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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>F.9. cube</title><link rel="stylesheet" type="text/css" href="stylesheet.css" /><link rev="made" href="pgsql-docs@lists.postgresql.org" /><meta name="generator" content="DocBook XSL Stylesheets V1.79.1" /><link rel="prev" href="citext.html" title="F.8. citext" /><link rel="next" href="dblink.html" title="F.10. dblink" /></head><body id="docContent" class="container-fluid col-10"><div xmlns="http://www.w3.org/TR/xhtml1/transitional" class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="5" align="center">F.9. cube</th></tr><tr><td width="10%" align="left"><a accesskey="p" href="citext.html" title="F.8. citext">Prev</a> </td><td width="10%" align="left"><a accesskey="u" href="contrib.html" title="Appendix F. Additional Supplied Modules">Up</a></td><th width="60%" align="center">Appendix F. Additional Supplied Modules</th><td width="10%" align="right"><a accesskey="h" href="index.html" title="PostgreSQL 13.4 Documentation">Home</a></td><td width="10%" align="right"> <a accesskey="n" href="dblink.html" title="F.10. dblink">Next</a></td></tr></table><hr></hr></div><div class="sect1" id="CUBE"><div class="titlepage"><div><div><h2 class="title" style="clear: both">F.9. cube</h2></div></div></div><div class="toc"><dl class="toc"><dt><span class="sect2"><a href="cube.html#id-1.11.7.18.5">F.9.1. Syntax</a></span></dt><dt><span class="sect2"><a href="cube.html#id-1.11.7.18.6">F.9.2. Precision</a></span></dt><dt><span class="sect2"><a href="cube.html#id-1.11.7.18.7">F.9.3. Usage</a></span></dt><dt><span class="sect2"><a href="cube.html#id-1.11.7.18.8">F.9.4. Defaults</a></span></dt><dt><span class="sect2"><a href="cube.html#id-1.11.7.18.9">F.9.5. Notes</a></span></dt><dt><span class="sect2"><a href="cube.html#id-1.11.7.18.10">F.9.6. Credits</a></span></dt></dl></div><a id="id-1.11.7.18.2" class="indexterm"></a><p>
+ This module implements a data type <code class="type">cube</code> for
+ representing multidimensional cubes.
+ </p><p>
+ This module is considered <span class="quote">“<span class="quote">trusted</span>”</span>, that is, it can be
+ installed by non-superusers who have <code class="literal">CREATE</code> privilege
+ on the current database.
+ </p><div class="sect2" id="id-1.11.7.18.5"><div class="titlepage"><div><div><h3 class="title">F.9.1. Syntax</h3></div></div></div><p>
+ <a class="xref" href="cube.html#CUBE-REPR-TABLE" title="Table F.2. Cube External Representations">Table F.2</a> shows the valid external
+ representations for the <code class="type">cube</code>
+ type. <em class="replaceable"><code>x</code></em>, <em class="replaceable"><code>y</code></em>, etc. denote
+ floating-point numbers.
