuncParam(context, argv[0], 0);
+  double x0 = sqlite3_value_double(argv[1]);
+  double y0 = sqlite3_value_double(argv[2]);
+  int v = 0;
+  int cnt = 0;
+  int ii;
+  if( p1==0 ) return;
+  for(ii=0; ii<p1->nVertex-1; ii++){
+    v = pointBeneathLine(x0,y0,GeoX(p1,ii), GeoY(p1,ii),
+                               GeoX(p1,ii+1),GeoY(p1,ii+1));
+    if( v==2 ) break;
+    cnt += v;
+  }
+  if( v!=2 ){
+    v = pointBeneathLine(x0,y0,GeoX(p1,ii), GeoY(p1,ii),
+                               GeoX(p1,0),  GeoY(p1,0));
+  }
+  if( v==2 ){
+    sqlite3_result_int(context, 1);
+  }else if( ((v+cnt)&1)==0 ){
+    sqlite3_result_int(context, 0);
+  }else{
+    sqlite3_result_int(context, 2);
+  }
+  sqlite3_free(p1);
+}
+
+/* Forward declaration */
+static int geopolyOverlap(GeoPoly *p1, GeoPoly *p2);
+
+/*
+** SQL function:    geopoly_within(P1,P2)
+**
+** Return +2 if P1 and P2 are the same polygon
+** Return +1 if P2 is contained within P1
+** Return 0 if any part of P2 is on the outside of P1
+**
+*/
+static void geopolyWithinFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p1 = geopolyFuncParam(context, argv[0], 0);
+  GeoPoly *p2 = geopolyFuncParam(context, argv[1], 0);
+  if( p1 && p2 ){
+    int x = geopolyOverlap(p1, p2);
+    if( x<0 ){
+      sqlite3_result_error_nomem(context);
+    }else{
+      sqlite3_result_int(context, x==2 ? 1 : x==4 ? 2 : 0);
+    }
+  }
+  sqlite3_free(p1);
+  sqlite3_free(p2);
+}
+
+/* Objects used by the overlap algorihm. */
+typedef struct GeoEvent GeoEvent;
+typedef struct GeoSegment GeoSegment;
+typedef struct GeoOverlap GeoOverlap;
+struct GeoEvent {
+  double x;              /* X coordinate at which event occurs */
+  int eType;             /* 0 for ADD, 1 for REMOVE */
+  GeoSegment *pSeg;      /* The segment to be added or removed */
+  GeoEvent *pNext;       /* Next event in the sorted list */
+};
+struct GeoSegment {
+  double C, B;           /* y = C*x + B */
+  double y;              /* Current y value */
+  float y0;              /* Initial y value */
+  unsigned char side;    /* 1 for p1, 2 for p2 */
+  unsigned int idx;      /* Which segment within the side */
+  GeoSegment *pNext;     /* Next segment in a list sorted by y */
+};
+struct GeoOverlap {
+  GeoEvent *aEvent;          /* Array of all events */
+  GeoSegment *aSegment;      /* Array of all segments */
+  int nEvent;                /* Number of events */
+  int nSegment;              /* Number of segments */
+};
+
+/*
+** Add a single segment and its associated events.
+*/
+static void geopolyAddOneSegment(
+  GeoOverlap *p,
+  GeoCoord x0,
+  GeoCoord y0,
+  GeoCoord x1,
+  GeoCoord y1,
+  unsigned char side,
+  unsigned int idx
+){
+  GeoSegment *pSeg;
+  GeoEvent *pEvent;
+  if( x0==x1 ) return;  /* Ignore vertical segments */
+  if( x0>x1 ){
+    GeoCoord t = x0;
+    x0 = x1;
+    x1 = t;
+    t = y0;
+    y0 = y1;
+    y1 = t;
+  }
+  pSeg = p->aSegment + p->nSegment;
+  p->nSegment++;
+  pSeg->C = (y1-y0)/(x1-x0);
+  pSeg->B = y1 - x1*pSeg->C;
+  pSeg->y0 = y0;
+  pSeg->side = side;
+  pSeg->idx = idx;
+  pEvent = p->aEvent + p->nEvent;
+  p->nEvent++;
+  pEvent->x = x0;
+  pEvent->eType = 0;
+  pEvent->pSeg = pSeg;
+  pEvent = p->aEvent + p->nEvent;
+  p->nEvent++;
+  pEvent->x = x1;
+  pEvent->eType = 1;
+  pEvent->pSeg = pSeg;
+}
+  
+
+
+/*
+** Insert all segments and events for polygon pPoly.
+*/
+static void geopolyAddSegments(
+  GeoOverlap *p,          /* Add segments to this Overlap object */
+  GeoPoly *pPoly,         /* Take all segments from this polygon */
+  unsigned char side      /* The side of pPoly */
+){
+  unsigned int i;
+  GeoCoord *x;
+  for(i=0; i<(unsigned)pPoly->nVertex-1; i++){
+    x = &GeoX(pPoly,i);
+    geopolyAddOneSegment(p, x[0], x[1], x[2], x[3], side, i);
+  }
+  x = &GeoX(pPoly,i);
+  geopolyAddOneSegment(p, x[0], x[1], pPoly->a[0], pPoly->a[1], side, i);
+}
+
+/*
+** Merge two lists of sorted events by X coordinate
+*/
+static GeoEvent *geopolyEventMerge(GeoEvent *pLeft, GeoEvent *pRight){
+  GeoEvent head, *pLast;
+  head.pNext = 0;
+  pLast = &head;
+  while( pRight && pLeft ){
+    if( pRight->x <= pLeft->x ){
+      pLast->pNext = pRight;
+      pLast = pRight;
+      pRight = pRight->pNext;
+    }else{
+      pLast->pNext = pLeft;
+      pLast = pLeft;
+      pLeft = pLeft->pNext;
+    }
+  }
+  pLast->pNext = pRight ? pRight : pLeft;
+  return head.pNext;  
+}
+
+/*
+** Sort an array of nEvent event objects into a list.
+*/
+static GeoEvent *geopolySortEventsByX(GeoEvent *aEvent, int nEvent){
+  int mx = 0;
+  int i, j;
+  GeoEvent *p;
+  GeoEvent *a[50];
+  for(i=0; i<nEvent; i++){
+    p = &aEvent[i];
+    p->pNext = 0;
+    for(j=0; j<mx && a[j]; j++){
+      p = geopolyEventMerge(a[j], p);
+      a[j] = 0;
+    }
+    a[j] = p;
+    if( j>=mx ) mx = j+1;
+  }
+  p = 0;
+  for(i=0; i<mx; i++){
+    p = geopolyEventMerge(a[i], p);
+  }
+  return p;
+}
+
+/*
+** Merge two lists of sorted segments by Y, and then by C.
+*/
+static GeoSegment *geopolySegmentMerge(GeoSegment *pLeft, GeoSegment *pRight){
+  GeoSegment head, *pLast;
+  head.pNext = 0;
+  pLast = &head;
+  while( pRight && pLeft ){
+    double r = pRight->y - pLeft->y;
+    if( r==0.0 ) r = pRight->C - pLeft->C;
+    if( r<0.0 ){
+      pLast->pNext = pRight;
+      pLast = pRight;
+      pRight = pRight->pNext;
+    }else{
+      pLast->pNext = pLeft;
+      pLast = pLeft;
+      pLeft = pLeft->pNext;
+    }
+  }
+  pLast->pNext = pRight ? pRight : pLeft;
+  return head.pNext;  
+}
+
+/*
+** Sort a list of GeoSegments in order of increasing Y and in the event of
+** a tie, increasing C (slope).
+*/
+static GeoSegment *geopolySortSegmentsByYAndC(GeoSegment *pList){
+  int mx = 0;
+  int i;
+  GeoSegment *p;
+  GeoSegment *a[50];
+  while( pList ){
+    p = pList;
+    pList = pList->pNext;
+    p->pNext = 0;
+    for(i=0; i<mx && a[i]; i++){
+      p = geopolySegmentMerge(a[i], p);
+      a[i] = 0;
+    }
+    a[i] = p;
+    if( i>=mx ) mx = i+1;
+  }
+  p = 0;
+  for(i=0; i<mx; i++){
+    p = geopolySegmentMerge(a[i], p);
+  }
+  return p;
+}
+
+/*
+** Determine the overlap between two polygons
+*/
+static int geopolyOverlap(GeoPoly *p1, GeoPoly *p2){
+  sqlite3_int64 nVertex = p1->nVertex + p2->nVertex + 2;
+  GeoOverlap *p;
+  sqlite3_int64 nByte;
+  GeoEvent *pThisEvent;
+  double rX;
+  int rc = 0;
+  int needSort = 0;
+  GeoSegment *pActive = 0;
+  GeoSegment *pSeg;
+  unsigned char aOverlap[4];
+
+  nByte = sizeof(GeoEvent)*nVertex*2 
+           + sizeof(GeoSegment)*nVertex 
+           + sizeof(GeoOverlap);
+  p = sqlite3_malloc64( nByte );
+  if( p==0 ) return -1;
+  p->aEvent = (GeoEvent*)&p[1];
+  p->aSegment = (GeoSegment*)&p->aEvent[nVertex*2];
+  p->nEvent = p->nSegment = 0;
+  geopolyAddSegments(p, p1, 1);
+  geopolyAddSegments(p, p2, 2);
+  pThisEvent = geopolySortEventsByX(p->aEvent, p->nEvent);
+  rX = pThisEvent && pThisEvent->x==0.0 ? -1.0 : 0.0;
+  memset(aOverlap, 0, sizeof(aOverlap));
+  while( pThisEvent ){
+    if( pThisEvent->x!=rX ){
+      GeoSegment *pPrev = 0;
+      int iMask = 0;
+      GEODEBUG(("Distinct X: %g\n", pThisEvent->x));
+      rX = pThisEvent->x;
+      if( needSort ){
+        GEODEBUG(("SORT\n"));
+        pActive = geopolySortSegmentsByYAndC(pActive);
+        needSort = 0;
+      }
+      for(pSeg=pActive; pSeg; pSeg=pSeg->pNext){
+        if( pPrev ){
+          if( pPrev->y!=pSeg->y ){
+            GEODEBUG(("MASK: %d\n", iMask));
+            aOverlap[iMask] = 1;
+          }
+        }
+        iMask ^= pSeg->side;
+        pPrev = pSeg;
+      }
+      pPrev = 0;
+      for(pSeg=pActive; pSeg; pSeg=pSeg->pNext){
+        double y = pSeg->C*rX + pSeg->B;
+        GEODEBUG(("Segment %d.%d %g->%g\n", pSeg->side, pSeg->idx, pSeg->y, y));
+        pSeg->y = y;
+        if( pPrev ){
+          if( pPrev->y>pSeg->y && pPrev->side!=pSeg->side ){
+            rc = 1;
+            GEODEBUG(("Crossing: %d.%d and %d.%d\n",
+                    pPrev->side, pPrev->idx,
+                    pSeg->side, pSeg->idx));
+            goto geopolyOverlapDone;
+          }else if( pPrev->y!=pSeg->y ){
+            GEODEBUG(("MASK: %d\n", iMask));
+            aOverlap[iMask] = 1;
+          }
+        }
+        iMask ^= pSeg->side;
+        pPrev = pSeg;
+      }
+    }
+    GEODEBUG(("%s %d.%d C=%g B=%g\n",
+      pThisEvent->eType ? "RM " : "ADD",
+      pThisEvent->pSeg->side, pThisEvent->pSeg->idx,
+      pThisEvent->pSeg->C,
+      pThisEvent->pSeg->B));
+    if( pThisEvent->eType==0 ){
+      /* Add a segment */
+      pSeg = pThisEvent->pSeg;
+      pSeg->y = pSeg->y0;
+      pSeg->pNext = pActive;
+      pActive = pSeg;
+      needSort = 1;
+    }else{
+      /* Remove a segment */
+      if( pActive==pThisEvent->pSeg ){
+        pActive = ALWAYS(pActive) ? pActive->pNext : 0;
+      }else{
+        for(pSeg=pActive; pSeg; pSeg=pSeg->pNext){
+          if( pSeg->pNext==pThisEvent->pSeg ){
+            pSeg->pNext = ALWAYS(pSeg->pNext) ? pSeg->pNext->pNext : 0;
+            break;
+          }
+        }
+      }
+    }
+    pThisEvent = pThisEvent->pNext;
+  }
+  if( aOverlap[3]==0 ){
+    rc = 0;
+  }else if( aOverlap[1]!=0 && aOverlap[2]==0 ){
+    rc = 3;
+  }else if( aOverlap[1]==0 && aOverlap[2]!=0 ){
+    rc = 2;
+  }else if( aOverlap[1]==0 && aOverlap[2]==0 ){
+    rc = 4;
+  }else{
+    rc = 1;
+  }
+
+geopolyOverlapDone:
+  sqlite3_free(p);
+  return rc;
+}
+
+/*
+** SQL function:    geopoly_overlap(P1,P2)
+**
+** Determine whether or not P1 and P2 overlap. Return value:
+**
+**   0     The two polygons are disjoint
+**   1     They overlap
+**   2     P1 is completely contained within P2
+**   3     P2 is completely contained within P1
+**   4     P1 and P2 are the same polygon
+**   NULL  Either P1 or P2 or both are not valid polygons
+*/
+static void geopolyOverlapFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p1 = geopolyFuncParam(context, argv[0], 0);
+  GeoPoly *p2 = geopolyFuncParam(context, argv[1], 0);
+  if( p1 && p2 ){
+    int x = geopolyOverlap(p1, p2);
+    if( x<0 ){
+      sqlite3_result_error_nomem(context);
+    }else{
+      sqlite3_result_int(context, x);
+    }
+  }
+  sqlite3_free(p1);
+  sqlite3_free(p2);
+}
+
+/*
+** Enable or disable debugging output
+*/
+static void geopolyDebugFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+#ifdef GEOPOLY_ENABLE_DEBUG
+  geo_debug = sqlite3_value_int(argv[0]);
+#endif
+}
+
+/* 
+** This function is the implementation of both the xConnect and xCreate
+** methods of the geopoly virtual table.
+**
+**   argv[0]   -> module name
+**   argv[1]   -> database name
+**   argv[2]   -> table name
+**   argv[...] -> column names...
+*/
+static int geopolyInit(
+  sqlite3 *db,                        /* Database connection */
+  void *pAux,                         /* One of the RTREE_COORD_* constants */
+  int argc, const char *const*argv,   /* Parameters to CREATE TABLE statement */
+  sqlite3_vtab **ppVtab,              /* OUT: New virtual table */
+  char **pzErr,                       /* OUT: Error message, if any */
+  int isCreate                        /* True for xCreate, false for xConnect */
+){
+  int rc = SQLITE_OK;
+  Rtree *pRtree;
+  sqlite3_int64 nDb;              /* Length of string argv[1] */
+  sqlite3_int64 nName;            /* Length of string argv[2] */
+  sqlite3_str *pSql;
+  char *zSql;
+  int ii;
+
+  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);
+
+  /* Allocate the sqlite3_vtab structure */
+  nDb = strlen(argv[1]);
+  nName = strlen(argv[2]);
+  pRtree = (Rtree *)sqlite3_malloc64(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->eCoordType = RTREE_COORD_REAL32;
+  pRtree->nDim = 2;
+  pRtree->nDim2 = 4;
+  memcpy(pRtree->zDb, argv[1], nDb);
+  memcpy(pRtree->zName, argv[2], nName);
+
+
+  /* Create/Connect to the underlying relational database schema. If
+  ** that is successful, call sqlite3_declare_vtab() to configure
+  ** the r-tree table schema.
+  */
+  pSql = sqlite3_str_new(db);
+  sqlite3_str_appendf(pSql, "CREATE TABLE x(_shape");
+  pRtree->nAux = 1;         /* Add one for _shape */
+  pRtree->nAuxNotNull = 1;  /* The _shape column is always not-null */
+  for(ii=3; ii<argc; ii++){
+    pRtree->nAux++;
+    sqlite3_str_appendf(pSql, ",%s", argv[ii]);
+  }
+  sqlite3_str_appendf(pSql, ");");
+  zSql = sqlite3_str_finish(pSql);
+  if( !zSql ){
+    rc = SQLITE_NOMEM;
+  }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
+    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
+  }
+  sqlite3_free(zSql);
+  if( rc ) goto geopolyInit_fail;
+  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
+
+  /* Figure out the node size to use. */
+  rc = getNodeSize(db, pRtree, isCreate, pzErr);
+  if( rc ) goto geopolyInit_fail;
+  rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate);
+  if( rc ){
+    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
+    goto geopolyInit_fail;
+  }
+
+  *ppVtab = (sqlite3_vtab *)pRtree;
+  return SQLITE_OK;
+
+geopolyInit_fail:
+  if( rc==SQLITE_OK ) rc = SQLITE_ERROR;
+  assert( *ppVtab==0 );
+  assert( pRtree->nBusy==1 );
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+
+/* 
+** GEOPOLY virtual table module xCreate method.
+*/
+static int geopolyCreate(
+  sqlite3 *db,
+  void *pAux,
+  int argc, const char *const*argv,
+  sqlite3_vtab **ppVtab,
+  char **pzErr
+){
+  return geopolyInit(db, pAux, argc, argv, ppVtab, pzErr, 1);
+}
+
+/* 
+** GEOPOLY virtual table module xConnect method.
+*/
+static int geopolyConnect(
+  sqlite3 *db,
+  void *pAux,
+  int argc, const char *const*argv,
+  sqlite3_vtab **ppVtab,
+  char **pzErr
+){
+  return geopolyInit(db, pAux, argc, argv, ppVtab, pzErr, 0);
+}
+
+
+/* 
+** GEOPOLY virtual table module xFilter method.
+**
+** Query plans:
+**
+**      1         rowid lookup
+**      2         search for objects overlapping the same bounding box
+**                that contains polygon argv[0]
+**      3         search for objects overlapping the same bounding box
+**                that contains polygon argv[0]
+**      4         full table scan
+*/
+static int geopolyFilter(
+  sqlite3_vtab_cursor *pVtabCursor,     /* The cursor to initialize */
+  int idxNum,                           /* Query plan */
+  const char *idxStr,                   /* Not Used */
+  int argc, sqlite3_value **argv        /* Parameters to the query plan */
+){
+  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
+  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
+  RtreeNode *pRoot = 0;
+  int rc = SQLITE_OK;
+  int iCell = 0;
+
+  rtreeReference(pRtree);
+
+  /* Reset the cursor to the same state as rtreeOpen() leaves it in. */
+  resetCursor(pCsr);
+
+  pCsr->iStrategy = idxNum;
+  if( idxNum==1 ){
+    /* Special case - lookup by rowid. */
+    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
+    RtreeSearchPoint *p;     /* Search point for the leaf */
+    i64 iRowid = sqlite3_value_int64(argv[0]);
+    i64 iNode = 0;
+    rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);
+    if( rc==SQLITE_OK && pLeaf!=0 ){
+      p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);
+      assert( p!=0 );  /* Always returns pCsr->sPoint */
+      pCsr->aNode[0] = pLeaf;
+      p->id = iNode;
+      p->eWithin = PARTLY_WITHIN;
+      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);
+      p->iCell = (u8)iCell;
+      RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
+    }else{
+      pCsr->atEOF = 1;
+    }
+  }else{
+    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
+    ** with the configured constraints. 
+    */
+    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
+    if( rc==SQLITE_OK && idxNum<=3 ){
+      RtreeCoord bbox[4];
+      RtreeConstraint *p;
+      assert( argc==1 );
+      assert( argv[0]!=0 );
+      geopolyBBox(0, argv[0], bbox, &rc);
+      if( rc ){
+        goto geopoly_filter_end;
+      }
+      pCsr->aConstraint = p = sqlite3_malloc(sizeof(RtreeConstraint)*4);
+      pCsr->nConstraint = 4;
+      if( p==0 ){
+        rc = SQLITE_NOMEM;
+      }else{
+        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*4);
+        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
+        if( idxNum==2 ){
+          /* Overlap query */
+          p->op = 'B';
+          p->iCoord = 0;
+          p->u.rValue = bbox[1].f;
+          p++;
+          p->op = 'D';
+          p->iCoord = 1;
+          p->u.rValue = bbox[0].f;
+          p++;
+          p->op = 'B';
+          p->iCoord = 2;
+          p->u.rValue = bbox[3].f;
+          p++;
+          p->op = 'D';
+          p->iCoord = 3;
+          p->u.rValue = bbox[2].f;
+        }else{
+          /* Within query */
+          p->op = 'D';
+          p->iCoord = 0;
+          p->u.rValue = bbox[0].f;
+          p++;
+          p->op = 'B';
+          p->iCoord = 1;
+          p->u.rValue = bbox[1].f;
+          p++;
+          p->op = 'D';
+          p->iCoord = 2;
+          p->u.rValue = bbox[2].f;
+          p++;
+          p->op = 'B';
+          p->iCoord = 3;
+          p->u.rValue = bbox[3].f;
+        }
+      }
+    }
+    if( rc==SQLITE_OK ){
+      RtreeSearchPoint *pNew;
+      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, (u8)(pRtree->iDepth+1));
+      if( pNew==0 ){
+        rc = SQLITE_NOMEM;
+        goto geopoly_filter_end;
+      }
+      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);
+    }
+  }
+
+geopoly_filter_end:
+  nodeRelease(pRtree, pRoot);
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+/*
+** 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        "rowid"       Direct lookup by rowid.
+**     2        "rtree"       R-tree overlap query using geopoly_overlap()
+**     3        "rtree"       R-tree within query using geopoly_within()
+**     4        "fullscan"    full-table scan.
+**   ------------------------------------------------
+*/
+static int geopolyBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
+  int ii;
+  int iRowidTerm = -1;
+  int iFuncTerm = -1;
+  int idxNum = 0;
+
+  for(ii=0; ii<pIdxInfo->nConstraint; ii++){
+    struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];
+    if( !p->usable ) continue;
+    if( p->iColumn<0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ  ){
+      iRowidTerm = ii;
+      break;
+    }
+    if( p->iColumn==0 && p->op>=SQLITE_INDEX_CONSTRAINT_FUNCTION ){
+      /* p->op==SQLITE_INDEX_CONSTRAINT_FUNCTION for geopoly_overlap()
+      ** p->op==(SQLITE_INDEX_CONTRAINT_FUNCTION+1) for geopoly_within().
+      ** See geopolyFindFunction() */
+      iFuncTerm = ii;
+      idxNum = p->op - SQLITE_INDEX_CONSTRAINT_FUNCTION + 2;
+    }
+  }
+
+  if( iRowidTerm>=0 ){
+    pIdxInfo->idxNum = 1;
+    pIdxInfo->idxStr = "rowid";
+    pIdxInfo->aConstraintUsage[iRowidTerm].argvIndex = 1;
+    pIdxInfo->aConstraintUsage[iRowidTerm].omit = 1;
+    pIdxInfo->estimatedCost = 30.0;
+    pIdxInfo->estimatedRows = 1;
+    pIdxInfo->idxFlags = SQLITE_INDEX_SCAN_UNIQUE;
+    return SQLITE_OK;
+  }
+  if( iFuncTerm>=0 ){
+    pIdxInfo->idxNum = idxNum;
+    pIdxInfo->idxStr = "rtree";
+    pIdxInfo->aConstraintUsage[iFuncTerm].argvIndex = 1;
+    pIdxInfo->aConstraintUsage[iFuncTerm].omit = 0;
+    pIdxInfo->estimatedCost = 300.0;
+    pIdxInfo->estimatedRows = 10;
+    return SQLITE_OK;
+  }
+  pIdxInfo->idxNum = 4;
+  pIdxInfo->idxStr = "fullscan";
+  pIdxInfo->estimatedCost = 3000000.0;
+  pIdxInfo->estimatedRows = 100000;
+  return SQLITE_OK;
+}
+
+
+/* 
+** GEOPOLY virtual table module xColumn method.
+*/
+static int geopolyColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
+  Rtree *pRtree = (Rtree *)cur->pVtab;
+  RtreeCursor *pCsr = (RtreeCursor *)cur;
+  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
+  int rc = SQLITE_OK;
+  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
+
+  if( rc ) return rc;
+  if( p==0 ) return SQLITE_OK;
+  if( i==0 && sqlite3_vtab_nochange(ctx) ) return SQLITE_OK;
+  if( i<=pRtree->nAux ){
+    if( !pCsr->bAuxValid ){
+      if( pCsr->pReadAux==0 ){
+        rc = sqlite3_prepare_v3(pRtree->db, pRtree->zReadAuxSql, -1, 0,
+                                &pCsr->pReadAux, 0);
+        if( rc ) return rc;
+      }
+      sqlite3_bind_int64(pCsr->pReadAux, 1, 
+          nodeGetRowid(pRtree, pNode, p->iCell));
+      rc = sqlite3_step(pCsr->pReadAux);
+      if( rc==SQLITE_ROW ){
+        pCsr->bAuxValid = 1;
+      }else{
+        sqlite3_reset(pCsr->pReadAux);
+        if( rc==SQLITE_DONE ) rc = SQLITE_OK;
+        return rc;
+      }
+    }
+    sqlite3_result_value(ctx, sqlite3_column_value(pCsr->pReadAux, i+2));
+  }
+  return SQLITE_OK;
+}
+
+
+/*
+** The xUpdate method for GEOPOLY module virtual tables.
+**
+** For DELETE:
+**
+**     argv[0] = the rowid to be deleted
+**
+** For INSERT:
+**
+**     argv[0] = SQL NULL
+**     argv[1] = rowid to insert, or an SQL NULL to select automatically
+**     argv[2] = _shape column
+**     argv[3] = first application-defined column....
+**
+** For UPDATE:
+**
+**     argv[0] = rowid to modify.  Never NULL
+**     argv[1] = rowid after the change.  Never NULL
+**     argv[2] = new value for _shape
+**     argv[3] = new value for first application-defined column....
+*/
+static int geopolyUpdate(
+  sqlite3_vtab *pVtab, 
+  int nData, 
+  sqlite3_value **aData, 
+  sqlite_int64 *pRowid
+){
+  Rtree *pRtree = (Rtree *)pVtab;
+  int rc = SQLITE_OK;
+  RtreeCell cell;                 /* New cell to insert if nData>1 */
+  i64 oldRowid;                   /* The old rowid */
+  int oldRowidValid;              /* True if oldRowid is valid */
+  i64 newRowid;                   /* The new rowid */
+  int newRowidValid;              /* True if newRowid is valid */
+  int coordChange = 0;            /* Change in coordinates */
+
+  if( pRtree->nNodeRef ){
+    /* Unable to write to the btree while another cursor is reading from it,
+    ** since the write might do a rebalance which would disrupt the read
+    ** cursor. */
+    return SQLITE_LOCKED_VTAB;
+  }
+  rtreeReference(pRtree);
+  assert(nData>=1);
+
+  oldRowidValid = sqlite3_value_type(aData[0])!=SQLITE_NULL;;
+  oldRowid = oldRowidValid ? sqlite3_value_int64(aData[0]) : 0;
+  newRowidValid = nData>1 && sqlite3_value_type(aData[1])!=SQLITE_NULL;
+  newRowid = newRowidValid ? sqlite3_value_int64(aData[1]) : 0;
+  cell.iRowid = newRowid;
+
+  if( nData>1                                 /* not a DELETE */
+   && (!oldRowidValid                         /* INSERT */
+        || !sqlite3_value_nochange(aData[2])  /* UPDATE _shape */
+        || oldRowid!=newRowid)                /* Rowid change */
+  ){
+    assert( aData[2]!=0 );
+    geopolyBBox(0, aData[2], cell.aCoord, &rc);
+    if( rc ){
+      if( rc==SQLITE_ERROR ){
+        pVtab->zErrMsg =
+          sqlite3_mprintf("_shape does not contain a valid polygon");
+      }
+      goto geopoly_update_end;
+    }
+    coordChange = 1;
+
+    /* If a rowid value was supplied, check if it is already present in 
+    ** the table. If so, the constraint has failed. */
+    if( newRowidValid && (!oldRowidValid || oldRowid!=newRowid) ){
+      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 = rtreeConstraintError(pRtree, 0);
+        }
+      }
+    }
+  }
+
+  /* If aData[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( rc==SQLITE_OK && (nData==1 || (coordChange && oldRowidValid)) ){
+    rc = rtreeDeleteRowid(pRtree, oldRowid);
+  }
+
+  /* If the aData[] array contains more than one element, elements
+  ** (aData[2]..aData[argc-1]) contain a new record to insert into
+  ** the r-tree structure.
+  */
+  if( rc==SQLITE_OK && nData>1 && coordChange ){
+    /* Insert the new record into the r-tree */
+    RtreeNode *pLeaf = 0;
+    if( !newRowidValid ){
+      rc = rtreeNewRowid(pRtree, &cell.iRowid);
+    }
+    *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);
+      rc2 = nodeRelease(pRtree, pLeaf);
+      if( rc==SQLITE_OK ){
+        rc = rc2;
+      }
+    }
+  }
+
+  /* Change the data */
+  if( rc==SQLITE_OK && nData>1 ){
+    sqlite3_stmt *pUp = pRtree->pWriteAux;
+    int jj;
+    int nChange = 0;
+    sqlite3_bind_int64(pUp, 1, cell.iRowid);
+    assert( pRtree->nAux>=1 );
+    if( sqlite3_value_nochange(aData[2]) ){
+      sqlite3_bind_null(pUp, 2);
+    }else{
+      GeoPoly *p = 0;
+      if( sqlite3_value_type(aData[2])==SQLITE_TEXT
+       && (p = geopolyFuncParam(0, aData[2], &rc))!=0
+       && rc==SQLITE_OK
+      ){
+        sqlite3_bind_blob(pUp, 2, p->hdr, 4+8*p->nVertex, SQLITE_TRANSIENT);
+      }else{
+        sqlite3_bind_value(pUp, 2, aData[2]);
+      }
+      sqlite3_free(p);
+      nChange = 1;
+    }
+    for(jj=1; jj<nData-2; jj++){
+      nChange++;
+      sqlite3_bind_value(pUp, jj+2, aData[jj+2]);
+    }
+    if( nChange ){
+      sqlite3_step(pUp);
+      rc = sqlite3_reset(pUp);
+    }
+  }
+
+geopoly_update_end:
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+/*
+** Report that geopoly_overlap() is an overloaded function suitable
+** for use in xBestIndex.
+*/
+static int geopolyFindFunction(
+  sqlite3_vtab *pVtab,
+  int nArg,
+  const char *zName,
+  void (**pxFunc)(sqlite3_context*,int,sqlite3_value**),
+  void **ppArg
+){
+  if( sqlite3_stricmp(zName, "geopoly_overlap")==0 ){
+    *pxFunc = geopolyOverlapFunc;
+    *ppArg = 0;
+    return SQLITE_INDEX_CONSTRAINT_FUNCTION;
+  }
+  if( sqlite3_stricmp(zName, "geopoly_within")==0 ){
+    *pxFunc = geopolyWithinFunc;
+    *ppArg = 0;
+    return SQLITE_INDEX_CONSTRAINT_FUNCTION+1;
+  }
+  return 0;
+}
+
+
+static sqlite3_module geopolyModule = {
+  3,                          /* iVersion */
+  geopolyCreate,              /* xCreate - create a table */
+  geopolyConnect,             /* xConnect - connect to an existing table */
+  geopolyBestIndex,           /* 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 */
+  geopolyFilter,              /* xFilter - configure scan constraints */
+  rtreeNext,                  /* xNext - advance a cursor */
+  rtreeEof,                   /* xEof */
+  geopolyColumn,              /* xColumn - read data */
+  rtreeRowid,                 /* xRowid - read data */
+  geopolyUpdate,              /* xUpdate - write data */
+  rtreeBeginTransaction,      /* xBegin - begin transaction */
+  rtreeEndTransaction,        /* xSync - sync transaction */
+  rtreeEndTransaction,        /* xCommit - commit transaction */
+  rtreeEndTransaction,        /* xRollback - rollback transaction */
+  geopolyFindFunction,        /* xFindFunction - function overloading */
+  rtreeRename,                /* xRename - rename the table */
+  rtreeSavepoint,             /* xSavepoint */
+  0,                          /* xRelease */
+  0,                          /* xRollbackTo */
+  rtreeShadowName             /* xShadowName */
+};
+
+static int sqlite3_geopoly_init(sqlite3 *db){
+  int rc = SQLITE_OK;
+  static const struct {
+    void (*xFunc)(sqlite3_context*,int,sqlite3_value**);
+    signed char nArg;
+    unsigned char bPure;
+    const char *zName;
+  } aFunc[] = {
+     { geopolyAreaFunc,          1, 1,    "geopoly_area"             },
+     { geopolyBlobFunc,          1, 1,    "geopoly_blob"             },
+     { geopolyJsonFunc,          1, 1,    "geopoly_json"             },
+     { geopolySvgFunc,          -1, 1,    "geopoly_svg"              },
+     { geopolyWithinFunc,        2, 1,    "geopoly_within"           },
+     { geopolyContainsPointFunc, 3, 1,    "geopoly_contains_point"   },
+     { geopolyOverlapFunc,       2, 1,    "geopoly_overlap"          },
+     { geopolyDebugFunc,         1, 0,    "geopoly_debug"            },
+     { geopolyBBoxFunc,          1, 1,    "geopoly_bbox"             },
+     { geopolyXformFunc,         7, 1,    "geopoly_xform"            },
+     { geopolyRegularFunc,       4, 1,    "geopoly_regular"          },
+     { geopolyCcwFunc,           1, 1,    "geopoly_ccw"              },
+  };
+  static const struct {
+    void (*xStep)(sqlite3_context*,int,sqlite3_value**);
+    void (*xFinal)(sqlite3_context*);
+    const char *zName;
+  } aAgg[] = {
+     { geopolyBBoxStep, geopolyBBoxFinal, "geopoly_group_bbox"    },
+  };
+  int i;
+  for(i=0; i<sizeof(aFunc)/sizeof(aFunc[0]) && rc==SQLITE_OK; i++){
+    int enc;
+    if( aFunc[i].bPure ){
+      enc = SQLITE_UTF8|SQLITE_DETERMINISTIC|SQLITE_INNOCUOUS;
+    }else{
+      enc = SQLITE_UTF8|SQLITE_DIRECTONLY;
+    }
+    rc = sqlite3_create_function(db, aFunc[i].zName, aFunc[i].nArg,
+                                 enc, 0,
+                                 aFunc[i].xFunc, 0, 0);
+  }
+  for(i=0; i<sizeof(aAgg)/sizeof(aAgg[0]) && rc==SQLITE_OK; i++){
+    rc = sqlite3_create_function(db, aAgg[i].zName, 1, 
+              SQLITE_UTF8|SQLITE_DETERMINISTIC|SQLITE_INNOCUOUS, 0,
+              0, aAgg[i].xStep, aAgg[i].xFinal);
+  }
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_module_v2(db, "geopoly", &geopolyModule, 0, 0);
+  }
+  return rc;
+}
diff --git a/ext/rtree/rtree.c b/ext/rtree/rtree.c
new file mode 100644
index 0000000..7daae9b
--- /dev/null
+++ b/ext/rtree/rtree.c
@@ -0,0 +1,4582 @@
+/*
+** 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.
+**
+*************************************************************************
+** This file contains code for implementations of the r-tree and r*-tree
+** algorithms packaged as an SQLite virtual table module.
+*/
+
+/*
+** Database Format of R-Tree Tables
+** --------------------------------
+**
+** The data structure for a single virtual r-tree table is stored in three 
+** native SQLite tables declared as follows. In each case, the '%' character
+** in the table name is replaced with the user-supplied name of the r-tree
+** table.
+**
+**   CREATE TABLE %_node(nodeno INTEGER PRIMARY KEY, data BLOB)
+**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
+**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER, ...)
+**
+** The data for each node of the r-tree structure is stored in the %_node
+** table. For each node that is not the root node of the r-tree, there is
+** an entry in the %_parent table associating the node with its parent.
+** And for each row of data in the table, there is an entry in the %_rowid
+** table that maps from the entries rowid to the id of the node that it
+** is stored on.  If the r-tree contains auxiliary columns, those are stored
+** on the end of the %_rowid table.
+**
+** The root node of an r-tree always exists, even if the r-tree table is
+** empty. The nodeno of the root node is always 1. All other nodes in the
+** table must be the same size as the root node. The content of each node
+** is formatted as follows:
+**
+**   1. If the node is the root node (node 1), then the first 2 bytes
+**      of the node contain the tree depth as a big-endian integer.
+**      For non-root nodes, the first 2 bytes are left unused.
+**
+**   2. The next 2 bytes contain the number of entries currently 
+**      stored in the node.
+**
+**   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) && !defined(SQLITE_OMIT_VIRTUALTABLE))
+
+#ifndef SQLITE_CORE
+  #include "sqlite3ext.h"
+  SQLITE_EXTENSION_INIT1
+#else
+  #include "sqlite3.h"
+#endif
+int sqlite3GetToken(const unsigned char*,int*); /* In the SQLite core */
+
+/*
+** If building separately, we will need some setup that is normally
+** found in sqliteInt.h
+*/
+#if !defined(SQLITE_AMALGAMATION)
+#include "sqlite3rtree.h"
+typedef sqlite3_int64 i64;
+typedef sqlite3_uint64 u64;
+typedef unsigned char u8;
+typedef unsigned short u16;
+typedef unsigned int u32;
+#if !defined(NDEBUG) && !defined(SQLITE_DEBUG)
+# define NDEBUG 1
+#endif
+#if defined(NDEBUG) && defined(SQLITE_DEBUG)
+# undef NDEBUG
+#endif
+#if defined(SQLITE_COVERAGE_TEST) || defined(SQLITE_MUTATION_TEST)
+# define SQLITE_OMIT_AUXILIARY_SAFETY_CHECKS 1
+#endif
+#if defined(SQLITE_OMIT_AUXILIARY_SAFETY_CHECKS)
+# define ALWAYS(X)      (1)
+# define NEVER(X)       (0)
+#elif !defined(NDEBUG)
+# define ALWAYS(X)      ((X)?1:(assert(0),0))
+# define NEVER(X)       ((X)?(assert(0),1):0)
+#else
+# define ALWAYS(X)      (X)
+# define NEVER(X)       (X)
+#endif
+#endif /* !defined(SQLITE_AMALGAMATION) */
+
+#include <string.h>
+#include <stdio.h>
+#include <assert.h>
+#include <stdlib.h>
+
+/*  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
+
+/* Maximum number of auxiliary columns */
+#define RTREE_MAX_AUX_COLUMN 100
+
+/* Size of hash table Rtree.aHash. This hash table is not expected to
+** ever contain very many entries, so a fixed number of buckets is 
+** used.
+*/
+#define HASHSIZE 97
+
+/* The xBestIndex method of this virtual table requires an estimate of
+** the number of rows in the virtual table to calculate the costs of
+** various strategies. If possible, this estimate is loaded from the
+** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
+** Otherwise, if no sqlite_stat1 entry is available, use 
+** RTREE_DEFAULT_ROWEST.
+*/
+#define RTREE_DEFAULT_ROWEST 1048576
+#define RTREE_MIN_ROWEST         100
+
+/* 
+** An rtree virtual-table object.
+*/
+struct Rtree {
+  sqlite3_vtab base;          /* Base class.  Must be first */
+  sqlite3 *db;                /* Host database connection */
+  int iNodeSize;              /* Size in bytes of each node in the node table */
+  u8 nDim;                    /* Number of dimensions */
+  u8 nDim2;                   /* Twice the number of dimensions */
+  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
+  u8 nBytesPerCell;           /* Bytes consumed per cell */
+  u8 inWrTrans;               /* True if inside write transaction */
+  u8 nAux;                    /* # of auxiliary columns in %_rowid */
+#ifdef SQLITE_ENABLE_GEOPOLY
+  u8 nAuxNotNull;             /* Number of initial not-null aux columns */
+#endif
+#ifdef SQLITE_DEBUG
+  u8 bCorrupt;                /* Shadow table corruption detected */
+#endif
+  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 */ 
+  u32 nBusy;                  /* Current number of users of this structure */
+  i64 nRowEst;                /* Estimated number of rows in this table */
+  u32 nCursor;                /* Number of open cursors */
+  u32 nNodeRef;               /* Number RtreeNodes with positive nRef */
+  char *zReadAuxSql;          /* SQL for statement to read aux data */
+
+  /* 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 */
+
+  /* Blob I/O on xxx_node */
+  sqlite3_blob *pNodeBlob;
+
+  /* Statements to read/write/delete a record from xxx_node */
+  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;
+
+  /* Statement for writing to the "aux:" fields, if there are any */
+  sqlite3_stmt *pWriteAux;
+
+  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
+};
+
+/* Possible values for Rtree.eCoordType: */
+#define RTREE_COORD_REAL32 0
+#define RTREE_COORD_INT32  1
+
+/*
+** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
+** only deal with integer coordinates.  No floating point operations
+** will be done.
+*/
+#ifdef SQLITE_RTREE_INT_ONLY
+  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */
+  typedef int RtreeValue;                  /* Low accuracy coordinate */
+# define RTREE_ZERO 0
+#else
+  typedef double RtreeDValue;              /* High accuracy coordinate */
+  typedef float RtreeValue;                /* Low accuracy coordinate */
+# define RTREE_ZERO 0.0
+#endif
+
+/*
+** Set the Rtree.bCorrupt flag
+*/
+#ifdef SQLITE_DEBUG
+# define RTREE_IS_CORRUPT(X) ((X)->bCorrupt = 1)
+#else
+# define RTREE_IS_CORRUPT(X)
+#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 
+** 3^40 is greater than 2^64, an r-tree structure always has a depth of
+** 40 or less.
+*/
+#define RTREE_MAX_DEPTH 40
+
+
+/*
+** Number of entries in the cursor RtreeNode cache.  The first entry is
+** used to cache the RtreeNode for RtreeCursor.sPoint.  The remaining
+** entries cache the RtreeNode for the first elements of the priority queue.
+*/
+#define RTREE_CACHE_SZ  5
+
+/* 
+** An rtree cursor object.
+*/
+struct RtreeCursor {
+  sqlite3_vtab_cursor base;         /* Base class.  Must be first */
+  u8 atEOF;                         /* True if at end of search */
+  u8 bPoint;                        /* True if sPoint is valid */
+  u8 bAuxValid;                     /* True if pReadAux 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 */
+  sqlite3_stmt *pReadAux;           /* Statement to read aux-data */
+  RtreeSearchPoint sPoint;          /* Cached next search point */
+  RtreeNode *aNode[RTREE_CACHE_SZ]; /* Rtree node cache */
+  u32 anQueue[RTREE_MAX_DEPTH+1];   /* Number of queued entries by iLevel */
+};
+
+/* Return the Rtree of a RtreeCursor */
+#define RTREE_OF_CURSOR(X)   ((Rtree*)((X)->base.pVtab))
+
+/*
+** A coordinate can be either a floating point number or a integer.  All
+** coordinates within a single R-Tree are always of the same time.
+*/
+union RtreeCoord {
+  RtreeValue f;      /* Floating point value */
+  int i;             /* Integer value */
+  u32 u;             /* Unsigned for byte-order conversions */
+};
+
+/*
+** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
+** formatted as a RtreeDValue (double or int64). This macro assumes that local
+** variable pRtree points to the Rtree structure associated with the
+** RtreeCoord.
+*/
+#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 */
+  union {
+    RtreeDValue rValue;             /* Constraint value. */
+    int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*);
+    int (*xQueryFunc)(sqlite3_rtree_query_info*);
+  } u;
+  sqlite3_rtree_query_info *pInfo;  /* xGeom and xQueryFunc argument */
+};
+
+/* Possible values for RtreeConstraint.op */
+#define RTREE_EQ    0x41  /* A */
+#define RTREE_LE    0x42  /* B */
+#define RTREE_LT    0x43  /* C */
+#define RTREE_GE    0x44  /* D */
+#define RTREE_GT    0x45  /* E */
+#define RTREE_MATCH 0x46  /* F: Old-style sqlite3_rtree_geometry_callback() */
+#define RTREE_QUERY 0x47  /* G: New-style sqlite3_rtree_query_callback() */
+
+/* Special operators available only on cursors.  Needs to be consecutive
+** with the normal values above, but must be less than RTREE_MATCH.  These
+** are used in the cursor for contraints such as x=NULL (RTREE_FALSE) or
+** x<'xyz' (RTREE_TRUE) */
+#define RTREE_TRUE  0x3f  /* ? */
+#define RTREE_FALSE 0x40  /* @ */
+
+/* 
+** An rtree structure node.
+*/
+struct RtreeNode {
+  RtreeNode *pParent;         /* Parent node */
+  i64 iNode;                  /* The node number */
+  int nRef;                   /* Number of references to this node */
+  int isDirty;                /* True if the node needs to be written to disk */
+  u8 *zData;                  /* Content of the node, as should be on disk */
+  RtreeNode *pNext;           /* Next node in this hash collision chain */
+};
+
+/* Return the number of cells in a node  */
+#define NCELL(pNode) readInt16(&(pNode)->zData[2])
+
+/* 
+** A single cell from a node, deserialized
+*/
+struct RtreeCell {
+  i64 iRowid;                                 /* Node or entry ID */
+  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];  /* Bounding box coordinates */
+};
+
+
+/*
+** This object becomes the sqlite3_user_data() for the SQL functions
+** that are created by sqlite3_rtree_geometry_callback() and
+** sqlite3_rtree_query_callback() and which appear on the right of MATCH
+** operators in order to constrain a search.
+**
+** xGeom and xQueryFunc are the callback functions.  Exactly one of 
+** xGeom and xQueryFunc fields is non-NULL, depending on whether the
+** SQL function was created using sqlite3_rtree_geometry_callback() or
+** sqlite3_rtree_query_callback().
+** 
+** This object is deleted automatically by the destructor mechanism in
+** sqlite3_create_function_v2().
+*/
+struct RtreeGeomCallback {
+  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
+  int (*xQueryFunc)(sqlite3_rtree_query_info*);
+  void (*xDestructor)(void*);
+  void *pContext;
+};
+
+/*
+** 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 iSize;                  /* Size of this object */
+  RtreeGeomCallback cb;       /* Info about the callback functions */
+  int nParam;                 /* Number of parameters to the SQL function */
+  sqlite3_value **apSqlParam; /* Original SQL parameter values */
+  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
+
+/* What version of GCC is being used.  0 means GCC is not being used .
+** Note that the GCC_VERSION macro will also be set correctly when using
+** clang, since clang works hard to be gcc compatible.  So the gcc
+** optimizations will also work when compiling with clang.
+*/
+#ifndef GCC_VERSION
+#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)
+#else
+# define GCC_VERSION 0
+#endif
+#endif
+
+/* The testcase() macro should already be defined in the amalgamation.  If
+** it is not, make it a no-op.
+*/
+#ifndef SQLITE_AMALGAMATION
+# if defined(SQLITE_COVERAGE_TEST) || defined(SQLITE_DEBUG)
+    unsigned int sqlite3RtreeTestcase = 0;
+#   define testcase(X)  if( X ){ sqlite3RtreeTestcase += __LINE__; }
+# else
+#   define testcase(X)
+# endif
+#endif
+
+/*
+** Make sure that the compiler intrinsics we desire are enabled when
+** compiling with an appropriate version of MSVC unless prevented by
+** the SQLITE_DISABLE_INTRINSIC define.
+*/
+#if !defined(SQLITE_DISABLE_INTRINSIC)
+#  if defined(_MSC_VER) && _MSC_VER>=1400
+#    if !defined(_WIN32_WCE)
+#      include <intrin.h>
+#      pragma intrinsic(_byteswap_ulong)
+#      pragma intrinsic(_byteswap_uint64)
+#    else
+#      include <cmnintrin.h>
+#    endif
+#  endif
+#endif
+
+/*
+** Macros to determine whether the machine is big or little endian,
+** and whether or not that determination is run-time or compile-time.
+**
+** For best performance, an attempt is made to guess at the byte-order
+** using C-preprocessor macros.  If that is unsuccessful, or if
+** -DSQLITE_RUNTIME_BYTEORDER=1 is set, then byte-order is determined
+** at run-time.
+*/
+#ifndef SQLITE_BYTEORDER
+#if defined(i386)     || defined(__i386__)   || defined(_M_IX86) ||    \
+    defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)  ||    \
+    defined(_M_AMD64) || defined(_M_ARM)     || defined(__x86)   ||    \
+    defined(__arm__)
+# define SQLITE_BYTEORDER    1234
+#elif defined(sparc)    || defined(__ppc__)
+# define SQLITE_BYTEORDER    4321
+#else
+# define SQLITE_BYTEORDER    0     /* 0 means "unknown at compile-time" */
+#endif
+#endif
+
+
+/* What version of MSVC is being used.  0 means MSVC is not being used */
+#ifndef MSVC_VERSION
+#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define MSVC_VERSION _MSC_VER
+#else
+# define MSVC_VERSION 0
+#endif
+#endif
+
+/*
+** Functions to deserialize a 16 bit integer, 32 bit real number and
+** 64 bit integer. The deserialized value is returned.
+*/
+static int readInt16(u8 *p){
+  return (p[0]<<8) + p[1];
+}
+static void readCoord(u8 *p, RtreeCoord *pCoord){
+  assert( ((((char*)p) - (char*)0)&3)==0 );  /* p is always 4-byte aligned */
+#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  pCoord->u = _byteswap_ulong(*(u32*)p);
+#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
+  pCoord->u = __builtin_bswap32(*(u32*)p);
+#elif SQLITE_BYTEORDER==4321
+  pCoord->u = *(u32*)p;
+#else
+  pCoord->u = (
+    (((u32)p[0]) << 24) + 
+    (((u32)p[1]) << 16) + 
+    (((u32)p[2]) <<  8) + 
+    (((u32)p[3]) <<  0)
+  );
+#endif
+}
+static i64 readInt64(u8 *p){
+#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  u64 x;
+  memcpy(&x, p, 8);
+  return (i64)_byteswap_uint64(x);
+#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
+  u64 x;
+  memcpy(&x, p, 8);
+  return (i64)__builtin_bswap64(x);
+#elif SQLITE_BYTEORDER==4321
+  i64 x;
+  memcpy(&x, p, 8);
+  return x;
+#else
+  return (i64)(
+    (((u64)p[0]) << 56) + 
+    (((u64)p[1]) << 48) + 
+    (((u64)p[2]) << 40) + 
+    (((u64)p[3]) << 32) + 
+    (((u64)p[4]) << 24) + 
+    (((u64)p[5]) << 16) + 
+    (((u64)p[6]) <<  8) + 
+    (((u64)p[7]) <<  0)
+  );
+#endif
+}
+
+/*
+** Functions to serialize a 16 bit integer, 32 bit real number and
+** 64 bit integer. The value returned is the number of bytes written
+** to the argument buffer (always 2, 4 and 8 respectively).
+*/
+static void writeInt16(u8 *p, int i){
+  p[0] = (i>> 8)&0xFF;
+  p[1] = (i>> 0)&0xFF;
+}
+static int writeCoord(u8 *p, RtreeCoord *pCoord){
+  u32 i;
+  assert( ((((char*)p) - (char*)0)&3)==0 );  /* p is always 4-byte aligned */
+  assert( sizeof(RtreeCoord)==4 );
+  assert( sizeof(u32)==4 );
+#if SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
+  i = __builtin_bswap32(pCoord->u);
+  memcpy(p, &i, 4);
+#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  i = _byteswap_ulong(pCoord->u);
+  memcpy(p, &i, 4);
+#elif SQLITE_BYTEORDER==4321
+  i = pCoord->u;
+  memcpy(p, &i, 4);
+#else
+  i = pCoord->u;
+  p[0] = (i>>24)&0xFF;
+  p[1] = (i>>16)&0xFF;
+  p[2] = (i>> 8)&0xFF;
+  p[3] = (i>> 0)&0xFF;
+#endif
+  return 4;
+}
+static int writeInt64(u8 *p, i64 i){
+#if SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
+  i = (i64)__builtin_bswap64((u64)i);
+  memcpy(p, &i, 8);
+#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  i = (i64)_byteswap_uint64((u64)i);
+  memcpy(p, &i, 8);
+#elif SQLITE_BYTEORDER==4321
+  memcpy(p, &i, 8);
+#else
+  p[0] = (i>>56)&0xFF;
+  p[1] = (i>>48)&0xFF;
+  p[2] = (i>>40)&0xFF;
+  p[3] = (i>>32)&0xFF;
+  p[4] = (i>>24)&0xFF;
+  p[5] = (i>>16)&0xFF;
+  p[6] = (i>> 8)&0xFF;
+  p[7] = (i>> 0)&0xFF;
+#endif
+  return 8;
+}
+
+/*
+** Increment the reference count of node p.
+*/
+static void nodeReference(RtreeNode *p){
+  if( p ){
+    assert( p->nRef>0 );
+    p->nRef++;
+  }
+}
+
+/*
+** Clear the content of node p (set all bytes to 0x00).
+*/
+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 unsigned int nodeHash(i64 iNode){
+  return ((unsigned)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;
+}
+
+/*
+** Add node pNode to the node hash table.
+*/
+static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){
+  int iHash;
+  assert( pNode->pNext==0 );
+  iHash = nodeHash(pNode->iNode);
+  pNode->pNext = pRtree->aHash[iHash];
+  pRtree->aHash[iHash] = pNode;
+}
+
+/*
+** Remove node pNode from the node hash table.
+*/
+static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
+  RtreeNode **pp;
+  if( pNode->iNode!=0 ){
+    pp = &pRtree->aHash[nodeHash(pNode->iNode)];
+    for( ; (*pp)!=pNode; pp = &(*pp)->pNext){ assert(*pp); }
+    *pp = pNode->pNext;
+    pNode->pNext = 0;
+  }
+}
+
+/*
+** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
+** indicating that node has not yet been assigned a node number. It is
+** assigned a node number when nodeWrite() is called to write the
+** node contents out to the database.
+*/
+static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent){
+  RtreeNode *pNode;
+  pNode = (RtreeNode *)sqlite3_malloc64(sizeof(RtreeNode) + pRtree->iNodeSize);
+  if( pNode ){
+    memset(pNode, 0, sizeof(RtreeNode) + pRtree->iNodeSize);
+    pNode->zData = (u8 *)&pNode[1];
+    pNode->nRef = 1;
+    pRtree->nNodeRef++;
+    pNode->pParent = pParent;
+    pNode->isDirty = 1;
+    nodeReference(pParent);
+  }
+  return pNode;
+}
+
+/*
+** Clear the Rtree.pNodeBlob object
+*/
+static void nodeBlobReset(Rtree *pRtree){
+  if( pRtree->pNodeBlob && pRtree->inWrTrans==0 && pRtree->nCursor==0 ){
+    sqlite3_blob *pBlob = pRtree->pNodeBlob;
+    pRtree->pNodeBlob = 0;
+    sqlite3_blob_close(pBlob);
+  }
+}
+
+/*
+** Obtain a reference to an r-tree node.
+*/
+static int nodeAcquire(
+  Rtree *pRtree,             /* R-tree structure */
+  i64 iNode,                 /* Node number to load */
+  RtreeNode *pParent,        /* Either the parent node or NULL */
+  RtreeNode **ppNode         /* OUT: Acquired node */
+){
+  int rc = SQLITE_OK;
+  RtreeNode *pNode = 0;
+
+  /* Check if the requested node is already in the hash table. If so,
+  ** increase its reference count and return it.
+  */
+  if( (pNode = nodeHashLookup(pRtree, iNode))!=0 ){
+    if( pParent && pParent!=pNode->pParent ){
+      RTREE_IS_CORRUPT(pRtree);
+      return SQLITE_CORRUPT_VTAB;
+    }
+    pNode->nRef++;
+    *ppNode = pNode;
+    return SQLITE_OK;
+  }
+
+  if( pRtree->pNodeBlob ){
+    sqlite3_blob *pBlob = pRtree->pNodeBlob;
+    pRtree->pNodeBlob = 0;
+    rc = sqlite3_blob_reopen(pBlob, iNode);
+    pRtree->pNodeBlob = pBlob;
+    if( rc ){
+      nodeBlobReset(pRtree);
+      if( rc==SQLITE_NOMEM ) return SQLITE_NOMEM;
+    }
+  }
+  if( pRtree->pNodeBlob==0 ){
+    char *zTab = sqlite3_mprintf("%s_node", pRtree->zName);
+    if( zTab==0 ) return SQLITE_NOMEM;
+    rc = sqlite3_blob_open(pRtree->db, pRtree->zDb, zTab, "data", iNode, 0,
+                           &pRtree->pNodeBlob);
+    sqlite3_free(zTab);
+  }
+  if( rc ){
+    nodeBlobReset(pRtree);
+    *ppNode = 0;
+    /* If unable to open an sqlite3_blob on the desired row, that can only
+    ** be because the shadow tables hold erroneous data. */
+    if( rc==SQLITE_ERROR ){
+      rc = SQLITE_CORRUPT_VTAB;
+      RTREE_IS_CORRUPT(pRtree);
+    }
+  }else if( pRtree->iNodeSize==sqlite3_blob_bytes(pRtree->pNodeBlob) ){
+    pNode = (RtreeNode *)sqlite3_malloc64(sizeof(RtreeNode)+pRtree->iNodeSize);
+    if( !pNode ){
+      rc = SQLITE_NOMEM;
+    }else{
+      pNode->pParent = pParent;
+      pNode->zData = (u8 *)&pNode[1];
+      pNode->nRef = 1;
+      pRtree->nNodeRef++;
+      pNode->iNode = iNode;
+      pNode->isDirty = 0;
+      pNode->pNext = 0;
+      rc = sqlite3_blob_read(pRtree->pNodeBlob, pNode->zData,
+                             pRtree->iNodeSize, 0);
+    }
+  }
+
+  /* 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( rc==SQLITE_OK && pNode && iNode==1 ){
+    pRtree->iDepth = readInt16(pNode->zData);
+    if( pRtree->iDepth>RTREE_MAX_DEPTH ){
+      rc = SQLITE_CORRUPT_VTAB;
+      RTREE_IS_CORRUPT(pRtree);
+    }
+  }
+
+  /* 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_VTAB.
+  */
+  if( pNode && rc==SQLITE_OK ){
+    if( NCELL(pNode)>((pRtree->iNodeSize-4)/pRtree->nBytesPerCell) ){
+      rc = SQLITE_CORRUPT_VTAB;
+      RTREE_IS_CORRUPT(pRtree);
+    }
+  }
+
+  if( rc==SQLITE_OK ){
+    if( pNode!=0 ){
+      nodeReference(pParent);
+      nodeHashInsert(pRtree, pNode);
+    }else{
+      rc = SQLITE_CORRUPT_VTAB;
+      RTREE_IS_CORRUPT(pRtree);
+    }
+    *ppNode = pNode;
+  }else{
+    if( pNode ){
+      pRtree->nNodeRef--;
+      sqlite3_free(pNode);
+    }
+    *ppNode = 0;
+  }
+
+  return rc;
+}
+
+/*
+** Overwrite cell iCell of node pNode with the contents of pCell.
+*/
+static void nodeOverwriteCell(
+  Rtree *pRtree,             /* The overall R-Tree */
+  RtreeNode *pNode,          /* The node into which the cell is to be written */
+  RtreeCell *pCell,          /* The cell to write */
+  int iCell                  /* Index into pNode into which pCell is written */
+){
+  int ii;
+  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
+  p += writeInt64(p, pCell->iRowid);
+  for(ii=0; ii<pRtree->nDim2; ii++){
+    p += writeCoord(p, &pCell->aCoord[ii]);
+  }
+  pNode->isDirty = 1;
+}
+
+/*
+** Remove the cell with index iCell from node pNode.
+*/
+static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
+  u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
+  u8 *pSrc = &pDst[pRtree->nBytesPerCell];
+  int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
+  memmove(pDst, pSrc, nByte);
+  writeInt16(&pNode->zData[2], NCELL(pNode)-1);
+  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,                /* 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){
+  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);
+    sqlite3_bind_null(p, 2);
+    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){
+  int rc = SQLITE_OK;
+  if( pNode ){
+    assert( pNode->nRef>0 );
+    assert( pRtree->nNodeRef>0 );
+    pNode->nRef--;
+    if( pNode->nRef==0 ){
+      pRtree->nNodeRef--;
+      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,       /* The overall R-Tree */
+  RtreeNode *pNode,    /* The node from which to extract the ID */
+  int iCell            /* The cell index from which to extract the ID */
+){
+  assert( iCell<NCELL(pNode) );
+  return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);
+}
+
+/*
+** Return coordinate iCoord from cell iCell in node pNode.
+*/
+static void nodeGetCoord(
+  Rtree *pRtree,               /* The overall R-Tree */
+  RtreeNode *pNode,            /* The node from which to extract a coordinate */
+  int iCell,                   /* The index of the cell within the node */
+  int iCoord,                  /* Which coordinate to extract */
+  RtreeCoord *pCoord           /* OUT: Space to write result to */
+){
+  readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
+}
+
+/*
+** Deserialize cell iCell of node pNode. Populate the structure pointed
+** to by pCell with the results.
+*/
+static void nodeGetCell(
+  Rtree *pRtree,               /* The overall R-Tree */
+  RtreeNode *pNode,            /* The node containing the cell to be read */
+  int iCell,                   /* Index of the cell within the node */
+  RtreeCell *pCell             /* OUT: Write the cell contents here */
+){
+  u8 *pData;
+  RtreeCoord *pCoord;
+  int ii = 0;
+  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
+  pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);
+  pCoord = pCell->aCoord;
+  do{
+    readCoord(pData, &pCoord[ii]);
+    readCoord(pData+4, &pCoord[ii+1]);
+    pData += 8;
+    ii += 2;
+  }while( ii<pRtree->nDim2 );
+}
+
+
+/* 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
+);
+
+/* 
+** Rtree virtual table module xCreate method.
+*/
+static int rtreeCreate(
+  sqlite3 *db,
+  void *pAux,
+  int argc, const char *const*argv,
+  sqlite3_vtab **ppVtab,
+  char **pzErr
+){
+  return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 1);
+}
+
+/* 
+** Rtree virtual table module xConnect method.
+*/
+static int rtreeConnect(
+  sqlite3 *db,
+  void *pAux,
+  int argc, const char *const*argv,
+  sqlite3_vtab **ppVtab,
+  char **pzErr
+){
+  return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 0);
+}
+
+/*
+** Increment the r-tree reference count.
+*/
+static void rtreeReference(Rtree *pRtree){
+  pRtree->nBusy++;
+}
+
+/*
+** Decrement the r-tree reference count. When the reference count reaches
+** zero the structure is deleted.
+*/
+static void rtreeRelease(Rtree *pRtree){
+  pRtree->nBusy--;
+  if( pRtree->nBusy==0 ){
+    pRtree->inWrTrans = 0;
+    assert( pRtree->nCursor==0 );
+    nodeBlobReset(pRtree);
+    assert( pRtree->nNodeRef==0 || pRtree->bCorrupt );
+    sqlite3_finalize(pRtree->pWriteNode);
+    sqlite3_finalize(pRtree->pDeleteNode);
+    sqlite3_finalize(pRtree->pReadRowid);
+    sqlite3_finalize(pRtree->pWriteRowid);
+    sqlite3_finalize(pRtree->pDeleteRowid);
+    sqlite3_finalize(pRtree->pReadParent);
+    sqlite3_finalize(pRtree->pWriteParent);
+    sqlite3_finalize(pRtree->pDeleteParent);
+    sqlite3_finalize(pRtree->pWriteAux);
+    sqlite3_free(pRtree->zReadAuxSql);
+    sqlite3_free(pRtree);
+  }
+}
+
+/* 
+** Rtree virtual table module xDisconnect method.
+*/
+static int rtreeDisconnect(sqlite3_vtab *pVtab){
+  rtreeRelease((Rtree *)pVtab);
+  return SQLITE_OK;
+}
+
+/* 
+** Rtree virtual table module xDestroy method.
