liquid_feedback_core

changeset 531:37d6d15919f1

pgLatLon is now a stand-alone extension for PostgreSQL
author jbe
date Sun Aug 21 17:31:44 2016 +0200 (2016-08-21)
parents 6bc81898fd3b
children 5855ff9e5c8f
files README pgLatLon/GNUmakefile pgLatLon/Makefile pgLatLon/README.html pgLatLon/README.mkd pgLatLon/create_test_db.data.sql pgLatLon/create_test_db.schema.sql pgLatLon/create_test_db.sh pgLatLon/latlon--0.1.sql pgLatLon/latlon-v0001.c pgLatLon/latlon.control pgLatLon/make-doc.sh
line diff
     1.1 --- a/README	Sun Aug 21 16:28:21 2016 +0200
     1.2 +++ b/README	Sun Aug 21 17:31:44 2016 +0200
     1.3 @@ -1,3 +1,7 @@
     1.4 +
     1.5 +LiquidFeedback Core requires the pgLatLon extension to be installed.
     1.6 +This extension may be obtained from:
     1.7 +http://www.public-software-group.org/pgLatLon
     1.8  
     1.9  Setup the database:
    1.10  $ createdb liquid_feedback
     2.1 --- a/pgLatLon/GNUmakefile	Sun Aug 21 16:28:21 2016 +0200
     2.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.3 @@ -1,7 +0,0 @@
     2.4 -EXTENSION = latlon
     2.5 -DATA = latlon--0.1.sql
     2.6 -MODULES = latlon-v0001
     2.7 -
     2.8 -PG_CONFIG = pg_config
     2.9 -PGXS := $(shell $(PG_CONFIG) --pgxs)
    2.10 -include $(PGXS)
     3.1 --- a/pgLatLon/Makefile	Sun Aug 21 16:28:21 2016 +0200
     3.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.3 @@ -1,8 +0,0 @@
     3.4 -all::
     3.5 -	gmake all
     3.6 -clean::
     3.7 -	gmake clean
     3.8 -install::
     3.9 -	gmake install
    3.10 -uninstall::
    3.11 -	gmake uninstall
     4.1 --- a/pgLatLon/README.html	Sun Aug 21 16:28:21 2016 +0200
     4.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     4.3 @@ -1,450 +0,0 @@
     4.4 -<html><head><title>pgLatLon v0.1 documentation</title></head><body>
     4.5 -<h1>pgLatLon v0.1 documentation</h1>
     4.6 -
     4.7 -<p>pgLatLon is a spatial database extension for the PostgreSQL object-relational
     4.8 -database management system providing geographic data types and spatial indexing
     4.9 -for the WGS-84 spheroid.</p>
    4.10 -
    4.11 -<p>While many other spatial databases still use imprecise bounding boxes for many
    4.12 -operations, pgLatLon supports more precise geometric calculations for all
    4.13 -implemented operators. Efficient indexing of geometric objects is provided
    4.14 -using fractal indices. Optimizations on bit level (including logarithmic
    4.15 -compression) allow for a highly memory-efficient non-overlapping index suitable
    4.16 -for huge datasets.</p>
    4.17 -
    4.18 -<p>Unlike competing spatial extensions for PostgreSQL, pgLatLon is available under
    4.19 -the permissive MIT/X11 license to avoid problems with viral licenses like the
    4.20 -GPLv2/v3.</p>
    4.21 -
    4.22 -<h2>Installation</h2>
    4.23 -
    4.24 -<h3>Automatic installation</h3>
    4.25 -
    4.26 -<p>Prerequisites:</p>
    4.27 -
    4.28 -<ul>
    4.29 -<li>Ensure that the <code>pg_config</code> binary is in your path (shipped with PostgreSQL).</li>
    4.30 -<li>Ensure that GNU Make is available (either as <code>make</code> or <code>gmake</code>).</li>
    4.31 -</ul>
    4.32 -
    4.33 -<p>Then simply type:</p>
    4.34 -
    4.35 -<pre><code>make install
    4.36 -</code></pre>
    4.37 -
    4.38 -<h3>Manual installation</h3>
    4.39 -
    4.40 -<p>It is also possible to compile and install the extension without GNU Make as
    4.41 -follows:</p>
    4.42 -
    4.43 -<pre><code>cc -Wall -O2 -fPIC -shared -I `pg_config --includedir-server` -o latlon-v0001.so latlon-v0001.c
    4.44 -cp latlon-v0001.so `pg_config --pkglibdir`
    4.45 -cp latlon.control `pg_config --sharedir`/extension/
    4.46 -cp latlon--0.1.sql `pg_config --sharedir`/extension/
    4.47 -</code></pre>
    4.48 -
    4.49 -<h3>Loading the extension</h3>
    4.50 -
    4.51 -<p>After installation, you can create a database and load the extension as
    4.52 -follows:</p>
    4.53 -
    4.54 -<pre><code>% createdb test_database
    4.55 -% psql test_database
    4.56 -psql (9.5.4)
    4.57 -Type "help" for help.
    4.58 -
    4.59 -test_database=# CREATE EXTENSION latlon;
    4.60 -</code></pre>
    4.61 -
    4.62 -<h2>Reference</h2>
    4.63 -
    4.64 -<h3>1. Types</h3>
    4.65 -
    4.66 -<p>pgLatLon provides four geographic types: <code>epoint</code>, <code>ebox</code>, <code>ecircle</code>, and
    4.67 -<code>ecluster</code>.</p>
    4.68 -
    4.69 -<h4><code>epoint</code></h4>
    4.70 -
    4.71 -<p>A point on the earth spheroid (WGS-84).</p>
    4.72 -
    4.73 -<p>The text input format is <code>'[N|S]&lt;float&gt; [E|W]&lt;float&gt;'</code>, where each float is in
    4.74 -degrees. Note the required white space between the latitude and longitude
    4.75 -components.  Each floating point number may have a sign, in which case <code>N</code>/<code>S</code>
    4.76 -or <code>E</code>/<code>W</code> are switched respectively (e.g. <code>E-5</code> is the same as <code>W5</code>).</p>
    4.77 -
    4.78 -<p>An <code>epoint</code> may also be created from two floating point numbers by calling
    4.79 -<code>epoint(latitude, longitude)</code>, where positive latitudes are used for the
    4.80 -northern hemisphere, negative latitudes are used for the southern hemisphere,
    4.81 -positive longitudes indicate positions east of the prime meridian, and negative
    4.82 -longitudes indicate positions west of the prime meridian.</p>
    4.83 -
    4.84 -<p>Latitudes exceeding -90 or +90 degrees are truncated to -90 or +90
    4.85 -respectively, in which case a warning will be issued. Longitudes exceeding -180
    4.86 -or +180 degrees will be converted to values between -180 and +180 (both
    4.87 -inclusive) by adding or substracting a multiple of 360 degrees, in which case a
    4.88 -notice will be issued.</p>
    4.89 -
    4.90 -<p>If the latitude is -90 or +90 (south pole or north pole), a longitude value is
    4.91 -still stored in the datum, and if a point is on the prime meridian or the
    4.92 -180th meridian, the east/west bit is also stored in the datum. In case of the
    4.93 -prime meridian, this is done by storing a floating point value of -0 for
    4.94 -0 degrees west and a value of +0 for 0 degrees east. In case of the
    4.95 -180th meridian, this is done by storing -180 or +180 respectively. The equality
    4.96 -operator, however, returns true when the same points on earth are described,
    4.97 -i.e. the longitude is ignored for the poles, and 180 degrees west is considered
    4.98 -to be equal to 180 degrees east.</p>
    4.99 -
   4.100 -<h4><code>ebox</code></h4>
   4.101 -
   4.102 -<p>An area on earth demarcated by a southern and northern latitude, and a western
   4.103 -and eastern longitude (all given in WGS-84).</p>
   4.104 -
   4.105 -<p>The text input format is
   4.106 -<code>'{N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt;'</code>, where each float is in
   4.107 -degrees. The ordering of the four white-space separated blocks is not
   4.108 -significant. To include the 180th meridian, one longitude boundary must be
   4.109 -equal to or exceed <code>W180</code> or <code>E180</code>, e.g. <code>'N10 N20 E170 E190'</code>.</p>
   4.110 -
   4.111 -<p>A special value is the empty area, denoted by the text represenation <code>'empty'</code>.
   4.112 -Such an <code>ebox</code> does not contain any point.</p>
   4.113 -
   4.114 -<p>An <code>ebox</code> may also be created from four floating point numbers by calling
   4.115 -<code>ebox(min_latitude, max_latitude, min_longitude, max_longitude)</code>, where
   4.116 -positive values are used for north and east, and negative values are used for
   4.117 -south and west. If <code>min_latitude</code> is strictly greater than <code>max_latitude</code>, an
   4.118 -empty <code>ebox</code> is created. If <code>min_longitude</code> is greater than <code>max_longitude</code> and
   4.119 -if both longitudes are between -180 and +180 degrees, then the area oriented in
   4.120 -such way that the 180th meridian is included.</p>
   4.121 -
   4.122 -<p>If the longitude span is less than 120 degrees, an <code>ebox</code> may be alternatively
   4.123 -created from two <code>epoints</code> in the following way: <code>ebox(epoint(lat1, lon1),
   4.124 -epoint(lat2, lon2))</code>. In this case <code>lat1</code> and <code>lat2</code> as well as <code>lon1</code> and
   4.125 -<code>lon2</code> can be swapped without any impact.</p>
   4.126 -
   4.127 -<h4><code>ecircle</code></h4>
   4.128 -
   4.129 -<p>An area containing all points not farther away from a given center point
   4.130 -(WGS-84) than a given radius.</p>
   4.131 -
   4.132 -<p>The text input format is <code>'{N|S}&lt;float&gt; {E|W}&lt;float&gt; &lt;float&gt;'</code>, where the first
   4.133 -two floats denote the center point in degrees and the third float denotes the
   4.134 -radius in meters. A radius equal to minus infinity denotes an empty circle
   4.135 -which contains no point at all (despite having a center), while a radius equal
   4.136 -to zero denotes a circle that includes a single point.</p>
   4.137 -
   4.138 -<p>An <code>ecircle</code> may also be created by calling <code>ecircle(epoint(...), radius)</code> or
   4.139 -from three floating point numbers by calling <code>ecircle(latitude, longitude,
   4.140 -radius)</code>.</p>
   4.141 -
   4.142 -<h4><code>ecluster</code></h4>
   4.143 -
   4.144 -<p>A collection of points, paths, polygons, and outlines on the WGS-84 spheroid.
   4.145 -Each path, polygon, or outline must cover a longitude range of less than
   4.146 -180 degrees to avoid ambiguities.</p>
   4.147 -
   4.148 -<p>The text input format is a white-space separated list of the following items:</p>
   4.149 -
   4.150 -<ul>
   4.151 -<li><code>point   ({N|S}&lt;float&gt; {E|W}&lt;float&gt;)</code></li>
   4.152 -<li><code>path    ({N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; ...)</code></li>
   4.153 -<li><code>outline ({N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; ...)</code></li>
   4.154 -<li><code>polygon ({N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; ...)</code></li>
   4.155 -</ul>
   4.156 -
   4.157 -<p>Paths are open by default (i.e. there is no connection from the last point in
   4.158 -the list to the first point in the list). Outlines and polygons, in contrast,
   4.159 -are automatically closed (i.e. there is a line segment from the last point in
   4.160 -the list to the first point in the list) which means the first point should not
   4.161 -be repeated as last point in the list. Polygons are filled, outlines are not.</p>
   4.162 -
   4.163 -<h3>2. Indices</h3>
   4.164 -
   4.165 -<p>Two kinds of indices are supported: B-tree and GiST indices.</p>
   4.166 -
   4.167 -<h4>B-tree indices</h4>
   4.168 -
   4.169 -<p>A B-tree index can be used for simple equality searches and is supported by the
   4.170 -<code>epoint</code>, <code>ebox</code>, and <code>ecircle</code> data types. B-tree indices can not be used for
   4.171 -geographic searches.</p>
   4.172 -
   4.173 -<h4>GiST indices</h4>
   4.174 -
   4.175 -<p>For geographic searches, GiST indices must be used. The <code>epoint</code>, <code>ecircle</code>,
   4.176 -and <code>ecluster</code> data types support GiST indexing. A GiST index for geographic
   4.177 -searches can be created as follows:</p>
   4.178 -
   4.179 -<pre><code>CREATE TABLE tbl (
   4.180 -        id              serial4         PRIMARY KEY,
   4.181 -        loc             epoint          NOT NULL );
   4.182 -
   4.183 -CREATE INDEX name_of_index ON tbl USING gist (loc);
   4.184 -</code></pre>
   4.185 -
   4.186 -<p>GiST indices also support nearest neighbor searches when using the distance
   4.187 -operator (<code>&lt;-&gt;</code>) in the ORDER BY clause.</p>
   4.188 -
   4.189 -<h4>Indices on other data types (e.g. GeoJSON)</h4>
   4.190 -
   4.191 -<p>Note that further types can be indexed by using an index on an expression with
   4.192 -a conversion function. One conversion function provided by pgLatLon is the
   4.193 -<code>GeoJSON_to_ecluster(float8, float8, text)</code> function:</p>
   4.194 -
   4.195 -<pre><code>CREATE TABLE tbl (
   4.196 -        id              serial4         PRIMARY KEY,
   4.197 -        loc             jsonb           NOT NULL );
   4.198 -
   4.199 -CREATE INDEX name_of_index ON tbl USING gist((GeoJSON_to_ecluster("loc")));
   4.200 -</code></pre>
   4.201 -
   4.202 -<p>When using the conversion function in an expression, the index will be used
   4.203 -automatically:</p>
   4.204 -
   4.205 -<pre><code>SELECT * FROM tbl WHERE GeoJSON_to_ecluster("loc") &amp;&amp; 'N50 E10 10000'::ecircle;
   4.206 -</code></pre>
   4.207 -
   4.208 -<h3>3. Operators</h3>
   4.209 -
   4.210 -<h4>Equality operator <code>=</code></h4>
   4.211 -
   4.212 -<p>Tests if two geographic objects are equal.</p>
   4.213 -
   4.214 -<p>The longitude is ignored for the poles, and 180 degrees west is considered to
   4.215 -be equal to 180 degrees east.</p>
   4.216 -
   4.217 -<p>For boxes and circles, two empty objects are considered equal. (Note that a
   4.218 -circle is not empty if the radius is zero but only if it is negative infinity,
   4.219 -i.e. smaller than zero.) Two circles with a positive infinite radius are also
   4.220 -considered equal.</p>
   4.221 -
   4.222 -<p>Implemented for:</p>
   4.223 -
   4.224 -<ul>
   4.225 -<li><code>epoint = epoint</code></li>
   4.226 -<li><code>ebox = ebox</code></li>
   4.227 -<li><code>ecircle = ecircle</code></li>
   4.228 -</ul>
   4.229 -
   4.230 -<p>The negation is the inequality operator (<code>&lt;&gt;</code> or <code>!=</code>).</p>
   4.231 -
   4.232 -<h4>Linear ordering operators <code>&lt;&lt;&lt;</code>, <code>&lt;&lt;&lt;=</code>, <code>&gt;&gt;&gt;=</code>, <code>&gt;&gt;&gt;</code></h4>
   4.233 -
   4.234 -<p>These operators create an arbitrary (but well-defined) linear ordering of
   4.235 -geographic objects, which is used internally for B-tree indexing and merge
   4.236 -joins. These operators will usually not be used by an application programmer.</p>
   4.237 -
   4.238 -<h4>Overlap operator <code>&amp;&amp;</code></h4>
   4.239 -
   4.240 -<p>Tests if two geographic objects have at least one point in common. Currently
   4.241 -implemented for:</p>
   4.242 -
   4.243 -<ul>
   4.244 -<li><code>epoint &amp;&amp; ebox</code></li>
   4.245 -<li><code>epoint &amp;&amp; ecircle</code></li>
   4.246 -<li><code>epoint &amp;&amp; ecluster</code></li>
   4.247 -<li><code>ebox &amp;&amp; ebox</code></li>
   4.248 -<li><code>ecircle &amp;&amp; ecircle</code></li>
   4.249 -<li><code>ecircle &amp;&amp; ecluster</code></li>
   4.250 -</ul>
   4.251 -
   4.252 -<p>The <code>&amp;&amp;</code> operator is commutative, i.e. <code>a &amp;&amp; b</code> is the same as <code>b &amp;&amp; a</code>. Each
   4.253 -commutation is supported as well.</p>
   4.254 -
   4.255 -<h4>Distance operator <code>&lt;-&gt;</code></h4>
   4.256 -
   4.257 -<p>Calculates the shortest distance between two geographic objects in meters (zero
   4.258 -if the objects are overlapping). Currently implemented for:</p>
   4.259 -
   4.260 -<ul>
   4.261 -<li><code>epoint &lt;-&gt; epoint</code></li>
   4.262 -<li><code>epoint &lt;-&gt; ecircle</code></li>
   4.263 -<li><code>epoint &lt;-&gt; ecluster</code></li>
   4.264 -<li><code>ecircle &lt;-&gt; ecircle</code></li>
   4.265 -<li><code>ecircle &lt;-&gt; ecluster</code></li>
   4.266 -</ul>
   4.267 -
   4.268 -<p>The <code>&lt;-&gt;</code> operator is commutative, i.e. <code>a &lt;-&gt; b</code> is the same as <code>b &lt;-&gt; a</code>.
