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><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="CUBE"
>F.9. cube</A
></H1
><P
> This module implements a data type <TT
CLASS="TYPE"
>cube</TT
> for
representing multidimensional cubes.
</P
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="AEN137538"
>F.9.1. Syntax</A
></H2
><P
> <A
HREF="cube.html#CUBE-REPR-TABLE"
>Table F-3</A
> shows the valid external
representations for the <TT
CLASS="TYPE"
>cube</TT
>
type. <TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
>, <TT
CLASS="REPLACEABLE"
><I
>y</I
></TT
>, etc. denote
floating-point numbers.
</P
><DIV
CLASS="TABLE"
><A
NAME="CUBE-REPR-TABLE"
></A
><P
><B
>Table F-3. Cube External Representations</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><THEAD
><TR
><TH
>External Syntax</TH
><TH
>Meaning</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
><TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
></TT
></TD
><TD
>A one-dimensional point
(or, zero-length one-dimensional interval)
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>(<TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
>)</TT
></TD
><TD
>Same as above</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><TT
CLASS="REPLACEABLE"
><I
>x1</I
></TT
>,<TT
CLASS="REPLACEABLE"
><I
>x2</I
></TT
>,...,<TT
CLASS="REPLACEABLE"
><I
>xn</I
></TT
></TT
></TD
><TD
>A point in n-dimensional space, represented internally as a
zero-volume cube
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>(<TT
CLASS="REPLACEABLE"
><I
>x1</I
></TT
>,<TT
CLASS="REPLACEABLE"
><I
>x2</I
></TT
>,...,<TT
CLASS="REPLACEABLE"
><I
>xn</I
></TT
>)</TT
></TD
><TD
>Same as above</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>(<TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
>),(<TT
CLASS="REPLACEABLE"
><I
>y</I
></TT
>)</TT
></TD
><TD
>A one-dimensional interval starting at <TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
> and ending at <TT
CLASS="REPLACEABLE"
><I
>y</I
></TT
> or vice versa; the
order does not matter
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>[(<TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
>),(<TT
CLASS="REPLACEABLE"
><I
>y</I
></TT
>)]</TT
></TD
><TD
>Same as above</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>(<TT
CLASS="REPLACEABLE"
><I
>x1</I
></TT
>,...,<TT
CLASS="REPLACEABLE"
><I
>xn</I
></TT
>),(<TT
CLASS="REPLACEABLE"
><I
>y1</I
></TT
>,...,<TT
CLASS="REPLACEABLE"
><I
>yn</I
></TT
>)</TT
></TD
><TD
>An n-dimensional cube represented by a pair of its diagonally
opposite corners
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>[(<TT
CLASS="REPLACEABLE"
><I
>x1</I
></TT
>,...,<TT
CLASS="REPLACEABLE"
><I
>xn</I
></TT
>),(<TT
CLASS="REPLACEABLE"
><I
>y1</I
></TT
>,...,<TT
CLASS="REPLACEABLE"
><I
>yn</I
></TT
>)]</TT
></TD
><TD
>Same as above</TD
></TR
></TBODY
></TABLE
></DIV
><P
> It does not matter which order the opposite corners of a cube are
entered in. The <TT
CLASS="TYPE"
>cube</TT
> functions
automatically swap values if needed to create a uniform
<SPAN
CLASS="QUOTE"
>"lower left — upper right"</SPAN
> internal representation.
When the corners coincide, <TT
CLASS="TYPE"
>cube</TT
> stores only one corner
along with an <SPAN
CLASS="QUOTE"
>"is point"</SPAN
> flag to avoid wasting space.
</P
><P
> White space is ignored on input, so
<TT
CLASS="LITERAL"
>[(<TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
>),(<TT
CLASS="REPLACEABLE"
><I
>y</I
></TT
>)]</TT
> is the same as
<TT
CLASS="LITERAL"
>[ ( <TT
CLASS="REPLACEABLE"
><I
>x</I
></TT
> ), ( <TT
CLASS="REPLACEABLE"
><I
>y</I
></TT
> ) ]</TT
>.
</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="AEN137619"
>F.9.2. Precision</A
></H2
><P
> Values are stored internally as 64-bit floating point numbers. This means
that numbers with more than about 16 significant digits will be truncated.