+*/
+static int rtreeDestroy(sqlite3_vtab *pVtab){
+  Rtree *pRtree = (Rtree *)pVtab;
+  int rc;
+  char *zCreate = sqlite3_mprintf(
+    "DROP TABLE '%q'.'%q_node';"
+    "DROP TABLE '%q'.'%q_rowid';"
+    "DROP TABLE '%q'.'%q_parent';",
+    pRtree->zDb, pRtree->zName, 
+    pRtree->zDb, pRtree->zName,
+    pRtree->zDb, pRtree->zName
+  );
+  if( !zCreate ){
+    rc = SQLITE_NOMEM;
+  }else{
+    nodeBlobReset(pRtree);
+    rc = sqlite3_exec(pRtree->db, zCreate, 0, 0, 0);
+    sqlite3_free(zCreate);
+  }
+  if( rc==SQLITE_OK ){
+    rtreeRelease(pRtree);
+  }
+
+  return rc;
+}
+
+/* 
+** Rtree virtual table module xOpen method.
+*/
+static int rtreeOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){
+  int rc = SQLITE_NOMEM;
+  Rtree *pRtree = (Rtree *)pVTab;
+  RtreeCursor *pCsr;
+
+  pCsr = (RtreeCursor *)sqlite3_malloc64(sizeof(RtreeCursor));
+  if( pCsr ){
+    memset(pCsr, 0, sizeof(RtreeCursor));
+    pCsr->base.pVtab = pVTab;
+    rc = SQLITE_OK;
+    pRtree->nCursor++;
+  }
+  *ppCursor = (sqlite3_vtab_cursor *)pCsr;
+
+  return rc;
+}
+
+
+/*
+** Reset a cursor back to its initial state.
+*/
+static void resetCursor(RtreeCursor *pCsr){
+  Rtree *pRtree = (Rtree *)(pCsr->base.pVtab);
+  int ii;
+  sqlite3_stmt *pStmt;
+  if( pCsr->aConstraint ){
+    int i;                        /* Used to iterate through constraint array */
+    for(i=0; i<pCsr->nConstraint; i++){
+      sqlite3_rtree_query_info *pInfo = pCsr->aConstraint[i].pInfo;
+      if( pInfo ){
+        if( pInfo->xDelUser ) pInfo->xDelUser(pInfo->pUser);
+        sqlite3_free(pInfo);
+      }
+    }
+    sqlite3_free(pCsr->aConstraint);
+    pCsr->aConstraint = 0;
+  }
+  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
+  sqlite3_free(pCsr->aPoint);
+  pStmt = pCsr->pReadAux;
+  memset(pCsr, 0, sizeof(RtreeCursor));
+  pCsr->base.pVtab = (sqlite3_vtab*)pRtree;
+  pCsr->pReadAux = pStmt;
+
+}
+
+/* 
+** Rtree virtual table module xClose method.
+*/
+static int rtreeClose(sqlite3_vtab_cursor *cur){
+  Rtree *pRtree = (Rtree *)(cur->pVtab);
+  RtreeCursor *pCsr = (RtreeCursor *)cur;
+  assert( pRtree->nCursor>0 );
+  resetCursor(pCsr);
+  sqlite3_finalize(pCsr->pReadAux);
+  sqlite3_free(pCsr);
+  pRtree->nCursor--;
+  nodeBlobReset(pRtree);
+  return SQLITE_OK;
+}
+
+/*
+** Rtree virtual table module xEof method.
+**
+** Return non-zero if the cursor does not currently point to a valid 
+** record (i.e if the scan has finished), or zero otherwise.
+*/
+static int rtreeEof(sqlite3_vtab_cursor *cur){
+  RtreeCursor *pCsr = (RtreeCursor *)cur;
+  return pCsr->atEOF;
+}
+
+/*
+** Convert raw bits from the on-disk RTree record into a coordinate value.
+** The on-disk format is big-endian and needs to be converted for little-
+** endian platforms.  The on-disk record stores integer coordinates if
+** eInt is true and it stores 32-bit floating point records if eInt is
+** false.  a[] is the four bytes of the on-disk record to be decoded.
+** Store the results in "r".
+**
+** There are five versions of this macro.  The last one is generic.  The
+** other four are various architectures-specific optimizations.
+*/
+#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+#define RTREE_DECODE_COORD(eInt, a, r) {                        \
+    RtreeCoord c;    /* Coordinate decoded */                   \
+    c.u = _byteswap_ulong(*(u32*)a);                            \
+    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
+}
+#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
+#define RTREE_DECODE_COORD(eInt, a, r) {                        \
+    RtreeCoord c;    /* Coordinate decoded */                   \
+    c.u = __builtin_bswap32(*(u32*)a);                          \
+    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
+}
+#elif 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 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 */
+){
+  sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */
+  int nCoord = pInfo->nCoord;                           /* No. of coordinates */
+  int rc;                                             /* Callback return code */
+  RtreeCoord c;                                       /* Translator union */
+  sqlite3_rtree_dbl aCoord[RTREE_MAX_DIMENSIONS*2];   /* Decoded coordinates */
+
+  assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );
+  assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );
+
+  if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){
+    pInfo->iRowid = readInt64(pCellData);
+  }
+  pCellData += 8;
+#ifndef SQLITE_RTREE_INT_ONLY
+  if( eInt==0 ){
+    switch( nCoord ){
+      case 10:  readCoord(pCellData+36, &c); aCoord[9] = c.f;
+                readCoord(pCellData+32, &c); aCoord[8] = c.f;
+      case 8:   readCoord(pCellData+28, &c); aCoord[7] = c.f;
+                readCoord(pCellData+24, &c); aCoord[6] = c.f;
+      case 6:   readCoord(pCellData+20, &c); aCoord[5] = c.f;
+                readCoord(pCellData+16, &c); aCoord[4] = c.f;
+      case 4:   readCoord(pCellData+12, &c); aCoord[3] = c.f;
+                readCoord(pCellData+8,  &c); aCoord[2] = c.f;
+      default:  readCoord(pCellData+4,  &c); aCoord[1] = c.f;
+                readCoord(pCellData,    &c); aCoord[0] = c.f;
+    }
+  }else
+#endif
+  {
+    switch( nCoord ){
+      case 10:  readCoord(pCellData+36, &c); aCoord[9] = c.i;
+                readCoord(pCellData+32, &c); aCoord[8] = c.i;
+      case 8:   readCoord(pCellData+28, &c); aCoord[7] = c.i;
+                readCoord(pCellData+24, &c); aCoord[6] = c.i;
+      case 6:   readCoord(pCellData+20, &c); aCoord[5] = c.i;
+                readCoord(pCellData+16, &c); aCoord[4] = c.i;
+      case 4:   readCoord(pCellData+12, &c); aCoord[3] = c.i;
+                readCoord(pCellData+8,  &c); aCoord[2] = c.i;
+      default:  readCoord(pCellData+4,  &c); aCoord[1] = c.i;
+                readCoord(pCellData,    &c); aCoord[0] = c.i;
+    }
+  }
+  if( pConstraint->op==RTREE_MATCH ){
+    int eWithin = 0;
+    rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,
+                              nCoord, aCoord, &eWithin);
+    if( eWithin==0 ) *peWithin = NOT_WITHIN;
+    *prScore = RTREE_ZERO;
+  }else{
+    pInfo->aCoord = aCoord;
+    pInfo->iLevel = pSearch->iLevel - 1;
+    pInfo->rScore = pInfo->rParentScore = pSearch->rScore;
+    pInfo->eWithin = pInfo->eParentWithin = pSearch->eWithin;
+    rc = pConstraint->u.xQueryFunc(pInfo);
+    if( pInfo->eWithin<*peWithin ) *peWithin = pInfo->eWithin;
+    if( pInfo->rScore<*prScore || *prScore<RTREE_ZERO ){
+      *prScore = pInfo->rScore;
+    }
+  }
+  return rc;
+}
+
+/* 
+** Check the internal RTree node given by pCellData against constraint p.
+** If this constraint cannot be satisfied by any child within the node,
+** set *peWithin to NOT_WITHIN.
+*/
+static void rtreeNonleafConstraint(
+  RtreeConstraint *p,        /* The constraint to test */
+  int eInt,                  /* True if RTree holds integer coordinates */
+  u8 *pCellData,             /* Raw cell content as appears on disk */
+  int *peWithin              /* Adjust downward, as appropriate */
+){
+  sqlite3_rtree_dbl val;     /* Coordinate value convert to a double */
+
+  /* p->iCoord might point to either a lower or upper bound coordinate
+  ** in a coordinate pair.  But make pCellData point to the lower bound.
+  */
+  pCellData += 8 + 4*(p->iCoord&0xfe);
+
+  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
+      || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_TRUE
+      || p->op==RTREE_FALSE );
+  assert( ((((char*)pCellData) - (char*)0)&3)==0 );  /* 4-byte aligned */
+  switch( p->op ){
+    case RTREE_TRUE:  return;   /* Always satisfied */
+    case RTREE_FALSE: break;    /* Never satisfied */
+    case RTREE_EQ:
+      RTREE_DECODE_COORD(eInt, pCellData, val);
+      /* val now holds the lower bound of the coordinate pair */
+      if( p->u.rValue>=val ){
+        pCellData += 4;
+        RTREE_DECODE_COORD(eInt, pCellData, val);
+        /* val now holds the upper bound of the coordinate pair */
+        if( p->u.rValue<=val ) return;
+      }
+      break;
+    case RTREE_LE:
+    case RTREE_LT:
+      RTREE_DECODE_COORD(eInt, pCellData, val);
+      /* val now holds the lower bound of the coordinate pair */
+      if( p->u.rValue>=val ) return;
+      break;
+
+    default:
+      pCellData += 4;
+      RTREE_DECODE_COORD(eInt, pCellData, val);
+      /* val now holds the upper bound of the coordinate pair */
+      if( p->u.rValue<=val ) return;
+      break;
+  }
+  *peWithin = NOT_WITHIN;
+}
+
+/*
+** Check the leaf RTree cell given by pCellData against constraint p.
+** If this constraint is not satisfied, set *peWithin to NOT_WITHIN.
+** If the constraint is satisfied, leave *peWithin unchanged.
+**
+** The constraint is of the form:  xN op $val
+**
+** The op is given by p->op.  The xN is p->iCoord-th coordinate in
+** pCellData.  $val is given by p->u.rValue.
+*/
+static void rtreeLeafConstraint(
+  RtreeConstraint *p,        /* The constraint to test */
+  int eInt,                  /* True if RTree holds integer coordinates */
+  u8 *pCellData,             /* Raw cell content as appears on disk */
+  int *peWithin              /* Adjust downward, as appropriate */
+){
+  RtreeDValue xN;      /* Coordinate value converted to a double */
+
+  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
+      || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_TRUE
+      || p->op==RTREE_FALSE );
+  pCellData += 8 + p->iCoord*4;
+  assert( ((((char*)pCellData) - (char*)0)&3)==0 );  /* 4-byte aligned */
+  RTREE_DECODE_COORD(eInt, pCellData, xN);
+  switch( p->op ){
+    case RTREE_TRUE:  return;   /* Always satisfied */
+    case RTREE_FALSE: break;    /* Never satisfied */
+    case RTREE_LE:    if( xN <= p->u.rValue ) return;  break;
+    case RTREE_LT:    if( xN <  p->u.rValue ) return;  break;
+    case RTREE_GE:    if( xN >= p->u.rValue ) return;  break;
+    case RTREE_GT:    if( xN >  p->u.rValue ) return;  break;
+    default:          if( xN == p->u.rValue ) return;  break;
+  }
+  *peWithin = NOT_WITHIN;
+}
+
+/*
+** One of the cells in node pNode is guaranteed to have a 64-bit 
+** integer value equal to iRowid. Return the index of this cell.
+*/
+static int nodeRowidIndex(
+  Rtree *pRtree, 
+  RtreeNode *pNode, 
+  i64 iRowid,
+  int *piIndex
+){
+  int ii;
+  int nCell = NCELL(pNode);
+  assert( nCell<200 );
+  for(ii=0; ii<nCell; ii++){
+    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
+      *piIndex = ii;
+      return SQLITE_OK;
+    }
+  }
+  RTREE_IS_CORRUPT(pRtree);
+  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( ALWAYS(pParent) ){
+    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
+  }else{
+    *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 two 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_realloc64(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<=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;
+      assert( ii==1 );
+      if( ALWAYS(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( ALWAYS(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 ){
+    u8 *pCellData;
+    pNode = rtreeNodeOfFirstSearchPoint(pCur, &rc);
+    if( rc ) return rc;
+    nCell = NCELL(pNode);
+    assert( nCell<200 );
+    pCellData = pNode->zData + (4+pRtree->nBytesPerCell*p->iCell);
+    while( p->iCell<nCell ){
+      sqlite3_rtree_dbl rScore = (sqlite3_rtree_dbl)-1;
+      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 ){
+          p->iCell++;
+          pCellData += pRtree->nBytesPerCell;
+          break;
+        }
+      }
+      if( eWithin==NOT_WITHIN ) continue;
+      p->iCell++;
+      x.iLevel = p->iLevel - 1;
+      if( x.iLevel ){
+        x.id = readInt64(pCellData);
+        for(ii=0; ii<pCur->nPoint; ii++){
+          if( pCur->aPoint[ii].id==x.id ){
+            RTREE_IS_CORRUPT(pRtree);
+            return SQLITE_CORRUPT_VTAB;
+          }
+        }
+        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 = (u8)eWithin;
+      p->id = x.id;
+      p->iCell = x.iCell;
+      RTREE_QUEUE_TRACE(pCur, "PUSH-S:");
+      break;
+    }
+    if( p->iCell>=nCell ){
+      RTREE_QUEUE_TRACE(pCur, "POP-Se:");
+      rtreeSearchPointPop(pCur);
+    }
+  }
+  pCur->atEOF = p==0;
+  return SQLITE_OK;
+}
+
+/* 
+** Rtree virtual table module xNext method.
+*/
+static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
+  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
+  int rc = SQLITE_OK;
+
+  /* Move to the next entry that matches the configured constraints. */
+  RTREE_QUEUE_TRACE(pCsr, "POP-Nx:");
+  if( pCsr->bAuxValid ){
+    pCsr->bAuxValid = 0;
+    sqlite3_reset(pCsr->pReadAux);
+  }
+  rtreeSearchPointPop(pCsr);
+  rc = rtreeStepToLeaf(pCsr);
+  return rc;
+}
+
+/* 
+** Rtree virtual table module xRowid method.
+*/
+static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){
+  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
+  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
+  int rc = SQLITE_OK;
+  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
+  if( rc==SQLITE_OK && ALWAYS(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( NEVER(p==0) ) return SQLITE_OK;
+  if( i==0 ){
+    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
+  }else if( i<=pRtree->nDim2 ){
+    nodeGetCoord(pRtree, pNode, p->iCell, i-1, &c);
+#ifndef SQLITE_RTREE_INT_ONLY
+    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
+      sqlite3_result_double(ctx, c.f);
+    }else
+#endif
+    {
+      assert( pRtree->eCoordType==RTREE_COORD_INT32 );
+      sqlite3_result_int(ctx, c.i);
+    }
+  }else{
+    if( !pCsr->bAuxValid ){
+      if( pCsr->pReadAux==0 ){
+        rc = sqlite3_prepare_v3(pRtree->db, pRtree->zReadAuxSql, -1, 0,
+                                &pCsr->pReadAux, 0);
+        if( rc ) return rc;
+      }
+      sqlite3_bind_int64(pCsr->pReadAux, 1, 
+          nodeGetRowid(pRtree, pNode, p->iCell));
+      rc = sqlite3_step(pCsr->pReadAux);
+      if( rc==SQLITE_ROW ){
+        pCsr->bAuxValid = 1;
+      }else{
+        sqlite3_reset(pCsr->pReadAux);
+        if( rc==SQLITE_DONE ) rc = SQLITE_OK;
+        return rc;
+      }
+    }
+    sqlite3_result_value(ctx,
+         sqlite3_column_value(pCsr->pReadAux, i - pRtree->nDim2 + 1));
+  }  
+  return SQLITE_OK;
+}
+
+/* 
+** Use nodeAcquire() to obtain the leaf node containing the record with 
+** rowid iRowid. If successful, set *ppLeaf to point to the node and
+** return SQLITE_OK. If there is no such record in the table, set
+** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
+** to zero and return an SQLite error code.
+*/
+static int findLeafNode(
+  Rtree *pRtree,              /* RTree to search */
+  i64 iRowid,                 /* The rowid searching for */
+  RtreeNode **ppLeaf,         /* Write the node here */
+  sqlite3_int64 *piNode       /* Write the node-id here */
+){
+  int rc;
+  *ppLeaf = 0;
+  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
+  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
+    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);
+    if( piNode ) *piNode = iNode;
+    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
+    sqlite3_reset(pRtree->pReadRowid);
+  }else{
+    rc = sqlite3_reset(pRtree->pReadRowid);
+  }
+  return rc;
+}
+
+/*
+** This function is called to configure the RtreeConstraint object passed
+** as the second argument for a MATCH constraint. The value passed as the
+** first argument to this function is the right-hand operand to the MATCH
+** operator.
+*/
+static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
+  RtreeMatchArg *pBlob, *pSrc;       /* BLOB returned by geometry function */
+  sqlite3_rtree_query_info *pInfo;   /* Callback information */
+
+  pSrc = sqlite3_value_pointer(pValue, "RtreeMatchArg");
+  if( pSrc==0 ) return SQLITE_ERROR;
+  pInfo = (sqlite3_rtree_query_info*)
+                sqlite3_malloc64( sizeof(*pInfo)+pSrc->iSize );
+  if( !pInfo ) return SQLITE_NOMEM;
+  memset(pInfo, 0, sizeof(*pInfo));
+  pBlob = (RtreeMatchArg*)&pInfo[1];
+  memcpy(pBlob, pSrc, pSrc->iSize);
+  pInfo->pContext = pBlob->cb.pContext;
+  pInfo->nParam = pBlob->nParam;
+  pInfo->aParam = pBlob->aParam;
+  pInfo->apSqlParam = pBlob->apSqlParam;
+
+  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. */
+  resetCursor(pCsr);
+
+  pCsr->iStrategy = idxNum;
+  if( idxNum==1 ){
+    /* Special case - lookup by rowid. */
+    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
+    RtreeSearchPoint *p;     /* Search point for the leaf */
+    i64 iRowid = sqlite3_value_int64(argv[0]);
+    i64 iNode = 0;
+    int eType = sqlite3_value_numeric_type(argv[0]);
+    if( eType==SQLITE_INTEGER
+     || (eType==SQLITE_FLOAT && sqlite3_value_double(argv[0])==iRowid)
+    ){
+      rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);
+    }else{
+      rc = SQLITE_OK;
+      pLeaf = 0;
+    }
+    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 = (u8)iCell;
+      RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
+    }else{
+      pCsr->atEOF = 1;
+    }
+  }else{
+    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
+    ** with the configured constraints. 
+    */
+    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
+    if( rc==SQLITE_OK && argc>0 ){
+      pCsr->aConstraint = sqlite3_malloc64(sizeof(RtreeConstraint)*argc);
+      pCsr->nConstraint = argc;
+      if( !pCsr->aConstraint ){
+        rc = SQLITE_NOMEM;
+      }else{
+        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);
+        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
+        assert( (idxStr==0 && argc==0)
+                || (idxStr && (int)strlen(idxStr)==argc*2) );
+        for(ii=0; ii<argc; ii++){
+          RtreeConstraint *p = &pCsr->aConstraint[ii];
+          int eType = sqlite3_value_numeric_type(argv[ii]);
+          p->op = idxStr[ii*2];
+          p->iCoord = idxStr[ii*2+1]-'0';
+          if( p->op>=RTREE_MATCH ){
+            /* A MATCH operator. The right-hand-side must be a blob that
+            ** can be cast into an RtreeMatchArg object. One created using
+            ** an sqlite3_rtree_geometry_callback() SQL user function.
+            */
+            rc = deserializeGeometry(argv[ii], p);
+            if( rc!=SQLITE_OK ){
+              break;
+            }
+            p->pInfo->nCoord = pRtree->nDim2;
+            p->pInfo->anQueue = pCsr->anQueue;
+            p->pInfo->mxLevel = pRtree->iDepth + 1;
+          }else if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
+#ifdef SQLITE_RTREE_INT_ONLY
+            p->u.rValue = sqlite3_value_int64(argv[ii]);
+#else
+            p->u.rValue = sqlite3_value_double(argv[ii]);
+#endif
+          }else{
+            p->u.rValue = RTREE_ZERO;
+            if( eType==SQLITE_NULL ){
+              p->op = RTREE_FALSE;
+            }else if( p->op==RTREE_LT || p->op==RTREE_LE ){
+              p->op = RTREE_TRUE;
+            }else{
+              p->op = RTREE_FALSE;
+            }
+          }
+        }
+      }
+    }
+    if( rc==SQLITE_OK ){
+      RtreeSearchPoint *pNew;
+      assert( pCsr->bPoint==0 );  /* Due to the resetCursor() call above */
+      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, (u8)(pRtree->iDepth+1));
+      if( NEVER(pNew==0) ){       /* Because pCsr->bPoint was FALSE */
+        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;
+}
+
+/*
+** 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.
+**   ------------------------------------------------
+**
+** If strategy 1 is used, then idxStr is not meaningful. If strategy
+** 2 is used, idxStr is formatted to contain 2 bytes for each 
+** constraint used. The first two bytes of idxStr correspond to 
+** the constraint in sqlite3_index_info.aConstraintUsage[] with
+** (argvIndex==1) etc.
+**
+** The first of each pair of bytes in idxStr identifies the constraint
+** operator as follows:
+**
+**   Operator    Byte Value
+**   ----------------------
+**      =        0x41 ('A')
+**     <=        0x42 ('B')
+**      <        0x43 ('C')
+**     >=        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;
+  int bMatch = 0;                 /* True if there exists a MATCH constraint */
+  i64 nRow;                       /* Estimated rows returned by this scan */
+
+  int iIdx = 0;
+  char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
+  memset(zIdxStr, 0, sizeof(zIdxStr));
+
+  /* Check if there exists a MATCH constraint - even an unusable one. If there
+  ** is, do not consider the lookup-by-rowid plan as using such a plan would
+  ** require the VDBE to evaluate the MATCH constraint, which is not currently
+  ** possible. */
+  for(ii=0; ii<pIdxInfo->nConstraint; ii++){
+    if( pIdxInfo->aConstraint[ii].op==SQLITE_INDEX_CONSTRAINT_MATCH ){
+      bMatch = 1;
+    }
+  }
+
+  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( bMatch==0 && 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). It is expected to return
+      ** a single row.
+      */ 
+      pIdxInfo->estimatedCost = 30.0;
+      pIdxInfo->estimatedRows = 1;
+      pIdxInfo->idxFlags = SQLITE_INDEX_SCAN_UNIQUE;
+      return SQLITE_OK;
+    }
+
+    if( p->usable
+    && ((p->iColumn>0 && p->iColumn<=pRtree->nDim2)
+        || 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;
+        case SQLITE_INDEX_CONSTRAINT_MATCH: op = RTREE_MATCH; break;
+        default:                            op = 0;           break;
+      }
+      if( op ){
+        zIdxStr[iIdx++] = op;
+        zIdxStr[iIdx++] = (char)(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;
+  }
+
+  nRow = pRtree->nRowEst >> (iIdx/2);
+  pIdxInfo->estimatedCost = (double)6.0 * (double)nRow;
+  pIdxInfo->estimatedRows = nRow;
+
+  return rc;
+}
+
+/*
+** Return the N-dimensional volumn of the cell stored in *p.
+*/
+static RtreeDValue cellArea(Rtree *pRtree, RtreeCell *p){
+  RtreeDValue area = (RtreeDValue)1;
+  assert( pRtree->nDim>=1 && pRtree->nDim<=5 );
+#ifndef SQLITE_RTREE_INT_ONLY
+  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
+    switch( pRtree->nDim ){
+      case 5:  area  = p->aCoord[9].f - p->aCoord[8].f;
+      case 4:  area *= p->aCoord[7].f - p->aCoord[6].f;
+      case 3:  area *= p->aCoord[5].f - p->aCoord[4].f;
+      case 2:  area *= p->aCoord[3].f - p->aCoord[2].f;
+      default: area *= p->aCoord[1].f - p->aCoord[0].f;
+    }
+  }else
+#endif
+  {
+    switch( pRtree->nDim ){
+      case 5:  area  = (i64)p->aCoord[9].i - (i64)p->aCoord[8].i;
+      case 4:  area *= (i64)p->aCoord[7].i - (i64)p->aCoord[6].i;
+      case 3:  area *= (i64)p->aCoord[5].i - (i64)p->aCoord[4].i;
+      case 2:  area *= (i64)p->aCoord[3].i - (i64)p->aCoord[2].i;
+      default: area *= (i64)p->aCoord[1].i - (i64)p->aCoord[0].i;
+    }
+  }
+  return area;
+}
+
+/*
+** Return the margin length of cell p. The margin length is the sum
+** of the objects size in each dimension.
+*/
+static RtreeDValue cellMargin(Rtree *pRtree, RtreeCell *p){
+  RtreeDValue margin = 0;
+  int ii = pRtree->nDim2 - 2;
+  do{
+    margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
+    ii -= 2;
+  }while( ii>=0 );
+  return margin;
+}
+
+/*
+** Store the union of cells p1 and p2 in p1.
+*/
+static void cellUnion(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
+  int ii = 0;
+  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
+    do{
+      p1->aCoord[ii].f = MIN(p1->aCoord[ii].f, p2->aCoord[ii].f);
+      p1->aCoord[ii+1].f = MAX(p1->aCoord[ii+1].f, p2->aCoord[ii+1].f);
+      ii += 2;
+    }while( ii<pRtree->nDim2 );
+  }else{
+    do{
+      p1->aCoord[ii].i = MIN(p1->aCoord[ii].i, p2->aCoord[ii].i);
+      p1->aCoord[ii+1].i = MAX(p1->aCoord[ii+1].i, p2->aCoord[ii+1].i);
+      ii += 2;
+    }while( ii<pRtree->nDim2 );
+  }
+}
+
+/*
+** Return true if the area covered by p2 is a subset of the area covered
+** by p1. False otherwise.
+*/
+static int cellContains(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
+  int ii;
+  int isInt = (pRtree->eCoordType==RTREE_COORD_INT32);
+  for(ii=0; ii<pRtree->nDim2; ii+=2){
+    RtreeCoord *a1 = &p1->aCoord[ii];
+    RtreeCoord *a2 = &p2->aCoord[ii];
+    if( (!isInt && (a2[0].f<a1[0].f || a2[1].f>a1[1].f)) 
+     || ( isInt && (a2[0].i<a1[0].i || a2[1].i>a1[1].i)) 
+    ){
+      return 0;
+    }
+  }
+  return 1;
+}
+
+/*
+** Return the amount cell p would grow by if it were unioned with pCell.
+*/
+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);
+}
+
+static RtreeDValue cellOverlap(
+  Rtree *pRtree, 
+  RtreeCell *p, 
+  RtreeCell *aCell, 
+  int nCell
+){
+  int ii;
+  RtreeDValue overlap = RTREE_ZERO;
+  for(ii=0; ii<nCell; ii++){
+    int jj;
+    RtreeDValue o = (RtreeDValue)1;
+    for(jj=0; jj<pRtree->nDim2; jj+=2){
+      RtreeDValue x1, x2;
+      x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
+      x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));
+      if( x2<x1 ){
+        o = (RtreeDValue)0;
+        break;
+      }else{
+        o = o * (x2-x1);
+      }
+    }
+    overlap += o;
+  }
+  return overlap;
+}
+
+
+/*
+** This function implements the ChooseLeaf algorithm from Gutman[84].
+** ChooseSubTree in r*tree terminology.
+*/
+static int ChooseLeaf(
+  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 = 0;
+  rc = nodeAcquire(pRtree, 1, 0, &pNode);
+
+  for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
+    int iCell;
+    sqlite3_int64 iBest = 0;
+
+    RtreeDValue fMinGrowth = RTREE_ZERO;
+    RtreeDValue fMinArea = RTREE_ZERO;
+
+    int nCell = NCELL(pNode);
+    RtreeCell cell;
+    RtreeNode *pChild = 0;
+
+    RtreeCell *aCell = 0;
+
+    /* Select the child node which will be enlarged the least if pCell
+    ** is inserted into it. Resolve ties by choosing the entry with
+    ** the smallest area.
+    */
+    for(iCell=0; iCell<nCell; iCell++){
+      int bBest = 0;
+      RtreeDValue growth;
+      RtreeDValue area;
+      nodeGetCell(pRtree, pNode, iCell, &cell);
+      growth = cellGrowth(pRtree, &cell, pCell);
+      area = cellArea(pRtree, &cell);
+      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
+        bBest = 1;
+      }
+      if( bBest ){
+        fMinGrowth = growth;
+        fMinArea = area;
+        iBest = cell.iRowid;
+      }
+    }
+
+    sqlite3_free(aCell);
+    rc = nodeAcquire(pRtree, iBest, pNode, &pChild);
+    nodeRelease(pRtree, pNode);
+    pNode = pChild;
+  }
+
+  *ppLeaf = pNode;
+  return rc;
+}
+
+/*
+** A cell with the same content as pCell has just been inserted into
+** the node pNode. This function updates the bounding box cells in
+** all ancestor elements.
+*/
+static int AdjustTree(
+  Rtree *pRtree,                    /* Rtree table */
+  RtreeNode *pNode,                 /* Adjust ancestry of this node. */
+  RtreeCell *pCell                  /* This cell was just inserted */
+){
+  RtreeNode *p = pNode;
+  int cnt = 0;
+  int rc;
+  while( p->pParent ){
+    RtreeNode *pParent = p->pParent;
+    RtreeCell cell;
+    int iCell;
+
+    cnt++;
+    if( NEVER(cnt>100) ){
+      RTREE_IS_CORRUPT(pRtree);
+      return SQLITE_CORRUPT_VTAB;
+    }
+    rc = nodeParentIndex(pRtree, p, &iCell);
+    if( NEVER(rc!=SQLITE_OK) ){
+      RTREE_IS_CORRUPT(pRtree);
+      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;
+  }
+  return SQLITE_OK;
+}
+
+/*
+** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
+*/
+static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
+  sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
+  sqlite3_bind_int64(pRtree->pWriteRowid, 2, iNode);
+  sqlite3_step(pRtree->pWriteRowid);
+  return sqlite3_reset(pRtree->pWriteRowid);
+}
+
+/*
+** Write mapping (iNode->iPar) to the <rtree>_parent table.
+*/
+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);
+
+
+/*
+** 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, 
+  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{
+        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++){
+        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 
+** (nIdx-1) in no particular order. This function sorts the values
+** in aIdx according to dimension iDim of the cells in aCell. The
+** minimum value of dimension iDim is considered first, the
+** maximum used to break ties.
+**
+** The aSpare array is used as temporary working space by the
+** sorting algorithm.
+*/
+static void SortByDimension(
+  Rtree *pRtree,
+  int *aIdx, 
+  int nIdx, 
+  int iDim, 
+  RtreeCell *aCell, 
+  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];
+
+    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 ){
+      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++){
+        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
+  }
+}
+
+/*
+** 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 = 0;
+  int iBestSplit = 0;
+  RtreeDValue fBestMargin = RTREE_ZERO;
+
+  sqlite3_int64 nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));
+
+  aaSorted = (int **)sqlite3_malloc64(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++){
+    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;
+      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);
+      area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
+      if( (nLeft==RTREE_MINCELLS(pRtree))
+       || (overlap<fBestOverlap)
+       || (overlap==fBestOverlap && area<fBestArea)
+      ){
+        iBestLeft = nLeft;
+        fBestOverlap = overlap;
+        fBestArea = area;
+      }
+    }
+
+    if( ii==0 || margin<fBestMargin ){
+      iBestDim = ii;
+      fBestMargin = margin;
+      iBestSplit = iBestLeft;
+    }
+  }
+
+  memcpy(pBboxLeft, &aCell[aaSorted[iBestDim][0]], sizeof(RtreeCell));
+  memcpy(pBboxRight, &aCell[aaSorted[iBestDim][iBestSplit]], sizeof(RtreeCell));
+  for(ii=0; ii<nCell; ii++){
+    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;
+}
+
+
+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 ){
+    RtreeNode *pChild = nodeHashLookup(pRtree, iRowid);
+    RtreeNode *p;
+    for(p=pNode; p; p=p->pParent){
+      if( p==pChild ) return SQLITE_CORRUPT_VTAB;
+    }
+    if( pChild ){
+      nodeRelease(pRtree, pChild->pParent);
+      nodeReference(pNode);
+      pChild->pParent = pNode;
+    }
+  }
+  if( NEVER(pNode==0) ) return SQLITE_ERROR;
+  return xSetMapping(pRtree, iRowid, pNode->iNode);
+}
+
+static int SplitNode(
+  Rtree *pRtree,
+  RtreeNode *pNode,
+  RtreeCell *pCell,
+  int iHeight
+){
+  int i;
+  int newCellIsRight = 0;
+
+  int rc = SQLITE_OK;
+  int nCell = NCELL(pNode);
+  RtreeCell *aCell;
+  int *aiUsed;
+
+  RtreeNode *pLeft = 0;
+  RtreeNode *pRight = 0;
+
+  RtreeCell leftbbox;
+  RtreeCell rightbbox;
+
+  /* Allocate an array and populate it with a copy of pCell and 
+  ** all cells from node pLeft. Then zero the original node.
+  */
+  aCell = sqlite3_malloc64((sizeof(RtreeCell)+sizeof(int))*(nCell+1));
+  if( !aCell ){
+    rc = SQLITE_NOMEM;
+    goto splitnode_out;
+  }
+  aiUsed = (int *)&aCell[nCell+1];
+  memset(aiUsed, 0, sizeof(int)*(nCell+1));
+  for(i=0; i<nCell; i++){
+    nodeGetCell(pRtree, pNode, i, &aCell[i]);
+  }
+  nodeZero(pRtree, pNode);
+  memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
+  nCell++;
+
+  if( pNode->iNode==1 ){
+    pRight = nodeNew(pRtree, pNode);
+    pLeft = nodeNew(pRtree, pNode);
+    pRtree->iDepth++;
+    pNode->isDirty = 1;
+    writeInt16(pNode->zData, pRtree->iDepth);
+  }else{
+    pLeft = pNode;
+    pRight = nodeNew(pRtree, pLeft->pParent);
+    pLeft->nRef++;
+  }
+
+  if( !pLeft || !pRight ){
+    rc = SQLITE_NOMEM;
+    goto splitnode_out;
+  }
+
+  memset(pLeft->zData, 0, pRtree->iNodeSize);
+  memset(pRight->zData, 0, pRtree->iNodeSize);
+
+  rc = splitNodeStartree(pRtree, aCell, nCell, pLeft, pRight,
+                         &leftbbox, &rightbbox);
+  if( rc!=SQLITE_OK ){
+    goto splitnode_out;
+  }
+
+  /* Ensure both child nodes have node numbers assigned to them by calling
+  ** nodeWrite(). Node pRight always needs a node number, as it was created
+  ** by nodeNew() above. But node pLeft sometimes already has a node number.
+  ** In this case avoid the all to nodeWrite().
+  */
+  if( SQLITE_OK!=(rc = nodeWrite(pRtree, pRight))
+   || (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
+  ){
+    goto splitnode_out;
+  }
+
+  rightbbox.iRowid = pRight->iNode;
+  leftbbox.iRowid = pLeft->iNode;
+
+  if( pNode->iNode==1 ){
+    rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
+    if( rc!=SQLITE_OK ){
+      goto splitnode_out;
+    }
+  }else{
+    RtreeNode *pParent = pLeft->pParent;
+    int iCell;
+    rc = nodeParentIndex(pRtree, pLeft, &iCell);
+    if( ALWAYS(rc==SQLITE_OK) ){
+      nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
+      rc = AdjustTree(pRtree, pParent, &leftbbox);
+      assert( rc==SQLITE_OK );
+    }
+    if( NEVER(rc!=SQLITE_OK) ){
+      goto splitnode_out;
+    }
+  }
+  if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
+    goto splitnode_out;
+  }
+
+  for(i=0; i<NCELL(pRight); i++){
+    i64 iRowid = nodeGetRowid(pRtree, pRight, i);
+    rc = updateMapping(pRtree, iRowid, pRight, iHeight);
+    if( iRowid==pCell->iRowid ){
+      newCellIsRight = 1;
+    }
+    if( rc!=SQLITE_OK ){
+      goto splitnode_out;
+    }
+  }
+  if( pNode->iNode==1 ){
+    for(i=0; i<NCELL(pLeft); i++){
+      i64 iRowid = nodeGetRowid(pRtree, pLeft, i);
+      rc = updateMapping(pRtree, iRowid, pLeft, iHeight);
+      if( rc!=SQLITE_OK ){
+        goto splitnode_out;
+      }
+    }
+  }else if( newCellIsRight==0 ){
+    rc = updateMapping(pRtree, pCell->iRowid, pLeft, iHeight);
+  }
+
+  if( rc==SQLITE_OK ){
+    rc = nodeRelease(pRtree, pRight);
+    pRight = 0;
+  }
+  if( rc==SQLITE_OK ){
+    rc = nodeRelease(pRtree, pLeft);
+    pLeft = 0;
+  }
+
+splitnode_out:
+  nodeRelease(pRtree, pRight);
+  nodeRelease(pRtree, pLeft);
+  sqlite3_free(aCell);
+  return rc;
+}
+
+/*
+** If node pLeaf is not the root of the r-tree and its pParent pointer is 
+** still NULL, load all ancestor nodes of pLeaf into memory and populate
+** the pLeaf->pParent chain all the way up to the root node.
+**
+** This operation is required when a row is deleted (or updated - an update
+** is implemented as a delete followed by an insert). SQLite provides the
+** rowid of the row to delete, which can be used to find the leaf on which
+** the entry resides (argument pLeaf). Once the leaf is located, this 
+** function is called to determine its ancestry.
+*/
+static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
+  int rc = SQLITE_OK;
+  RtreeNode *pChild = pLeaf;
+  while( rc==SQLITE_OK && pChild->iNode!=1 && pChild->pParent==0 ){
+    int rc2 = SQLITE_OK;          /* sqlite3_reset() return code */
+    sqlite3_bind_int64(pRtree->pReadParent, 1, pChild->iNode);
+    rc = sqlite3_step(pRtree->pReadParent);
+    if( rc==SQLITE_ROW ){
+      RtreeNode *pTest;           /* Used to test for reference loops */
+      i64 iNode;                  /* Node number of parent node */
+
+      /* Before setting pChild->pParent, test that we are not creating a
+      ** loop of references (as we would if, say, pChild==pParent). We don't
+      ** want to do this as it leads to a memory leak when trying to delete
+      ** the referenced counted node structures.
+      */
+      iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
+      for(pTest=pLeaf; pTest && pTest->iNode!=iNode; pTest=pTest->pParent);
+      if( pTest==0 ){
+        rc2 = nodeAcquire(pRtree, iNode, 0, &pChild->pParent);
+      }
+    }
+    rc = sqlite3_reset(pRtree->pReadParent);
+    if( rc==SQLITE_OK ) rc = rc2;
+    if( rc==SQLITE_OK && !pChild->pParent ){
+      RTREE_IS_CORRUPT(pRtree);
+      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 = 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);
+    testcase( rc!=SQLITE_OK );
+  }
+  rc2 = nodeRelease(pRtree, pParent);
+  if( rc==SQLITE_OK ){
+    rc = rc2;
+  }
+  if( rc!=SQLITE_OK ){
+    return rc;
+  }
+
+  /* Remove the xxx_node entry. */
+  sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
+  sqlite3_step(pRtree->pDeleteNode);
+  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
+    return rc;
+  }
+
+  /* Remove the xxx_parent entry. */
+  sqlite3_bind_int64(pRtree->pDeleteParent, 1, pNode->iNode);
+  sqlite3_step(pRtree->pDeleteParent);
+  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteParent)) ){
+    return rc;
+  }
+  
+  /* Remove the node from the in-memory hash table and link it into
+  ** the Rtree.pDeleted list. Its contents will be re-inserted later on.
+  */
+  nodeHashDelete(pRtree, pNode);
+  pNode->iNode = iHeight;
+  pNode->pNext = pRtree->pDeleted;
+  pNode->nRef++;
+  pRtree->pDeleted = pNode;
+
+  return SQLITE_OK;
+}
+
+static int fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
+  RtreeNode *pParent = pNode->pParent;
+  int rc = SQLITE_OK; 
+  if( pParent ){
+    int ii; 
+    int nCell = NCELL(pNode);
+    RtreeCell box;                            /* Bounding box for pNode */
+    nodeGetCell(pRtree, pNode, 0, &box);
+    for(ii=1; ii<nCell; ii++){
+      RtreeCell cell;
+      nodeGetCell(pRtree, pNode, ii, &cell);
+      cellUnion(pRtree, &box, &cell);
+    }
+    box.iRowid = pNode->iNode;
+    rc = nodeParentIndex(pRtree, pNode, &ii);
+    if( rc==SQLITE_OK ){
+      nodeOverwriteCell(pRtree, pParent, &box, ii);
+      rc = fixBoundingBox(pRtree, pParent);
+    }
+  }
+  return rc;
+}
+
+/*
+** Delete the cell at index iCell of node pNode. After removing the
+** cell, adjust the r-tree data structure if required.
+*/
+static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){
+  RtreeNode *pParent;
+  int rc;
+
+  if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
+    return rc;
+  }
+
+  /* Remove the cell from the node. This call just moves bytes around
+  ** the in-memory node image, so it cannot fail.
+  */
+  nodeDeleteCell(pRtree, pNode, iCell);
+
+  /* If the node is not the tree root and now has less than the minimum
+  ** number of cells, remove it from the tree. Otherwise, update the
+  ** cell in the parent node so that it tightly contains the updated
+  ** node.
+  */
+  pParent = pNode->pParent;
+  assert( pParent || pNode->iNode==1 );
+  if( pParent ){
+    if( NCELL(pNode)<RTREE_MINCELLS(pRtree) ){
+      rc = removeNode(pRtree, pNode, iHeight);
+    }else{
+      rc = fixBoundingBox(pRtree, pNode);
+    }
+  }
+
+  return rc;
+}
+
+static int Reinsert(
+  Rtree *pRtree, 
+  RtreeNode *pNode, 
+  RtreeCell *pCell, 
+  int iHeight
+){
+  int *aOrder;
+  int *aSpare;
+  RtreeCell *aCell;
+  RtreeDValue *aDistance;
+  int nCell;
+  RtreeDValue aCenterCoord[RTREE_MAX_DIMENSIONS];
+  int iDim;
+  int ii;
+  int rc = SQLITE_OK;
+  int n;
+
+  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_malloc64(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[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]/(nCell*(RtreeDValue)2));
+  }
+
+  for(ii=0; ii<nCell; ii++){
+    aDistance[ii] = RTREE_ZERO;
+    for(iDim=0; iDim<pRtree->nDim; iDim++){
+      RtreeDValue coord = (DCOORD(aCell[ii].aCoord[iDim*2+1]) - 
+                               DCOORD(aCell[ii].aCoord[iDim*2]));
+      aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
+    }
+  }
+
+  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);
+    if( p->iRowid==pCell->iRowid ){
+      if( iHeight==0 ){
+        rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);
+      }else{
+        rc = parentWrite(pRtree, p->iRowid, pNode->iNode);
+      }
+    }
+  }
+  if( rc==SQLITE_OK ){
+    rc = fixBoundingBox(pRtree, pNode);
+  }
+  for(; rc==SQLITE_OK && ii<nCell; ii++){
+    /* Find a node to store this cell in. pNode->iNode currently contains
+    ** the height of the sub-tree headed by the cell.
+    */
+    RtreeNode *pInsert;
+    RtreeCell *p = &aCell[aOrder[ii]];
+    rc = ChooseLeaf(pRtree, p, iHeight, &pInsert);
+    if( rc==SQLITE_OK ){
+      int rc2;
+      rc = rtreeInsertCell(pRtree, pInsert, p, iHeight);
+      rc2 = nodeRelease(pRtree, pInsert);
+      if( rc==SQLITE_OK ){
+        rc = rc2;
+      }
+    }
+  }
+
+  sqlite3_free(aCell);
+  return rc;
+}
+
+/*
+** Insert cell pCell into node pNode. Node pNode is the head of a 
+** subtree iHeight high (leaf nodes have iHeight==0).
+*/
+static int rtreeInsertCell(
+  Rtree *pRtree,
+  RtreeNode *pNode,
+  RtreeCell *pCell,
+  int iHeight
+){
+  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( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
+      rc = SplitNode(pRtree, pNode, pCell, iHeight);
+    }else{
+      pRtree->iReinsertHeight = iHeight;
+      rc = Reinsert(pRtree, pNode, pCell, iHeight);
+    }
+  }else{
+    rc = AdjustTree(pRtree, pNode, pCell);
+    if( ALWAYS(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, (int)pNode->iNode, &pInsert);
+    if( rc==SQLITE_OK ){
+      int rc2;
+      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 rtreeNewRowid(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 = 0;           /* 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);
+  }
+
+#ifdef CORRUPT_DB
+  assert( pLeaf!=0 || rc!=SQLITE_OK || CORRUPT_DB );
+#endif
+
+  /* Delete the cell in question from the leaf node. */
+  if( rc==SQLITE_OK && pLeaf ){
+    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 = 0;
+    i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
+    rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);  /* tag-20210916a */
+    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;
+    pRtree->nNodeRef--;
+    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) */
+
+/*
+** A constraint has failed while inserting a row into an rtree table. 
+** Assuming no OOM error occurs, this function sets the error message 
+** (at pRtree->base.zErrMsg) to an appropriate value and returns
+** SQLITE_CONSTRAINT.
+**
+** Parameter iCol is the index of the leftmost column involved in the
+** constraint failure. If it is 0, then the constraint that failed is
+** the unique constraint on the id column. Otherwise, it is the rtree
+** (c1<=c2) constraint on columns iCol and iCol+1 that has failed.
+**
+** If an OOM occurs, SQLITE_NOMEM is returned instead of SQLITE_CONSTRAINT.
+*/
+static int rtreeConstraintError(Rtree *pRtree, int iCol){
+  sqlite3_stmt *pStmt = 0;
+  char *zSql; 
+  int rc;
+
+  assert( iCol==0 || iCol%2 );
+  zSql = sqlite3_mprintf("SELECT * FROM %Q.%Q", pRtree->zDb, pRtree->zName);
+  if( zSql ){
+    rc = sqlite3_prepare_v2(pRtree->db, zSql, -1, &pStmt, 0);
+  }else{
+    rc = SQLITE_NOMEM;
+  }
+  sqlite3_free(zSql);
+
+  if( rc==SQLITE_OK ){
+    if( iCol==0 ){
+      const char *zCol = sqlite3_column_name(pStmt, 0);
+      pRtree->base.zErrMsg = sqlite3_mprintf(
+          "UNIQUE constraint failed: %s.%s", pRtree->zName, zCol
+      );
+    }else{
+      const char *zCol1 = sqlite3_column_name(pStmt, iCol);
+      const char *zCol2 = sqlite3_column_name(pStmt, iCol+1);
+      pRtree->base.zErrMsg = sqlite3_mprintf(
+          "rtree constraint failed: %s.(%s<=%s)", pRtree->zName, zCol1, zCol2
+      );
+    }
+  }
+
+  sqlite3_finalize(pStmt);
+  return (rc==SQLITE_OK ? SQLITE_CONSTRAINT : rc);
+}
+
+
+
+/*
+** The xUpdate method for rtree module virtual tables.
+*/
+static int rtreeUpdate(
+  sqlite3_vtab *pVtab, 
+  int nData, 
+  sqlite3_value **aData, 
+  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 */
+
+  if( pRtree->nNodeRef ){
+    /* Unable to write to the btree while another cursor is reading from it,
+    ** since the write might do a rebalance which would disrupt the read
+    ** cursor. */
+    return SQLITE_LOCKED_VTAB;
+  }
+  rtreeReference(pRtree);
+  assert(nData>=1);
+
+  memset(&cell, 0, sizeof(cell));
+
+  /* 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( nData>1 ){
+    int ii;
+    int nn = nData - 4;
+
+    if( nn > pRtree->nDim2 ) nn = pRtree->nDim2;
+    /* Populate the cell.aCoord[] array. The first coordinate is aData[3].
+    **
+    ** NB: nData can only be less than nDim*2+3 if the rtree is mis-declared
+    ** with "column" that are interpreted as table constraints.
+    ** Example:  CREATE VIRTUAL TABLE bad USING rtree(x,y,CHECK(y>5));
+    ** This problem was discovered after years of use, so we silently ignore
+    ** these kinds of misdeclared tables to avoid breaking any legacy.
+    */
+
+#ifndef SQLITE_RTREE_INT_ONLY
+    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
+      for(ii=0; ii<nn; ii+=2){
+        cell.aCoord[ii].f = rtreeValueDown(aData[ii+3]);
+        cell.aCoord[ii+1].f = rtreeValueUp(aData[ii+4]);
+        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
+          rc = rtreeConstraintError(pRtree, ii+1);
+          goto constraint;
+        }
+      }
+    }else
+#endif
+    {
+      for(ii=0; ii<nn; ii+=2){
+        cell.aCoord[ii].i = sqlite3_value_int(aData[ii+3]);
+        cell.aCoord[ii+1].i = sqlite3_value_int(aData[ii+4]);
+        if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
+          rc = rtreeConstraintError(pRtree, ii+1);
+          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(aData[2])!=SQLITE_NULL ){
+      cell.iRowid = sqlite3_value_int64(aData[2]);
+      if( sqlite3_value_type(aData[0])==SQLITE_NULL
+       || sqlite3_value_int64(aData[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 = rtreeConstraintError(pRtree, 0);
+            goto constraint;
+          }
+        }
+      }
+      bHaveRowid = 1;
+    }
+  }
+
+  /* If aData[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(aData[0])!=SQLITE_NULL ){
+    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(aData[0]));
+  }
+
+  /* If the aData[] array contains more than one element, elements
+  ** (aData[2]..aData[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( bHaveRowid==0 ){
+      rc = rtreeNewRowid(pRtree, &cell.iRowid);
+    }
+    *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);
+      rc2 = nodeRelease(pRtree, pLeaf);
+      if( rc==SQLITE_OK ){
+        rc = rc2;
+      }
+    }
+    if( rc==SQLITE_OK && pRtree->nAux ){
+      sqlite3_stmt *pUp = pRtree->pWriteAux;
+      int jj;
+      sqlite3_bind_int64(pUp, 1, *pRowid);
+      for(jj=0; jj<pRtree->nAux; jj++){
+        sqlite3_bind_value(pUp, jj+2, aData[pRtree->nDim2+3+jj]);
+      }
+      sqlite3_step(pUp);
+      rc = sqlite3_reset(pUp);
+    }
+  }
+
+constraint:
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+/*
+** Called when a transaction starts.
+*/
+static int rtreeBeginTransaction(sqlite3_vtab *pVtab){
+  Rtree *pRtree = (Rtree *)pVtab;
+  assert( pRtree->inWrTrans==0 );
+  pRtree->inWrTrans++;
+  return SQLITE_OK;
+}
+
+/*
+** Called when a transaction completes (either by COMMIT or ROLLBACK).
+** The sqlite3_blob object should be released at this point.
+*/
+static int rtreeEndTransaction(sqlite3_vtab *pVtab){
+  Rtree *pRtree = (Rtree *)pVtab;
+  pRtree->inWrTrans = 0;
+  nodeBlobReset(pRtree);
+  return SQLITE_OK;
+}
+
+/*
+** The xRename method for rtree module virtual tables.
+*/
+static int rtreeRename(sqlite3_vtab *pVtab, const char *zNewName){
+  Rtree *pRtree = (Rtree *)pVtab;
+  int rc = SQLITE_NOMEM;
+  char *zSql = sqlite3_mprintf(
+    "ALTER TABLE %Q.'%q_node'   RENAME TO \"%w_node\";"
+    "ALTER TABLE %Q.'%q_parent' RENAME TO \"%w_parent\";"
+    "ALTER TABLE %Q.'%q_rowid'  RENAME TO \"%w_rowid\";"
+    , pRtree->zDb, pRtree->zName, zNewName 
+    , pRtree->zDb, pRtree->zName, zNewName 
+    , pRtree->zDb, pRtree->zName, zNewName
+  );
+  if( zSql ){
+    nodeBlobReset(pRtree);
+    rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);
+    sqlite3_free(zSql);
+  }
+  return rc;
+}
+
+/*
+** The xSavepoint method.
+**
+** This module does not need to do anything to support savepoints. However,
+** it uses this hook to close any open blob handle. This is done because a 
+** DROP TABLE command - which fortunately always opens a savepoint - cannot 
+** succeed if there are any open blob handles. i.e. if the blob handle were
+** not closed here, the following would fail:
+**
+**   BEGIN;
+**     INSERT INTO rtree...
+**     DROP TABLE <tablename>;    -- Would fail with SQLITE_LOCKED
+**   COMMIT;
+*/
+static int rtreeSavepoint(sqlite3_vtab *pVtab, int iSavepoint){
+  Rtree *pRtree = (Rtree *)pVtab;
+  u8 iwt = pRtree->inWrTrans;
+  UNUSED_PARAMETER(iSavepoint);
+  pRtree->inWrTrans = 0;
+  nodeBlobReset(pRtree);
+  pRtree->inWrTrans = iwt;
+  return SQLITE_OK;
+}
+
+/*
+** 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 = RTREE_MIN_ROWEST;
+
+  rc = sqlite3_table_column_metadata(
+      db, pRtree->zDb, "sqlite_stat1",0,0,0,0,0,0
+  );
+  if( rc!=SQLITE_OK ){
+    pRtree->nRowEst = RTREE_DEFAULT_ROWEST;
+    return rc==SQLITE_ERROR ? SQLITE_OK : rc;
+  }
+  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);
+    }
+    sqlite3_free(zSql);
+  }
+  pRtree->nRowEst = MAX(nRow, RTREE_MIN_ROWEST);
+  return rc;
+}
+
+
+/*
+** Return true if zName is the extension on one of the shadow tables used
+** by this module.
+*/
+static int rtreeShadowName(const char *zName){
+  static const char *azName[] = {
+    "node", "parent", "rowid"
+  };
+  unsigned int i;
+  for(i=0; i<sizeof(azName)/sizeof(azName[0]); i++){
+    if( sqlite3_stricmp(zName, azName[i])==0 ) return 1;
+  }
+  return 0;
+}
+
+static sqlite3_module rtreeModule = {
+  3,                          /* 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 */
+  rtreeBeginTransaction,      /* xBegin - begin transaction */
+  rtreeEndTransaction,        /* xSync - sync transaction */
+  rtreeEndTransaction,        /* xCommit - commit transaction */
+  rtreeEndTransaction,        /* xRollback - rollback transaction */
+  0,                          /* xFindFunction - function overloading */
+  rtreeRename,                /* xRename - rename the table */
+  rtreeSavepoint,             /* xSavepoint */
+  0,                          /* xRelease */
+  0,                          /* xRollbackTo */
+  rtreeShadowName             /* xShadowName */
+};
+
+static int rtreeSqlInit(
+  Rtree *pRtree, 
+  sqlite3 *db, 
+  const char *zDb, 
+  const char *zPrefix, 
+  int isCreate
+){
+  int rc = SQLITE_OK;
+
+  #define N_STATEMENT 8
+  static const char *azSql[N_STATEMENT] = {
+    /* Write the xxx_node table */
+    "INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(?1, ?2)",
+    "DELETE FROM '%q'.'%q_node' WHERE nodeno = ?1",
+
+    /* Read and write the xxx_rowid table */
+    "SELECT nodeno FROM '%q'.'%q_rowid' WHERE rowid = ?1",
+    "INSERT OR REPLACE INTO '%q'.'%q_rowid' VALUES(?1, ?2)",
+    "DELETE FROM '%q'.'%q_rowid' WHERE rowid = ?1",
+
+    /* Read and write the xxx_parent table */
+    "SELECT parentnode FROM '%q'.'%q_parent' WHERE nodeno = ?1",
+    "INSERT OR REPLACE INTO '%q'.'%q_parent' VALUES(?1, ?2)",
+    "DELETE FROM '%q'.'%q_parent' WHERE nodeno = ?1"
+  };
+  sqlite3_stmt **appStmt[N_STATEMENT];
+  int i;
+  const int f = SQLITE_PREPARE_PERSISTENT|SQLITE_PREPARE_NO_VTAB;
+
+  pRtree->db = db;
+
+  if( isCreate ){
+    char *zCreate;
+    sqlite3_str *p = sqlite3_str_new(db);
+    int ii;
+    sqlite3_str_appendf(p,
+       "CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY,nodeno",
+       zDb, zPrefix);
+    for(ii=0; ii<pRtree->nAux; ii++){
+      sqlite3_str_appendf(p,",a%d",ii);
+    }
+    sqlite3_str_appendf(p,
+      ");CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY,data);",
+      zDb, zPrefix);
+    sqlite3_str_appendf(p,
+    "CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY,parentnode);",
+      zDb, zPrefix);
+    sqlite3_str_appendf(p,
+       "INSERT INTO \"%w\".\"%w_node\"VALUES(1,zeroblob(%d))",
+       zDb, zPrefix, pRtree->iNodeSize);
+    zCreate = sqlite3_str_finish(p);
+    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->pWriteNode;
+  appStmt[1] = &pRtree->pDeleteNode;
+  appStmt[2] = &pRtree->pReadRowid;
+  appStmt[3] = &pRtree->pWriteRowid;
+  appStmt[4] = &pRtree->pDeleteRowid;
+  appStmt[5] = &pRtree->pReadParent;
+  appStmt[6] = &pRtree->pWriteParent;
+  appStmt[7] = &pRtree->pDeleteParent;
+
+  rc = rtreeQueryStat1(db, pRtree);
+  for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
+    char *zSql;
+    const char *zFormat;
+    if( i!=3 || pRtree->nAux==0 ){
+       zFormat = azSql[i];
+    }else {
+       /* An UPSERT is very slightly slower than REPLACE, but it is needed
+       ** if there are auxiliary columns */
+       zFormat = "INSERT INTO\"%w\".\"%w_rowid\"(rowid,nodeno)VALUES(?1,?2)"
+                  "ON CONFLICT(rowid)DO UPDATE SET nodeno=excluded.nodeno";
+    }
+    zSql = sqlite3_mprintf(zFormat, zDb, zPrefix);
+    if( zSql ){
+      rc = sqlite3_prepare_v3(db, zSql, -1, f, appStmt[i], 0); 
+    }else{
+      rc = SQLITE_NOMEM;
+    }
+    sqlite3_free(zSql);
+  }
+  if( pRtree->nAux ){
+    pRtree->zReadAuxSql = sqlite3_mprintf(
+       "SELECT * FROM \"%w\".\"%w_rowid\" WHERE rowid=?1",
+       zDb, zPrefix);
+    if( pRtree->zReadAuxSql==0 ){
+      rc = SQLITE_NOMEM;
+    }else{
+      sqlite3_str *p = sqlite3_str_new(db);
+      int ii;
+      char *zSql;
+      sqlite3_str_appendf(p, "UPDATE \"%w\".\"%w_rowid\"SET ", zDb, zPrefix);
+      for(ii=0; ii<pRtree->nAux; ii++){
+        if( ii ) sqlite3_str_append(p, ",", 1);
+#ifdef SQLITE_ENABLE_GEOPOLY
+        if( ii<pRtree->nAuxNotNull ){
+          sqlite3_str_appendf(p,"a%d=coalesce(?%d,a%d)",ii,ii+2,ii);
+        }else
+#endif
+        {
+          sqlite3_str_appendf(p,"a%d=?%d",ii,ii+2);
+        }
+      }
+      sqlite3_str_appendf(p, " WHERE rowid=?1");
+      zSql = sqlite3_str_finish(p);
+      if( zSql==0 ){
+        rc = SQLITE_NOMEM;
+      }else{
+        rc = sqlite3_prepare_v3(db, zSql, -1, f, &pRtree->pWriteAux, 0); 
+        sqlite3_free(zSql);
+      }
+    }
+  }
+
+  return rc;
+}
+
+/*
+** The second argument to this function contains the text of an SQL statement
+** that returns a single integer value. The statement is compiled and executed
+** using database connection db. If successful, the integer value returned
+** is written to *piVal and SQLITE_OK returned. Otherwise, an SQLite error
+** code is returned and the value of *piVal after returning is not defined.
+*/
+static int getIntFromStmt(sqlite3 *db, const char *zSql, int *piVal){
+  int rc = SQLITE_NOMEM;
+  if( zSql ){
+    sqlite3_stmt *pStmt = 0;
+    rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);
+    if( rc==SQLITE_OK ){
+      if( SQLITE_ROW==sqlite3_step(pStmt) ){
+        *piVal = sqlite3_column_int(pStmt, 0);
+      }
+      rc = sqlite3_finalize(pStmt);
+    }
+  }
+  return rc;
+}
+
+/*
+** This function is called from within the xConnect() or xCreate() method to
+** determine the node-size used by the rtree table being created or connected
+** to. If successful, pRtree->iNodeSize is populated and SQLITE_OK returned.
+** Otherwise, an SQLite error code is returned.
+**
+** If this function is being called as part of an xConnect(), then the rtree
+** table already exists. In this case the node-size is determined by inspecting
+** 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 */
+  char **pzErr                    /* OUT: Error message, if any */
+){
+  int rc;
+  char *zSql;
+  if( isCreate ){
+    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));
+    }else if( pRtree->iNodeSize<(512-64) ){
+      rc = SQLITE_CORRUPT_VTAB;
+      RTREE_IS_CORRUPT(pRtree);
+      *pzErr = sqlite3_mprintf("undersize RTree blobs in \"%q_node\"",
+                               pRtree->zName);
+    }
+  }
+
+  sqlite3_free(zSql);
+  return rc;
+}
+
+/*
+** Return the length of a token
+*/
+static int rtreeTokenLength(const char *z){
+  int dummy = 0;
+  return sqlite3GetToken((const unsigned char*)z,&dummy);
+}
+
+/* 
+** This function is the implementation of both the xConnect and xCreate
+** methods of the r-tree virtual table.
+**
+**   argv[0]   -> module name
+**   argv[1]   -> database name
+**   argv[2]   -> table name
+**   argv[...] -> column names...
+*/
+static int rtreeInit(
+  sqlite3 *db,                        /* Database connection */
+  void *pAux,                         /* One of the RTREE_COORD_* constants */
+  int argc, const char *const*argv,   /* Parameters to CREATE TABLE statement */
+  sqlite3_vtab **ppVtab,              /* OUT: New virtual table */
+  char **pzErr,                       /* OUT: Error message, if any */
+  int isCreate                        /* True for xCreate, false for xConnect */
+){
+  int rc = SQLITE_OK;
+  Rtree *pRtree;
+  int nDb;              /* Length of string argv[1] */
+  int nName;            /* Length of string argv[2] */
+  int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);
+  sqlite3_str *pSql;
+  char *zSql;
+  int ii = 4;
+  int iErr;
+
+  const char *aErrMsg[] = {
+    0,                                                    /* 0 */
+    "Wrong number of columns for an rtree table",         /* 1 */
+    "Too few columns for an rtree table",                 /* 2 */
+    "Too many columns for an rtree table",                /* 3 */
+    "Auxiliary rtree columns must be last"                /* 4 */
+  };
+
+  assert( RTREE_MAX_AUX_COLUMN<256 ); /* Aux columns counted by a u8 */
+  if( argc<6 || argc>RTREE_MAX_AUX_COLUMN+3 ){
+    *pzErr = sqlite3_mprintf("%s", aErrMsg[2 + (argc>=6)]);
+    return SQLITE_ERROR;
+  }
+
+  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);
+
+  /* Allocate the sqlite3_vtab structure */
+  nDb = (int)strlen(argv[1]);
+  nName = (int)strlen(argv[2]);
+  pRtree = (Rtree *)sqlite3_malloc64(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->eCoordType = (u8)eCoordType;
+  memcpy(pRtree->zDb, argv[1], nDb);
+  memcpy(pRtree->zName, argv[2], nName);
+
+
+  /* Create/Connect to the underlying relational database schema. If
+  ** that is successful, call sqlite3_declare_vtab() to configure
+  ** the r-tree table schema.