   4.269 -Each commutation is supported as well.</p>
   4.270 -
   4.271 -<p>For short distances, the result is very accurate (i.e. respects the dimensions
   4.272 -of the WGS-84 spheroid). For longer distances in the order of magnitude of
   4.273 -earth's radius or greater, the value is only approximate (but the error is
   4.274 -still less than 0.2% as long as no polygons with very long edges are involved).</p>
   4.275 -
   4.276 -<p>The functions <code>distance(epoint, epoint)</code> and <code>distance(ecluster, epoint)</code> can
   4.277 -be used as an alias for this operator.</p>
   4.278 -
   4.279 -<p>Note: In case of radial searches with a fixed radius, this operator should
   4.280 -not be used. Instead, an <code>ecircle</code> should be created and used in combination
   4.281 -with the overlap operator (<code>&amp;&amp;</code>). Alternatively, the functions
   4.282 -<code>distance_within(epoint, epoint, float8)</code> or <code>distance_within(ecluster, epoint,
   4.283 -float8)</code> can be used for fixed-radius searches.</p>
   4.284 -
   4.285 -<h3>4. Functions</h3>
   4.286 -
   4.287 -<h4><code>center(circle)</code></h4>
   4.288 -
   4.289 -<p>Returns the center of an <code>ecircle</code> as an <code>epoint</code>.</p>
   4.290 -
   4.291 -<h4><code>distance(epoint, epoint)</code></h4>
   4.292 -
   4.293 -<p>Calculates the distance between two <code>epoint</code> datums in meters. This function is
   4.294 -an alias for the distance operator <code>&lt;-&gt;</code>.</p>
   4.295 -
   4.296 -<p>Note: In case of radial searches with a fixed radius, this function should not be
   4.297 -used. Use <code>distance_within(epoint, epoint, float8)</code> instead.</p>
   4.298 -
   4.299 -<h4><code>distance(ecluster, epoint)</code></h4>
   4.300 -
   4.301 -<p>Calculates the distance from an <code>ecluster</code> to an <code>epoint</code> in meters. This
   4.302 -function is an alias for the distance operator <code>&lt;-&gt;</code>.</p>
   4.303 -
   4.304 -<p>Note: In case of radial searches with a fixed radius, this function should not be
   4.305 -used. Use <code>distance_within(epoint, epoint, float8)</code> instead.</p>
   4.306 -
   4.307 -<h4><code>distance_within(</code>variable <code>epoint,</code> fixed <code>epoint,</code> radius <code>float8)</code></h4>
   4.308 -
   4.309 -<p>Checks if the distance between two <code>epoint</code> datums is not greater than a given
   4.310 -value (search radius).</p>
   4.311 -
   4.312 -<p>Note: In case of radial searches with a fixed radius, the first argument must
   4.313 -be used for the table column, while the second argument must be used for the
   4.314 -search center. Otherwise an existing index cannot be used.</p>
   4.315 -
   4.316 -<h4><code>distance_within(</code>variable <code>ecluster,</code> fixed <code>epoint,</code> radius <code>float8)</code></h4>
   4.317 -
   4.318 -<p>Checks if the distance from an <code>ecluster</code> to an <code>epoint</code> is not greater than a
   4.319 -given value (search radius).</p>
   4.320 -
   4.321 -<h4><code>ebox(</code>latmin <code>float8,</code> latmax <code>float8,</code> lonmin <code>float8,</code> lonmax <code>float8)</code></h4>
   4.322 -
   4.323 -<p>Creates a new <code>ebox</code> with the given boundaries.
   4.324 -See "1. Types", subsection <code>ebox</code> for details.</p>
   4.325 -
   4.326 -<h4><code>ebox(epoint, epoint)</code></h4>
   4.327 -
   4.328 -<p>Creates a new <code>ebox</code>. This function may only be used if the longitude
   4.329 -difference is less than or equal to 120 degrees.
   4.330 -See "1. Types", subsection <code>ebox</code> for details.</p>
   4.331 -
   4.332 -<h4><code>ecircle(epoint, float8)</code></h4>
   4.333 -
   4.334 -<p>Creates an <code>ecircle</code> with the given center point and radius.</p>
   4.335 -
   4.336 -<h4><code>ecircle(</code>latitude <code>float8,</code> longitude <code>float8,</code> radius <code>float8)</code></h4>
   4.337 -
   4.338 -<p>Creates an <code>ecircle</code> with the given center point and radius.</p>
   4.339 -
   4.340 -<h4><code>ecluster_concat(ecluster, ecluster)</code></h4>
   4.341 -
   4.342 -<p>Combines two clusters to form a new <code>ecluster</code> by uniting all entries of both
   4.343 -clusters. Note that two overlapping areas of polygons annihilate each other
   4.344 -(which may be used to create polygons with holes).</p>
   4.345 -
   4.346 -<h4><code>ecluster_concat(ecluster[])</code></h4>
   4.347 -
   4.348 -<p>Creates a new <code>ecluster</code> that unites all entries of all clusters in the passed
   4.349 -array. Note that two overlapping areas of polygons annihilate each other (which
   4.350 -may be used to create polygons with holes).</p>
   4.351 -
   4.352 -<h4><code>ecluster_create_multipoint(epoint[])</code></h4>
   4.353 -
   4.354 -<p>Creates a new <code>ecluster</code> which contains multiple points.</p>
   4.355 -
   4.356 -<h4><code>ecluster_create_outline(epoint[])</code></h4>
   4.357 -
   4.358 -<p>Creates a new <code>ecluster</code> that is an outline given by the passed points.</p>
   4.359 -
   4.360 -<h4><code>ecluster_create_path(epoint[])</code></h4>
   4.361 -
   4.362 -<p>Creates a new <code>ecluster</code> that is a path given by the passed points.</p>
   4.363 -
   4.364 -<h4><code>ecluster_create_polygon(epoint[])</code></h4>
   4.365 -
   4.366 -<p>Creates a new <code>ecluster</code> that is a polygon given by the passed points.</p>
   4.367 -
   4.368 -<h4><code>ecluster_extract_outlines(ecluster)</code></h4>
   4.369 -
   4.370 -<p>Set-returning function that returns the outlines of an <code>ecluster</code> as <code>epoint[]</code>
   4.371 -rows.</p>
   4.372 -
   4.373 -<h4><code>ecluster_extract_paths(ecluster)</code></h4>
   4.374 -
   4.375 -<p>Set-returning function that returns the paths of an <code>ecluster</code> as <code>epoint[]</code>
   4.376 -rows.</p>
   4.377 -
   4.378 -<h4><code>ecluster_extract_points(ecluster)</code></h4>
   4.379 -
   4.380 -<p>Set-returning function that returns the points of an <code>ecluster</code> as <code>epoint</code>
   4.381 -rows.</p>
   4.382 -
   4.383 -<h4><code>ecluster_extract_polygons(ecluster)</code></h4>
   4.384 -
   4.385 -<p>Set-returning function that returns the polygons of an <code>ecluster</code> as <code>epoint[]</code>
   4.386 -rows.</p>
   4.387 -
   4.388 -<h4><code>empty_ebox</code>()</h4>
   4.389 -
   4.390 -<p>Returns the empty <code>ebox</code>.
   4.391 -See "1. Types", subsection <code>ebox</code> for details.</p>
   4.392 -
   4.393 -<h4><code>epoint(</code>latitude <code>float8,</code> longitude <code>float8)</code></h4>
   4.394 -
   4.395 -<p>Returns an <code>epoint</code> with the given latitude and longitude.</p>
   4.396 -
   4.397 -<h4><code>epoint_latlon(</code>latitude <code>float8,</code> longitude <code>float8)</code></h4>
   4.398 -
   4.399 -<p>Alias for <code>epoint(float8, float8)</code>.</p>
   4.400 -
   4.401 -<h4><code>epoint_lonlat(</code>longitude <code>float8,</code> latitude <code>float8)</code></h4>
   4.402 -
   4.403 -<p>Same as <code>epoint(float8, float8)</code> but with arguments reversed.</p>
   4.404 -
   4.405 -<h4><code>GeoJSON_to_epoint(jsonb, text)</code></h4>
   4.406 -
   4.407 -<p>Maps a GeoJSON object of type "Point" or "Feature" (which contains a
   4.408 -"Point") to an <code>epoint</code> datum. For any other JSON objects, NULL is returned.</p>
   4.409 -
   4.410 -<p>The second parameter (which defaults to <code>epoint_lonlat</code>) may be set to a name
   4.411 -of a conversion function that transforms two coordinates (two <code>float8</code>
   4.412 -parameters) to an <code>epoint</code>.</p>
   4.413 -
   4.414 -<h4><code>GeoJSON_to_ecluster(jsonb, text)</code></h4>
   4.415 -
   4.416 -<p>Maps a (valid) GeoJSON object to an <code>ecluster</code>. Note that this function
   4.417 -does not check whether the JSONB object is a valid GeoJSON object.</p>
   4.418 -
   4.419 -<p>The second parameter (which defaults to <code>epoint_lonlat</code>) may be set to a name
   4.420 -of a conversion function that transforms two coordinates (two <code>float8</code>
   4.421 -parameters) to an <code>epoint</code>.</p>
   4.422 -
   4.423 -<h4><code>max_latitude(ebox)</code></h4>
   4.424 -
   4.425 -<p>Returns the northern boundary of a given <code>ebox</code> in degrees between -90 and +90.</p>
   4.426 -
   4.427 -<h4><code>max_longitude(ebox)</code></h4>
   4.428 -
   4.429 -<p>Returns the eastern boundary of a given <code>ebox</code> in degrees between -180 and +180
   4.430 -(both inclusive).</p>
   4.431 -
   4.432 -<h4><code>min_latitude(ebox)</code></h4>
   4.433 -
   4.434 -<p>Returns the southern boundary of a given <code>ebox</code> in degrees between -90 and +90.</p>
   4.435 -
   4.436 -<h4><code>min_longitude(ebox)</code></h4>
   4.437 -
   4.438 -<p>Returns the western boundary of a given <code>ebox</code> in degrees between -180 and +180
   4.439 -(both inclusive).</p>
   4.440 -
   4.441 -<h4><code>latitude(epoint)</code></h4>
   4.442 -
   4.443 -<p>Returns the latitude value of an <code>epoint</code> in degrees between -90 and +90.</p>
   4.444 -
   4.445 -<h4><code>longitude(epoint)</code></h4>
   4.446 -
   4.447 -<p>Returns the longitude value of an <code>epoint</code> in degrees between -180 and +180
   4.448 -(both inclusive).</p>
   4.449 -
   4.450 -<h4><code>radius(ecircle)</code></h4>
   4.451 -
   4.452 -<p>Returns the radius of an <code>ecircle</code> in meters.</p>
   4.453 -</body></html>
     5.1 --- a/pgLatLon/README.mkd	Sun Aug 21 16:28:21 2016 +0200
     5.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     5.3 @@ -1,438 +0,0 @@
     5.4 -pgLatLon v0.1 documentation
     5.5 -===========================
     5.6 -
     5.7 -pgLatLon is a spatial database extension for the PostgreSQL object-relational
     5.8 -database management system providing geographic data types and spatial indexing
     5.9 -for the WGS-84 spheroid.
    5.10 -
    5.11 -While many other spatial databases still use imprecise bounding boxes for many
    5.12 -operations, pgLatLon supports more precise geometric calculations for all
    5.13 -implemented operators. Efficient indexing of geometric objects is provided
    5.14 -using fractal indices. Optimizations on bit level (including logarithmic
    5.15 -compression) allow for a highly memory-efficient non-overlapping index suitable
    5.16 -for huge datasets.
    5.17 -
    5.18 -Unlike competing spatial extensions for PostgreSQL, pgLatLon is available under
    5.19 -the permissive MIT/X11 license to avoid problems with viral licenses like the
    5.20 -GPLv2/v3.
    5.21 -
    5.22 -
    5.23 -Installation
    5.24 -------------
    5.25 -
    5.26 -### Automatic installation
    5.27 -
    5.28 -Prerequisites:
    5.29 -
    5.30 -* Ensure that the `pg_config` binary is in your path (shipped with PostgreSQL).
    5.31 -* Ensure that GNU Make is available (either as `make` or `gmake`).
    5.32 -
    5.33 -Then simply type:
    5.34 -
    5.35 -    make install
    5.36 -
    5.37 -### Manual installation    
    5.38 -
    5.39 -It is also possible to compile and install the extension without GNU Make as
    5.40 -follows:
    5.41 -
    5.42 -    cc -Wall -O2 -fPIC -shared -I `pg_config --includedir-server` -o latlon-v0001.so latlon-v0001.c
    5.43 -    cp latlon-v0001.so `pg_config --pkglibdir`
    5.44 -    cp latlon.control `pg_config --sharedir`/extension/
    5.45 -    cp latlon--0.1.sql `pg_config --sharedir`/extension/
    5.46 -
    5.47 -### Loading the extension
    5.48 -
    5.49 -After installation, you can create a database and load the extension as
    5.50 -follows:
    5.51 -
    5.52 -    % createdb test_database
    5.53 -    % psql test_database
    5.54 -    psql (9.5.4)
    5.55 -    Type "help" for help.
    5.56 -
    5.57 -    test_database=# CREATE EXTENSION latlon;
    5.58 -
    5.59 -
    5.60 -Reference
    5.61 ----------
    5.62 -
    5.63 -### 1. Types
    5.64 -
    5.65 -pgLatLon provides four geographic types: `epoint`, `ebox`, `ecircle`, and
    5.66 -`ecluster`.
    5.67 -
    5.68 -#### `epoint`
    5.69 -
    5.70 -A point on the earth spheroid (WGS-84).
    5.71 -
    5.72 -The text input format is `'[N|S]<float> [E|W]<float>'`, where each float is in
    5.73 -degrees. Note the required white space between the latitude and longitude
    5.74 -components.  Each floating point number may have a sign, in which case `N`/`S`
    5.75 -or `E`/`W` are switched respectively (e.g. `E-5` is the same as `W5`).
    5.76 -
    5.77 -An `epoint` may also be created from two floating point numbers by calling
    5.78 -`epoint(latitude, longitude)`, where positive latitudes are used for the
    5.79 -northern hemisphere, negative latitudes are used for the southern hemisphere,
    5.80 -positive longitudes indicate positions east of the prime meridian, and negative
    5.81 -longitudes indicate positions west of the prime meridian.
    5.82 -
    5.83 -Latitudes exceeding -90 or +90 degrees are truncated to -90 or +90
    5.84 -respectively, in which case a warning will be issued. Longitudes exceeding -180
    5.85 -or +180 degrees will be converted to values between -180 and +180 (both
    5.86 -inclusive) by adding or substracting a multiple of 360 degrees, in which case a
    5.87 -notice will be issued.
    5.88 -
    5.89 -If the latitude is -90 or +90 (south pole or north pole), a longitude value is
    5.90 -still stored in the datum, and if a point is on the prime meridian or the
    5.91 -180th meridian, the east/west bit is also stored in the datum. In case of the
    5.92 -prime meridian, this is done by storing a floating point value of -0 for
    5.93 -0 degrees west and a value of +0 for 0 degrees east. In case of the
    5.94 -180th meridian, this is done by storing -180 or +180 respectively. The equality
    5.95 -operator, however, returns true when the same points on earth are described,
    5.96 -i.e. the longitude is ignored for the poles, and 180 degrees west is considered
    5.97 -to be equal to 180 degrees east.
    5.98 -
    5.99 -#### `ebox`
   5.100 -
   5.101 -An area on earth demarcated by a southern and northern latitude, and a western
   5.102 -and eastern longitude (all given in WGS-84).
   5.103 -
   5.104 -The text input format is
   5.105 -`'{N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float>'`, where each float is in
   5.106 -degrees. The ordering of the four white-space separated blocks is not
   5.107 -significant. To include the 180th meridian, one longitude boundary must be
   5.108 -equal to or exceed `W180` or `E180`, e.g. `'N10 N20 E170 E190'`.
   5.109 -
   5.110 -A special value is the empty area, denoted by the text represenation `'empty'`.
   5.111 -Such an `ebox` does not contain any point.
   5.112 -
   5.113 -An `ebox` may also be created from four floating point numbers by calling
   5.114 -`ebox(min_latitude, max_latitude, min_longitude, max_longitude)`, where
   5.115 -positive values are used for north and east, and negative values are used for
   5.116 -south and west. If `min_latitude` is strictly greater than `max_latitude`, an
   5.117 -empty `ebox` is created. If `min_longitude` is greater than `max_longitude` and
   5.118 -if both longitudes are between -180 and +180 degrees, then the area oriented in
   5.119 -such way that the 180th meridian is included.
   5.120 -
   5.121 -If the longitude span is less than 120 degrees, an `ebox` may be alternatively
   5.122 -created from two `epoints` in the following way: `ebox(epoint(lat1, lon1),
   5.123 -epoint(lat2, lon2))`. In this case `lat1` and `lat2` as well as `lon1` and
   5.124 -`lon2` can be swapped without any impact.
   5.125 -
   5.126 -#### `ecircle`
   5.127 -
   5.128 -An area containing all points not farther away from a given center point
   5.129 -(WGS-84) than a given radius.
   5.130 -
   5.131 -The text input format is `'{N|S}<float> {E|W}<float> <float>'`, where the first
   5.132 -two floats denote the center point in degrees and the third float denotes the
   5.133 -radius in meters. A radius equal to minus infinity denotes an empty circle
   5.134 -which contains no point at all (despite having a center), while a radius equal
   5.135 -to zero denotes a circle that includes a single point.
   5.136 -
   5.137 -An `ecircle` may also be created by calling `ecircle(epoint(...), radius)` or
   5.138 -from three floating point numbers by calling `ecircle(latitude, longitude,
   5.139 -radius)`.
   5.140 -
   5.141 -#### `ecluster`
   5.142 -
   5.143 -A collection of points, paths, polygons, and outlines on the WGS-84 spheroid.
   5.144 -Each path, polygon, or outline must cover a longitude range of less than
   5.145 -180 degrees to avoid ambiguities.
   5.146 -
   5.147 -The text input format is a white-space separated list of the following items:
   5.148 -
   5.149 -* `point   ({N|S}<float> {E|W}<float>)`
   5.150 -* `path    ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)`
   5.151 -* `outline ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)`
   5.152 -* `polygon ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)`
   5.153 -
   5.154 -Paths are open by default (i.e. there is no connection from the last point in
   5.155 -the list to the first point in the list). Outlines and polygons, in contrast,
   5.156 -are automatically closed (i.e. there is a line segment from the last point in
   5.157 -the list to the first point in the list) which means the first point should not
   5.158 -be repeated as last point in the list. Polygons are filled, outlines are not.
   5.159 -
   5.160 -### 2. Indices
   5.161 -
   5.162 -Two kinds of indices are supported: B-tree and GiST indices.
   5.163 -
   5.164 -#### B-tree indices
   5.165 -
   5.166 -A B-tree index can be used for simple equality searches and is supported by the
   5.167 -`epoint`, `ebox`, and `ecircle` data types. B-tree indices can not be used for
   5.168 -geographic searches.
   5.169 -
   5.170 -#### GiST indices
   5.171 -
   5.172 -For geographic searches, GiST indices must be used. The `epoint`, `ecircle`,
   5.173 -and `ecluster` data types support GiST indexing. A GiST index for geographic
   5.174 -searches can be created as follows:
   5.175 -
   5.176 -    CREATE TABLE tbl (
   5.177 -            id              serial4         PRIMARY KEY,
   5.178 -            loc             epoint          NOT NULL );
   5.179 -
   5.180 -    CREATE INDEX name_of_index ON tbl USING gist (loc);
   5.181 -
   5.182 -GiST indices also support nearest neighbor searches when using the distance
   5.183 -operator (`<->`) in the ORDER BY clause.