+ </p><div class="table" id="CUBE-REPR-TABLE"><p class="title"><strong>Table F.2. Cube External Representations</strong></p><div class="table-contents"><table class="table" summary="Cube External Representations" border="1"><colgroup><col /><col /></colgroup><thead><tr><th>External Syntax</th><th>Meaning</th></tr></thead><tbody><tr><td><code class="literal"><em class="replaceable"><code>x</code></em></code></td><td>A one-dimensional point
+ (or, zero-length one-dimensional interval)
+ </td></tr><tr><td><code class="literal">(<em class="replaceable"><code>x</code></em>)</code></td><td>Same as above</td></tr><tr><td><code class="literal"><em class="replaceable"><code>x1</code></em>,<em class="replaceable"><code>x2</code></em>,...,<em class="replaceable"><code>xn</code></em></code></td><td>A point in n-dimensional space, represented internally as a
+ zero-volume cube
+ </td></tr><tr><td><code class="literal">(<em class="replaceable"><code>x1</code></em>,<em class="replaceable"><code>x2</code></em>,...,<em class="replaceable"><code>xn</code></em>)</code></td><td>Same as above</td></tr><tr><td><code class="literal">(<em class="replaceable"><code>x</code></em>),(<em class="replaceable"><code>y</code></em>)</code></td><td>A one-dimensional interval starting at <em class="replaceable"><code>x</code></em> and ending at <em class="replaceable"><code>y</code></em> or vice versa; the
+ order does not matter
+ </td></tr><tr><td><code class="literal">[(<em class="replaceable"><code>x</code></em>),(<em class="replaceable"><code>y</code></em>)]</code></td><td>Same as above</td></tr><tr><td><code class="literal">(<em class="replaceable"><code>x1</code></em>,...,<em class="replaceable"><code>xn</code></em>),(<em class="replaceable"><code>y1</code></em>,...,<em class="replaceable"><code>yn</code></em>)</code></td><td>An n-dimensional cube represented by a pair of its diagonally
+ opposite corners
+ </td></tr><tr><td><code class="literal">[(<em class="replaceable"><code>x1</code></em>,...,<em class="replaceable"><code>xn</code></em>),(<em class="replaceable"><code>y1</code></em>,...,<em class="replaceable"><code>yn</code></em>)]</code></td><td>Same as above</td></tr></tbody></table></div></div><br class="table-break" /><p>
+ It does not matter which order the opposite corners of a cube are
+ entered in. The <code class="type">cube</code> functions
+ automatically swap values if needed to create a uniform
+ <span class="quote">“<span class="quote">lower left — upper right</span>”</span> internal representation.
+ When the corners coincide, <code class="type">cube</code> stores only one corner
+ along with an <span class="quote">“<span class="quote">is point</span>”</span> flag to avoid wasting space.
+ </p><p>
+ White space is ignored on input, so
+ <code class="literal">[(<em class="replaceable"><code>x</code></em>),(<em class="replaceable"><code>y</code></em>)]</code> is the same as
+ <code class="literal">[ ( <em class="replaceable"><code>x</code></em> ), ( <em class="replaceable"><code>y</code></em> ) ]</code>.
+ </p></div><div class="sect2" id="id-1.11.7.18.6"><div class="titlepage"><div><div><h3 class="title">F.9.2. Precision</h3></div></div></div><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" id="id-1.11.7.18.7"><div class="titlepage"><div><div><h3 class="title">F.9.3. Usage</h3></div></div></div><p>
+ <a class="xref" href="cube.html#CUBE-OPERATORS-TABLE" title="Table F.3. Cube Operators">Table F.3</a> shows the specialized operators
+ provided for type <code class="type">cube</code>.
+ </p><div class="table" id="CUBE-OPERATORS-TABLE"><p class="title"><strong>Table F.3. Cube Operators</strong></p><div class="table-contents"><table class="table" summary="Cube Operators" border="1"><colgroup><col /></colgroup><thead><tr><th class="func_table_entry"><p class="func_signature">
+ Operator
+ </p>
+ <p>
+ Description
+ </p></th></tr></thead><tbody><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">&amp;&amp;</code> <code class="type">cube</code>
+ → <code class="returnvalue">boolean</code>
+ </p>
+ <p>
+ Do the cubes overlap?
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">@&gt;</code> <code class="type">cube</code>
+ → <code class="returnvalue">boolean</code>
+ </p>
+ <p>
+ Does the first cube contain the second?
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">&lt;@</code> <code class="type">cube</code>
+ → <code class="returnvalue">boolean</code>
+ </p>
+ <p>
+ Is the first cube contained in the second?
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">-&gt;</code> <code class="type">integer</code>
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Extracts the <em class="parameter"><code>n</code></em>-th coordinate of the cube
+ (counting from 1).