+  */
+  pSql = sqlite3_str_new(db);
+  sqlite3_str_appendf(pSql, "CREATE TABLE x(%.*s INT", 
+                      rtreeTokenLength(argv[3]), argv[3]);
+  for(ii=4; ii<argc; ii++){
+    const char *zArg = argv[ii];
+    if( zArg[0]=='+' ){
+      pRtree->nAux++;
+      sqlite3_str_appendf(pSql, ",%.*s", rtreeTokenLength(zArg+1), zArg+1);
+    }else if( pRtree->nAux>0 ){
+      break;
+    }else{
+      static const char *azFormat[] = {",%.*s REAL", ",%.*s INT"};
+      pRtree->nDim2++;
+      sqlite3_str_appendf(pSql, azFormat[eCoordType],
+                          rtreeTokenLength(zArg), zArg);
+    }
+  }
+  sqlite3_str_appendf(pSql, ");");
+  zSql = sqlite3_str_finish(pSql);
+  if( !zSql ){
+    rc = SQLITE_NOMEM;
+  }else if( ii<argc ){
+    *pzErr = sqlite3_mprintf("%s", aErrMsg[4]);
+    rc = SQLITE_ERROR;
+  }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
+    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
+  }
+  sqlite3_free(zSql);
+  if( rc ) goto rtreeInit_fail;
+  pRtree->nDim = pRtree->nDim2/2;
+  if( pRtree->nDim<1 ){
+    iErr = 2;
+  }else if( pRtree->nDim2>RTREE_MAX_DIMENSIONS*2 ){
+    iErr = 3;
+  }else if( pRtree->nDim2 % 2 ){
+    iErr = 1;
+  }else{
+    iErr = 0;
+  }
+  if( iErr ){
+    *pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
+    goto rtreeInit_fail;
+  }
+  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
+
+  /* Figure out the node size to use. */
+  rc = getNodeSize(db, pRtree, isCreate, pzErr);
+  if( rc ) goto rtreeInit_fail;
+  rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate);
+  if( rc ){
+    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
+    goto rtreeInit_fail;
+  }
+
+  *ppVtab = (sqlite3_vtab *)pRtree;
+  return SQLITE_OK;
+
+rtreeInit_fail:
+  if( rc==SQLITE_OK ) rc = SQLITE_ERROR;
+  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: (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){
+  RtreeNode node;
+  Rtree tree;
+  int ii;
+  int nData;
+  int errCode;
+  sqlite3_str *pOut;
+
+  UNUSED_PARAMETER(nArg);
+  memset(&node, 0, sizeof(RtreeNode));
+  memset(&tree, 0, sizeof(Rtree));
+  tree.nDim = (u8)sqlite3_value_int(apArg[0]);
+  if( tree.nDim<1 || tree.nDim>5 ) return;
+  tree.nDim2 = tree.nDim*2;
+  tree.nBytesPerCell = 8 + 8 * tree.nDim;
+  node.zData = (u8 *)sqlite3_value_blob(apArg[1]);
+  if( node.zData==0 ) return;
+  nData = sqlite3_value_bytes(apArg[1]);
+  if( nData<4 ) return;
+  if( nData<NCELL(&node)*tree.nBytesPerCell ) return;
+
+  pOut = sqlite3_str_new(0);
+  for(ii=0; ii<NCELL(&node); ii++){
+    RtreeCell cell;
+    int jj;
+
+    nodeGetCell(&tree, &node, ii, &cell);
+    if( ii>0 ) sqlite3_str_append(pOut, " ", 1);
+    sqlite3_str_appendf(pOut, "{%lld", cell.iRowid);
+    for(jj=0; jj<tree.nDim2; jj++){
+#ifndef SQLITE_RTREE_INT_ONLY
+      sqlite3_str_appendf(pOut, " %g", (double)cell.aCoord[jj].f);
+#else
+      sqlite3_str_appendf(pOut, " %d", cell.aCoord[jj].i);
+#endif
+    }
+    sqlite3_str_append(pOut, "}", 1);
+  }
+  errCode = sqlite3_str_errcode(pOut);
+  sqlite3_result_text(ctx, sqlite3_str_finish(pOut), -1, sqlite3_free);
+  sqlite3_result_error_code(ctx, errCode);
+}
+
+/* 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]);
+    if( zBlob ){
+      sqlite3_result_int(ctx, readInt16(zBlob));
+    }else{
+      sqlite3_result_error_nomem(ctx);
+    }
+  }
+}
+
+/*
+** Context object passed between the various routines that make up the
+** implementation of integrity-check function rtreecheck().
+*/
+typedef struct RtreeCheck RtreeCheck;
+struct RtreeCheck {
+  sqlite3 *db;                    /* Database handle */
+  const char *zDb;                /* Database containing rtree table */
+  const char *zTab;               /* Name of rtree table */
+  int bInt;                       /* True for rtree_i32 table */
+  int nDim;                       /* Number of dimensions for this rtree tbl */
+  sqlite3_stmt *pGetNode;         /* Statement used to retrieve nodes */
+  sqlite3_stmt *aCheckMapping[2]; /* Statements to query %_parent/%_rowid */
+  int nLeaf;                      /* Number of leaf cells in table */
+  int nNonLeaf;                   /* Number of non-leaf cells in table */
+  int rc;                         /* Return code */
+  char *zReport;                  /* Message to report */
+  int nErr;                       /* Number of lines in zReport */
+};
+
+#define RTREE_CHECK_MAX_ERROR 100
+
+/*
+** Reset SQL statement pStmt. If the sqlite3_reset() call returns an error,
+** and RtreeCheck.rc==SQLITE_OK, set RtreeCheck.rc to the error code.
+*/
+static void rtreeCheckReset(RtreeCheck *pCheck, sqlite3_stmt *pStmt){
+  int rc = sqlite3_reset(pStmt);
+  if( pCheck->rc==SQLITE_OK ) pCheck->rc = rc;
+}
+
+/*
+** The second and subsequent arguments to this function are a format string
+** and printf style arguments. This function formats the string and attempts
+** to compile it as an SQL statement.
+**
+** If successful, a pointer to the new SQL statement is returned. Otherwise,
+** NULL is returned and an error code left in RtreeCheck.rc.
+*/
+static sqlite3_stmt *rtreeCheckPrepare(
+  RtreeCheck *pCheck,             /* RtreeCheck object */
+  const char *zFmt, ...           /* Format string and trailing args */
+){
+  va_list ap;
+  char *z;
+  sqlite3_stmt *pRet = 0;
+
+  va_start(ap, zFmt);
+  z = sqlite3_vmprintf(zFmt, ap);
+
+  if( pCheck->rc==SQLITE_OK ){
+    if( z==0 ){
+      pCheck->rc = SQLITE_NOMEM;
+    }else{
+      pCheck->rc = sqlite3_prepare_v2(pCheck->db, z, -1, &pRet, 0);
+    }
+  }
+
+  sqlite3_free(z);
+  va_end(ap);
+  return pRet;
+}
+
+/*
+** The second and subsequent arguments to this function are a printf()
+** style format string and arguments. This function formats the string and
+** appends it to the report being accumuated in pCheck.
+*/
+static void rtreeCheckAppendMsg(RtreeCheck *pCheck, const char *zFmt, ...){
+  va_list ap;
+  va_start(ap, zFmt);
+  if( pCheck->rc==SQLITE_OK && pCheck->nErr<RTREE_CHECK_MAX_ERROR ){
+    char *z = sqlite3_vmprintf(zFmt, ap);
+    if( z==0 ){
+      pCheck->rc = SQLITE_NOMEM;
+    }else{
+      pCheck->zReport = sqlite3_mprintf("%z%s%z", 
+          pCheck->zReport, (pCheck->zReport ? "\n" : ""), z
+      );
+      if( pCheck->zReport==0 ){
+        pCheck->rc = SQLITE_NOMEM;
+      }
+    }
+    pCheck->nErr++;
+  }
+  va_end(ap);
+}
+
+/*
+** This function is a no-op if there is already an error code stored
+** in the RtreeCheck object indicated by the first argument. NULL is
+** returned in this case.
+**
+** Otherwise, the contents of rtree table node iNode are loaded from
+** the database and copied into a buffer obtained from sqlite3_malloc().
+** If no error occurs, a pointer to the buffer is returned and (*pnNode)
+** is set to the size of the buffer in bytes.
+**
+** Or, if an error does occur, NULL is returned and an error code left
+** in the RtreeCheck object. The final value of *pnNode is undefined in
+** this case.
+*/
+static u8 *rtreeCheckGetNode(RtreeCheck *pCheck, i64 iNode, int *pnNode){
+  u8 *pRet = 0;                   /* Return value */
+
+  if( pCheck->rc==SQLITE_OK && pCheck->pGetNode==0 ){
+    pCheck->pGetNode = rtreeCheckPrepare(pCheck,
+        "SELECT data FROM %Q.'%q_node' WHERE nodeno=?", 
+        pCheck->zDb, pCheck->zTab
+    );
+  }
+
+  if( pCheck->rc==SQLITE_OK ){
+    sqlite3_bind_int64(pCheck->pGetNode, 1, iNode);
+    if( sqlite3_step(pCheck->pGetNode)==SQLITE_ROW ){
+      int nNode = sqlite3_column_bytes(pCheck->pGetNode, 0);
+      const u8 *pNode = (const u8*)sqlite3_column_blob(pCheck->pGetNode, 0);
+      pRet = sqlite3_malloc64(nNode);
+      if( pRet==0 ){
+        pCheck->rc = SQLITE_NOMEM;
+      }else{
+        memcpy(pRet, pNode, nNode);
+        *pnNode = nNode;
+      }
+    }
+    rtreeCheckReset(pCheck, pCheck->pGetNode);
+    if( pCheck->rc==SQLITE_OK && pRet==0 ){
+      rtreeCheckAppendMsg(pCheck, "Node %lld missing from database", iNode);
+    }
+  }
+
+  return pRet;
+}
+
+/*
+** This function is used to check that the %_parent (if bLeaf==0) or %_rowid
+** (if bLeaf==1) table contains a specified entry. The schemas of the
+** two tables are:
+**
+**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
+**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER, ...)
+**
+** In both cases, this function checks that there exists an entry with
+** IPK value iKey and the second column set to iVal.
+**
+*/
+static void rtreeCheckMapping(
+  RtreeCheck *pCheck,             /* RtreeCheck object */
+  int bLeaf,                      /* True for a leaf cell, false for interior */
+  i64 iKey,                       /* Key for mapping */
+  i64 iVal                        /* Expected value for mapping */
+){
+  int rc;
+  sqlite3_stmt *pStmt;
+  const char *azSql[2] = {
+    "SELECT parentnode FROM %Q.'%q_parent' WHERE nodeno=?1",
+    "SELECT nodeno FROM %Q.'%q_rowid' WHERE rowid=?1"
+  };
+
+  assert( bLeaf==0 || bLeaf==1 );
+  if( pCheck->aCheckMapping[bLeaf]==0 ){
+    pCheck->aCheckMapping[bLeaf] = rtreeCheckPrepare(pCheck,
+        azSql[bLeaf], pCheck->zDb, pCheck->zTab
+    );
+  }
+  if( pCheck->rc!=SQLITE_OK ) return;
+
+  pStmt = pCheck->aCheckMapping[bLeaf];
+  sqlite3_bind_int64(pStmt, 1, iKey);
+  rc = sqlite3_step(pStmt);
+  if( rc==SQLITE_DONE ){
+    rtreeCheckAppendMsg(pCheck, "Mapping (%lld -> %lld) missing from %s table",
+        iKey, iVal, (bLeaf ? "%_rowid" : "%_parent")
+    );
+  }else if( rc==SQLITE_ROW ){
+    i64 ii = sqlite3_column_int64(pStmt, 0);
+    if( ii!=iVal ){
+      rtreeCheckAppendMsg(pCheck, 
+          "Found (%lld -> %lld) in %s table, expected (%lld -> %lld)",
+          iKey, ii, (bLeaf ? "%_rowid" : "%_parent"), iKey, iVal
+      );
+    }
+  }
+  rtreeCheckReset(pCheck, pStmt);
+}
+
+/*
+** Argument pCell points to an array of coordinates stored on an rtree page.
+** This function checks that the coordinates are internally consistent (no
+** x1>x2 conditions) and adds an error message to the RtreeCheck object
+** if they are not.
+**
+** Additionally, if pParent is not NULL, then it is assumed to point to
+** the array of coordinates on the parent page that bound the page 
+** containing pCell. In this case it is also verified that the two
+** sets of coordinates are mutually consistent and an error message added
+** to the RtreeCheck object if they are not.
+*/
+static void rtreeCheckCellCoord(
+  RtreeCheck *pCheck, 
+  i64 iNode,                      /* Node id to use in error messages */
+  int iCell,                      /* Cell number to use in error messages */
+  u8 *pCell,                      /* Pointer to cell coordinates */
+  u8 *pParent                     /* Pointer to parent coordinates */
+){
+  RtreeCoord c1, c2;
+  RtreeCoord p1, p2;
+  int i;
+
+  for(i=0; i<pCheck->nDim; i++){
+    readCoord(&pCell[4*2*i], &c1);
+    readCoord(&pCell[4*(2*i + 1)], &c2);
+
+    /* printf("%e, %e\n", c1.u.f, c2.u.f); */
+    if( pCheck->bInt ? c1.i>c2.i : c1.f>c2.f ){
+      rtreeCheckAppendMsg(pCheck, 
+          "Dimension %d of cell %d on node %lld is corrupt", i, iCell, iNode
+      );
+    }
+
+    if( pParent ){
+      readCoord(&pParent[4*2*i], &p1);
+      readCoord(&pParent[4*(2*i + 1)], &p2);
+
+      if( (pCheck->bInt ? c1.i<p1.i : c1.f<p1.f) 
+       || (pCheck->bInt ? c2.i>p2.i : c2.f>p2.f)
+      ){
+        rtreeCheckAppendMsg(pCheck, 
+            "Dimension %d of cell %d on node %lld is corrupt relative to parent"
+            , i, iCell, iNode
+        );
+      }
+    }
+  }
+}
+
+/*
+** Run rtreecheck() checks on node iNode, which is at depth iDepth within
+** the r-tree structure. Argument aParent points to the array of coordinates
+** that bound node iNode on the parent node.
+**
+** If any problems are discovered, an error message is appended to the
+** report accumulated in the RtreeCheck object.
+*/
+static void rtreeCheckNode(
+  RtreeCheck *pCheck,
+  int iDepth,                     /* Depth of iNode (0==leaf) */
+  u8 *aParent,                    /* Buffer containing parent coords */
+  i64 iNode                       /* Node to check */
+){
+  u8 *aNode = 0;
+  int nNode = 0;
+
+  assert( iNode==1 || aParent!=0 );
+  assert( pCheck->nDim>0 );
+
+  aNode = rtreeCheckGetNode(pCheck, iNode, &nNode);
+  if( aNode ){
+    if( nNode<4 ){
+      rtreeCheckAppendMsg(pCheck, 
+          "Node %lld is too small (%d bytes)", iNode, nNode
+      );
+    }else{
+      int nCell;                  /* Number of cells on page */
+      int i;                      /* Used to iterate through cells */
+      if( aParent==0 ){
+        iDepth = readInt16(aNode);
+        if( iDepth>RTREE_MAX_DEPTH ){
+          rtreeCheckAppendMsg(pCheck, "Rtree depth out of range (%d)", iDepth);
+          sqlite3_free(aNode);
+          return;
+        }
+      }
+      nCell = readInt16(&aNode[2]);
+      if( (4 + nCell*(8 + pCheck->nDim*2*4))>nNode ){
+        rtreeCheckAppendMsg(pCheck, 
+            "Node %lld is too small for cell count of %d (%d bytes)", 
+            iNode, nCell, nNode
+        );
+      }else{
+        for(i=0; i<nCell; i++){
+          u8 *pCell = &aNode[4 + i*(8 + pCheck->nDim*2*4)];
+          i64 iVal = readInt64(pCell);
+          rtreeCheckCellCoord(pCheck, iNode, i, &pCell[8], aParent);
+
+          if( iDepth>0 ){
+            rtreeCheckMapping(pCheck, 0, iVal, iNode);
+            rtreeCheckNode(pCheck, iDepth-1, &pCell[8], iVal);
+            pCheck->nNonLeaf++;
+          }else{
+            rtreeCheckMapping(pCheck, 1, iVal, iNode);
+            pCheck->nLeaf++;
+          }
+        }
+      }
+    }
+    sqlite3_free(aNode);
+  }
+}
+
+/*
+** The second argument to this function must be either "_rowid" or
+** "_parent". This function checks that the number of entries in the
+** %_rowid or %_parent table is exactly nExpect. If not, it adds
+** an error message to the report in the RtreeCheck object indicated
+** by the first argument.
+*/
+static void rtreeCheckCount(RtreeCheck *pCheck, const char *zTbl, i64 nExpect){
+  if( pCheck->rc==SQLITE_OK ){
+    sqlite3_stmt *pCount;
+    pCount = rtreeCheckPrepare(pCheck, "SELECT count(*) FROM %Q.'%q%s'",
+        pCheck->zDb, pCheck->zTab, zTbl
+    );
+    if( pCount ){
+      if( sqlite3_step(pCount)==SQLITE_ROW ){
+        i64 nActual = sqlite3_column_int64(pCount, 0);
+        if( nActual!=nExpect ){
+          rtreeCheckAppendMsg(pCheck, "Wrong number of entries in %%%s table"
+              " - expected %lld, actual %lld" , zTbl, nExpect, nActual
+          );
+        }
+      }
+      pCheck->rc = sqlite3_finalize(pCount);
+    }
+  }
+}
+
+/*
+** This function does the bulk of the work for the rtree integrity-check.
+** It is called by rtreecheck(), which is the SQL function implementation.
+*/
+static int rtreeCheckTable(
+  sqlite3 *db,                    /* Database handle to access db through */
+  const char *zDb,                /* Name of db ("main", "temp" etc.) */
+  const char *zTab,               /* Name of rtree table to check */
+  char **pzReport                 /* OUT: sqlite3_malloc'd report text */
+){
+  RtreeCheck check;               /* Common context for various routines */
+  sqlite3_stmt *pStmt = 0;        /* Used to find column count of rtree table */
+  int bEnd = 0;                   /* True if transaction should be closed */
+  int nAux = 0;                   /* Number of extra columns. */
+
+  /* Initialize the context object */
+  memset(&check, 0, sizeof(check));
+  check.db = db;
+  check.zDb = zDb;
+  check.zTab = zTab;
+
+  /* If there is not already an open transaction, open one now. This is
+  ** to ensure that the queries run as part of this integrity-check operate
+  ** on a consistent snapshot.  */
+  if( sqlite3_get_autocommit(db) ){
+    check.rc = sqlite3_exec(db, "BEGIN", 0, 0, 0);
+    bEnd = 1;
+  }
+
+  /* Find the number of auxiliary columns */
+  if( check.rc==SQLITE_OK ){
+    pStmt = rtreeCheckPrepare(&check, "SELECT * FROM %Q.'%q_rowid'", zDb, zTab);
+    if( pStmt ){
+      nAux = sqlite3_column_count(pStmt) - 2;
+      sqlite3_finalize(pStmt);
+    }else 
+    if( check.rc!=SQLITE_NOMEM ){
+      check.rc = SQLITE_OK;
+    }
+  }
+
+  /* Find number of dimensions in the rtree table. */
+  pStmt = rtreeCheckPrepare(&check, "SELECT * FROM %Q.%Q", zDb, zTab);
+  if( pStmt ){
+    int rc;
+    check.nDim = (sqlite3_column_count(pStmt) - 1 - nAux) / 2;
+    if( check.nDim<1 ){
+      rtreeCheckAppendMsg(&check, "Schema corrupt or not an rtree");
+    }else if( SQLITE_ROW==sqlite3_step(pStmt) ){
+      check.bInt = (sqlite3_column_type(pStmt, 1)==SQLITE_INTEGER);
+    }
+    rc = sqlite3_finalize(pStmt);
+    if( rc!=SQLITE_CORRUPT ) check.rc = rc;
+  }
+
+  /* Do the actual integrity-check */
+  if( check.nDim>=1 ){
+    if( check.rc==SQLITE_OK ){
+      rtreeCheckNode(&check, 0, 0, 1);
+    }
+    rtreeCheckCount(&check, "_rowid", check.nLeaf);
+    rtreeCheckCount(&check, "_parent", check.nNonLeaf);
+  }
+
+  /* Finalize SQL statements used by the integrity-check */
+  sqlite3_finalize(check.pGetNode);
+  sqlite3_finalize(check.aCheckMapping[0]);
+  sqlite3_finalize(check.aCheckMapping[1]);
+
+  /* If one was opened, close the transaction */
+  if( bEnd ){
+    int rc = sqlite3_exec(db, "END", 0, 0, 0);
+    if( check.rc==SQLITE_OK ) check.rc = rc;
+  }
+  *pzReport = check.zReport;
+  return check.rc;
+}
+
+/*
+** Usage:
+**
+**   rtreecheck(<rtree-table>);
+**   rtreecheck(<database>, <rtree-table>);
+**
+** Invoking this SQL function runs an integrity-check on the named rtree
+** table. The integrity-check verifies the following:
+**
+**   1. For each cell in the r-tree structure (%_node table), that:
+**
+**       a) for each dimension, (coord1 <= coord2).
+**
+**       b) unless the cell is on the root node, that the cell is bounded
+**          by the parent cell on the parent node.
+**
+**       c) for leaf nodes, that there is an entry in the %_rowid 
+**          table corresponding to the cell's rowid value that 
+**          points to the correct node.
+**
+**       d) for cells on non-leaf nodes, that there is an entry in the 
+**          %_parent table mapping from the cell's child node to the
+**          node that it resides on.
+**
+**   2. That there are the same number of entries in the %_rowid table
+**      as there are leaf cells in the r-tree structure, and that there
+**      is a leaf cell that corresponds to each entry in the %_rowid table.
+**
+**   3. That there are the same number of entries in the %_parent table
+**      as there are non-leaf cells in the r-tree structure, and that 
+**      there is a non-leaf cell that corresponds to each entry in the 
+**      %_parent table.
+*/
+static void rtreecheck(
+  sqlite3_context *ctx, 
+  int nArg, 
+  sqlite3_value **apArg
+){
+  if( nArg!=1 && nArg!=2 ){
+    sqlite3_result_error(ctx, 
+        "wrong number of arguments to function rtreecheck()", -1
+    );
+  }else{
+    int rc;
+    char *zReport = 0;
+    const char *zDb = (const char*)sqlite3_value_text(apArg[0]);
+    const char *zTab;
+    if( nArg==1 ){
+      zTab = zDb;
+      zDb = "main";
+    }else{
+      zTab = (const char*)sqlite3_value_text(apArg[1]);
+    }
+    rc = rtreeCheckTable(sqlite3_context_db_handle(ctx), zDb, zTab, &zReport);
+    if( rc==SQLITE_OK ){
+      sqlite3_result_text(ctx, zReport ? zReport : "ok", -1, SQLITE_TRANSIENT);
+    }else{
+      sqlite3_result_error_code(ctx, rc);
+    }
+    sqlite3_free(zReport);
+  }
+}
+
+/* Conditionally include the geopoly code */
+#ifdef SQLITE_ENABLE_GEOPOLY
+# include "geopoly.c"
+#endif
+
+/*
+** 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 ){
+    rc = sqlite3_create_function(db, "rtreecheck", -1, utf8, 0,rtreecheck, 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);
+  }
+#ifdef SQLITE_ENABLE_GEOPOLY
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_geopoly_init(db);
+  }
+#endif
+
+  return rc;
+}
+
+/*
+** This routine deletes the RtreeGeomCallback object that was attached
+** one of the SQL functions create by sqlite3_rtree_geometry_callback()
+** or sqlite3_rtree_query_callback().  In other words, this routine is the
+** destructor for an RtreeGeomCallback objecct.  This routine is called when
+** the corresponding SQL function is deleted.
+*/
+static void rtreeFreeCallback(void *p){
+  RtreeGeomCallback *pInfo = (RtreeGeomCallback*)p;
+  if( pInfo->xDestructor ) pInfo->xDestructor(pInfo->pContext);
+  sqlite3_free(p);
+}
+
+/*
+** This routine frees the BLOB that is returned by geomCallback().
+*/
+static void rtreeMatchArgFree(void *pArg){
+  int i;
+  RtreeMatchArg *p = (RtreeMatchArg*)pArg;
+  for(i=0; i<p->nParam; i++){
+    sqlite3_value_free(p->apSqlParam[i]);
+  }
+  sqlite3_free(p);
+}
+
+/*
+** Each call to sqlite3_rtree_geometry_callback() or
+** sqlite3_rtree_query_callback() creates an ordinary SQLite
+** scalar function that is implemented by this routine.
+**
+** All this function does is construct an RtreeMatchArg object that
+** contains the geometry-checking callback routines and a list of
+** parameters to this function, then return that RtreeMatchArg object
+** as a BLOB.
+**
+** The R-Tree MATCH operator will read the returned BLOB, deserialize
+** the RtreeMatchArg object, and use the RtreeMatchArg object to figure
+** out which elements of the R-Tree should be returned by the query.
+*/
+static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
+  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
+  RtreeMatchArg *pBlob;
+  sqlite3_int64 nBlob;
+  int memErr = 0;
+
+  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue)
+           + nArg*sizeof(sqlite3_value*);
+  pBlob = (RtreeMatchArg *)sqlite3_malloc64(nBlob);
+  if( !pBlob ){
+    sqlite3_result_error_nomem(ctx);
+  }else{
+    int i;
+    pBlob->iSize = nBlob;
+    pBlob->cb = pGeomCtx[0];
+    pBlob->apSqlParam = (sqlite3_value**)&pBlob->aParam[nArg];
+    pBlob->nParam = nArg;
+    for(i=0; i<nArg; i++){
+      pBlob->apSqlParam[i] = sqlite3_value_dup(aArg[i]);
+      if( pBlob->apSqlParam[i]==0 ) memErr = 1;
+#ifdef SQLITE_RTREE_INT_ONLY
+      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
+#else
+      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
+#endif
+    }
+    if( memErr ){
+      sqlite3_result_error_nomem(ctx);
+      rtreeMatchArgFree(pBlob);
+    }else{
+      sqlite3_result_pointer(ctx, pBlob, "RtreeMatchArg", rtreeMatchArgFree);
+    }
+  }
+}
+
+/*
+** Register a new geometry function for use with the r-tree MATCH operator.
+*/
+int sqlite3_rtree_geometry_callback(
+  sqlite3 *db,                  /* Register SQL function on this connection */
+  const char *zGeom,            /* Name of the new SQL function */
+  int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*), /* Callback */
+  void *pContext                /* Extra data associated with the callback */
+){
+  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */
+
+  /* Allocate and populate the context object. */
+  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
+  if( !pGeomCtx ) return SQLITE_NOMEM;
+  pGeomCtx->xGeom = xGeom;
+  pGeomCtx->xQueryFunc = 0;
+  pGeomCtx->xDestructor = 0;
+  pGeomCtx->pContext = pContext;
+  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
+      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
+  );
+}
+
+/*
+** Register a new 2nd-generation geometry function for use with the
+** r-tree MATCH operator.
+*/
+int sqlite3_rtree_query_callback(
+  sqlite3 *db,                 /* Register SQL function on this connection */
+  const char *zQueryFunc,      /* Name of new SQL function */
+  int (*xQueryFunc)(sqlite3_rtree_query_info*), /* Callback */
+  void *pContext,              /* Extra data passed into the callback */
+  void (*xDestructor)(void*)   /* Destructor for the extra data */
+){
+  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */
+
+  /* Allocate and populate the context object. */
+  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
+  if( !pGeomCtx ){
+    if( xDestructor ) xDestructor(pContext);
+    return SQLITE_NOMEM;
+  }
+  pGeomCtx->xGeom = 0;
+  pGeomCtx->xQueryFunc = xQueryFunc;
+  pGeomCtx->xDestructor = xDestructor;
+  pGeomCtx->pContext = pContext;
+  return sqlite3_create_function_v2(db, zQueryFunc, -1, SQLITE_ANY, 
+      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
+  );
+}
+
+#if !SQLITE_CORE
+#ifdef _WIN32
+__declspec(dllexport)
+#endif
+int sqlite3_rtree_init(
+  sqlite3 *db,
+  char **pzErrMsg,
+  const sqlite3_api_routines *pApi
+){
+  SQLITE_EXTENSION_INIT2(pApi)
+  return sqlite3RtreeInit(db);
+}
+#endif
+
+#endif
diff --git a/ext/rtree/rtree.h b/ext/rtree/rtree.h
new file mode 100644
index 0000000..8f41500
--- /dev/null
+++ b/ext/rtree/rtree.h
@@ -0,0 +1,30 @@
+/*
+** 2008 May 26
+**
+** The author disclaims copyright to this source code.  In place of
+** a legal notice, here is a blessing:
+**
+**    May you do good and not evil.
+**    May you find forgiveness for yourself and forgive others.
+**    May you share freely, never taking more than you give.
+**
+******************************************************************************
+**
+** This header file is used by programs that want to link against the
+** RTREE library.  All it does is declare the sqlite3RtreeInit() interface.
+*/
+#include "sqlite3.h"
+
+#ifdef SQLITE_OMIT_VIRTUALTABLE
+# undef SQLITE_ENABLE_RTREE
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif  /* __cplusplus */
+
+int sqlite3RtreeInit(sqlite3 *db);
+
+#ifdef __cplusplus
+}  /* extern "C" */
+#endif  /* __cplusplus */
diff --git a/ext/rtree/rtree1.test b/ext/rtree/rtree1.test
new file mode 100644
index 0000000..0341553
--- /dev/null
+++ b/ext/rtree/rtree1.test
@@ -0,0 +1,759 @@
+# 2008 Feb 19
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+}
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+set testprefix rtree1
+
+# Test plan:
+#
+#   rtree-1.*: Creating/destroying r-tree tables.
+#   rtree-2.*: Test the implicit constraints - unique rowid and
+#              (coord[N]<=coord[N+1]) for even values of N. Also
+#              automatic assigning of rowid values.
+#   rtree-3.*: Linear scans of r-tree data.
+#   rtree-4.*: Test INSERT
+#   rtree-5.*: Test DELETE
+#   rtree-6.*: Test UPDATE
+#   rtree-7.*: Test renaming an r-tree table.
+#   rtree-8.*: Test constrained scans of r-tree data.
+#
+#   rtree-12.*: Test that on-conflict clauses are supported.
+#   rtree-13.*: Test that bug [d2889096e7bdeac6d] has been fixed.
+#   rtree-14.*: Test if a non-integer is inserted into the PK column of an
+#               r-tree table, it is converted to an integer before being
+#               inserted. Also that if a non-numeric is inserted into one
+#               of the min/max dimension columns, it is converted to the
+#               required type before being inserted.
+#   rtree-15.*: Check that DROP TABLE works within a transaction that
+#               writes to an r-tree table.
+#
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+#----------------------------------------------------------------------------
+# Test cases rtree-1.* test CREATE and DROP table statements.
+#
+
+# Test creating and dropping an rtree table.
+#
+do_test rtree-1.1.1 {
+  execsql { CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2) }
+} {}
+do_test rtree-1.1.2a {
+  execsql { SELECT name FROM sqlite_master ORDER BY name }
+} {t1 t1_node t1_parent t1_rowid}
+do_execsql_test rtree-1.1.2b {
+  SELECT name FROM pragma_table_list WHERE type='shadow' ORDER BY name;
+} {t1_node t1_parent t1_rowid}
+do_test rtree-1.1.3 {
+  execsql { 
+    DROP TABLE t1; 
+    SELECT name FROM sqlite_master ORDER BY name;
+  }
+} {}
+
+# Test creating and dropping an rtree table with an odd name in
+# an attached database.
+#
+do_test rtree-1.2.1 {
+  file delete -force test2.db
+  execsql {
+    ATTACH 'test2.db' AS aux;
+    CREATE VIRTUAL TABLE aux.'a" "b' USING rtree(ii, x1, x2, y1, y2);
+  }
+} {}
+do_test rtree-1.2.2 {
+  execsql { SELECT name FROM sqlite_master ORDER BY name }
+} {}
+do_test rtree-1.2.3 {
+  execsql { SELECT name FROM aux.sqlite_master ORDER BY name }
+} {{a" "b} {a" "b_node} {a" "b_parent} {a" "b_rowid}}
+do_test rtree-1.2.4 {
+  execsql { 
+    DROP TABLE aux.'a" "b'; 
+    SELECT name FROM aux.sqlite_master ORDER BY name;
+  }
+} {}
+
+# Test that the logic for checking the number of columns specified
+# for an rtree table. Acceptable values are odd numbers between 3 and
+# 11, inclusive.
+#
+set cols [list i1 i2 i3 i4 i5 i6 i7 i8 i9 iA iB iC iD iE iF iG iH iI iJ iK]
+for {set nCol 1} {$nCol<[llength $cols]} {incr nCol} {
+
+  set columns [join [lrange $cols 0 [expr {$nCol-1}]] ,]
+
+  set X {0 {}}
+  if {$nCol%2 == 0}  { set X {1 {Wrong number of columns for an rtree table}} }
+  if {$nCol < 3}     { set X {1 {Too few columns for an rtree table}} }
+  if {$nCol > 11}    { set X {1 {Too many columns for an rtree table}} }
+
+  do_test rtree-1.3.$nCol {
+    catchsql " 
+      CREATE VIRTUAL TABLE t1 USING rtree($columns);
+    "
+  } $X
+
+  catchsql { DROP TABLE t1 }
+}
+do_catchsql_test rtree-1.3.1000 {
+  CREATE VIRTUAL TABLE t1000 USING rtree;
+} {1 {Too few columns for an rtree table}}
+
+# Like execsql except display output as integer where that can be
+# done without loss of information.
+#
+proc execsql_intout {sql} {
+  set out {}
+  foreach term [execsql $sql] {
+    regsub {\.0$} $term {} term
+    lappend out $term
+  }
+  return $out
+}
+
+# Test that it is possible to open an existing database that contains
+# r-tree tables.
+#
+do_execsql_test rtree-1.4.1a {
+  CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2);
+  INSERT INTO t1 VALUES(1, 5.0, 10.0);
+  SELECT substr(hex(data),1,40) FROM t1_node;
+} {00000001000000000000000140A0000041200000}
+do_execsql_test rtree-1.4.1b {
+  INSERT INTO t1 VALUES(2, 15.0, 20.0);
+} {}
+do_test rtree-1.4.2 {
+  db close
+  sqlite3 db test.db
+  execsql_intout { SELECT * FROM t1 ORDER BY ii }
+} {1 5 10 2 15 20}
+do_test rtree-1.4.3 {
+  execsql { DROP TABLE t1 }
+} {}
+
+# Test that it is possible to create an r-tree table with ridiculous
+# column names.
+#
+do_test rtree-1.5.1 {
+  execsql_intout {
+    CREATE VIRTUAL TABLE t1 USING rtree("the key", "x dim.", "x2'dim");
+    INSERT INTO t1 VALUES(1, 2, 3);
+    SELECT "the key", "x dim.", "x2'dim" FROM t1;
+  }
+} {1 2 3}
+do_test rtree-1.5.1 {
+  execsql { DROP TABLE t1 }
+} {}
+
+# Force the r-tree constructor to fail.
+#
+do_test rtree-1.6.1 {
+  execsql { CREATE TABLE t1_rowid(a); }
+  catchsql {
+    CREATE VIRTUAL TABLE t1 USING rtree("the key", "x dim.", "x2'dim");
+  }
+} {1 {table "t1_rowid" already exists}}
+do_test rtree-1.6.1 {
+  execsql { DROP TABLE t1_rowid }
+} {}
+
+#----------------------------------------------------------------------------
+# Test cases rtree-2.* 
+#
+do_test rtree-2.1.1 {
+  execsql { 
+    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
+    SELECT * FROM t1;
+  }
+} {}
+
+do_test rtree-2.1.2 {
+  execsql { INSERT INTO t1 VALUES(NULL, 1, 3, 2, 4) }
+  execsql_intout { SELECT * FROM t1 }
+} {1 1 3 2 4}
+do_test rtree-2.1.3 {
+  execsql { INSERT INTO t1 VALUES(NULL, 1, 3, 2, 4) }
+  execsql { SELECT rowid FROM t1 ORDER BY rowid }
+} {1 2}
+do_test rtree-2.1.3 {
+  execsql { INSERT INTO t1 VALUES(NULL, 1, 3, 2, 4) }
+  execsql { SELECT ii FROM t1 ORDER BY ii }
+} {1 2 3}
+
+do_test rtree-2.2.1 {
+  catchsql { INSERT INTO t1 VALUES(2, 1, 3, 2, 4) }
+} {1 {UNIQUE constraint failed: t1.ii}}
+do_test rtree-2.2.2 {
+  catchsql { INSERT INTO t1 VALUES(4, 1, 3, 4, 2) }
+} {1 {rtree constraint failed: t1.(y1<=y2)}}
+do_test rtree-2.2.3 {
+  catchsql { INSERT INTO t1 VALUES(4, 3, 1, 2, 4) }
+} {1 {rtree constraint failed: t1.(x1<=x2)}}
+do_test rtree-2.2.4 {
+  execsql { SELECT ii FROM t1 ORDER BY ii }
+} {1 2 3}
+
+do_test rtree-2.X {
+  execsql { DROP TABLE t1 }
+} {}
+
+#----------------------------------------------------------------------------
+# Test cases rtree-3.* test linear scans of r-tree table data. To test
+# this we have to insert some data into an r-tree, but that is not the
+# focus of these tests.
+#
+do_test rtree-3.1.1 {
+  execsql { 
+    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
+    SELECT * FROM t1;
+  }
+} {}
+do_test rtree-3.1.2 {
+  execsql_intout { 
+    INSERT INTO t1 VALUES(5, 1, 3, 2, 4);
+    SELECT * FROM t1;
+  }
+} {5 1 3 2 4}
+do_test rtree-3.1.3 {
+  execsql_intout {
+    INSERT INTO t1 VALUES(6, 2, 6, 4, 8);
+    SELECT * FROM t1;
+  }
+} {5 1 3 2 4 6 2 6 4 8}
+
+# Test the constraint on the coordinates (c[i]<=c[i+1] where (i%2==0)):
+do_test rtree-3.2.1 {
+  catchsql { INSERT INTO t1 VALUES(7, 2, 6, 4, 3) }
+} {1 {rtree constraint failed: t1.(y1<=y2)}}
+do_test rtree-3.2.2 {
+  catchsql { INSERT INTO t1 VALUES(8, 2, 6, 3, 3) }
+} {0 {}}
+
+#----------------------------------------------------------------------------
+# Test cases rtree-5.* test DELETE operations.
+#
+do_test rtree-5.1.1 {
+  execsql { CREATE VIRTUAL TABLE t2 USING rtree(ii, x1, x2) }
+} {}
+do_test rtree-5.1.2 {
+  execsql_intout { 
+    INSERT INTO t2 VALUES(1, 10, 20);
+    INSERT INTO t2 VALUES(2, 30, 40);
+    INSERT INTO t2 VALUES(3, 50, 60);
+    SELECT * FROM t2 ORDER BY ii;
+  }
+} {1 10 20 2 30 40 3 50 60}
+do_test rtree-5.1.3 {
+  execsql_intout { 
+    DELETE FROM t2 WHERE ii=2;
+    SELECT * FROM t2 ORDER BY ii;
+  }
+} {1 10 20 3 50 60}
+do_test rtree-5.1.4 {
+  execsql_intout { 
+    DELETE FROM t2 WHERE ii=1;
+    SELECT * FROM t2 ORDER BY ii;
+  }
+} {3 50 60}
+do_test rtree-5.1.5 {
+  execsql { 
+    DELETE FROM t2 WHERE ii=3;
+    SELECT * FROM t2 ORDER BY ii;
+  }
+} {}
+do_test rtree-5.1.6 {
+  execsql { SELECT * FROM t2_rowid }
+} {}
+
+#----------------------------------------------------------------------------
+# Test cases rtree-5.* test UPDATE operations.
+#
+do_test rtree-6.1.1 {
+  execsql { CREATE VIRTUAL TABLE t3 USING rtree(ii, x1, x2, y1, y2) }
+} {}
+do_test rtree-6.1.2 {
+  execsql_intout {
+    INSERT INTO t3 VALUES(1, 2, 3, 4, 5);
+    UPDATE t3 SET x2=5;
+    SELECT * FROM t3;
+  }
+} {1 2 5 4 5}
+do_test rtree-6.1.3 {
+  execsql { UPDATE t3 SET ii = 2 }
+  execsql_intout { SELECT * FROM t3 }
+} {2 2 5 4 5}
+
+#----------------------------------------------------------------------------
+# Test cases rtree-7.* test rename operations.
+#
+do_test rtree-7.1.1 {
+  execsql {
+    CREATE VIRTUAL TABLE t4 USING rtree(ii, x1, x2, y1, y2, z1, z2);
+    INSERT INTO t4 VALUES(1, 2, 3, 4, 5, 6, 7);
+  }
+} {}
+do_test rtree-7.1.2 {
+  execsql { ALTER TABLE t4 RENAME TO t5 }
+  execsql_intout { SELECT * FROM t5 }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.1.3 {
+  db close
+  sqlite3 db test.db
+  execsql_intout { SELECT * FROM t5 }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.1.4 {
+  execsql { ALTER TABLE t5 RENAME TO 'raisara "one"'''}
+  execsql_intout { SELECT * FROM "raisara ""one""'" }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.1.5 {
+  execsql_intout { SELECT * FROM 'raisara "one"''' }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.1.6 {
+  execsql { ALTER TABLE "raisara ""one""'" RENAME TO "abc 123" }
+  execsql_intout { SELECT * FROM "abc 123" }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.1.7 {
+  db close
+  sqlite3 db test.db
+  execsql_intout { SELECT * FROM "abc 123" }
+} {1 2 3 4 5 6 7}
+
+# An error midway through a rename operation.
+do_test rtree-7.2.1 {
+  execsql { 
+    CREATE TABLE t4_node(a);
+  }
+  catchsql { ALTER TABLE "abc 123" RENAME TO t4 }
+} {1 {SQL logic error}}
+do_test rtree-7.2.2 {
+  execsql_intout { SELECT * FROM "abc 123" }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.2.3 {
+  execsql { 
+    DROP TABLE t4_node;
+    CREATE TABLE t4_rowid(a);
+  }
+  catchsql { ALTER TABLE "abc 123" RENAME TO t4 }
+} {1 {SQL logic error}}
+do_test rtree-7.2.4 {
+  db close
+  sqlite3 db test.db
+  execsql_intout { SELECT * FROM "abc 123" }
+} {1 2 3 4 5 6 7}
+do_test rtree-7.2.5 {
+  execsql { DROP TABLE t4_rowid }
+  execsql { ALTER TABLE "abc 123" RENAME TO t4 }
+  execsql_intout { SELECT * FROM t4 }
+} {1 2 3 4 5 6 7}
+
+
+#----------------------------------------------------------------------------
+# Test cases rtree-8.*
+#
+
+# Test that the function to determine if a leaf cell is part of the
+# result set works.
+do_test rtree-8.1.1 {
+  execsql {
+    CREATE VIRTUAL TABLE t6 USING rtree(ii, x1, x2);
+    INSERT INTO t6 VALUES(1, 3, 7);
+    INSERT INTO t6 VALUES(2, 4, 6);
+  }
+} {}
+do_test rtree-8.1.2 { execsql { SELECT ii FROM t6 WHERE x1>2 } }   {1 2}
+do_test rtree-8.1.3 { execsql { SELECT ii FROM t6 WHERE x1>3 } }   {2}
+do_test rtree-8.1.4 { execsql { SELECT ii FROM t6 WHERE x1>4 } }   {}
+do_test rtree-8.1.5 { execsql { SELECT ii FROM t6 WHERE x1>5 } }   {}
+do_test rtree-8.1.6 { execsql { SELECT ii FROM t6 WHERE x1>''} }   {}
+do_test rtree-8.1.7 { execsql { SELECT ii FROM t6 WHERE x1>null}}  {}
+do_test rtree-8.1.8 { execsql { SELECT ii FROM t6 WHERE x1>'2'} }   {1 2}
+do_test rtree-8.1.9 { execsql { SELECT ii FROM t6 WHERE x1>'3'} }   {2}
+do_test rtree-8.2.2 { execsql { SELECT ii FROM t6 WHERE x1>=2 } }  {1 2}
+do_test rtree-8.2.3 { execsql { SELECT ii FROM t6 WHERE x1>=3 } }  {1 2}
+do_test rtree-8.2.4 { execsql { SELECT ii FROM t6 WHERE x1>=4 } }  {2}
+do_test rtree-8.2.5 { execsql { SELECT ii FROM t6 WHERE x1>=5 } }  {}
+do_test rtree-8.2.6 { execsql { SELECT ii FROM t6 WHERE x1>=''} }  {}
+do_test rtree-8.2.7 { execsql { SELECT ii FROM t6 WHERE x1>=null}} {}
+do_test rtree-8.2.8 { execsql { SELECT ii FROM t6 WHERE x1>='4'} } {2}
+do_test rtree-8.2.9 { execsql { SELECT ii FROM t6 WHERE x1>='5'} } {}
+do_test rtree-8.3.2 { execsql { SELECT ii FROM t6 WHERE x1<2 } }   {}
+do_test rtree-8.3.3 { execsql { SELECT ii FROM t6 WHERE x1<3 } }   {}
+do_test rtree-8.3.4 { execsql { SELECT ii FROM t6 WHERE x1<4 } }   {1}
+do_test rtree-8.3.5 { execsql { SELECT ii FROM t6 WHERE x1<5 } }   {1 2}
+do_test rtree-8.3.6 { execsql { SELECT ii FROM t6 WHERE x1<''} }   {1 2}
+do_test rtree-8.3.7 { execsql { SELECT ii FROM t6 WHERE x1<null}}  {}
+do_test rtree-8.3.8 { execsql { SELECT ii FROM t6 WHERE x1<'3'} }  {}
+do_test rtree-8.3.9 { execsql { SELECT ii FROM t6 WHERE x1<'4'} }  {1}
+do_test rtree-8.4.2 { execsql { SELECT ii FROM t6 WHERE x1<=2 } }  {}
+do_test rtree-8.4.3 { execsql { SELECT ii FROM t6 WHERE x1<=3 } }  {1}
+do_test rtree-8.4.4 { execsql { SELECT ii FROM t6 WHERE x1<=4 } }  {1 2}
+do_test rtree-8.4.5 { execsql { SELECT ii FROM t6 WHERE x1<=5 } }  {1 2}
+do_test rtree-8.4.6 { execsql { SELECT ii FROM t6 WHERE x1<=''} }  {1 2}
+do_test rtree-8.4.7 { execsql { SELECT ii FROM t6 WHERE x1<=null}} {}
+do_test rtree-8.5.2 { execsql { SELECT ii FROM t6 WHERE x1=2 } }   {}
+do_test rtree-8.5.3 { execsql { SELECT ii FROM t6 WHERE x1=3 } }   {1}
+do_test rtree-8.5.4 { execsql { SELECT ii FROM t6 WHERE x1=4 } }   {2}
+do_test rtree-8.5.5 { execsql { SELECT ii FROM t6 WHERE x1=5 } }   {}
+do_test rtree-8.5.6 { execsql { SELECT ii FROM t6 WHERE x1=''} }   {}
+do_test rtree-8.5.7 { execsql { SELECT ii FROM t6 WHERE x1=null}}  {}
+
+
+#----------------------------------------------------------------------------
+# Test cases rtree-9.*
+#
+# Test that ticket #3549 is fixed.
+do_test rtree-9.1 {
+  execsql {
+    CREATE TABLE foo (id INTEGER PRIMARY KEY);
+    CREATE VIRTUAL TABLE bar USING rtree (id, minX, maxX, minY, maxY);
+    INSERT INTO foo VALUES (null);
+    INSERT INTO foo SELECT null FROM foo;
+    INSERT INTO foo SELECT null FROM foo;
+    INSERT INTO foo SELECT null FROM foo;
+    INSERT INTO foo SELECT null FROM foo;
+    INSERT INTO foo SELECT null FROM foo;
+    INSERT INTO foo SELECT null FROM foo;
+    DELETE FROM foo WHERE id > 40;
+    INSERT INTO bar SELECT NULL, 0, 0, 0, 0 FROM foo;
+  }
+} {}
+
+# This used to crash.
+do_test rtree-9.2 {
+  execsql {
+    SELECT count(*) FROM bar b1, bar b2, foo s1 WHERE s1.id = b1.id;
+  }
+} {1600}
+do_test rtree-9.3 {
+  execsql {
+    SELECT count(*) FROM bar b1, bar b2, foo s1 
+    WHERE b1.minX <= b2.maxX AND s1.id = b1.id;
+  }
+} {1600}
+
+#-------------------------------------------------------------------------
+# Ticket #3970: Check that the error message is meaningful when a 
+# keyword is used as a column name.
+#
+do_test rtree-10.1 {
+  catchsql { CREATE VIRTUAL TABLE t7 USING rtree(index, x1, y1, x2, y2) }
+} {1 {near "index": syntax error}}
+
+#-------------------------------------------------------------------------
+# Test last_insert_rowid().
+# 
+do_test rtree-11.1 {
+  execsql {
+    CREATE VIRTUAL TABLE t8 USING rtree(idx, x1, x2, y1, y2);
+    INSERT INTO t8 VALUES(1, 1.0, 1.0, 2.0, 2.0);
+    SELECT last_insert_rowid();
+  }
+} {1}
+do_test rtree-11.2 {
+  execsql {
+    INSERT INTO t8 VALUES(NULL, 1.0, 1.0, 2.0, 2.0);
+    SELECT last_insert_rowid();
+  }
+} {2}
+
+#-------------------------------------------------------------------------
+# Test on-conflict clause handling.
+#
+db_delete_and_reopen
+do_execsql_test 12.0.1 {
+  CREATE VIRTUAL TABLE t1 USING rtree_i32(idx, x1, x2, y1, y2);
+  INSERT INTO t1 VALUES(1,   1, 2, 3, 4);
+  SELECT substr(hex(data),1,56) FROM t1_node;
+} {00000001000000000000000100000001000000020000000300000004}
+do_execsql_test 12.0.2 {
+  INSERT INTO t1 VALUES(2,   2, 3, 4, 5);
+  INSERT INTO t1 VALUES(3,   3, 4, 5, 6);
+
+  CREATE TABLE source(idx, x1, x2, y1, y2);
+  INSERT INTO source VALUES(5, 8, 8, 8, 8);
+  INSERT INTO source VALUES(2, 7, 7, 7, 7);
+}
+db_save_and_close
+foreach {tn sql_template testdata} {
+  1    "INSERT %CONF% INTO t1 VALUES(2, 7, 7, 7, 7)" {
+    ROLLBACK 0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
+    ABORT    0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    FAIL     0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    REPLACE  0 0 {1 1 2 3 4   2 7 7 7 7   3 3 4 5 6   4 4 5 6 7}
+  }
+
+  2    "INSERT %CONF% INTO t1 SELECT * FROM source" {
+    ROLLBACK 1 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
+    ABORT    1 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    IGNORE   1 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7  5 8 8 8 8}
+    FAIL     1 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7  5 8 8 8 8}
+    REPLACE  1 0 {1 1 2 3 4   2 7 7 7 7   3 3 4 5 6   4 4 5 6 7  5 8 8 8 8}
+  }
+
+  3    "UPDATE %CONF% t1 SET idx = 2 WHERE idx = 4" {
+    ROLLBACK 0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
+    ABORT    0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    FAIL     0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    REPLACE  0 0 {1 1 2 3 4   2 4 5 6 7   3 3 4 5 6}
+  }
+
+  3    "UPDATE %CONF% t1 SET idx = ((idx+1)%5)+1 WHERE idx > 2" {
+    ROLLBACK 1 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
+    ABORT    1 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    IGNORE   1 0 {1 1 2 3 4   2 2 3 4 5               4 4 5 6 7   5 3 4 5 6}
+    FAIL     1 1 {1 1 2 3 4   2 2 3 4 5               4 4 5 6 7   5 3 4 5 6}
+    REPLACE  1 0 {1 4 5 6 7   2 2 3 4 5                           5 3 4 5 6}
+  }
+
+  4    "INSERT %CONF% INTO t1 VALUES(2, 7, 6, 7, 7)" {
+    ROLLBACK 0 2 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
+    ABORT    0 2 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    FAIL     0 2 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+    REPLACE  0 2 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
+  }
+
+} {
+  foreach {mode uses error data} $testdata {
+    db_restore_and_reopen
+
+    set sql [string map [list %CONF% "OR $mode"] $sql_template]
+    set testname "12.$tn.[string tolower $mode]"
+
+    execsql {
+      BEGIN;
+        INSERT INTO t1 VALUES(4,   4, 5, 6, 7);
+    }
+
+    set res(0) {0 {}}
+    set res(1) {1 {UNIQUE constraint failed: t1.idx}}
+    set res(2) {1 {rtree constraint failed: t1.(x1<=x2)}}
+
+    do_catchsql_test $testname.1 $sql $res($error)
+    do_test $testname.2 [list sql_uses_stmt db $sql] $uses
+    do_execsql_test $testname.3 { SELECT * FROM t1 ORDER BY idx } $data
+
+    do_rtree_integrity_test $testname.4 t1
+    db close
+  }
+}
+
+#-------------------------------------------------------------------------
+# Test that bug [d2889096e7bdeac6d] has been fixed.
+#
+reset_db
+do_execsql_test 13.1 {
+  CREATE VIRTUAL TABLE t9 USING rtree(id, xmin, xmax);
+  INSERT INTO t9 VALUES(1,0,0);            
+  INSERT INTO t9 VALUES(2,0,0);
+  SELECT * FROM t9 WHERE id IN (1, 2);
+} {1 0.0 0.0 2 0.0 0.0}
+
+do_execsql_test 13.2 {
+  WITH r(x) AS (
+    SELECT 1 UNION ALL
+    SELECT 2 UNION ALL
+    SELECT 3
+  )
+  SELECT * FROM r CROSS JOIN t9 WHERE id=x;
+} {1 1 0.0 0.0 2 2 0.0 0.0}
+
+#-------------------------------------------------------------------------
+# Test if a non-integer is inserted into the PK column of an r-tree
+# table, it is converted to an integer before being inserted. Also
+# that if a non-numeric is inserted into one of the min/max dimension
+# columns, it is converted to the required type before being inserted.
+#
+do_execsql_test 14.1 {
+  CREATE VIRTUAL TABLE t10 USING rtree(ii, x1, x2);
+}
+
+do_execsql_test 14.2 {
+  INSERT INTO t10 VALUES(NULL,   1, 2);
+  INSERT INTO t10 VALUES(NULL,   2, 3);
+  INSERT INTO t10 VALUES('4xxx', 3, 4);
+  INSERT INTO t10 VALUES(5.0,    4, 5);
+  INSERT INTO t10 VALUES(6.4,    5, 6);
+}
+do_execsql_test 14.3 {
+  SELECT * FROM t10;
+} {
+  1 1.0 2.0   2 2.0 3.0   4 3.0 4.0   5 4.0 5.0   6 5.0 6.0
+}
+
+do_execsql_test 14.4 {
+  DELETE FROM t10;
+  INSERT INTO t10 VALUES(1, 'one', 'two');
+  INSERT INTO t10 VALUES(2, '52xyz', '81...');
+}
+do_execsql_test 14.5 {
+  SELECT * FROM t10;
+} {
+  1 0.0 0.0
+  2 52.0 81.0
+}
+do_execsql_test 14.6 {
+  INSERT INTO t10 VALUES(0,10,20);
+  SELECT * FROM t10 WHERE ii=NULL;
+} {}
+do_execsql_test 14.7 {
+  SELECT * FROM t10 WHERE ii='xyz';
+} {}
+do_execsql_test 14.8 {
+  SELECT * FROM t10 WHERE ii='0.0';
+} {0 10.0 20.0}
+do_execsql_test 14.9 {
+  SELECT * FROM t10 WHERE ii=0.0;
+} {0 10.0 20.0}
+
+
+do_execsql_test 14.104 {
+  DROP TABLE t10;
+  CREATE VIRTUAL TABLE t10 USING rtree_i32(ii, x1, x2);
+  INSERT INTO t10 VALUES(1, 'one', 'two');
+  INSERT INTO t10 VALUES(2, '52xyz', '81...');
+  INSERT INTO t10 VALUES(3, 42.3, 49.9);
+}
+do_execsql_test 14.105 {
+  SELECT * FROM t10;
+} {
+  1 0 0
+  2 52 81
+  3 42 49
+}
+
+#-------------------------------------------------------------------------
+#
+do_execsql_test 15.0 {
+  CREATE VIRTUAL TABLE rt USING rtree(id, x1,x2, y1,y2);
+  CREATE TEMP TABLE t13(a, b, c);
+}
+do_execsql_test 15.1 {
+  BEGIN;
+  INSERT INTO rt VALUES(1,2,3,4,5);
+}
+do_execsql_test 15.2 {
+  DROP TABLE t13;
+  COMMIT;
+}
+
+# Test cases for the new auxiliary columns feature
+#
+do_catchsql_test 16.100 {
+  CREATE VIRTUAL TABLE t16 USING rtree(id,x0,x1,y0,+aux1,x1);
+} {1 {Auxiliary rtree columns must be last}}
+do_test 16.110 {
+  set sql {
+    CREATE VIRTUAL TABLE t16 USING rtree(
+      id, x00, x01, x10, x11, x20, x21, x30, x31, x40, x41
+  }
+  for {set i 12} {$i<=100} {incr i} {
+     append sql ", +a$i"
+  }
+  append sql ");"
+  execsql $sql
+} {}
+do_test 16.120 {
+  set sql {
+    CREATE VIRTUAL TABLE t16b USING rtree(
+      id, x00, x01, x10, x11, x20, x21, x30, x31, x40, x41
+  }
+  for {set i 12} {$i<=101} {incr i} {
+     append sql ", +a$i"
+  }
+  append sql ");"
+  catchsql $sql
+} {1 {Too many columns for an rtree table}}
+
+do_execsql_test 16.130 {
+  DROP TABLE IF EXISTS rt1;
+  CREATE VIRTUAL TABLE rt1 USING rtree(id, x1, x2, +aux);
+  INSERT INTO rt1 VALUES(1, 1, 2, 'aux1');
+  INSERT INTO rt1 VALUES(2, 2, 3, 'aux2');
+  INSERT INTO rt1 VALUES(3, 3, 4, 'aux3');
+  INSERT INTO rt1 VALUES(4, 4, 5, 'aux4');
+  SELECT * FROM rt1 WHERE id IN (1, 2, 3, 4);
+} {1 1.0 2.0 aux1 2 2.0 3.0 aux2 3 3.0 4.0 aux3 4 4.0 5.0 aux4}
+
+reset_db
+do_execsql_test 17.0 {
+  CREATE VIRTUAL TABLE t1 USING rtree(id, x1 PRIMARY KEY, x2, y1, y2);
+  CREATE VIRTUAL TABLE t2 USING rtree(id, x1, x2, y1, y2 UNIQUE);
+}
+do_execsql_test 17.1 {
+  REINDEX t1;
+  REINDEX t2;
+} {}
+
+do_execsql_test 17.2 {
+  REINDEX;
+} {}
+
+reset_db
+do_execsql_test 18.0 {
+  CREATE VIRTUAL TABLE rt0 USING rtree(c0, c1, c2);
+  INSERT INTO rt0(c0,c1,c2) VALUES(9,2,3);
+  SELECT c0 FROM rt0 WHERE rt0.c1 > '-1'; 
+  SELECT rt0.c1 > '-1' FROM rt0;
+} {9 1}
+
+expand_all_sql db
+
+# 2020-02-28 ticket e63b4d1a65546532
+reset_db
+do_execsql_test 19.0 {
+  CREATE VIRTUAL TABLE rt0 USING rtree(a,b,c);
+  INSERT INTO rt0(a,b,c) VALUES(0,0.0,0.0);
+  CREATE VIEW v0(x) AS SELECT DISTINCT rt0.b FROM rt0;
+  SELECT v0.x FROM v0, rt0;
+} {0.0}
+do_execsql_test 19.1 {
+  SELECT v0.x FROM v0, rt0 WHERE v0.x = rt0.b;
+} {0.0}
+
+# 2022-06-20 https://sqlite.org/forum/forumpost/57bdf2217d
+#
+reset_db
+do_execsql_test 20.0 {
+  CREATE VIRTUAL TABLE rt0 USING rtree(id, x0, x1);
+  CREATE TABLE t0(a INT);
+  CREATE TABLE t1(b INT);
+  INSERT INTO rt0 VALUES(0, 0, 0);
+}
+do_catchsql_test 20.1 {
+  SELECT * FROM t1 JOIN t0 ON x0>a RIGHT JOIN rt0 ON true WHERE +x0 = 0;
+} {1 {ON clause references tables to its right}}
+do_catchsql_test 20.2 {
+  SELECT * FROM t1 JOIN t0 ON x0>a RIGHT JOIN rt0 ON true WHERE x0 = 0;
+} {1 {ON clause references tables to its right}}
+db null -
+do_execsql_test 20.3 {
+  SELECT * FROM t1 JOIN t0 ON true RIGHT JOIN rt0 ON x0>a WHERE +x0 = 0;
+} {- - 0 0.0 0.0}
+do_execsql_test 20.4 {
+  SELECT * FROM t1 JOIN t0 ON true RIGHT JOIN rt0 ON x0>a WHERE x0 = 0;
+} {- - 0 0.0 0.0}
+
+finish_test
diff --git a/ext/rtree/rtree2.test b/ext/rtree/rtree2.test
new file mode 100644
index 0000000..31c1914
--- /dev/null
+++ b/ext/rtree/rtree2.test
@@ -0,0 +1,147 @@
+# 2008 Feb 19
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+set ::NROW   1000
+set ::NDEL     10
+set ::NSELECT 100
+
+if {[info exists G(isquick)] && $G(isquick)} {
+  set ::NROW 100
+  set ::NSELECT 10
+}
+
+foreach module {rtree_i32 rtree} {
+  if {$module=="rtree_i32"} {set etype INT} {set etype REAL}
+  for {set nDim 1} {$nDim <= 5} {incr nDim} {
+  
+    do_test rtree2-$module.$nDim.1 {
+      set cols [list]
+      foreach c [list c0 c1 c2 c3 c4 c5 c6 c7 c8 c9] {
+        lappend cols "$c $etype"
+      }
+      set cols [join [lrange $cols 0 [expr {$nDim*2-1}]] ", "]
+      execsql " 
+        CREATE VIRTUAL TABLE t1 USING ${module}(ii, $cols);
+        CREATE TABLE t2 (ii, $cols);
+      "
+    } {}
+  
+    do_test rtree2-$module.$nDim.2 {
+      db transaction {
+        for {set ii 0} {$ii < $::NROW} {incr ii} {
+          #puts "Row $ii"
+          set values [list]
+          for {set jj 0} {$jj<$nDim*2} {incr jj} {
+            lappend values [expr int(rand()*1000)]
+          }
+          set values [join $values ,]
+          #puts [rtree_treedump db t1]
+          #puts "INSERT INTO t2 VALUES($ii, $values)"
+          set rc [catch {db eval "INSERT INTO t1 VALUES($ii, $values)"}]
+          if {$rc} {
+            incr ii -1
+          } else {
+            db eval "INSERT INTO t2 VALUES($ii, $values)"
+          }
+          #if {[rtree_check db t1]} {
+            #puts [rtree_treedump db t1]
+            #exit
+          #}
+        }
+      }
+  
+      set t1 [execsql {SELECT * FROM t1 ORDER BY ii}]
+      set t2 [execsql {SELECT * FROM t2 ORDER BY ii}]
+      set rc [expr {$t1 eq $t2}]
+      if {$rc != 1} {
+        puts $t1
+        puts $t2
+      }
+      set rc
+    } {1}
+  
+    do_rtree_integrity_test rtree2-$module.$nDim.3 t1
+  
+    set OPS [list < > <= >= =]
+    for {set ii 0} {$ii < $::NSELECT} {incr ii} {
+      do_test rtree2-$module.$nDim.4.$ii.1 {
+        set where [list]
+        foreach look_three_dots! {. . .} {
+          set colidx [expr int(rand()*($nDim*2+1))-1]
+          if {$colidx<0} {
+            set col ii
+          } else {
+            set col "c$colidx"
+          }
+          set op  [lindex $OPS [expr int(rand()*[llength $OPS])]]
+          set val [expr int(rand()*1000)]
+          lappend where "$col $op $val"
+        }
+        set where [join $where " AND "]
+  
+        set t1 [execsql "SELECT * FROM t1 WHERE $where ORDER BY ii"]
+        set t2 [execsql "SELECT * FROM t2 WHERE $where ORDER BY ii"]
+        set rc [expr {$t1 eq $t2}]
+        if {$rc != 1} {
+          #puts $where
+          puts $t1
+          puts $t2
+          #puts [rtree_treedump db t1]
+          #breakpoint
+          #set t1 [execsql "SELECT * FROM t1 WHERE $where ORDER BY ii"]
+          #exit
+        }
+        set rc
+      } {1}
+    }
+  
+    for {set ii 0} {$ii < $::NROW} {incr ii $::NDEL} {
+      #puts [rtree_treedump db t1]
+      do_test rtree2-$module.$nDim.5.$ii.1 {
+        execsql "DELETE FROM t2 WHERE ii <= $::ii"
+        execsql "DELETE FROM t1 WHERE ii <= $::ii"
+  
+        set t1 [execsql {SELECT * FROM t1 ORDER BY ii}]
+        set t2 [execsql {SELECT * FROM t2 ORDER BY ii}]
+        set rc [expr {$t1 eq $t2}]
+        if {$rc != 1} {
+          puts $t1
+          puts $t2
+        }
+        set rc
+      } {1}
+      do_rtree_integrity_test rtree2-$module.$nDim.5.$ii.2 t1
+    }
+  
+    do_test rtree2-$module.$nDim.6 {
+      execsql {
+        DROP TABLE t1;
+        DROP TABLE t2;
+      }
+    } {}
+  }
+}
+
+finish_test
diff --git a/ext/rtree/rtree3.test b/ext/rtree/rtree3.test
new file mode 100644
index 0000000..c980863
--- /dev/null
+++ b/ext/rtree/rtree3.test
@@ -0,0 +1,270 @@
+# 2008 Feb 19
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing that the r-tree correctly handles
+# out-of-memory conditions.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source $testdir/tester.tcl
+source $testdir/malloc_common.tcl
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+set ::TMPDBERROR [list 1 \
+  {unable to open a temporary database file for storing temporary tables}
+]
+
+# Test summary:
+#
+#   rtree3-1: Test OOM in simple CREATE TABLE, INSERT, DELETE and SELECT 
+#             commands on an almost empty table.