</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="AEN137622"
>F.9.3. Usage</A
></H2
><P
> <A
HREF="cube.html#CUBE-OPERATORS-TABLE"
>Table F-4</A
> shows the operators provided for
type <TT
CLASS="TYPE"
>cube</TT
>.
</P
><DIV
CLASS="TABLE"
><A
NAME="CUBE-OPERATORS-TABLE"
></A
><P
><B
>Table F-4. Cube Operators</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><THEAD
><TR
><TH
>Operator</TH
><TH
>Result</TH
><TH
>Description</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
>a = b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cubes a and b are identical.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a && b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cubes a and b overlap.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a @> b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a contains the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a <@ b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a is contained in the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a < b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a is less than the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a <= b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a is less than or equal to the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a > b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a is greater than the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a >= b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a is greater than or equal to the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a <> b</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>The cube a is not equal to the cube b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a -> n</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Get <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
>-th coordinate of cube (counting from 1).</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a ~> n</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
> Get <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
>-th coordinate of cube in following way:
n = 2 * k - 1 means lower bound of <TT
CLASS="REPLACEABLE"
><I
>k</I
></TT
>-th
dimension, n = 2 * k means upper bound of
<TT
CLASS="REPLACEABLE"
><I
>k</I
></TT
>-th dimension. This operator is designed
for KNN-GiST support.
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a <-> b</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Euclidean distance between a and b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a <#> b</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Taxicab (L-1 metric) distance between a and b.</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>a <=> b</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Chebyshev (L-inf metric) distance between a and b.</TD
></TR
></TBODY
></TABLE
></DIV
><P
> (Before PostgreSQL 8.2, the containment operators <TT
CLASS="LITERAL"
>@></TT
> and <TT
CLASS="LITERAL"
><@</TT
> were
respectively called <TT
CLASS="LITERAL"
>@</TT
> and <TT
CLASS="LITERAL"
>~</TT
>. These names are still available, but are
deprecated and will eventually be retired. Notice that the old names
are reversed from the convention formerly followed by the core geometric
data types!)
</P
><P
> The scalar ordering operators (<TT
CLASS="LITERAL"
><</TT
>, <TT
CLASS="LITERAL"
>>=</TT
>, etc)
do not make a lot of sense for any practical purpose but sorting. These
operators first compare the first coordinates, and if those are equal,
compare the second coordinates, etc. They exist mainly to support the
b-tree index operator class for <TT
CLASS="TYPE"
>cube</TT
>, which can be useful for
example if you would like a UNIQUE constraint on a <TT
CLASS="TYPE"
>cube</TT
> column.
</P
><P
> The <TT
CLASS="FILENAME"
>cube</TT
> module also provides a GiST index operator class for
<TT
CLASS="TYPE"
>cube</TT
> values.
A <TT
CLASS="TYPE"
>cube</TT
> GiST index can be used to search for values using the
<TT
CLASS="LITERAL"
>=</TT
>, <TT
CLASS="LITERAL"
>&&</TT
>, <TT
CLASS="LITERAL"
>@></TT
>, and
<TT
CLASS="LITERAL"
><@</TT
> operators in <TT
CLASS="LITERAL"
>WHERE</TT
> clauses.
</P
><P
> In addition, a <TT
CLASS="TYPE"
>cube</TT
> GiST index can be used to find nearest
neighbors using the metric operators
<TT
CLASS="LITERAL"
><-></TT
>, <TT
CLASS="LITERAL"
><#></TT
>, and
<TT
CLASS="LITERAL"
><=></TT
> in <TT
CLASS="LITERAL"
>ORDER BY</TT
> clauses.
For example, the nearest neighbor of the 3-D point (0.5, 0.5, 0.5)
could be found efficiently with:
</P><PRE
CLASS="PROGRAMLISTING"
>SELECT c FROM test ORDER BY c <-> cube(array[0.5,0.5,0.5]) LIMIT 1;</PRE
><P>
</P
><P
> The <TT
CLASS="LITERAL"
>~></TT
> operator can also be used in this way to
efficiently retrieve the first few values sorted by a selected coordinate.