   5.184 -
   5.185 -#### Indices on other data types (e.g. GeoJSON)
   5.186 -
   5.187 -Note that further types can be indexed by using an index on an expression with
   5.188 -a conversion function. One conversion function provided by pgLatLon is the
   5.189 -`GeoJSON_to_ecluster(float8, float8, text)` function:
   5.190 -
   5.191 -    CREATE TABLE tbl (
   5.192 -            id              serial4         PRIMARY KEY,
   5.193 -            loc             jsonb           NOT NULL );
   5.194 -
   5.195 -    CREATE INDEX name_of_index ON tbl USING gist((GeoJSON_to_ecluster("loc")));
   5.196 -
   5.197 -When using the conversion function in an expression, the index will be used
   5.198 -automatically:
   5.199 -
   5.200 -    SELECT * FROM tbl WHERE GeoJSON_to_ecluster("loc") && 'N50 E10 10000'::ecircle;
   5.201 -
   5.202 -### 3. Operators
   5.203 -
   5.204 -#### Equality operator `=`
   5.205 -
   5.206 -Tests if two geographic objects are equal.
   5.207 -
   5.208 -The longitude is ignored for the poles, and 180 degrees west is considered to
   5.209 -be equal to 180 degrees east.
   5.210 -
   5.211 -For boxes and circles, two empty objects are considered equal. (Note that a
   5.212 -circle is not empty if the radius is zero but only if it is negative infinity,
   5.213 -i.e. smaller than zero.) Two circles with a positive infinite radius are also
   5.214 -considered equal.
   5.215 -
   5.216 -Implemented for:
   5.217 -
   5.218 -* `epoint = epoint`
   5.219 -* `ebox = ebox`
   5.220 -* `ecircle = ecircle`
   5.221 -
   5.222 -The negation is the inequality operator (`<>` or `!=`).
   5.223 -
   5.224 -#### Linear ordering operators `<<<`, `<<<=`, `>>>=`, `>>>`
   5.225 -
   5.226 -These operators create an arbitrary (but well-defined) linear ordering of
   5.227 -geographic objects, which is used internally for B-tree indexing and merge
   5.228 -joins. These operators will usually not be used by an application programmer.
   5.229 -
   5.230 -#### Overlap operator `&&`
   5.231 -
   5.232 -Tests if two geographic objects have at least one point in common. Currently
   5.233 -implemented for:
   5.234 -
   5.235 -* `epoint && ebox`
   5.236 -* `epoint && ecircle`
   5.237 -* `epoint && ecluster`
   5.238 -* `ebox && ebox`
   5.239 -* `ecircle && ecircle`
   5.240 -* `ecircle && ecluster`
   5.241 -
   5.242 -The `&&` operator is commutative, i.e. `a && b` is the same as `b && a`. Each
   5.243 -commutation is supported as well.
   5.244 -
   5.245 -#### Distance operator `<->`
   5.246 -
   5.247 -Calculates the shortest distance between two geographic objects in meters (zero
   5.248 -if the objects are overlapping). Currently implemented for:
   5.249 -
   5.250 -* `epoint <-> epoint`
   5.251 -* `epoint <-> ecircle`
   5.252 -* `epoint <-> ecluster`
   5.253 -* `ecircle <-> ecircle`
   5.254 -* `ecircle <-> ecluster`
   5.255 -
   5.256 -The `<->` operator is commutative, i.e. `a <-> b` is the same as `b <-> a`.
   5.257 -Each commutation is supported as well.
   5.258 -
   5.259 -For short distances, the result is very accurate (i.e. respects the dimensions
   5.260 -of the WGS-84 spheroid). For longer distances in the order of magnitude of
   5.261 -earth's radius or greater, the value is only approximate (but the error is
   5.262 -still less than 0.2% as long as no polygons with very long edges are involved).
   5.263 -
   5.264 -The functions `distance(epoint, epoint)` and `distance(ecluster, epoint)` can
   5.265 -be used as an alias for this operator.
   5.266 -
   5.267 -Note: In case of radial searches with a fixed radius, this operator should
   5.268 -not be used. Instead, an `ecircle` should be created and used in combination
   5.269 -with the overlap operator (`&&`). Alternatively, the functions
   5.270 -`distance_within(epoint, epoint, float8)` or `distance_within(ecluster, epoint,
   5.271 -float8)` can be used for fixed-radius searches.
   5.272 -
   5.273 -### 4. Functions
   5.274 -
   5.275 -#### `center(circle)`
   5.276 -
   5.277 -Returns the center of an `ecircle` as an `epoint`.
   5.278 -
   5.279 -#### `distance(epoint, epoint)`
   5.280 -
   5.281 -Calculates the distance between two `epoint` datums in meters. This function is
   5.282 -an alias for the distance operator `<->`.
   5.283 -
   5.284 -Note: In case of radial searches with a fixed radius, this function should not be
   5.285 -used. Use `distance_within(epoint, epoint, float8)` instead.
   5.286 -
   5.287 -#### `distance(ecluster, epoint)`
   5.288 -
   5.289 -Calculates the distance from an `ecluster` to an `epoint` in meters. This
   5.290 -function is an alias for the distance operator `<->`.
   5.291 -
   5.292 -Note: In case of radial searches with a fixed radius, this function should not be
   5.293 -used. Use `distance_within(epoint, epoint, float8)` instead.
   5.294 -
   5.295 -#### `distance_within(`variable `epoint,` fixed `epoint,` radius `float8)`
   5.296 -
   5.297 -Checks if the distance between two `epoint` datums is not greater than a given
   5.298 -value (search radius).
   5.299 -
   5.300 -Note: In case of radial searches with a fixed radius, the first argument must
   5.301 -be used for the table column, while the second argument must be used for the
   5.302 -search center. Otherwise an existing index cannot be used.
   5.303 -
   5.304 -#### `distance_within(`variable `ecluster,` fixed `epoint,` radius `float8)`
   5.305 -
   5.306 -Checks if the distance from an `ecluster` to an `epoint` is not greater than a
   5.307 -given value (search radius).
   5.308 -
   5.309 -#### `ebox(`latmin `float8,` latmax `float8,` lonmin `float8,` lonmax `float8)`
   5.310 -
   5.311 -Creates a new `ebox` with the given boundaries.
   5.312 -See "1. Types", subsection `ebox` for details.
   5.313 -
   5.314 -#### `ebox(epoint, epoint)`
   5.315 -
   5.316 -Creates a new `ebox`. This function may only be used if the longitude
   5.317 -difference is less than or equal to 120 degrees.
   5.318 -See "1. Types", subsection `ebox` for details.
   5.319 -
   5.320 -#### `ecircle(epoint, float8)`
   5.321 -
   5.322 -Creates an `ecircle` with the given center point and radius.
   5.323 -
   5.324 -#### `ecircle(`latitude `float8,` longitude `float8,` radius `float8)`
   5.325 -
   5.326 -Creates an `ecircle` with the given center point and radius.
   5.327 -
   5.328 -#### `ecluster_concat(ecluster, ecluster)`
   5.329 -
   5.330 -Combines two clusters to form a new `ecluster` by uniting all entries of both
   5.331 -clusters. Note that two overlapping areas of polygons annihilate each other
   5.332 -(which may be used to create polygons with holes).
   5.333 -
   5.334 -#### `ecluster_concat(ecluster[])`
   5.335 -
   5.336 -Creates a new `ecluster` that unites all entries of all clusters in the passed
   5.337 -array. Note that two overlapping areas of polygons annihilate each other (which
   5.338 -may be used to create polygons with holes).
   5.339 -
   5.340 -#### `ecluster_create_multipoint(epoint[])`
   5.341 -
   5.342 -Creates a new `ecluster` which contains multiple points.
   5.343 -
   5.344 -#### `ecluster_create_outline(epoint[])`
   5.345 -
   5.346 -Creates a new `ecluster` that is an outline given by the passed points.
   5.347 -
   5.348 -#### `ecluster_create_path(epoint[])`
   5.349 -
   5.350 -Creates a new `ecluster` that is a path given by the passed points.
   5.351 -
   5.352 -#### `ecluster_create_polygon(epoint[])`
   5.353 -
   5.354 -Creates a new `ecluster` that is a polygon given by the passed points.
   5.355 -
   5.356 -#### `ecluster_extract_outlines(ecluster)`
   5.357 -
   5.358 -Set-returning function that returns the outlines of an `ecluster` as `epoint[]`
   5.359 -rows.
   5.360 -
   5.361 -#### `ecluster_extract_paths(ecluster)`
   5.362 -
   5.363 -Set-returning function that returns the paths of an `ecluster` as `epoint[]`
   5.364 -rows.
   5.365 -
   5.366 -#### `ecluster_extract_points(ecluster)`
   5.367 -
   5.368 -Set-returning function that returns the points of an `ecluster` as `epoint`
   5.369 -rows.
   5.370 -
   5.371 -#### `ecluster_extract_polygons(ecluster)`
   5.372 -
   5.373 -Set-returning function that returns the polygons of an `ecluster` as `epoint[]`
   5.374 -rows.
   5.375 -
   5.376 -#### `empty_ebox`()
   5.377 -
   5.378 -Returns the empty `ebox`.
   5.379 -See "1. Types", subsection `ebox` for details.
   5.380 -
   5.381 -#### `epoint(`latitude `float8,` longitude `float8)`
   5.382 -
   5.383 -Returns an `epoint` with the given latitude and longitude.
   5.384 -
   5.385 -#### `epoint_latlon(`latitude `float8,` longitude `float8)`
   5.386 -
   5.387 -Alias for `epoint(float8, float8)`.
   5.388 -
   5.389 -#### `epoint_lonlat(`longitude `float8,` latitude `float8)`
   5.390 -
   5.391 -Same as `epoint(float8, float8)` but with arguments reversed.
   5.392 -
   5.393 -#### `GeoJSON_to_epoint(jsonb, text)`
   5.394 -
   5.395 -Maps a GeoJSON object of type "Point" or "Feature" (which contains a
   5.396 -"Point") to an `epoint` datum. For any other JSON objects, NULL is returned.
   5.397 -
   5.398 -The second parameter (which defaults to `epoint_lonlat`) may be set to a name
   5.399 -of a conversion function that transforms two coordinates (two `float8`
   5.400 -parameters) to an `epoint`.
   5.401 -
   5.402 -#### `GeoJSON_to_ecluster(jsonb, text)`
   5.403 -
   5.404 -Maps a (valid) GeoJSON object to an `ecluster`. Note that this function
   5.405 -does not check whether the JSONB object is a valid GeoJSON object.
   5.406 -
   5.407 -The second parameter (which defaults to `epoint_lonlat`) may be set to a name
   5.408 -of a conversion function that transforms two coordinates (two `float8`
   5.409 -parameters) to an `epoint`.
   5.410 -
   5.411 -#### `max_latitude(ebox)`
   5.412 -
   5.413 -Returns the northern boundary of a given `ebox` in degrees between -90 and +90.
   5.414 -
   5.415 -#### `max_longitude(ebox)`
   5.416 -
   5.417 -Returns the eastern boundary of a given `ebox` in degrees between -180 and +180
   5.418 -(both inclusive).
   5.419 -
   5.420 -#### `min_latitude(ebox)`
   5.421 -
   5.422 -Returns the southern boundary of a given `ebox` in degrees between -90 and +90.
   5.423 -
   5.424 -#### `min_longitude(ebox)`
   5.425 -
   5.426 -Returns the western boundary of a given `ebox` in degrees between -180 and +180
   5.427 -(both inclusive).
   5.428 -
   5.429 -#### `latitude(epoint)`
   5.430 -
   5.431 -Returns the latitude value of an `epoint` in degrees between -90 and +90.
   5.432 -
   5.433 -#### `longitude(epoint)`
   5.434 -
   5.435 -Returns the longitude value of an `epoint` in degrees between -180 and +180
   5.436 -(both inclusive).
   5.437 -
   5.438 -#### `radius(ecircle)`
   5.439 -
   5.440 -Returns the radius of an `ecircle` in meters.
   5.441 -
     6.1 --- a/pgLatLon/create_test_db.data.sql	Sun Aug 21 16:28:21 2016 +0200
     6.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     6.3 @@ -1,6 +0,0 @@
     6.4 -
     6.5 -INSERT INTO "test" ("location", "area") SELECT
     6.6 -  epoint((asin(2*random()-1) / pi()) * 180, (2*random()-1) * 180),
     6.7 -  ecircle((asin(2*random()-1) / pi()) * 180, (2*random()-1) * 180, -ln(1-random()) * 1000)
     6.8 -  FROM generate_series(1, 10000);
     6.9 -
     7.1 --- a/pgLatLon/create_test_db.schema.sql	Sun Aug 21 16:28:21 2016 +0200
     7.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     7.3 @@ -1,11 +0,0 @@
     7.4 -
     7.5 -CREATE EXTENSION latlon;
     7.6 -
     7.7 -CREATE TABLE "test" (
     7.8 -        "id"            SERIAL4         PRIMARY KEY,
     7.9 -        "location"      EPOINT          NOT NULL,
    7.10 -        "area"          ECIRCLE         NOT NULL );
    7.11 -
    7.12 -CREATE INDEX "test_location_key" ON "test" USING gist ("location");
    7.13 -CREATE INDEX "test_area_key"     ON "test" USING gist ("area");
    7.14 -
     8.1 --- a/pgLatLon/create_test_db.sh	Sun Aug 21 16:28:21 2016 +0200
     8.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     8.3 @@ -1,8 +0,0 @@
     8.4 -#!/bin/sh
     8.5 -dropdb latlon_test --if-exists
     8.6 -createdb latlon_test || exit 1
     8.7 -psql -v ON_ERROR_STOP=1 -f create_test_db.schema.sql latlon_test || exit 1
     8.8 -for i in 1 2 3 4 5 6 7 8 9 10
     8.9 -do
    8.10 -psql -v ON_ERROR_STOP=1 -f create_test_db.data.sql latlon_test || exit 1
    8.11 -done
     9.1 --- a/pgLatLon/latlon--0.1.sql	Sun Aug 21 16:28:21 2016 +0200
     9.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     9.3 @@ -1,1205 +0,0 @@
     9.4 -
     9.5 -----------------------------------------
     9.6 --- forward declarations (shell types) --
     9.7 -----------------------------------------
     9.8 -
     9.9 -CREATE TYPE epoint;
    9.10 -CREATE TYPE ebox;
    9.11 -CREATE TYPE ecircle;
    9.12 -CREATE TYPE ecluster;
    9.13 -
    9.14 -
    9.15 -------------------------------------------------------------
    9.16 --- dummy input/output functions for dummy index key types --
    9.17 -------------------------------------------------------------
    9.18 -
    9.19 -CREATE FUNCTION ekey_point_in_dummy(cstring)
    9.20 -  RETURNS ekey_point
    9.21 -  LANGUAGE C IMMUTABLE STRICT
    9.22 -  AS '$libdir/latlon-v0001', 'pgl_notimpl';
    9.23 -
    9.24 -CREATE FUNCTION ekey_point_out_dummy(ekey_point)
    9.25 -  RETURNS cstring
    9.26 -  LANGUAGE C IMMUTABLE STRICT
    9.27 -  AS '$libdir/latlon-v0001', 'pgl_notimpl';
    9.28 -
    9.29 -CREATE FUNCTION ekey_area_in_dummy(cstring)
    9.30 -  RETURNS ekey_area
    9.31 -  LANGUAGE C IMMUTABLE STRICT
    9.32 -  AS '$libdir/latlon-v0001', 'pgl_notimpl';
    9.33 -
    9.34 -CREATE FUNCTION ekey_area_out_dummy(ekey_area)
    9.35 -  RETURNS cstring
    9.36 -  LANGUAGE C IMMUTABLE STRICT
    9.37 -  AS '$libdir/latlon-v0001', 'pgl_notimpl';
    9.38 -
    9.39 -
    9.40 ---------------------------
    9.41 --- text input functions --
    9.42 ---------------------------
    9.43 -
    9.44 -CREATE FUNCTION epoint_in(cstring)
    9.45 -  RETURNS epoint
    9.46 -  LANGUAGE C IMMUTABLE STRICT
    9.47 -  AS '$libdir/latlon-v0001', 'pgl_epoint_in';
    9.48 -
    9.49 -CREATE FUNCTION ebox_in(cstring)
    9.50 -  RETURNS ebox
    9.51 -  LANGUAGE C IMMUTABLE STRICT
    9.52 -  AS '$libdir/latlon-v0001', 'pgl_ebox_in';
    9.53 -
    9.54 -CREATE FUNCTION ecircle_in(cstring)
    9.55 -  RETURNS ecircle
    9.56 -  LANGUAGE C IMMUTABLE STRICT
    9.57 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_in';
    9.58 -
    9.59 -CREATE FUNCTION ecluster_in(cstring)
    9.60 -  RETURNS ecluster
    9.61 -  LANGUAGE C IMMUTABLE STRICT
    9.62 -  AS '$libdir/latlon-v0001', 'pgl_ecluster_in';
    9.63 -
    9.64 -
    9.65 ----------------------------
    9.66 --- text output functions --
    9.67 ----------------------------
    9.68 -
    9.69 -CREATE FUNCTION epoint_out(epoint)
    9.70 -  RETURNS cstring
    9.71 -  LANGUAGE C IMMUTABLE STRICT
    9.72 -  AS '$libdir/latlon-v0001', 'pgl_epoint_out';
    9.73 -
    9.74 -CREATE FUNCTION ebox_out(ebox)
    9.75 -  RETURNS cstring
    9.76 -  LANGUAGE C IMMUTABLE STRICT
    9.77 -  AS '$libdir/latlon-v0001', 'pgl_ebox_out';
    9.78 -
    9.79 -CREATE FUNCTION ecircle_out(ecircle)