+#
+#   rtree3-2: Test OOM in a DROP TABLE command.
+#
+#   rtree3-3a: Test OOM during a transaction to insert 100 pseudo-random rows.
+#
+#   rtree3-3b: Test OOM during a transaction deleting all entries in the
+#              database constructed in [rtree3-3a] in pseudo-random order.
+#
+#   rtree3-4a: OOM during "SELECT count(*) FROM ..." on a big table.
+#
+#   rtree3-4b: OOM while deleting rows from a big table.
+#
+#   rtree3-5: Test OOM while inserting rows into a big table.
+#
+#   rtree3-6: Test OOM while deleting all rows of a table, one at a time.
+#
+#   rtree3-7: OOM during an ALTER TABLE RENAME TABLE command.
+#
+#   rtree3-8: Test OOM while registering the r-tree module with sqlite.
+#
+#   rtree3-11: OOM following a constraint failure
+#
+do_faultsim_test rtree3-1 -faults oom* -prep {
+  faultsim_delete_and_reopen
+} -body {
+  execsql {
+    BEGIN TRANSACTION;
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
+    INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
+    INSERT INTO rt VALUES(NULL, 13, 15, 17, 19);
+    DELETE FROM rt WHERE ii = 1;
+    SELECT * FROM rt;
+    SELECT ii FROM rt WHERE ii = 2;
+    COMMIT;
+  }
+}
+
+do_test rtree3-2.prep {
+  faultsim_delete_and_reopen
+  execsql {
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
+    INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
+  }
+  faultsim_save_and_close
+} {}
+do_faultsim_test rtree3-2 -faults oom* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  execsql { DROP TABLE rt } 
+}
+
+do_malloc_test rtree3-3.prep {
+  faultsim_delete_and_reopen
+  execsql {
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2, +a1, +a2);
+    INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
+  }
+  faultsim_save_and_close
+} {}
+
+do_faultsim_test rtree3-3a -faults oom* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  db eval BEGIN
+  for {set ii 0} {$ii < 100} {incr ii} {
+    set f [expr rand()]
+    db eval {INSERT INTO rt VALUES(NULL, $f*10.0, $f*10.0, $f*15.0, $f*15.0)}
+  }
+  db eval COMMIT
+}
+faultsim_save_and_close
+
+do_faultsim_test rtree3-3b -faults oom* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  db eval BEGIN
+  for {set ii 0} {$ii < 100} {incr ii} {
+    set f [expr rand()]
+    db eval { DELETE FROM rt WHERE x1<($f*10.0) AND x1>($f*10.5) }
+  }
+  db eval COMMIT
+} 
+
+do_test rtree3-4.prep {
+  faultsim_delete_and_reopen
+  execsql {
+    BEGIN;
+    PRAGMA page_size = 512;
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
+  }
+  for {set i 0} {$i < 1500} {incr i} {
+    execsql { INSERT INTO rt VALUES($i, $i, $i+1, $i, $i+1) }
+  }
+  execsql { COMMIT }
+  faultsim_save_and_close
+} {}
+
+do_faultsim_test rtree3-4a -faults oom-* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  db eval { SELECT count(*) FROM rt }
+} -test {
+  faultsim_test_result {0 1500}
+}
+
+do_faultsim_test rtree3-4b -faults oom-transient -prep {
+  faultsim_restore_and_reopen
+} -body {
+  db eval { DELETE FROM rt WHERE ii BETWEEN 1 AND 100 }
+} -test {
+  faultsim_test_result {0 {}}
+}
+
+do_test rtree3-5.prep {
+  faultsim_delete_and_reopen
+  execsql {
+    BEGIN;
+    PRAGMA page_size = 512;
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
+  }
+  for {set i 0} {$i < 100} {incr i} {
+    execsql { INSERT INTO rt VALUES($i, $i, $i+1, $i, $i+1) }
+  }
+  execsql { COMMIT }
+  faultsim_save_and_close
+} {}
+do_faultsim_test rtree3-5 -faults oom-* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  for {set i 100} {$i < 110} {incr i} {
+    execsql { INSERT INTO rt VALUES($i, $i, $i+1, $i, $i+1) }
+  }
+} -test {
+  faultsim_test_result {0 {}}
+}
+
+do_test rtree3-6.prep {
+  faultsim_delete_and_reopen
+  execsql {
+    BEGIN;
+    PRAGMA page_size = 512;
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
+  }
+  for {set i 0} {$i < 50} {incr i} {
+    execsql { INSERT INTO rt VALUES($i, $i, $i+1, $i, $i+1) }
+  }
+  execsql { COMMIT }
+  faultsim_save_and_close
+} {}
+do_faultsim_test rtree3-6 -faults oom-* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  execsql BEGIN
+  for {set i 0} {$i < 50} {incr i} {
+    execsql { DELETE FROM rt WHERE ii=$i }
+  }
+  execsql COMMIT
+} -test {
+  faultsim_test_result {0 {}}
+}
+
+do_test rtree3-7.prep {
+  faultsim_delete_and_reopen
+  execsql { CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2) }
+  faultsim_save_and_close
+} {}
+do_faultsim_test rtree3-7 -faults oom-* -prep {
+  faultsim_restore_and_reopen
+} -body {
+  execsql { ALTER TABLE rt RENAME TO rt2 } 
+} -test {
+  faultsim_test_result {0 {}} $::TMPDBERROR
+}
+
+do_faultsim_test rtree3-8 -faults oom-* -prep {
+  catch { db close }
+} -body {
+  sqlite3 db test.db
+} 
+
+do_faultsim_test rtree3-9 -faults oom-* -prep {
+  sqlite3 db :memory:
+} -body {
+  set rc [register_cube_geom db]
+  if {$rc != "SQLITE_OK"} { error $rc }
+} -test {
+  faultsim_test_result {0 {}} {1 SQLITE_NOMEM}
+}
+
+do_test rtree3-10.prep {
+  faultsim_delete_and_reopen
+  execsql { 
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2, z1, z2);
+    INSERT INTO rt VALUES(1,  10, 10, 10, 11, 11, 11);
+    INSERT INTO rt VALUES(2,  5, 6, 6, 7, 7, 8);
+  }
+  faultsim_save_and_close
+} {}
+do_faultsim_test rtree3-10 -faults oom-* -prep {
+  faultsim_restore_and_reopen
+  register_cube_geom db
+  execsql { SELECT * FROM rt }
+} -body {
+  execsql { SELECT ii FROM rt WHERE ii MATCH cube(4.5, 5.5, 6.5, 1, 1, 1) }
+} -test {
+  faultsim_test_result {0 2}
+}
+
+
+do_test rtree3-11.prep {
+  faultsim_delete_and_reopen
+  execsql { 
+    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
+    INSERT INTO rt VALUES(1, 2, 3, 4, 5);
+  }
+  faultsim_save_and_close
+} {}
+do_faultsim_test rtree3-10.1 -faults oom-* -prep {
+  faultsim_restore_and_reopen
+  execsql { SELECT * FROM rt }
+} -body {
+  execsql { INSERT INTO rt VALUES(1, 2, 3, 4, 5) }
+} -test {
+  faultsim_test_result {1 {UNIQUE constraint failed: rt.ii}} \
+                       {1 {constraint failed}}
+}
+do_faultsim_test rtree3-10.2 -faults oom-* -prep {
+  faultsim_restore_and_reopen
+  execsql { SELECT * FROM rt }
+} -body {
+  execsql { INSERT INTO rt VALUES(2, 2, 3, 5, 4) }
+} -test {
+  faultsim_test_result {1 {rtree constraint failed: rt.(y1<=y2)}} \
+                       {1 {constraint failed}}
+}
+
+finish_test
diff --git a/ext/rtree/rtree4.test b/ext/rtree/rtree4.test
new file mode 100644
index 0000000..a73921d
--- /dev/null
+++ b/ext/rtree/rtree4.test
@@ -0,0 +1,254 @@
+# 2008 May 23
+#
+# 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.
+#
+#***********************************************************************
+#
+# Randomized test cases for the rtree extension.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+set ::NROW 2500
+if {[info exists G(isquick)] && $G(isquick)} {
+  set ::NROW 250
+}
+
+ifcapable !rtree_int_only {
+  # Return a floating point number between -X and X.
+  # 
+  proc rand {X} {
+    return [expr {int((rand()-0.5)*1024.0*$X)/512.0}]
+  }
+  
+  # Return a positive floating point number less than or equal to X
+  #
+  proc randincr {X} {
+    while 1 {
+      set r [expr {int(rand()*$X*32.0)/32.0}]
+      if {$r>0.0} {return $r}
+    }
+  }
+} else {
+  # For rtree_int_only, return an number between -X and X.
+  # 
+  proc rand {X} {
+    return [expr {int((rand()-0.5)*2*$X)}]
+  }
+  
+  # Return a positive integer less than or equal to X
+  #
+  proc randincr {X} {
+    while 1 {
+      set r [expr {int(rand()*$X)+1}]
+      if {$r>0} {return $r}
+    }
+  }
+}
+  
+# Scramble the $inlist into a random order.
+#
+proc scramble {inlist} {
+  set y {}
+  foreach x $inlist {
+    lappend y [list [expr {rand()}] $x]
+  }
+  set y [lsort $y]
+  set outlist {}
+  foreach x $y {
+    lappend outlist [lindex $x 1]
+  }
+  return $outlist
+}
+
+# Always use the same random seed so that the sequence of tests
+# is repeatable.
+#
+expr {srand(1234)}
+
+# Run these tests for all number of dimensions between 1 and 5.
+#
+for {set nDim 1} {$nDim<=5} {incr nDim} {
+
+  # Construct an rtree virtual table and an ordinary btree table
+  # to mirror it.  The ordinary table should be much slower (since
+  # it has to do a full table scan) but should give the exact same
+  # answers.
+  #
+  do_test rtree4-$nDim.1 {
+    set clist {}
+    set cklist {}
+    for {set i 0} {$i<$nDim} {incr i} {
+      lappend clist mn$i mx$i
+      lappend cklist "mn$i<mx$i"
+    }
+    db eval "DROP TABLE IF EXISTS rx"
+    db eval "DROP TABLE IF EXISTS bx"
+    db eval "CREATE VIRTUAL TABLE rx USING rtree(id, [join $clist ,])"
+    db eval "CREATE TABLE bx(id INTEGER PRIMARY KEY,\
+                [join $clist ,], CHECK( [join $cklist { AND }] ))"
+  } {}
+
+  # Do many insertions of small objects.  Do both overlapping and
+  # contained-within queries after each insert to verify that all
+  # is well.
+  #
+  unset -nocomplain where
+  for {set i 1} {$i<$::NROW} {incr i} {
+    # Do a random insert
+    #
+    do_test rtree4-$nDim.2.$i.1 {
+      set vlist {}
+      for {set j 0} {$j<$nDim} {incr j} {
+        set mn [rand 10000]
+        set mx [expr {$mn+[randincr 50]}]
+        lappend vlist $mn $mx
+      }
+      db eval "INSERT INTO rx VALUES(NULL, [join $vlist ,])"
+      db eval "INSERT INTO bx VALUES(NULL, [join $vlist ,])"
+    } {}
+
+    # Do a contained-in query on all dimensions
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn [rand 10000]
+      set mx [expr {$mn+[randincr 500]}]
+      lappend where mn$j>=$mn mx$j<=$mx
+    }
+    set where "WHERE [join $where { AND }]"
+    do_test rtree4-$nDim.2.$i.2 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do an overlaps query on all dimensions
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn [rand 10000]
+      set mx [expr {$mn+[randincr 500]}]
+      lappend where mx$j>=$mn mn$j<=$mx
+    }
+    set where "WHERE [join $where { AND }]"
+    do_test rtree4-$nDim.2.$i.3 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do a contained-in query with surplus contraints at the beginning.
+    # This should force a full-table scan on the rtree.
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      lappend where mn$j>-10000 mx$j<10000
+    }
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn [rand 10000]
+      set mx [expr {$mn+[randincr 500]}]
+      lappend where mn$j>=$mn mx$j<=$mx
+    }
+    set where "WHERE [join $where { AND }]"
+    do_test rtree4-$nDim.2.$i.3 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do an overlaps query with surplus contraints at the beginning.
+    # This should force a full-table scan on the rtree.
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      lappend where mn$j>=-10000 mx$j<=10000
+    }
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn [rand 10000]
+      set mx [expr {$mn+[randincr 500]}]
+      lappend where mx$j>$mn mn$j<$mx
+    }
+    set where "WHERE [join $where { AND }]"
+    do_test rtree4-$nDim.2.$i.4 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do a contained-in query with surplus contraints at the end
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn [rand 10000]
+      set mx [expr {$mn+[randincr 500]}]
+      lappend where mn$j>=$mn mx$j<$mx
+    }
+    for {set j [expr {$nDim-1}]} {$j>=0} {incr j -1} {
+      lappend where mn$j>=-10000 mx$j<10000
+    }
+    set where "WHERE [join $where { AND }]"
+    do_test rtree4-$nDim.2.$i.5 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do an overlaps query with surplus contraints at the end
+    #
+    set where {}
+    for {set j [expr {$nDim-1}]} {$j>=0} {incr j -1} {
+      set mn [rand 10000]
+      set mx [expr {$mn+[randincr 500]}]
+      lappend where mx$j>$mn mn$j<=$mx
+    }
+    for {set j 0} {$j<$nDim} {incr j} {
+      lappend where mx$j>-10000 mn$j<=10000
+    }
+    set where "WHERE [join $where { AND }]"
+    do_test rtree4-$nDim.2.$i.6 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do a contained-in query with surplus contraints where the 
+    # constraints appear in a random order.
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn1 [rand 10000]
+      set mn2 [expr {$mn1+[randincr 100]}]
+      set mx1 [expr {$mn2+[randincr 400]}]
+      set mx2 [expr {$mx1+[randincr 100]}]
+      lappend where mn$j>=$mn1 mn$j>$mn2 mx$j<$mx1 mx$j<=$mx2
+    }
+    set where "WHERE [join [scramble $where] { AND }]"
+    do_test rtree4-$nDim.2.$i.7 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+
+    # Do an overlaps query with surplus contraints where the
+    # constraints appear in a random order.
+    #
+    set where {}
+    for {set j 0} {$j<$nDim} {incr j} {
+      set mn1 [rand 10000]
+      set mn2 [expr {$mn1+[randincr 100]}]
+      set mx1 [expr {$mn2+[randincr 400]}]
+      set mx2 [expr {$mx1+[randincr 100]}]
+      lappend where mx$j>=$mn1 mx$j>$mn2 mn$j<$mx1 mn$j<=$mx2
+    }
+    set where "WHERE [join [scramble $where] { AND }]"
+    do_test rtree4-$nDim.2.$i.8 {
+      list $where [db eval "SELECT id FROM rx $where ORDER BY id"]
+    } [list $where [db eval "SELECT id FROM bx $where ORDER BY id"]]
+  }
+
+  do_rtree_integrity_test rtree4-$nDim.3 rx
+}
+
+expand_all_sql db
+finish_test
diff --git a/ext/rtree/rtree5.test b/ext/rtree/rtree5.test
new file mode 100644
index 0000000..92bb690
--- /dev/null
+++ b/ext/rtree/rtree5.test
@@ -0,0 +1,83 @@
+# 2008 Jul 14
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension when it is
+# configured to store values as 32 bit integers.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+do_test rtree5-1.0 {
+  execsql { CREATE VIRTUAL TABLE t1 USING rtree_i32(id, x1, x2, y1, y2) }
+} {}
+do_test rtree5-1.1 {
+  execsql { INSERT INTO t1 VALUES(1, 5, 10, 4, 11.2) }
+} {}
+do_test rtree5-1.2 { 
+  execsql { SELECT * FROM t1 }
+} {1 5 10 4 11}
+do_test rtree5-1.3 { 
+  execsql { SELECT typeof(x1) FROM t1 }
+} {integer}
+
+do_test rtree5-1.4 { 
+  execsql { SELECT x1==5 FROM t1 }
+} {1}
+do_test rtree5-1.5 { 
+  execsql { SELECT x1==5.2 FROM t1 }
+} {0}
+do_test rtree5-1.6 { 
+  execsql { SELECT x1==5.0 FROM t1 }
+} {1}
+
+do_test rtree5-1.7 { 
+  execsql { SELECT count(*) FROM t1 WHERE x1==5 }
+} {1}
+ifcapable !rtree_int_only {
+  do_test rtree5-1.8 { 
+    execsql { SELECT count(*) FROM t1 WHERE x1==5.2 }
+  } {0}
+}
+do_test rtree5-1.9 { 
+  execsql { SELECT count(*) FROM t1 WHERE x1==5.0 }
+} {1}
+
+do_test rtree5-1.10 { 
+  execsql { SELECT (1<<31)-5, (1<<31)-1, -1*(1<<31), -1*(1<<31)+5 }
+} {2147483643 2147483647 -2147483648 -2147483643}
+do_test rtree5-1.11 { 
+  execsql { 
+    INSERT INTO t1 VALUES(2, (1<<31)-5, (1<<31)-1, -1*(1<<31), -1*(1<<31)+5) 
+  }
+} {}
+do_test rtree5-1.12 { 
+  execsql { SELECT * FROM t1 WHERE id=2 }
+} {2 2147483643 2147483647 -2147483648 -2147483643}
+do_test rtree5-1.13 { 
+  execsql { 
+    SELECT * FROM t1 WHERE 
+        x1=2147483643 AND x2=2147483647 AND 
+        y1=-2147483648 AND y2=-2147483643
+  }
+} {2 2147483643 2147483647 -2147483648 -2147483643}
+do_rtree_integrity_test rtree5-1.14 t1
+
+expand_all_sql db
+finish_test
diff --git a/ext/rtree/rtree6.test b/ext/rtree/rtree6.test
new file mode 100644
index 0000000..b6dfe99
--- /dev/null
+++ b/ext/rtree/rtree6.test
@@ -0,0 +1,181 @@
+# 2008 Sep 1
+#
+# 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.
+#
+#***********************************************************************
+# 
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source $testdir/tester.tcl
+set testprefix rtree6
+
+ifcapable {!rtree || rtree_int_only} {
+  finish_test
+  return
+}
+
+#   Operator    Byte Value
+#   ----------------------
+#      =        0x41 ('A')
+#     <=        0x42 ('B')
+#      <        0x43 ('C')
+#     >=        0x44 ('D')
+#      >        0x45 ('E')
+#   ----------------------
+
+proc rtree_strategy {sql} {
+  set ret [list]
+  db eval "explain $sql" a {
+    if {$a(opcode) eq "VFilter"} {
+      lappend ret $a(p4)
+    }
+  }
+  set ret
+}
+
+proc query_plan {sql} {
+  set ret [list]
+  db eval "explain query plan $sql" a {
+    lappend ret $a(detail)
+  }
+  set ret
+}
+
+do_test rtree6-1.1 {
+  execsql {
+    CREATE TABLE t2(k INTEGER PRIMARY KEY, v);
+    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
+  }
+} {}
+
+do_test rtree6-1.2 {
+  rtree_strategy {SELECT * FROM t1 WHERE x1>10}
+} {E0}
+do_test rtree6-1.2.1 {
+  rtree_strategy {SELECT * FROM t1 WHERE x1>10 AND x2 LIKE '%x%'}
+} {E0}
+
+do_test rtree6-1.3 {
+  rtree_strategy {SELECT * FROM t1 WHERE x1<10}
+} {C0}
+
+do_test rtree6-1.4 {
+  rtree_strategy {SELECT * FROM t1,t2 WHERE k=ii AND x1<10}
+} {C0}
+
+do_test rtree6-1.5 {
+  rtree_strategy {SELECT * FROM t1,t2 WHERE k=+ii AND x1<10}
+} {C0}
+
+do_eqp_test rtree6.2.1 {
+  SELECT * FROM t1,t2 WHERE k=+ii AND x1<10
+} {
+  QUERY PLAN
+  |--SCAN t1 VIRTUAL TABLE INDEX 2:C0
+  `--SEARCH t2 USING INTEGER PRIMARY KEY (rowid=?)
+}
+
+do_eqp_test rtree6.2.2 {
+  SELECT * FROM t1,t2 WHERE k=ii AND x1<10
+} {
+  QUERY PLAN
+  |--SCAN t1 VIRTUAL TABLE INDEX 2:C0
+  `--SEARCH t2 USING INTEGER PRIMARY KEY (rowid=?)
+}
+
+do_eqp_test rtree6.2.3 {
+  SELECT * FROM t1,t2 WHERE k=ii
+} {
+  QUERY PLAN
+  |--SCAN t1 VIRTUAL TABLE INDEX 2:
+  `--SEARCH t2 USING INTEGER PRIMARY KEY (rowid=?)
+}
+
+do_eqp_test rtree6.2.4.1 {
+  SELECT * FROM t1,t2 WHERE v=+ii and x1<10 and x2>10
+} {
+  QUERY PLAN
+  |--SCAN t1 VIRTUAL TABLE INDEX 2:C0E1
+  `--SEARCH t2 USING AUTOMATIC COVERING INDEX (v=?)
+}
+do_eqp_test rtree6.2.4.2 {
+  SELECT * FROM t1,t2 WHERE v=10 and x1<10 and x2>10
+} {
+  QUERY PLAN
+  |--SCAN t1 VIRTUAL TABLE INDEX 2:C0E1
+  `--SEARCH t2 USING AUTOMATIC PARTIAL COVERING INDEX (v=?)
+}
+
+do_eqp_test rtree6.2.5 {
+  SELECT * FROM t1,t2 WHERE k=ii AND x1<v
+} {
+  QUERY PLAN
+  |--SCAN t1 VIRTUAL TABLE INDEX 2:
+  `--SEARCH t2 USING INTEGER PRIMARY KEY (rowid=?)
+}
+
+do_execsql_test rtree6-3.1 {
+  CREATE VIRTUAL TABLE t3 USING rtree(id, x1, x2, y1, y2);
+  INSERT INTO t3 VALUES(NULL, 1, 1, 2, 2);
+  SELECT * FROM t3 WHERE 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5;
+} {1 1.0 1.0 2.0 2.0}
+
+do_test rtree6.3.2 {
+  rtree_strategy {
+    SELECT * FROM t3 WHERE 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 
+  }
+} {E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0}
+do_test rtree6.3.3 {
+  rtree_strategy {
+    SELECT * FROM t3 WHERE 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5
+  }
+} {E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0}
+
+do_execsql_test rtree6-3.4 {
+  SELECT * FROM t3 WHERE x1>0.5 AND x1>0.8 AND x1>1.1
+} {}
+do_execsql_test rtree6-3.5 {
+  SELECT * FROM t3 WHERE 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
+    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>1.1
+} {}
+
+#-------------------------------------------------------------------------
+reset_db
+do_execsql_test 4.0 {
+  CREATE VIRTUAL TABLE t1 USING rtree(id,x0,x1,y0,y1);
+}
+do_execsql_test 4.1 {
+  DELETE FROM t1 WHERE x0>1 AND x1<2 OR y0<92;
+}
+
+expand_all_sql db
+finish_test
diff --git a/ext/rtree/rtree7.test b/ext/rtree/rtree7.test
new file mode 100644
index 0000000..1556179
--- /dev/null
+++ b/ext/rtree/rtree7.test
@@ -0,0 +1,73 @@
+# 2010 February 16
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# 
+# Test that nothing goes wrong if an rtree table is created, then the
+# database page-size is modified. At one point (3.6.22), this was causing
+# malfunctions.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+
+ifcapable !rtree||!vacuum {
+  finish_test
+  return
+}
+
+# Like execsql except display output as integer where that can be
+# done without loss of information.
+#
+proc execsql_intout {sql} {
+  set out {}
+  foreach term [execsql $sql] {
+    regsub {\.0$} $term {} term
+    lappend out $term
+  }
+  return $out
+}
+
+do_test rtree7-1.1 {
+  execsql {
+    PRAGMA page_size = 1024;
+    CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, y1, y2);
+    INSERT INTO rt VALUES(1, 1, 2, 3, 4);
+  }
+} {}
+do_test rtree7-1.2 {
+  execsql_intout { SELECT * FROM rt }
+} {1 1 2 3 4}
+do_test rtree7-1.3 {
+  execsql_intout { 
+    PRAGMA page_size = 2048;
+    VACUUM;
+    SELECT * FROM rt;
+  }
+} {1 1 2 3 4}
+do_test rtree7-1.4 {
+  for {set i 2} {$i <= 51} {incr i} {
+    execsql { INSERT INTO rt VALUES($i, 1, 2, 3, 4) }
+  }
+  execsql_intout { SELECT sum(x1), sum(x2), sum(y1), sum(y2) FROM rt }
+} {51 102 153 204}
+do_test rtree7-1.5 {
+  execsql_intout { 
+    PRAGMA page_size = 512;
+    VACUUM;
+    SELECT sum(x1), sum(x2), sum(y1), sum(y2) FROM rt
+  }
+} {51 102 153 204}
+
+do_rtree_integrity_test rtree7-1.6 rt
+
+finish_test
diff --git a/ext/rtree/rtree8.test b/ext/rtree/rtree8.test
new file mode 100644
index 0000000..12e75a6
--- /dev/null
+++ b/ext/rtree/rtree8.test
@@ -0,0 +1,209 @@
+# 2010 February 16
+#
+# 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.
+#
+#***********************************************************************
+# 
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+#-------------------------------------------------------------------------
+# The following block of tests - rtree8-1.* - feature reading and writing
+# an r-tree table while there exist open cursors on it.
+#
+proc populate_t1 {n} {
+  execsql { DELETE FROM t1 }
+  for {set i 1} {$i <= $n} {incr i} {
+    execsql { INSERT INTO t1 VALUES($i, $i, $i+2) }
+  }
+}
+
+# A DELETE while a cursor is reading the table.
+#
+do_test rtree8-1.1.1 {
+  execsql { PRAGMA page_size = 512 }
+  execsql { CREATE VIRTUAL TABLE t1 USING rtree_i32(id, x1, x2) }
+  populate_t1 5
+} {}
+do_test rtree8-1.1.2 {
+  set res [list]
+  set rc [catch {
+    db eval { SELECT * FROM t1 } { 
+      lappend res $x1 $x2
+      if {$id==3} { db eval { DELETE FROM t1 WHERE id>3 } }
+    }
+  } msg];
+  lappend rc $msg
+  set rc
+} {1 {database table is locked}}
+do_test rtree8-1.1.2b {
+  db eval { SELECT * FROM t1 ORDER BY +id } { 
+    if {$id==3} { db eval { DELETE FROM t1 WHERE id>3 } }
+  }
+  db eval {SELECT x1, x2 FROM t1}
+} {1 3 2 4 3 5}
+do_test rtree8-1.1.3 {
+  execsql { SELECT * FROM t1 }
+} {1 1 3 2 2 4 3 3 5}
+
+# Many SELECTs on the same small table.
+#
+proc nested_select {n} {
+  set ::max $n
+  db eval { SELECT * FROM t1 } {
+    if {$id == $n} { nested_select [expr $n+1] }
+  }
+  return $::max
+}
+do_test rtree8-1.2.1 { populate_t1 50  } {}
+do_test rtree8-1.2.2 { nested_select 1 } {51}
+
+# This test runs many SELECT queries simultaneously against a large 
+# table, causing a collision in the hash-table used to store r-tree 
+# nodes internally.
+#
+populate_t1 1500
+do_rtree_integrity_test rtree8-1.3.0 t1
+do_execsql_test rtree8-1.3.1 { SELECT max(nodeno) FROM t1_node } {164}
+do_test rtree8-1.3.2 {
+  set rowids [execsql {SELECT min(rowid) FROM t1_rowid GROUP BY nodeno}]
+  set stmt_list [list]
+  foreach row $rowids {
+    set stmt [sqlite3_prepare db "SELECT * FROM t1 WHERE id = $row" -1 tail]
+    sqlite3_step $stmt
+    lappend res_list [sqlite3_column_int $stmt 0]
+    lappend stmt_list $stmt 
+  }
+} {}
+do_test rtree8-1.3.3 { set res_list } $rowids
+do_execsql_test rtree8-1.3.4 { SELECT count(*) FROM t1 } {1500}
+do_test rtree8-1.3.5 { 
+  foreach stmt $stmt_list { sqlite3_finalize $stmt }
+} {}
+
+
+#-------------------------------------------------------------------------
+# The following block of tests - rtree8-2.* - test a couple of database
+# corruption cases. In this case things are not corrupted at the b-tree
+# level, but the contents of the various tables used internally by an
+# r-tree table are inconsistent.
+#
+populate_t1 50
+do_execsql_test rtree8-2.1.1 { SELECT max(nodeno) FROM t1_node } {5}
+sqlite3_db_config db DEFENSIVE 0
+do_execsql_test rtree8-2.1.2 { DELETE FROM t1_node } {}
+for {set i 1} {$i <= 50} {incr i} {
+  do_catchsql_test rtree8-2.1.3.$i { 
+    SELECT * FROM t1 WHERE id = $i 
+  } {1 {database disk image is malformed}}
+}
+do_catchsql_test rtree8-2.1.4 { 
+  SELECT * FROM t1
+} {1 {database disk image is malformed}}
+do_catchsql_test rtree8-2.1.5 { 
+  DELETE FROM t1
+} {1 {database disk image is malformed}}
+
+do_execsql_test rtree8-2.1.6 { 
+  DROP TABLE t1;
+  CREATE VIRTUAL TABLE t1 USING rtree_i32(id, x1, x2);
+} {}
+
+
+populate_t1 50
+sqlite3_db_config db DEFENSIVE 0
+do_execsql_test rtree8-2.2.1 {
+  DELETE FROM t1_parent
+} {}
+do_catchsql_test rtree8-2.2.2 {
+  DELETE FROM t1 WHERE id=25
+} {1 {database disk image is malformed}}
+do_execsql_test rtree8-2.2.3 { 
+  DROP TABLE t1;
+  CREATE VIRTUAL TABLE t1 USING rtree_i32(id, x1, x2);
+} {}
+
+
+#-------------------------------------------------------------------------
+# Test that trying to use the MATCH operator with the r-tree module does
+# not confuse it. 
+#
+populate_t1 10
+do_catchsql_test rtree8-3.1 { 
+  SELECT * FROM t1 WHERE x1 MATCH '1234'
+} {1 {SQL logic error}}
+
+#-------------------------------------------------------------------------
+# Test a couple of invalid arguments to rtreedepth().
+#
+do_catchsql_test rtree8-4.1 {
+  SELECT rtreedepth('hello world')
+} {1 {Invalid argument to rtreedepth()}}
+do_catchsql_test rtree8-4.2 {
+  SELECT rtreedepth(X'00')
+} {1 {Invalid argument to rtreedepth()}}
+
+
+#-------------------------------------------------------------------------
+# Delete half of a lopsided tree.
+#
+do_execsql_test rtree8-5.1 { 
+  CREATE VIRTUAL TABLE t2 USING rtree_i32(id, x1, x2) 
+} {}
+do_test rtree8-5.2 {
+  execsql BEGIN
+  for {set i 0} {$i < 100} {incr i} {
+    execsql { INSERT INTO t2 VALUES($i, 100, 101) }
+  }
+  for {set i 100} {$i < 200} {incr i} {
+    execsql { INSERT INTO t2 VALUES($i, 1000, 1001) }
+  }
+  execsql COMMIT
+} {}
+do_rtree_integrity_test rtree8-5.3 t2
+do_test rtree8-5.4 {
+  execsql BEGIN
+  for {set i 0} {$i < 200} {incr i} {
+    execsql { DELETE FROM t2 WHERE id = $i }
+  }
+  execsql COMMIT
+} {}
+do_rtree_integrity_test rtree8-5.5 t2
+
+# 2018-05-24
+# The following script caused an assertion fault and/or segfault
+# prior to the fix that prevents simultaneous reads and writes on
+# the same rtree virtual table.
+#
+do_test rtree8-6.1 {
+  db close
+  sqlite3 db :memory:
+  db eval {
+    PRAGMA page_size=512;
+    CREATE VIRTUAL TABLE t1 USING rtree(id,x1,x2,y1,y2);
+    WITH RECURSIVE c(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM c WHERE x<49)
+    INSERT INTO t1 SELECT x, x, x+1, x, x+1 FROM c;
+  }
+  set rc [catch {
+    db eval {SELECT id FROM t1} x {
+      db eval {DELETE FROM t1 WHERE id=$x(id)}
+    }
+  } msg]
+  lappend rc $msg
+} {1 {database table is locked}}
+
+
+
+
+finish_test
diff --git a/ext/rtree/rtree9.test b/ext/rtree/rtree9.test
new file mode 100644
index 0000000..f39a82e
--- /dev/null
+++ b/ext/rtree/rtree9.test
@@ -0,0 +1,129 @@
+# 2010 August 28
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# This file contains tests for the r-tree module. Specifically, it tests
+# that custom r-tree queries (geometry callbacks) work.
+# 
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+ifcapable rtree_int_only { finish_test; return }
+
+register_cube_geom db
+
+do_execsql_test rtree9-1.1 {
+  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, y1, y2, z1, z2);
+  INSERT INTO rt VALUES(1, 1, 2, 1, 2, 1, 2);
+} {}
+do_execsql_test rtree9-1.2 {
+  SELECT * FROM rt WHERE id MATCH cube(0, 0, 0, 2, 2, 2);
+} {1 1.0 2.0 1.0 2.0 1.0 2.0}
+do_execsql_test rtree9-1.3 {
+  SELECT * FROM rt WHERE id MATCH cube(3, 3, 3, 2, 2, 2);
+} {}
+do_execsql_test rtree9-1.4 {
+  DELETE FROM rt;
+} {}
+
+unset -nocomplain x
+for {set i 0} {$i < 1000} {incr i} {
+  set x [expr $i%10]
+  set y [expr ($i/10)%10]
+  set z [expr ($i/100)%10]
+  execsql { INSERT INTO rt VALUES($i, $x, $x+1, $y, $y+1, $z, $z+1) }
+}
+do_rtree_integrity_test rtree9-2.0 rt
+do_execsql_test rtree9-2.1 {
+  SELECT id FROM rt WHERE id MATCH cube(2.5, 2.5, 2.5, 1, 1, 1) ORDER BY id;
+} {222 223 232 233 322 323 332 333}
+do_execsql_test rtree9-2.2 {
+  SELECT id FROM rt WHERE id MATCH cube(5.5, 5.5, 5.5, 1, 1, 1) ORDER BY id;
+} {555 556 565 566 655 656 665 666}
+
+
+do_execsql_test rtree9-3.0 {
+  CREATE VIRTUAL TABLE rt32 USING rtree_i32(id, x1, x2, y1, y2, z1, z2);
+} {} 
+for {set i 0} {$i < 1000} {incr i} {
+  set x [expr $i%10]
+  set y [expr ($i/10)%10]
+  set z [expr ($i/100)%10]
+  execsql { INSERT INTO rt32 VALUES($i, $x, $x+1, $y, $y+1, $z, $z+1) }
+}
+do_rtree_integrity_test rtree9-3.1 rt32
+do_execsql_test rtree9-3.2 {
+  SELECT id FROM rt32 WHERE id MATCH cube(3, 3, 3, 1, 1, 1) ORDER BY id;
+} {222 223 224 232 233 234 242 243 244 322 323 324 332 333 334 342 343 344 422 423 424 432 433 434 442 443 444}
+do_execsql_test rtree9-3.3 {
+  SELECT id FROM rt32 WHERE id MATCH cube(5.5, 5.5, 5.5, 1, 1, 1) ORDER BY id;
+} {555 556 565 566 655 656 665 666}
+
+
+do_catchsql_test rtree9-4.1 {
+  SELECT id FROM rt32 WHERE id MATCH cube(5.5, 5.5, 1, 1, 1) ORDER BY id;
+} {1 {SQL logic error}}
+for {set x 2} {$x<200} {incr x 2} {
+  do_catchsql_test rtree9-4.2.[expr $x/2] {
+    SELECT id FROM rt WHERE id MATCH randomblob($x)
+  } {1 {SQL logic error}}
+}
+do_catchsql_test rtree9-4.3 {
+  SELECT id FROM rt WHERE id MATCH CAST( 
+    (cube(5.5, 5.5, 5.5, 1, 1, 1) || X'1234567812345678') AS blob 
+  )
+} {1 {SQL logic error}}
+
+
+#-------------------------------------------------------------------------
+# Test the example 2d "circle" geometry callback.
+#
+register_circle_geom db
+
+do_execsql_test rtree9-5.1 {
+  CREATE VIRTUAL TABLE rt2 USING rtree(id, xmin, xmax, ymin, ymax);
+
+  INSERT INTO rt2 VALUES(1,    1,   2,  1,  2);
+  INSERT INTO rt2 VALUES(2,    1,   2, -2, -1);
+  INSERT INTO rt2 VALUES(3,    -2, -1, -2, -1);
+  INSERT INTO rt2 VALUES(4,    -2, -1,  1,  2);
+
+  INSERT INTO rt2 VALUES(5,    2,   3,  2,  3);
+  INSERT INTO rt2 VALUES(6,    2,   3, -3, -2);
+  INSERT INTO rt2 VALUES(7,    -3, -2, -3, -2);
+  INSERT INTO rt2 VALUES(8,    -3, -2,  2,  3);
+
+  INSERT INTO rt2 VALUES(9,    1.8,   3,  1.8,  3);
+  INSERT INTO rt2 VALUES(10,   1.8,   3, -3, -1.8);
+  INSERT INTO rt2 VALUES(11,   -3, -1.8, -3, -1.8);
+  INSERT INTO rt2 VALUES(12,   -3, -1.8,  1.8,  3);
+
+  INSERT INTO rt2 VALUES(13,   -15, 15, 1.8, 2.2);
+  INSERT INTO rt2 VALUES(14,   -15, 15, -2.2, -1.8);
+  INSERT INTO rt2 VALUES(15,   1.8, 2.2, -15, 15);
+  INSERT INTO rt2 VALUES(16,   -2.2, -1.8, -15, 15);
+
+  INSERT INTO rt2 VALUES(17,   -100, 100, -100, 100);
+} {}
+
+do_execsql_test rtree9-5.2 {
+  SELECT id FROM rt2 WHERE id MATCH circle(0.0, 0.0, 2.0);
+} {1 2 3 4 13 14 15 16 17}
+
+do_execsql_test rtree9-5.3 {
+  UPDATE rt2 SET xmin=xmin+5, ymin=ymin+5, xmax=xmax+5, ymax=ymax+5;
+  SELECT id FROM rt2 WHERE id MATCH circle(5.0, 5.0, 2.0);
+} {1 2 3 4 13 14 15 16 17}
+do_rtree_integrity_test rtree9-5.4 rt2
+
+finish_test
diff --git a/ext/rtree/rtreeA.test b/ext/rtree/rtreeA.test
new file mode 100644
index 0000000..301cd4f
--- /dev/null
+++ b/ext/rtree/rtreeA.test
@@ -0,0 +1,262 @@
+# 2010 September 22
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# This file contains tests for the r-tree module. Specifically, it tests
+# that corrupt or inconsistent databases do not cause crashes in the r-tree
+# module.
+# 
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+proc create_t1 {} {
+  db close
+  forcedelete test.db
+  sqlite3 db test.db
+  execsql {
+    PRAGMA page_size = 1024;
+    CREATE VIRTUAL TABLE t1 USING rtree(id, x1, x2, y1, y2);
+  }
+}
+proc populate_t1 {} {
+  execsql BEGIN
+  for {set i 0} {$i < 500} {incr i} {
+    set x2 [expr $i+5]
+    set y2 [expr $i+5]
+    execsql { INSERT INTO t1 VALUES($i, $i, $x2, $i, $y2) }
+  }
+  execsql COMMIT
+  sqlite3_db_config db DEFENSIVE 0
+}
+
+proc truncate_node {nodeno nTrunc} {
+  set blob [db one {SELECT data FROM t1_node WHERE nodeno=$nodeno}]
+  if {$nTrunc<0} {set nTrunc "end-$nTrunc"}
+  set blob [string range $blob 0 $nTrunc]
+  db eval { UPDATE t1_node SET data = $blob WHERE nodeno=$nodeno }
+}
+
+proc set_tree_depth {tbl {newvalue ""}} {
+  set blob [db one "SELECT data FROM ${tbl}_node WHERE nodeno=1"]
+
+  if {$newvalue == ""} {
+    binary scan $blob Su oldvalue
+    return $oldvalue
+  }
+
+  set blob [binary format Sua* $newvalue [string range $blob 2 end]]
+  db eval "UPDATE ${tbl}_node SET data = \$blob WHERE nodeno=1"
+  return [set_tree_depth $tbl]
+}
+
+proc set_entry_count {tbl nodeno {newvalue ""}} {
+  set blob [db one "SELECT data FROM ${tbl}_node WHERE nodeno=$nodeno"]
+
+  if {$newvalue == ""} {
+    binary scan [string range $blob 2 end] Su oldvalue
+    return $oldvalue
+  }
+
+  set blob [binary format a*Sua* \
+    [string range $blob 0 1] $newvalue [string range $blob 4 end]
+  ]
+  db eval "UPDATE ${tbl}_node SET data = \$blob WHERE nodeno=$nodeno"
+  return [set_entry_count $tbl $nodeno]
+}
+
+
+proc do_corruption_tests {prefix args} {
+  set testarray [lindex $args end]
+  set errormsg {database disk image is malformed}
+
+  foreach {z value} [lrange $args 0 end-1] {
+    set n [string length $z]
+    if {$n>=2 && [string equal -length $n $z "-error"]} {
+      set errormsg $value
+    }
+  }
+
+  foreach {tn sql} $testarray {
+    do_catchsql_test $prefix.$tn $sql [list 1 $errormsg]
+  }
+}
+
+#-------------------------------------------------------------------------
+# Test the libraries response if the %_node table is completely empty
+# (i.e. the root node is missing), or has been removed from the database
+# entirely.
+#
+create_t1
+populate_t1
+do_execsql_test rtreeA-1.0 {
+  DELETE FROM t1_node;
+} {}
+
+do_corruption_tests rtreeA-1.1 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+  4   "SELECT * FROM t1 WHERE x1<10 AND x2>12"
+}
+
+do_execsql_test rtreeA-1.1.1 {
+  SELECT rtreecheck('main', 't1')
+} {{Node 1 missing from database
+Wrong number of entries in %_rowid table - expected 0, actual 500
+Wrong number of entries in %_parent table - expected 0, actual 23}}
+
+do_execsql_test  rtreeA-1.2.0 { DROP TABLE t1_node } {}
+do_corruption_tests rtreeA-1.2 -error "database disk image is malformed" {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+  4   "SELECT * FROM t1 WHERE x1<10 AND x2>12"
+}
+
+#-------------------------------------------------------------------------
+# Test the libraries response if some of the entries in the %_node table 
+# are the wrong size.
+#
+create_t1
+populate_t1
+do_test rtreeA-2.1.0 {
+  set nodes [db eval {select nodeno FROM t1_node}]
+  foreach {a b c} $nodes { truncate_node $c 200 }
+} {}
+do_corruption_tests rtreeA-2.1 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+  4   "SELECT * FROM t1 WHERE x1<10 AND x2>12"
+}
+
+create_t1
+populate_t1
+do_test rtreeA-2.2.0 { truncate_node 1 200 } {}
+do_corruption_tests rtreeA-2.2 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE +rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+  4   "SELECT * FROM t1 WHERE x1<10 AND x2>12"
+}
+
+#-------------------------------------------------------------------------
+# Set the "depth" of the tree stored on the root node incorrectly. Test
+# that this does not cause any problems.
+#
+create_t1
+populate_t1
+do_test rtreeA-3.1.0.1 { set_tree_depth t1 } {1}
+do_test rtreeA-3.1.0.2 { set_tree_depth t1 3 } {3}
+do_corruption_tests rtreeA-3.1 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE +rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+}
+
+do_execsql_test rtreeA-3.1.0.3 {
+  SELECT rtreecheck('main', 't1')!='ok'
+} {1}
+
+do_test rtreeA-3.2.0 { set_tree_depth t1 1000 } {1000}
+do_corruption_tests rtreeA-3.2 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE +rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+}
+
+create_t1
+populate_t1
+do_test rtreeA-3.3.0 { 
+  execsql { DELETE FROM t1 WHERE rowid = 0 }
+  set_tree_depth t1 65535
+} {65535}
+do_corruption_tests rtreeA-3.3 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE +rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+}
+
+do_execsql_test rtreeA-3.3.3.4 {
+  SELECT rtreecheck('main', 't1')
+} {{Rtree depth out of range (65535)
+Wrong number of entries in %_rowid table - expected 0, actual 499
+Wrong number of entries in %_parent table - expected 0, actual 23}}
+
+#-------------------------------------------------------------------------
+# Set the "number of entries" field on some nodes incorrectly.
+#
+create_t1
+populate_t1
+do_test rtreeA-4.1.0 { 
+  set_entry_count t1 1 4000
+} {4000}
+do_corruption_tests rtreeA-4.1 {
+  1   "SELECT * FROM t1"
+  2   "SELECT * FROM t1 WHERE +rowid=5"
+  3   "INSERT INTO t1 VALUES(1000, 1, 2, 3, 4)"
+  4   "SELECT * FROM t1 WHERE x1<10 AND x2>12"
+}
+
+#-------------------------------------------------------------------------
+# Remove entries from the %_parent table and check that this does not
+# cause a crash.
+#
+create_t1
+populate_t1
+do_execsql_test rtreeA-5.1.0 { DELETE FROM t1_parent } {}
+do_corruption_tests rtreeA-5.1 {
+  1   "DELETE FROM t1 WHERE +rowid = 5"
+  2   "DELETE FROM t1"
+}
+
+do_execsql_test rtreeA-5.2 {
+  SELECT rtreecheck('main', 't1')!='ok'
+} {1}
+
+#-------------------------------------------------------------------------
+# Add some bad entries to the %_parent table.
+#
+create_t1
+populate_t1
+do_execsql_test rtreeA-6.1.0 { 
+  UPDATE t1_parent set parentnode = parentnode+1
+} {}
+do_corruption_tests rtreeA-6.1 {
+  1   "DELETE FROM t1 WHERE rowid = 5"
+  2   "UPDATE t1 SET x1=x1+1, x2=x2+1"
+}
+
+do_execsql_test rtreeA-6.2 {
+  SELECT rtreecheck('main', 't1')!='ok'
+} {1}
+
+#-------------------------------------------------------------------------
+# Truncated blobs in the _node table.
+#
+create_t1
+populate_t1
+sqlite3 db test.db
+sqlite3_db_config db DEFENSIVE 0
+do_execsql_test rtreeA-7.100 { 
+  UPDATE t1_node SET data=x'' WHERE rowid=1;
+} {}
+do_catchsql_test rtreeA-7.110 {
+  SELECT * FROM t1 WHERE x1>0 AND x1<100 AND x2>0 AND x2<100;
+} {1 {undersize RTree blobs in "t1_node"}}
+do_test rtreeA-7.120 {
+  sqlite3_extended_errcode db
+} {SQLITE_CORRUPT_VTAB}
+
+
+finish_test
diff --git a/ext/rtree/rtreeB.test b/ext/rtree/rtreeB.test
new file mode 100644
index 0000000..6fc3104
--- /dev/null
+++ b/ext/rtree/rtreeB.test
@@ -0,0 +1,50 @@
+# 2011 March 2
+#
+# 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.
+#
+#***********************************************************************
+# Make sure the rtreenode() testing function can handle entries with
+# 64-bit rowids.
+# 
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+ifcapable rtree_int_only {
+  do_test rtreeB-1.1-intonly {
+    db eval {
+      CREATE VIRTUAL TABLE t1 USING rtree(ii, x0, y0, x1, y1);
+      INSERT INTO t1 VALUES(1073741824, 0.0, 0.0, 100.0, 100.0);
+      INSERT INTO t1 VALUES(2147483646, 0.0, 0.0, 200.0, 200.0);
+      INSERT INTO t1 VALUES(4294967296, 0.0, 0.0, 300.0, 300.0);
+      INSERT INTO t1 VALUES(8589934592, 20.0, 20.0, 150.0, 150.0);
+      INSERT INTO t1 VALUES(9223372036854775807, 150, 150, 400, 400);
+      SELECT rtreenode(2, data) FROM t1_node;
+    }
+  } {{{1073741824 0 0 100 100} {2147483646 0 0 200 200} {4294967296 0 0 300 300} {8589934592 20 20 150 150} {9223372036854775807 150 150 400 400}}}
+} else {  
+  do_test rtreeB-1.1 {
+    db eval {
+      CREATE VIRTUAL TABLE t1 USING rtree(ii, x0, y0, x1, y1);
+      INSERT INTO t1 VALUES(1073741824, 0.0, 0.0, 100.0, 100.0);
+      INSERT INTO t1 VALUES(2147483646, 0.0, 0.0, 200.0, 200.0);
+      INSERT INTO t1 VALUES(4294967296, 0.0, 0.0, 300.0, 300.0);
+      INSERT INTO t1 VALUES(8589934592, 20.0, 20.0, 150.0, 150.0);
+      INSERT INTO t1 VALUES(9223372036854775807, 150, 150, 400, 400);
+      SELECT rtreenode(2, data) FROM t1_node;
+    }
+  } {{{1073741824 0 0 100 100} {2147483646 0 0 200 200} {4294967296 0 0 300 300} {8589934592 20 20 150 150} {9223372036854775807 150 150 400 400}}}
+}
+
+do_rtree_integrity_test rtreeB-1.2 t1
+
+finish_test
diff --git a/ext/rtree/rtreeC.test b/ext/rtree/rtreeC.test
new file mode 100644
index 0000000..bddc7d3
--- /dev/null
+++ b/ext/rtree/rtreeC.test
@@ -0,0 +1,378 @@
+# 2011 March 2
+#
+# 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.
+#
+#***********************************************************************
+# Make sure the rtreenode() testing function can handle entries with
+# 64-bit rowids.
+# 
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+set testprefix rtreeC
+
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE r_tree USING rtree(id, min_x, max_x, min_y, max_y);
+  CREATE TABLE t(x, y);
+}
+
+do_eqp_test 1.1 {
+  SELECT * FROM r_tree, t 
+  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
+} {
+  QUERY PLAN
+  |--SCAN t
+  `--SCAN r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0
+}
+
+do_eqp_test 1.2 {
+  SELECT * FROM t, r_tree
+  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
+} {
+  QUERY PLAN
+  |--SCAN t
+  `--SCAN r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0
+}
+
+do_eqp_test 1.3 {
+  SELECT * FROM t, r_tree
+  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
+} {
+  QUERY PLAN
+  |--SCAN t
+  `--SCAN r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0
+}
+
+do_eqp_test 1.5 {
+  SELECT * FROM t, r_tree
+} {
+  QUERY PLAN
+  |--SCAN r_tree VIRTUAL TABLE INDEX 2:
+  `--SCAN t
+}
+
+do_execsql_test 2.0 {
+  INSERT INTO t VALUES(0, 0);
+  INSERT INTO t VALUES(0, 1);
+  INSERT INTO t VALUES(0, 2);
+  INSERT INTO t VALUES(0, 3);
+  INSERT INTO t VALUES(0, 4);
+  INSERT INTO t VALUES(0, 5);
+  INSERT INTO t VALUES(0, 6);
+  INSERT INTO t VALUES(0, 7);
+  INSERT INTO t VALUES(0, 8);
+  INSERT INTO t VALUES(0, 9);
+
+  INSERT INTO t SELECT x+1, y FROM t;
+  INSERT INTO t SELECT x+2, y FROM t;
+  INSERT INTO t SELECT x+4, y FROM t;
+  INSERT INTO r_tree SELECT NULL, x-1, x+1, y-1, y+1 FROM t;
+  ANALYZE;
+}
+
+db close
+sqlite3 db test.db
+
+do_eqp_test 2.1 {
+  SELECT * FROM r_tree, t 
+  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
+} {
+  QUERY PLAN
+  |--SCAN t
+  `--SCAN r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0
+}
+
+do_eqp_test 2.2 {
+  SELECT * FROM t, r_tree
+  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
+} {
+  QUERY PLAN
+  |--SCAN t
+  `--SCAN r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0
+}
+
+do_eqp_test 2.3 {
+  SELECT * FROM t, r_tree
+  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
+} {
+  QUERY PLAN
+  |--SCAN t
+  `--SCAN r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0
+}
+
+do_eqp_test 2.5 {
+  SELECT * FROM t, r_tree
+} {
+  QUERY PLAN
+  |--SCAN r_tree VIRTUAL TABLE INDEX 2:
+  `--SCAN t
+}
+
+#-------------------------------------------------------------------------
+# Test that the special CROSS JOIN handling works with rtree tables.
+#
+do_execsql_test 3.1 {
+  CREATE TABLE t1(x);
+  CREATE TABLE t2(y);
+  CREATE VIRTUAL TABLE t3 USING rtree(z, x1,x2, y1,y2);
+}
+
+do_eqp_test 3.2.1 { SELECT * FROM t1 CROSS JOIN t2 } {
+  QUERY PLAN
+  |--SCAN t1
+  `--SCAN t2
+}
+do_eqp_test 3.2.2 { SELECT * FROM t2 CROSS JOIN t1 } {
+  QUERY PLAN
+  |--SCAN t2
+  `--SCAN t1
+}
+
+do_eqp_test 3.3.1 { SELECT * FROM t1 CROSS JOIN t3 } {
+  QUERY PLAN
+  |--SCAN t1
+  `--SCAN t3 VIRTUAL TABLE INDEX 2:
+}
+do_eqp_test 3.3.2 { SELECT * FROM t3 CROSS JOIN t1 } {
+  QUERY PLAN
+  |--SCAN t3 VIRTUAL TABLE INDEX 2:
+  `--SCAN t1
+}
+
+#--------------------------------------------------------------------
+# Test that LEFT JOINs are not reordered if the right-hand-side is
+# a virtual table.
+#
+reset_db
+do_execsql_test 4.1 {
+  CREATE TABLE t1(a);
+  CREATE VIRTUAL TABLE t2 USING rtree(b, x1,x2);
+
+  INSERT INTO t1 VALUES(1);
+  INSERT INTO t1 VALUES(2);
+
+  INSERT INTO t2 VALUES(1, 0.0, 0.1);
+  INSERT INTO t2 VALUES(3, 0.0, 0.1);
+}
+
+do_execsql_test 4.2 {
+  SELECT a, b FROM t1 LEFT JOIN t2 ON (+a = +b);
+} {1 1 2 {}}
+
+do_execsql_test 4.3 {
+  SELECT b, a FROM t2 LEFT JOIN t1 ON (+a = +b);
+} {1 1 3 {}}
+
+#--------------------------------------------------------------------
+# Test that the sqlite_stat1 data is used correctly.
+#
+reset_db
+do_execsql_test 5.1 {
+  CREATE TABLE t1(x INT PRIMARY KEY, y);
+  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, +d1);
+
+  INSERT INTO t1(x) VALUES(1);
+  INSERT INTO t1(x) SELECT x+1 FROM t1;   --   2
+  INSERT INTO t1(x) SELECT x+2 FROM t1;   --   4
+  INSERT INTO t1(x) SELECT x+4 FROM t1;   --   8
+  INSERT INTO t1(x) SELECT x+8 FROM t1;   --  16
+  INSERT INTO t1(x) SELECT x+16 FROM t1;  --  32
+  INSERT INTO t1(x) SELECT x+32 FROM t1;  --  64
+  INSERT INTO t1(x) SELECT x+64 FROM t1;  -- 128
+  INSERT INTO t1(x) SELECT x+128 FROM t1; -- 256
+  INSERT INTO t1(x) SELECT x+256 FROM t1; -- 512
+  INSERT INTO t1(x) SELECT x+512 FROM t1; --1024
+
+  INSERT INTO rt SELECT x, x, x+1, printf('x%04xy',x) FROM t1 WHERE x<=5;
+}
+do_rtree_integrity_test 5.1.1 rt
+
+# First test a query with no ANALYZE data at all. The outer loop is
+# real table "t1".
+#
+do_eqp_test 5.2 {
+  SELECT * FROM t1, rt WHERE x==id;
+} {
+  QUERY PLAN
+  |--SCAN t1
+  `--SCAN rt VIRTUAL TABLE INDEX 1:
+}
+
+# Now create enough ANALYZE data to tell SQLite that virtual table "rt"
+# contains very few rows. This causes it to move "rt" to the outer loop.
+#
+do_execsql_test 5.3 {
+  ANALYZE;
+  DELETE FROM sqlite_stat1 WHERE tbl='t1';
+}
+db close
+sqlite3 db test.db
+do_eqp_test 5.4 {
+  SELECT * FROM t1, rt WHERE x==id;
+} {
+  QUERY PLAN
+  |--SCAN rt VIRTUAL TABLE INDEX 2:
+  `--SEARCH t1 USING INDEX sqlite_autoindex_t1_1 (x=?)
+}
+
+# Delete the ANALYZE data. "t1" should be the outer loop again.
+#
+do_execsql_test 5.5 { DROP TABLE sqlite_stat1; }
+db close
+sqlite3 db test.db
+do_eqp_test 5.6 {
+  SELECT * FROM t1, rt WHERE x==id;
+} {
+  QUERY PLAN
+  |--SCAN t1
+  `--SCAN rt VIRTUAL TABLE INDEX 1:
+}
+
+# This time create and attach a database that contains ANALYZE data for
+# tables of the same names as those used internally by virtual table
+# "rt". Check that the rtree module is not fooled into using this data.
+# Table "t1" should remain the outer loop.
+#
+do_test 5.7 {
+  db backup test.db2
+  sqlite3 db2 test.db2
+  db2 eval {
+    ANALYZE;
+    DELETE FROM sqlite_stat1 WHERE tbl='t1';
+  }
+  db2 close
+  db close
+  sqlite3 db test.db
+  execsql { ATTACH 'test.db2' AS aux; }
+} {}
+do_eqp_test 5.8 {
+  SELECT * FROM t1, rt WHERE x==id;
+} {
+  QUERY PLAN
+  |--SCAN t1
+  `--SCAN rt VIRTUAL TABLE INDEX 1:
+}
+
+#--------------------------------------------------------------------
+# Test that having a second connection drop the sqlite_stat1 table
+# before it is required by rtreeConnect() does not cause problems.
+#
+ifcapable rtree {
+  reset_db
+  do_execsql_test 6.1 {
+    CREATE TABLE t1(x);
+    CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2);
+    INSERT INTO t1 VALUES(1);
+    INSERT INTO rt VALUES(1,2,3);
+    ANALYZE;
+  }
+  db close
+  sqlite3 db test.db
+  do_execsql_test 6.2 { SELECT * FROM t1 } {1}
+  
+  do_test 6.3 {
+    sqlite3 db2 test.db
+    db2 eval { DROP TABLE sqlite_stat1 }
+    db2 close
+    execsql { SELECT * FROM rt }
+  } {1 2.0 3.0}
+  db close
+}
+
+#--------------------------------------------------------------------
+# Test that queries featuring LEFT or CROSS JOINS are handled correctly.
+# Handled correctly in this case means:
+#
+#   * Terms with prereqs that appear to the left of a LEFT JOIN against
+#     the virtual table are always available to xBestIndex.
+#
+#   * Terms with prereqs that appear to the right of a LEFT JOIN against
+#     the virtual table are never available to xBestIndex.
+#
+# And the same behaviour for CROSS joins.
+#
+reset_db
+do_execsql_test 7.0 {
+  CREATE TABLE xdir(x1);
+  CREATE TABLE ydir(y1);
+  CREATE VIRTUAL TABLE rt USING rtree_i32(id, xmin, xmax, ymin, ymax);
+
+  INSERT INTO xdir VALUES(5);
+  INSERT INTO ydir VALUES(10);
+
+  INSERT INTO rt VALUES(1, 2, 7, 12, 14);      -- Not a hit
+  INSERT INTO rt VALUES(2, 2, 7, 8, 12);       -- A hit!
+  INSERT INTO rt VALUES(3, 7, 11, 8, 12);      -- Not a hit!
+  INSERT INTO rt VALUES(4, 5, 5, 10, 10);      -- A hit!