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">~&gt;</code> <code class="type">integer</code>
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Extracts the <em class="parameter"><code>n</code></em>-th coordinate of the cube,
+ counting in the following way: <em class="parameter"><code>n</code></em> = 2
+ * <em class="parameter"><code>k</code></em> - 1 means lower bound
+ of <em class="parameter"><code>k</code></em>-th dimension, <em class="parameter"><code>n</code></em> = 2
+ * <em class="parameter"><code>k</code></em> means upper bound of
+ <em class="parameter"><code>k</code></em>-th dimension. Negative
+ <em class="parameter"><code>n</code></em> denotes the inverse value of the corresponding
+ positive coordinate. This operator is designed for KNN-GiST support.
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">&lt;-&gt;</code> <code class="type">cube</code>
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Computes the Euclidean distance between the two cubes.
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">&lt;#&gt;</code> <code class="type">cube</code>
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Computes the taxicab (L-1 metric) distance between the two cubes.
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="type">cube</code> <code class="literal">&lt;=&gt;</code> <code class="type">cube</code>
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Computes the Chebyshev (L-inf metric) distance between the two cubes.
+ </p></td></tr></tbody></table></div></div><br class="table-break" /><p>
+ (Before PostgreSQL 8.2, the containment operators <code class="literal">@&gt;</code> and <code class="literal">&lt;@</code> were
+ respectively called <code class="literal">@</code> and <code class="literal">~</code>. 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>
+ In addition to the above operators, the usual comparison
+ operators shown in <a class="xref" href="functions-comparison.html#FUNCTIONS-COMPARISON-OP-TABLE" title="Table 9.1. Comparison Operators">Table 9.1</a> are
+ available for type <code class="type">cube</code>. 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 <code class="type">cube</code>, which can be useful for
+ example if you would like a UNIQUE constraint on a <code class="type">cube</code> column.
+ Otherwise, this ordering is not of much practical use.
+ </p><p>
+ The <code class="filename">cube</code> module also provides a GiST index operator class for
+ <code class="type">cube</code> values.
+ A <code class="type">cube</code> GiST index can be used to search for values using the
+ <code class="literal">=</code>, <code class="literal">&amp;&amp;</code>, <code class="literal">@&gt;</code>, and
+ <code class="literal">&lt;@</code> operators in <code class="literal">WHERE</code> clauses.
+ </p><p>
+ In addition, a <code class="type">cube</code> GiST index can be used to find nearest
+ neighbors using the metric operators
+ <code class="literal">&lt;-&gt;</code>, <code class="literal">&lt;#&gt;</code>, and
+ <code class="literal">&lt;=&gt;</code> in <code class="literal">ORDER BY</code> 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 &lt;-&gt; cube(array[0.5,0.5,0.5]) LIMIT 1;
+</pre><p>
+ </p><p>
+ The <code class="literal">~&gt;</code> 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 ~&gt; 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 ~&gt; 3 DESC LIMIT 5;
+</pre><p>
+ </p><p>
+ <a class="xref" href="cube.html#CUBE-FUNCTIONS-TABLE" title="Table F.4. Cube Functions">Table F.4</a> shows the available functions.
+ </p><div class="table" id="CUBE-FUNCTIONS-TABLE"><p class="title"><strong>Table F.4. Cube Functions</strong></p><div class="table-contents"><table class="table" summary="Cube Functions" border="1"><colgroup><col /></colgroup><thead><tr><th class="func_table_entry"><p class="func_signature">
+ Function
+ </p>
+ <p>
+ Description
+ </p>
+ <p>
+ Example(s)
+ </p></th></tr></thead><tbody><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube</code> ( <code class="type">float8</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Makes a one dimensional cube with both coordinates the same.
+ </p>
+ <p>
+ <code class="literal">cube(1)</code>
+ → <code class="returnvalue">(1)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube</code> ( <code class="type">float8</code>, <code class="type">float8</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Makes a one dimensional cube.