    9.80 -  RETURNS cstring
    9.81 -  LANGUAGE C IMMUTABLE STRICT
    9.82 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_out';
    9.83 -
    9.84 -CREATE FUNCTION ecluster_out(ecluster)
    9.85 -  RETURNS cstring
    9.86 -  LANGUAGE C IMMUTABLE STRICT
    9.87 -  AS '$libdir/latlon-v0001', 'pgl_ecluster_out';
    9.88 -
    9.89 -
    9.90 ---------------------------
    9.91 --- binary I/O functions --
    9.92 ---------------------------
    9.93 -
    9.94 -CREATE FUNCTION epoint_recv(internal)
    9.95 -  RETURNS epoint
    9.96 -  LANGUAGE C IMMUTABLE STRICT
    9.97 -  AS '$libdir/latlon-v0001', 'pgl_epoint_recv';
    9.98 -
    9.99 -CREATE FUNCTION ebox_recv(internal)
   9.100 -  RETURNS ebox
   9.101 -  LANGUAGE C IMMUTABLE STRICT
   9.102 -  AS '$libdir/latlon-v0001', 'pgl_ebox_recv';
   9.103 -
   9.104 -CREATE FUNCTION ecircle_recv(internal)
   9.105 -  RETURNS ecircle
   9.106 -  LANGUAGE C IMMUTABLE STRICT
   9.107 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_recv';
   9.108 -
   9.109 -CREATE FUNCTION epoint_send(epoint)
   9.110 -  RETURNS bytea
   9.111 -  LANGUAGE C IMMUTABLE STRICT
   9.112 -  AS '$libdir/latlon-v0001', 'pgl_epoint_send';
   9.113 -
   9.114 -CREATE FUNCTION ebox_send(ebox)
   9.115 -  RETURNS bytea
   9.116 -  LANGUAGE C IMMUTABLE STRICT
   9.117 -  AS '$libdir/latlon-v0001', 'pgl_ebox_send';
   9.118 -
   9.119 -CREATE FUNCTION ecircle_send(ecircle)
   9.120 -  RETURNS bytea
   9.121 -  LANGUAGE C IMMUTABLE STRICT
   9.122 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_send';
   9.123 -
   9.124 -
   9.125 ------------------------------------------------
   9.126 --- type definitions of dummy index key types --
   9.127 ------------------------------------------------
   9.128 -
   9.129 -CREATE TYPE ekey_point (
   9.130 -  internallength = 8,
   9.131 -  input = ekey_point_in_dummy,
   9.132 -  output = ekey_point_out_dummy,
   9.133 -  alignment = char );
   9.134 -
   9.135 -CREATE TYPE ekey_area (
   9.136 -  internallength = 9,
   9.137 -  input = ekey_area_in_dummy,
   9.138 -  output = ekey_area_out_dummy,
   9.139 -  alignment = char );
   9.140 -
   9.141 -
   9.142 -------------------------------------------
   9.143 --- definitions of geographic data types --
   9.144 -------------------------------------------
   9.145 -
   9.146 -CREATE TYPE epoint (
   9.147 -  internallength = 16,
   9.148 -  input = epoint_in,
   9.149 -  output = epoint_out,
   9.150 -  receive = epoint_recv,
   9.151 -  send = epoint_send,
   9.152 -  alignment = double );
   9.153 -
   9.154 -CREATE TYPE ebox (
   9.155 -  internallength = 32,
   9.156 -  input = ebox_in,
   9.157 -  output = ebox_out,
   9.158 -  receive = ebox_recv,
   9.159 -  send = ebox_send,
   9.160 -  alignment = double );
   9.161 -
   9.162 -CREATE TYPE ecircle (
   9.163 -  internallength = 24,
   9.164 -  input = ecircle_in,
   9.165 -  output = ecircle_out,
   9.166 -  receive = ecircle_recv,
   9.167 -  send = ecircle_send,
   9.168 -  alignment = double );
   9.169 -
   9.170 -CREATE TYPE ecluster (
   9.171 -  internallength = VARIABLE,
   9.172 -  input = ecluster_in,
   9.173 -  output = ecluster_out,
   9.174 -  alignment = double,
   9.175 -  storage = external );
   9.176 -
   9.177 -
   9.178 ---------------------
   9.179 --- B-tree support --
   9.180 ---------------------
   9.181 -
   9.182 --- begin of B-tree support for epoint
   9.183 -
   9.184 -CREATE FUNCTION epoint_btree_lt(epoint, epoint)
   9.185 -  RETURNS boolean
   9.186 -  LANGUAGE C IMMUTABLE STRICT
   9.187 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_lt';
   9.188 -
   9.189 -CREATE FUNCTION epoint_btree_le(epoint, epoint)
   9.190 -  RETURNS boolean
   9.191 -  LANGUAGE C IMMUTABLE STRICT
   9.192 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_le';
   9.193 -
   9.194 -CREATE FUNCTION epoint_btree_eq(epoint, epoint)
   9.195 -  RETURNS boolean
   9.196 -  LANGUAGE C IMMUTABLE STRICT
   9.197 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_eq';
   9.198 -
   9.199 -CREATE FUNCTION epoint_btree_ne(epoint, epoint)
   9.200 -  RETURNS boolean
   9.201 -  LANGUAGE C IMMUTABLE STRICT
   9.202 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_ne';
   9.203 -
   9.204 -CREATE FUNCTION epoint_btree_ge(epoint, epoint)
   9.205 -  RETURNS boolean
   9.206 -  LANGUAGE C IMMUTABLE STRICT
   9.207 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_ge';
   9.208 -
   9.209 -CREATE FUNCTION epoint_btree_gt(epoint, epoint)
   9.210 -  RETURNS boolean
   9.211 -  LANGUAGE C IMMUTABLE STRICT
   9.212 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_gt';
   9.213 -
   9.214 -CREATE OPERATOR <<< (
   9.215 -  leftarg = epoint,
   9.216 -  rightarg = epoint,
   9.217 -  procedure = epoint_btree_lt,
   9.218 -  commutator = >>>,
   9.219 -  negator = >>>=,
   9.220 -  restrict = scalarltsel,
   9.221 -  join = scalarltjoinsel
   9.222 -);
   9.223 -
   9.224 -CREATE OPERATOR <<<= (
   9.225 -  leftarg = epoint,
   9.226 -  rightarg = epoint,
   9.227 -  procedure = epoint_btree_le,
   9.228 -  commutator = >>>=,
   9.229 -  negator = >>>,
   9.230 -  restrict = scalarltsel,
   9.231 -  join = scalarltjoinsel
   9.232 -);
   9.233 -
   9.234 -CREATE OPERATOR = (
   9.235 -  leftarg = epoint,
   9.236 -  rightarg = epoint,
   9.237 -  procedure = epoint_btree_eq,
   9.238 -  commutator = =,
   9.239 -  negator = <>,
   9.240 -  restrict = eqsel,
   9.241 -  join = eqjoinsel,
   9.242 -  merges
   9.243 -);
   9.244 -
   9.245 -CREATE OPERATOR <> (
   9.246 -  leftarg = epoint,
   9.247 -  rightarg = epoint,
   9.248 -  procedure = epoint_btree_eq,
   9.249 -  commutator = <>,
   9.250 -  negator = =,
   9.251 -  restrict = neqsel,
   9.252 -  join = neqjoinsel
   9.253 -);
   9.254 -
   9.255 -CREATE OPERATOR >>>= (
   9.256 -  leftarg = epoint,
   9.257 -  rightarg = epoint,
   9.258 -  procedure = epoint_btree_ge,
   9.259 -  commutator = <<<=,
   9.260 -  negator = <<<,
   9.261 -  restrict = scalargtsel,
   9.262 -  join = scalargtjoinsel
   9.263 -);
   9.264 -
   9.265 -CREATE OPERATOR >>> (
   9.266 -  leftarg = epoint,
   9.267 -  rightarg = epoint,
   9.268 -  procedure = epoint_btree_gt,
   9.269 -  commutator = <<<,
   9.270 -  negator = <<<=,
   9.271 -  restrict = scalargtsel,
   9.272 -  join = scalargtjoinsel
   9.273 -);
   9.274 -
   9.275 -CREATE FUNCTION epoint_btree_cmp(epoint, epoint)
   9.276 -  RETURNS int4
   9.277 -  LANGUAGE C IMMUTABLE STRICT
   9.278 -  AS '$libdir/latlon-v0001', 'pgl_btree_epoint_cmp';
   9.279 -
   9.280 -CREATE OPERATOR CLASS epoint_btree_ops
   9.281 -  DEFAULT FOR TYPE epoint USING btree AS
   9.282 -  OPERATOR 1 <<< ,
   9.283 -  OPERATOR 2 <<<= ,
   9.284 -  OPERATOR 3 = ,
   9.285 -  OPERATOR 4 >>>= ,
   9.286 -  OPERATOR 5 >>> ,
   9.287 -  FUNCTION 1 epoint_btree_cmp(epoint, epoint);
   9.288 -
   9.289 --- end of B-tree support for epoint
   9.290 -
   9.291 --- begin of B-tree support for ebox
   9.292 -
   9.293 -CREATE FUNCTION ebox_btree_lt(ebox, ebox)
   9.294 -  RETURNS boolean
   9.295 -  LANGUAGE C IMMUTABLE STRICT
   9.296 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_lt';
   9.297 -
   9.298 -CREATE FUNCTION ebox_btree_le(ebox, ebox)
   9.299 -  RETURNS boolean
   9.300 -  LANGUAGE C IMMUTABLE STRICT
   9.301 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_le';
   9.302 -
   9.303 -CREATE FUNCTION ebox_btree_eq(ebox, ebox)
   9.304 -  RETURNS boolean
   9.305 -  LANGUAGE C IMMUTABLE STRICT
   9.306 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_eq';
   9.307 -
   9.308 -CREATE FUNCTION ebox_btree_ne(ebox, ebox)
   9.309 -  RETURNS boolean
   9.310 -  LANGUAGE C IMMUTABLE STRICT
   9.311 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_ne';
   9.312 -
   9.313 -CREATE FUNCTION ebox_btree_ge(ebox, ebox)
   9.314 -  RETURNS boolean
   9.315 -  LANGUAGE C IMMUTABLE STRICT
   9.316 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_ge';
   9.317 -
   9.318 -CREATE FUNCTION ebox_btree_gt(ebox, ebox)
   9.319 -  RETURNS boolean
   9.320 -  LANGUAGE C IMMUTABLE STRICT
   9.321 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_gt';
   9.322 -
   9.323 -CREATE OPERATOR <<< (
   9.324 -  leftarg = ebox,
   9.325 -  rightarg = ebox,
   9.326 -  procedure = ebox_btree_lt,
   9.327 -  commutator = >>>,
   9.328 -  negator = >>>=,
   9.329 -  restrict = scalarltsel,
   9.330 -  join = scalarltjoinsel
   9.331 -);
   9.332 -
   9.333 -CREATE OPERATOR <<<= (
   9.334 -  leftarg = ebox,
   9.335 -  rightarg = ebox,
   9.336 -  procedure = ebox_btree_le,
   9.337 -  commutator = >>>=,
   9.338 -  negator = >>>,
   9.339 -  restrict = scalarltsel,
   9.340 -  join = scalarltjoinsel
   9.341 -);
   9.342 -
   9.343 -CREATE OPERATOR = (
   9.344 -  leftarg = ebox,
   9.345 -  rightarg = ebox,
   9.346 -  procedure = ebox_btree_eq,
   9.347 -  commutator = =,
   9.348 -  negator = <>,
   9.349 -  restrict = eqsel,
   9.350 -  join = eqjoinsel,
   9.351 -  merges
   9.352 -);
   9.353 -
   9.354 -CREATE OPERATOR <> (
   9.355 -  leftarg = ebox,
   9.356 -  rightarg = ebox,
   9.357 -  procedure = ebox_btree_eq,
   9.358 -  commutator = <>,
   9.359 -  negator = =,
   9.360 -  restrict = neqsel,
   9.361 -  join = neqjoinsel
   9.362 -);
   9.363 -
   9.364 -CREATE OPERATOR >>>= (
   9.365 -  leftarg = ebox,
   9.366 -  rightarg = ebox,
   9.367 -  procedure = ebox_btree_ge,
   9.368 -  commutator = <<<=,
   9.369 -  negator = <<<,
   9.370 -  restrict = scalargtsel,
   9.371 -  join = scalargtjoinsel
   9.372 -);
   9.373 -
   9.374 -CREATE OPERATOR >>> (
   9.375 -  leftarg = ebox,
   9.376 -  rightarg = ebox,
   9.377 -  procedure = ebox_btree_gt,
   9.378 -  commutator = <<<,
   9.379 -  negator = <<<=,
   9.380 -  restrict = scalargtsel,
   9.381 -  join = scalargtjoinsel
   9.382 -);
   9.383 -
   9.384 -CREATE FUNCTION ebox_btree_cmp(ebox, ebox)
   9.385 -  RETURNS int4
   9.386 -  LANGUAGE C IMMUTABLE STRICT
   9.387 -  AS '$libdir/latlon-v0001', 'pgl_btree_ebox_cmp';
   9.388 -
   9.389 -CREATE OPERATOR CLASS ebox_btree_ops
   9.390 -  DEFAULT FOR TYPE ebox USING btree AS
   9.391 -  OPERATOR 1 <<< ,
   9.392 -  OPERATOR 2 <<<= ,
   9.393 -  OPERATOR 3 = ,
   9.394 -  OPERATOR 4 >>>= ,
   9.395 -  OPERATOR 5 >>> ,
   9.396 -  FUNCTION 1 ebox_btree_cmp(ebox, ebox);
   9.397 -
   9.398 --- end of B-tree support for ebox
   9.399 -
   9.400 --- begin of B-tree support for ecircle
   9.401 -
   9.402 -CREATE FUNCTION ecircle_btree_lt(ecircle, ecircle)
   9.403 -  RETURNS boolean
   9.404 -  LANGUAGE C IMMUTABLE STRICT
   9.405 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_lt';
   9.406 -
   9.407 -CREATE FUNCTION ecircle_btree_le(ecircle, ecircle)
   9.408 -  RETURNS boolean
   9.409 -  LANGUAGE C IMMUTABLE STRICT
   9.410 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_le';
   9.411 -
   9.412 -CREATE FUNCTION ecircle_btree_eq(ecircle, ecircle)
   9.413 -  RETURNS boolean
   9.414 -  LANGUAGE C IMMUTABLE STRICT
   9.415 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_eq';
   9.416 -
   9.417 -CREATE FUNCTION ecircle_btree_ne(ecircle, ecircle)
   9.418 -  RETURNS boolean
   9.419 -  LANGUAGE C IMMUTABLE STRICT
   9.420 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_ne';
   9.421 -
   9.422 -CREATE FUNCTION ecircle_btree_ge(ecircle, ecircle)
   9.423 -  RETURNS boolean
   9.424 -  LANGUAGE C IMMUTABLE STRICT
   9.425 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_ge';
   9.426 -
   9.427 -CREATE FUNCTION ecircle_btree_gt(ecircle, ecircle)
   9.428 -  RETURNS boolean
   9.429 -  LANGUAGE C IMMUTABLE STRICT
   9.430 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_gt';
   9.431 -
   9.432 -CREATE OPERATOR <<< (
   9.433 -  leftarg = ecircle,
   9.434 -  rightarg = ecircle,
   9.435 -  procedure = ecircle_btree_lt,
   9.436 -  commutator = >>>,
   9.437 -  negator = >>>=,
   9.438 -  restrict = scalarltsel,
   9.439 -  join = scalarltjoinsel
   9.440 -);
   9.441 -
   9.442 -CREATE OPERATOR <<<= (
   9.443 -  leftarg = ecircle,
   9.444 -  rightarg = ecircle,
   9.445 -  procedure = ecircle_btree_le,
   9.446 -  commutator = >>>=,
   9.447 -  negator = >>>,
   9.448 -  restrict = scalarltsel,
   9.449 -  join = scalarltjoinsel
   9.450 -);
   9.451 -
   9.452 -CREATE OPERATOR = (
   9.453 -  leftarg = ecircle,
   9.454 -  rightarg = ecircle,
   9.455 -  procedure = ecircle_btree_eq,
   9.456 -  commutator = =,
   9.457 -  negator = <>,
   9.458 -  restrict = eqsel,
   9.459 -  join = eqjoinsel,
   9.460 -  merges
   9.461 -);
   9.462 -
   9.463 -CREATE OPERATOR <> (
   9.464 -  leftarg = ecircle,
   9.465 -  rightarg = ecircle,
   9.466 -  procedure = ecircle_btree_eq,
   9.467 -  commutator = <>,
   9.468 -  negator = =,
   9.469 -  restrict = neqsel,
   9.470 -  join = neqjoinsel
   9.471 -);
   9.472 -
   9.473 -CREATE OPERATOR >>>= (
   9.474 -  leftarg = ecircle,
   9.475 -  rightarg = ecircle,
   9.476 -  procedure = ecircle_btree_ge,
   9.477 -  commutator = <<<=,
   9.478 -  negator = <<<,
   9.479 -  restrict = scalargtsel,
   9.480 -  join = scalargtjoinsel
   9.481 -);
   9.482 -
   9.483 -CREATE OPERATOR >>> (
   9.484 -  leftarg = ecircle,
   9.485 -  rightarg = ecircle,
   9.486 -  procedure = ecircle_btree_gt,
   9.487 -  commutator = <<<,
   9.488 -  negator = <<<=,
   9.489 -  restrict = scalargtsel,
   9.490 -  join = scalargtjoinsel
   9.491 -);
   9.492 -
   9.493 -CREATE FUNCTION ecircle_btree_cmp(ecircle, ecircle)
   9.494 -  RETURNS int4
   9.495 -  LANGUAGE C IMMUTABLE STRICT
   9.496 -  AS '$libdir/latlon-v0001', 'pgl_btree_ecircle_cmp';
   9.497 -
   9.498 -CREATE OPERATOR CLASS ecircle_btree_ops
   9.499 -  DEFAULT FOR TYPE ecircle USING btree AS
   9.500 -  OPERATOR 1 <<< ,
   9.501 -  OPERATOR 2 <<<= ,
   9.502 -  OPERATOR 3 = ,
   9.503 -  OPERATOR 4 >>>= ,
   9.504 -  OPERATOR 5 >>> ,
   9.505 -  FUNCTION 1 ecircle_btree_cmp(ecircle, ecircle);
   9.506 -
   9.507 --- end of B-tree support for ecircle
   9.508 -
   9.509 -
   9.510 -----------------
   9.511 --- type casts --
   9.512 -----------------
   9.513 -
   9.514 -CREATE FUNCTION cast_epoint_to_ebox(epoint)
   9.515 -  RETURNS ebox
   9.516 -  LANGUAGE C IMMUTABLE STRICT
   9.517 -  AS '$libdir/latlon-v0001', 'pgl_epoint_to_ebox';
   9.518 -
   9.519 -CREATE CAST (epoint AS ebox) WITH FUNCTION cast_epoint_to_ebox(epoint);
   9.520 -
   9.521 -CREATE FUNCTION cast_epoint_to_ecircle(epoint)
   9.522 -  RETURNS ecircle
   9.523 -  LANGUAGE C IMMUTABLE STRICT
   9.524 -  AS '$libdir/latlon-v0001', 'pgl_epoint_to_ecircle';
   9.525 -
   9.526 -CREATE CAST (epoint AS ecircle) WITH FUNCTION cast_epoint_to_ecircle(epoint);
   9.527 -
   9.528 -CREATE FUNCTION cast_epoint_to_ecluster(epoint)
   9.529 -  RETURNS ecluster
   9.530 -  LANGUAGE C IMMUTABLE STRICT
   9.531 -  AS '$libdir/latlon-v0001', 'pgl_epoint_to_ecluster';
   9.532 -
   9.533 -CREATE CAST (epoint AS ecluster) WITH FUNCTION cast_epoint_to_ecluster(epoint);
   9.534 -
   9.535 -CREATE FUNCTION cast_ebox_to_ecluster(ebox)
   9.536 -  RETURNS ecluster
   9.537 -  LANGUAGE C IMMUTABLE STRICT
   9.538 -  AS '$libdir/latlon-v0001', 'pgl_ebox_to_ecluster';
   9.539 -
   9.540 -CREATE CAST (ebox AS ecluster) WITH FUNCTION cast_ebox_to_ecluster(ebox);