For example, to get the first few cubes ordered by the first coordinate
(lower left corner) ascending one could use the following query:
</P><PRE
CLASS="PROGRAMLISTING"
>SELECT c FROM test ORDER BY c ~> 1 LIMIT 5;</PRE
><P>
And to get 2-D cubes ordered by the first coordinate of the upper right
corner descending:
</P><PRE
CLASS="PROGRAMLISTING"
>SELECT c FROM test ORDER BY c ~> 3 DESC LIMIT 5;</PRE
><P>
</P
><P
> <A
HREF="cube.html#CUBE-FUNCTIONS-TABLE"
>Table F-5</A
> shows the available functions.
</P
><DIV
CLASS="TABLE"
><A
NAME="CUBE-FUNCTIONS-TABLE"
></A
><P
><B
>Table F-5. Cube Functions</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><COL><THEAD
><TR
><TH
>Function</TH
><TH
>Result</TH
><TH
>Description</TH
><TH
>Example</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
>cube(float8)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a one dimensional cube with both coordinates the same.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube(1) == '(1)'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube(float8, float8)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a one dimensional cube.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube(1,2) == '(1),(2)'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube(float8[])</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a zero-volume cube using the coordinates
defined by the array.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube(ARRAY[1,2]) == '(1,2)'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube(float8[], float8[])</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a cube with upper right and lower left
coordinates as defined by the two arrays, which must be of the
same length.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube(ARRAY[1,2], ARRAY[3,4]) == '(1,2),(3,4)'
</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube(cube, float8)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a new cube by adding a dimension on to an existing cube,
with the same values for both endpoints of the new coordinate. This
is useful for building cubes piece by piece from calculated values.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube('(1,2),(3,4)'::cube, 5) == '(1,2,5),(3,4,5)'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube(cube, float8, float8)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a new cube by adding a dimension on to an existing
cube. This is useful for building cubes piece by piece from calculated
values.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube('(1,2),(3,4)'::cube, 5, 6) == '(1,2,5),(3,4,6)'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_dim(cube)</TT
></TD
><TD
><TT
CLASS="TYPE"
>integer</TT
></TD
><TD
>Returns the number of dimensions of the cube.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube_dim('(1,2),(3,4)') == '2'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_ll_coord(cube, integer)</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Returns the <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
>-th coordinate value for the lower
left corner of the cube.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube_ll_coord('(1,2),(3,4)', 2) == '2'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_ur_coord(cube, integer)</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Returns the <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
>-th coordinate value for the
upper right corner of the cube.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube_ur_coord('(1,2),(3,4)', 2) == '4'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_is_point(cube)</TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>Returns true if the cube is a point, that is,
the two defining corners are the same.</TD
><TD
> </TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_distance(cube, cube)</TT
></TD
><TD
><TT
CLASS="TYPE"
>float8</TT
></TD
><TD
>Returns the distance between two cubes. If both
cubes are points, this is the normal distance function.
</TD
><TD
> </TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_subset(cube, integer[])</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Makes a new cube from an existing cube, using a list of
dimension indexes from an array. Can be used to extract the endpoints
of a single dimension, or to drop dimensions, or to reorder them as
desired.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2]) == '(3),(7)'</TT
>
<TT
CLASS="LITERAL"
>cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]) ==
'(5,3,1,1),(8,7,6,6)'</TT
>
</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_union(cube, cube)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Produces the union of two cubes.
</TD
><TD
> </TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_inter(cube, cube)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Produces the intersection of two cubes.
</TD
><TD
> </TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>cube_enlarge(c cube, r double, n integer)</TT
></TD
><TD
><TT
CLASS="TYPE"
>cube</TT
></TD
><TD
>Increases the size of the cube by the specified
radius <TT
CLASS="REPLACEABLE"
><I
>r</I
></TT
> in at least <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
> dimensions.
If the radius is negative the cube is shrunk instead.
All defined dimensions are changed by the radius <TT
CLASS="REPLACEABLE"
><I
>r</I
></TT
>.
Lower-left coordinates are decreased by <TT
CLASS="REPLACEABLE"
><I
>r</I
></TT
> and
upper-right coordinates are increased by <TT
CLASS="REPLACEABLE"
><I
>r</I
></TT
>. If a
lower-left coordinate is increased to more than the corresponding
upper-right coordinate (this can only happen when <TT
CLASS="REPLACEABLE"
><I
>r</I
></TT
>
< 0) than both coordinates are set to their average.