+ </p>
+ <p>
+ <code class="literal">cube(1,2)</code>
+ → <code class="returnvalue">(1),(2)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube</code> ( <code class="type">float8[]</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Makes a zero-volume cube using the coordinates defined by the array.
+ </p>
+ <p>
+ <code class="literal">cube(ARRAY[1,2,3])</code>
+ → <code class="returnvalue">(1, 2, 3)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube</code> ( <code class="type">float8[]</code>, <code class="type">float8[]</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Makes a cube with upper right and lower left coordinates as defined by
+ the two arrays, which must be of the same length.
+ </p>
+ <p>
+ <code class="literal">cube(ARRAY[1,2], ARRAY[3,4])</code>
+ → <code class="returnvalue">(1, 2),(3, 4)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube</code> ( <code class="type">cube</code>, <code class="type">float8</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ 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.
+ </p>
+ <p>
+ <code class="literal">cube('(1,2),(3,4)'::cube, 5)</code>
+ → <code class="returnvalue">(1, 2, 5),(3, 4, 5)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube</code> ( <code class="type">cube</code>, <code class="type">float8</code>, <code class="type">float8</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ 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.
+ </p>
+ <p>
+ <code class="literal">cube('(1,2),(3,4)'::cube, 5, 6)</code>
+ → <code class="returnvalue">(1, 2, 5),(3, 4, 6)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_dim</code> ( <code class="type">cube</code> )
+ → <code class="returnvalue">integer</code>
+ </p>
+ <p>
+ Returns the number of dimensions of the cube.
+ </p>
+ <p>
+ <code class="literal">cube_dim('(1,2),(3,4)')</code>
+ → <code class="returnvalue">2</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_ll_coord</code> ( <code class="type">cube</code>, <code class="type">integer</code> )
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Returns the <em class="parameter"><code>n</code></em>-th coordinate value for the lower
+ left corner of the cube.
+ </p>
+ <p>
+ <code class="literal">cube_ll_coord('(1,2),(3,4)', 2)</code>
+ → <code class="returnvalue">2</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_ur_coord</code> ( <code class="type">cube</code>, <code class="type">integer</code> )
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Returns the <em class="parameter"><code>n</code></em>-th coordinate value for the
+ upper right corner of the cube.
+ </p>
+ <p>
+ <code class="literal">cube_ur_coord('(1,2),(3,4)', 2)</code>
+ → <code class="returnvalue">4</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_is_point</code> ( <code class="type">cube</code> )
+ → <code class="returnvalue">boolean</code>
+ </p>
+ <p>
+ Returns true if the cube is a point, that is,
+ the two defining corners are the same.
+ </p>
+ <p>
+ <code class="literal">cube_is_point(cube(1,1))</code>
+ → <code class="returnvalue">t</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_distance</code> ( <code class="type">cube</code>, <code class="type">cube</code> )
+ → <code class="returnvalue">float8</code>
+ </p>
+ <p>
+ Returns the distance between two cubes. If both
+ cubes are points, this is the normal distance function.
+ </p>
+ <p>
+ <code class="literal">cube_distance('(1,2)', '(3,4)')</code>
+ → <code class="returnvalue">2.8284271247461903</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_subset</code> ( <code class="type">cube</code>, <code class="type">integer[]</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ 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.
+ </p>
+ <p>
+ <code class="literal">cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2])</code>
+ → <code class="returnvalue">(3),(7)</code>
+ </p>
+ <p>
+ <code class="literal">cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1])</code>
+ → <code class="returnvalue">(5, 3, 1, 1),(8, 7, 6, 6)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_union</code> ( <code class="type">cube</code>, <code class="type">cube</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Produces the union of two cubes.
+ </p>
+ <p>
+ <code class="literal">cube_union('(1,2)', '(3,4)')</code>
+ → <code class="returnvalue">(1, 2),(3, 4)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_inter</code> ( <code class="type">cube</code>, <code class="type">cube</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Produces the intersection of two cubes.
