local-test-sqlite3-delta-01/afc-sqlite3/ext/rtree/rtreedoc.test

# 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 ORDER BY +A.id;
} {
  28215
  28216
  28262
  28269
  28286
  28287
  28291
  28293
  28298
  28313
  28320
  28322
  28336
}

# 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 10, actual 11}}
execsql ROLLBACK



finish_test