   9.541 -
   9.542 -
   9.543 ----------------------------
   9.544 --- constructor functions --
   9.545 ----------------------------
   9.546 -
   9.547 -CREATE FUNCTION epoint(float8, float8)
   9.548 -  RETURNS epoint
   9.549 -  LANGUAGE C IMMUTABLE STRICT
   9.550 -  AS '$libdir/latlon-v0001', 'pgl_create_epoint';
   9.551 -
   9.552 -CREATE FUNCTION epoint_latlon(float8, float8)
   9.553 -  RETURNS epoint
   9.554 -  LANGUAGE SQL IMMUTABLE STRICT AS $$
   9.555 -    SELECT epoint($1, $2)
   9.556 -  $$;
   9.557 -
   9.558 -CREATE FUNCTION epoint_lonlat(float8, float8)
   9.559 -  RETURNS epoint
   9.560 -  LANGUAGE SQL IMMUTABLE STRICT AS $$
   9.561 -    SELECT epoint($2, $1)
   9.562 -  $$;
   9.563 -
   9.564 -CREATE FUNCTION empty_ebox()
   9.565 -  RETURNS ebox
   9.566 -  LANGUAGE C IMMUTABLE STRICT
   9.567 -  AS '$libdir/latlon-v0001', 'pgl_create_empty_ebox';
   9.568 -
   9.569 -CREATE FUNCTION ebox(float8, float8, float8, float8)
   9.570 -  RETURNS ebox
   9.571 -  LANGUAGE C IMMUTABLE STRICT
   9.572 -  AS '$libdir/latlon-v0001', 'pgl_create_ebox';
   9.573 -
   9.574 -CREATE FUNCTION ebox(epoint, epoint)
   9.575 -  RETURNS ebox
   9.576 -  LANGUAGE C IMMUTABLE STRICT
   9.577 -  AS '$libdir/latlon-v0001', 'pgl_create_ebox_from_epoints';
   9.578 -
   9.579 -CREATE FUNCTION ecircle(float8, float8, float8)
   9.580 -  RETURNS ecircle
   9.581 -  LANGUAGE C IMMUTABLE STRICT
   9.582 -  AS '$libdir/latlon-v0001', 'pgl_create_ecircle';
   9.583 -
   9.584 -CREATE FUNCTION ecircle(epoint, float8)
   9.585 -  RETURNS ecircle
   9.586 -  LANGUAGE C IMMUTABLE STRICT
   9.587 -  AS '$libdir/latlon-v0001', 'pgl_create_ecircle_from_epoint';
   9.588 -
   9.589 -CREATE FUNCTION ecluster_concat(ecluster[])
   9.590 -  RETURNS ecluster
   9.591 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.592 -    SELECT array_to_string($1, ' ')::ecluster
   9.593 -  $$;
   9.594 -
   9.595 -CREATE FUNCTION ecluster_concat(ecluster, ecluster)
   9.596 -  RETURNS ecluster
   9.597 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.598 -    SELECT ($1::text || ' ' || $2::text)::ecluster
   9.599 -  $$;
   9.600 -
   9.601 -CREATE FUNCTION ecluster_create_multipoint(epoint[])
   9.602 -  RETURNS ecluster
   9.603 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.604 -    SELECT
   9.605 -      array_to_string(array_agg('point (' || unnest || ')'), ' ')::ecluster
   9.606 -    FROM unnest($1)
   9.607 -  $$;
   9.608 -
   9.609 -CREATE FUNCTION ecluster_create_path(epoint[])
   9.610 -  RETURNS ecluster
   9.611 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.612 -    SELECT CASE WHEN "str" = '' THEN 'empty'::ecluster ELSE
   9.613 -      ('path (' || array_to_string($1, ' ') || ')')::ecluster
   9.614 -    END
   9.615 -    FROM array_to_string($1, ' ') AS "str"
   9.616 -  $$;
   9.617 -
   9.618 -CREATE FUNCTION ecluster_create_outline(epoint[])
   9.619 -  RETURNS ecluster
   9.620 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.621 -    SELECT CASE WHEN "str" = '' THEN 'empty'::ecluster ELSE
   9.622 -      ('outline (' || array_to_string($1, ' ') || ')')::ecluster
   9.623 -    END
   9.624 -    FROM array_to_string($1, ' ') AS "str"
   9.625 -  $$;
   9.626 -
   9.627 -CREATE FUNCTION ecluster_create_polygon(epoint[])
   9.628 -  RETURNS ecluster
   9.629 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.630 -    SELECT CASE WHEN "str" = '' THEN 'empty'::ecluster ELSE
   9.631 -      ('polygon (' || array_to_string($1, ' ') || ')')::ecluster
   9.632 -    END
   9.633 -    FROM array_to_string($1, ' ') AS "str"
   9.634 -  $$;
   9.635 -
   9.636 -
   9.637 -----------------------
   9.638 --- getter functions --
   9.639 -----------------------
   9.640 -
   9.641 -CREATE FUNCTION latitude(epoint)
   9.642 -  RETURNS float8
   9.643 -  LANGUAGE C IMMUTABLE STRICT
   9.644 -  AS '$libdir/latlon-v0001', 'pgl_epoint_lat';
   9.645 -
   9.646 -CREATE FUNCTION longitude(epoint)
   9.647 -  RETURNS float8
   9.648 -  LANGUAGE C IMMUTABLE STRICT
   9.649 -  AS '$libdir/latlon-v0001', 'pgl_epoint_lon';
   9.650 -
   9.651 -CREATE FUNCTION min_latitude(ebox)
   9.652 -  RETURNS float8
   9.653 -  LANGUAGE C IMMUTABLE STRICT
   9.654 -  AS '$libdir/latlon-v0001', 'pgl_ebox_lat_min';
   9.655 -
   9.656 -CREATE FUNCTION max_latitude(ebox)
   9.657 -  RETURNS float8
   9.658 -  LANGUAGE C IMMUTABLE STRICT
   9.659 -  AS '$libdir/latlon-v0001', 'pgl_ebox_lat_max';
   9.660 -
   9.661 -CREATE FUNCTION min_longitude(ebox)
   9.662 -  RETURNS float8
   9.663 -  LANGUAGE C IMMUTABLE STRICT
   9.664 -  AS '$libdir/latlon-v0001', 'pgl_ebox_lon_min';
   9.665 -
   9.666 -CREATE FUNCTION max_longitude(ebox)
   9.667 -  RETURNS float8
   9.668 -  LANGUAGE C IMMUTABLE STRICT
   9.669 -  AS '$libdir/latlon-v0001', 'pgl_ebox_lon_max';
   9.670 -
   9.671 -CREATE FUNCTION center(ecircle)
   9.672 -  RETURNS epoint
   9.673 -  LANGUAGE C IMMUTABLE STRICT
   9.674 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_center';
   9.675 -
   9.676 -CREATE FUNCTION radius(ecircle)
   9.677 -  RETURNS float8
   9.678 -  LANGUAGE C IMMUTABLE STRICT
   9.679 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_radius';
   9.680 -
   9.681 -CREATE FUNCTION ecluster_extract_points(ecluster)
   9.682 -  RETURNS SETOF epoint
   9.683 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.684 -    SELECT "match"[2]::epoint
   9.685 -    FROM regexp_matches($1::text, e'(^| )point \\(([^)]+)\\)', 'g') AS "match"
   9.686 -  $$;
   9.687 -
   9.688 -CREATE FUNCTION ecluster_extract_paths(ecluster)
   9.689 -  RETURNS SETOF epoint[]
   9.690 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.691 -    SELECT (
   9.692 -      SELECT array_agg("m2"[1]::epoint)
   9.693 -      FROM regexp_matches("m1"[2], e'[^ ]+ [^ ]+', 'g') AS "m2"
   9.694 -    )
   9.695 -    FROM regexp_matches($1::text, e'(^| )path \\(([^)]+)\\)', 'g') AS "m1"
   9.696 -  $$;
   9.697 -
   9.698 -CREATE FUNCTION ecluster_extract_outlines(ecluster)
   9.699 -  RETURNS SETOF epoint[]
   9.700 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.701 -    SELECT (
   9.702 -      SELECT array_agg("m2"[1]::epoint)
   9.703 -      FROM regexp_matches("m1"[2], e'[^ ]+ [^ ]+', 'g') AS "m2"
   9.704 -    )
   9.705 -    FROM regexp_matches($1::text, e'(^| )outline \\(([^)]+)\\)', 'g') AS "m1"
   9.706 -  $$;
   9.707 -
   9.708 -CREATE FUNCTION ecluster_extract_polygons(ecluster)
   9.709 -  RETURNS SETOF epoint[]
   9.710 -  LANGUAGE sql IMMUTABLE STRICT AS $$
   9.711 -    SELECT (
   9.712 -      SELECT array_agg("m2"[1]::epoint)
   9.713 -      FROM regexp_matches("m1"[2], e'[^ ]+ [^ ]+', 'g') AS "m2"
   9.714 -    )
   9.715 -    FROM regexp_matches($1::text, e'(^| )polygon \\(([^)]+)\\)', 'g') AS "m1"
   9.716 -  $$;
   9.717 -
   9.718 -
   9.719 ----------------
   9.720 --- operators --
   9.721 ----------------
   9.722 -
   9.723 -CREATE FUNCTION epoint_ebox_overlap_proc(epoint, ebox)
   9.724 -  RETURNS boolean
   9.725 -  LANGUAGE C IMMUTABLE STRICT
   9.726 -  AS '$libdir/latlon-v0001', 'pgl_epoint_ebox_overlap';
   9.727 -
   9.728 -CREATE FUNCTION epoint_ecircle_overlap_proc(epoint, ecircle)
   9.729 -  RETURNS boolean
   9.730 -  LANGUAGE C IMMUTABLE STRICT
   9.731 -  AS '$libdir/latlon-v0001', 'pgl_epoint_ecircle_overlap';
   9.732 -
   9.733 -CREATE FUNCTION epoint_ecluster_overlap_proc(epoint, ecluster)
   9.734 -  RETURNS boolean
   9.735 -  LANGUAGE C IMMUTABLE STRICT
   9.736 -  AS '$libdir/latlon-v0001', 'pgl_epoint_ecluster_overlap';
   9.737 -
   9.738 -CREATE FUNCTION ebox_overlap_proc(ebox, ebox)
   9.739 -  RETURNS boolean
   9.740 -  LANGUAGE C IMMUTABLE STRICT
   9.741 -  AS '$libdir/latlon-v0001', 'pgl_ebox_overlap';
   9.742 -
   9.743 -CREATE FUNCTION ecircle_overlap_proc(ecircle, ecircle)
   9.744 -  RETURNS boolean
   9.745 -  LANGUAGE C IMMUTABLE STRICT
   9.746 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_overlap';
   9.747 -
   9.748 -CREATE FUNCTION ecircle_ecluster_overlap_proc(ecircle, ecluster)
   9.749 -  RETURNS boolean
   9.750 -  LANGUAGE C IMMUTABLE STRICT
   9.751 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_ecluster_overlap';
   9.752 -
   9.753 -CREATE FUNCTION epoint_distance_proc(epoint, epoint)
   9.754 -  RETURNS float8
   9.755 -  LANGUAGE C IMMUTABLE STRICT
   9.756 -  AS '$libdir/latlon-v0001', 'pgl_epoint_distance';
   9.757 -
   9.758 -CREATE FUNCTION epoint_ecircle_distance_proc(epoint, ecircle)
   9.759 -  RETURNS float8
   9.760 -  LANGUAGE C IMMUTABLE STRICT
   9.761 -  AS '$libdir/latlon-v0001', 'pgl_epoint_ecircle_distance';
   9.762 -
   9.763 -CREATE FUNCTION epoint_ecluster_distance_proc(epoint, ecluster)
   9.764 -  RETURNS float8
   9.765 -  LANGUAGE C IMMUTABLE STRICT
   9.766 -  AS '$libdir/latlon-v0001', 'pgl_epoint_ecluster_distance';
   9.767 -
   9.768 -CREATE FUNCTION ecircle_distance_proc(ecircle, ecircle)
   9.769 -  RETURNS float8
   9.770 -  LANGUAGE C IMMUTABLE STRICT
   9.771 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_distance';
   9.772 -
   9.773 -CREATE FUNCTION ecircle_ecluster_distance_proc(ecircle, ecluster)
   9.774 -  RETURNS float8
   9.775 -  LANGUAGE C IMMUTABLE STRICT
   9.776 -  AS '$libdir/latlon-v0001', 'pgl_ecircle_ecluster_distance';
   9.777 -
   9.778 -CREATE OPERATOR && (
   9.779 -  leftarg = epoint,
   9.780 -  rightarg = ebox,
   9.781 -  procedure = epoint_ebox_overlap_proc,
   9.782 -  commutator = &&,
   9.783 -  restrict = areasel,
   9.784 -  join = areajoinsel
   9.785 -);
   9.786 -
   9.787 -CREATE FUNCTION epoint_ebox_overlap_commutator(ebox, epoint)
   9.788 -  RETURNS boolean
   9.789 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   9.790 -
   9.791 -CREATE OPERATOR && (
   9.792 -  leftarg = ebox,
   9.793 -  rightarg = epoint,
   9.794 -  procedure = epoint_ebox_overlap_commutator,
   9.795 -  commutator = &&,
   9.796 -  restrict = areasel,
   9.797 -  join = areajoinsel
   9.798 -);
   9.799 -
   9.800 -CREATE OPERATOR && (
   9.801 -  leftarg = epoint,
   9.802 -  rightarg = ecircle,
   9.803 -  procedure = epoint_ecircle_overlap_proc,
   9.804 -  commutator = &&,
   9.805 -  restrict = areasel,
   9.806 -  join = areajoinsel
   9.807 -);
   9.808 -
   9.809 -CREATE FUNCTION epoint_ecircle_overlap_commutator(ecircle, epoint)
   9.810 -  RETURNS boolean
   9.811 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   9.812 -
   9.813 -CREATE OPERATOR && (
   9.814 -  leftarg = ecircle,
   9.815 -  rightarg = epoint,
   9.816 -  procedure = epoint_ecircle_overlap_commutator,
   9.817 -  commutator = &&,
   9.818 -  restrict = areasel,
   9.819 -  join = areajoinsel
   9.820 -);
   9.821 -
   9.822 -CREATE OPERATOR && (
   9.823 -  leftarg = epoint,
   9.824 -  rightarg = ecluster,
   9.825 -  procedure = epoint_ecluster_overlap_proc,
   9.826 -  commutator = &&,
   9.827 -  restrict = areasel,
   9.828 -  join = areajoinsel
   9.829 -);
   9.830 -
   9.831 -CREATE FUNCTION epoint_ecluster_overlap_commutator(ecluster, epoint)
   9.832 -  RETURNS boolean
   9.833 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   9.834 -
   9.835 -CREATE OPERATOR && (
   9.836 -  leftarg = ecluster,
   9.837 -  rightarg = epoint,
   9.838 -  procedure = epoint_ecluster_overlap_commutator,
   9.839 -  commutator = &&,
   9.840 -  restrict = areasel,
   9.841 -  join = areajoinsel
   9.842 -);
   9.843 -
   9.844 -CREATE OPERATOR && (
   9.845 -  leftarg = ebox,
   9.846 -  rightarg = ebox,
   9.847 -  procedure = ebox_overlap_proc,
   9.848 -  commutator = &&,
   9.849 -  restrict = areasel,
   9.850 -  join = areajoinsel
   9.851 -);
   9.852 -
   9.853 -CREATE OPERATOR && (
   9.854 -  leftarg = ecircle,
   9.855 -  rightarg = ecircle,
   9.856 -  procedure = ecircle_overlap_proc,
   9.857 -  commutator = &&,
   9.858 -  restrict = areasel,
   9.859 -  join = areajoinsel
   9.860 -);
   9.861 -
   9.862 -CREATE OPERATOR && (
   9.863 -  leftarg = ecircle,
   9.864 -  rightarg = ecluster,
   9.865 -  procedure = ecircle_ecluster_overlap_proc,
   9.866 -  commutator = &&,
   9.867 -  restrict = areasel,
   9.868 -  join = areajoinsel
   9.869 -);
   9.870 -
   9.871 -CREATE FUNCTION ecircle_ecluster_overlap_commutator(ecluster, ecircle)
   9.872 -  RETURNS boolean
   9.873 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   9.874 -
   9.875 -CREATE OPERATOR && (
   9.876 -  leftarg = ecluster,
   9.877 -  rightarg = ecircle,
   9.878 -  procedure = ecircle_ecluster_overlap_commutator,
   9.879 -  commutator = &&,
   9.880 -  restrict = areasel,
   9.881 -  join = areajoinsel
   9.882 -);
   9.883 -
   9.884 -CREATE OPERATOR <-> (
   9.885 -  leftarg = epoint,
   9.886 -  rightarg = epoint,
   9.887 -  procedure = epoint_distance_proc,
   9.888 -  commutator = <->
   9.889 -);
   9.890 -
   9.891 -CREATE OPERATOR <-> (
   9.892 -  leftarg = epoint,
   9.893 -  rightarg = ecircle,
   9.894 -  procedure = epoint_ecircle_distance_proc,
   9.895 -  commutator = <->
   9.896 -);
   9.897 -
   9.898 -CREATE FUNCTION epoint_ecircle_distance_commutator(ecircle, epoint)
   9.899 -  RETURNS float8
   9.900 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 <-> $1';
   9.901 -
   9.902 -CREATE OPERATOR <-> (
   9.903 -  leftarg = ecircle,
   9.904 -  rightarg = epoint,
   9.905 -  procedure = epoint_ecircle_distance_commutator,
   9.906 -  commutator = <->
   9.907 -);
   9.908 -
   9.909 -CREATE OPERATOR <-> (
   9.910 -  leftarg = epoint,
   9.911 -  rightarg = ecluster,
   9.912 -  procedure = epoint_ecluster_distance_proc,
   9.913 -  commutator = <->
   9.914 -);
   9.915 -
   9.916 -CREATE FUNCTION epoint_ecluster_distance_commutator(ecluster, epoint)
   9.917 -  RETURNS float8
   9.918 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 <-> $1';
   9.919 -
   9.920 -CREATE OPERATOR <-> (
   9.921 -  leftarg = ecluster,
   9.922 -  rightarg = epoint,
   9.923 -  procedure = epoint_ecluster_distance_commutator,
   9.924 -  commutator = <->
   9.925 -);
   9.926 -
   9.927 -CREATE OPERATOR <-> (
   9.928 -  leftarg = ecircle,
   9.929 -  rightarg = ecircle,
   9.930 -  procedure = ecircle_distance_proc,
   9.931 -  commutator = <->
   9.932 -);
   9.933 -
   9.934 -CREATE OPERATOR <-> (
   9.935 -  leftarg = ecircle,
   9.936 -  rightarg = ecluster,
   9.937 -  procedure = ecircle_ecluster_distance_proc,
   9.938 -  commutator = <->
   9.939 -);
   9.940 -
   9.941 -CREATE FUNCTION ecircle_ecluster_distance_commutator(ecluster, ecircle)
   9.942 -  RETURNS float8
   9.943 -  LANGUAGE sql IMMUTABLE AS 'SELECT $2 <-> $1';
   9.944 -
   9.945 -CREATE OPERATOR <-> (
   9.946 -  leftarg = ecluster,
   9.947 -  rightarg = ecircle,
   9.948 -  procedure = ecircle_ecluster_distance_commutator,
   9.949 -  commutator = <->
   9.950 -);
   9.951 -
   9.952 -
   9.953 -----------------
   9.954 --- GiST index --
   9.955 -----------------
   9.956 -
   9.957 -CREATE FUNCTION pgl_gist_consistent(internal, internal, smallint, oid, internal)
   9.958 -  RETURNS boolean
   9.959 -  LANGUAGE C STRICT
   9.960 -  AS '$libdir/latlon-v0001', 'pgl_gist_consistent';
   9.961 -
   9.962 -CREATE FUNCTION pgl_gist_union(internal, internal)
   9.963 -  RETURNS internal
   9.964 -  LANGUAGE C STRICT
   9.965 -  AS '$libdir/latlon-v0001', 'pgl_gist_union';
   9.966 -