+
+}
+
+proc do_eqp_execsql_test {tn sql res1 res2} {
+  do_eqp_test $tn.1 $sql $res1
+  do_execsql_test $tn.2 $sql $res2
+}
+
+do_eqp_execsql_test 7.1 {
+  SELECT id FROM xdir, rt, ydir 
+  ON (y1 BETWEEN ymin AND ymax)
+  WHERE (x1 BETWEEN xmin AND xmax);
+} {
+  QUERY PLAN
+  |--SCAN xdir
+  |--SCAN ydir
+  `--SCAN rt VIRTUAL TABLE INDEX 2:B2D3B0D1
+} {
+  2 4
+}
+
+do_eqp_execsql_test 7.2 {
+  SELECT * FROM xdir, rt LEFT JOIN ydir 
+  ON (y1 BETWEEN ymin AND ymax)
+  WHERE (x1 BETWEEN xmin AND xmax);
+} {
+  QUERY PLAN
+  |--SCAN xdir
+  |--SCAN rt VIRTUAL TABLE INDEX 2:B0D1
+  `--SCAN ydir LEFT-JOIN
+} {
+  5 1 2 7 12 14 {}
+  5 2 2 7  8 12 10
+  5 4 5 5 10 10 10
+}
+
+do_eqp_execsql_test 7.3 {
+  SELECT id FROM xdir, rt CROSS JOIN ydir 
+  ON (y1 BETWEEN ymin AND ymax)
+  WHERE (x1 BETWEEN xmin AND xmax);
+} {
+  QUERY PLAN
+  |--SCAN xdir
+  |--SCAN rt VIRTUAL TABLE INDEX 2:B0D1
+  `--SCAN ydir
+} {
+  2 4
+}
+
+do_eqp_execsql_test 7.4 {
+  SELECT id FROM rt, xdir CROSS JOIN ydir 
+  ON (y1 BETWEEN ymin AND ymax)
+  WHERE (x1 BETWEEN xmin AND xmax);
+} {
+  QUERY PLAN
+  |--SCAN xdir
+  |--SCAN rt VIRTUAL TABLE INDEX 2:B0D1
+  `--SCAN ydir
+} {
+  2 4
+}
+
+finish_test
diff --git a/ext/rtree/rtreeD.test b/ext/rtree/rtreeD.test
new file mode 100644
index 0000000..7f92898
--- /dev/null
+++ b/ext/rtree/rtreeD.test
@@ -0,0 +1,55 @@
+# 2014 March 11
+#
+# 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.
+#
+#***********************************************************************
+#
+# Miscellaneous tests for errors in the rtree constructor.
+#
+
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+source $testdir/lock_common.tcl
+ifcapable !rtree||!builtin_test {
+  finish_test
+  return
+}
+set testprefix rtreeD
+
+#-------------------------------------------------------------------------
+# Test that if an SQLITE_BUSY is encountered within the vtable 
+# constructor, a relevant error message is returned.
+#
+do_multiclient_test tn {
+  do_test 1.$tn.1 {
+    sql1 {
+      CREATE TABLE t1(a, b);
+      INSERT INTO t1 VALUES(1,2);
+      CREATE VIRTUAL TABLE rt USING rtree(id, minx, maxx, miny, maxy);
+      INSERT INTO rt VALUES(1,2,3,4,5);
+    }
+  } {}
+
+  do_test 1.$tn.2 {
+    sql2 { SELECT * FROM t1; }
+  } {1 2}
+
+  do_test 1.$tn.3 {
+    sql1 { BEGIN EXCLUSIVE; INSERT INTO t1 VALUES(3, 4); }
+  } {}
+
+  do_test 1.$tn.4 {
+    list [catch { sql2 { SELECT * FROM rt } } msg] $msg
+  } {1 {database is locked}}
+}
+
+finish_test
diff --git a/ext/rtree/rtreeE.test b/ext/rtree/rtreeE.test
new file mode 100644
index 0000000..72dcc94
--- /dev/null
+++ b/ext/rtree/rtreeE.test
@@ -0,0 +1,143 @@
+# 2010 August 28
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# This file contains tests for the r-tree module. Specifically, it tests
+# that new-style custom r-tree queries (geometry callbacks) work.
+# 
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+ifcapable rtree_int_only { finish_test; return }
+
+
+#-------------------------------------------------------------------------
+# Test the example 2d "circle" geometry callback.
+#
+register_circle_geom db
+
+do_execsql_test rtreeE-1.0.0 {
+  PRAGMA page_size=512;
+  CREATE VIRTUAL TABLE rt1 USING rtree(id,x0,x1,y0,y1);
+  
+  /* A tight pattern of small boxes near 0,0 */
+  WITH RECURSIVE
+    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
+    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
+  INSERT INTO rt1 SELECT x+5*y, x, x+2, y, y+2 FROM x, y;
+
+  /* A looser pattern of small boxes near 100, 0 */
+  WITH RECURSIVE
+    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
+    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
+  INSERT INTO rt1 SELECT 100+x+5*y, x*3+100, x*3+102, y*3, y*3+2 FROM x, y;
+
+  /* A looser pattern of larger boxes near 0, 200 */
+  WITH RECURSIVE
+    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
+    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
+  INSERT INTO rt1 SELECT 200+x+5*y, x*7, x*7+15, y*7+200, y*7+215 FROM x, y;
+} {}
+do_rtree_integrity_test rtreeE-1.0.1 rt1
+
+# Queries against each of the three clusters */
+do_execsql_test rtreeE-1.1 {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle(0.0, 0.0, 50.0, 3) ORDER BY id;
+} {0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24}
+do_execsql_test rtreeE-1.1x {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle('x:0 y:0 r:50.0 e:3') ORDER BY id;
+} {0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24}
+do_execsql_test rtreeE-1.2 {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle(100.0, 0.0, 50.0, 3) ORDER BY id;
+} {100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124}
+do_execsql_test rtreeE-1.3 {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle(0.0, 200.0, 50.0, 3) ORDER BY id;
+} {200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224}
+
+# The Qcircle geometry function gives a lower score to larger leaf-nodes.
+# This causes the 200s to sort before the 100s and the 0s to sort before
+# last.
+#
+do_execsql_test rtreeE-1.4 {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle('r:1000 e:3') AND id%100==0
+} {200 100 0}
+
+# Exclude odd rowids on a depth-first search
+do_execsql_test rtreeE-1.5 {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle('r:1000 e:4') ORDER BY +id
+} {0 2 4 6 8 10 12 14 16 18 20 22 24 100 102 104 106 108 110 112 114 116 118 120 122 124 200 202 204 206 208 210 212 214 216 218 220 222 224}
+
+# Exclude odd rowids on a breadth-first search.
+do_execsql_test rtreeE-1.6 {
+  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,5) ORDER BY +id
+} {0 2 4 6 8 10 12 14 16 18 20 22 24 100 102 104 106 108 110 112 114 116 118 120 122 124 200 202 204 206 208 210 212 214 216 218 220 222 224}
+
+# Test that rtree prefers MATCH to lookup-by-rowid.
+#
+do_execsql_test rtreeE-1.7 {
+  SELECT id FROM rt1 WHERE id=18 AND id MATCH Qcircle(0,0,1000,5)
+} {18}
+
+
+# Construct a large 2-D RTree with thousands of random entries.
+#
+do_test rtreeE-2.1 {
+  db eval {
+    CREATE TABLE t2(id,x0,x1,y0,y1);
+    CREATE VIRTUAL TABLE rt2 USING rtree(id,x0,x1,y0,y1);
+    BEGIN;
+  }
+  expr srand(0)
+  for {set i 1} {$i<=10000} {incr i} {
+    set dx [expr {int(rand()*40)+1}]
+    set dy [expr {int(rand()*40)+1}]
+    set x0 [expr {int(rand()*(10000 - $dx))}]
+    set x1 [expr {$x0+$dx}]
+    set y0 [expr {int(rand()*(10000 - $dy))}]
+    set y1 [expr {$y0+$dy}]
+    set id [expr {$i+10000}]
+    db eval {INSERT INTO t2 VALUES($id,$x0,$x1,$y0,$y1)}
+  }
+  db eval {
+    INSERT INTO rt2 SELECT * FROM t2;
+    COMMIT;
+  }
+} {}
+do_rtree_integrity_test rtreeE-2.1.1 rt2
+
+for {set i 1} {$i<=200} {incr i} {
+  set dx [expr {int(rand()*100)}]
+  set dy [expr {int(rand()*100)}]
+  set x0 [expr {int(rand()*(10000 - $dx))}]
+  set x1 [expr {$x0+$dx}]
+  set y0 [expr {int(rand()*(10000 - $dy))}]
+  set y1 [expr {$y0+$dy}]
+  set ans [db eval {SELECT id FROM t2 WHERE x1>=$x0 AND x0<=$x1 AND y1>=$y0 AND y0<=$y1 ORDER BY id}]
+  do_execsql_test rtreeE-2.2.$i {
+    SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch($x0,$x1,$y0,$y1) ORDER BY id
+  } $ans
+}
+
+# Run query that have very deep priority queues
+#
+set ans [db eval {SELECT id FROM t2 WHERE x1>=0 AND x0<=5000 AND y1>=0 AND y0<=5000 ORDER BY id}]
+do_execsql_test rtreeE-2.3 {
+  SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch(0,5000,0,5000) ORDER BY id
+} $ans
+set ans [db eval {SELECT id FROM t2 WHERE x1>=0 AND x0<=10000 AND y1>=0 AND y0<=10000 ORDER BY id}]
+do_execsql_test rtreeE-2.4 {
+  SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch(0,10000,0,10000) ORDER BY id
+} $ans
+
+
+finish_test
diff --git a/ext/rtree/rtreeF.test b/ext/rtree/rtreeF.test
new file mode 100644
index 0000000..561770d
--- /dev/null
+++ b/ext/rtree/rtreeF.test
@@ -0,0 +1,84 @@
+# 2014-08-21
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# This file contains tests for the r-tree module.
+#
+# This file contains test cases for the ticket
+# [369d57fb8e5ccdff06f197a37147a88f9de95cda] (2014-08-21)
+#
+#  The following SQL causes an assertion fault while running
+#  sqlite3_prepare() on the DELETE statement:
+#
+#     CREATE TABLE t1(x);
+#     CREATE TABLE t2(y);
+#     CREATE VIRTUAL TABLE t3 USING rtree(a,b,c);
+#     CREATE TRIGGER t2del AFTER DELETE ON t2 WHEN (SELECT 1 from t1) BEGIN 
+#       DELETE FROM t3 WHERE a=old.y; 
+#     END;
+#     DELETE FROM t2 WHERE y=1;
+# 
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+do_execsql_test rtreeF-1.1 {
+  CREATE TABLE t1(x);
+  CREATE TABLE t2(y);
+  CREATE VIRTUAL TABLE t3 USING rtree(a,b,c);
+  CREATE TRIGGER t2dwl AFTER DELETE ON t2 WHEN (SELECT 1 from t1) BEGIN 
+    DELETE FROM t3 WHERE a=old.y; 
+  END;
+
+  INSERT INTO t1(x) VALUES(999);
+  INSERT INTO t2(y) VALUES(1),(2),(3),(4),(5);
+  INSERT INTO t3(a,b,c) VALUES(1,2,3),(2,3,4),(3,4,5),(4,5,6),(5,6,7);
+
+  SELECT a FROM t3 ORDER BY a;
+  SELECT '|';
+  SELECT y FROM t2 ORDER BY y;
+} {1 2 3 4 5 | 1 2 3 4 5}
+do_execsql_test rtreeF-1.2 {
+  DELETE FROM t2 WHERE y=3;
+
+  SELECT a FROM t3 ORDER BY a;
+  SELECT '|';
+  SELECT y FROM t2 ORDER BY y;
+} {1 2 4 5 | 1 2 4 5}
+do_execsql_test rtreeF-1.3 {
+  DELETE FROM t1;
+  DELETE FROM t2 WHERE y=5;
+
+  SELECT a FROM t3 ORDER BY a;
+  SELECT '|';
+  SELECT y FROM t2 ORDER BY y;
+} {1 2 4 5 | 1 2 4}
+do_execsql_test rtreeF-1.4 {
+  INSERT INTO t1 DEFAULT VALUES;
+  DELETE FROM t2 WHERE y=5;
+
+  SELECT a FROM t3 ORDER BY a;
+  SELECT '|';
+  SELECT y FROM t2 ORDER BY y;
+} {1 2 4 5 | 1 2 4}
+do_execsql_test rtreeF-1.5 {
+  DELETE FROM t2 WHERE y=2;
+
+  SELECT a FROM t3 ORDER BY a;
+  SELECT '|';
+  SELECT y FROM t2 ORDER BY y;
+} {1 4 5 | 1 4}
+
+do_rtree_integrity_test rtreeF-1.6 t3
+
+finish_test
diff --git a/ext/rtree/rtreeG.test b/ext/rtree/rtreeG.test
new file mode 100644
index 0000000..12225d5
--- /dev/null
+++ b/ext/rtree/rtreeG.test
@@ -0,0 +1,69 @@
+# 2016-05-32
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# This file contains tests for the r-tree module.
+#
+# Verify that no invalid SQL is run during initialization
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+db close
+sqlite3_shutdown
+test_sqlite3_log [list lappend ::log]
+set ::log [list]
+sqlite3 db test.db
+
+
+set ::log {}
+do_execsql_test rtreeG-1.1 {
+  CREATE VIRTUAL TABLE t1 USING rtree(id,x0,x1,y0,y1);
+} {}
+do_test rtreeG-1.1log {
+  set ::log
+} {}
+
+do_execsql_test rtreeG-1.2 {
+  INSERT INTO t1 VALUES(1,10,15,5,23),(2,20,21,5,23),(3,10,15,20,30);
+  SELECT id from t1 WHERE x0>8 AND x1<16 AND y0>2 AND y1<25;
+} {1}
+do_rtree_integrity_test rtreeG-1.2.integrity t1
+do_test rtreeG-1.2log {
+  set ::log
+} {}
+
+db close
+sqlite3 db test.db
+do_execsql_test rtreeG-1.3 {
+  SELECT id from t1 WHERE x0>8 AND x1<16 AND y0>2 AND y1<25;
+} {1}
+do_test rtreeG-1.3log {
+  set ::log
+} {}
+
+do_execsql_test rtreeG-1.4 {
+  DROP TABLE t1;
+} {}
+do_test rtreeG-1.4log {
+  set ::log
+} {}
+
+expand_all_sql db
+db close
+sqlite3_shutdown
+test_sqlite3_log
+sqlite3_initialize
+sqlite3 db test.db
+
+finish_test
diff --git a/ext/rtree/rtreeH.test b/ext/rtree/rtreeH.test
new file mode 100644
index 0000000..e26107f
--- /dev/null
+++ b/ext/rtree/rtreeH.test
@@ -0,0 +1,103 @@
+# 2018-05-16
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# This file contains tests for the r-tree module, specifically the
+# auxiliary column mechanism.
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+do_execsql_test rtreeH-100 {
+  CREATE VIRTUAL TABLE t1 USING rtree(id,x0,x1,y0,y1,+label,+other);
+  INSERT INTO t1(x0,x1,y0,y1,label) VALUES
+    (0,10,0,10,'lower-left corner'),
+    (0,10,90,100,'upper-left corner'),
+    (90,100,0,10,'lower-right corner'),
+    (90,100,90,100,'upper-right corner'),
+    (40,60,40,60,'center'),
+    (0,5,0,100,'left edge'),
+    (95,100,0,100,'right edge'),
+    (0,100,0,5,'bottom edge'),
+    (0,100,95,100,'top edge'),
+    (0,100,0,100,'the whole thing'),
+    (0,50,0,100,'left half'),
+    (51,100,0,100,'right half'),
+    (0,100,0,50,'bottom half'),
+    (0,100,51,100,'top half');
+} {}
+do_execsql_test rtreeH-101 {
+  SELECT * FROM t1_rowid ORDER BY rowid
+} {1 1 {lower-left corner} {} 2 1 {upper-left corner} {} 3 1 {lower-right corner} {} 4 1 {upper-right corner} {} 5 1 center {} 6 1 {left edge} {} 7 1 {right edge} {} 8 1 {bottom edge} {} 9 1 {top edge} {} 10 1 {the whole thing} {} 11 1 {left half} {} 12 1 {right half} {} 13 1 {bottom half} {} 14 1 {top half} {}}
+
+do_execsql_test rtreeH-102 {
+  SELECT * FROM t1 WHERE rowid=5;
+} {5 40.0 60.0 40.0 60.0 center {}}
+do_execsql_test rtreeH-102b {
+  SELECT * FROM t1 WHERE rowid=5.0;
+} {5 40.0 60.0 40.0 60.0 center {}}
+do_execsql_test rtreeH-102c {
+  SELECT * FROM t1 WHERE rowid='5';
+} {5 40.0 60.0 40.0 60.0 center {}}
+do_execsql_test rtreeH-102d {
+  SELECT * FROM t1 WHERE rowid='0005';
+} {5 40.0 60.0 40.0 60.0 center {}}
+do_execsql_test rtreeH-102e {
+  SELECT * FROM t1 WHERE rowid='+5.0e+0';
+} {5 40.0 60.0 40.0 60.0 center {}}
+do_execsql_test rtreeH-103 {
+  SELECT * FROM t1 WHERE label='center';
+} {5 40.0 60.0 40.0 60.0 center {}}
+
+do_execsql_test rtreeH-104 {
+  SELECT * FROM t1 WHERE rowid='+5.0e+0x';
+} {}
+do_execsql_test rtreeH-105 {
+  SELECT * FROM t1 WHERE rowid=x'35';
+} {}
+do_execsql_test rtreeH-106 {
+  SELECT * FROM t1 WHERE rowid=null;
+} {}
+
+
+do_rtree_integrity_test rtreeH-110 t1
+
+do_execsql_test rtreeH-120 {
+  SELECT label FROM t1 WHERE x1<=50 ORDER BY id
+} {{lower-left corner} {upper-left corner} {left edge} {left half}}
+do_execsql_test rtreeH-121 {
+  SELECT label FROM t1 WHERE x1<=50 AND label NOT LIKE '%corner%' ORDER BY id
+} {{left edge} {left half}}
+
+do_execsql_test rtreeH-200 {
+  WITH RECURSIVE
+    c1(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM c1 WHERE x<99),
+    c2(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM c2 WHERE y<99)
+  INSERT INTO t1(id, x0,x1,y0,y1,label)
+    SELECT 1000+x+y*100, x, x+1, y, y+1, printf('box-%d,%d',x,y) FROM c1, c2;
+} {}
+
+do_execsql_test rtreeH-210 {
+  SELECT label FROM t1 WHERE x0>=48 AND x1<=50 AND y0>=48 AND y1<=50
+     ORDER BY id;
+} {box-48,48 box-49,48 box-48,49 box-49,49}
+
+do_execsql_test rtreeH-300 {
+  UPDATE t1 SET label='x'||label
+    WHERE x0>=49 AND x1<=50 AND y0>=49 AND y1<=50;
+  SELECT label FROM t1 WHERE x0>=48 AND x1<=50 AND y0>=48 AND y1<=50
+     ORDER BY id;
+} {box-48,48 box-49,48 box-48,49 xbox-49,49}
+
+
+finish_test
diff --git a/ext/rtree/rtreeI.test b/ext/rtree/rtreeI.test
new file mode 100644
index 0000000..0bc910e
--- /dev/null
+++ b/ext/rtree/rtreeI.test
@@ -0,0 +1,74 @@
+# 2019-12-05
+#
+# 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.
+#
+#***********************************************************************
+# Additional test cases
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+ifcapable !rtree { finish_test ; return }
+
+# The following is a test of rowvalue handling on virtual tables that
+# deal with inequalities and that set the OMIT flag on terms of the
+# WHERE clause.  This is not specific to rtree.  We just use rtree because
+# it is a convenient test platform since it has all the right
+# characteristics.
+#
+do_execsql_test rtreeI-1.10 {
+  CREATE TABLE t1(a);
+  INSERT INTO t1 VALUES(2);
+  CREATE VIRTUAL TABLE t2 USING rtree(id,x0,x1);
+  INSERT INTO t2(id,x0,x1) VALUES(1,2,3);
+} {}
+do_execsql_test rtreeI-1.20 {
+  SELECT 123 FROM t1, t2 WHERE (a,0)>(x0,0);
+} {}
+do_execsql_test rtreeI-1.21 {
+  SELECT 123 FROM t1, t2 WHERE (a,0.1)>(x0,0);
+} {123}
+do_execsql_test rtreeI-1.22 {
+  SELECT 123 FROM t1, t2 WHERE (a,0)>=(x0,0);
+} {123}
+do_execsql_test rtreeI-1.23 {
+  SELECT 123 FROM t1, t2 WHERE (a,0)<=(x0,0);
+} {123}
+do_execsql_test rtreeI-1.24 {
+  SELECT 123 FROM t1, t2 WHERE (a,0)<(x0,0);
+} {}
+do_execsql_test rtreeI-1.30 {
+  SELECT 123 FROM t1, t2 WHERE (x0,0)<(a,0);
+} {}
+do_execsql_test rtreeI-1.31 {
+  SELECT 123 FROM t1, t2 WHERE (x0,0)<(a,0.1);
+} {123}
+do_execsql_test rtreeI-1.40 {
+  SELECT 123 FROM t1, t2 WHERE x1<5 AND id<99 AND (a,0)>(x0,0);
+} {}
+do_execsql_test rtreeI-1.41 {
+  SELECT 123 FROM t1, t2 WHERE x1<5 AND id<99 AND (a,0.5)>(x0,0);
+} {123}
+do_execsql_test rtreeI-1.42 {
+  SELECT 123 FROM t1, t2 WHERE x1<5 AND id<99 AND (a,0)>=(x0,0);
+} {123}
+do_execsql_test rtreeI-1.43 {
+  SELECT 123 FROM t1, t2 WHERE x1<5 AND id<99 AND (a,0)<(x0,0);
+} {}
+do_execsql_test rtreeI-1.50 {
+  SELECT 123 FROM t1, t2 WHERE 5>x1 AND 99>id AND (x0,0)<(a,0);
+} {}
+do_execsql_test rtreeI-1.51 {
+  SELECT 123 FROM t1, t2 WHERE 5>x1 AND 99>id AND (x0,0)<(a,0.5);
+} {123}
+
+
+
+finish_test
diff --git a/ext/rtree/rtree_perf.tcl b/ext/rtree/rtree_perf.tcl
new file mode 100644
index 0000000..e42e685
--- /dev/null
+++ b/ext/rtree/rtree_perf.tcl
@@ -0,0 +1,74 @@
+
+set testdir [file join [file dirname $argv0] .. .. test]
+source $testdir/tester.tcl
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+set NROW   10000
+set NQUERY   500
+
+puts "Generating $NROW rows of data..."
+set data [list]
+for {set ii 0} {$ii < $NROW} {incr ii} {
+  set x1 [expr {rand()*1000}]
+  set x2 [expr {$x1+rand()*50}]
+  set y1 [expr {rand()*1000}]
+  set y2 [expr {$y1+rand()*50}]
+  lappend data $x1 $x2 $y1 $y2
+}
+puts "Finished generating data"
+
+
+set sql1 {CREATE TABLE btree(ii INTEGER PRIMARY KEY, x1, x2, y1, y2)}
+set sql2 {CREATE VIRTUAL TABLE rtree USING rtree(ii, x1, x2, y1, y2)}
+puts "Creating tables:"
+puts "  $sql1"
+puts "  $sql2"
+db eval $sql1
+db eval $sql2
+
+db eval "pragma cache_size=100"
+
+puts -nonewline "Inserting into btree... "
+flush stdout
+set btree_time [time {db transaction {
+  set ii 1
+  foreach {x1 x2 y1 y2} $data {
+    db eval {INSERT INTO btree VALUES($ii, $x1, $x2, $y1, $y2)}
+    incr ii
+  }
+}}]
+puts "$btree_time"
+
+puts -nonewline "Inserting into rtree... "
+flush stdout
+set rtree_time [time {db transaction {
+  set ii 1
+  foreach {x1 x2 y1 y2} $data {
+    incr ii
+    db eval {INSERT INTO rtree VALUES($ii, $x1, $x2, $y1, $y2)}
+  }
+}}]
+puts "$rtree_time"
+
+
+puts -nonewline "Selecting from btree... "
+flush stdout
+set btree_select_time [time {
+  foreach {x1 x2 y1 y2} [lrange $data 0 [expr $NQUERY*4-1]] {
+    db eval {SELECT * FROM btree WHERE x1<$x1 AND x2>$x2 AND y1<$y1 AND y2>$y2}
+ }
+}]
+puts "$btree_select_time"
+
+puts -nonewline "Selecting from rtree... "
+flush stdout
+set rtree_select_time [time {
+  foreach {x1 x2 y1 y2} [lrange $data 0 [expr $NQUERY*4-1]] {
+    db eval {SELECT * FROM rtree WHERE x1<$x1 AND x2>$x2 AND y1<$y1 AND y2>$y2}
+  }
+}]
+puts "$rtree_select_time"
diff --git a/ext/rtree/rtree_util.tcl b/ext/rtree/rtree_util.tcl
new file mode 100644
index 0000000..afa588e
--- /dev/null
+++ b/ext/rtree/rtree_util.tcl
@@ -0,0 +1,197 @@
+# 2008 Feb 19
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+#
+# This file contains Tcl code that may be useful for testing or
+# analyzing r-tree structures created with this module. It is
+# used by both test procedures and the r-tree viewer application.
+#
+
+
+#--------------------------------------------------------------------------
+# PUBLIC API:
+#
+#   rtree_depth
+#   rtree_ndim
+#   rtree_node
+#   rtree_mincells
+#   rtree_check
+#   rtree_dump
+#   rtree_treedump
+#
+
+proc rtree_depth {db zTab} {
+  $db one "SELECT rtreedepth(data) FROM ${zTab}_node WHERE nodeno=1"
+}
+
+proc rtree_nodedepth {db zTab iNode} {
+  set iDepth [rtree_depth $db $zTab]
+  
+  set ii $iNode
+  while {$ii != 1} {
+    set sql "SELECT parentnode FROM ${zTab}_parent WHERE nodeno = $ii"
+    set ii [db one $sql]
+    incr iDepth -1
+  }
+  
+  return $iDepth
+}
+
+# Return the number of dimensions of the rtree.
+#
+proc rtree_ndim {db zTab} {
+  set nDim [expr {(([llength [$db eval "pragma table_info($zTab)"]]/6)-1)/2}]
+}
+
+# Return the contents of rtree node $iNode.
+#
+proc rtree_node {db zTab iNode {iPrec 6}} {
+  set nDim [rtree_ndim $db $zTab]
+  set sql "
+    SELECT rtreenode($nDim, data) FROM ${zTab}_node WHERE nodeno = $iNode
+  "
+  set node [db one $sql]
+
+  set nCell [llength $node]
+  set nCoord [expr $nDim*2]
+  for {set ii 0} {$ii < $nCell} {incr ii} {
+    for {set jj 1} {$jj <= $nCoord} {incr jj} {
+      set newval [format "%.${iPrec}f" [lindex $node $ii $jj]]
+      lset node $ii $jj $newval
+    }
+  }
+  set node
+}
+
+proc rtree_mincells {db zTab} {
+  set n [$db one "select length(data) FROM ${zTab}_node LIMIT 1"]
+  set nMax [expr {int(($n-4)/(8+[rtree_ndim $db $zTab]*2*4))}]
+  return [expr {int($nMax/3)}]
+}
+
+# An integrity check for the rtree $zTab accessible via database 
+# connection $db.
+#
+proc rtree_check {db zTab} {
+  array unset ::checked
+ 
+  # Check each r-tree node.
+  set rc [catch {
+    rtree_node_check $db $zTab 1 [rtree_depth $db $zTab]
+  } msg]
+  if {$rc && $msg ne ""} { error $msg }
+
+  # Check that the _rowid and _parent tables have the right 
+  # number of entries.
+  set nNode   [$db one "SELECT count(*) FROM ${zTab}_node"]
+  set nRow    [$db one "SELECT count(*) FROM ${zTab}"]
+  set nRowid  [$db one "SELECT count(*) FROM ${zTab}_rowid"]
+  set nParent [$db one "SELECT count(*) FROM ${zTab}_parent"]
+
+  if {$nNode != ($nParent+1)} { 
+    error "Wrong number of entries in ${zTab}_parent"
+  }
+  if {$nRow != $nRowid} { 
+    error "Wrong number of entries in ${zTab}_rowid"
+  }
+  
+  return $rc
+}
+
+proc rtree_node_check {db zTab iNode iDepth} {
+  if {[info exists ::checked($iNode)]} { error "Second ref to $iNode" }
+  set ::checked($iNode) 1
+
+  set node [rtree_node $db $zTab $iNode]
+  if {$iNode!=1 && [llength $node]==0} { error "No such node: $iNode" }
+
+  if {$iNode != 1 && [llength $node]<[rtree_mincells $db $zTab]} {
+    puts "Node $iNode: Has only [llength $node] cells"
+    error ""
+  }
+  if {$iNode == 1 && [llength $node]==1 && [rtree_depth $db $zTab]>0} {
+    set depth [rtree_depth $db $zTab]
+    puts "Node $iNode: Has only 1 child (tree depth is $depth)"
+    error ""
+  }
+
+  set nDim [expr {([llength [lindex $node 0]]-1)/2}]
+
+  if {$iDepth > 0} {
+    set d [expr $iDepth-1]
+    foreach cell $node {
+      set shouldbe [rtree_node_check $db $zTab [lindex $cell 0] $d]
+      if {$cell ne $shouldbe} {
+        puts "Node $iNode: Cell is: {$cell}, should be {$shouldbe}"
+        error ""
+      }
+    }
+  }
+
+  set mapping_table "${zTab}_parent" 
+  set mapping_sql "SELECT parentnode FROM $mapping_table WHERE rowid = \$rowid"
+  if {$iDepth==0} { 
+    set mapping_table "${zTab}_rowid"
+    set mapping_sql "SELECT nodeno FROM $mapping_table WHERE rowid = \$rowid"
+  }
+  foreach cell $node {
+    set rowid [lindex $cell 0]
+    set mapping [db one $mapping_sql]
+    if {$mapping != $iNode} {
+      puts "Node $iNode: $mapping_table entry for cell $rowid is $mapping"
+      error ""
+    }
+  }
+
+  set ret [list $iNode]
+  for {set ii 1} {$ii <= $nDim*2} {incr ii} {
+    set f [lindex $node 0 $ii]
+    foreach cell $node {
+      set f2 [lindex $cell $ii]
+      if {($ii%2)==1 && $f2<$f} {set f $f2}
+      if {($ii%2)==0 && $f2>$f} {set f $f2}
+    }
+    lappend ret $f
+  }
+  return $ret
+}
+
+proc rtree_dump {db zTab} {
+  set zRet ""
+  set nDim [expr {(([llength [$db eval "pragma table_info($zTab)"]]/6)-1)/2}]
+  set sql "SELECT nodeno, rtreenode($nDim, data) AS node FROM ${zTab}_node"
+  $db eval $sql {
+    append zRet [format "% -10s %s\n" $nodeno $node]
+  }
+  set zRet
+}
+
+proc rtree_nodetreedump {db zTab zIndent iDepth iNode} {
+  set ret ""
+  set node [rtree_node $db $zTab $iNode 1]
+  append ret [format "%-3d %s%s\n" $iNode $zIndent $node]
+  if {$iDepth>0} {
+    foreach cell $node {
+      set i [lindex $cell 0]
+      append ret [rtree_nodetreedump $db $zTab "$zIndent  " [expr $iDepth-1] $i]
+    }
+  }
+  set ret
+}
+
+proc rtree_treedump {db zTab} {
+  set d [rtree_depth $db $zTab]
+  rtree_nodetreedump $db $zTab "" $d 1
+}
+
+proc do_rtree_integrity_test {tn tbl} {
+  uplevel [list do_execsql_test $tn "SELECT rtreecheck('$tbl')" ok]
+}
+
diff --git a/ext/rtree/rtreecheck.test b/ext/rtree/rtreecheck.test
new file mode 100644
index 0000000..17f359a
--- /dev/null
+++ b/ext/rtree/rtreecheck.test
@@ -0,0 +1,160 @@
+# 2017 August 17
+#
+# 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.
+#
+#***********************************************************************
+#
+#
+
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source $testdir/tester.tcl
+set testprefix rtreecheck
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+proc swap_int32 {blob i0 i1} {
+  binary scan $blob I* L
+
+  set a [lindex $L $i0]
+  set b [lindex $L $i1]
+
+  lset L $i0 $b
+  lset L $i1 $a
+
+  binary format I* $L
+}
+
+proc set_int32 {blob idx val} {
+  binary scan $blob I* L
+  lset L $idx $val
+  binary format I* $L
+}
+
+do_catchsql_test 1.0 {
+  SELECT rtreecheck();
+} {1 {wrong number of arguments to function rtreecheck()}}
+
+do_catchsql_test 1.1 {
+  SELECT rtreecheck(0,0,0);
+} {1 {wrong number of arguments to function rtreecheck()}}
+
+
+proc setup_simple_db {{module rtree}} {
+  reset_db
+  db func swap_int32 swap_int32
+  execsql "
+    CREATE VIRTUAL TABLE r1 USING $module (id, x1, x2, y1, y2);
+    INSERT INTO r1 VALUES(1,  5, 5, 5, 5);  --  3
+    INSERT INTO r1 VALUES(2,  6, 6, 6, 6);  --  9
+    INSERT INTO r1 VALUES(3,  7, 7, 7, 7);  -- 15
+    INSERT INTO r1 VALUES(4,  8, 8, 8, 8);  -- 21
+    INSERT INTO r1 VALUES(5,  9, 9, 9, 9);  -- 27
+  "
+  sqlite3_db_config db DEFENSIVE 0
+}
+
+setup_simple_db
+do_execsql_test 2.1 { 
+  SELECT rtreecheck('r1') 
+} {ok}
+
+do_execsql_test 2.2 {
+  UPDATE r1_node SET data = swap_int32(data, 3, 9);
+  UPDATE r1_node SET data = swap_int32(data, 23, 29);
+}
+
+do_execsql_test 2.3 { 
+  SELECT rtreecheck('r1') 
+} {{Dimension 0 of cell 0 on node 1 is corrupt
+Dimension 1 of cell 3 on node 1 is corrupt}}
+
+setup_simple_db
+do_execsql_test 2.4 {
+  DELETE FROM r1_rowid WHERE rowid = 3;
+  SELECT rtreecheck('r1') 
+} {{Mapping (3 -> 1) missing from %_rowid table
+Wrong number of entries in %_rowid table - expected 5, actual 4}}
+
+setup_simple_db
+do_execsql_test 2.5 {
+  UPDATE r1_rowid SET nodeno=2 WHERE rowid=3;
+  SELECT rtreecheck('r1') 
+} {{Found (3 -> 2) in %_rowid table, expected (3 -> 1)}}
+
+reset_db
+do_execsql_test 3.0 { 
+  CREATE VIRTUAL TABLE r1 USING rtree_i32(id, x1, x2);
+  INSERT INTO r1 VALUES(1, 0x7FFFFFFF*-1, 0x7FFFFFFF);
+  INSERT INTO r1 VALUES(2, 0x7FFFFFFF*-1, 5);
+  INSERT INTO r1 VALUES(3, -5, 5);
+  INSERT INTO r1 VALUES(4, 5, 0x11111111);
+  INSERT INTO r1 VALUES(5, 5, 0x00800000);
+  INSERT INTO r1 VALUES(6, 5, 0x00008000);
+  INSERT INTO r1 VALUES(7, 5, 0x00000080);
+  INSERT INTO r1 VALUES(8, 5, 0x40490fdb);
+  INSERT INTO r1 VALUES(9, 0x7f800000, 0x7f900000);
+  SELECT rtreecheck('r1') 
+} {ok}
+
+do_execsql_test 3.1 { 
+  CREATE VIRTUAL TABLE r2 USING rtree_i32(id, x1, x2);
+  INSERT INTO r2 VALUES(2, -1*(1<<31), -1*(1<<31)+5);
+  SELECT rtreecheck('r2') 
+} {ok}
+
+sqlite3_db_config db DEFENSIVE 0
+do_execsql_test 3.2 {
+  BEGIN;
+    UPDATE r2_node SET data = X'123456';
+    SELECT rtreecheck('r2')!='ok';
+} {1}
+
+do_execsql_test 3.3 {
+  ROLLBACK;
+  UPDATE r2_node SET data = X'00001234';
+  SELECT rtreecheck('r2')!='ok';
+} {1}
+
+do_execsql_test 4.0 {
+  CREATE TABLE notanrtree(i);
+  SELECT rtreecheck('notanrtree');
+} {{Schema corrupt or not an rtree}}
+
+#-------------------------------------------------------------------------
+#
+reset_db
+db func set_int32 set_int32
+do_execsql_test 5.0 {
+  CREATE VIRTUAL TABLE r3 USING rtree_i32(id, x1, x2, y1, y2);
+  WITH x(i) AS (
+    SELECT 1 UNION ALL SELECT i+1 FROM x WHERE i<1000
+  )
+  INSERT INTO r3 SELECT i, i, i, i, i FROM x;
+}
+sqlite3_db_config db DEFENSIVE 0
+do_execsql_test 5.1 {
+  BEGIN;
+    UPDATE r3_node SET data = set_int32(data, 3, 5000);
+    UPDATE r3_node SET data = set_int32(data, 4, 5000);
+    SELECT rtreecheck('r3')=='ok'
+} 0
+do_execsql_test 5.2 {
+  ROLLBACK;
+  BEGIN;
+    UPDATE r3_node SET data = set_int32(data, 3, 0);
+    UPDATE r3_node SET data = set_int32(data, 4, 0);
+    SELECT rtreecheck('r3')=='ok'
+} 0
+
+finish_test
diff --git a/ext/rtree/rtreecirc.test b/ext/rtree/rtreecirc.test
new file mode 100644
index 0000000..d77ed04
--- /dev/null
+++ b/ext/rtree/rtreecirc.test
@@ -0,0 +1,66 @@
+# 2018 Dec 22
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#*************************************************************************
+# This file implements regression tests for SQLite library.  The
+# focus of this script is testing the FTS5 module.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+}
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+set testprefix rtreecirc
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, y1, y2);
+  SELECT name FROM sqlite_master ORDER BY 1;
+} {
+  rt rt_node rt_parent rt_rowid
+}
+db_save_and_close
+
+foreach {tn schema sql} {
+  1 {
+    CREATE TRIGGER tr1 AFTER INSERT ON rt_node BEGIN
+      SELECT * FROM rt;
+    END;
+  } {
+    INSERT INTO rt VALUES(1, 2, 3, 4, 5);
+  }
+  2 {
+    CREATE TRIGGER tr1 AFTER INSERT ON rt_parent BEGIN
+      SELECT * FROM rt;
+    END;
+  } {
+    INSERT INTO rt VALUES(1, 2, 3, 4, 5);
+  }
+  3 {
+    CREATE TRIGGER tr1 AFTER INSERT ON rt_rowid BEGIN
+      SELECT * FROM rt;
+    END;
+  } {
+    INSERT INTO rt VALUES(1, 2, 3, 4, 5);
+  }
+} {
+  db_restore_and_reopen
+  do_execsql_test  1.1.$tn.1 $schema
+  do_catchsql_test 1.1.$tn.2 $sql {1 {no such table: main.rt}}
+  db close
+}
+
+
+finish_test
+
diff --git a/ext/rtree/rtreeconnect.test b/ext/rtree/rtreeconnect.test
new file mode 100644
index 0000000..16d04d9
--- /dev/null
+++ b/ext/rtree/rtreeconnect.test
@@ -0,0 +1,56 @@
+# 2017 August 17
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension. Specifically,
+# the impact of an SQLITE_SCHEMA error within the rtree module xConnect
+# callback.
+#
+
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source $testdir/tester.tcl
+set testprefix rtreeconnect
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE r1 USING rtree(id, x1, x2, y1, y2);
+  CREATE TABLE t1(id, x1, x2, y1, y2);
+  CREATE TABLE log(l);
+
+  CREATE TRIGGER tr1 AFTER INSERT ON t1 BEGIN
+    INSERT INTO r1 VALUES(new.id, new.x1, new.x2, new.y1, new.y2);
+    INSERT INTO log VALUES('r1: ' || new.id);
+  END;
+}
+
+db close
+sqlite3 db  test.db
+sqlite3 db2 test.db
+
+do_test 1.1 {
+  db eval { INSERT INTO log VALUES('startup'); }
+  db2 eval { CREATE TABLE newtable(x,y); }
+} {}
+
+do_execsql_test 1.2 {
+  INSERT INTO t1 VALUES(1, 2, 3, 4, 5);
+}
+
+db2 close
+db close
+
+finish_test
diff --git a/ext/rtree/rtreedoc.test b/ext/rtree/rtreedoc.test
new file mode 100644
index 0000000..b64faa2
--- /dev/null
+++ b/ext/rtree/rtreedoc.test
@@ -0,0 +1,1583 @@
+# 2021 September 13
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+}
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+set testprefix rtreedoc
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+# This command returns the number of columns in table $tbl within the
+# database opened by database handle $db
+proc column_count {db tbl} {
+  set nCol 0
+  $db eval "PRAGMA table_info = $tbl" { incr nCol }
+  return $nCol
+}
+
+proc column_name_list {db tbl} {
+  set lCol [list]
+  $db eval "PRAGMA table_info = $tbl" { 
+    lappend lCol $name
+  }
+  return $lCol
+}
+unset -nocomplain res
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-1
+
+# EVIDENCE-OF: R-15060-13876 A 1-dimensional R*Tree thus has 3 columns.
+do_execsql_test 1.1.1 { CREATE VIRTUAL TABLE rt1 USING rtree(id, x1,x2) }
+do_test         1.1.2 { column_count db rt1 } 3
+
+# EVIDENCE-OF: R-19353-19546 A 2-dimensional R*Tree has 5 columns.
+do_execsql_test 1.2.1 { CREATE VIRTUAL TABLE rt2 USING rtree(id,x1,x2, y1,y2) }
+do_test         1.2.2 { column_count db rt2 } 5
+
+# EVIDENCE-OF: R-13615-19528 A 3-dimensional R*Tree has 7 columns.
+do_execsql_test 1.3.1 { 
+  CREATE VIRTUAL TABLE rt3 USING rtree(id, x1,x2, y1,y2, z1,z2) 
+}
+do_test         1.3.2 { column_count db rt3 } 7
+
+# EVIDENCE-OF: R-53479-41922 A 4-dimensional R*Tree has 9 columns.
+do_execsql_test 1.4.1 { 
+  CREATE VIRTUAL TABLE rt4 USING rtree(id, x1,x2, y1,y2, z1,z2, v1,v2) 
+}
+do_test         1.4.2 { column_count db rt4 } 9
+
+# EVIDENCE-OF: R-13981-28768 And a 5-dimensional R*Tree has 11 columns.
+do_execsql_test 1.5.1 { 
+  CREATE VIRTUAL TABLE rt5 USING rtree(id, x1,x2, y1,y2, z1,z2, v1,v2, w1,w2)
+}
+do_test         1.5.2 { column_count db rt5 } 11
+
+
+# Attempt to create r-tree tables with 6 and 7 dimensions.
+#
+# EVIDENCE-OF: R-61533-25862 The SQLite R*Tree implementation does not
+# support R*Trees wider than 5 dimensions.
+do_catchsql_test 2.1.1 { 
+  CREATE VIRTUAL TABLE rt6 USING rtree(
+    id, x1,x2, y1,y2, z1,z2, v1,v2, w1,w2, a1,a2
+  )
+} {1 {Too many columns for an rtree table}}
+do_catchsql_test 2.1.2 { 
+  CREATE VIRTUAL TABLE rt6 USING rtree(
+    id, x1,x2, y1,y2, z1,z2, v1,v2, w1,w2, a1,a2, b1, b2
+  )
+} {1 {Too many columns for an rtree table}}
+
+# Attempt to create r-tree tables with no columns, a single column, or
+# an even number of columns. This and the tests above establish that:
+#
+# EVIDENCE-OF: R-16717-50504 Each R*Tree index is a virtual table with
+# an odd number of columns between 3 and 11.
+foreach {tn cols err} {
+  1 ""                        "Too few columns for an rtree table"
+  2 "x"                       "Too few columns for an rtree table"
+  3 "x,y"                     "Too few columns for an rtree table"
+  4 "a,b,c,d"                 "Wrong number of columns for an rtree table"
+  5 "a,b,c,d,e,f"             "Wrong number of columns for an rtree table"
+  6 "a,b,c,d,e,f,g,h"         "Wrong number of columns for an rtree table"
+  7 "a,b,c,d,e,f,g,h,i,j"     "Wrong number of columns for an rtree table"
+  8 "a,b,c,d,e,f,g,h,i,j,k,l" "Too many columns for an rtree table"
+} {
+  do_catchsql_test 3.$tn "
+    CREATE VIRTUAL TABLE xyz USING rtree($cols)
+  " [list 1 $err]
+}
+
+# EVIDENCE-OF: R-17874-21123 The first column of an SQLite R*Tree is
+# similar to an integer primary key column of a normal SQLite table.
+#
+# EVIDENCE-OF: R-46619-65417 The first column is always a 64-bit signed
+# integer primary key.
+#
+# EVIDENCE-OF: R-46866-24036 It may only store a 64-bit signed integer
+# value.
+#
+# EVIDENCE-OF: R-00250-64843 If an attempt is made to insert any other
+# non-integer value into this column, the r-tree module silently
+# converts it to an integer before writing it into the database.
+#
+do_execsql_test 4.0 { CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2) }
+foreach {tn val res} {
+  1 10    10
+  2 10.6  10
+  3 10.99 10
+  4 '123' 123
+  5 X'313233'  123
+  6 -10   -10
+  7  9223372036854775807 9223372036854775807 
+  8 -9223372036854775808 -9223372036854775808 
+  9  '9223372036854775807' 9223372036854775807
+  10  '-9223372036854775808' -9223372036854775808
+  11  'hello+world' 0
+} {
+  do_execsql_test 4.$tn.1 "
+    DELETE FROM rt;
+    INSERT INTO rt VALUES($val, 10, 20);
+  "
+  do_execsql_test 4.$tn.2 {
+    SELECT typeof(id), id FROM rt
+  } [list integer $res]
+}
+
+# EVIDENCE-OF: R-15544-29079 Inserting a NULL value into this column
+# causes SQLite to automatically generate a new unique primary key
+# value.
+do_execsql_test 5.1 {
+  DELETE FROM rt;
+  INSERT INTO rt VALUES(100, 1, 2);
+  INSERT INTO rt VALUES(NULL, 1, 2);
+}
+do_execsql_test 5.2 { SELECT id FROM rt } {100 101}
+do_execsql_test 5.3 { 
+  INSERT INTO rt VALUES(9223372036854775807, 1, 2);
+  INSERT INTO rt VALUES(NULL, 1, 2);
+}
+do_execsql_test 5.4 {
+  SELECT count(*) FROM rt;
+} 4
+do_execsql_test 5.5 {
+  SELECT id IN(100, 101, 9223372036854775807) FROM rt ORDER BY 1;
+} {0 1 1 1}
+
+
+# EVIDENCE-OF: R-64317-38978 The other columns are pairs, one pair per
+# dimension, containing the minimum and maximum values for that
+# dimension, respectively.
+#
+# Show this by observing that attempts to insert rows with max>min fail.
+#
+do_execsql_test 6.1 {
+  CREATE VIRTUAL TABLE rtF USING rtree(id, x1,x2, y1,y2);
+  CREATE VIRTUAL TABLE rtI USING rtree_i32(id, x1,x2, y1,y2, z1,z2);
+}
+foreach {tn x1 x2 y1 y2 ok} {
+  1   10.3 20.1   30.9 40.2   1
+  2   10.3 20.1   40.2 30.9   0
+  3   10.3 30.9   20.1 40.2   1
+  4   20.1 10.3   30.9 40.2   0
+} {
+  do_test 6.2.$tn {
+    catch { db eval { INSERT INTO rtF VALUES(NULL, $x1, $x2, $y1, $y2) } }
+  } [expr $ok==0]
+}
+foreach {tn x1 x2 y1 y2 z1 z2 ok} {
+  1   10 20   30 40  50 60  1
+  2   10 20   30 40  60 50  0
+  3   10 20   30 50  40 60  1
+  4   10 20   40 30  50 60  0
+  5   10 30   20 40  50 60  1
+  6   20 10   30 40  50 60  0
+} {
+  do_test 6.3.$tn {
+    catch { db eval { INSERT INTO rtI VALUES(NULL,$x1,$x2,$y1,$y2,$z1,$z2) } }
+  } [expr $ok==0]
+}
+
+# EVIDENCE-OF: R-08054-15429 The min/max-value pair columns are stored
+# as 32-bit floating point values for "rtree" virtual tables or as
+# 32-bit signed integers in "rtree_i32" virtual tables.
+#
+# Show this by showing that large values are rounded in ways consistent
+# with those two 32-bit types.
+do_execsql_test 7.1 {
+  DELETE FROM rtI;
+  INSERT INTO rtI VALUES(
+    0, -2000000000, 2000000000, -5000000000, 5000000000,
+    -1000000000000, 10000000000000
+  );
+  SELECT * FROM rtI;
+} {
+  0 -2000000000 2000000000 -705032704 705032704 727379968 1316134912
+}
+do_execsql_test 7.2 {
+  DELETE FROM rtF;
+  INSERT INTO rtF VALUES(
+    0, -2000000000, 2000000000, 
+    -1000000000000, 10000000000000
+  );
+  SELECT * FROM rtF;
+} {
+  0 -2000000000.0 2000000000.0 -1000000126976.0 10000000876544.0
+}
+
+# EVIDENCE-OF: R-47371-54529 Unlike regular SQLite tables which can
+# store data in a variety of datatypes and formats, the R*Tree rigidly
+# enforce these storage types.
+#
+# EVIDENCE-OF: R-39153-14977 If any other type of value is inserted into
+# such a column, the r-tree module silently converts it to the required
+# type before writing the new record to the database.
+do_execsql_test 8.1 {
+  DELETE FROM rtI;
+  INSERT INTO rtI VALUES(
+    1, 'hello world', X'616263', NULL, 44.5, 1000, 9999.9999
+  );
+  SELECT * FROM rtI;
+} {
+  1   0 0    0 44    1000 9999
+}
+
+do_execsql_test 8.2 {
+  SELECT 
+    typeof(x1), typeof(x2), typeof(y1), typeof(y2), typeof(z1), typeof(z2)
+  FROM rtI
+} {integer integer integer integer integer integer}
+
+do_execsql_test 8.3 {
+  DELETE FROM rtF;
+  INSERT INTO rtF VALUES(
+    1, 'hello world', X'616263', NULL, 44
+  );
+  SELECT * FROM rtF;
+} {
+  1   0.0 0.0    0.0 44.0
+}
+do_execsql_test 8.4 {
+  SELECT 
+    typeof(x1), typeof(x2), typeof(y1), typeof(y2)
+  FROM rtF
+} {real real real real}
+
+
+
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3.1 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-2
+reset_db
+
+foreach {tn name clist} {
+  1 t1 "id x1 x2"
+  2 t2 "id x1 x2   y1 y2   z1 z2"
+} {
+# EVIDENCE-OF: R-15142-18077 A new R*Tree index is created as follows:
+# CREATE VIRTUAL TABLE <name> USING rtree(<column-names>);
+  do_execsql_test 1.$tn.1 "
+    CREATE VIRTUAL TABLE $name USING rtree([join $clist ,])
+  "
+
+# EVIDENCE-OF: R-51698-09302 The <name> is the name your
+# application chooses for the R*Tree index and <column-names> is a
+# comma separated list of between 3 and 11 columns.
+  do_test 1.$tn.2 { column_name_list db $name } [list {*}$clist]
+
+# EVIDENCE-OF: R-50130-53472 The virtual <name> table creates
+# three shadow tables to actually store its content.
+  do_execsql_test 1.$tn.3 {
+    SELECT count(*) FROM sqlite_schema
+  } [expr 1+3]
+
+# EVIDENCE-OF: R-45256-35998 The names of these shadow tables are:
+# <name>_node <name>_rowid <name>_parent
+  do_execsql_test 1.$tn.4 {
+    SELECT name FROM sqlite_schema WHERE rootpage>0 ORDER BY 1
+  } [list ${name}_node ${name}_parent ${name}_rowid]
+
+  do_execsql_test 1.$tn.5 "DROP TABLE $name"
+}
+
+# EVIDENCE-OF: R-11241-54478 As an example, consider creating a
+# two-dimensional R*Tree index for use in spatial queries: CREATE
+# VIRTUAL TABLE demo_index USING rtree( id, -- Integer primary key minX,
+# maxX, -- Minimum and maximum X coordinate minY, maxY -- Minimum and
+# maximum Y coordinate );
+do_execsql_test 2.0 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(
+      id,              -- Integer primary key
+      minX, maxX,      -- Minimum and maximum X coordinate
+      minY, maxY       -- Minimum and maximum Y coordinate
+  );
+  INSERT INTO demo_index VALUES(1,2,3,4,5);
+  INSERT INTO demo_index VALUES(6,7,8,9,10);
+}
+
+# EVIDENCE-OF: R-02287-33529 The shadow tables are ordinary SQLite data
+# tables.
+#
+# Ordinary tables. With ordinary sqlite_schema entries.
+do_execsql_test 2.1 {
+  SELECT type, name, sql FROM sqlite_schema WHERE sql NOT LIKE '%virtual%'
+} {
+  table demo_index_rowid 
+    {CREATE TABLE "demo_index_rowid"(rowid INTEGER PRIMARY KEY,nodeno)} 
+  table demo_index_node
+    {CREATE TABLE "demo_index_node"(nodeno INTEGER PRIMARY KEY,data)} 
+  table demo_index_parent
+    {CREATE TABLE "demo_index_parent"(nodeno INTEGER PRIMARY KEY,parentnode)}
+}
+
+# EVIDENCE-OF: R-10863-13089 You can query them directly if you like,
+# though this unlikely to reveal anything particularly useful.
+#
+# Querying:
+do_execsql_test 2.2 {
+  SELECT count(*) FROM demo_index_node;
+  SELECT count(*) FROM demo_index_rowid;
+  SELECT count(*) FROM demo_index_parent;
+} {1 2 0}
+
+# EVIDENCE-OF: R-05650-46070 And you can UPDATE, DELETE, INSERT or even
+# DROP the shadow tables, though doing so will corrupt your R*Tree
+# index.
+do_execsql_test 2.3 {
+  DELETE FROM demo_index_rowid;
+  INSERT INTO demo_index_parent VALUES(2, 3);
+  UPDATE demo_index_node SET data = 'hello world'
+}
+do_catchsql_test 2.4 {
+  SELECT * FROM demo_index WHERE minX>10 AND maxX<30
+} {1 {database disk image is malformed}}
+do_execsql_test 2.5 {
+  DROP TABLE demo_index_rowid
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3.1.1 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-3
+reset_db
+
+# EVIDENCE-OF: R-44253-50720 In the argments to "rtree" in the CREATE
+# VIRTUAL TABLE statement, the names of the columns are taken from the
+# first token of each argument. All subsequent tokens within each
+# argument are silently ignored.
+#
+foreach {tn cols lCol} {
+  1 {(id TEXT, x1 TEXT, x2 TEXT, y1 TEXT, y2 TEXT)} {id x1 x2 y1 y2}
+  2 {(id TEXT, x1 UNIQUE, x2 TEXT, y1 NOT NULL, y2 TEXT)} {id x1 x2 y1 y2}
+  3 {(id, x1 DEFAULT 4, x2 TEXT, y1 NOT NULL, y2 TEXT)} {id x1 x2 y1 y2}
+} {
+  do_execsql_test 1.$tn.1 " CREATE VIRTUAL TABLE abc USING rtree $cols "
+  do_test 1.$tn.2 { column_name_list db abc } $lCol
+
+# EVIDENCE-OF: R-52032-06717 This means, for example, that if you try to
+# give a column a type affinity or add a constraint such as UNIQUE or
+# NOT NULL or DEFAULT to a column, those extra tokens are accepted as
+# valid, but they do not change the behavior of the rtree.
+
+  # Show there are no UNIQUE constraints
+  do_execsql_test 1.$tn.3 {
+    INSERT INTO abc VALUES(1, 10.0, 20.0, 10.0, 20.0);
+    INSERT INTO abc VALUES(2, 10.0, 20.0, 10.0, 20.0);
+  }
+
+  # Show the default values have not been modified
+  do_execsql_test 1.$tn.4 {
+    INSERT INTO abc DEFAULT VALUES;
+    SELECT * FROM abc WHERE rowid NOT IN (1,2)
+  } {3 0.0 0.0 0.0 0.0}
+
+  # Show that there are no NOT NULL constraints
+  do_execsql_test 1.$tn.5 {
+    INSERT INTO abc VALUES(NULL, NULL, NULL, NULL, NULL);
+    SELECT * FROM abc WHERE rowid NOT IN (1,2,3)
+  } {4 0.0 0.0 0.0 0.0}
+
+# EVIDENCE-OF: R-06893-30579 In an RTREE virtual table, the first column
+# always has a type affinity of INTEGER and all other data columns have
+# a type affinity of REAL.
+  do_execsql_test 1.$tn.5 {
+    INSERT INTO abc VALUES('5', '5', '5', '5', '5');
+    SELECT * FROM abc WHERE rowid NOT IN (1,2,3,4)
+  } {5 5.0 5.0 5.0 5.0}
+  do_execsql_test 1.$tn.6 {
+    SELECT type FROM pragma_table_info('abc') ORDER BY cid
+  } {INT REAL REAL REAL REAL}
+
+  do_execsql_test 1.$tn.7 " CREATE VIRTUAL TABLE abc2 USING rtree_i32 $cols "
+
+# EVIDENCE-OF: R-06224-52418 In an RTREE_I32 virtual table, all columns
+# have type affinity of INTEGER.
+  do_execsql_test 1.$tn.8 {
+    INSERT INTO abc2 VALUES('6.0', '6.0', '6.0', '6.0', '6.0');
+    SELECT * FROM abc2
+  } {6 6 6 6 6}
+  do_execsql_test 1.$tn.9 {
+    SELECT type FROM pragma_table_info('abc2') ORDER BY cid
+  } {INT INT INT INT INT}
+
+
+  do_execsql_test 1.$tn.10 {
+    DROP TABLE abc;
+    DROP TABLE abc2;
+  }
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3.2 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-4
+reset_db
+
+# EVIDENCE-OF: R-36195-31555 The usual INSERT, UPDATE, and DELETE
+# commands work on an R*Tree index just like on regular tables.
+#
+# Create a regular table and an rtree table. Perform INSERT, UPDATE and
+# DELETE operations, then observe that the contents of the two tables
+# are identical.
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2);
+  CREATE TABLE t1(id INTEGER PRIMARY KEY, x1 REAL, x2 REAL);
+}
+foreach {tn sql} {
+  1 "INSERT INTO %TBL% VALUES(5, 11,12)"
+  2 "INSERT INTO %TBL% VALUES(11, -11,14.5)"
+  3 "UPDATE %TBL% SET x1=-99 WHERE id=11"
+  4 "DELETE FROM %TBL% WHERE x2=14.5"
+  5 "DELETE FROM %TBL%"
+} {
+  set sql1 [string map {%TBL% rt} $sql]
+  set sql2 [string map {%TBL% t1} $sql]
+  do_execsql_test 1.$tn.0 $sql1
+  do_execsql_test 1.$tn.1 $sql2
+
+  set data1 [execsql {SELECT * FROM rt ORDER BY 1}]
+  set data2 [execsql {SELECT * FROM t1 ORDER BY 1}]
+
+  set res [expr {$data1==$data2}]
+  do_test 1.$tn.2 {set res} 1 
+}
+
+# EVIDENCE-OF: R-56987-45305
+do_execsql_test 2.0 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(
+      id,              -- Integer primary key
+      minX, maxX,      -- Minimum and maximum X coordinate
+      minY, maxY       -- Minimum and maximum Y coordinate
+  );
+
+  INSERT INTO demo_index VALUES
+    (28215, -80.781227, -80.604706, 35.208813, 35.297367),
+    (28216, -80.957283, -80.840599, 35.235920, 35.367825),
+    (28217, -80.960869, -80.869431, 35.133682, 35.208233),
+    (28226, -80.878983, -80.778275, 35.060287, 35.154446),
+    (28227, -80.745544, -80.555382, 35.130215, 35.236916),
+    (28244, -80.844208, -80.841988, 35.223728, 35.225471),
+    (28262, -80.809074, -80.682938, 35.276207, 35.377747),
+    (28269, -80.851471, -80.735718, 35.272560, 35.407925),
+    (28270, -80.794983, -80.728966, 35.059872, 35.161823),
+    (28273, -80.994766, -80.875259, 35.074734, 35.172836),
+    (28277, -80.876793, -80.767586, 35.001709, 35.101063),
+    (28278, -81.058029, -80.956375, 35.044701, 35.223812),
+    (28280, -80.844208, -80.841972, 35.225468, 35.227203),
+    (28282, -80.846382, -80.844193, 35.223972, 35.225655);
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3.3 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-5
+
+do_execsql_test 1.0 {
+  INSERT INTO demo_index 
+    SELECT NULL, minX, maxX, minY+0.2, maxY+0.2 FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX+0.2, maxX+0.2, minY, maxY FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX, maxX, minY+0.4, maxY+0.4 FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX+0.4, maxX+0.4, minY, maxY FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX, maxX, minY+0.8, maxY+0.8 FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX+0.8, maxX+0.8, minY, maxY FROM demo_index;
+
+  SELECT count(*) FROM demo_index;
+} {896}
+
+proc do_vmstep_test {tn sql expr} {
+  execsql $sql
+  set step [db status vmstep]
+  do_test $tn.$step "expr {[subst $expr]}" 1
+}
+
+# EVIDENCE-OF: R-45880-07724 Any valid query will work against an R*Tree
+# index.
+do_execsql_test 1.1.0 {
+  CREATE TABLE demo_tbl AS SELECT * FROM demo_index;
+}
+foreach {tn sql} {
+  1  {SELECT * FROM %TBL% ORDER BY 1}
+  2  {SELECT max(minX) FROM %TBL% ORDER BY 1}
+  3  {SELECT max(minX) FROM %TBL% GROUP BY round(minY) ORDER BY 1}
+} {
+  set sql1 [string map {%TBL% demo_index} $sql]
+  set sql2 [string map {%TBL% demo_tbl} $sql]
+
+  do_execsql_test 1.1.$tn $sql1 [execsql $sql2]
+}
+
+# EVIDENCE-OF: R-60814-18273 The R*Tree implementation just makes some
+# kinds of queries especially efficient.
+#
+# The second query is more efficient than the first.
+do_vmstep_test 1.2.1 {SELECT * FROM demo_index WHERE +rowid=28269} {$step>2000}
+do_vmstep_test 1.2.2 {SELECT * FROM demo_index WHERE rowid=28269} {$step<100}
+
+# EVIDENCE-OF: R-37800-50174 Queries against the primary key are
+# efficient: SELECT * FROM demo_index WHERE id=28269;
+do_vmstep_test 2.2 { SELECT * FROM demo_index WHERE id=28269 } {$step < 100}
+
+# EVIDENCE-OF: R-35847-18866 The big reason for using an R*Tree is so
+# that you can efficiently do range queries against the coordinate
+# ranges.
+#
+# EVIDENCE-OF: R-49927-54202
+do_vmstep_test 2.3 { 
+  SELECT id FROM demo_index
+    WHERE minX<=-80.77470 AND maxX>=-80.77470
+    AND minY<=35.37785  AND maxY>=35.37785;
+} {$step < 100}
+
+# EVIDENCE-OF: R-12823-37176 The query above will quickly locate all
+# zipcodes that contain the SQLite main office in their bounding box,
+# even if the R*Tree contains many entries.
+#
+do_execsql_test 2.4 { 
+  SELECT id FROM demo_index
+    WHERE minX<=-80.77470 AND maxX>=-80.77470
+    AND minY<=35.37785  AND maxY>=35.37785;
+} {
+  28322 28269 
+}
+
+# EVIDENCE-OF: R-07351-00257 For example, to find all zipcode bounding
+# boxes that overlap with the 28269 zipcode: SELECT A.id FROM demo_index
+# AS A, demo_index AS B WHERE A.maxX>=B.minX AND A.minX<=B.maxX
+# AND A.maxY>=B.minY AND A.minY<=B.maxY AND B.id=28269;
+#
+# Also check that it is efficient
+#
+# EVIDENCE-OF: R-39094-01937 This second query will find both 28269
+# entry (since every bounding box overlaps with itself) and also other
+# zipcode that is close enough to 28269 that their bounding boxes
+# overlap.
+#
+# 28269 is there in the result.