If <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
> is greater than the number of defined dimensions
and the cube is being enlarged (<TT
CLASS="REPLACEABLE"
><I
>r</I
></TT
> > 0), then extra
dimensions are added to make <TT
CLASS="REPLACEABLE"
><I
>n</I
></TT
> altogether;
0 is used as the initial value for the extra coordinates.
This function is useful for creating bounding boxes around a point for
searching for nearby points.
</TD
><TD
> <TT
CLASS="LITERAL"
>cube_enlarge('(1,2),(3,4)', 0.5, 3) ==
'(0.5,1.5,-0.5),(3.5,4.5,0.5)'</TT
>
</TD
></TR
></TBODY
></TABLE
></DIV
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="AEN137894"
>F.9.4. Defaults</A
></H2
><P
> I believe this union:
</P
><PRE
CLASS="PROGRAMLISTING"
>select cube_union('(0,5,2),(2,3,1)', '0');
cube_union
-------------------
(0, 0, 0),(2, 5, 2)
(1 row)</PRE
><P
> does not contradict common sense, neither does the intersection
</P
><PRE
CLASS="PROGRAMLISTING"
>select cube_inter('(0,-1),(1,1)', '(-2),(2)');
cube_inter
-------------
(0, 0),(1, 0)
(1 row)</PRE
><P
> In all binary operations on differently-dimensioned cubes, I assume the
lower-dimensional one to be a Cartesian projection, i. e., having zeroes
in place of coordinates omitted in the string representation. The above
examples are equivalent to:
</P
><PRE
CLASS="PROGRAMLISTING"
>cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)');
cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');</PRE
><P
> The following containment predicate uses the point syntax,
while in fact the second argument is internally represented by a box.
This syntax makes it unnecessary to define a separate point type
and functions for (box,point) predicates.
</P
><PRE
CLASS="PROGRAMLISTING"
>select cube_contains('(0,0),(1,1)', '0.5,0.5');
cube_contains
--------------
t
(1 row)</PRE
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="AEN137904"
>F.9.5. Notes</A
></H2
><P
> For examples of usage, see the regression test <TT
CLASS="FILENAME"
>sql/cube.sql</TT
>.
</P
><P
> To make it harder for people to break things, there
is a limit of 100 on the number of dimensions of cubes. This is set
in <TT
CLASS="FILENAME"
>cubedata.h</TT
> if you need something bigger.
</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="AEN137910"
>F.9.6. Credits</A
></H2
><P
> Original author: Gene Selkov, Jr. <CODE
CLASS="EMAIL"
><<A
HREF="mailto:selkovjr@mcs.anl.gov"
>selkovjr@mcs.anl.gov</A
>></CODE
>,
Mathematics and Computer Science Division, Argonne National Laboratory.
</P
><P
> My thanks are primarily to Prof. Joe Hellerstein
(<A
HREF="https://dsf.berkeley.edu/jmh/"
TARGET="_top"
>https://dsf.berkeley.edu/jmh/</A
>) for elucidating the
gist of the GiST (<A
HREF="http://gist.cs.berkeley.edu/"
TARGET="_top"
>http://gist.cs.berkeley.edu/</A
>), and
to his former student Andy Dong for his example written for Illustra.
I am also grateful to all Postgres developers, present and past, for
enabling myself to create my own world and live undisturbed in it. And I
would like to acknowledge my gratitude to Argonne Lab and to the
U.S. Department of Energy for the years of faithful support of my database
research.
</P
><P
> Minor updates to this package were made by Bruno Wolff III
<CODE
CLASS="EMAIL"
><<A
HREF="mailto:bruno@wolff.to"
>bruno@wolff.to</A
>></CODE
> in August/September of 2002. These include
changing the precision from single precision to double precision and adding
some new functions.
</P
><P
> Additional updates were made by Joshua Reich <CODE
CLASS="EMAIL"
><<A
HREF="mailto:josh@root.net"
>josh@root.net</A
>></CODE
> in
July 2006. These include <TT
CLASS="LITERAL"
>cube(float8[], float8[])</TT
> and
cleaning up the code to use the V1 call protocol instead of the deprecated
V0 protocol.
</P
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