   9.967 -CREATE FUNCTION pgl_gist_compress_epoint(internal)
   9.968 -  RETURNS internal
   9.969 -  LANGUAGE C STRICT
   9.970 -  AS '$libdir/latlon-v0001', 'pgl_gist_compress_epoint';
   9.971 -
   9.972 -CREATE FUNCTION pgl_gist_compress_ecircle(internal)
   9.973 -  RETURNS internal
   9.974 -  LANGUAGE C STRICT
   9.975 -  AS '$libdir/latlon-v0001', 'pgl_gist_compress_ecircle';
   9.976 -
   9.977 -CREATE FUNCTION pgl_gist_compress_ecluster(internal)
   9.978 -  RETURNS internal
   9.979 -  LANGUAGE C STRICT
   9.980 -  AS '$libdir/latlon-v0001', 'pgl_gist_compress_ecluster';
   9.981 -
   9.982 -CREATE FUNCTION pgl_gist_decompress(internal)
   9.983 -  RETURNS internal
   9.984 -  LANGUAGE C STRICT
   9.985 -  AS '$libdir/latlon-v0001', 'pgl_gist_decompress';
   9.986 -
   9.987 -CREATE FUNCTION pgl_gist_penalty(internal, internal, internal)
   9.988 -  RETURNS internal
   9.989 -  LANGUAGE C STRICT
   9.990 -  AS '$libdir/latlon-v0001', 'pgl_gist_penalty';
   9.991 -
   9.992 -CREATE FUNCTION pgl_gist_picksplit(internal, internal)
   9.993 -  RETURNS internal
   9.994 -  LANGUAGE C STRICT
   9.995 -  AS '$libdir/latlon-v0001', 'pgl_gist_picksplit';
   9.996 -
   9.997 -CREATE FUNCTION pgl_gist_same(internal, internal, internal)
   9.998 -  RETURNS internal
   9.999 -  LANGUAGE C STRICT
  9.1000 -  AS '$libdir/latlon-v0001', 'pgl_gist_same';
  9.1001 -
  9.1002 -CREATE FUNCTION pgl_gist_distance(internal, internal, smallint, oid)
  9.1003 -  RETURNS internal
  9.1004 -  LANGUAGE C STRICT
  9.1005 -  AS '$libdir/latlon-v0001', 'pgl_gist_distance';
  9.1006 -
  9.1007 -CREATE OPERATOR CLASS epoint_ops
  9.1008 -  DEFAULT FOR TYPE epoint USING gist AS
  9.1009 -  OPERATOR 11 = ,
  9.1010 -  OPERATOR 22 && (epoint, ebox),
  9.1011 -  OPERATOR 23 && (epoint, ecircle),
  9.1012 -  OPERATOR 24 && (epoint, ecluster),
  9.1013 -  OPERATOR 31 <-> (epoint, epoint) FOR ORDER BY float_ops,
  9.1014 -  OPERATOR 33 <-> (epoint, ecircle) FOR ORDER BY float_ops,
  9.1015 -  OPERATOR 34 <-> (epoint, ecluster) FOR ORDER BY float_ops,
  9.1016 -  FUNCTION 1 pgl_gist_consistent(internal, internal, smallint, oid, internal),
  9.1017 -  FUNCTION 2 pgl_gist_union(internal, internal),
  9.1018 -  FUNCTION 3 pgl_gist_compress_epoint(internal),
  9.1019 -  FUNCTION 4 pgl_gist_decompress(internal),
  9.1020 -  FUNCTION 5 pgl_gist_penalty(internal, internal, internal),
  9.1021 -  FUNCTION 6 pgl_gist_picksplit(internal, internal),
  9.1022 -  FUNCTION 7 pgl_gist_same(internal, internal, internal),
  9.1023 -  FUNCTION 8 pgl_gist_distance(internal, internal, smallint, oid),
  9.1024 -  STORAGE ekey_point;
  9.1025 -
  9.1026 -CREATE OPERATOR CLASS ecircle_ops
  9.1027 -  DEFAULT FOR TYPE ecircle USING gist AS
  9.1028 -  OPERATOR 13 = ,
  9.1029 -  OPERATOR 21 && (ecircle, epoint),
  9.1030 -  OPERATOR 23 && (ecircle, ecircle),
  9.1031 -  OPERATOR 24 && (ecircle, ecluster),
  9.1032 -  OPERATOR 31 <-> (ecircle, epoint) FOR ORDER BY float_ops,
  9.1033 -  OPERATOR 33 <-> (ecircle, ecircle) FOR ORDER BY float_ops,
  9.1034 -  OPERATOR 34 <-> (ecircle, ecluster) FOR ORDER BY float_ops,
  9.1035 -  FUNCTION 1 pgl_gist_consistent(internal, internal, smallint, oid, internal),
  9.1036 -  FUNCTION 2 pgl_gist_union(internal, internal),
  9.1037 -  FUNCTION 3 pgl_gist_compress_ecircle(internal),
  9.1038 -  FUNCTION 4 pgl_gist_decompress(internal),
  9.1039 -  FUNCTION 5 pgl_gist_penalty(internal, internal, internal),
  9.1040 -  FUNCTION 6 pgl_gist_picksplit(internal, internal),
  9.1041 -  FUNCTION 7 pgl_gist_same(internal, internal, internal),
  9.1042 -  FUNCTION 8 pgl_gist_distance(internal, internal, smallint, oid),
  9.1043 -  STORAGE ekey_area;
  9.1044 -
  9.1045 -CREATE OPERATOR CLASS ecluster_ops
  9.1046 -  DEFAULT FOR TYPE ecluster USING gist AS
  9.1047 -  OPERATOR 21 && (ecluster, epoint),
  9.1048 -  FUNCTION 1 pgl_gist_consistent(internal, internal, smallint, oid, internal),
  9.1049 -  FUNCTION 2 pgl_gist_union(internal, internal),
  9.1050 -  FUNCTION 3 pgl_gist_compress_ecluster(internal),
  9.1051 -  FUNCTION 4 pgl_gist_decompress(internal),
  9.1052 -  FUNCTION 5 pgl_gist_penalty(internal, internal, internal),
  9.1053 -  FUNCTION 6 pgl_gist_picksplit(internal, internal),
  9.1054 -  FUNCTION 7 pgl_gist_same(internal, internal, internal),
  9.1055 -  FUNCTION 8 pgl_gist_distance(internal, internal, smallint, oid),
  9.1056 -  STORAGE ekey_area;
  9.1057 -
  9.1058 -
  9.1059 ----------------------
  9.1060 --- alias functions --
  9.1061 ----------------------
  9.1062 -
  9.1063 -CREATE FUNCTION distance(epoint, epoint)
  9.1064 -  RETURNS float8
  9.1065 -  LANGUAGE sql IMMUTABLE AS 'SELECT $1 <-> $2';
  9.1066 -
  9.1067 -CREATE FUNCTION distance(ecluster, epoint)
  9.1068 -  RETURNS float8
  9.1069 -  LANGUAGE sql IMMUTABLE AS 'SELECT $1 <-> $2';
  9.1070 -
  9.1071 -CREATE FUNCTION distance_within(epoint, epoint, float8)
  9.1072 -  RETURNS boolean
  9.1073 -  LANGUAGE sql IMMUTABLE AS 'SELECT $1 && ecircle($2, $3)';
  9.1074 -
  9.1075 -CREATE FUNCTION distance_within(ecluster, epoint, float8)
  9.1076 -  RETURNS boolean
  9.1077 -  LANGUAGE sql IMMUTABLE AS 'SELECT $1 && ecircle($2, $3)';
  9.1078 -
  9.1079 -
  9.1080 ---------------------------------
  9.1081 --- other data storage formats --
  9.1082 ---------------------------------
  9.1083 -
  9.1084 -CREATE FUNCTION coords_to_epoint(float8, float8, text = 'epoint_lonlat')
  9.1085 -  RETURNS epoint
  9.1086 -  LANGUAGE plpgsql IMMUTABLE STRICT AS $$
  9.1087 -    DECLARE
  9.1088 -      "result" epoint;
  9.1089 -    BEGIN
  9.1090 -      IF $3 = 'epoint_lonlat' THEN
  9.1091 -        -- avoid dynamic command execution for better performance
  9.1092 -        RETURN epoint($2, $1);
  9.1093 -      END IF;
  9.1094 -      IF $3 = 'epoint' OR $3 = 'epoint_latlon' THEN
  9.1095 -        -- avoid dynamic command execution for better performance
  9.1096 -        RETURN epoint($1, $2);
  9.1097 -      END IF;
  9.1098 -      EXECUTE 'SELECT ' || $3 || '($1, $2)' INTO STRICT "result" USING $1, $2;
  9.1099 -      RETURN "result";
  9.1100 -    END;
  9.1101 -  $$;
  9.1102 -
  9.1103 -CREATE FUNCTION GeoJSON_to_epoint(jsonb, text = 'epoint_lonlat')
  9.1104 -  RETURNS epoint
  9.1105 -  LANGUAGE sql IMMUTABLE STRICT AS $$
  9.1106 -    SELECT CASE
  9.1107 -    WHEN $1->>'type' = 'Point' THEN
  9.1108 -      coords_to_epoint(
  9.1109 -        ($1->'coordinates'->>1)::float8,
  9.1110 -        ($1->'coordinates'->>0)::float8,
  9.1111 -        $2
  9.1112 -      )
  9.1113 -    WHEN $1->>'type' = 'Feature' THEN
  9.1114 -      GeoJSON_to_epoint($1->'geometry', $2)
  9.1115 -    ELSE
  9.1116 -      NULL
  9.1117 -    END
  9.1118 -  $$;
  9.1119 -
  9.1120 -CREATE FUNCTION GeoJSON_to_ecluster(jsonb, text = 'epoint_lonlat')
  9.1121 -  RETURNS ecluster
  9.1122 -  LANGUAGE sql IMMUTABLE STRICT AS $$
  9.1123 -    SELECT CASE $1->>'type'
  9.1124 -    WHEN 'Point' THEN
  9.1125 -      coords_to_epoint(
  9.1126 -        ($1->'coordinates'->>1)::float8,
  9.1127 -        ($1->'coordinates'->>0)::float8,
  9.1128 -        $2
  9.1129 -      )::ecluster
  9.1130 -    WHEN 'MultiPoint' THEN
  9.1131 -      ( SELECT ecluster_create_multipoint(array_agg(
  9.1132 -          coords_to_epoint(
  9.1133 -            ("coord"->>1)::float8,
  9.1134 -            ("coord"->>0)::float8,
  9.1135 -            $2
  9.1136 -          )
  9.1137 -        ))
  9.1138 -        FROM jsonb_array_elements($1->'coordinates') AS "coord"
  9.1139 -      )
  9.1140 -    WHEN 'LineString' THEN
  9.1141 -      ( SELECT ecluster_create_path(array_agg(
  9.1142 -          coords_to_epoint(
  9.1143 -            ("coord"->>1)::float8,
  9.1144 -            ("coord"->>0)::float8,
  9.1145 -            $2
  9.1146 -          )
  9.1147 -        ))
  9.1148 -        FROM jsonb_array_elements($1->'coordinates') AS "coord"
  9.1149 -      )
  9.1150 -    WHEN 'MultiLineString' THEN
  9.1151 -      ( SELECT ecluster_concat(array_agg(
  9.1152 -          ( SELECT ecluster_create_path(array_agg(
  9.1153 -              coords_to_epoint(
  9.1154 -                ("coord"->>1)::float8,
  9.1155 -                ("coord"->>0)::float8,
  9.1156 -                $2
  9.1157 -              )
  9.1158 -            ))
  9.1159 -            FROM jsonb_array_elements("coord_array") AS "coord"
  9.1160 -          )
  9.1161 -        ))
  9.1162 -        FROM jsonb_array_elements($1->'coordinates') AS "coord_array"
  9.1163 -      )
  9.1164 -    WHEN 'Polygon' THEN
  9.1165 -      ( SELECT ecluster_concat(array_agg(
  9.1166 -          ( SELECT ecluster_create_polygon(array_agg(
  9.1167 -              coords_to_epoint(
  9.1168 -                ("coord"->>1)::float8,
  9.1169 -                ("coord"->>0)::float8,
  9.1170 -                $2
  9.1171 -              )
  9.1172 -            ))
  9.1173 -            FROM jsonb_array_elements("coord_array") AS "coord"
  9.1174 -          )
  9.1175 -        ))
  9.1176 -        FROM jsonb_array_elements($1->'coordinates') AS "coord_array"
  9.1177 -      )
  9.1178 -    WHEN 'MultiPolygon' THEN
  9.1179 -      ( SELECT ecluster_concat(array_agg(
  9.1180 -          ( SELECT ecluster_concat(array_agg(
  9.1181 -              ( SELECT ecluster_create_polygon(array_agg(
  9.1182 -                  coords_to_epoint(
  9.1183 -                    ("coord"->>1)::float8,
  9.1184 -                    ("coord"->>0)::float8,
  9.1185 -                    $2
  9.1186 -                  )
  9.1187 -                ))
  9.1188 -                FROM jsonb_array_elements("coord_array") AS "coord"
  9.1189 -              )
  9.1190 -            ))
  9.1191 -            FROM jsonb_array_elements("coord_array_array") AS "coord_array"
  9.1192 -          )
  9.1193 -        ))
  9.1194 -        FROM jsonb_array_elements($1->'coordinates') AS "coord_array_array"
  9.1195 -      )
  9.1196 -    WHEN 'Feature' THEN
  9.1197 -      GeoJSON_to_ecluster($1->'geometry', $2)
  9.1198 -    WHEN 'FeatureCollection' THEN
  9.1199 -      ( SELECT ecluster_concat(array_agg(
  9.1200 -          GeoJSON_to_ecluster("feature", $2)
  9.1201 -        ))
  9.1202 -        FROM jsonb_array_elements($1->'features') AS "feature"
  9.1203 -      )
  9.1204 -    ELSE
  9.1205 -      NULL
  9.1206 -    END
  9.1207 -  $$;
  9.1208 -
    10.1 --- a/pgLatLon/latlon-v0001.c	Sun Aug 21 16:28:21 2016 +0200
    10.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
    10.3 @@ -1,2710 +0,0 @@
    10.4 -
    10.5 -/*-------------*
    10.6 - *  C prelude  *
    10.7 - *-------------*/
    10.8 -
    10.9 -#include "postgres.h"
   10.10 -#include "fmgr.h"
   10.11 -#include "libpq/pqformat.h"
   10.12 -#include "access/gist.h"
   10.13 -#include "access/stratnum.h"
   10.14 -#include "utils/array.h"
   10.15 -#include <math.h>
   10.16 -
   10.17 -#ifdef PG_MODULE_MAGIC
   10.18 -PG_MODULE_MAGIC;
   10.19 -#endif
   10.20 -
   10.21 -#if INT_MAX < 2147483647
   10.22 -#error Expected int type to be at least 32 bit wide
   10.23 -#endif
   10.24 -
   10.25 -
   10.26 -/*---------------------------------*
   10.27 - *  distance calculation on earth  *
   10.28 - *  (using WGS-84 spheroid)        *
   10.29 - *---------------------------------*/
   10.30 -
   10.31 -/*  WGS-84 spheroid with following parameters:
   10.32 -    semi-major axis  a = 6378137
   10.33 -    semi-minor axis  b = a * (1 - 1/298.257223563)
   10.34 -    estimated diameter = 2 * (2*a+b)/3
   10.35 -*/
   10.36 -#define PGL_SPHEROID_A 6378137.0            /* semi major axis */
   10.37 -#define PGL_SPHEROID_F (1.0/298.257223563)  /* flattening */
   10.38 -#define PGL_SPHEROID_B (PGL_SPHEROID_A * (1.0-PGL_SPHEROID_F))
   10.39 -#define PGL_EPS2       ( ( PGL_SPHEROID_A * PGL_SPHEROID_A - \
   10.40 -                           PGL_SPHEROID_B * PGL_SPHEROID_B ) / \
   10.41 -                         ( PGL_SPHEROID_A * PGL_SPHEROID_A ) )
   10.42 -#define PGL_SUBEPS2    (1.0-PGL_EPS2)
   10.43 -#define PGL_DIAMETER   ((4.0*PGL_SPHEROID_A + 2.0*PGL_SPHEROID_B) / 3.0)
   10.44 -#define PGL_SCALE      (PGL_SPHEROID_A / PGL_DIAMETER)  /* semi-major ref. */
   10.45 -#define PGL_FADELIMIT  (PGL_DIAMETER * M_PI / 6.0)      /* 1/6 circumference */
   10.46 -#define PGL_MAXDIST    (PGL_DIAMETER * M_PI / 2.0)      /* maximum distance */
   10.47 -
   10.48 -/* calculate distance between two points on earth (given in degrees) */
   10.49 -static inline double pgl_distance(
   10.50 -  double lat1, double lon1, double lat2, double lon2
   10.51 -) {
   10.52 -  float8 lat1cos, lat1sin, lat2cos, lat2sin, lon2cos, lon2sin;
   10.53 -  float8 nphi1, nphi2, x1, z1, x2, y2, z2, g, s, t;
   10.54 -  /* normalize delta longitude (lon2 > 0 && lon1 = 0) */
   10.55 -  /* lon1 = 0 (not used anymore) */
   10.56 -  lon2 = fabs(lon2-lon1);
   10.57 -  /* convert to radians (first divide, then multiply) */
   10.58 -  lat1 = (lat1 / 180.0) * M_PI;
   10.59 -  lat2 = (lat2 / 180.0) * M_PI;
   10.60 -  lon2 = (lon2 / 180.0) * M_PI;
   10.61 -  /* make lat2 >= lat1 to ensure reversal-symmetry despite floating point
   10.62 -     operations (lon2 >= lon1 is already ensured in a previous step) */
   10.63 -  if (lat2 < lat1) { float8 swap = lat1; lat1 = lat2; lat2 = swap; }
   10.64 -  /* calculate 3d coordinates on scaled ellipsoid which has an average diameter
   10.65 -     of 1.0 */
   10.66 -  lat1cos = cos(lat1); lat1sin = sin(lat1);
   10.67 -  lat2cos = cos(lat2); lat2sin = sin(lat2);
   10.68 -  lon2cos = cos(lon2); lon2sin = sin(lon2);
   10.69 -  nphi1 = PGL_SCALE / sqrt(1 - PGL_EPS2 * lat1sin * lat1sin);
   10.70 -  nphi2 = PGL_SCALE / sqrt(1 - PGL_EPS2 * lat2sin * lat2sin);
   10.71 -  x1 = nphi1 * lat1cos;
   10.72 -  z1 = nphi1 * PGL_SUBEPS2 * lat1sin;
   10.73 -  x2 = nphi2 * lat2cos * lon2cos;
   10.74 -  y2 = nphi2 * lat2cos * lon2sin;
   10.75 -  z2 = nphi2 * PGL_SUBEPS2 * lat2sin;
   10.76 -  /* calculate tunnel distance through scaled (diameter 1.0) ellipsoid */
   10.77 -  g = sqrt((x2-x1)*(x2-x1) + y2*y2 + (z2-z1)*(z2-z1));
   10.78 -  /* convert tunnel distance through scaled ellipsoid to approximated surface
   10.79 -     distance on original ellipsoid */
   10.80 -  if (g > 1.0) g = 1.0;
   10.81 -  s = PGL_DIAMETER * asin(g);
   10.82 -  /* return result only if small enough to be precise (less than 1/3 of
   10.83 -     maximum possible distance) */
   10.84 -  if (s <= PGL_FADELIMIT) return s;
   10.85 -  /* determine antipodal point of second point (i.e. mirror second point) */
   10.86 -  lat2 = -lat2; lon2 = lon2 - M_PI;
   10.87 -  lat2cos = cos(lat2); lat2sin = sin(lat2);
   10.88 -  lon2cos = cos(lon2); lon2sin = sin(lon2);
   10.89 -  /* calculate 3d coordinates of antipodal point on scaled ellipsoid */
   10.90 -  nphi2 = PGL_SCALE / sqrt(1 - PGL_EPS2 * lat2sin * lat2sin);
   10.91 -  x2 = nphi2 * lat2cos * lon2cos;
   10.92 -  y2 = nphi2 * lat2cos * lon2sin;
   10.93 -  z2 = nphi2 * PGL_SUBEPS2 * lat2sin;
   10.94 -  /* calculate tunnel distance to antipodal point through scaled ellipsoid */
   10.95 -  g = sqrt((x2-x1)*(x2-x1) + y2*y2 + (z2-z1)*(z2-z1));
   10.96 -  /* convert tunnel distance to antipodal point through scaled ellipsoid to
   10.97 -     approximated surface distance to antipodal point on original ellipsoid */
   10.98 -  if (g > 1.0) g = 1.0;