+ </p>
+ <p>
+ <code class="literal">cube_inter('(1,2)', '(3,4)')</code>
+ → <code class="returnvalue">(3, 4),(1, 2)</code>
+ </p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
+ <code class="function">cube_enlarge</code> ( <em class="parameter"><code>c</code></em> <code class="type">cube</code>, <em class="parameter"><code>r</code></em> <code class="type">double</code>, <em class="parameter"><code>n</code></em> <code class="type">integer</code> )
+ → <code class="returnvalue">cube</code>
+ </p>
+ <p>
+ Increases the size of the cube by the specified
+ radius <em class="parameter"><code>r</code></em> in at least <em class="parameter"><code>n</code></em>
+ dimensions. If the radius is negative the cube is shrunk instead.
+ All defined dimensions are changed by the
+ radius <em class="parameter"><code>r</code></em>. Lower-left coordinates are decreased
+ by <em class="parameter"><code>r</code></em> and upper-right coordinates are increased
+ by <em class="parameter"><code>r</code></em>. If a lower-left coordinate is increased
+ to more than the corresponding upper-right coordinate (this can only
+ happen when <em class="parameter"><code>r</code></em> &lt; 0) than both coordinates are
+ set to their average. If <em class="parameter"><code>n</code></em> is greater than the
+ number of defined dimensions and the cube is being enlarged
+ (<em class="parameter"><code>r</code></em> &gt; 0), then extra dimensions are added to
+ make <em class="parameter"><code>n</code></em> 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.
+ </p>
+ <p>
+ <code class="literal">cube_enlarge('(1,2),(3,4)', 0.5, 3)</code>
+ → <code class="returnvalue">(0.5, 1.5, -0.5),(3.5, 4.5, 0.5)</code>
+ </p></td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2" id="id-1.11.7.18.8"><div class="titlepage"><div><div><h3 class="title">F.9.4. Defaults</h3></div></div></div><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" id="id-1.11.7.18.9"><div class="titlepage"><div><div><h3 class="title">F.9.5. Notes</h3></div></div></div><p>
+ For examples of usage, see the regression test <code class="filename">sql/cube.sql</code>.
+ </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 <code class="filename">cubedata.h</code> if you need something bigger.
+ </p></div><div class="sect2" id="id-1.11.7.18.10"><div class="titlepage"><div><div><h3 class="title">F.9.6. Credits</h3></div></div></div><p>
+ Original author: Gene Selkov, Jr. <code class="email">&lt;<a class="email" href="mailto:selkovjr@mcs.anl.gov">selkovjr@mcs.anl.gov</a>&gt;</code>,
+ Mathematics and Computer Science Division, Argonne National Laboratory.
+ </p><p>
+ My thanks are primarily to Prof. Joe Hellerstein
+ (<a class="ulink" href="https://dsf.berkeley.edu/jmh/" target="_top">https://dsf.berkeley.edu/jmh/</a>) for elucidating the
+ gist of the GiST (<a class="ulink" 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">&lt;<a class="email" href="mailto:bruno@wolff.to">bruno@wolff.to</a>&gt;</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">&lt;<a class="email" href="mailto:josh@root.net">josh@root.net</a>&gt;</code> in
+ July 2006. These include <code class="literal">cube(float8[], float8[])</code> and
+ cleaning up the code to use the V1 call protocol instead of the deprecated
+ V0 protocol.
+ </p></div></div><div xmlns="http://www.w3.org/TR/xhtml1/transitional" class="navfooter"><hr></hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="citext.html" title="F.8. citext">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="contrib.html" title="Appendix F. Additional Supplied Modules">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="dblink.html" title="F.10. dblink">Next</a></td></tr><tr><td width="40%" align="left" valign="top">F.8. citext </td><td width="20%" align="center"><a accesskey="h" href="index.html" title="PostgreSQL 13.4 Documentation">Home</a></td><td width="40%" align="right" valign="top"> F.10. dblink</td></tr></table></div></body></html> \ No newline at end of file