+#
+do_vmstep_test 2.5.1 {
+  SELECT A.id FROM demo_index AS A, demo_index AS B
+    WHERE A.maxX>=B.minX AND A.minX<=B.maxX
+    AND A.maxY>=B.minY AND A.minY<=B.maxY
+    AND B.id=28269
+} {$step < 100}
+do_execsql_test 2.5.2 {
+  SELECT A.id FROM demo_index AS A, demo_index AS B
+    WHERE A.maxX>=B.minX AND A.minX<=B.maxX
+    AND A.maxY>=B.minY AND A.minY<=B.maxY
+    AND B.id=28269;
+} {
+  28293 28216 28322 28286 28269 
+  28215 28336 28262 28291 28320 
+  28313 28298 28287
+}
+
+# EVIDENCE-OF: R-02723-34107 Note that it is not necessary for all
+# coordinates in an R*Tree index to be constrained in order for the
+# index search to be efficient.
+#
+# EVIDENCE-OF: R-22490-27246 One might, for example, want to query all
+# objects that overlap with the 35th parallel: SELECT id FROM demo_index
+# WHERE maxY>=35.0 AND minY<=35.0;
+do_vmstep_test 2.6.1 {
+  SELECT id FROM demo_index
+   WHERE maxY>=35.0  AND minY<=35.0;
+} {$step < 100}
+do_execsql_test 2.6.2 {
+  SELECT id FROM demo_index
+   WHERE maxY>=35.0  AND minY<=35.0;
+} {}
+
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3.4 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-6
+reset_db
+
+# EVIDENCE-OF: R-08327-00674 By default, coordinates are stored in an
+# R*Tree using 32-bit floating point values.
+#
+# EVIDENCE-OF: R-22000-53613 The default virtual table ("rtree") stores
+# coordinates as single-precision (4-byte) floating point numbers.
+#
+# Show this by showing that rounding is consistent with 32-bit float
+# rounding.
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rt USING rtree(id, a,b);
+}
+do_execsql_test 1.1 {
+  INSERT INTO rt VALUES(14, -1000000000000, 1000000000000);
+  SELECT * FROM rt;
+} {14 -1000000126976.0 1000000126976.0}
+
+# EVIDENCE-OF: R-39127-51288 When a coordinate cannot be exactly
+# represented by a 32-bit floating point number, the lower-bound
+# coordinates are rounded down and the upper-bound coordinates are
+# rounded up.
+foreach {tn val} {
+  1 100000000000
+  2 200000000000
+  3 300000000000
+  4 400000000000
+
+  5 -100000000000
+  6 -200000000000
+  7 -300000000000
+  8 -400000000000
+} {
+  set val [expr $val]
+  do_execsql_test 2.$tn.0 {DELETE FROM rt}
+  do_execsql_test 2.$tn.1 {INSERT INTO rt VALUES(23, $val, $val)}
+  do_execsql_test 2.$tn.2 {
+    SELECT $val>=a, $val<=b, a!=b FROM rt
+  } {1 1 1}
+}
+
+do_execsql_test 3.0 {
+  DROP TABLE rt;
+  CREATE VIRTUAL TABLE rt USING rtree(id, x1,x2, y1,y2);
+}
+
+# EVIDENCE-OF: R-45870-62834 Thus, bounding boxes might be slightly
+# larger than specified, but will never be any smaller.
+foreach {tn x1 x2 y1 y2} {
+  1 100000000000 200000000000 300000000000 400000000000
+} {
+  set val [expr $val]
+  do_execsql_test 3.$tn.0 {DELETE FROM rt}
+  do_execsql_test 3.$tn.1 {INSERT INTO rt VALUES(23, $x1, $x2, $y1, $y2)}
+  do_execsql_test 3.$tn.2 {
+    SELECT (x2-x1)*(y2-y1) >= ($x2-$x1)*($y2-$y1) FROM rt
+  } {1}
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 3.5 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-7
+reset_db
+
+# EVIDENCE-OF: R-55979-39402 It is the nature of the Guttman R-Tree
+# algorithm that any write might radically restructure the tree, and in
+# the process change the scan order of the nodes.
+#
+# In the test below, the INSERT marked "THIS INSERT!!" does not affect
+# the results of queries with an ORDER BY, but does affect the results
+# of one without an ORDER BY. Therefore the INSERT changed the scan 
+# order.
+do_execsql_test 1.0 { 
+  CREATE VIRTUAL TABLE rt USING rtree(id, minX, maxX);
+  WITH s(i) AS (
+    SELECT 1 UNION ALL SELECT i+1 FROM s WHERE i<51
+  )
+  INSERT INTO rt SELECT NULL, i%10, (i%10)+5 FROM s
+}
+do_execsql_test 1.1 { SELECT count(*) FROM rt_node } 1
+do_test 1.2 {
+  set res1 [db eval {SELECT * FROM rt WHERE maxX < 30}]
+  set res1o [db eval {SELECT * FROM rt WHERE maxX < 30 ORDER BY +id}]
+
+  db eval { INSERT INTO rt VALUES(NULL, 50, 50) }   ;# THIS INSERT!!
+
+  set res2 [db eval {SELECT * FROM rt WHERE maxX < 30}]
+  set res2o [db eval {SELECT * FROM rt WHERE maxX < 30 ORDER BY +id}]
+  list [expr {$res1==$res2}] [expr {$res1o==$res2o}]
+} {0 1}
+
+do_execsql_test 1.3 { SELECT count(*) FROM rt_node } 3
+
+# EVIDENCE-OF: R-00683-48865 For this reason, it is not generally
+# possible to modify the R-Tree in the middle of a query of the R-Tree.
+# Attempts to do so will fail with a SQLITE_LOCKED "database table is
+# locked" error.
+#
+# SQLITE_LOCKED==6
+#
+do_test 1.4 {
+  set nCnt 3
+  db eval { SELECT * FROM rt WHERE minX>0 AND maxX<12 } {
+    incr nCnt -1
+    if {$nCnt==0} {
+      set rc [catch {db eval {
+        INSERT INTO rt VALUES(NULL, 51, 51);
+      }} msg]
+      set errorcode [db errorcode]
+      break
+    }
+  }
+
+  list $errorcode $rc $msg
+} {6 1 {database table is locked}}
+
+# EVIDENCE-OF: R-19740-29710 So, for example, suppose an application
+# runs one query against an R-Tree like this: SELECT id FROM demo_index
+# WHERE maxY>=35.0 AND minY<=35.0; Then for each "id" value
+# returned, suppose the application creates an UPDATE statement like the
+# following and binds the "id" value returned against the "?1"
+# parameter: UPDATE demo_index SET maxY=maxY+0.5 WHERE id=?1;
+#
+# EVIDENCE-OF: R-52919-32711 Then the UPDATE might fail with an
+# SQLITE_LOCKED error.
+do_execsql_test 2.0 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(
+      id,              -- Integer primary key
+      minX, maxX,      -- Minimum and maximum X coordinate
+      minY, maxY       -- Minimum and maximum Y coordinate
+  );
+  INSERT INTO demo_index VALUES
+    (28215, -80.781227, -80.604706, 35.208813, 35.297367),
+    (28216, -80.957283, -80.840599, 35.235920, 35.367825),
+    (28217, -80.960869, -80.869431, 35.133682, 35.208233),
+    (28226, -80.878983, -80.778275, 35.060287, 35.154446);
+}
+do_test 2.1 {
+  db eval { SELECT id FROM demo_index WHERE maxY>=35.0  AND minY<=35.0 } {
+    set rc [catch { 
+      db eval { UPDATE demo_index SET maxY=maxY+0.5 WHERE id=$id } 
+    } msg]
+    set errorcode [db errorcode]
+    break
+  }
+  list $errorcode $rc $msg
+} {6 1 {database table is locked}}
+
+# EVIDENCE-OF: R-32604-49843 Ordinary tables in SQLite are able to read
+# and write at the same time.
+#
+do_execsql_test 3.0 {
+  CREATE TABLE x1(a INTEGER PRIMARY KEY, b, c);
+  INSERT INTO x1 VALUES(1, 1, 1);
+  INSERT INTO x1 VALUES(2, 2, 2);
+  INSERT INTO x1 VALUES(3, 3, 3);
+  INSERT INTO x1 VALUES(4, 4, 4);
+}
+do_test 3.1 {
+  unset -nocomplain res
+  set res [list]
+  db eval { SELECT * FROM x1 } {
+    lappend res $a $b $c
+    switch -- $a {
+      1 {
+        db eval { INSERT INTO x1 VALUES(5, 5, 5) }
+      }
+      2 {
+        db eval { UPDATE x1 SET c=20 WHERE a=2 }
+      }
+      3 {
+        db eval { DELETE FROM x1 WHERE c IN (3,4) }
+      }
+    }
+  }
+  set res
+} {1 1 1 2 2 2 3 3 3 5 5 5}
+do_execsql_test 3.2 {
+  SELECT * FROM x1
+} {1 1 1  2 2 20  5 5 5}
+
+# EVIDENCE-OF: R-06177-00576 And R-Tree can appear to read and write at
+# the same time in some circumstances, if it can figure out how to
+# reliably run the query to completion before starting the update.
+#
+# In 8.2, it can, it 8.1, it cannot.
+do_test 8.1 {
+  db eval { SELECT * FROM rt } {
+    set rc [catch { db eval { INSERT INTO rt VALUES(53,53,53) } } msg]
+    break;
+  }
+  list $rc $msg
+} {1 {database table is locked}}
+do_test 8.2 {
+  db eval { SELECT * FROM rt ORDER BY +id } {
+    set rc [catch { db eval { INSERT INTO rt VALUES(53,53,53) } } msg]
+    break
+  }
+  list $rc $msg
+} {0 {}}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 4 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-8
+reset_db
+
+# EVIDENCE-OF: R-21062-30088 For the example above, one might create an
+# auxiliary table as follows: CREATE TABLE demo_data( id INTEGER PRIMARY
+# KEY, -- primary key objname TEXT, -- name of the object objtype TEXT,
+# -- object type boundary BLOB -- detailed boundary of object );
+#
+# One might.
+#
+do_execsql_test 1.0 {
+  CREATE TABLE demo_data(
+      id INTEGER PRIMARY KEY,  -- primary key
+      objname TEXT,            -- name of the object
+      objtype TEXT,            -- object type
+      boundary BLOB            -- detailed boundary of object
+  );
+}
+
+do_execsql_test 1.1 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(
+      id,              -- Integer primary key
+      minX, maxX,      -- Minimum and maximum X coordinate
+      minY, maxY       -- Minimum and maximum Y coordinate
+  );
+
+  INSERT INTO demo_index VALUES
+    (28215, -80.781227, -80.604706, 35.208813, 35.297367),
+    (28216, -80.957283, -80.840599, 35.235920, 35.367825),
+    (28217, -80.960869, -80.869431, 35.133682, 35.208233),
+    (28226, -80.878983, -80.778275, 35.060287, 35.154446),
+    (28227, -80.745544, -80.555382, 35.130215, 35.236916),
+    (28244, -80.844208, -80.841988, 35.223728, 35.225471),
+    (28262, -80.809074, -80.682938, 35.276207, 35.377747),
+    (28269, -80.851471, -80.735718, 35.272560, 35.407925),
+    (28270, -80.794983, -80.728966, 35.059872, 35.161823),
+    (28273, -80.994766, -80.875259, 35.074734, 35.172836),
+    (28277, -80.876793, -80.767586, 35.001709, 35.101063),
+    (28278, -81.058029, -80.956375, 35.044701, 35.223812),
+    (28280, -80.844208, -80.841972, 35.225468, 35.227203),
+    (28282, -80.846382, -80.844193, 35.223972, 35.225655);
+
+  INSERT INTO demo_index 
+    SELECT NULL, minX, maxX, minY+0.2, maxY+0.2 FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX+0.2, maxX+0.2, minY, maxY FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX, maxX, minY+0.4, maxY+0.4 FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX+0.4, maxX+0.4, minY, maxY FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX, maxX, minY+0.8, maxY+0.8 FROM demo_index;
+  INSERT INTO demo_index 
+    SELECT NULL, minX+0.8, maxX+0.8, minY, maxY FROM demo_index;
+
+  INSERT INTO demo_data(id) SELECT id FROM demo_index;
+
+  SELECT count(*) FROM demo_index;
+} {896}
+
+set ::contained_in 0
+proc contained_in {args} {incr ::contained_in ; return 0}
+db func contained_in contained_in
+
+# EVIDENCE-OF: R-32671-43888 Then an efficient way to find the specific
+# ZIP code for the main SQLite office would be to run a query like this:
+# SELECT objname FROM demo_data, demo_index WHERE
+# demo_data.id=demo_index.id AND contained_in(demo_data.boundary,
+# 35.37785, -80.77470) AND minX<=-80.77470 AND maxX>=-80.77470 AND
+# minY<=35.37785 AND maxY>=35.37785;
+do_vmstep_test 1.2 {
+  SELECT objname FROM demo_data, demo_index
+    WHERE demo_data.id=demo_index.id
+    AND contained_in(demo_data.boundary, 35.37785, -80.77470)
+    AND minX<=-80.77470 AND maxX>=-80.77470
+    AND minY<=35.37785  AND maxY>=35.37785;
+} {$step<100}
+set ::contained_in1 $::contained_in
+
+# EVIDENCE-OF: R-32761-23915 One would get the same answer without the
+# use of the R*Tree index using the following simpler query: SELECT
+# objname FROM demo_data WHERE contained_in(demo_data.boundary,
+# 35.37785, -80.77470);
+set ::contained_in 0
+do_vmstep_test 1.3 {
+  SELECT objname FROM demo_data
+    WHERE contained_in(demo_data.boundary, 35.37785, -80.77470);
+} {$step>3200}
+
+# EVIDENCE-OF: R-40261-32799 The problem with this latter query is that
+# it must apply the contained_in() function to all entries in the
+# demo_data table.
+#
+# 896 of them, IIRC.
+do_test 1.4 {
+  set ::contained_in
+} 896
+
+# EVIDENCE-OF: R-24212-52761 The use of the R*Tree in the penultimate
+# query reduces the number of calls to contained_in() function to a
+# small subset of the entire table.
+#
+# 2 is a small subset of 896.
+#
+# EVIDENCE-OF: R-39057-63901 The R*Tree index did not find the exact
+# answer itself, it merely limited the search space.
+#
+# contained_in() filtered out those 2 rows.
+do_test 1.5 {
+  set ::contained_in1
+} {2}
+
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 4.1 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-9
+reset_db
+
+# EVIDENCE-OF: R-46566-43213 Beginning with SQLite version 3.24.0
+# (2018-06-04), r-tree tables can have auxiliary columns that store
+# arbitrary data. Auxiliary columns can be used in place of secondary
+# tables such as "demo_data".
+#
+# EVIDENCE-OF: R-41287-48160 Auxiliary columns are marked with a "+"
+# symbol before the column name.
+#
+# This interface cannot conveniently be used to prove anything about 
+# versions of SQLite prior to 3.24.0.
+#
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rta USING rtree(
+    id, u1,u2,  v1,v2,   +aux
+  );
+
+  INSERT INTO rta(aux) VALUES(NULL);
+  INSERT INTO rta(aux) VALUES(45);
+  INSERT INTO rta(aux) VALUES(22.3);
+  INSERT INTO rta(aux) VALUES('hello');
+  INSERT INTO rta(aux) VALUES(X'ABCD');
+
+  SELECT typeof(aux), quote(aux) FROM rta;
+} {
+  null NULL
+  integer 45
+  real 22.3
+  text 'hello'
+  blob X'ABCD'
+}
+
+# EVIDENCE-OF: R-30514-26093 Auxiliary columns must come after all of
+# the coordinate boundary columns.
+foreach {tn cols} {
+  1 "id x1,x2, +extra,  y1,y2"
+  2 "extra, +id x1,x2, y1,y2"
+  3 "id, x1,+x2, extra, y1,y2"
+} {
+  do_catchsql_test 2.$tn "
+    CREATE VIRTUAL TABLE rrr USING rtree($cols)
+  " {1 {Auxiliary rtree columns must be last}}
+}
+do_catchsql_test 3.0 {
+  CREATE VIRTUAL TABLE rrr USING rtree(+id, extra, x1, x2);
+} {1 {near "+": syntax error}}
+
+# EVIDENCE-OF: R-01280-03635 An RTREE table can have no more than 100
+# columns total. In other words, the count of columns including the
+# integer primary key column, the coordinate boundary columns, and all
+# auxiliary columns must be 100 or less.
+do_catchsql_test 3.1 {
+  CREATE VIRTUAL TABLE r1 USING rtree(intid, u1,u2,
+    +c00, +c01, +c02, +c03, +c04, +c05, +c06, +c07, +c08, +c09,
+    +c10, +c11, +c12, +c13, +c14, +c15, +c16, +c17, +c18, +c19,
+    +c20, +c21, +c22, +c23, +c24, +c25, +c26, +c27, +c28, +c29,
+    +c30, +c31, +c32, +c33, +c34, +c35, +c36, +c37, +c38, +c39,
+    +c40, +c41, +c42, +c43, +c44, +c45, +c46, +c47, +c48, +c49,
+    +c50, +c51, +c52, +c53, +c54, +c55, +c56, +c57, +c58, +c59,
+    +c60, +c61, +c62, +c63, +c64, +c65, +c66, +c67, +c68, +c69,
+    +c70, +c71, +c72, +c73, +c74, +c75, +c76, +c77, +c78, +c79,
+    +c80, +c81, +c82, +c83, +c84, +c85, +c86, +c87, +c88, +c89,
+    +c90, +c91, +c92, +c93, +c94, +c95, +c96
+  );
+} {0 {}}
+do_catchsql_test 3.2 {
+  DROP TABLE r1;
+  CREATE VIRTUAL TABLE r1 USING rtree(intid, u1,u2,
+    +c00, +c01, +c02, +c03, +c04, +c05, +c06, +c07, +c08, +c09,
+    +c10, +c11, +c12, +c13, +c14, +c15, +c16, +c17, +c18, +c19,
+    +c20, +c21, +c22, +c23, +c24, +c25, +c26, +c27, +c28, +c29,
+    +c30, +c31, +c32, +c33, +c34, +c35, +c36, +c37, +c38, +c39,
+    +c40, +c41, +c42, +c43, +c44, +c45, +c46, +c47, +c48, +c49,
+    +c50, +c51, +c52, +c53, +c54, +c55, +c56, +c57, +c58, +c59,
+    +c60, +c61, +c62, +c63, +c64, +c65, +c66, +c67, +c68, +c69,
+    +c70, +c71, +c72, +c73, +c74, +c75, +c76, +c77, +c78, +c79,
+    +c80, +c81, +c82, +c83, +c84, +c85, +c86, +c87, +c88, +c89,
+    +c90, +c91, +c92, +c93, +c94, +c95, +c96, +c97
+  );
+} {1 {Too many columns for an rtree table}}
+do_catchsql_test 3.3 {
+  CREATE VIRTUAL TABLE r1 USING rtree(intid, u1,u2, v1,v2,
+    +c00, +c01, +c02, +c03, +c04, +c05, +c06, +c07, +c08, +c09,
+    +c10, +c11, +c12, +c13, +c14, +c15, +c16, +c17, +c18, +c19,
+    +c20, +c21, +c22, +c23, +c24, +c25, +c26, +c27, +c28, +c29,
+    +c30, +c31, +c32, +c33, +c34, +c35, +c36, +c37, +c38, +c39,
+    +c40, +c41, +c42, +c43, +c44, +c45, +c46, +c47, +c48, +c49,
+    +c50, +c51, +c52, +c53, +c54, +c55, +c56, +c57, +c58, +c59,
+    +c60, +c61, +c62, +c63, +c64, +c65, +c66, +c67, +c68, +c69,
+    +c70, +c71, +c72, +c73, +c74, +c75, +c76, +c77, +c78, +c79,
+    +c80, +c81, +c82, +c83, +c84, +c85, +c86, +c87, +c88, +c89,
+    +c90, +c91, +c92, +c93, +c94,
+  );
+} {0 {}}
+do_catchsql_test 3.4 {
+  DROP TABLE r1;
+  CREATE VIRTUAL TABLE r1 USING rtree(intid, u1,u2, v1,v2,
+    +c00, +c01, +c02, +c03, +c04, +c05, +c06, +c07, +c08, +c09,
+    +c10, +c11, +c12, +c13, +c14, +c15, +c16, +c17, +c18, +c19,
+    +c20, +c21, +c22, +c23, +c24, +c25, +c26, +c27, +c28, +c29,
+    +c30, +c31, +c32, +c33, +c34, +c35, +c36, +c37, +c38, +c39,
+    +c40, +c41, +c42, +c43, +c44, +c45, +c46, +c47, +c48, +c49,
+    +c50, +c51, +c52, +c53, +c54, +c55, +c56, +c57, +c58, +c59,
+    +c60, +c61, +c62, +c63, +c64, +c65, +c66, +c67, +c68, +c69,
+    +c70, +c71, +c72, +c73, +c74, +c75, +c76, +c77, +c78, +c79,
+    +c80, +c81, +c82, +c83, +c84, +c85, +c86, +c87, +c88, +c89,
+    +c90, +c91, +c92, +c93, +c94, +c95,
+  );
+} {1 {Too many columns for an rtree table}}
+
+# EVIDENCE-OF: R-05552-15084
+do_execsql_test 4.0 {
+  CREATE VIRTUAL TABLE demo_index2 USING rtree(
+      id,              -- Integer primary key
+      minX, maxX,      -- Minimum and maximum X coordinate
+      minY, maxY,      -- Minimum and maximum Y coordinate
+      +objname TEXT,   -- name of the object
+      +objtype TEXT,   -- object type
+      +boundary BLOB   -- detailed boundary of object
+  );
+}
+do_execsql_test 4.1 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(
+      id,              -- Integer primary key
+      minX, maxX,      -- Minimum and maximum X coordinate
+      minY, maxY       -- Minimum and maximum Y coordinate
+  );
+  CREATE TABLE demo_data(
+      id INTEGER PRIMARY KEY,  -- primary key
+      objname TEXT,            -- name of the object
+      objtype TEXT,            -- object type
+      boundary BLOB            -- detailed boundary of object
+  );
+
+  INSERT INTO demo_index2(id) VALUES(1);
+  INSERT INTO demo_index(id) VALUES(1);
+  INSERT INTO demo_data(id) VALUES(1);
+}
+do_test 4.2 {
+  catch { array unset R }
+  db eval {SELECT * FROM demo_index2} R { set r1 [array names R] }
+  catch { array unset R }
+  db eval {SELECT * FROM demo_index NATURAL JOIN demo_data } R { 
+    set r2 [array names R] 
+  }
+  expr {$r1==$r2}
+} {1}
+
+# EVIDENCE-OF: R-26099-32169 SELECT objname FROM demo_index2 WHERE
+# contained_in(boundary, 35.37785, -80.77470) AND minX<=-80.77470 AND
+# maxX>=-80.77470 AND minY<=35.37785 AND maxY>=35.37785;
+do_execsql_test 4.3.1 {
+  DELETE FROM demo_index2;
+  INSERT INTO demo_index2(id,minX,maxX,minY,maxY) VALUES
+    (28215, -80.781227, -80.604706, 35.208813, 35.297367),
+    (28216, -80.957283, -80.840599, 35.235920, 35.367825),
+    (28217, -80.960869, -80.869431, 35.133682, 35.208233),
+    (28226, -80.878983, -80.778275, 35.060287, 35.154446),
+    (28227, -80.745544, -80.555382, 35.130215, 35.236916),
+    (28244, -80.844208, -80.841988, 35.223728, 35.225471),
+    (28262, -80.809074, -80.682938, 35.276207, 35.377747),
+    (28269, -80.851471, -80.735718, 35.272560, 35.407925),
+    (28270, -80.794983, -80.728966, 35.059872, 35.161823),
+    (28273, -80.994766, -80.875259, 35.074734, 35.172836),
+    (28277, -80.876793, -80.767586, 35.001709, 35.101063),
+    (28278, -81.058029, -80.956375, 35.044701, 35.223812),
+    (28280, -80.844208, -80.841972, 35.225468, 35.227203),
+    (28282, -80.846382, -80.844193, 35.223972, 35.225655);
+}
+set ::contained_in 0
+proc contained_in {args} {
+  incr ::contained_in
+  return 0
+}
+db func contained_in contained_in
+do_execsql_test 4.3.2 {
+  SELECT objname FROM demo_index2
+    WHERE contained_in(boundary, 35.37785, -80.77470)
+    AND minX<=-80.77470 AND maxX>=-80.77470
+    AND minY<=35.37785  AND maxY>=35.37785;
+}
+do_test 4.3.3 {
+  # Function invoked only once because r-tree filtering happened first.
+  set ::contained_in
+} 1
+set ::contained_in 0
+do_execsql_test 4.3.4 {
+  SELECT objname FROM demo_index2
+    WHERE contained_in(boundary, 35.37785, -80.77470)
+}
+do_test 4.3.3 {
+  # Function invoked 14 times because no r-tree filtering. Inefficient.
+  set ::contained_in
+} 14
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 4.1.1 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-9
+reset_db
+
+# EVIDENCE-OF: R-24021-02490 For auxiliary columns, only the name of the
+# column matters. The type affinity is ignored.
+#
+# EVIDENCE-OF: R-39906-44154 Constraints such as NOT NULL, UNIQUE,
+# REFERENCES, or CHECK are also ignored.
+do_execsql_test 1.0 { PRAGMA foreign_keys = on }
+foreach {tn auxcol nm} {
+  1 "+extra INTEGER" extra
+  2 "+extra TEXT"    extra
+  3 "+extra BLOB"    extra
+  4 "+extra REAL"    extra
+
+  5 "+col NOT NULL"                 col
+  6 "+col CHECK (col IS NOT NULL)"  col
+  7 "+col REFERENCES tbl(x)"        col
+} {
+  do_execsql_test 1.$tn.1 "
+    CREATE VIRTUAL TABLE rt USING rtree_i32(k, a,b, $auxcol)
+  "
+
+  # Check that the aux column has no affinity. Or NOT NULL constraint.
+  # And that the aux column is the child key of an FK constraint.
+  #
+  do_execsql_test 1.$tn.2 "
+    INSERT INTO rt($nm) VALUES(NULL), (45), (-123.2), ('456'), (X'ABCD');
+    SELECT typeof($nm), quote($nm) FROM rt;
+  " {
+    null NULL
+    integer 45
+    real -123.2
+    text '456'
+    blob X'ABCD'
+  }
+
+  # Check that there is no UNIQUE constraint either.
+  #
+  do_execsql_test 1.$tn.3 "
+    INSERT INTO rt($nm) VALUES('xyz'), ('xyz'), ('xyz');
+  "
+
+  do_execsql_test 1.$tn.2 {
+    DROP TABLE rt
+  }
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 5 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-10
+
+# EVIDENCE-OF: R-21011-43790 If integer coordinates are desired, declare
+# the table using "rtree_i32" instead: CREATE VIRTUAL TABLE intrtree
+# USING rtree_i32(id,x0,x1,y0,y1,z0,z1);
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE intrtree USING rtree_i32(id,x0,x1,y0,y1,z0,z1);
+  INSERT INTO intrtree DEFAULT VALUES;
+  SELECT typeof(x0) FROM intrtree;
+} {integer}
+
+# EVIDENCE-OF: R-09193-49806 An rtree_i32 stores coordinates as 32-bit
+# signed integers.
+#
+# Show that coordinates are cast in a way consistent with casting to
+# a signed 32-bit integer.
+do_execsql_test 1.1 {
+  DELETE FROM intrtree;
+  INSERT INTO intrtree VALUES(333,
+      1<<44, (1<<44)+1,
+      10000000000, 10000000001,
+      -10000000001, -10000000000
+  );
+  SELECT * FROM intrtree;
+} {
+  333 0 1 1410065408 1410065409 -1410065409 -1410065408
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 7.1 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-11
+reset_db
+
+# This command assumes that the argument is a node blob for a 2 dimensional
+# i32 r-tree table. It decodes and returns a list of cells from the node
+# as a list. Each cell is itself a list of the following form:
+#
+#    {$rowid $minX $maxX $minY $maxY}
+#
+# For internal (non-leaf) nodes, the rowid is replaced by the child node
+# number.
+#
+proc rnode {aData} {
+  set nDim 2
+
+  set nData [string length $aData]
+  set nBytePerCell [expr (8 + 2*$nDim*4)]
+  binary scan [string range $aData 2 3] S nCell
+
+  set res [list]
+  for {set i 0} {$i < $nCell} {incr i} {
+    set iOff [expr $i*$nBytePerCell+4]
+    set cell [string range $aData $iOff [expr $iOff+$nBytePerCell-1]]
+    binary scan $cell WIIII rowid x1 x2 y1 y2
+    lappend res [list $rowid $x1 $x2 $y1 $y2]
+  }
+
+  return $res
+}
+
+# aData must be a node blob. This command returns true if the node contains
+# rowid $rowid, or false otherwise.
+#
+proc rnode_contains {aData rowid} {
+  set L [rnode $aData]
+  foreach cell $L {
+    set r [lindex $cell 0]
+    if {$r==$rowid} { return 1 }
+  }
+  return 0
+}
+
+proc rnode_replace_cell {aData iCell cell} {
+  set aCell [binary format WIIII {*}$cell]
+  set nDim 2
+  set nBytePerCell [expr (8 + 2*$nDim*4)]
+  set iOff [expr $iCell*$nBytePerCell+4]
+
+  set aNew [binary format a*a*a* \
+      [string range $aData 0 $iOff-1]     \
+      $aCell     \
+      [string range $aData $iOff+$nBytePerCell end] \
+  ]
+  return $aNew
+}
+
+db function rnode rnode
+db function rnode_contains rnode_contains
+db function rnode_replace_cell rnode_replace_cell
+
+foreach {tn nm} {
+  1 x1
+  2 asdfghjkl
+  3 hello_world
+} {
+  do_execsql_test 1.$tn.1 "
+    CREATE VIRTUAL TABLE $nm USING rtree(a,b,c,d,e);
+  "
+
+  # EVIDENCE-OF: R-33789-46762 The content of an R*Tree index is actually
+  # stored in three ordinary SQLite tables with names derived from the
+  # name of the R*Tree.
+  #
+  # EVIDENCE-OF: R-39849-06566 This is their schema: CREATE TABLE
+  # %_node(nodeno INTEGER PRIMARY KEY, data) CREATE TABLE %_parent(nodeno
+  # INTEGER PRIMARY KEY, parentnode) CREATE TABLE %_rowid(rowid INTEGER
+  # PRIMARY KEY, nodeno)
+  #
+  # EVIDENCE-OF: R-07489-10051 The "%" in the name of each shadow table is
+  # replaced by the name of the R*Tree virtual table. So, if the name of
+  # the R*Tree table is "xyz" then the three shadow tables would be
+  # "xyz_node", "xyz_parent", and "xyz_rowid".
+  do_execsql_test 1.$tn.2 {
+    SELECT sql FROM sqlite_schema WHERE name!=$nm ORDER BY 1
+  } [string map [list % $nm] "
+    {CREATE TABLE \"%_node\"(nodeno INTEGER PRIMARY KEY,data)}
+    {CREATE TABLE \"%_parent\"(nodeno INTEGER PRIMARY KEY,parentnode)}
+    {CREATE TABLE \"%_rowid\"(rowid INTEGER PRIMARY KEY,nodeno)}
+  "]
+
+  do_execsql_test 1.$tn "DROP TABLE $nm"
+}
+
+
+# EVIDENCE-OF: R-51070-59303 There is one entry in the %_node table for
+# each R*Tree node.
+#
+# The following creates a 6 node r-tree structure.
+#
+do_execsql_test 2.0 {
+  CREATE VIRTUAL TABLE r1 USING rtree_i32(i, x1,x2, y1,y2);
+  WITH t(i) AS (
+    VALUES(1) UNION SELECT i+1 FROM t WHERE i<110
+  )
+  INSERT INTO r1 SELECT i, (i%10), (i%10)+2, (i%6), (i%7)+6 FROM t;
+}
+do_execsql_test 2.1 {
+  SELECT count(*) FROM r1_node;
+} 6
+
+# EVIDENCE-OF: R-27261-09153 All nodes other than the root have an entry
+# in the %_parent shadow table that identifies the parent node.
+#
+# In this case nodes 2-6 are the children of node 1.
+#
+do_execsql_test 2.3 {
+  SELECT nodeno, parentnode FROM r1_parent
+} {2 1  3 1  4 1  5 1  6 1}
+
+# EVIDENCE-OF: R-02358-35037 The %_rowid shadow table maps entry rowids
+# to the node that contains that entry.
+#
+do_execsql_test 2.4 {
+  SELECT 'failed' FROM r1_rowid WHERE 0==rnode_contains(
+    (SELECT data FROM r1_node WHERE nodeno=r1_rowid.nodeno), rowid
+  )
+}
+do_test 2.5 {
+  db eval { SELECT nodeno, data FROM r1_node WHERE nodeno!=1 } {
+    set L [rnode $data]
+    foreach cell $L {
+      set rowid [lindex $cell 0]
+      set rowid_nodeno 0
+      db eval {SELECT nodeno AS rowid_nodeno FROM r1_rowid WHERE rowid=$rowid} {
+        break
+      }
+      if {$rowid_nodeno!=$nodeno} { error "data mismatch!" }
+    }
+  }
+} {}
+
+# EVIDENCE-OF: R-65201-22208 Extra columns appended to the %_rowid table
+# hold the content of auxiliary columns.
+#
+# EVIDENCE-OF: R-44161-28345 The names of these extra %_rowid columns
+# are probably not the same as the actual auxiliary column names.
+#
+# In this case, the auxiliary columns are named "e1" and "e2". The
+# extra %_rowid columns are named "a0" and "a1".
+#
+do_execsql_test 3.0 {
+  CREATE VIRTUAL TABLE rtaux USING rtree(id, x1,x2, y1,y2, +e1, +e2);
+  SELECT sql FROM sqlite_schema WHERE name='rtaux_rowid';
+} {
+  {CREATE TABLE "rtaux_rowid"(rowid INTEGER PRIMARY KEY,nodeno,a0,a1)}
+}
+do_execsql_test 3.1 {
+  INSERT INTO rtaux(e1, e2) VALUES('hello', 'world'), (123, 456);
+}
+do_execsql_test 3.2 {
+  SELECT a0, a1 FROM rtaux_rowid;
+} {
+  hello world  123 456
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 7.2 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc-12
+reset_db
+forcedelete test.db2
+
+db function rnode rnode
+db function rnode_contains rnode_contains
+db function rnode_replace_cell rnode_replace_cell
+
+# EVIDENCE-OF: R-13571-45795 The scalar SQL function rtreecheck(R) or
+# rtreecheck(S,R) runs an integrity check on the rtree table named R
+# contained within database S.
+#
+# EVIDENCE-OF: R-36011-59963 The function returns a human-language
+# description of any problems found, or the string 'ok' if everything is
+# ok.
+#
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rt1 USING rtree(id, a, b);
+  WITH s(i) AS (
+    VALUES(1) UNION ALL SELECT i+1 FROM s WHERE i<200
+  )
+  INSERT INTO rt1 SELECT i, i, i FROM s;
+
+  ATTACH 'test.db2' AS 'aux';
+  CREATE VIRTUAL TABLE aux.rt1 USING rtree(id, a, b);
+  INSERT INTO aux.rt1 SELECT * FROM rt1;
+}
+
+do_execsql_test 1.1.1 { SELECT rtreecheck('rt1'); } {ok}
+do_execsql_test 1.1.2 { SELECT rtreecheck('main', 'rt1'); } {ok}
+do_execsql_test 1.1.3 { SELECT rtreecheck('aux', 'rt1'); } {ok}
+do_catchsql_test 1.1.4 { 
+  SELECT rtreecheck('nosuchdb', 'rt1'); 
+} {1 {SQL logic error}}
+
+# Corrupt the table in database 'main':
+do_execsql_test 1.2.1 { UPDATE rt1_node SET nodeno=21 WHERE nodeno=3; }
+do_execsql_test 1.2.1 { SELECT rtreecheck('rt1')=='ok'; } {0}
+do_execsql_test 1.2.2 { SELECT rtreecheck('main', 'rt1')=='ok'; } {0}
+do_execsql_test 1.2.3 { SELECT rtreecheck('aux', 'rt1')=='ok'; } {1}
+do_execsql_test 1.2.4 { UPDATE rt1_node SET nodeno=3 WHERE nodeno=21; }
+
+# Corrupt the table in database 'aux':
+do_execsql_test 1.2.1 { UPDATE aux.rt1_node SET nodeno=21 WHERE nodeno=3; }
+do_execsql_test 1.2.1 { SELECT rtreecheck('rt1')=='ok'; } {1}
+do_execsql_test 1.2.2 { SELECT rtreecheck('main', 'rt1')=='ok'; } {1}
+do_execsql_test 1.2.3 { SELECT rtreecheck('aux', 'rt1')=='ok'; } {0}
+do_execsql_test 1.2.4 { UPDATE rt1_node SET nodeno=3 WHERE nodeno=21; }
+
+# EVIDENCE-OF: R-45759-33459 Example: To verify that an R*Tree named
+# "demo_index" is well-formed and internally consistent, run: SELECT
+# rtreecheck('demo_index');
+do_execsql_test 2.0 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(id, x1,x2, y1,y2);
+  INSERT INTO demo_index SELECT id, a, b, a, b FROM rt1;
+}
+do_execsql_test 2.1 { SELECT rtreecheck('demo_index') } {ok}
+do_execsql_test 2.2 {
+  UPDATE demo_index_rowid SET nodeno=44 WHERE rowid=44;
+  SELECT rtreecheck('demo_index');
+} {{Found (44 -> 44) in %_rowid table, expected (44 -> 4)}}
+
+
+do_execsql_test 3.0 {
+  CREATE VIRTUAL TABLE rt2 USING rtree_i32(id, a, b, c, d);
+  WITH s(i) AS (
+    VALUES(1) UNION ALL SELECT i+1 FROM s WHERE i<200
+  )
+  INSERT INTO rt2 SELECT i, i, i+2, i, i+2 FROM s;
+}
+
+# EVIDENCE-OF: R-02555-31045 for each dimension, (coord1 <= coord2).
+#
+execsql BEGIN
+do_test 3.1 {
+  set cell [
+    lindex [execsql {SELECT rnode(data) FROM rt2_node WHERE nodeno=3}] 0 3
+  ]
+  set cell [list [lindex $cell 0]       \
+    [lindex $cell 2] [lindex $cell 1]   \
+    [lindex $cell 3] [lindex $cell 4]   \
+  ]
+  execsql { 
+    UPDATE rt2_node SET data=rnode_replace_cell(data, 3, $cell) WHERE nodeno=3 
+  }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Dimension 0 of cell 3 on node 3 is corrupt}}
+execsql ROLLBACK
+
+# EVIDENCE-OF: R-13844-15873 unless the cell is on the root node, that
+# the cell is bounded by the parent cell on the parent node.
+#
+execsql BEGIN
+do_test 3.2 {
+  set cell [
+    lindex [execsql {SELECT rnode(data) FROM rt2_node WHERE nodeno=3}] 0 3
+  ]
+  lset cell 3 450
+  lset cell 4 451
+  execsql { 
+    UPDATE rt2_node SET data=rnode_replace_cell(data, 3, $cell) WHERE nodeno=3 
+  }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Dimension 1 of cell 3 on node 3 is corrupt relative to parent}}
+execsql ROLLBACK
+
+# EVIDENCE-OF: R-02505-03621 for leaf nodes, that there is an entry in
+# the %_rowid table corresponding to the cell's rowid value that points
+# to the correct node.
+#
+execsql BEGIN
+do_test 3.3 {
+  execsql { 
+    UPDATE rt2_rowid SET rowid=452 WHERE rowid=100
+  }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Mapping (100 -> 6) missing from %_rowid table}}
+execsql ROLLBACK
+
+# EVIDENCE-OF: R-50927-02218 for cells on non-leaf nodes, that there is
+# an entry in the %_parent table mapping from the cell's child node to
+# the node that it resides on.
+#
+execsql BEGIN
+do_test 3.4.1 {
+  execsql { 
+    UPDATE rt2_parent SET parentnode=123 WHERE nodeno=3
+  }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Found (3 -> 123) in %_parent table, expected (3 -> 1)}}
+execsql ROLLBACK
+execsql BEGIN
+do_test 3.4.2 {
+  execsql { 
+    UPDATE rt2_parent SET nodeno=123 WHERE nodeno=3
+  }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Mapping (3 -> 1) missing from %_parent table}}
+execsql ROLLBACK
+
+# EVIDENCE-OF: R-23235-09153 That there are the same number of entries
+# in the %_rowid table as there are leaf cells in the r-tree structure,
+# and that there is a leaf cell that corresponds to each entry in the
+# %_rowid table.
+execsql BEGIN
+do_test 3.5 {
+  execsql { INSERT INTO rt2_rowid VALUES(1000, 1000) }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Wrong number of entries in %_rowid table - expected 200, actual 201}}
+execsql ROLLBACK
+
+# EVIDENCE-OF: R-62800-43436 That there are the same number of entries
+# in the %_parent table as there are non-leaf cells in the r-tree
+# structure, and that there is a non-leaf cell that corresponds to each
+# entry in the %_parent table.
+execsql BEGIN
+do_test 3.6 {
+  execsql { INSERT INTO rt2_parent VALUES(1000, 1000) }
+  execsql { SELECT rtreecheck('rt2') }
+} {{Wrong number of entries in %_parent table - expected 9, actual 10}}
+execsql ROLLBACK
+
+
+
+finish_test
diff --git a/ext/rtree/rtreedoc2.test b/ext/rtree/rtreedoc2.test
new file mode 100644
index 0000000..ca0c6b3
--- /dev/null
+++ b/ext/rtree/rtreedoc2.test
@@ -0,0 +1,346 @@
+# 2021 September 13
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+}
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+set testprefix rtreedoc2
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 6 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc2-1
+
+# EVIDENCE-OF: R-35254-48865 A call to one of the above APIs creates a
+# new SQL function named by the second parameter (zQueryFunc or zGeom).
+#
+# [register_circle_geom db] registers new geometry callback "Qcircle"
+# and legacy implementation "circle". Test that these do actually appear.
+#
+do_execsql_test 1.1.0 {
+  SELECT * FROM pragma_function_list WHERE name IN('circle', 'qcircle');
+} {
+}
+do_test 1.1 {
+  register_circle_geom db
+} {SQLITE_OK}
+do_execsql_test 1.1.2 {
+  SELECT * FROM pragma_function_list WHERE name = 'circle' AND enc='utf8';
+} {
+  circle 0 s utf8 -1 0
+}
+do_execsql_test 1.1.3 {
+  SELECT * FROM pragma_function_list WHERE name = 'qcircle' AND enc='utf8';
+} {
+  qcircle 0 s utf8 -1 0
+} 
+
+do_execsql_test 1.2.0 { SELECT circle(1, 2, 3); } {{}}
+do_execsql_test 1.2.1 { SELECT qcircle(1, 2, 3); } {{}}
+
+# EVIDENCE-OF: R-61427-46983
+do_execsql_test 1.3.0 {
+  CREATE VIRTUAL TABLE demo_index USING rtree(id, x1,x2, y1,y2);
+  INSERT INTO demo_index VALUES(10, 45,45,  24,24);
+  INSERT INTO demo_index VALUES(20, 50,50,  28,28);
+  INSERT INTO demo_index VALUES(30, 43,43,  22,22);
+}
+do_execsql_test 1.3.1 {
+  SELECT id FROM demo_index WHERE id MATCH circle(45.3, 22.9, 5.0)
+} {10 30}
+
+# EVIDENCE-OF: R-16907-50223 The SQL syntax for custom queries is the
+# same regardless of which interface, sqlite3_rtree_geometry_callback()
+# or sqlite3_rtree_query_callback(), is used to register the SQL
+# function.
+do_execsql_test 1.3.2 {
+  SELECT id FROM demo_index WHERE id MATCH qcircle(45.3, 22.9, 5.0, 1)
+} {10 30}
+
+
+# EVIDENCE-OF: R-59634-51678 When that SQL function appears on the
+# right-hand side of the MATCH operator and the left-hand side of the
+# MATCH operator is any column in the R*Tree virtual table, then the
+# callback defined by the third argument (xQueryFunc or xGeom) is
+# invoked to determine if a particular object or subtree overlaps the
+# desired region.
+proc box_geom {args} {
+  lappend ::box_geom [concat [lindex $args 0] [lrange $args 2 end-1]]
+  return ""
+}
+register_box_geom db box_geom
+set box_geom [list]
+do_execsql_test 1.3.2 {
+  SELECT id FROM demo_index WHERE id MATCH box(43,46, 21,25);
+} {10 30}
+do_test 1.3.3 {
+  set ::box_geom
+} [list {*}{
+  {box {43.0 46.0 21.0 25.0} {45.0 45.0 24.0 24.0}}
+  {box {43.0 46.0 21.0 25.0} {50.0 50.0 28.0 28.0}} 
+  {box {43.0 46.0 21.0 25.0} {43.0 43.0 22.0 22.0}}
+}]
+
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+# Section 6 of documentation.
+#-------------------------------------------------------------------------
+#-------------------------------------------------------------------------
+set testprefix rtreedoc2-2
+
+# EVIDENCE-OF: R-02424-24769 The second argument is the number of
+# coordinates in each r-tree entry, and is always the same for any given
+# R*Tree.
+#
+# EVIDENCE-OF: R-40260-16838 The number of coordinates is 2 for a
+# 1-dimensional R*Tree, 4 for a 2-dimensional R*Tree, 6 for a
+# 3-dimensional R*Tree, and so forth.
+#
+# The second argument refered to above is the length of the list passed
+# as the 3rd parameter to the Tcl script.
+#
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rt1 USING rtree(id, x1,x2);
+  CREATE VIRTUAL TABLE rt2 USING rtree(id, x1,x2, y1,y2);
+  CREATE VIRTUAL TABLE rt3 USING rtree(id, x1,x2, y1,y2, z1,z2);
+
+  INSERT INTO rt1 DEFAULT VALUES;
+  INSERT INTO rt2 DEFAULT VALUES;
+  INSERT INTO rt3 DEFAULT VALUES;
+}
+foreach {tn tbl nCoord} {
+  1 rt1 2     
+  2 rt2 4
+  3 rt3 6
+} {
+  set ::box_geom [list]
+  do_catchsql_test 1.$tn.1 "
+    SELECT id FROM $tbl WHERE id MATCH box();
+  " {1 {SQL logic error}}
+
+  do_test 1.$tn.2 {
+    llength [lindex $::box_geom 0 2]
+  } $nCoord
+}
+
+# EVIDENCE-OF: R-28051-48608 If xGeom returns anything other than
+# SQLITE_OK, then the r-tree query will abort with an error.
+proc box_geom {args} {
+  error "an error!"
+}
+do_catchsql_test 2.0 {
+  SELECT * FROM rt2 WHERE id MATCH box(22,23, 24,25); 
+} {1 {SQL logic error}}
+
+do_execsql_test 3.0 {
+  INSERT INTO rt1 VALUES(10, 10, 10);
+  INSERT INTO rt1 VALUES(11, 11, 11);
+  INSERT INTO rt1 VALUES(12, 12, 12);
+  INSERT INTO rt1 VALUES(13, 13, 13);
+  INSERT INTO rt1 VALUES(14, 14, 14);
+}
+
+# EVIDENCE-OF: R-53759-57366 The exact same sqlite3_rtree_geometry
+# structure is used for every callback for same MATCH operator in the
+# same query.
+proc box_geom {args} {
+  lappend ::ptr_list [lindex $args 4]
+  return 0
+}
+set ::ptr_list [list]
+do_execsql_test 3.1 {
+  SELECT * FROM rt1 WHERE id MATCH box(1,1);
+}
+do_test 3.2 {
+  set val [lindex $::ptr_list 0]
+  foreach p $::ptr_list {
+    if {$p!=$val} {error "pointer mismatch"}
+  }
+} {}
+
+# EVIDENCE-OF: R-60247-35692 The contents of the sqlite3_rtree_geometry
+# structure are initialized by SQLite but are not subsequently modified.
+proc box_geom {args} {
+  lappend ::box_geom [concat [lindex $args 0] [lrange $args 2 end-1]]
+  if {[llength $::box_geom]==3} {
+    return "zero"
+  }
+  return ""
+}
+set ::box_geom [list]
+do_catchsql_test 3.2 {
+  SELECT * FROM rt1 WHERE id MATCH box(1,1);
+} {1 {SQL logic error}}
+do_test 3.3 {
+  set ::box_geom
+} [list {*}{
+  {box {1.0 1.0} {0.0 0.0}} 
+  {box {1.0 1.0} {10.0 10.0}} 
+  {box {1.0 1.0} {11.0 11.0}} 
+  {box 0.0 {12.0 12.0}}
+}]
+
+# EVIDENCE-OF: R-31246-29731 The pContext member of the
+# sqlite3_rtree_geometry structure is always set to a copy of the
+# pContext argument passed to sqlite3_rtree_geometry_callback() when the
+# callback is registered.
+reset_db
+do_execsql_test 4.0 {
+  CREATE VIRTUAL TABLE r1 USING rtree(id, minX,maxX, minY,maxY);
+  WITH s(i) AS (
+    VALUES(1) UNION ALL SELECT i+1 FROM s WHERE i<120
+  )
+  INSERT INTO r1 SELECT i,i,i+1,  200,201 FROM s;
+}
+set ctx [register_box_geom db box_geom]
+set ::box_geom [list]
+proc box_geom {args} {
+  lappend ::box_geom [lindex $args 1]
+  return ""
+}
+do_execsql_test 4.1 {
+  SELECT count(*) FROM r1 WHERE id MATCH box(0,150,199,201)
+} 120
+do_test 4.2 {
+  foreach g $::box_geom {
+    if {$g!=$ctx} {error "pointer mismatch"}
+  }
+} {}
+
+# EVIDENCE-OF: R-09904-19077 The aParam[] array (size nParam) contains
+# the parameter values passed to the SQL function on the right-hand side
+# of the MATCH operator.
+proc box_geom {args} {
+  set ::box_geom [lindex $args 2]
+}
+foreach {tn q vals} {
+  1 "SELECT count(*) FROM r1 WHERE id MATCH box(1,2,3)" {1.0 2.0 3.0}
+  2 "SELECT count(*) FROM r1 WHERE id MATCH box(10001)" {10001.0}
+  3 "SELECT count(*) FROM r1 WHERE id MATCH box(-10001)" {-10001.0}
+} {
+  do_catchsql_test 5.$tn.1 $q {1 {SQL logic error}}
+  do_test 5.$tn.2 { set ::box_geom } $vals
+}
+
+do_execsql_test 5.0 {
+  CREATE VIRTUAL TABLE myrtree USING rtree(id, x1,x2);
+  INSERT INTO myrtree VALUES(1, 1, 1);
+  INSERT INTO myrtree VALUES(2, 2, 2);
+  INSERT INTO myrtree VALUES(3, 3, 3);
+}
+
+# EVIDENCE-OF: R-44448-00687 The pUser and xDelUser members of the
+# sqlite3_rtree_geometry structure are initially set to NULL.
+set ::box_geom_calls 0
+proc box_geom {args} {
+  incr ::box_geom_calls
+  return user_is_zero
+}
+do_execsql_test 5.1.1 {
+  SELECT * FROM myrtree WHERE id MATCH box(4, 5);
+} 
+do_test 5.1.2 { set ::box_geom_calls } 3
+
+
+# EVIDENCE-OF: R-55837-00155 The pUser variable may be set by the
+# callback implementation to any arbitrary value that may be useful to
+# subsequent invocations of the callback within the same query (for
+# example, a pointer to a complicated data structure used to test for
+# region intersection).
+#
+# EVIDENCE-OF: R-34745-08839 If the xDelUser variable is set to a
+# non-NULL value, then after the query has finished running SQLite
+# automatically invokes it with the value of the pUser variable as the
+# only argument.
+#
+set ::box_geom_calls 0
+proc box_geom {args} {
+  incr ::box_geom_calls
+  switch -- $::box_geom_calls {
+    1 {
+      return user_is_zero
+    }
+    2 {
+      return [list user box_geom_finalizer]
+    }
+  }
+  return ""
+}
+proc box_geom_finalizer {} {
+  set ::box_geom_finalizer "::box_geom_calls is $::box_geom_calls"
+}
+do_execsql_test 5.1.1 {
+  SELECT * FROM myrtree WHERE id MATCH box(4, 5);
+} 
+do_test 5.1.2 { set ::box_geom_calls } 3
+do_test 5.1.3 {
+  set ::box_geom_finalizer
+} {::box_geom_calls is 3}
+ 
+
+# EVIDENCE-OF: R-28176-28813 The xGeom callback always does a
+# depth-first search of the r-tree.
+#
+# For a breadth first search, final test case would return "B L" only.
+#
+do_execsql_test 6.0 {
+  CREATE VIRTUAL TABLE xyz USING rtree(x, x1,x2, y1,y2);
+  WITH s(i) AS (
+    VALUES(1) UNION ALL SELECT i+1 FROM s WHERE i<15
+  )
+  INSERT INTO xyz SELECT NULL, one.i,one.i+1,  two.i,two.i+1 FROM s one, s two;
+}
+do_execsql_test 6.1 {
+  SELECT count(*) FROM xyz_node
+} {10}
+proc box_geom {args} {
+  set coords [lindex $args 3]
+  set area [expr {
+    ([lindex $coords 1]-[lindex $coords 0]) * 
+    ([lindex $coords 3]-[lindex $coords 2])
+  }]
+  if {$area==1} {
+    lappend ::box_geom_calls L
+  } else {
+    lappend ::box_geom_calls B
+  }
+}
+set ::box_geom_calls [list]
+do_execsql_test 6.2 {
+  SELECT count(*) FROM xyz WHERE x MATCH box(0,20,0,20)
+} 225
+do_test 6.3 {
+  set prev ""
+  set box_calls [list]
+  foreach c $::box_geom_calls {
+    if {$c!=$prev} {
+      lappend ::box_calls $c
+      set prev $c
+    }
+  }
+  set ::box_calls
+} {B L B L B L B L B L B L B L B L B L}
+
+
+finish_test
+
diff --git a/ext/rtree/rtreedoc3.test b/ext/rtree/rtreedoc3.test
new file mode 100644
index 0000000..0403409
--- /dev/null
+++ b/ext/rtree/rtreedoc3.test
@@ -0,0 +1,292 @@
+# 2021 September 13
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing the r-tree extension.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+}
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+set testprefix rtreedoc3
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+
+# This command assumes that the argument is a node blob for a 2 dimensional
+# i32 r-tree table. It decodes and returns a list of cells from the node
+# as a list. Each cell is itself a list of the following form:
+#
+#    {$rowid $minX $maxX $minY $maxY}
+#
+# For internal (non-leaf) nodes, the rowid is replaced by the child node
+# number.
+#
+proc rnode_cells {aData} {
+  set nDim 2
+
+  set nData [string length $aData]
+  set nBytePerCell [expr (8 + 2*$nDim*4)]
+  binary scan [string range $aData 2 3] S nCell
+
+  set res [list]
+  for {set i 0} {$i < $nCell} {incr i} {
+    set iOff [expr $i*$nBytePerCell+4]
+    set cell [string range $aData $iOff [expr $iOff+$nBytePerCell-1]]
+    binary scan $cell WIIII rowid x1 x2 y1 y2
+    lappend res [list $rowid $x1 $x2 $y1 $y2]
+  }
+
+  return $res
+}
+
+# Interpret the first two bytes of the blob passed as the only parameter
+# as a 16-bit big-endian integer and return the value. If this blob is
+# the root node of an r-tree, this value is the height of the tree.
+#
+proc rnode_height {aData} {
+  binary scan [string range $aData 0 1] S nHeight
+  return $nHeight
+}
+
+# Return a blob containing node iNode of r-tree "rt".
+#
+proc rt_node_get {iNode} {
+  db one { SELECT data FROM rt_node WHERE nodeno=$iNode }
+}
+
+
+#--------------------------------------------------------------
+# API:
+#
+#    pq_init 
+#      Initialize a new test.
+#
+#    pq_test_callback
+#      Invoked each time the xQueryCallback function is called. This Tcl
+#      command checks that the arguments that SQLite passed to xQueryCallback
+#      are as expected.
+#
+#    pq_test_row
+#      Invoked each time a row is returned. Checks that the row returned
+#      was predicted by the documentation.
+#
+# DATA STRUCTURE:
+#    The priority queue is stored as a Tcl list. The order of elements in 
+#    the list is unimportant - it is just used as a set here. Each element
+#    in the priority queue is itself a list. The first element is the
+#    priority value for the entry (a real). Following this is a list of
+#    key-value pairs that make up the entries fields.
+#
+proc pq_init {} {
+  global Q 
+  set Q(pri_queue)  [list]
+
+  set nHeight [rnode_height [rt_node_get 1]]
+  set nCell [llength [rnode_cells [rt_node_get 1]]]
+
+  # EVIDENCE-OF: R-54708-13595 An R*Tree query is initialized by making
+  # the root node the only entry in a priority queue sorted by rScore.
+  lappend Q(pri_queue) [list 0.0 [list \
+    iLevel [expr $nHeight+1] \
+    iChild 1                 \
+    iCurrent   0             \
+  ]]
+}
+
+proc pq_extract {} {
+  global Q
+  if {[llength $Q(pri_queue)]==0} {
+    error "priority queue is empty!"
+  }
+
+  # Find the priority queue entry with the lowest score.
+  #
+  # EVIDENCE-OF: R-47257-47871 Smaller scores are processed first.
+  set iBest 0
+  set rBestScore [lindex $Q(pri_queue) 0 0]
+  for {set ii 1} {$ii < [llength $Q(pri_queue)]} {incr ii} {
+    set rScore [expr [lindex $Q(pri_queue) $ii 0]]
+    if {$rScore<$rBestScore} {
+      set rBestScore $rScore
+      set iBest $ii
+    }
+  }
+
+  # Extract the entry with the lowest score from the queue and return it. 
+  #
+  # EVIDENCE-OF: R-60002-49798 The query proceeds by extracting the entry
+  # from the priority queue that has the lowest score.
+  set ret [lindex $Q(pri_queue) $iBest]
+  set Q(pri_queue) [lreplace $Q(pri_queue) $iBest $iBest]
+
+  return $ret
+}
+
+proc pq_new_entry {rScore iLevel cell} {
+  global Q
+
+  set rowid_name "iChild"
+  if {$iLevel==0} { set rowid_name "iRowid" }
+
+  set kv [list]
+  lappend kv aCoord [lrange $cell 1 end]
+  lappend kv iLevel $iLevel
+
+  if {$iLevel==0} {
+    lappend kv iRowid [lindex $cell 0]
+  } else {
+    lappend kv iChild [lindex $cell 0]
+    lappend kv iCurrent 0
+  }
+
+  lappend Q(pri_queue) [list $rScore $kv]
+}
+
+proc pq_test_callback {L res} {
+  #pq_debug "pq_test_callback $L -> $res"
+  global Q
+
+  array set G $L    ;# "Got" - as in stuff passed to xQuery
+
+  # EVIDENCE-OF: R-65127-42665 If the extracted priority queue entry is a
+  # node (a subtree), then the next child of that node is passed to the
+  # xQueryFunc callback.
+  #
+  # If it had been a leaf, the row should have been returned, instead of
+  # xQueryCallback being called on a child - as is happening here.
+  foreach {rParentScore parent} [pq_extract] {}
+  array set P $parent ;# "Parent" - as in parent of expected cell
+  if {$P(iLevel)==0} { error "query callback mismatch (1)" }
+  set child_node [rnode_cells [rt_node_get $P(iChild)]]
+  set expected_cell [lindex $child_node $P(iCurrent)]
+  set expected_coords [lrange $expected_cell 1 end]
+  if {[llength $expected_coords] != [llength $G(aCoord)]} {
+  puts [array get P]
+  puts "E: $expected_coords  G: $G(aCoord)"
+    error "coordinate mismatch in query callback (1)"
+  }
+  foreach a [lrange $expected_cell 1 end] b $G(aCoord) {
+    if {$a!=$b} { error "coordinate mismatch in query callback (2)" }
+  }
+
+  # Check level is as expected
+  #
+  if {$G(iLevel) != $P(iLevel)-1} {
+    error "iLevel mismatch in query callback (1)"
+  }
+
+  # Unless the callback returned NOT_WITHIN, add the entry to the priority
+  # queue.
+  #
+  # EVIDENCE-OF: R-28754-35153 Those subelements for which the xQueryFunc
+  # callback sets eWithin to PARTLY_WITHIN or FULLY_WITHIN are added to
+  # the priority queue using the score supplied by the callback.
+  #
+  # EVIDENCE-OF: R-08681-45277 Subelements that return NOT_WITHIN are
+  # discarded.
+  set r [lindex $res 0]
+  set rScore [lindex $res 1]
+  if {$r!="fully" && $r!="partly" && $r!="not"} {
+    error "unknown result: $r - expected \"fully\", \"partly\" or \"not\""
+  }
+  if {$r!="not"} {
+    pq_new_entry $rScore [expr $P(iLevel)-1] $expected_cell
+  }
+
+  # EVIDENCE-OF: R-07194-63805 If the node has more children then it is
+  # returned to the priority queue. Otherwise it is discarded.
+  incr P(iCurrent)
+  if {$P(iCurrent)<[llength $child_node]} {
+    lappend Q(pri_queue) [list $rParentScore [array get P]]
+  }
+}
+
+proc pq_test_result {id x1 x2 y1 y2} {
+  #pq_debug "pq_test_result $id $x1 $x2 $y1 $y2"
+  foreach {rScore next} [pq_extract] {}
+
+  # The extracted entry must be a leaf (otherwise, xQueryCallback would
+  # have been called on the extracted entries children instead of just
+  # returning the data).
+  #
+  # EVIDENCE-OF: R-13214-54017 If that entry is a leaf (meaning that it is
+  # an actual R*Tree entry and not a subtree) then that entry is returned
+  # as one row of the query result.
+  array set N $next
+  if {$N(iLevel)!=0} { error "result row mismatch (1)" }
+
+  if {$x1!=[lindex $N(aCoord) 0] || $x2!=[lindex $N(aCoord) 1]
+   || $y1!=[lindex $N(aCoord) 2] || $y2!=[lindex $N(aCoord) 3]
+  } {
+    if {$N(iLevel)!=0} { error "result row mismatch (2)" }
+  }
+
+  if {$id!=$N(iRowid)} { error "result row mismatch (3)" }
+}
+
+proc pq_done {} {
+  global Q
+  # EVIDENCE-OF: R-57438-45968 The query runs until the priority queue is
+  # empty.
+  if {[llength $Q(pri_queue)]>0} {
+    error "priority queue is not empty!"
+  }
+}
+
+proc pq_debug {caption} {
+  global Q
+
+  puts "**** $caption ****"
+  set i 0
+  foreach q [lsort -real -index 0 $Q(pri_queue)] { 
+    puts "PQ $i: $q" 
+    incr i
+  }
+}
+
+#--------------------------------------------------------------
+
+proc box_query {a} {
+  set res [list fully [expr rand()]]
+  pq_test_callback $a $res
+  return $res
+}
+
+register_box_query db box_query
+
+do_execsql_test 1.0 {
+  CREATE VIRTUAL TABLE rt USING rtree_i32(id,  x1,x2,  y1,y2);
+  WITH s(i) AS (
+    SELECT 0 UNION ALL SELECT i+1 FROM s WHERE i<64
+  )
+  INSERT INTO rt SELECT NULL, a.i, a.i+1, b.i, b.i+1 FROM s a, s b;
+}
+
+proc box_query {a} {
+  set res [list fully [expr rand()]]
+  pq_test_callback $a $res
+  return $res
+}
+
+pq_init
+db eval { SELECT id, x1,x2, y1,y2 FROM rt WHERE id MATCH qbox() } {
+  pq_test_result $id $x1 $x2 $y1 $y2
+}
+pq_done
+
+finish_test
+
+
diff --git a/ext/rtree/rtreefuzz001.test b/ext/rtree/rtreefuzz001.test
new file mode 100644
index 0000000..58fd179
--- /dev/null
+++ b/ext/rtree/rtreefuzz001.test
@@ -0,0 +1,1211 @@
+# 2012-12-21
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+#
+# Test cases for corrupt database files.