   10.99 -  t = PGL_DIAMETER * asin(g);
  10.100 -  /* surface distance between original points can now be approximated by
  10.101 -     substracting antipodal distance from maximum possible distance;
  10.102 -     return result only if small enough (less than 1/3 of maximum possible
  10.103 -     distance) */
  10.104 -  if (t <= PGL_FADELIMIT) return PGL_MAXDIST-t;
  10.105 -  /* otherwise crossfade direct and antipodal result to ensure monotonicity */
  10.106 -  return (
  10.107 -    (s * (t-PGL_FADELIMIT) + (PGL_MAXDIST-t) * (s-PGL_FADELIMIT)) /
  10.108 -    (s + t - 2*PGL_FADELIMIT)
  10.109 -  );
  10.110 -}
  10.111 -
  10.112 -/* finite distance that can not be reached on earth */
  10.113 -#define PGL_ULTRA_DISTANCE (3 * PGL_MAXDIST)
  10.114 -
  10.115 -
  10.116 -/*--------------------------------*
  10.117 - *  simple geographic data types  *
  10.118 - *--------------------------------*/
  10.119 -
  10.120 -/* point on earth given by latitude and longitude in degrees */
  10.121 -/* (type "epoint" in SQL) */
  10.122 -typedef struct {
  10.123 -  double lat;  /* between  -90 and  90 (both inclusive) */
  10.124 -  double lon;  /* between -180 and 180 (both inclusive) */
  10.125 -} pgl_point;
  10.126 -
  10.127 -/* box delimited by two parallels and two meridians (all in degrees) */
  10.128 -/* (type "ebox" in SQL) */
  10.129 -typedef struct {
  10.130 -  double lat_min;  /* between  -90 and  90 (both inclusive) */
  10.131 -  double lat_max;  /* between  -90 and  90 (both inclusive) */
  10.132 -  double lon_min;  /* between -180 and 180 (both inclusive) */
  10.133 -  double lon_max;  /* between -180 and 180 (both inclusive) */
  10.134 -  /* if lat_min > lat_max, then box is empty */
  10.135 -  /* if lon_min > lon_max, then 180th meridian is crossed */
  10.136 -} pgl_box;
  10.137 -
  10.138 -/* circle on earth surface (for radial searches with fixed radius) */
  10.139 -/* (type "ecircle" in SQL) */
  10.140 -typedef struct {
  10.141 -  pgl_point center;
  10.142 -  double radius; /* positive (including +0 but excluding -0), or -INFINITY */
  10.143 -  /* A negative radius (i.e. -INFINITY) denotes nothing (i.e. no point),
  10.144 -     zero radius (0) denotes a single point,
  10.145 -     a finite radius (0 < radius < INFINITY) denotes a filled circle, and
  10.146 -     a radius of INFINITY is valid and means complete coverage of earth. */
  10.147 -} pgl_circle;
  10.148 -
  10.149 -
  10.150 -/*----------------------------------*
  10.151 - *  geographic "cluster" data type  *
  10.152 - *----------------------------------*/
  10.153 -
  10.154 -/* A cluster is a collection of points, paths, outlines, and polygons. If two
  10.155 -   polygons in a cluster overlap, the area covered by both polygons does not
  10.156 -   belong to the cluster. This way, a cluster can be used to describe complex
  10.157 -   shapes like polygons with holes. Outlines are non-filled polygons. Paths are
  10.158 -   open by default (i.e. the last point in the list is not connected with the
  10.159 -   first point in the list). Note that each outline or polygon in a cluster
  10.160 -   must cover a longitude range of less than 180 degrees to avoid ambiguities.
  10.161 -   Areas which are larger may be split into multiple polygons. */
  10.162 -
  10.163 -/* maximum number of points in a cluster */
  10.164 -/* (limited to avoid integer overflows, e.g. when allocating memory) */
  10.165 -#define PGL_CLUSTER_MAXPOINTS 16777216
  10.166 -
  10.167 -/* types of cluster entries */
  10.168 -#define PGL_ENTRY_POINT   1  /* a point */
  10.169 -#define PGL_ENTRY_PATH    2  /* a path from first point to last point */
  10.170 -#define PGL_ENTRY_OUTLINE 3  /* a non-filled polygon with given vertices */
  10.171 -#define PGL_ENTRY_POLYGON 4  /* a filled polygon with given vertices */
  10.172 -
  10.173 -/* Entries of a cluster are described by two different structs: pgl_newentry
  10.174 -   and pgl_entry. The first is used only during construction of a cluster, the
  10.175 -   second is used in all other cases (e.g. when reading clusters from the
  10.176 -   database, performing operations, etc). */
  10.177 -
  10.178 -/* entry for new geographic cluster during construction of that cluster */
  10.179 -typedef struct {
  10.180 -  int32_t entrytype;
  10.181 -  int32_t npoints;
  10.182 -  pgl_point *points;  /* pointer to an array of points (pgl_point) */
  10.183 -} pgl_newentry;
  10.184 -
  10.185 -/* entry of geographic cluster */
  10.186 -typedef struct {
  10.187 -  int32_t entrytype;  /* type of entry: point, path, outline, polygon */
  10.188 -  int32_t npoints;    /* number of stored points (set to 1 for point entry) */
  10.189 -  int32_t offset;     /* offset of pgl_point array from cluster base address */
  10.190 -  /* use macro PGL_ENTRY_POINTS to obtain a pointer to the array of points */
  10.191 -} pgl_entry;
  10.192 -
  10.193 -/* geographic cluster which is a collection of points, (open) paths, polygons,
  10.194 -   and outlines (non-filled polygons) */
  10.195 -typedef struct {
  10.196 -  char header[VARHDRSZ];  /* PostgreSQL header for variable size data types */
  10.197 -  int32_t nentries;       /* number of stored points */
  10.198 -  pgl_circle bounding;    /* bounding circle */
  10.199 -  /* Note: bounding circle ensures alignment of pgl_cluster for points */
  10.200 -  pgl_entry entries[FLEXIBLE_ARRAY_MEMBER];  /* var-length data */
  10.201 -} pgl_cluster;
  10.202 -
  10.203 -/* macro to determine memory alignment of points */
  10.204 -/* (needed to store pgl_point array after entries in pgl_cluster) */
  10.205 -typedef struct { char dummy; pgl_point aligned; } pgl_point_alignment;
  10.206 -#define PGL_POINT_ALIGNMENT offsetof(pgl_point_alignment, aligned)
  10.207 -
  10.208 -/* macro to extract a pointer to the array of points of a cluster entry */
  10.209 -#define PGL_ENTRY_POINTS(cluster, idx) \
  10.210 -  ((pgl_point *)(((intptr_t)cluster)+(cluster)->entries[idx].offset))
  10.211 -
  10.212 -/* convert pgl_newentry array to pgl_cluster */
  10.213 -static pgl_cluster *pgl_new_cluster(int nentries, pgl_newentry *entries) {
  10.214 -  int i;              /* index of current entry */
  10.215 -  int npoints = 0;    /* number of points in whole cluster */
  10.216 -  int entry_npoints;  /* number of points in current entry */
  10.217 -  int points_offset = PGL_POINT_ALIGNMENT * (
  10.218 -    ( offsetof(pgl_cluster, entries) +
  10.219 -      nentries * sizeof(pgl_entry) +
  10.220 -      PGL_POINT_ALIGNMENT - 1
  10.221 -    ) / PGL_POINT_ALIGNMENT
  10.222 -  );  /* offset of pgl_point array from base address (considering alignment) */
  10.223 -  pgl_cluster *cluster;  /* new cluster to be returned */
  10.224 -  /* determine total number of points */
  10.225 -  for (i=0; i<nentries; i++) npoints += entries[i].npoints;
  10.226 -  /* allocate memory for cluster (including entries and points) */
  10.227 -  cluster = palloc(points_offset + npoints * sizeof(pgl_point));
  10.228 -  /* re-count total number of points to determine offset for each entry */
  10.229 -  npoints = 0;
  10.230 -  /* copy entries and points */
  10.231 -  for (i=0; i<nentries; i++) {
  10.232 -    /* determine number of points in entry */
  10.233 -    entry_npoints = entries[i].npoints;
  10.234 -    /* copy entry */
  10.235 -    cluster->entries[i].entrytype = entries[i].entrytype;
  10.236 -    cluster->entries[i].npoints = entry_npoints;
  10.237 -    /* calculate offset (in bytes) of pgl_point array */
  10.238 -    cluster->entries[i].offset = points_offset + npoints * sizeof(pgl_point);
  10.239 -    /* copy points */
  10.240 -    memcpy(
  10.241 -      PGL_ENTRY_POINTS(cluster, i),
  10.242 -      entries[i].points,
  10.243 -      entry_npoints * sizeof(pgl_point)
  10.244 -    );
  10.245 -    /* update total number of points processed */
  10.246 -    npoints += entry_npoints;
  10.247 -  }
  10.248 -  /* set number of entries in cluster */
  10.249 -  cluster->nentries = nentries;
  10.250 -  /* set PostgreSQL header for variable sized data */
  10.251 -  SET_VARSIZE(cluster, points_offset + npoints * sizeof(pgl_point));
  10.252 -  /* return newly created cluster */
  10.253 -  return cluster;
  10.254 -}
  10.255 -
  10.256 -
  10.257 -/*----------------------------------------*
  10.258 - *  C functions on geographic data types  *
  10.259 - *----------------------------------------*/
  10.260 -
  10.261 -/* round latitude or longitude to 12 digits after decimal point */
  10.262 -static inline double pgl_round(double val) {
  10.263 -  return round(val * 1e12) / 1e12;
  10.264 -}
  10.265 -
  10.266 -/* compare two points */
  10.267 -/* (equality when same point on earth is described, otherwise an arbitrary
  10.268 -   linear order) */
  10.269 -static int pgl_point_cmp(pgl_point *point1, pgl_point *point2) {
  10.270 -  double lon1, lon2;  /* modified longitudes for special cases */
  10.271 -  /* use latitude as first ordering criterion */
  10.272 -  if (point1->lat < point2->lat) return -1;
  10.273 -  if (point1->lat > point2->lat) return 1;
  10.274 -  /* determine modified longitudes (considering special case of poles and
  10.275 -     180th meridian which can be described as W180 or E180) */
  10.276 -  if (point1->lat == -90 || point1->lat == 90) lon1 = 0;
  10.277 -  else if (point1->lon == 180) lon1 = -180;
  10.278 -  else lon1 = point1->lon;
  10.279 -  if (point2->lat == -90 || point2->lat == 90) lon2 = 0;
  10.280 -  else if (point2->lon == 180) lon2 = -180;
  10.281 -  else lon2 = point2->lon;
  10.282 -  /* use (modified) longitude as secondary ordering criterion */
  10.283 -  if (lon1 < lon2) return -1;
  10.284 -  if (lon1 > lon2) return 1;
  10.285 -  /* no difference found, points are equal */
  10.286 -  return 0;
  10.287 -}
  10.288 -
  10.289 -/* compare two boxes */
  10.290 -/* (equality when same box on earth is described, otherwise an arbitrary linear
  10.291 -   order) */
  10.292 -static int pgl_box_cmp(pgl_box *box1, pgl_box *box2) {
  10.293 -  /* two empty boxes are equal, and an empty box is always considered "less
  10.294 -     than" a non-empty box */
  10.295 -  if (box1->lat_min> box1->lat_max && box2->lat_min<=box2->lat_max) return -1;
  10.296 -  if (box1->lat_min> box1->lat_max && box2->lat_min> box2->lat_max) return 0;
  10.297 -  if (box1->lat_min<=box1->lat_max && box2->lat_min> box2->lat_max) return 1;
  10.298 -  /* use southern border as first ordering criterion */
  10.299 -  if (box1->lat_min < box2->lat_min) return -1;
  10.300 -  if (box1->lat_min > box2->lat_min) return 1;
  10.301 -  /* use northern border as second ordering criterion */
  10.302 -  if (box1->lat_max < box2->lat_max) return -1;
  10.303 -  if (box1->lat_max > box2->lat_max) return 1;
  10.304 -  /* use western border as third ordering criterion */
  10.305 -  if (box1->lon_min < box2->lon_min) return -1;
  10.306 -  if (box1->lon_min > box2->lon_min) return 1;
  10.307 -  /* use eastern border as fourth ordering criterion */
  10.308 -  if (box1->lon_max < box2->lon_max) return -1;
  10.309 -  if (box1->lon_max > box2->lon_max) return 1;
  10.310 -  /* no difference found, boxes are equal */
  10.311 -  return 0;
  10.312 -}
  10.313 -
  10.314 -/* compare two circles */
  10.315 -/* (equality when same circle on earth is described, otherwise an arbitrary
  10.316 -   linear order) */
  10.317 -static int pgl_circle_cmp(pgl_circle *circle1, pgl_circle *circle2) {
  10.318 -  /* two circles with same infinite radius (positive or negative infinity) are
  10.319 -     considered equal independently of center point */
  10.320 -  if (
  10.321 -    !isfinite(circle1->radius) && !isfinite(circle2->radius) &&
  10.322 -    circle1->radius == circle2->radius
  10.323 -  ) return 0;
  10.324 -  /* use radius as first ordering criterion */
  10.325 -  if (circle1->radius < circle2->radius) return -1;
  10.326 -  if (circle1->radius > circle2->radius) return 1;
  10.327 -  /* use center point as secondary ordering criterion */
  10.328 -  return pgl_point_cmp(&(circle1->center), &(circle2->center));
  10.329 -}
  10.330 -
  10.331 -/* set box to empty box*/
  10.332 -static void pgl_box_set_empty(pgl_box *box) {
  10.333 -  box->lat_min = INFINITY;
  10.334 -  box->lat_max = -INFINITY;
  10.335 -  box->lon_min = 0;
  10.336 -  box->lon_max = 0;
  10.337 -}
  10.338 -
  10.339 -/* check if point is inside a box */
  10.340 -static bool pgl_point_in_box(pgl_point *point, pgl_box *box) {
  10.341 -  return (
  10.342 -    point->lat >= box->lat_min && point->lat <= box->lat_max && (
  10.343 -      (box->lon_min > box->lon_max) ? (
  10.344 -        /* box crosses 180th meridian */
  10.345 -        point->lon >= box->lon_min || point->lon <= box->lon_max
  10.346 -      ) : (
  10.347 -        /* box does not cross the 180th meridian */
  10.348 -        point->lon >= box->lon_min && point->lon <= box->lon_max
  10.349 -      )
  10.350 -    )
  10.351 -  );
  10.352 -}
  10.353 -
  10.354 -/* check if two boxes overlap */
  10.355 -static bool pgl_boxes_overlap(pgl_box *box1, pgl_box *box2) {
  10.356 -  return (
  10.357 -    box2->lat_max >= box2->lat_min &&  /* ensure box2 is not empty */
  10.358 -    ( box2->lat_min >= box1->lat_min || box2->lat_max >= box1->lat_min ) &&
  10.359 -    ( box2->lat_min <= box1->lat_max || box2->lat_max <= box1->lat_max ) && (
  10.360 -      (
  10.361 -        /* check if one and only one box crosses the 180th meridian */
  10.362 -        ((box1->lon_min > box1->lon_max) ? 1 : 0) ^
  10.363 -        ((box2->lon_min > box2->lon_max) ? 1 : 0)
  10.364 -      ) ? (
  10.365 -        /* exactly one box crosses the 180th meridian */
  10.366 -        box2->lon_min >= box1->lon_min || box2->lon_max >= box1->lon_min ||
  10.367 -        box2->lon_min <= box1->lon_max || box2->lon_max <= box1->lon_max
  10.368 -      ) : (
  10.369 -        /* no box or both boxes cross the 180th meridian */
  10.370 -        (
  10.371 -          (box2->lon_min >= box1->lon_min || box2->lon_max >= box1->lon_min) &&
  10.372 -          (box2->lon_min <= box1->lon_max || box2->lon_max <= box1->lon_max)
  10.373 -        ) ||
  10.374 -        /* handle W180 == E180 */
  10.375 -        ( box1->lon_min == -180 && box2->lon_max == 180 ) ||
  10.376 -        ( box2->lon_min == -180 && box1->lon_max == 180 )
  10.377 -      )
  10.378 -    )
  10.379 -  );
  10.380 -}
  10.381 -
  10.382 -/* check unambiguousness of east/west orientation of cluster entries and set
  10.383 -   bounding circle of cluster */
  10.384 -static bool pgl_finalize_cluster(pgl_cluster *cluster) {
  10.385 -  int i, j;                 /* i: index of entry, j: index of point in entry */
  10.386 -  int npoints;              /* number of points in entry */
  10.387 -  int total_npoints = 0;    /* total number of points in cluster */
  10.388 -  pgl_point *points;        /* points in entry */
  10.389 -  int lon_dir;              /* first point of entry west (-1) or east (+1) */
  10.390 -  double lon_break = 0;     /* antipodal longitude of first point in entry */
  10.391 -  double lon_min, lon_max;  /* covered longitude range of entry */
  10.392 -  double value;             /* temporary variable */