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+} 
+source $testdir/tester.tcl
+
+ifcapable !deserialize||!rtree {
+  finish_test
+  return
+}
+database_may_be_corrupt
+
+do_test rtreefuzz001-100 {
+  sqlite3 db {}
+  db deserialize [decode_hexdb {
+| size 24576 pagesize 4096 filename c1b.db
+| page 1 offset 0
+|      0: 53 51 4c 69 74 65 20 66 6f 72 6d 61 74 20 33 00   SQLite format 3.
+|     16: 10 00 01 01 00 40 20 20 00 00 00 03 00 00 00 06   .....@  ........
+|     32: 00 00 00 00 00 00 00 00 00 00 00 03 00 00 00 04   ................
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+|   2672: 00 00 00 06 44 40 80 00 00 40 a0 00 00 40 c0 00   ....D@...@...@..
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+|   2864: 04 00 93 24 00 01 00 02 00 00 00 00 00 00 00 03   ...$............
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+|   2896: 00 00 00 00 00 00 00 02 00 00 00 00 41 20 00 00   ............A ..
+|   2912: 00 00 00 00 41 20 00 00 00 00 00 00 00 00 00 00   ....A ..........
+|   4080: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 05 03   ................
+| page 4 offset 12288
+|      0: 0d 00 00 00 00 10 00 00 00 00 00 00 00 00 00 00   ................
+| page 5 offset 16384
+|      0: 0d 00 00 00 03 01 87 00 0b 2d 06 5a 01 87 00 00   .........-.Z....
+|    384: 00 00 00 00 00 00 00 89 50 03 04 00 93 24 00 00   ........P....$..
+|    400: 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00   ................
+|    688: 00 00 00 00 42 c8 00 00 42 4c 00 00 42 00 00 00   ....B...BL..B...
+|    720: 03 eb 40 40 00 00 40 80 00 00 00 00 00 00 3f 80   ..@@..@.......?.
+|    736: 00 00 00 00 00 00 00 00 03 ea 40 00 00 00 40 40   ..........@...@@
+|    752: 00 00 00 00 00 00 3f 80 00 00 00 00 00 00 00 00   ......?.........
+|    768: 03 e9 3f 80 00 00 40 00 00 00 00 00 00 00 3f 80   ..?...@.......?.
+|    784: 00 00 00 00 00 00 00 00 03 e8 00 00 00 00 3f 80   ..............?.
+|    800: 00 00 00 00 00 00 3f 80 00 00 00 00 00 00 00 00   ......?.........
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+|   1760: 00 00 00 00 01 00 00 00 00 41 20 00 00 00 00 00   .........A .....
+|   1776: 00 41 0e 00 00 00 00 00 00 00 00 04 4d 3f 80 00   .A..........M?..
+|   1792: 00 40 00 00 00 3f 80 00 00 40 00 00 00 00 00 00   .@...?...@......
+|   1808: 00 00 00 04 b1 3f 80 00 00 40 00 00 00 40 00 00   .....?...@...@..
+|   1824: 00 40 40 00 00 00 00 00 00 00 00 05 15 3f 80 00   .@@..........?..
+|   1840: 00 40 00 00 00 40 40 00 00 40 80 00 00 00 00 00   .@...@@..@......
+|   1856: 00 00 00 05 79 3f 80 00 00 40 00 00 00 40 80 00   ....y?...@...@..
+|   1872: 00 40 a0 00 00 00 00 00 00 00 00 05 dd 3f 80 00   .@...........?..
+|   1888: 00 40 00 00 00 40 a0 00 00 40 c0 00 00 00 00 00   .@...@...@......
+|   1904: 00 00 00 04 4e 40 00 00 00 40 40 00 00 3f 80 00   ....N@...@@..?..
+|   1920: 00 40 00 00 00 00 00 00 00 00 00 04 b2 40 00 00   .@...........@..
+|   1936: 00 40 40 00 00 40 00 00 00 40 40 00 00 00 00 00   .@@..@...@@.....
+|   1952: 00 00 00 05 16 40 00 00 00 40 40 00 00 40 40 00   .....@...@@..@@.
+|   1968: 00 40 80 00 00 00 00 00 00 00 00 05 7a 40 00 00   .@..........z@..
+|   1984: 00 40 40 00 00 40 80 00 00 40 a0 00 00 00 00 00   .@@..@...@......
+|   2000: 00 00 00 05 de 40 00 00 00 40 40 00 00 40 a0 00   .....@...@@..@..
+|   2016: 00 40 c0 00 00 00 00 00 00 00 00 04 4f 40 40 00   .@..........O@@.
+|   2032: 00 40 80 00 00 3f 80 00 00 40 00 00 00 00 00 00   .@...?...@......
+|   2048: 00 00 00 04 b3 40 40 00 00 40 80 00 00 40 00 00   .....@@..@...@..
+|   2064: 00 40 40 00 00 00 00 00 00 00 00 05 17 40 40 00   .@@..........@@.
+|   2080: 00 40 80 00 00 40 40 00 00 40 80 00 00 00 00 00   .@...@@..@......
+|   2096: 00 00 00 05 7b 40 40 00 00 40 80 00 00 40 80 00   .....@@..@...@..
+|   2112: 00 40 a0 00 00 00 00 00 00 00 00 05 df 40 40 00   .@...........@@.
+|   2128: 00 40 80 00 00 40 a0 00 00 40 c0 00 00 00 00 00   .@...@...@......
+|   2144: 00 00 00 03 ec 40 80 00 00 40 a0 00 00 00 00 00   .....@...@......
+|   2160: 00 3f 80 00 00 00 00 00 00 00 00 04 50 40 80 00   .?..........P@..
+|   2176: 00 40 a0 00 00 3f 80 00 00 40 00 00 00 00 00 00   .@...?...@......
+|   2192: 00 00 00 04 b4 40 80 00 00 40 a0 00 00 40 00 00   .....@...@...@..
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+|   2240: 00 00 00 05 7c 40 80 00 00 40 a0 00 00 40 80 00   ....|@...@...@..
+|   2256: 00 40 a0 00 00 00 00 00 00 00 00 05 e0 40 80 00   .@...........@..
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+|   2288: 00 00 00 03 f0 41 00 00 00 41 10 00 00 00 00 00   .....A...A......
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+|   2336: 00 00 00 04 b8 41 00 00 00 41 10 00 00 40 00 00   .....A...A...@..
+|   2352: 00 40 40 00 00 00 00 00 00 00 00 05 1c 41 00 00   .@@..........A..
+|   2368: 00 41 10 00 00 40 40 00 00 40 80 00 00 00 00 00   .A...@@..@......
+|   2384: 00 00 00 05 80 41 00 00 00 41 10 00 00 40 80 00   .....A...A...@..
+|   2400: 00 40 a0 00 00 00 00 00 00 00 00 05 e4 41 00 00   .@...........A..
+|   2416: 00 41 10 00 00 40 a0 00 00 40 c0 00 00 00 00 00   .A...@...@......
+|   2432: 00 00 00 06 48 41 00 00 00 41 10 00 00 40 c0 00   ....HA...A...@..
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+|   2480: 00 00 00 07 10 41 00 00 00 41 10 00 00 41 00 00   .....A...A...A..
+|   2496: 00 41 10 00 00 00 00 00 00 00 00 03 f1 41 10 00   .A...........A..
+|   2512: 00 41 20 00 00 00 00 00 00 3f 80 00 00 00 00 00   .A ......?......
+|   2528: 00 00 00 04 55 41 10 00 00 41 20 00 00 3f 80 00   ....UA...A ..?..
+|   2544: 00 40 00 00 00 00 00 00 00 00 00 04 b9 41 10 00   .@...........A..
+|   2560: 00 41 20 00 00 40 00 00 00 40 40 00 00 00 00 00   .A ..@...@@.....
+|   2576: 00 00 00 05 1d 41 10 00 00 41 20 00 00 40 40 00   .....A...A ..@@.
+|   2592: 00 40 80 00 00 00 00 00 00 00 00 05 81 41 10 00   .@...........A..
+|   2608: 00 41 20 00 00 40 80 00 00 40 a0 00 00 00 00 00   .A ..@...@......
+|   2624: 00 00 00 05 e5 41 10 00 00 41 20 00 00 40 a0 00   .....A...A ..@..
+|   2640: 00 40 c0 00 00 00 00 00 00 00 00 06 49 41 10 00   .@..........IA..
+|   2656: 00 41 20 00 00 40 c0 00 00 40 e0 00 00 00 00 00   .A ..@...@......
+|   2672: 00 00 00 06 ad 41 10 00 00 41 20 00 00 40 e0 00   .....A...A ..@..
+|   2688: 00 41 00 00 00 00 00 00 00 00 00 07 11 41 10 00   .A...........A..
+|   2704: 00 41 20 00 00 41 00 00 00 41 10 00 00 00 00 00   .A ..A...A......
+|   2848: 00 00 00 00 00 00 00 00 00 00 00 00 00 89 50 01   ..............P.
+|   2864: 04 00 93 24 00 01 00 04 00 00 00 00 00 00 00 03   ...$............
+|   2880: 00 00 00 00 40 80 00 00 00 00 00 00 3f 80 00 00   ....@.......?...
+|   2896: 00 00 00 00 00 00 00 02 00 00 00 00 41 20 00 00   ............A ..
+|   2912: 00 00 00 00 41 10 00 00 00 00 00 00 00 00 00 04   ....A...........
+|   2928: 00 00 00 00 41 20 00 00 40 c0 00 00 41 20 00 00   ....A ..@...A ..
+|   2944: 00 00 00 00 00 00 00 05 40 a0 00 00 41 00 00 00   ........@...A...
+|   2960: 00 00 00 00 41 20 00 00 00 00 00 00 00 00 00 00   ....A ..........
+| page 6 offset 20480
+|      0: 0d 00 00 00 02 06 5a 00 0b 2d 06 5a 00 00 00 00   ......Z..-.Z....
+|   1616: 00 00 00 00 00 00 00 00 00 00 89 50 05 04 00 93   ...........P....
+|   1632: 24 00 00 00 1c 00 00 00 00 00 00 03 ed 40 a0 00   $............@..
+|   1648: 00 40 c0 00 00 00 00 00 00 3f 80 00 00 00 00 00   .@.......?......
+|   1664: 00 00 00 04 51 40 a0 00 00 40 c0 00 00 3f 80 00   ....Q@...@...?..
+|   1680: 00 40 00 00 00 00 00 00 00 00 00 04 b5 40 a0 00   .@...........@..
+|   1696: 00 40 c0 00 00 40 00 00 00 40 40 00 00 00 00 00   .@...@...@@.....
+|   1712: 00 00 00 05 19 40 a0 00 00 40 c0 00 00 40 40 00   .....@...@...@@.
+|   1728: 00 40 80 00 00 00 00 00 00 00 00 05 7d 40 a0 00   .@...........@..
+|   1744: 00 40 c0 00 00 40 80 00 00 40 a0 00 00 00 00 00   .@...@...@......
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+|   1808: 00 00 00 06 a9 40 a0 00 00 40 c0 00 00 40 e0 00   .....@...@...@..
+|   1824: 00 41 00 00 00 00 00 00 00 00 00 07 0d 40 a0 00   .A...........@..
+|   1840: 00 40 c0 00 00 41 00 00 00 41 10 00 00 00 00 00   .@...A...A......
+|   1856: 00 00 00 03 ee 40 c0 00 00 40 e0 00 00 00 00 00   .....@...@......
+|   1872: 00 3f 80 00 00 00 00 00 00 00 00 04 52 40 c0 00   .?..........R@..
+|   1888: 00 40 e0 00 00 3f 80 00 00 40 00 00 00 00 00 00   .@...?...@......
+|   1904: 00 00 00 04 b6 40 c0 00 00 40 e0 00 00 40 00 00   .....@...@...@..
+|   1920: 00 40 40 00 00 00 00 00 00 00 00 05 1a 40 c0 00   .@@..........@..
+|   1936: 00 40 e0 00 00 40 40 00 00 40 80 00 00 00 00 00   .@...@@..@......
+|   1952: 00 00 00 05 7e 40 c0 00 00 40 e0 00 00 40 80 00   ....~@...@...@..
+|   1968: 00 40 a0 00 00 00 00 00 00 00 00 05 e2 40 c0 00   .@...........@..
+|   1984: 00 40 e0 00 00 40 a0 00 00 40 c0 00 00 00 00 00   .@...@...@......
+|   2000: 00 00 00 06 46 40 c0 00 00 40 e0 00 00 40 c0 00   ....F@...@...@..
+|   2016: 00 40 e0 00 00 00 00 00 00 00 00 06 aa 40 c0 00   .@...........@..
+|   2032: 00 40 e0 00 00 40 e0 00 00 41 00 00 00 00 00 00   .@...@...A......
+|   2048: 00 00 00 07 0e 40 c0 00 00 40 e0 00 00 41 00 00   .....@...@...A..
+|   2064: 00 41 10 00 00 00 00 00 00 00 00 03 ef 40 e0 00   .A...........@..
+|   2080: 00 41 00 00 00 00 00 00 00 3f 80 00 00 00 00 00   .A.......?......
+|   2096: 00 00 00 04 53 40 e0 00 00 41 00 00 00 3f 80 00   ....S@...A...?..
+|   2112: 00 40 00 00 00 00 00 00 00 00 00 04 b7 40 e0 00   .@...........@..
+|   2128: 00 41 00 00 00 40 00 00 00 40 40 00 00 00 00 00   .A...@...@@.....
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+|   2160: 00 40 80 00 00 00 00 00 00 00 00 05 7f 40 e0 00   .@...........@..
+|   2176: 00 41 00 00 00 40 80 00 00 40 a0 00 00 00 00 00   .A...@...@......
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+|   2208: 00 40 c0 00 00 00 00 00 00 00 00 06 47 40 e0 00   .@..........G@..
+|   2224: 00 41 00 00 00 40 c0 00 00 40 e0 00 00 00 00 00   .A...@...@......
+|   2240: 00 00 00 06 ab 40 e0 00 00 41 00 00 00 40 e0 00   .....@...A...@..
+|   2256: 00 41 00 00 00 00 00 00 00 00 00 07 0f 40 e0 00   .A...........@..
+|   2272: 00 41 00 00 00 41 00 00 00 41 10 00 00 00 00 00   .A...A...A......
+|   2288: 00 00 00 07 73 40 e0 00 00 41 00 00 00 41 10 00   ....s@...A...A..
+|   2304: 00 41 20 00 00 00 00 00 00 00 00 00 00 00 00 00   .A .............
+|   2848: 00 00 00 00 00 00 00 00 00 00 00 00 00 89 50 04   ..............P.
+|   2864: 04 00 93 24 00 00 00 18 00 00 00 00 00 00 06 43   ...$...........C
+|   2880: 40 40 00 00 40 80 00 00 40 c0 00 00 40 e0 00 00   @@..@...@...@...
+|   2896: 00 00 00 00 00 00 06 42 40 00 00 00 40 40 00 00   .......B@...@@..
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+|   2944: 00 00 00 00 00 00 06 40 00 00 00 00 3f 80 00 00   .......@....?...
+|   2960: 40 c0 00 00 40 e0 00 00 00 00 00 00 00 00 06 44   @...@..........D
+|   2976: 40 80 00 00 40 a0 00 00 40 c0 00 00 40 e0 00 00   @...@...@...@...
+|   2992: 00 00 00 00 00 00 06 a7 40 40 00 00 40 80 00 00   ........@@..@...
+|   3008: 40 e0 00 00 41 00 00 00 00 00 00 00 00 00 06 a6   @...A...........
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+|   3120: 40 00 00 00 40 40 00 00 41 00 00 00 41 10 00 00   @...@@..A...A...
+|   3136: 00 00 00 00 00 00 07 09 3f 80 00 00 40 00 00 00   ........?...@...
+|   3152: 41 00 00 00 41 10 00 00 00 00 00 00 00 00 07 08   A...A...........
+|   3168: 00 00 00 00 3f 80 00 00 41 00 00 00 41 10 00 00   ....?...A...A...
+|   3184: 00 00 00 00 00 00 07 0b 40 40 00 00 40 80 00 00   ........@@..@...
+|   3200: 41 00 00 00 41 10 00 00 00 00 00 00 00 00 07 0c   A...A...........
+|   3216: 40 80 00 00 40 a0 00 00 41 00 00 00 41 10 00 00   @...@...A...A...
+|   3232: 00 00 00 00 00 00 07 6e 40 00 00 00 40 40 00 00   .......n@...@@..
+|   3248: 41 10 00 00 41 20 00 00 00 00 00 00 00 00 07 6d   A...A .........m
+|   3264: 3f 80 00 00 40 00 00 00 41 10 00 00 41 20 00 00   ?...@...A...A ..
+|   3280: 00 00 00 00 00 00 07 6c 00 00 00 00 3f 80 00 00   .......l....?...
+|   3296: 41 10 00 00 41 20 00 00 00 00 00 00 00 00 07 6f   A...A .........o
+|   3312: 40 40 00 00 40 80 00 00 41 10 00 00 41 20 00 00   @@..@...A...A ..
+|   3328: 00 00 00 00 00 00 07 70 40 80 00 00 40 a0 00 00   .......p@...@...
+|   3344: 41 10 00 00 41 20 00 00 00 00 00 00 00 00 07 71   A...A .........q
+|   3360: 40 a0 00 00 40 c0 00 00 41 10 00 00 41 20 00 00   @...@...A...A ..
+|   3376: 00 00 00 00 00 00 07 72 40 c0 00 00 40 e0 00 00   .......r@...@...
+|   3392: 41 10 00 00 41 20 00 00 00 00 00 00 00 00 07 74   A...A .........t
+|   3408: 41 00 00 00 41 10 00 00 41 10 00 00 41 20 00 00   A...A...A...A ..
+|   3424: 00 00 00 00 00 00 07 75 41 10 00 00 41 20 00 00   .......uA...A ..
+|   3440: 41 10 00 00 41 20 00 00 00 00 00 00 00 00 00 00   A...A ..........
+| end c1b.db
+  }]
+  catchsql {
+     PRAGMA writable_schema = 1;
+     SELECT rtreecheck('t1');
+  }
+} {1 {SQL logic error}}
+
+do_test rtreefuzz001-200 {
+  sqlite3 db {}
+  db deserialize [decode_hexdb {
+| size 16384 pagesize 4096 filename c3.db
+| page 1 offset 0
+|      0: 53 51 4c 69 74 65 20 66 6f 72 6d 61 74 20 33 00   SQLite format 3.
+|     16: 10 00 01 01 00 40 20 20 00 00 00 00 00 00 00 04   .....@  ........
+|     32: 00 00 00 00 01 00 00 00 00 00 00 04 00 00 00 04   ................
+|     48: 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00   ................
+|     96: 00 00 00 00 0d 00 00 00 04 0e 9c 00 0f ad 0f 4f   ...............O
+|    112: 0e fc 0e 9c 00 00 00 00 00 00 00 00 00 00 00 00   ................
+|   3728: 00 00 00 00 00 00 00 00 00 00 00 00 5e 04 07 17   ............^...
+|   3744: 1f 1f 01 81 0b 74 61 62 6c 65 74 31 5f 70 61 72   .....tablet1_par
+|   3760: 65 6e 74 74 31 5f 70 61 72 65 6e 74 04 43 52 45   entt1_parent.CRE
+|   3776: 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 70 61   ATE TABLE .t1_pa
+|   3792: 72 65 6e 74 22 28 6e 6f 64 65 6e 6f 20 49 4e 54   rent.(nodeno INT
+|   3808: 45 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59   EGER PRIMARY KEY
+|   3824: 2c 70 61 72 65 6e 74 6e 6f 64 65 29 51 03 06 17   ,parentnode)Q...
+|   3840: 1b 1b 01 7b 74 61 62 6c 65 74 31 5f 6e 6f 64 65   ....tablet1_node
+|   3856: 74 31 5f 6e 6f 64 65 03 43 52 45 41 54 45 20 54   t1_node.CREATE T
+|   3872: 41 42 4c 45 20 22 74 31 5f 6e 6f 64 65 22 28 6e   ABLE .t1_node.(n
+|   3888: 6f 64 65 6e 6f 20 49 4e 54 45 47 45 52 20 50 52   odeno INTEGER PR
+|   3904: 49 4d 41 52 59 20 4b 45 59 2c 64 61 74 61 29 5c   IMARY KEY,data).
+|   3920: 02 07 17 1d 1d 01 81 0b 74 61 62 6c 65 74 31 5f   ........tablet1_
+|   3936: 72 6f 77 69 64 74 31 5f 72 6f 77 69 64 02 43 52   rowidt1_rowid.CR
+|   3952: 45 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 72   EATE TABLE .t1_r
+|   3968: 6f 77 69 64 22 28 72 6f 77 69 64 20 49 4e 54 45   owid.(rowid INTE
+|   3984: 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59 2c   GER PRIMARY KEY,
+|   4000: 6e 6f 64 65 6e 6f 2c 61 30 2c 61 31 29 51 01 07   nodeno,a0,a1)Q..
+|   4016: 17 11 11 08 81 0f 74 61 62 6c 65 74 31 74 31 43   ......tablet1t1C
+|   4032: 52 45 41 54 45 20 56 49 52 54 55 41 4c 20 54 41   REATE VIRTUAL TA
+|   4048: 42 4c 45 20 74 31 20 55 53 49 4e 47 20 72 74 72   BLE t1 USING rtr
+|   4064: 65 65 28 69 64 2c 78 30 2c 78 31 2c 79 30 2c 79   ee(id,x0,x1,y0,y
+|   4080: 31 2c 2b 6c 61 62 65 6c 2c 2b 6f 74 68 65 72 29   1,+label,+other)
+| page 2 offset 4096
+|      0: 0d 00 00 00 0e 0e f7 00 0f e8 0f d0 0f b7 0f 9e   ................
+|     16: 0f 91 0f 81 0f 70 0f 5e 0f 4f 0f 39 0f 29 0f 18   .....p.^.O.9.)..
+|     32: 0f 06 0e f7 00 00 00 00 00 00 00 00 00 00 00 00   ................
+|   3824: 00 00 00 00 00 00 00 0d 0e 05 00 09 1d 00 74 6f   ..............to
+|   3840: 70 20 68 61 6c 66 10 0d 05 00 09 23 00 62 6f 74   p half.....#.bot
+|   3856: 74 6f 6d 20 68 61 6c 66 0f 0c 05 00 09 21 00 72   tom half.....!.r
+|   3872: 69 67 68 74 20 68 61 6c 66 0e 0b 05 00 09 1f 00   ight half.......
+|   3888: 6c 65 66 74 20 68 61 6c 66 14 0a 05 00 09 2b 00   left half.....+.
+|   3904: 74 68 65 20 77 68 6f 6c 65 20 74 68 69 6e 67 0d   the whole thing.
+|   3920: 09 05 00 09 1d 00 74 6f 70 20 65 64 67 65 10 08   ......top edge..
+|   3936: 05 00 09 23 00 62 6f 74 74 6f 6d 20 65 64 67 65   ...#.bottom edge
+|   3952: 0f 07 05 00 09 21 00 72 69 67 68 74 20 65 64 67   .....!.right edg
+|   3968: 65 0e 06 05 00 09 1f 00 6c 65 66 74 20 65 64 67   e.......left edg
+|   3984: 65 0b 05 05 00 09 19 00 63 65 6e 74 65 72 17 04   e.......center..
+|   4000: 05 00 09 31 00 75 70 70 65 72 2d 72 69 67 68 74   ...1.upper-right
+|   4016: 20 63 6f 72 6e 65 72 17 03 05 00 09 31 00 6c 6f    corner.....1.lo
+|   4032: 77 65 72 2d 72 69 67 68 74 27 60 f6 32 6e 65 72   wer-right'`.2ner
+|   4048: 16 02 05 00 09 2f 00 75 70 70 65 72 2d 6c 65 66   ...../.upper-lef
+|   4064: 74 20 63 6f 72 6e 65 72 16 01 05 00 09 2f 00 6c   t corner...../.l
+|   4080: 6f 77 65 72 2d 6c 65 66 74 20 63 6f 72 6e 65 72   ower-left corner
+| page 3 offset 8192
+|      0: 0d 00 00 00 02 0b 2d 00 0b 2d 00 00 00 00 00 00   ......-..-......
+|   2848: 00 00 00 00 00 00 00 00 00 00 00 00 00 89 50 01   ..............P.
+|   2864: 04 00 93 24 00 00 00 0e 00 00 00 00 00 00 00 01   ...$............
+|   2880: 00 00 00 00 41 20 00 00 00 00 00 00 41 20 01 00   ....A ......A ..
+|   2896: 00 00 00 00 00 00 00 02 00 00 00 00 41 00 00 04   ............A...
+|   2912: 2b 40 00 0c 42 c8 00 00 00 00 00 00 00 00 00 03   +@..B...........
+|   2928: 42 b4 00 00 42 c8 00 00 00 00 00 00 41 20 00 00   B...B.......A ..
+|   2944: 00 00 00 00 00 00 00 04 42 b4 00 00 42 c8 00 00   ........B...B...
+|   2960: 42 b4 00 00 42 c8 00 00 00 00 00 00 00 00 00 05   B...B...........
+|   2976: 42 20 00 00 42 70 00 00 42 20 00 00 42 70 00 00   B ..Bp..B ..Bp..
+|   2992: 00 00 00 00 00 00 00 60 00 00 00 04 0a 00 00 00   .......`........
+|   3008: 00 00 00 42 c8 00 00 00 00 00 00 00 00 00 07 42   ...B...........B
+|   3024: be 00 00 42 c8 00 00 00 00 00 00 42 c8 00 00 00   ...B.......B....
+|   3040: 00 00 00 00 00 00 08 00 00 00 00 42 c8 00 00 00   ...........B....
+|   3056: 00 00 00 40 a0 00 00 00 00 00 00 00 00 00 09 00   ...@............
+|   3072: 00 00 00 42 c8 00 00 42 be 00 00 42 c8 00 00 00   ...B...B...B....
+|   3088: 00 00 00 00 00 00 0a 00 00 00 00 42 c8 00 00 00   ...........B....
+|   3104: 00 00 00 42 c8 00 00 00 00 00 00 00 00 00 0b 00   ...B............
+|   3120: 00 00 00 42 48 00 00 00 00 00 04 2c 80 00 00 00   ...BH......,....
+|   3136: 00 00 00 00 00 00 c4 24 c0 00 04 2c 80 00 00 00   .......$...,....
+|   3152: 00 00 04 2c 80 00 00 00 00 00 00 00 00 00 d0 00   ...,............
+|   3168: 00 00 04 2c 80 00 00 00 00 00 04 24 80 00 00 00   ...,.......$....
+|   3184: 00 00 00 00 00 00 e0 00 00 00 04 2c 80 00 04 24   ...........,...$
+|   3200: c0 00 04 2c 00 00 00 00 00 00 00 00 00 00 00 00   ...,............
+| page 4 offset 12288
+|      0: 0d 00 00 00 00 10 00 00 00 00 00 00 00 00 00 00   ................
+| end c3.db
+  }]
+  catchsql {
+    WITH RECURSIVE
+      c1(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM c1 WHERE x<99),
+      c2(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM c2 WHERE y<99)
+    INSERT INTO t1(id, x0,x1,y0,y1,label)
+      SELECT 1000+x+y*100, x, x+1, y, y+1, printf('box-%d,%d',x,y) FROM c1, c2;
+  }
+} {1 {database disk image is malformed}}
+do_test rtreefuzz001-210 {
+  catchsql {
+    SELECT rtreecheck('t1');
+  }
+} {/1 .*corrupt.*/}
+
+do_test rtreefuzz001-300 {
+  sqlite3 db {}
+  db deserialize [decode_hexdb {
+| size 16384 pagesize 4096 filename c4.db
+| page 1 offset 0
+|      0: 53 51 4c 69 74 65 20 66 6f 72 6d 61 74 20 33 00   SQLite format 3.
+|     16: 10 00 01 01 00 40 20 20 00 00 00 00 00 00 00 04   .....@  ........
+|     32: 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 04   ................
+|     96: 00 00 00 00 0d 00 00 00 04 0e 9c 00 0f ad 0f 4f   ...............O
+|    112: 0e fc 0e 9c 00 00 00 00 00 00 00 00 00 00 00 00   ................
+|   3728: 00 00 00 00 00 00 00 00 00 00 00 00 5e 04 07 17   ............^...
+|   3744: 1f 1f 01 81 0b 74 61 62 6c 65 74 31 5f 70 61 72   .....tablet1_par
+|   3760: 65 6e 74 74 31 5f 70 61 72 65 6e 74 04 43 52 45   entt1_parent.CRE
+|   3776: 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 70 61   ATE TABLE .t1_pa
+|   3792: 72 65 6e 74 22 28 6e 6f 64 65 6e 6f 20 49 4e 54   rent.(nodeno INT
+|   3808: 45 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59   EGER PRIMARY KEY
+|   3824: 2c 70 61 72 65 6e 74 6e 6f 64 65 29 51 03 06 17   ,parentnode)Q...
+|   3840: 1b 1b 01 7b 74 61 62 6c 65 74 31 5f 6e 6f 64 65   ....tablet1_node
+|   3856: 74 31 5f 6e 6f 64 65 03 43 52 45 41 54 45 20 54   t1_node.CREATE T
+|   3872: 41 42 4c 45 20 22 74 31 5f 6e 6f 64 65 22 28 6e   ABLE .t1_node.(n
+|   3888: 6f 64 65 6e 6f 20 49 4e 54 45 47 45 52 20 50 52   odeno INTEGER PR
+|   3904: 49 4d 41 52 59 20 4b 45 59 2c 64 61 74 61 29 5c   IMARY KEY,data).
+|   3920: 02 07 17 1d 1d 01 81 0b 74 61 62 6c 65 74 31 5f   ........tablet1_
+|   3936: 72 6f 77 69 64 74 31 5f 72 6f 77 69 64 02 43 52   rowidt1_rowid.CR
+|   3952: 45 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 72   EATE TABLE .t1_r
+|   3968: 6f 77 69 64 22 28 72 6f 77 69 64 20 49 4e 54 45   owid.(rowid INTE
+|   3984: 47 45 72 20 50 52 49 4d 41 52 59 20 4b 45 59 2c   GEr PRIMARY KEY,
+|   4000: 6e 6f 64 65 6e 6f 2c 61 30 2c 61 31 29 51 01 07   nodeno,a0,a1)Q..
+|   4016: 17 11 11 08 81 0f 74 61 62 6c 65 74 31 74 31 43   ......tablet1t1C
+|   4032: 52 45 41 54 45 20 56 49 52 54 55 41 4c 20 54 41   REATE VIRTUAL TA
+|   4048: 42 4c 45 20 74 31 20 55 53 49 4e 47 20 72 74 72   BLE t1 USING rtr
+|   4064: 65 65 28 69 64 2c 78 30 2c 78 31 2c 79 30 2c 79   ee(id,x0,x1,y0,y
+|   4080: 31 2c 2b 6c 61 62 65 6c 2c 2b 6f 74 68 65 72 29   1,+label,+other)
+| page 2 offset 4096
+|      0: 0d 00 00 00 0e 0e f7 00 0f e8 0f 00 fb 70 f9 e0   .............p..
+|     16: f9 10 f8 10 f7 00 f5 e0 f4 f0 f3 90 f2 90 f1 80   ................
+|     32: f0 60 ef 00 00 00 00 00 00 00 00 00 00 00 00 00   .`..............
+|   3824: 00 00 00 00 00 00 00 0d 0e 05 00 09 1d 00 74 6f   ..............to
+|   3840: 70 20 68 61 6c 66 10 0d 05 00 09 23 00 62 6f 74   p half.....#.bot
+|   3856: 74 6f 6d 20 68 61 6c 66 0f 0c 05 00 09 21 00 72   tom half.....!.r
+|   3872: 69 67 68 74 20 68 61 6c 66 0e 0b 05 00 09 1f 00   ight half.......
+|   3888: 6c 65 66 74 20 68 61 6c 66 14 0a 05 00 09 2b 00   left half.....+.
+|   3904: 00 03 98 20 49 98 2f 6c 62 05 74 68 69 6e 67 0d   ... I./lb.thing.
+|   3920: 09 05 00 09 1d 00 74 6f 70 20 65 64 67 65 10 08   ......top edge..
+|   3936: 05 00 09 23 00 62 6f 74 74 6f 6d 20 65 64 67 65   ...#.bottom edge
+|   3952: 0f 07 05 00 09 21 00 72 69 67 68 74 20 65 64 67   .....!.right edg
+|   3968: 65 0e 06 05 00 09 1f 00 6c 65 66 74 20 65 64 67   e.......left edg
+|   3984: 65 0b 05 05 00 09 19 00 63 65 6e 74 65 72 17 04   e.......center..
+|   4000: 05 00 09 31 00 75 70 70 65 72 2d 72 69 67 68 74   ...1.upper-right
+|   4016: 20 63 6f 72 6e 65 72 17 03 05 00 09 31 00 6c 6f    corner.....1.lo
+|   4032: 77 65 72 2d 72 69 67 68 74 20 63 6f 72 6e 65 72   wer-right corner
+|   4048: 16 02 05 00 09 2f 00 75 70 70 65 72 2d 6c 65 66   ...../.upper-lef
+|   4064: 74 20 63 6f 72 6e 65 72 16 01 05 00 09 2f 00 6c   t corner...../.l
+|   4080: 6f 77 65 72 2d 6c 65 66 74 20 63 6f 72 6e 65 72   ower-left corner
+| page 3 offset 8192
+|      0: 0d 00 00 00 01 0b 2d 00 0b 2d 00 00 00 00 00 00   ......-..-......
+|   2848: 00 00 00 00 00 00 00 00 00 00 00 00 00 89 50 01   ..............P.
+|   2864: 04 00 93 24 00 00 00 0e 00 00 00 00 00 00 00 01   ...$............
+|   2880: 00 00 00 04 01 20 00 00 00 00 00 04 12 00 00 00   ..... ..........
+|   2896: 00 00 00 00 00 00 00 23 00 00 00 00 41 20 00 00   .......#....A ..
+|   2912: 42 b4 00 00 42 c8 00 00 00 00 00 00 00 00 00 03   B...B...........
+|   2928: 42 b4 00 00 42 c8 00 00 00 00 00 00 41 20 00 00   B...B.......A ..
+|   2944: 00 00 00 00 00 00 00 04 42 b4 00 00 42 c8 00 00   ........B...B...
+|   2960: 42 b4 00 00 42 c8 00 00 00 00 00 00 00 00 00 05   B...B...........
+|   2976: 42 20 00 00 42 70 00 00 42 20 00 00 42 70 00 00   B ..Bp..B ..Bp..
+|   2992: 00 00 00 00 00 00 00 06 00 00 00 00 40 a0 00 00   ............@...
+|   3008: 00 00 00 04 2c 80 00 00 00 00 00 00 00 00 00 74   ....,..........t
+|   3024: 2b e0 00 04 2c 80 00 04 2c 80 00 00 00 00 00 00   +...,...,.......
+|   3040: 00 00 00 80 00 00 00 04 2c 80 00 00 00 00 00 04   ........,.......
+|   3056: 0a 00 00 00 00 00 b0 80 00 00 04 2c 80 00 04 2b   ...........,...+
+|   3072: e0 00 04 2c 80 00 00 00 00 00 00 00 00 00 a0 00   ...,............
+|   3088: 00 00 04 2c 80 00 00 00 00 00 04 2c 80 00 00 00   ...,.......,....
+|   3104: 00 00 00 00 00 00 b0 00 00 00 04 24 80 00 00 00   ...........$....
+|   3120: 00 00 04 2c 80 00 00 00 00 00 00 00 50 00 91 f0   ...,........P...
+|   3136: 06 c6 56 67 42 06 86 16 c6 61 40 a0 50 00 92 b0   ..VgB....a@.P...
+|   3152: 07 46 86 52 07 76 86 f6 c6 52 07 46 86 96 e6 70   .F.R.v...R.F...p
+|   3168: d0 90 50 00 91 d0 07 46 f7 02 06 56 46 76 51 00   ..P....F...VFvQ.
+|   3184: 80 50 00 92 30 06 26 f7 47 46 f6 d2 06 56 46 76   .P..0.&.GF...VFv
+|   3200: 50 f0 70 50 00 92 10 07 26 96 76 87 42 06 56 46   P.pP....&.v.B.VF
+|   3216: 76 50 e0 60 50 00 91 f0 06 c6 56 67 42 06 56 46   vP.`P.....VgB.VF
+|   3232: 76 50 b0 50 50 00 91 90 06 36 56 e7 46 57 21 70   vP.PP....6V.FW!p
+|   3248: 40 50 00 93 10 07 57 07 06 57 22 d7 26 96 76 87   @P....W..W..&.v.
+|   3264: 42 06 36 f7 26 e6 57 21 70 30 50 00 93 10 06 c6   B.6.&.W!p0P.....
+|   3280: f7 76 57 22 d7 26 96 76 87 42 06 36 f7 26 e6 57   .vW..&.v.B.6.&.W
+|   3296: 21 60 20 50 00 92 f0 07 57 07 06 57 22 d6 c6 56   !` P....W..W...V
+|   3312: 60 00 00 c4 24 c0 00 04 2c 80 00 00 00 00 00 04   `...$...,.......
+|   3328: 2c 80 00 00 00 00 00 00 00 00 00 d0 00 00 00 04   ,...............
+|   3344: 2c 80 00 00 00 00 00 04 24 80 00 00 00 00 00 00   ,.......$.......
+|   3360: 00 00 00 e0 00 00 00 04 2c 80 00 04 24 c0 00 04   ........,...$...
+|   3376: 2c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00   ,...............
+| page 4 offset 12288
+|      0: 0d 00 00 00 00 10 00 00 00 00 00 00 00 00 00 00   ................
+| end c4.db
+  }]
+  catchsql {
+    UPDATE t1 SET label='x';
+  }
+} {1 {rtree constraint failed: t1.(y0<=y1)}}
+do_test rtreefuzz001-310 {
+  catchsql {
+    SELECT rtreecheck('t1');
+  }
+} {/1 .*corrupt.*/}
+
+do_test rtreefuzz001-400 {
+  sqlite3 db {}
+  db deserialize [decode_hexdb {
+| size 16384 pagesize 4096 filename c7.db
+| page 1 offset 0
+|      0: 53 51 4c 69 74 65 20 66 6f 72 6d 61 74 20 33 00   SQLite format 3.
+|     16: 10 00 01 01 00 40 20 20 00 00 00 00 00 00 00 04   .....@  ........
+|     32: 00 00 00 00 01 00 00 00 00 00 00 04 00 00 00 04   ................
+|     48: 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00   ................
+|     96: 00 00 00 00 0d 00 00 00 04 0e 9c 00 0f ad 0f 4f   ...............O
+|    112: 0e fc 0e 9c 00 00 00 00 00 00 00 00 00 00 00 00   ................
+|   3728: 00 00 00 00 00 00 00 00 00 00 00 00 5e 04 07 17   ............^...
+|   3744: 1f 1f 01 81 0b 74 61 62 6c 65 74 31 5f 70 61 72   .....tablet1_par
+|   3760: 65 6e 74 74 31 5f 70 61 72 65 6e 74 04 43 52 45   entt1_parent.CRE
+|   3776: 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 70 61   ATE TABLE .t1_pa
+|   3792: 72 65 6e 74 22 28 6e 6f 64 65 6e 6f 20 49 4e 54   rent.(nodeno INT
+|   3808: 45 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59   EGER PRIMARY KEY
+|   3824: 2c 70 61 72 65 6e 74 6e 6f 64 65 29 51 03 06 17   ,parentnode)Q...
+|   3840: 1b 1b 01 7b 74 61 62 6c 65 74 31 5f 6e 6f 64 65   ....tablet1_node
+|   3856: 74 31 5f 6e 6f 64 65 03 43 52 45 41 54 45 20 54   t1_node.CREATE T
+|   3872: 41 42 4c 45 20 22 74 31 5f 6e 6f 64 65 22 28 6e   ABLE .t1_node.(n
+|   3888: 6f 64 65 6e 6f 20 49 4e 54 45 47 45 52 20 50 52   odeno INTEGER PR
+|   3904: 49 4d 41 52 59 20 4b 45 59 2c 64 61 74 61 29 5c   IMARY KEY,data).
+|   3920: 02 07 17 1d 1d 01 81 0b 74 61 62 6c 65 74 31 5f   ........tablet1_
+|   3936: 72 6f 77 69 64 74 31 5f 72 6f 77 69 64 02 43 52   rowidt1_rowid.CR
+|   3952: 45 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 72   EATE TABLE .t1_r
+|   3968: 6f 77 69 64 22 28 72 6f 77 69 64 20 49 4e 54 45   owid.(rowid INTE
+|   3984: 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59 2c   GER PRIMARY KEY,
+|   4000: 6e 6f 64 65 6e 6f 2c 61 30 2c 61 31 29 51 01 07   nodeno,a0,a1)Q..
+|   4016: 17 11 11 08 81 0f 74 61 62 6c 65 74 31 74 31 43   ......tablet1t1C
+|   4032: 52 45 41 54 45 20 56 49 52 54 55 41 4c 20 54 41   REATE VIRTUAL TA
+|   4048: 42 4c 45 20 74 31 20 55 53 49 4e 47 20 72 74 72   BLE t1 USING rtr
+|   4064: 65 65 28 69 64 2c 78 30 2c 78 31 2c 79 30 2c 79   ee(id,x0,x1,y0,y
+|   4080: 31 2c 2b 6c 61 62 65 6c 2c 2b 6f 74 68 65 72 29   1,+label,+other)
+| page 2 offset 4096
+|      0: 0d 00 00 00 0e 0e f7 00 0f e8 0f d0 0f b7 0f 9e   ................
+|     16: 0f 91 0f 81 0f 70 0f 5e 0f 4f 0f 39 0f 29 0f 18   .....p.^.O.9.)..
+|     32: 0f 06 0e f7 00 00 00 00 00 00 00 00 00 00 00 00   ................
+|   3824: 00 00 00 00 00 00 00 0d 0e 05 00 09 1d 00 74 6f   ..............to
+|   3840: 70 20 68 61 6c 66 10 0d 05 00 09 23 00 62 6f 74   p half.....#.bot
+|   3856: 74 6f 6d 20 68 61 6c 66 0f 0c 05 00 09 21 00 72   tom half.....!.r
+|   3872: 69 67 68 74 20 68 61 6c 66 0e 0b 05 00 09 1f 00   ight half.......
+|   3888: 6c 65 66 74 20 68 61 6c 66 14 0a 05 00 09 2b 00   left half.....+.
+|   3904: 74 68 65 20 77 68 6f 6c 65 20 74 68 69 6e 67 0d   the whole thing.
+|   3920: 09 05 00 09 1d 00 74 6f 70 20 65 64 67 65 10 08   ......top edge..
+|   3936: 05 00 09 23 00 62 6f 74 74 6f 6d 20 65 64 67 65   ...#.bottom edge
+|   3952: 0f 07 05 00 09 21 00 72 69 67 68 74 20 65 64 67   .....!.right edg
+|   3968: 65 0e 06 05 00 09 1f 00 6c 65 66 74 20 65 64 67   e.......left edg
+|   3984: 65 0b 05 05 00 09 19 00 23 65 6e 74 65 72 17 04   e.......#enter..
+|   4000: 05 00 09 31 00 75 70 70 65 72 2d 72 69 67 68 74   ...1.upper-right
+|   4016: 20 63 6f 72 6e 65 72 17 03 05 00 09 31 00 6c 6f    corner.....1.lo
+|   4032: 77 65 72 2d 72 69 67 68 74 20 63 6f 72 6e 65 72   wer-right corner
+|   4048: 16 02 05 00 09 2f 00 75 70 70 65 72 2d 6c 65 66   ...../.upper-lef
+|   4064: 74 20 63 6f 72 6e 65 72 16 01 05 00 09 2f 00 6c   t corner...../.l
+|   4080: 6f 77 65 72 2d 6c 65 66 74 20 63 6f 72 6e 65 72   ower-left corner
+| page 3 offset 8192
+|      0: 0d 00 00 00 02 0b 2d 00 0b 2d 00 00 00 00 00 00   ......-..-......
+|   2848: 00 00 00 00 00 00 00 00 00 00 00 00 00 89 50 01   ..............P.
+|   2864: 04 00 93 24 00 00 00 00 00 00 00 00 08 00 00 00   ...$............
+|   2880: 00 42 c8 00 00 00 00 00 00 40 a0 00 00 00 00 00   .B.......@......
+|   2896: 00 00 00 00 42 c8 00 00 00 00 00 00 00 00 00 07   ....B...........
+|   2912: 42 be 00 00 42 c8 00 00 00 00 00 00 42 c8 00 00   B...B.......B...
+|   2928: 00 00 00 00 00 00 00 08 00 00 00 00 42 c8 00 00   ............B...
+|   2944: 00 00 00 00 40 a0 00 00 00 00 00 00 00 00 00 09   ....@...........
+|   2960: 00 00 00 00 42 c8 00 00 42 be 00 00 42 c8 00 00   ....B...B...B...
+|   2976: 00 00 00 00 00 00 00 0a 00 00 00 00 42 c8 00 00   ............B...
+|   2992: 00 00 00 00 42 c8 00 00 00 00 00 00 00 00 00 0b   ....B...........
+|   3008: 00 00 00 00 42 48 00 00 00 00 00 04 2c 80 00 00   ....BH......,...
+|   3024: 00 00 00 00 00 00 00 c4 00 00 00 00 00 42 c8 00   .............B..
+|   3040: 00 00 00 00 00 00 00 00 07 42 be 00 00 42 c8 00   .........B...B..
+|   3056: 00 00 00 00 00 42 c8 00 00 00 00 00 00 00 00 00   .....B..........
+|   3072: 08 00 00 00 00 42 c8 00 00 00 00 00 00 40 a0 00   .....B.......@..
+|   3088: 00 00 00 00 00 00 00 00 09 00 00 00 00 42 c8 00   .............B..
+|   3104: 00 42 be 00 00 42 c8 00 00 00 00 00 00 00 00 00   .B...B..........
+|   3120: 0a 00 00 00 00 42 c8 00 00 00 00 00 00 42 c8 00   .....B.......B..
+|   3136: 00 00 00 00 00 00 00 00 0b 00 00 00 00 42 48 00   .............BH.
+|   3152: 00 00 00 00 04 2c 80 00 00 00 00 00 00 00 00 00   .....,..........
+|   3168: c4 24 c0 00 04 2c 80 00 00 00 00 00 04 2c 80 00   .$...,.......,..
+|   3184: 00 00 00 00 00 00 00 00 d0 00 00 00 04 2c 80 00   .............,..
+|   3200: 00 00 00 00 04 24 80 00 00 00 00 00 00 00 00 00   .....$..........
+|   3216: e0 00 00 00 04 2c 80 00 04 24 c0 00 04 2c 00 00   .....,...$...,..
+| page 4 offset 12288
+|      0: 0d 00 00 00 00 10 00 00 00 00 00 00 0e 00 00 00   ................
+|     16: 00 42 c8 00 00 42 4c 00 00 42 c8 00 00 00 00 00   .B...BL..B......
+|     32: 00 00 00 0a 00 00 00 00 42 c8 00 00 00 00 00 00   ........B.......
+|     48: 42 c8 00 00 00 00 00 00 00 00 00 0b 00 00 00 00   B...............
+|     64: 42 48 00 00 00 00 00 04 2c 80 00 00 00 00 00 00   BH......,.......
+|     80: 00 00 00 c4 24 c0 00 04 2c 80 00 00 00 00 00 04   ....$...,.......
+|     96: 2c 80 00 00 00 00 00 00 00 00 00 d0 00 00 00 04   ,...............
+|    112: 2c 80 00 00 00 00 00 04 24 80 00 00 00 00 00 00   ,.......$.......
+|    128: 00 00 00 e0 00 00 00 04 2c 80 00 04 24 c0 00 04   ........,...$...
+|    144: 2c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00   ,...............
+| end c7.db
+  }]
+  catchsql {
+    WITH RECURSIVE
+      c1(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM c1 WHERE x<8),
+      c2(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM c2 WHERE y<5)
+    INSERT INTO t1(id, x0,x1,y0,y1,label)
+      SELECT 1000+x+y*100, x, x+1, y, y+1, printf('box-%d,%d',x,y) FROM c1, c2;
+  }
+} {1 {database disk image is malformed}}
+
+do_test rtreefuzz001-500 {
+  sqlite3 db {}
+  db deserialize [decode_hexdb {
+| size 16384 pagesize 4096 filename crash-2e81f5dce5cbd4.db
+| page 1 offset 0
+|      0: 53 51 4c 69 74 65 20 66 6f 72 6d 61 74 20 33 00   SQLite format 3.
+|     16: 10 00 01 01 00 40 20 20 00 00 00 00 00 00 00 00   .....@  ........
+|     96: 00 00 00 00 0d 00 00 00 05 0e 6d 00 0f c8 0f 7b   ..........m.....
+|    112: 0f 20 0e cd 0e 6d 00 00 00 00 00 00 00 00 00 00   . ...m..........
+|   3680: 00 00 00 00 00 00 00 00 00 00 00 00 00 5e 05 07   .............^..
+|   3696: 17 1f 1f 01 81 0b 74 61 62 6c 65 74 31 5f 70 61   ......tablet1_pa
+|   3712: 72 65 6e 74 74 31 5f 70 61 72 65 6e 74 05 43 52   rentt1_parent.CR
+|   3728: 45 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f 70   EATE TABLE .t1_p
+|   3744: 61 72 65 6e 74 22 28 6e 6f 64 65 6e 6f 20 49 4e   arent.(nodeno IN
+|   3760: 54 45 47 45 42 20 50 52 49 4d 41 52 59 20 4b 45   TEGEB PRIMARY KE
+|   3776: 59 2c 70 61 72 65 6e 74 6e 6f 64 65 29 51 04 06   Y,parentnode)Q..
+|   3792: 17 1b 1b 01 7b 74 61 62 6c 65 74 31 5f 6e 6f 64   .....tablet1_nod
+|   3808: 65 74 31 5f 6e 6f 64 65 04 43 52 45 41 54 45 20   et1_node.CREATE 
+|   3824: 54 41 42 4c 45 20 22 74 31 5f 6e 6f 64 65 22 28   TABLE .t1_node.(
+|   3840: 6e 6f 64 65 6e 6f 20 49 4e 54 45 47 45 52 20 50   nodeno INTEGER P
+|   3856: 52 49 4d 41 52 59 20 4b 45 59 2c 64 61 74 61 29   RIMARY KEY,data)
+|   3872: 59 03 07 17 1d 1d 01 81 05 74 61 62 6c 65 84 31   Y........table.1
+|   3888: 5f 72 6f 77 69 64 74 31 5f 72 6f 87 69 64 03 43   _rowidt1_ro.id.C
+|   3904: 52 45 41 54 45 20 54 41 42 4c 45 20 22 74 31 5f   REATE TABLE .t1_
+|   3920: 72 6f 77 69 64 22 28 72 6f 77 69 64 20 49 4e 54   rowid.(rowid INT
+|   3936: 45 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59   EGER PRIMARY KEY
+|   3952: 2c 6e f8 64 65 6e 6f 2c 61 30 29 4b 02 07 17 11   ,n.deno,a0)K....
+|   3968: 11 08 81 03 74 22 62 6c 65 74 31 74 31 43 52 45   ....t.blet1t1CRE
+|   3984: 41 54 45 20 56 49 52 54 55 41 4c 20 54 41 42 4c   ATE VIRTUAL TABL
+|   4000: 45 20 74 31 20 55 53 49 4e 47 20 72 74 72 65 65   E t1 USING rtree
+|   4016: 5f 69 33 32 28 69 cc 2c 78 30 2c 78 31 2c 79 30   _i32(i.,x0,x1,y0
+|   4032: 2c 79 31 2c 2b 65 78 29 36 01 06 17 17 17 01 4d   ,y1,+ex)6......M
+|   4048: 74 61 62 6c 65 63 6f 6f 72 64 63 6f 6f 72 64 02   tablecoordcoord.
+|   4064: 43 52 45 41 54 45 20 54 41 42 4c 45 20 63 6f 6f   CREATE TABLE coo
+|   4080: 71 64 28 76 20 49 4e 54 2c 20 77 20 49 4e 54 29   qd(v INT, w INT)
+| page 2 offset 4096
+|   4016: 00 00 00 00 00 00 00 00 00 00 00 05 0a 03 01 01   ................
+|   4032: 0a 02 05 09 03 01 01 09 02 05 08 03 01 01 08 02   ................
+|   4048: 05 07 03 01 01 07 02 05 06 03 11 01 06 02 05 05   ................
+|   4064: 03 01 01 05 02 05 04 03 01 01 04 02 05 03 03 01   ................
+|   4080: 01 03 02 05 02 03 01 01 02 02 04 01 03 09 01 02   ................
+| page 3 offset 8192
+|      0: 0d 0e 4f 00 64 0b 5a 12 0d bb 0d 84 0f eb 0d c6   ..O.d.Z.........
+|     16: 0f d7 0e cc 0f c1 0f b6 0f ab 0f 9f 0f 94 0d 8f   ................
+|     32: 0f 86 0d d1 0f 62 0f 67 0f 5c 0f 51 1f 46 0f 3a   .....b.g...Q.F.:
+|     48: 0f 30 0d 9a 0f 21 0d dc 0f 00 00 00 00 00 00 00   .0...!..........
+|   2896: 00 00 00 00 00 00 00 00 00 00 0a ce 1a 04 00 01   ................
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+| end crash-2e81f5dce5cbd4.db}]
+  execsql { PRAGMA writable_schema = 1;}
+  catchsql {UPDATE t1 SET ex= ex ISNULL}
+} {1 {database disk image is malformed}}
+
+do_test rtreefuzz001-600 {
+  sqlite3 db {}
+  db deserialize [decode_hexdb {
+| size 20480 pagesize 4096 filename crash-7b37d80f000235.db
+| page 1 offset 0
+|      0: 53 51 4c 69 74 65 20 66 6f 72 6d 61 74 20 33 00   SQLite format 3.
+|     16: 10 00 01 01 00 40 20 20 00 00 00 00 00 00 00 05   .....@  ........
+|     32: 00 00 00 00 00 00 00 00 00 00 10 06 00 00 00 04   ................
+|     96: 00 00 00 00 0d 00 00 00 05 0e 49 00 0f 99 0f 40   ..........I....@
+|    112: 0e da 0e 8f 0e 49 00 00 00 00 00 00 00 00 00 00   .....I..........
+|   3648: 00 00 00 00 00 00 00 00 00 44 05 06 17 15 15 08   .........D......
+|   3664: 6f 74 61 62 6c 65 67 65 6f 31 67 65 6f 31 43 52   otablegeo1geo1CR
+|   3680: 45 41 54 45 20 56 49 52 54 55 41 4c 20 54 41 42   EATE VIRTUAL TAB
+|   3696: 4c 45 20 67 65 6f 31 20 55 53 49 4e 47 20 67 65   LE geo1 USING ge
+|   3712: 6f 70 6f 6c 79 28 74 79 70 65 2c 63 6c 72 29 49   opoly(type,clr)I
+|   3728: 04 06 17 1f 1f 01 63 74 61 62 6c 65 71 75 65 72   ......ctablequer
+|   3744: 79 70 6f 6c 79 71 75 65 72 79 70 6f 6c 79 05 43   ypolyquerypoly.C
+|   3760: 52 45 41 54 45 20 54 41 42 4c 45 20 71 75 65 72   REATE TABLE quer
+|   3776: 79 70 6f 6c 79 28 70 6f 6c 79 20 4a 53 4f 4e 2c   ypoly(poly JSON,
+|   3792: 20 63 6c 72 20 54 45 58 54 29 64 03 07 17 23 23    clr TEXT)d...##
+|   3808: 01 81 0f 74 61 62 6c 65 67 65 6f 31 5f 70 61 72   ...tablegeo1_par
+|   3824: 65 6e 74 67 65 6f 31 5f 70 61 72 65 6e 74 04 43   entgeo1_parent.C
+|   3840: 52 45 41 54 45 20 54 41 42 4c 45 20 22 67 65 6f   REATE TABLE .geo
+|   3856: 31 5f 70 61 72 65 6e 74 22 28 6e 6f 64 65 6e 6f   1_parent.(nodeno
+|   3872: 20 49 4e 54 45 47 45 52 20 50 52 49 4d 41 52 59    INTEGER PRIMARY
+|   3888: 20 4b 45 59 2c 70 61 72 65 6e 74 6e 6f 64 85 29    KEY,parentnod.)
+|   3904: 57 02 06 17 1f 1f 01 7f 74 61 62 6c 65 67 65 6f   W.......tablegeo
+|   3920: 31 5f 6e 6f 64 65 67 65 6f 31 5f 6e 6f 64 65 03   1_nodegeo1_node.
+|   3936: 43 52 45 41 54 45 20 54 41 42 4c 45 20 22 67 65   CREATE TABLE .ge
+|   3952: 6f 31 5f 6e 6f 64 65 22 28 6e 6f 64 65 6e 6f 20   o1_node.(nodeno 
+|   3968: 49 4e 54 45 47 45 52 20 50 52 49 4d 41 52 59 20   INTEGER PRIMARY 
+|   3984: 4b 45 59 2c 64 61 74 61 29 65 01 07 17 21 21 01   KEY,data)e...!!.
+|   4000: 81 15 74 61 62 6c 65 67 65 6f 31 5f 72 6f 77 69   ..tablegeo1_rowi
+|   4016: 64 67 65 6f 31 5f 72 6f 77 69 64 02 43 52 45 41   dgeo1_rowid.CREA
+|   4032: 54 45 20 54 41 42 4c 45 20 22 67 65 6f 31 5f 72   TE TABLE .geo1_r
+|   4048: 6f 77 69 64 22 28 72 6f 77 69 64 20 49 4e 54 45   owid.(rowid INTE
+|   4064: 47 45 52 20 50 52 49 4d 41 52 59 20 4b 45 59 2c   GER PRIMARY KEY,
+|   4080: 6e 6f 64 65 6e 6f 2c 61 30 2c 61 31 2c 61 32 29   nodeno,a0,a1,a2)
+| page 2 offset 4096
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+|   3584: 00 40 3f 44 00 c0 20 44 00 c0 46 44 00 c0 20 44   .@?D.. D..FD.. D
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+|   3664: 44 a4 60 1d 44 61 72 72 6f 77 2d 35 30 72 65 64   D.`.Darrow-50red
+|   3680: 36 74 06 00 09 54 1b 17 01 00 00 04 00 80 0d 44   6t...T.........D
+|   3696: 00 00 f2 42 0a d7 04 44 00 00 ca 42 0a 77 05 44   ...B...D...B.w.D
+|   3712: 0a 57 c1 42 00 20 0e 44 0a 57 e9 42 6c 69 6e 65   .W.B. .D.W.Bline
+|   3728: 2d 34 30 67 72 65 65 6e 36 72 06 00 09 54 1b 17   -40green6r...T..
+|   3744: 01 00 00 04 00 00 7b 43 00 00 ea 42 29 5c 58 43   .......C...B).XC
+|   3760: 00 00 c2 42 29 dc 5a 43 0a 57 b9 42 00 80 7d 43   ...B).ZC.W.B...C
+|   3776: 0a 57 e1 42 6c 69 6e 65 2d 34 30 67 72 65 65 6e   .W.Bline-40green
+|   3792: 36 54 06 00 09 54 1b 17 01 00 00 04 00 00 a2 43   6T...T.........C
+|   3808: 00 00 24 44 00 00 b6 43 00 00 24 44 00 00 b6 43   ..$D...C..$D...C
+|   3824: 00 40 25 44 00 00 a2 43 00 40 25 44 6c 69 6e 65   .@%D...C.@%Dline
+|   3840: 2d 34 30 62 6c 61 63 6b 3e 37 06 00 09 64 1d 15   -40black>7...d..
+|   3856: 01 00 00 05 00 80 f0 43 00 00 54 43 66 16 01 44   .......C..TCf..D
+|   3872: 66 a6 30 43 cd ec 09 44 00 00 54 43 8f 0a 09 44   f.0C...D..TC...D
+|   3888: a4 d0 73 43 66 16 01 44 9a 59 77 43 68 6f 75 73   ..sCf..D.YwChous
+|   3904: 65 2d 37 30 62 6c 75 65 3e 35 06 00 09 64 1d 15   e-70blue>5...d..
+|   3920: 01 00 00 05 00 00 a2 43 00 00 5a 43 cd ac b3 43   .......C..ZC...C
+|   3936: 66 a6 36 43 9a 59 c5 43 00 00 5a 43 1f 95 c3 43   f.6C.Y.C..ZC...C
+|   3952: a4 d0 79 43 cd ac b3 43 9a 59 7d 43 68 6f 75 73   ..yC...C.Y.Chous
+|   3968: 65 2d 37 30 62 6c 75 65 3f 2c 06 00 09 64 1d 17   e-70blue?,...d..
+|   3984: 01 00 00 05 00 00 f5 43 00 00 2f 43 00 00 07 44   .......C../C...D
+|   4000: 00 00 2f 43 00 00 07 44 00 00 61 43 00 c0 00 44   ../C...D..aC...D
+|   4016: 00 00 75 43 00 00 f5 43 00 00 61 43 68 6f 75 73   ..uC...C..aChous
+|   4032: 65 2d 37 30 62 6c 61 63 6b 35 1f 06 10 09 54 19   e-70black5....T.
+|   4048: 17 01 00 00 04 00 00 9b 43 00 00 67 43 0a 57 92   ........C..gC.W.
+|   4064: 43 00 00 5d 43 0a 57 97 43 14 ae 4b 42 ff ff a0   C..]C.W.C..KB...
+|   4080: 43 14 ae 55 43 62 6f 78 2d 32 30 67 72 65 65 6e   C..UCbox-20green
+| page 3 offset 8192
+|      0: 0d 00 00 00 01 0b 2d 00 0b 2e 00 00 00 00 00 00   ......-.........
+|   2848: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 50   ...............P
+|   2864: 01 04 00 93 24 00 00 00 0a 00 00 00 00 00 00 01   ....$...........
+|   2880: 0a 43 b5 80 00 43 c9 fd 71 43 9f 82 8f 43 ad 80   .C...C..qC...C..
+|   2896: 00 00 00 00 00 00 00 00 72 43 58 5c 29 43 7d 80   ........rCX.)C..
+|   2912: 00 42 b9 57 0a 42 ea 00 00 00 00 00 00 00 00 00   .B.W.B..........
+|   2928: 35 43 a2 00 00 43 c5 59 9a 43 36 a6 66 43 7d 59   5C...C.Y.C6.fC.Y
+|   2944: 9a 00 00 00 00 00 00 00 1f 43 92 57 0a 43 a0 00   .........C.W.C..
+|   2960: 00 43 4b ae 14 43 67 00 00 00 00 00 00 00 00 00   .CK..Cg.........
+|   2976: 37 43 f0 80 00 44 09 ec cd 43 30 a6 66 43 77 59   7C...D...C0.fCwY
+|   2992: 9a 00 00 00 00 00 00 00 2c 43 f5 00 00 44 07 00   ........,C...D..
+|   3008: 00 43 2f 00 00 43 75 00 00 00 00 00 00 00 00 00   .C/..Cu.........
+|   3024: 74 44 04 d7 0a 44 0e 20 00 42 c1 57 0a 42 f2 00   tD...D. .B.W.B..
+|   3040: 00 00 00 00 00 00 00 00 ce 44 3f 40 00 44 46 c0   .........D?@.DF.
+|   3056: 00 44 20 c0 00 44 28 40 00 00 00 00 00 00 00 00   .D ..D(@........
+|   3072: be 44 54 40 00 44 5f 13 33 44 1b 36 66 44 23 c0   .DT@.D_.3D.6fD#.
+|   3088: 00 00 00 00 00 00 00 00 54 43 a2 00 00 43 b6 00   ........TC...C..
+|   3104: 00 44 24 00 00 44 25 40 00 00 00 00 00 00 00 00   .D$..D%@........
+|   3120: 54 43 a2 00 00 43 b6 00 00 44 24 00 00 44 25 40   TC...C...D$..D%@
+|   3136: 00 00 00 00 00 00 00 00 54 43 a2 00 00 43 b6 00   ........TC...C..
+|   3152: 00 44 24 00 00 44 25 40 00 00 00 00 00 00 00 00   .D$..D%@........
+|   3168: 54 43 a2 00 00 43 b6 00 00 44 24 00 00 44 25 40   TC...C...D$..D%@
+|   3184: 00 00 00 00 00 00 00 00 54 43 a2 00 00 43 b6 00   ........TC...C..
+|   3200: 00 44 24 00 00 44 25 40 00 00 00 00 00 00 00 00   .D$..D%@........
+|   3216: 54 43 a2 00 00 43 b6 00 00 44 24 00 00 44 25 40   TC...C...D$..D%@
+|   3232: 00 00 00 00 00 00 00 00 54 43 a2 00 00 43 b6 00   ........TC...C..
+|   3248: 00 44 24 00 00 44 25 40 00 00 00 00 00 00 00 00   .D$..D%@........
+|   3264: 54 43 a2 00 00 43 b6 00 00 44 24 00 00 44 25 40   TC...C...D$..D%@
+|   3280: 00 00 00 00 00 00 00 00 54 43 a2 00 00 43 b6 00   ........TC...C..
+|   3296: 00 44 24 00 00 44 25 40 00 00 00 00 00 00 00 00   .D$..D%@........
+|   3312: 54 43 a2 00 00 43 b6 00 00 44 24 00 00 44 25 40   TC...C...D$..D%@
+|   3328: 00 00 00 00 00 00 00 00 54 43 a2 00 00 43 b6 00   ........TC...C..
+|   3344: 00 44 24 00 00 44 25 40 00 00 00 00 00 00 00 01   .D$..D%@........
+|   3360: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3376: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3392: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3408: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3424: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3440: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3456: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3472: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3488: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3504: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3520: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3536: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3552: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3568: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3584: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3600: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3616: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3632: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3648: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+|   3664: 00 00 00 00 00 00 00 01 36 44 53 e0 00 44 56 bb   ........6DS..DV.
+|   3680: 64 43 71 34 bc 43 7d 00 00 00 00 00 00 00 00 01   dCq4.C..........
+|   3696: 36 44 53 e0 00 44 56 bb 64 43 71 34 bc 43 7d 00   6DS..DV.dCq4.C..
+| page 4 offset 12288
+|      0: 0d 00 00 00 00 10 00 00 00 00 00 00 00 00 00 00   ................
+| page 5 offset 16384
+|      0: 0d 00 00 00 01 0f 8f 00 00 00 00 00 00 00 00 00   ................
+|   3968: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6f   ...............o
+|   3984: 01 04 81 57 19 5b 5b 33 30 30 2c 33 30 30 5d 2c   ...W.[[300,300],
+|   4000: 5b 34 30 30 2c 33 35 30 5d 2c 5b 35 30 30 2c 32   [400,350],[500,2
+|   4016: 35 30 5d 2c 5b 34 38 30 2c 35 30 30 5d 2c 5b 34   50],[480,500],[4
+|   4032: 30 30 2c 34 38 30 5d 2c 5c 33 30 30 2c 35 35 30   00,480],.300,550
+|   4048: 5d 2c 5b 32 38 30 2c 34 35 30 5d 2c 5b 33 32 30   ],[280,450],[320
+|   4064: 2c 34 30 30 5d 2c 5b 32 38 30 2c 33 35 30 5d 2c   ,400],[280,350],
+|   4080: 5b 33 30 30 2c 33 30 00 00 00 00 00 00 00 00 00   [300,30.........
+| end crash-7b37d80f000235.db
+}]} {}
+
+ifcapable geopoly {
+
+do_catchsql_test rtreefuzz001-601 {
+  SAVEPOINT one;
+  UPDATE geo1 SET clr=CASE WHEN rowid IN ( SELECT geo1.rowid FROM geo1, querypoly ) THEN 'e' ELSE 'blue' END;
+} {1 {database disk image is malformed}}
+
+do_catchsql_test rtreefuzz001-602 {
+  SELECT geopoly_svg(_shape, printf('j',geo1.clr)) 
+    FROM geo1, querypoly WHERE geopoly_overlap(_shape, poly);
+} {1 {database disk image is malformed}}
+
+} ;# ifcapable geopoly
+
+finish_test
diff --git a/ext/rtree/sqlite3rtree.h b/ext/rtree/sqlite3rtree.h
new file mode 100644
index 0000000..9976c2d
--- /dev/null
+++ b/ext/rtree/sqlite3rtree.h
@@ -0,0 +1,117 @@
+/*
+** 2010 August 30
+**
+** 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.
+**
+*************************************************************************
+*/
+
+#ifndef _SQLITE3RTREE_H_
+#define _SQLITE3RTREE_H_
+
+#include <sqlite3.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+typedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;
+typedef struct sqlite3_rtree_query_info sqlite3_rtree_query_info;
+
+/* The double-precision datatype used by RTree depends on the
+** SQLITE_RTREE_INT_ONLY compile-time option.
+*/
+#ifdef SQLITE_RTREE_INT_ONLY
+  typedef sqlite3_int64 sqlite3_rtree_dbl;
+#else
+  typedef double sqlite3_rtree_dbl;
+#endif
+
+/*
+** Register a geometry callback named zGeom that can be used as part of an
+** R-Tree geometry query as follows:
+**
+**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)
+*/
+int sqlite3_rtree_geometry_callback(
+  sqlite3 *db,
+  const char *zGeom,
+  int (*xGeom)(sqlite3_rtree_geometry*, int, sqlite3_rtree_dbl*,int*),
+  void *pContext
+);
+
+
+/*
+** A pointer to a structure of the following type is passed as the first
+** argument to callbacks registered using rtree_geometry_callback().
+*/
+struct sqlite3_rtree_geometry {
+  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */
+  int nParam;                     /* Size of array aParam[] */
+  sqlite3_rtree_dbl *aParam;      /* Parameters passed to SQL geom function */
+  void *pUser;                    /* Callback implementation user data */
+  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */
+};
+
+/*
+** Register a 2nd-generation geometry callback named zScore that can be 
+** used as part of an R-Tree geometry query as follows:
+**
+**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zQueryFunc(... params ...)
+*/
+int sqlite3_rtree_query_callback(
+  sqlite3 *db,
+  const char *zQueryFunc,
+  int (*xQueryFunc)(sqlite3_rtree_query_info*),
+  void *pContext,
+  void (*xDestructor)(void*)
+);
+
+
+/*
+** A pointer to a structure of the following type is passed as the 
+** argument to scored geometry callback registered using
+** sqlite3_rtree_query_callback().
+**
+** Note that the first 5 fields of this structure are identical to
+** sqlite3_rtree_geometry.  This structure is a subclass of
+** sqlite3_rtree_geometry.
+*/
+struct sqlite3_rtree_query_info {
+  void *pContext;                   /* pContext from when function registered */
+  int nParam;                       /* Number of function parameters */
+  sqlite3_rtree_dbl *aParam;        /* value of function parameters */
+  void *pUser;                      /* callback can use this, if desired */
+  void (*xDelUser)(void*);          /* function to free pUser */
+  sqlite3_rtree_dbl *aCoord;        /* Coordinates of node or entry to check */
+  unsigned int *anQueue;            /* Number of pending entries in the queue */
+  int nCoord;                       /* Number of coordinates */
+  int iLevel;                       /* Level of current node or entry */
+  int mxLevel;                      /* The largest iLevel value in the tree */
+  sqlite3_int64 iRowid;             /* Rowid for current entry */
+  sqlite3_rtree_dbl rParentScore;   /* Score of parent node */
+  int eParentWithin;                /* Visibility of parent node */
+  int eWithin;                      /* OUT: Visibility */
+  sqlite3_rtree_dbl rScore;         /* OUT: Write the score here */
+  /* The following fields are only available in 3.8.11 and later */
+  sqlite3_value **apSqlParam;       /* Original SQL values of parameters */
+};
+
+/*
+** Allowed values for sqlite3_rtree_query.eWithin and .eParentWithin.
+*/
+#define NOT_WITHIN       0   /* Object completely outside of query region */
+#define PARTLY_WITHIN    1   /* Object partially overlaps query region */
+#define FULLY_WITHIN     2   /* Object fully contained within query region */
+
+
+#ifdef __cplusplus
+}  /* end of the 'extern "C"' block */
+#endif
+
+#endif  /* ifndef _SQLITE3RTREE_H_ */
diff --git a/ext/rtree/test_rtreedoc.c b/ext/rtree/test_rtreedoc.c
new file mode 100644
index 0000000..cdbcb2e
--- /dev/null
+++ b/ext/rtree/test_rtreedoc.c
@@ -0,0 +1,348 @@
+/*
+** 2010 August 28
+**
+** The author disclaims copyright to this source code.  In place of
+** a legal notice, here is a blessing:
+**
+**    May you do good and not evil.
+**    May you find forgiveness for yourself and forgive others.
+**    May you share freely, never taking more than you give.
+**
+*************************************************************************
+** Code for testing all sorts of SQLite interfaces. This code
+** is not included in the SQLite library. 
+*/
+
+#include "sqlite3.h"
+#if defined(INCLUDE_SQLITE_TCL_H)
+#  include "sqlite_tcl.h"
+#else
+#  include "tcl.h"
+#endif
+
+/* Solely for the UNUSED_PARAMETER() macro. */
+#include "sqliteInt.h"
+
+#ifdef SQLITE_ENABLE_RTREE
+
+typedef struct BoxGeomCtx BoxGeomCtx;
+struct BoxGeomCtx {
+  Tcl_Interp *interp;
+  Tcl_Obj *pScript;
+};
+
+typedef struct BoxQueryCtx BoxQueryCtx;
+struct BoxQueryCtx {
+  Tcl_Interp *interp;
+  Tcl_Obj *pScript;
+};
+
+static void testDelUser(void *pCtx){
+  BoxGeomCtx *p = (BoxGeomCtx*)pCtx;
+  Tcl_EvalObjEx(p->interp, p->pScript, 0);
+  Tcl_DecrRefCount(p->pScript);
+  sqlite3_free(p);
+}
+
+static int invokeTclGeomCb(
+  const char *zName, 
+  sqlite3_rtree_geometry *p, 
+  int nCoord,
+  sqlite3_rtree_dbl *aCoord
+){
+  int rc = SQLITE_OK;
+  if( p->pContext ){
+    char aPtr[64];
+    BoxGeomCtx *pCtx = (BoxGeomCtx*)p->pContext;
+    Tcl_Interp *interp = pCtx->interp;
+    Tcl_Obj *pScript = 0;
+    Tcl_Obj *pParam = 0;
+    Tcl_Obj *pCoord = 0;
+    int ii;
+    Tcl_Obj *pRes;
+
+
+    pScript = Tcl_DuplicateObj(pCtx->pScript);
+    Tcl_IncrRefCount(pScript);
+    Tcl_ListObjAppendElement(interp, pScript, Tcl_NewStringObj(zName,-1));
+
+    sqlite3_snprintf(sizeof(aPtr)-1, aPtr, "%p", (void*)p->pContext);
+    Tcl_ListObjAppendElement(interp, pScript, Tcl_NewStringObj(aPtr,-1));
+
+    pParam = Tcl_NewObj();
+    for(ii=0; ii<p->nParam; ii++){
+      Tcl_ListObjAppendElement(
+          interp, pParam, Tcl_NewDoubleObj(p->aParam[ii])
+      );
+    }
+    Tcl_ListObjAppendElement(interp, pScript, pParam);
+
+    pCoord = Tcl_NewObj();
+    for(ii=0; ii<nCoord; ii++){
+      Tcl_ListObjAppendElement(interp, pCoord, Tcl_NewDoubleObj(aCoord[ii]));
+    }
+    Tcl_ListObjAppendElement(interp, pScript, pCoord);
+
+    sqlite3_snprintf(sizeof(aPtr)-1, aPtr, "%p", (void*)p);
+    Tcl_ListObjAppendElement(interp, pScript, Tcl_NewStringObj(aPtr,-1));
+
+    rc = Tcl_EvalObjEx(interp, pScript, 0);
+    if( rc!=TCL_OK ){
+      rc = SQLITE_ERROR;
+    }else{
+      int nObj = 0;
+      Tcl_Obj **aObj = 0;
+
+      pRes = Tcl_GetObjResult(interp);
+      if( Tcl_ListObjGetElements(interp, pRes, &nObj, &aObj) ) return TCL_ERROR;
+      if( nObj>0 ){
+        const char *zCmd = Tcl_GetString(aObj[0]);
+        if( 0==sqlite3_stricmp(zCmd, "zero") ){
+          p->aParam[0] = 0.0;
+          p->nParam = 1;
+        }
+        else if( 0==sqlite3_stricmp(zCmd, "user") ){
+          if( p->pUser || p->xDelUser ){
+            rc = SQLITE_ERROR;
+          }else{
+            BoxGeomCtx *pBGCtx = sqlite3_malloc(sizeof(BoxGeomCtx));
+            if( pBGCtx==0 ){
+              rc = SQLITE_NOMEM;
+            }else{
+              pBGCtx->interp = interp;
+              pBGCtx->pScript = Tcl_DuplicateObj(pRes);
+              Tcl_IncrRefCount(pBGCtx->pScript);
+              Tcl_ListObjReplace(interp, pBGCtx->pScript, 0, 1, 0, 0);
+              p->pUser = (void*)pBGCtx;
+              p->xDelUser = testDelUser;
+            }
+          }
+        }
+        else if( 0==sqlite3_stricmp(zCmd, "user_is_zero") ){
+          if( p->pUser || p->xDelUser ) rc = SQLITE_ERROR;
+        }
+      }
+    }
+  }
+  return rc;
+}
+
+/*
+# EVIDENCE-OF: R-00693-36727 The legacy xGeom callback is invoked with
+# four arguments.
+
+# EVIDENCE-OF: R-50437-53270 The first argument is a pointer to an
+# sqlite3_rtree_geometry structure which provides information about how
+# the SQL function was invoked.
+
+# EVIDENCE-OF: R-00090-24248 The third argument, aCoord[], is an array
+# of nCoord coordinates that defines a bounding box to be tested.
+
+# EVIDENCE-OF: R-28207-40885 The last argument is a pointer into which
+# the callback result should be written.
+
+*/
+static int box_geom(
+  sqlite3_rtree_geometry *p,      /* R-50437-53270 */
+  int nCoord,                     /* R-02424-24769 */
+  sqlite3_rtree_dbl *aCoord,      /* R-00090-24248 */
+  int *pRes                       /* R-28207-40885 */
+){
+  int ii;
+
+  if( p->nParam!=nCoord ){
+    invokeTclGeomCb("box", p, nCoord, aCoord);
+    return SQLITE_ERROR;
+  }
+  if( invokeTclGeomCb("box", p, nCoord, aCoord) ) return SQLITE_ERROR;
+
+  for(ii=0; ii<nCoord; ii+=2){
+    if( aCoord[ii]>p->aParam[ii+1] || aCoord[ii+1]<p->aParam[ii] ){
+      /* R-28207-40885 */
+      *pRes = 0;
+      return SQLITE_OK;
+    }
+  }
+
+  /* R-28207-40885 */
+  *pRes = 1;
+
+  return SQLITE_OK;
+}
+
+static int SQLITE_TCLAPI register_box_geom(
+  void * clientData,
+  Tcl_Interp *interp,
+  int objc,
+  Tcl_Obj *CONST objv[]
+){
+  extern int getDbPointer(Tcl_Interp*, const char*, sqlite3**);
+  extern const char *sqlite3ErrName(int);
+  sqlite3 *db;
+  BoxGeomCtx *pCtx;
+  char aPtr[64];
+
+  if( objc!=3 ){
+    Tcl_WrongNumArgs(interp, 1, objv, "DB SCRIPT");
+    return TCL_ERROR;
+  }
+  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;
+
+  pCtx = (BoxGeomCtx*)ckalloc(sizeof(BoxGeomCtx*));
+  pCtx->interp = interp;
+  pCtx->pScript = Tcl_DuplicateObj(objv[2]);
+  Tcl_IncrRefCount(pCtx->pScript);
+
+  sqlite3_rtree_geometry_callback(db, "box", box_geom, (void*)pCtx);
+
+  sqlite3_snprintf(64, aPtr, "%p", (void*)pCtx);
+  Tcl_SetObjResult(interp, Tcl_NewStringObj(aPtr, -1));
+  return TCL_OK;
+}
+
+static int box_query(sqlite3_rtree_query_info *pInfo){
+  const char *azParentWithin[] = {"not", "partly", "fully", 0};
+  BoxQueryCtx *pCtx = (BoxQueryCtx*)pInfo->pContext;
+  Tcl_Interp *interp = pCtx->interp;
+  Tcl_Obj *pEval;
+  Tcl_Obj *pArg;
+  Tcl_Obj *pTmp = 0;
+  int rc;
+  int ii;
+
+  pEval = Tcl_DuplicateObj(pCtx->pScript);
+  Tcl_IncrRefCount(pEval);
+  pArg = Tcl_NewObj();
+  Tcl_IncrRefCount(pArg);
+
+  /* aParam[] */
+  pTmp = Tcl_NewObj();
+  Tcl_IncrRefCount(pTmp);
+  for(ii=0; ii<pInfo->nParam; ii++){
+    Tcl_Obj *p = Tcl_NewDoubleObj(pInfo->aParam[ii]);
+    Tcl_ListObjAppendElement(interp, pTmp, p);
+  }
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("aParam", -1));
+  Tcl_ListObjAppendElement(interp, pArg, pTmp);
+  Tcl_DecrRefCount(pTmp);
+
+  /* aCoord[] */
+  pTmp = Tcl_NewObj();
+  Tcl_IncrRefCount(pTmp);
+  for(ii=0; ii<pInfo->nCoord; ii++){
+    Tcl_Obj *p = Tcl_NewDoubleObj(pInfo->aCoord[ii]);
+    Tcl_ListObjAppendElement(interp, pTmp, p);
+  }
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("aCoord", -1));
+  Tcl_ListObjAppendElement(interp, pArg, pTmp);
+  Tcl_DecrRefCount(pTmp);
+
+  /* anQueue[] */
+  pTmp = Tcl_NewObj();
+  Tcl_IncrRefCount(pTmp);
+  for(ii=0; ii<=pInfo->mxLevel; ii++){
+    Tcl_Obj *p = Tcl_NewIntObj((int)pInfo->anQueue[ii]);
+    Tcl_ListObjAppendElement(interp, pTmp, p);
+  }
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("anQueue", -1));
+  Tcl_ListObjAppendElement(interp, pArg, pTmp);
+  Tcl_DecrRefCount(pTmp);
+  
+  /* iLevel */
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("iLevel", -1));
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewIntObj(pInfo->iLevel));
+
+  /* mxLevel */
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("mxLevel", -1));
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewIntObj(pInfo->mxLevel));
+
+  /* iRowid */
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("iRowid", -1));
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewWideIntObj(pInfo->iRowid));
+
+  /* rParentScore */
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("rParentScore", -1));
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewDoubleObj(pInfo->rParentScore));
+
+  /* eParentWithin */
+  assert( pInfo->eParentWithin==0 
+       || pInfo->eParentWithin==1 
+       || pInfo->eParentWithin==2 
+  );
+  Tcl_ListObjAppendElement(interp, pArg, Tcl_NewStringObj("eParentWithin", -1));
+  Tcl_ListObjAppendElement(interp, pArg, 
+      Tcl_NewStringObj(azParentWithin[pInfo->eParentWithin], -1)
+  );
+
+  Tcl_ListObjAppendElement(interp, pEval, pArg);
+  rc = Tcl_EvalObjEx(interp, pEval, 0) ? SQLITE_ERROR : SQLITE_OK;
+
+  if( rc==SQLITE_OK ){
+    double rScore = 0.0;
+    int nObj = 0;
+    int eP = 0;
+    Tcl_Obj **aObj = 0;
+    Tcl_Obj *pRes = Tcl_GetObjResult(interp);
+
+    if( Tcl_ListObjGetElements(interp, pRes, &nObj, &aObj) 
+     || nObj!=2 
+     || Tcl_GetDoubleFromObj(interp, aObj[1], &rScore)
+     || Tcl_GetIndexFromObj(interp, aObj[0], azParentWithin, "value", 0, &eP)
+    ){
+      rc = SQLITE_ERROR;
+    }else{
+      pInfo->rScore = rScore;
+      pInfo->eParentWithin = eP;
+    }
+  }
+
+  Tcl_DecrRefCount(pArg);
+  Tcl_DecrRefCount(pEval);
+  return rc;
+}
+
+static void box_query_destroy(void *p){
+  BoxQueryCtx *pCtx = (BoxQueryCtx*)p;
+  Tcl_DecrRefCount(pCtx->pScript);
+  ckfree((char*)pCtx);
+}
+
+static int SQLITE_TCLAPI register_box_query(
+  void * clientData,
+  Tcl_Interp *interp,
+  int objc,
+  Tcl_Obj *CONST objv[]
+){
+  extern int getDbPointer(Tcl_Interp*, const char*, sqlite3**);
+  extern const char *sqlite3ErrName(int);
+  sqlite3 *db;
+  BoxQueryCtx *pCtx;
+
+  if( objc!=3 ){
+    Tcl_WrongNumArgs(interp, 1, objv, "DB SCRIPT");
+    return TCL_ERROR;
+  }
+  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;
+
+  pCtx = (BoxQueryCtx*)ckalloc(sizeof(BoxQueryCtx));
+  pCtx->interp = interp;
+  pCtx->pScript = Tcl_DuplicateObj(objv[2]);
+  Tcl_IncrRefCount(pCtx->pScript);
+
+  sqlite3_rtree_query_callback(
+      db, "qbox", box_query, (void*)pCtx, box_query_destroy
+  );
+
+  Tcl_ResetResult(interp);
+  return TCL_OK;
+}
+#endif /* SQLITE_ENABLE_RTREE */
+
+
+int Sqlitetestrtreedoc_Init(Tcl_Interp *interp){
+#ifdef SQLITE_ENABLE_RTREE
+  Tcl_CreateObjCommand(interp, "register_box_geom", register_box_geom, 0, 0);
+  Tcl_CreateObjCommand(interp, "register_box_query", register_box_query, 0, 0);
+#endif /* SQLITE_ENABLE_RTREE */
+  return TCL_OK;
+}
diff --git a/ext/rtree/tkt3363.test b/ext/rtree/tkt3363.test
new file mode 100644
index 0000000..db05ed5
--- /dev/null
+++ b/ext/rtree/tkt3363.test
@@ -0,0 +1,50 @@
+# 2008 Sep 08
+#
+# 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.
+#
+#***********************************************************************
+#
+# The focus of this file is testing that ticket #3363 is fixed.
+#
+
+if {![info exists testdir]} {
+  set testdir [file join [file dirname [info script]] .. .. test]
+}
+source [file join [file dirname [info script]] rtree_util.tcl]
+source $testdir/tester.tcl
+
+ifcapable !rtree {
+  finish_test
+  return
+}
+
+do_test tkt3363.1.1 {
+  execsql { CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2) }
+} {}
+
+do_test tkt3363.1.2 {
+  for {set ii 1} {$ii < 50} {incr ii} {
+    set x 1000000
+    set y [expr 4000000 + $ii*10]
+    execsql { INSERT INTO t1 VALUES($ii, $x, $x, $y, $y) }
+  }
+} {}
+
+do_test tkt3363.1.3 {
+  execsql { 
+    SELECT count(*) FROM t1 WHERE +y2>4000425.0;
+  }
+} {7}
+
+do_test tkt3363.1.4 {
+  execsql { 
+    SELECT count(*) FROM t1 WHERE y2>4000425.0;
+  }
+} {7}
+
+finish_test
diff --git a/ext/rtree/util/randomshape.tcl b/ext/rtree/util/randomshape.tcl
new file mode 100644
index 0000000..98725bc
--- /dev/null
+++ b/ext/rtree/util/randomshape.tcl
@@ -0,0 +1,87 @@
+#!/usr/bin/tclsh
+#
+# This script generates a cluster of random polygons that are useful
+# for testing the geopoly extension.
+#
+# Usage:
+#
+#    tclsh randomshape.tcl | tee x.sql | sqlite3 >x.html
+#
+# The output files are x.sql and x.html.  Run the above multiple times
+# until an interesting "x.html" file is found, then use the "x.sql" inputs
+# to construct test cases.
+#
+proc randomenclosure {cx cy p1 p2 p3 p4} {
+  set r 0
+  set pi 3.145926
+  set pi2 [expr {$pi*2}]
+  set x0 [expr {$cx + rand()*$p3 + $p4}]
+  set ans "\[\[$x0,$cy\]"
+  while {1} {
+    set r [expr {$r+$p1+$p2*rand()}]
+    if {$r>=$pi2} break
+    set m [expr {rand()*$p3 + $p4}]
+    set x [expr {$cx+$m*cos($r)}]
+    set y [expr {$cy+$m*sin($r)}]
+    append ans ",\[$x,$y\]"
+  }
+  append ans ",\[$x0,$cy\]\]"
+  return $ans
+}
+proc randomshape1 {} {
+  set cx [expr {100+int(rand()*800)}]
+  set cy [expr {100+int(rand()*600)}]
+  set p1 [expr {rand()*0.1}]
+  set p2 [expr {rand()*0.5+0.5}]
+  set p3 [expr {rand()*100+25}]
+  set p4 [expr {rand()*25}]
+  return [randomenclosure $cx $cy $p1 $p2 $p3 $p4]
+}
+proc randomshape1_sm {} {
+  set cx [expr {100+int(rand()*800)}]
+  set cy [expr {100+int(rand()*600)}]
+  set p1 [expr {rand()*0.1}]
+  set p2 [expr {rand()*0.5+0.5}]
+  set p3 [expr {rand()*10+25}]
+  set p4 [expr {rand()*5}]
+  return [randomenclosure $cx $cy $p1 $p2 $p3 $p4]
+}
+proc randomshape2 {} {
+  set cx [expr {400+int(rand()*200)}]
+  set cy [expr {300+int(rand()*200)}]
+  set p1 [expr {rand()*0.05}]
+  set p2 [expr {rand()*0.5+0.5}]
+  set p3 [expr {rand()*50+200}]
+  set p4 [expr {rand()*50+100}]
+  return [randomenclosure $cx $cy $p1 $p2 $p3 $p4]
+}
+proc randomcolor {} {
+  set n [expr {int(rand()*5)}]
+  return [lindex {red orange green blue purple} $n]
+}
+
+puts {.print '<html>'}
+puts {.print '<svg width="1000" height="800" style="border:1px solid black">'}
+puts {CREATE TABLE t1(poly,clr);}
+puts {CREATE TABLE t2(poly,clr);}
+for {set i 0} {$i<30} {incr i} {
+  puts "INSERT INTO t1(rowid,poly,clr)"
+  puts " VALUES($i,'[randomshape1]','[randomcolor]');"
+}
+for {set i 30} {$i<80} {incr i} {
+  puts "INSERT INTO t1(rowid,poly,clr)"
+  puts " VALUES($i,'[randomshape1_sm]','[randomcolor]');"
+}
+for {set i 100} {$i<105} {incr i} {
+  puts "INSERT INTO t2(rowid,poly,clr)"
+  puts " VALUES($i,'[randomshape2]','[randomcolor]');"
+}
+
+puts {DELETE FROM t1 WHERE geopoly_json(poly) IS NULL;}
+puts {SELECT geopoly_svg(poly,
+   printf('style="fill:none;stroke:%s;stroke-width:1;"',clr))
+  FROM t1;}
+puts {SELECT geopoly_svg(poly,
+   printf('style="fill:none;stroke:%s;stroke-width:2;"',clr))
+  FROM t2;}
+puts {.print '<svg>'}
diff --git a/ext/rtree/viewrtree.tcl b/ext/rtree/viewrtree.tcl
new file mode 100644
index 0000000..794677f
--- /dev/null
+++ b/ext/rtree/viewrtree.tcl
@@ -0,0 +1,188 @@
+
+load ./libsqlite3.dylib
+#package require sqlite3
+source [file join [file dirname $argv0] rtree_util.tcl]
+
+wm title . "SQLite r-tree viewer"
+
+if {[llength $argv]!=1} {
+  puts stderr "Usage: $argv0 <database-file>"
+  puts stderr ""
+  exit
+}
+sqlite3 db [lindex $argv 0]
+
+canvas .c -background white -width 400 -height 300 -highlightthickness 0
+
+button .b -text "Parent Node" -command {
+  set sql "SELECT parentnode FROM $::O(zTab)_parent WHERE nodeno = $::O(iNode)"
+  set ::O(iNode) [db one $sql]
+  if {$::O(iNode) eq ""} {set ::O(iNode) 1}
+  view_node
+}
+
+set O(iNode) 1
+set O(zTab) ""
+set O(listbox_captions)  [list]
+set O(listbox_itemmap)   [list]
+set O(listbox_highlight) -1
+
+listbox   .l -listvariable ::O(listbox_captions) -yscrollcommand {.ls set}
+scrollbar .ls -command {.l yview}
+label     .status -font courier -anchor w
+label     .title -anchor w -text "Node 1:" -background white -borderwidth 0
+
+
+set rtree_tables [list]
+db eval {
+  SELECT name 
+  FROM sqlite_master 
+  WHERE type='table' AND sql LIKE '%virtual%table%using%rtree%'
+} {
+  set nCol [expr [llength [db eval "pragma table_info($name)"]]/6]
+  if {$nCol != 5} {
+    puts stderr "Not viewing $name - is not 2-dimensional"
+  } else {
+    lappend rtree_tables [list Table $name]
+  }
+}
+if {$rtree_tables eq ""} {
+  puts stderr "Cannot find an r-tree table in database [lindex $argv 0]"
+  puts stderr ""
+  exit
+}
+eval tk_optionMenu .select option_var $rtree_tables
+trace add variable option_var write set_option_var
+proc set_option_var {args} {
+  set ::O(zTab) [lindex $::option_var 1]
+  set ::O(iNode) 1
+  view_node
+}
+set ::O(zTab) [lindex $::rtree_tables 0 1]
+
+bind .l <1> {listbox_click [.l nearest %y]}
+bind .l <Motion> {listbox_mouseover [.l nearest %y]}
+bind .l <Leave>  {listbox_mouseover -1}
+
+proc listbox_click {sel} {
+  if {$sel ne ""} {
+    set ::O(iNode) [lindex $::O(listbox_captions) $sel 1]
+    view_node
+  }
+}
+proc listbox_mouseover {i} {
+  set oldid [lindex $::O(listbox_itemmap) $::O(listbox_highlight)]
+  .c itemconfigure $oldid -fill ""
+
+  .l selection clear 0 end
+  .status configure -text ""
+  if {$i>=0} {
+    set id [lindex $::O(listbox_itemmap) $i]
+    .c itemconfigure $id -fill grey
+    .c lower $id
+    set ::O(listbox_highlight) $i
+    .l selection set $i
+    .status configure -text [cell_report db $::O(zTab) $::O(iNode) $i]
+  }
+}
+
+grid configure .select  -row 0 -column 0 -columnspan 2 -sticky nsew
+grid configure .b       -row 1 -column 0 -columnspan 2 -sticky nsew
+grid configure .l       -row 2 -column 0               -sticky nsew
+grid configure .status  -row 3 -column 0 -columnspan 3 -sticky nsew
+
+grid configure .title   -row 0 -column 2               -sticky nsew
+grid configure .c       -row 1 -column 2 -rowspan 2    -sticky nsew
+grid configure .ls      -row 2 -column 1               -sticky nsew
+
+grid columnconfigure . 2 -weight 1
+grid rowconfigure    . 2 -weight 1
+
+proc node_bbox {data} {
+  set xmin 0
+  set xmax 0
+  set ymin 0
+  set ymax 0
+  foreach {rowid xmin xmax ymin ymax} [lindex $data 0] break
+  foreach cell [lrange $data 1 end] {
+    foreach {rowid x1 x2 y1 y2} $cell break
+    if {$x1 < $xmin} {set xmin $x1}
+    if {$x2 > $xmax} {set xmax $x2}
+    if {$y1 < $ymin} {set ymin $y1}
+    if {$y2 > $ymax} {set ymax $y2}
+  }
+  list $xmin $xmax $ymin $ymax
+}
+
+proc view_node {} {
+  set iNode $::O(iNode)
+  set zTab $::O(zTab)
+
+  set data [rtree_node db $zTab $iNode 12]
+  set depth [rtree_nodedepth db $zTab $iNode]
+
+  .c delete all
+  set ::O(listbox_captions) [list]
+  set ::O(listbox_itemmap) [list]
+  set $::O(listbox_highlight) -1
+
+  .b configure -state normal
+  if {$iNode == 1} {.b configure -state disabled}
+  .title configure -text "Node $iNode: [cell_report db $zTab $iNode -1]"
+
+  foreach {xmin xmax ymin ymax} [node_bbox $data] break
+  set total_area 0.0
+
+  set xscale [expr {double([winfo width .c]-20)/($xmax-$xmin)}]
+  set yscale [expr {double([winfo height .c]-20)/($ymax-$ymin)}]
+
+  set xoff [expr {10.0 - $xmin*$xscale}]
+  set yoff [expr {10.0 - $ymin*$yscale}]
+
+  foreach cell $data {
+    foreach {rowid x1 x2 y1 y2} $cell break
+    set total_area [expr {$total_area + ($x2-$x1)*($y2-$y1)}]
+    set x1 [expr {$x1*$xscale + $xoff}]
+    set x2 [expr {$x2*$xscale + $xoff}]
+    set y1 [expr {$y1*$yscale + $yoff}]
+    set y2 [expr {$y2*$yscale + $yoff}]
+
+    set id [.c create rectangle $x1 $y1 $x2 $y2]
+    if {$depth>0} {
+      lappend ::O(listbox_captions) "Node $rowid"
+      lappend ::O(listbox_itemmap) $id
+    }
+  }
+}
+
+proc cell_report {db zTab iParent iCell} {
+  set data [rtree_node db $zTab $iParent 12]
+  set cell [lindex $data $iCell]
+
+  foreach {xmin xmax ymin ymax} [node_bbox $data] break
+  set total_area [expr ($xmax-$xmin)*($ymax-$ymin)]
+
+  if {$cell eq ""} {
+    set cell_area 0.0
+    foreach cell $data {
+      foreach {rowid x1 x2 y1 y2} $cell break
+      set cell_area [expr $cell_area+($x2-$x1)*($y2-$y1)]
+    }
+    set cell_area [expr $cell_area/[llength $data]]
+    set zReport [format "Size = %.1f x %.1f    Average child area = %.1f%%" \
+      [expr $xmax-$xmin] [expr $ymax-$ymin] [expr 100.0*$cell_area/$total_area]\
+    ]
+    append zReport "   Sub-tree height: [rtree_nodedepth db $zTab $iParent]"
+  } else {
+    foreach {rowid x1 x2 y1 y2} $cell break
+    set cell_area  [expr ($x2-$x1)*($y2-$y1)]
+    set zReport [format "Size = %.1f x %.1f    Area = %.1f%%" \
+      [expr $x2-$x1] [expr $y2-$y1] [expr 100.0*$cell_area/$total_area]
+    ]
+  }
+
+  return $zReport
+}
+
+view_node
+bind .c <Configure> view_node
diff --git a/ext/rtree/visual01.txt b/ext/rtree/visual01.txt
new file mode 100644
index 0000000..281d610
--- /dev/null
+++ b/ext/rtree/visual01.txt
@@ -0,0 +1,602 @@
+#!sqlite3
+#
+# This is a visual test case for the geopoly virtual table.
+#
+# Run this script in the sqlite3 CLI, and redirect output into an
+# HTML file.  This display the HTML in a webbrowser.
+#
+
+/* Test data.
+** Lots of shapes to be displayed over a 1000x800 canvas.
+*/
+CREATE TEMP TABLE basis(name TEXT, jshape TEXT);
+INSERT INTO basis(name,jshape) VALUES
+  ('box-20','[[0,0],[20,0],[20,20],[0,20],[0,0]]'),
+  ('house-70','[[0,0],[50,0],[50,50],[25,70],[0,50],[0,0]]'),
+  ('line-40','[[0,0],[40,0],[40,5],[0,5],[0,0]]'),
+  ('line-80','[[0,0],[80,0],[80,7],[0,7],[0,0]]'),
+  ('arrow-50','[[0,0],[25,25],[0,50],[15,25],[0,0]]'),
+  ('triangle-30','[[0,0],[30,0],[15,30],[0,0]]'),
+  ('angle-30','[[0,0],[30,0],[30,30],[26,30],[26,4],[0,4],[0,0]]'),
+  ('star-10','[[1,0],[5,2],[9,0],[7,4],[10,8],[7,7],[5,10],[3,7],[0,8],[3,4],[1,0]]');
+CREATE TEMP TABLE xform(A,B,C,D,clr);
+INSERT INTO xform(A,B,clr) VALUES
+  (1,0,'black'),
+  (0.707,0.707,'blue'),
+  (0.5,0.866,'red'),
+  (-0.866,0.5,'green');
+CREATE TEMP TABLE xyoff(id1,id2,xoff,yoff,PRIMARY KEY(id1,id2,xoff,yoff))
+  WITHOUT ROWID;
+INSERT INTO xyoff VALUES(1,1,811,659);
+INSERT INTO xyoff VALUES(1,1,235,550);
+INSERT INTO xyoff VALUES(1,1,481,620);
+INSERT INTO xyoff VALUES(1,1,106,494);
+INSERT INTO xyoff VALUES(1,1,487,106);
+INSERT INTO xyoff VALUES(1,1,817,595);
+INSERT INTO xyoff VALUES(1,1,240,504);
+INSERT INTO xyoff VALUES(1,1,806,457);
+INSERT INTO xyoff VALUES(1,1,608,107);
+INSERT INTO xyoff VALUES(1,1,768,662);
+INSERT INTO xyoff VALUES(1,2,808,528);
+INSERT INTO xyoff VALUES(1,2,768,528);
+INSERT INTO xyoff VALUES(1,2,771,171);
+INSERT INTO xyoff VALUES(1,2,275,671);
+INSERT INTO xyoff VALUES(1,2,326,336);
+INSERT INTO xyoff VALUES(1,2,690,688);
+INSERT INTO xyoff VALUES(1,2,597,239);
+INSERT INTO xyoff VALUES(1,2,317,528);
+INSERT INTO xyoff VALUES(1,2,366,223);
+INSERT INTO xyoff VALUES(1,2,621,154);
+INSERT INTO xyoff VALUES(1,3,829,469);
+INSERT INTO xyoff VALUES(1,3,794,322);
+INSERT INTO xyoff VALUES(1,3,358,387);
+INSERT INTO xyoff VALUES(1,3,184,444);
+INSERT INTO xyoff VALUES(1,3,729,500);
+INSERT INTO xyoff VALUES(1,3,333,523);
+INSERT INTO xyoff VALUES(1,3,117,595);
+INSERT INTO xyoff VALUES(1,3,496,201);
+INSERT INTO xyoff VALUES(1,3,818,601);
+INSERT INTO xyoff VALUES(1,3,541,343);
+INSERT INTO xyoff VALUES(1,4,603,248);
+INSERT INTO xyoff VALUES(1,4,761,649);
+INSERT INTO xyoff VALUES(1,4,611,181);
+INSERT INTO xyoff VALUES(1,4,607,233);
+INSERT INTO xyoff VALUES(1,4,860,206);
+INSERT INTO xyoff VALUES(1,4,310,231);
+INSERT INTO xyoff VALUES(1,4,727,539);
+INSERT INTO xyoff VALUES(1,4,660,661);
+INSERT INTO xyoff VALUES(1,4,403,133);
+INSERT INTO xyoff VALUES(1,4,619,331);
+INSERT INTO xyoff VALUES(2,1,712,578);
+INSERT INTO xyoff VALUES(2,1,567,313);
+INSERT INTO xyoff VALUES(2,1,231,423);
+INSERT INTO xyoff VALUES(2,1,490,175);
+INSERT INTO xyoff VALUES(2,1,898,353);
+INSERT INTO xyoff VALUES(2,1,589,483);
+INSERT INTO xyoff VALUES(2,1,188,462);
+INSERT INTO xyoff VALUES(2,1,720,106);
+INSERT INTO xyoff VALUES(2,1,793,380);
+INSERT INTO xyoff VALUES(2,1,154,396);
+INSERT INTO xyoff VALUES(2,2,324,218);
+INSERT INTO xyoff VALUES(2,2,120,327);
+INSERT INTO xyoff VALUES(2,2,655,133);
+INSERT INTO xyoff VALUES(2,2,516,603);
+INSERT INTO xyoff VALUES(2,2,529,572);
+INSERT INTO xyoff VALUES(2,2,481,212);
+INSERT INTO xyoff VALUES(2,2,802,107);
+INSERT INTO xyoff VALUES(2,2,234,509);
+INSERT INTO xyoff VALUES(2,2,501,269);
+INSERT INTO xyoff VALUES(2,2,349,553);
+INSERT INTO xyoff VALUES(2,3,495,685);
+INSERT INTO xyoff VALUES(2,3,897,372);
+INSERT INTO xyoff VALUES(2,3,350,681);
+INSERT INTO xyoff VALUES(2,3,832,257);
+INSERT INTO xyoff VALUES(2,3,778,149);
+INSERT INTO xyoff VALUES(2,3,683,426);
+INSERT INTO xyoff VALUES(2,3,693,217);
+INSERT INTO xyoff VALUES(2,3,746,317);
+INSERT INTO xyoff VALUES(2,3,805,369);
+INSERT INTO xyoff VALUES(2,3,336,585);
+INSERT INTO xyoff VALUES(2,4,890,255);
+INSERT INTO xyoff VALUES(2,4,556,565);
+INSERT INTO xyoff VALUES(2,4,865,555);
+INSERT INTO xyoff VALUES(2,4,230,293);
+INSERT INTO xyoff VALUES(2,4,247,251);
+INSERT INTO xyoff VALUES(2,4,730,563);
+INSERT INTO xyoff VALUES(2,4,318,282);
+INSERT INTO xyoff VALUES(2,4,220,431);
+INSERT INTO xyoff VALUES(2,4,828,336);
+INSERT INTO xyoff VALUES(2,4,278,525);
+INSERT INTO xyoff VALUES(3,1,324,656);
+INSERT INTO xyoff VALUES(3,1,625,362);
+INSERT INTO xyoff VALUES(3,1,155,570);
+INSERT INTO xyoff VALUES(3,1,267,433);
+INSERT INTO xyoff VALUES(3,1,599,121);
+INSERT INTO xyoff VALUES(3,1,873,498);
+INSERT INTO xyoff VALUES(3,1,789,520);
+INSERT INTO xyoff VALUES(3,1,656,378);
+INSERT INTO xyoff VALUES(3,1,831,601);
+INSERT INTO xyoff VALUES(3,1,256,471);
+INSERT INTO xyoff VALUES(3,2,332,258);
+INSERT INTO xyoff VALUES(3,2,305,463);
+INSERT INTO xyoff VALUES(3,2,796,341);
+INSERT INTO xyoff VALUES(3,2,830,229);
+INSERT INTO xyoff VALUES(3,2,413,271);
+INSERT INTO xyoff VALUES(3,2,269,140);
+INSERT INTO xyoff VALUES(3,2,628,441);
+INSERT INTO xyoff VALUES(3,2,747,643);
+INSERT INTO xyoff VALUES(3,2,584,435);
+INSERT INTO xyoff VALUES(3,2,784,314);
+INSERT INTO xyoff VALUES(3,3,722,233);
+INSERT INTO xyoff VALUES(3,3,815,421);
+INSERT INTO xyoff VALUES(3,3,401,267);
+INSERT INTO xyoff VALUES(3,3,451,650);
+INSERT INTO xyoff VALUES(3,3,329,485);
+INSERT INTO xyoff VALUES(3,3,878,370);
+INSERT INTO xyoff VALUES(3,3,162,616);
+INSERT INTO xyoff VALUES(3,3,844,183);
+INSERT INTO xyoff VALUES(3,3,161,216);
+INSERT INTO xyoff VALUES(3,3,176,676);
+INSERT INTO xyoff VALUES(3,4,780,128);
+INSERT INTO xyoff VALUES(3,4,566,121);
+INSERT INTO xyoff VALUES(3,4,646,120);
+INSERT INTO xyoff VALUES(3,4,223,557);
+INSERT INTO xyoff VALUES(3,4,251,117);
+INSERT INTO xyoff VALUES(3,4,139,209);
+INSERT INTO xyoff VALUES(3,4,813,597);
+INSERT INTO xyoff VALUES(3,4,454,538);
+INSERT INTO xyoff VALUES(3,4,616,198);
+INSERT INTO xyoff VALUES(3,4,210,159);
+INSERT INTO xyoff VALUES(4,1,208,415);
+INSERT INTO xyoff VALUES(4,1,326,665);
+INSERT INTO xyoff VALUES(4,1,612,133);
+INSERT INTO xyoff VALUES(4,1,537,513);
+INSERT INTO xyoff VALUES(4,1,638,438);
+INSERT INTO xyoff VALUES(4,1,808,269);
+INSERT INTO xyoff VALUES(4,1,552,121);
+INSERT INTO xyoff VALUES(4,1,100,189);
+INSERT INTO xyoff VALUES(4,1,643,664);
+INSERT INTO xyoff VALUES(4,1,726,378);
+INSERT INTO xyoff VALUES(4,2,478,409);
+INSERT INTO xyoff VALUES(4,2,497,507);
+INSERT INTO xyoff VALUES(4,2,233,148);
+INSERT INTO xyoff VALUES(4,2,587,237);
+INSERT INTO xyoff VALUES(4,2,604,166);
+INSERT INTO xyoff VALUES(4,2,165,455);
+INSERT INTO xyoff VALUES(4,2,320,258);
+INSERT INTO xyoff VALUES(4,2,353,496);
+INSERT INTO xyoff VALUES(4,2,347,495);
+INSERT INTO xyoff VALUES(4,2,166,622);
+INSERT INTO xyoff VALUES(4,3,461,332);
+INSERT INTO xyoff VALUES(4,3,685,278);
+INSERT INTO xyoff VALUES(4,3,427,594);
+INSERT INTO xyoff VALUES(4,3,467,346);
+INSERT INTO xyoff VALUES(4,3,125,548);
+INSERT INTO xyoff VALUES(4,3,597,680);
+INSERT INTO xyoff VALUES(4,3,820,445);
+INSERT INTO xyoff VALUES(4,3,144,330);
+INSERT INTO xyoff VALUES(4,3,557,434);
+INSERT INTO xyoff VALUES(4,3,254,315);
+INSERT INTO xyoff VALUES(4,4,157,339);
+INSERT INTO xyoff VALUES(4,4,249,220);
+INSERT INTO xyoff VALUES(4,4,391,323);
+INSERT INTO xyoff VALUES(4,4,589,429);
+INSERT INTO xyoff VALUES(4,4,859,592);
+INSERT INTO xyoff VALUES(4,4,337,680);
+INSERT INTO xyoff VALUES(4,4,410,288);
+INSERT INTO xyoff VALUES(4,4,636,596);
+INSERT INTO xyoff VALUES(4,4,734,433);
+INSERT INTO xyoff VALUES(4,4,559,549);
+INSERT INTO xyoff VALUES(5,1,549,607);
+INSERT INTO xyoff VALUES(5,1,584,498);
+INSERT INTO xyoff VALUES(5,1,699,116);
+INSERT INTO xyoff VALUES(5,1,525,524);
+INSERT INTO xyoff VALUES(5,1,304,667);
+INSERT INTO xyoff VALUES(5,1,302,232);
+INSERT INTO xyoff VALUES(5,1,403,149);
+INSERT INTO xyoff VALUES(5,1,824,403);
+INSERT INTO xyoff VALUES(5,1,697,203);
+INSERT INTO xyoff VALUES(5,1,293,689);
+INSERT INTO xyoff VALUES(5,2,199,275);
+INSERT INTO xyoff VALUES(5,2,395,393);
+INSERT INTO xyoff VALUES(5,2,657,642);
+INSERT INTO xyoff VALUES(5,2,200,655);
+INSERT INTO xyoff VALUES(5,2,882,234);
+INSERT INTO xyoff VALUES(5,2,483,565);
+INSERT INTO xyoff VALUES(5,2,755,640);
+INSERT INTO xyoff VALUES(5,2,810,305);
+INSERT INTO xyoff VALUES(5,2,731,655);
+INSERT INTO xyoff VALUES(5,2,466,690);
+INSERT INTO xyoff VALUES(5,3,563,584);
+INSERT INTO xyoff VALUES(5,3,491,117);
+INSERT INTO xyoff VALUES(5,3,779,292);
+INSERT INTO xyoff VALUES(5,3,375,637);
+INSERT INTO xyoff VALUES(5,3,253,553);
+INSERT INTO xyoff VALUES(5,3,797,514);
+INSERT INTO xyoff VALUES(5,3,229,480);
+INSERT INTO xyoff VALUES(5,3,257,194);
+INSERT INTO xyoff VALUES(5,3,449,555);
+INSERT INTO xyoff VALUES(5,3,849,630);
+INSERT INTO xyoff VALUES(5,4,329,286);
+INSERT INTO xyoff VALUES(5,4,640,197);
+INSERT INTO xyoff VALUES(5,4,104,150);
+INSERT INTO xyoff VALUES(5,4,438,272);
+INSERT INTO xyoff VALUES(5,4,773,226);
+INSERT INTO xyoff VALUES(5,4,441,650);
+INSERT INTO xyoff VALUES(5,4,242,340);
+INSERT INTO xyoff VALUES(5,4,301,435);
+INSERT INTO xyoff VALUES(5,4,171,397);
+INSERT INTO xyoff VALUES(5,4,541,619);
+INSERT INTO xyoff VALUES(6,1,651,301);
+INSERT INTO xyoff VALUES(6,1,637,137);
+INSERT INTO xyoff VALUES(6,1,765,643);
+INSERT INTO xyoff VALUES(6,1,173,296);
+INSERT INTO xyoff VALUES(6,1,263,192);
+INSERT INTO xyoff VALUES(6,1,791,302);
+INSERT INTO xyoff VALUES(6,1,860,601);
+INSERT INTO xyoff VALUES(6,1,780,445);
+INSERT INTO xyoff VALUES(6,1,462,214);
+INSERT INTO xyoff VALUES(6,1,802,207);
+INSERT INTO xyoff VALUES(6,2,811,685);
+INSERT INTO xyoff VALUES(6,2,533,531);
+INSERT INTO xyoff VALUES(6,2,390,614);
+INSERT INTO xyoff VALUES(6,2,260,580);
+INSERT INTO xyoff VALUES(6,2,116,377);
+INSERT INTO xyoff VALUES(6,2,860,458);
+INSERT INTO xyoff VALUES(6,2,438,590);
+INSERT INTO xyoff VALUES(6,2,604,562);
+INSERT INTO xyoff VALUES(6,2,241,242);
+INSERT INTO xyoff VALUES(6,2,667,298);
+INSERT INTO xyoff VALUES(6,3,787,698);
+INSERT INTO xyoff VALUES(6,3,868,521);
+INSERT INTO xyoff VALUES(6,3,412,587);
+INSERT INTO xyoff VALUES(6,3,640,131);
+INSERT INTO xyoff VALUES(6,3,748,410);
+INSERT INTO xyoff VALUES(6,3,257,244);
+INSERT INTO xyoff VALUES(6,3,411,195);
+INSERT INTO xyoff VALUES(6,3,464,356);
+INSERT INTO xyoff VALUES(6,3,157,339);
+INSERT INTO xyoff VALUES(6,3,434,505);
+INSERT INTO xyoff VALUES(6,4,480,671);
+INSERT INTO xyoff VALUES(6,4,519,228);
+INSERT INTO xyoff VALUES(6,4,404,513);
+INSERT INTO xyoff VALUES(6,4,120,538);
+INSERT INTO xyoff VALUES(6,4,403,663);
+INSERT INTO xyoff VALUES(6,4,477,677);
+INSERT INTO xyoff VALUES(6,4,690,154);
+INSERT INTO xyoff VALUES(6,4,606,498);
+INSERT INTO xyoff VALUES(6,4,430,665);
+INSERT INTO xyoff VALUES(6,4,499,273);
+INSERT INTO xyoff VALUES(7,1,118,526);
+INSERT INTO xyoff VALUES(7,1,817,522);
+INSERT INTO xyoff VALUES(7,1,388,638);
+INSERT INTO xyoff VALUES(7,1,181,265);
+INSERT INTO xyoff VALUES(7,1,442,332);
+INSERT INTO xyoff VALUES(7,1,475,282);
+INSERT INTO xyoff VALUES(7,1,722,633);
+INSERT INTO xyoff VALUES(7,1,104,394);
+INSERT INTO xyoff VALUES(7,1,631,262);
+INSERT INTO xyoff VALUES(7,1,372,392);
+INSERT INTO xyoff VALUES(7,2,600,413);
+INSERT INTO xyoff VALUES(7,2,386,223);
+INSERT INTO xyoff VALUES(7,2,839,174);
+INSERT INTO xyoff VALUES(7,2,293,410);
+INSERT INTO xyoff VALUES(7,2,281,391);
+INSERT INTO xyoff VALUES(7,2,859,387);
+INSERT INTO xyoff VALUES(7,2,478,347);
+INSERT INTO xyoff VALUES(7,2,646,690);
+INSERT INTO xyoff VALUES(7,2,713,234);
+INSERT INTO xyoff VALUES(7,2,199,588);
+INSERT INTO xyoff VALUES(7,3,389,256);
+INSERT INTO xyoff VALUES(7,3,349,542);
+INSERT INTO xyoff VALUES(7,3,363,345);
+INSERT INTO xyoff VALUES(7,3,751,302);
+INSERT INTO xyoff VALUES(7,3,423,386);
+INSERT INTO xyoff VALUES(7,3,267,444);
+INSERT INTO xyoff VALUES(7,3,243,182);
+INSERT INTO xyoff VALUES(7,3,453,658);
+INSERT INTO xyoff VALUES(7,3,126,345);
+INSERT INTO xyoff VALUES(7,3,120,472);
+INSERT INTO xyoff VALUES(7,4,359,654);
+INSERT INTO xyoff VALUES(7,4,339,516);
+INSERT INTO xyoff VALUES(7,4,710,452);
+INSERT INTO xyoff VALUES(7,4,810,560);
+INSERT INTO xyoff VALUES(7,4,644,692);
+INSERT INTO xyoff VALUES(7,4,826,327);
+INSERT INTO xyoff VALUES(7,4,465,462);
+INSERT INTO xyoff VALUES(7,4,310,456);
+INSERT INTO xyoff VALUES(7,4,577,613);
+INSERT INTO xyoff VALUES(7,4,502,555);
+INSERT INTO xyoff VALUES(8,1,601,620);
+INSERT INTO xyoff VALUES(8,1,372,683);
+INSERT INTO xyoff VALUES(8,1,758,399);
+INSERT INTO xyoff VALUES(8,1,485,552);
+INSERT INTO xyoff VALUES(8,1,159,563);
+INSERT INTO xyoff VALUES(8,1,536,303);
+INSERT INTO xyoff VALUES(8,1,122,263);
+INSERT INTO xyoff VALUES(8,1,836,435);
+INSERT INTO xyoff VALUES(8,1,544,146);
+INSERT INTO xyoff VALUES(8,1,270,277);
+INSERT INTO xyoff VALUES(8,2,849,281);
+INSERT INTO xyoff VALUES(8,2,563,242);
+INSERT INTO xyoff VALUES(8,2,704,463);
+INSERT INTO xyoff VALUES(8,2,102,165);
+INSERT INTO xyoff VALUES(8,2,797,524);
+INSERT INTO xyoff VALUES(8,2,612,426);
+INSERT INTO xyoff VALUES(8,2,345,372);
+INSERT INTO xyoff VALUES(8,2,820,376);
+INSERT INTO xyoff VALUES(8,2,789,156);
+INSERT INTO xyoff VALUES(8,2,321,466);
+INSERT INTO xyoff VALUES(8,3,150,332);
+INSERT INTO xyoff VALUES(8,3,136,152);
+INSERT INTO xyoff VALUES(8,3,468,528);
+INSERT INTO xyoff VALUES(8,3,409,192);
+INSERT INTO xyoff VALUES(8,3,820,216);
+INSERT INTO xyoff VALUES(8,3,847,249);
+INSERT INTO xyoff VALUES(8,3,801,267);
+INSERT INTO xyoff VALUES(8,3,181,670);
+INSERT INTO xyoff VALUES(8,3,398,563);
+INSERT INTO xyoff VALUES(8,3,439,576);
+INSERT INTO xyoff VALUES(8,4,123,309);
+INSERT INTO xyoff VALUES(8,4,190,496);
+INSERT INTO xyoff VALUES(8,4,571,531);
+INSERT INTO xyoff VALUES(8,4,290,255);
+INSERT INTO xyoff VALUES(8,4,244,412);
+INSERT INTO xyoff VALUES(8,4,264,596);
+INSERT INTO xyoff VALUES(8,4,253,420);
+INSERT INTO xyoff VALUES(8,4,847,536);
+INSERT INTO xyoff VALUES(8,4,120,288);
+INSERT INTO xyoff VALUES(8,4,331,639);
+
+/* Create the geopoly object from test data above */
+CREATE VIRTUAL TABLE geo1 USING geopoly(type,clr);
+INSERT INTO geo1(_shape,type,clr)
+  SELECT geopoly_xform(jshape,A,B,-B,A,xoff,yoff), basis.name, xform.clr
+    FROM basis, xform, xyoff
+   WHERE xyoff.id1=basis.rowid AND xyoff.id2=xform.rowid;
+
+
+/* Query polygon */
+CREATE TEMP TABLE querypoly(poly JSON, clr TEXT);
+INSERT INTO querypoly(clr, poly) VALUES
+  ('orange', '[[300,300],[400,350],[500,250],[480,500],[400,480],[300,550],[280,450],[320,400],[280,350],[300,300]]');
+
+/* Generate the HTML */
+.print '<html>'
+.print '<h1>Everything</h1>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape, 
+         printf('style="fill:none;stroke:%s;stroke-width:1"',clr)
+       )
+  FROM geo1;
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Overlap Query</h1>'
+.print '<pre>'
+.print 'SELECT *'
+.print '  FROM geo1, querypoly'
+.print ' WHERE geopoly_overlap(_shape, poly);'
+.print 
+EXPLAIN QUERY PLAN
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_overlap(_shape, poly);
+.print '</pre>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_overlap(_shape, poly);
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Overlap Query And Result Bounding Box</h1>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_overlap(_shape, poly);
+SELECT geopoly_svg(geopoly_bbox(poly),
+         'style="fill:none;stroke:black;stroke-width:3"'
+       )
+  FROM querypoly;
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+SELECT geopoly_svg(geopoly_group_bbox(_shape),
+         'style="fill:none;stroke:red;stroke-width:3"'
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_overlap(_shape, poly);
+.print '</svg>'
+
+.print '<h1>Bounding-Box Overlap Query</h1>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       ),
+       geopoly_svg(geopoly_bbox(_shape),
+         'style="fill:none;stroke:black;stroke-width:1"'
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_overlap(geopoly_bbox(_shape), geopoly_bbox(poly));
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+SELECT geopoly_svg(geopoly_bbox(poly),
+         'style="fill:none;stroke:black;stroke-width:3"'
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Within Query</h1>'
+.print '<pre>'
+.print 'SELECT *'
+.print '  FROM geo1, querypoly'
+.print ' WHERE geopoly_within(_shape, poly);'
+.print 
+EXPLAIN QUERY PLAN
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_within(_shape, poly);
+.print '</pre>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_within(_shape, poly);
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Bounding-Box WITHIN Query</h1>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       ),
+       geopoly_svg(geopoly_bbox(_shape),
+         'style="fill:none;stroke:black;stroke-width:1"'
+       )
+  FROM geo1, querypoly
+ WHERE geopoly_within(geopoly_bbox(_shape), geopoly_bbox(poly));
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+SELECT geopoly_svg(geopoly_bbox(poly),
+         'style="fill:none;stroke:black;stroke-width:3"'
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Not Overlap Query</h1>'
+.print '<pre>'
+.print 'SELECT *'
+.print '  FROM geo1, querypoly'
+.print ' WHERE NOT geopoly_overlap(_shape, poly);'
+.print 
+EXPLAIN QUERY PLAN
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE NOT geopoly_overlap(_shape, poly);
+.print '</pre>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE NOT geopoly_overlap(_shape, poly);
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Not Within Query</h1>'
+.print '<pre>'
+.print 'SELECT *'
+.print '  FROM geo1, querypoly'
+.print ' WHERE NOT geopoly_within(_shape, poly);'
+.print 
+EXPLAIN QUERY PLAN
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE NOT geopoly_within(_shape, poly);
+.print '</pre>'
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1, querypoly
+ WHERE NOT geopoly_within(_shape, poly);
+SELECT geopoly_svg(poly, 
+         printf('style="fill:%s;fill-opacity:0.5;"',clr)
+       )
+  FROM querypoly;
+.print '</svg>'
+
+.print '<h1>Color-Change For Overlapping Elements</h1>'
+BEGIN;
+UPDATE geo1
+   SET clr=CASE WHEN rowid IN (SELECT geo1.rowid FROM geo1, querypoly
+                                WHERE geopoly_overlap(_shape,poly))
+           THEN 'red' ELSE 'blue' END;
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1;
+SELECT geopoly_svg(poly,'style="fill:none;stroke:black;stroke-width:2"')
+  FROM querypoly;
+ROLLBACK;
+.print '</svg>'
+
+.print '<h1>Color-Change And Move Overlapping Elements</h1>'
+BEGIN;
+UPDATE geo1
+   SET clr=CASE WHEN rowid IN (SELECT geo1.rowid FROM geo1, querypoly
+                                WHERE geopoly_overlap(_shape,poly))
+           THEN 'red' ELSE '#76ccff' END;
+UPDATE geo1
+   SET _shape=geopoly_xform(_shape,1,0,0,1,300,0)
+ WHERE geopoly_overlap(_shape,(SELECT poly FROM querypoly));
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1;
+SELECT geopoly_svg(poly,'style="fill:none;stroke:black;stroke-width:2"')
+  FROM querypoly;
+--ROLLBACK;
+.print '</svg>'
+
+
+.print '<h1>Overlap With Translated Query Polygon</h1>'
+UPDATE querypoly SET poly=geopoly_xform(poly,1,0,0,1,300,0);
+.print '<svg width="1000" height="800" style="border:1px solid black">'
+SELECT geopoly_svg(_shape,
+         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
+       )
+  FROM geo1
+ WHERE geopoly_overlap(_shape,(SELECT poly FROM querypoly));
+SELECT geopoly_svg(poly,'style="fill:none;stroke:black;stroke-width:2"')
+  FROM querypoly;
+ROLLBACK;
+.print '</svg>'
+
+.print '<h1>Regular Polygons</h1>'
+.print '<svg width="1000" height="200" style="border:1px solid black">'
+SELECT geopoly_svg(geopoly_regular(100,100,40,3),'style="fill:none;stroke:red;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(200,100,40,4),'style="fill:none;stroke:orange;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(300,100,40,5),'style="fill:none;stroke:green;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(400,100,40,6),'style="fill:none;stroke:blue;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(500,100,40,7),'style="fill:none;stroke:purple;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(600,100,40,8),'style="fill:none;stroke:red;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(700,100,40,10),'style="fill:none;stroke:orange;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(800,100,40,20),'style="fill:none;stroke:green;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(900,100,40,30),'style="fill:none;stroke:blue;stroke-width:1"');
+.print '</svg>'
+
+.print '</html>'