  10.393 -  /* reset bounding circle center to empty circle at 0/0 coordinates */
  10.394 -  cluster->bounding.center.lat = 0;
  10.395 -  cluster->bounding.center.lon = 0;
  10.396 -  cluster->bounding.radius = -INFINITY;
  10.397 -  /* if cluster is not empty */
  10.398 -  if (cluster->nentries != 0) {
  10.399 -    /* iterate over all cluster entries and ensure they each cover a longitude
  10.400 -       range less than 180 degrees */
  10.401 -    for (i=0; i<cluster->nentries; i++) {
  10.402 -      /* get properties of entry */
  10.403 -      npoints = cluster->entries[i].npoints;
  10.404 -      points = PGL_ENTRY_POINTS(cluster, i);
  10.405 -      /* get longitude of first point of entry */
  10.406 -      value = points[0].lon;
  10.407 -      /* initialize lon_min and lon_max with longitude of first point */
  10.408 -      lon_min = value;
  10.409 -      lon_max = value;
  10.410 -      /* determine east/west orientation of first point and calculate antipodal
  10.411 -         longitude (Note: rounding required here) */
  10.412 -      if      (value < 0) { lon_dir = -1; lon_break = pgl_round(value + 180); }
  10.413 -      else if (value > 0) { lon_dir =  1; lon_break = pgl_round(value - 180); }
  10.414 -      else lon_dir = 0;
  10.415 -      /* iterate over all other points in entry */
  10.416 -      for (j=1; j<npoints; j++) {
  10.417 -        /* consider longitude wrap-around */
  10.418 -        value = points[j].lon;
  10.419 -        if      (lon_dir<0 && value>lon_break) value = pgl_round(value - 360);
  10.420 -        else if (lon_dir>0 && value<lon_break) value = pgl_round(value + 360);
  10.421 -        /* update lon_min and lon_max */
  10.422 -        if      (value < lon_min) lon_min = value;
  10.423 -        else if (value > lon_max) lon_max = value;
  10.424 -        /* return false if 180 degrees or more are covered */
  10.425 -        if (lon_max - lon_min >= 180) return false;
  10.426 -      }
  10.427 -    }
  10.428 -    /* iterate over all points of all entries and calculate arbitrary center
  10.429 -       point for bounding circle (best if center point minimizes the radius,
  10.430 -       but some error is allowed here) */
  10.431 -    for (i=0; i<cluster->nentries; i++) {
  10.432 -      /* get properties of entry */
  10.433 -      npoints = cluster->entries[i].npoints;
  10.434 -      points = PGL_ENTRY_POINTS(cluster, i);
  10.435 -      /* check if first entry */
  10.436 -      if (i==0) {
  10.437 -        /* get longitude of first point of first entry in whole cluster */
  10.438 -        value = points[0].lon;
  10.439 -        /* initialize lon_min and lon_max with longitude of first point of
  10.440 -           first entry in whole cluster (used to determine if whole cluster
  10.441 -           covers a longitude range of 180 degrees or more) */
  10.442 -        lon_min = value;
  10.443 -        lon_max = value;
  10.444 -        /* determine east/west orientation of first point and calculate
  10.445 -           antipodal longitude (Note: rounding not necessary here) */
  10.446 -        if      (value < 0) { lon_dir = -1; lon_break = value + 180; }
  10.447 -        else if (value > 0) { lon_dir =  1; lon_break = value - 180; }
  10.448 -        else lon_dir = 0;
  10.449 -      }
  10.450 -      /* iterate over all points in entry */
  10.451 -      for (j=0; j<npoints; j++) {
  10.452 -        /* longitude wrap-around (Note: rounding not necessary here) */
  10.453 -        value = points[j].lon;
  10.454 -        if      (lon_dir < 0 && value > lon_break) value -= 360;
  10.455 -        else if (lon_dir > 0 && value < lon_break) value += 360;
  10.456 -        if      (value < lon_min) lon_min = value;
  10.457 -        else if (value > lon_max) lon_max = value;
  10.458 -        /* set bounding circle to cover whole earth if more than 180 degrees
  10.459 -           are covered */
  10.460 -        if (lon_max - lon_min >= 180) {
  10.461 -          cluster->bounding.center.lat = 0;
  10.462 -          cluster->bounding.center.lon = 0;
  10.463 -          cluster->bounding.radius = INFINITY;
  10.464 -          return true;
  10.465 -        }
  10.466 -        /* add point to bounding circle center (for average calculation) */
  10.467 -        cluster->bounding.center.lat += points[j].lat;
  10.468 -        cluster->bounding.center.lon += value;
  10.469 -      }
  10.470 -      /* count total number of points */
  10.471 -      total_npoints += npoints;
  10.472 -    }
  10.473 -    /* determine average latitude and longitude of cluster */
  10.474 -    cluster->bounding.center.lat /= total_npoints;
  10.475 -    cluster->bounding.center.lon /= total_npoints;
  10.476 -    /* normalize longitude of center of cluster bounding circle */
  10.477 -    if (cluster->bounding.center.lon < -180) {
  10.478 -      cluster->bounding.center.lon += 360;
  10.479 -    }
  10.480 -    else if (cluster->bounding.center.lon > 180) {
  10.481 -      cluster->bounding.center.lon -= 360;
  10.482 -    }
  10.483 -    /* round bounding circle center (useful if it is used by other functions) */
  10.484 -    cluster->bounding.center.lat = pgl_round(cluster->bounding.center.lat);
  10.485 -    cluster->bounding.center.lon = pgl_round(cluster->bounding.center.lon);
  10.486 -    /* calculate radius of bounding circle */
  10.487 -    for (i=0; i<cluster->nentries; i++) {
  10.488 -      npoints = cluster->entries[i].npoints;
  10.489 -      points = PGL_ENTRY_POINTS(cluster, i);
  10.490 -      for (j=0; j<npoints; j++) {
  10.491 -        value = pgl_distance(
  10.492 -          cluster->bounding.center.lat, cluster->bounding.center.lon,
  10.493 -          points[j].lat, points[j].lon
  10.494 -        );
  10.495 -        if (value > cluster->bounding.radius) cluster->bounding.radius = value;
  10.496 -      }
  10.497 -    }
  10.498 -  }
  10.499 -  /* return true (east/west orientation is unambiguous) */
  10.500 -  return true;
  10.501 -}
  10.502 -
  10.503 -/* check if point is inside cluster */
  10.504 -static bool pgl_point_in_cluster(pgl_point *point, pgl_cluster *cluster) {
  10.505 -  int i, j, k;  /* i: entry, j: point in entry, k: next point in entry */
  10.506 -  int entrytype;         /* type of entry */
  10.507 -  int npoints;           /* number of points in entry */
  10.508 -  pgl_point *points;     /* array of points in entry */
  10.509 -  int lon_dir = 0;       /* first vertex west (-1) or east (+1) */
  10.510 -  double lon_break = 0;  /* antipodal longitude of first vertex */
  10.511 -  double lat0 = point->lat;  /* latitude of point */
  10.512 -  double lon0;           /* (adjusted) longitude of point */
  10.513 -  double lat1, lon1;     /* latitude and (adjusted) longitude of vertex */
  10.514 -  double lat2, lon2;     /* latitude and (adjusted) longitude of next vertex */
  10.515 -  double lon;            /* longitude of intersection */
  10.516 -  int counter = 0;       /* counter for intersections east of point */
  10.517 -  /* points outside bounding circle are always assumed to be non-overlapping */
  10.518 -  /* (necessary for consistent table and index scans) */
  10.519 -  if (
  10.520 -    pgl_distance(
  10.521 -      point->lat, point->lon,
  10.522 -      cluster->bounding.center.lat, cluster->bounding.center.lon
  10.523 -    ) > cluster->bounding.radius
  10.524 -  ) return false;
  10.525 -  /* iterate over all entries */
  10.526 -  for (i=0; i<cluster->nentries; i++) {
  10.527 -    /* get properties of entry */
  10.528 -    entrytype = cluster->entries[i].entrytype;
  10.529 -    npoints = cluster->entries[i].npoints;
  10.530 -    points = PGL_ENTRY_POINTS(cluster, i);
  10.531 -    /* determine east/west orientation of first point of entry and calculate
  10.532 -       antipodal longitude */
  10.533 -    lon_break = points[0].lon;
  10.534 -    if      (lon_break < 0) { lon_dir = -1; lon_break += 180; }
  10.535 -    else if (lon_break > 0) { lon_dir =  1; lon_break -= 180; }
  10.536 -    else lon_dir = 0;
  10.537 -    /* get longitude of point */
  10.538 -    lon0 = point->lon;
  10.539 -    /* consider longitude wrap-around for point */
  10.540 -    if      (lon_dir < 0 && lon0 > lon_break) lon0 = pgl_round(lon0 - 360);
  10.541 -    else if (lon_dir > 0 && lon0 < lon_break) lon0 = pgl_round(lon0 + 360);
  10.542 -    /* iterate over all edges and vertices */
  10.543 -    for (j=0; j<npoints; j++) {
  10.544 -      /* return true if point is on vertex of polygon */
  10.545 -      if (pgl_point_cmp(point, &(points[j])) == 0) return true;
  10.546 -      /* calculate index of next vertex */
  10.547 -      k = (j+1) % npoints;
  10.548 -      /* skip last edge unless entry is (closed) outline or polygon */
  10.549 -      if (
  10.550 -        k == 0 &&
  10.551 -        entrytype != PGL_ENTRY_OUTLINE &&
  10.552 -        entrytype != PGL_ENTRY_POLYGON
  10.553 -      ) continue;
  10.554 -      /* get latitude and longitude values of edge */
  10.555 -      lat1 = points[j].lat;
  10.556 -      lat2 = points[k].lat;
  10.557 -      lon1 = points[j].lon;
  10.558 -      lon2 = points[k].lon;
  10.559 -      /* consider longitude wrap-around for edge */
  10.560 -      if      (lon_dir < 0 && lon1 > lon_break) lon1 = pgl_round(lon1 - 360);
  10.561 -      else if (lon_dir > 0 && lon1 < lon_break) lon1 = pgl_round(lon1 + 360);
  10.562 -      if      (lon_dir < 0 && lon2 > lon_break) lon2 = pgl_round(lon2 - 360);
  10.563 -      else if (lon_dir > 0 && lon2 < lon_break) lon2 = pgl_round(lon2 + 360);
  10.564 -      /* return true if point is on horizontal (west to east) edge of polygon */
  10.565 -      if (
  10.566 -        lat0 == lat1 && lat0 == lat2 &&
  10.567 -        ( (lon0 >= lon1 && lon0 <= lon2) || (lon0 >= lon2 && lon0 <= lon1) )
  10.568 -      ) return true;
  10.569 -      /* check if edge crosses east/west line of point */
  10.570 -      if ((lat1 < lat0 && lat2 >= lat0) || (lat2 < lat0 && lat1 >= lat0)) {
  10.571 -        /* calculate longitude of intersection */
  10.572 -        lon = (lon1 * (lat2-lat0) + lon2 * (lat0-lat1)) / (lat2-lat1);
  10.573 -        /* return true if intersection goes (approximately) through point */
  10.574 -        if (pgl_round(lon) == lon0) return true;
  10.575 -        /* count intersection if east of point and entry is polygon*/
  10.576 -        if (entrytype == PGL_ENTRY_POLYGON && lon > lon0) counter++;
  10.577 -      }
  10.578 -    }
  10.579 -  }
  10.580 -  /* return true if number of intersections is odd */
  10.581 -  return counter & 1;
  10.582 -}
  10.583 -
  10.584 -/* calculate (approximate) distance between point and cluster */
  10.585 -static double pgl_point_cluster_distance(pgl_point *point, pgl_cluster *cluster) {
  10.586 -  int i, j, k;  /* i: entry, j: point in entry, k: next point in entry */
  10.587 -  int entrytype;         /* type of entry */
  10.588 -  int npoints;           /* number of points in entry */
  10.589 -  pgl_point *points;     /* array of points in entry */
  10.590 -  int lon_dir = 0;       /* first vertex west (-1) or east (+1) */
  10.591 -  double lon_break = 0;  /* antipodal longitude of first vertex */
  10.592 -  double lon_min = 0;    /* minimum (adjusted) longitude of entry vertices */
  10.593 -  double lon_max = 0;    /* maximum (adjusted) longitude of entry vertices */
  10.594 -  double lat0 = point->lat;  /* latitude of point */
  10.595 -  double lon0;           /* (adjusted) longitude of point */
  10.596 -  double lat1, lon1;     /* latitude and (adjusted) longitude of vertex */
  10.597 -  double lat2, lon2;     /* latitude and (adjusted) longitude of next vertex */
  10.598 -  double s;              /* scalar for vector calculations */
  10.599 -  double dist;           /* distance calculated in one step */
  10.600 -  double min_dist = INFINITY;   /* minimum distance */
  10.601 -  /* distance is zero if point is contained in cluster */
  10.602 -  if (pgl_point_in_cluster(point, cluster)) return 0;
  10.603 -  /* iterate over all entries */
  10.604 -  for (i=0; i<cluster->nentries; i++) {
  10.605 -    /* get properties of entry */
  10.606 -    entrytype = cluster->entries[i].entrytype;
  10.607 -    npoints = cluster->entries[i].npoints;
  10.608 -    points = PGL_ENTRY_POINTS(cluster, i);
  10.609 -    /* determine east/west orientation of first point of entry and calculate
  10.610 -       antipodal longitude */
  10.611 -    lon_break = points[0].lon;
  10.612 -    if      (lon_break < 0) { lon_dir = -1; lon_break += 180; }
  10.613 -    else if (lon_break > 0) { lon_dir =  1; lon_break -= 180; }
  10.614 -    else lon_dir = 0;
  10.615 -    /* determine covered longitude range */
  10.616 -    for (j=0; j<npoints; j++) {
  10.617 -      /* get longitude of vertex */
  10.618 -      lon1 = points[j].lon;
  10.619 -      /* adjust longitude to fix potential wrap-around */
  10.620 -      if      (lon_dir < 0 && lon1 > lon_break) lon1 -= 360;
  10.621 -      else if (lon_dir > 0 && lon1 < lon_break) lon1 += 360;
  10.622 -      /* update minimum and maximum longitude of polygon */
  10.623 -      if (j == 0 || lon1 < lon_min) lon_min = lon1;
  10.624 -      if (j == 0 || lon1 > lon_max) lon_max = lon1;
  10.625 -    }
  10.626 -    /* adjust longitude wrap-around according to full longitude range */
  10.627 -    lon_break = (lon_max + lon_min) / 2;
  10.628 -    if      (lon_break < 0) { lon_dir = -1; lon_break += 180; }
  10.629 -    else if (lon_break > 0) { lon_dir =  1; lon_break -= 180; }
  10.630 -    /* get longitude of point */
  10.631 -    lon0 = point->lon;
  10.632 -    /* consider longitude wrap-around for point */
  10.633 -    if      (lon_dir < 0 && lon0 > lon_break) lon0 -= 360;
  10.634 -    else if (lon_dir > 0 && lon0 < lon_break) lon0 += 360;
  10.635 -    /* iterate over all edges and vertices */
  10.636 -    for (j=0; j<npoints; j++) {
  10.637 -      /* get latitude and longitude values of current point */
  10.638 -      lat1 = points[j].lat;
  10.639 -      lon1 = points[j].lon;
  10.640 -      /* consider longitude wrap-around for current point */
  10.641 -      if      (lon_dir < 0 && lon1 > lon_break) lon1 -= 360;
  10.642 -      else if (lon_dir > 0 && lon1 < lon_break) lon1 += 360;
  10.643 -      /* calculate distance to vertex */
  10.644 -      dist = pgl_distance(lat0, lon0, lat1, lon1);
  10.645 -      /* store calculated distance if smallest */
  10.646 -      if (dist < min_dist) min_dist = dist;
  10.647 -      /* calculate index of next vertex */
  10.648 -      k = (j+1) % npoints;
  10.649 -      /* skip last edge unless entry is (closed) outline or polygon */
  10.650 -      if (
  10.651 -        k == 0 &&
  10.652 -        entrytype != PGL_ENTRY_OUTLINE &&
  10.653 -        entrytype != PGL_ENTRY_POLYGON
  10.654 -      ) continue;
  10.655 -      /* get latitude and longitude values of next point */
  10.656 -      lat2 = points[k].lat;
  10.657 -      lon2 = points[k].lon;
  10.658 -      /* consider longitude wrap-around for next point */
  10.659 -      if      (lon_dir < 0 && lon2 > lon_break) lon2 -= 360;
  10.660 -      else if (lon_dir > 0 && lon2 < lon_break) lon2 += 360;
  10.661 -      /* go to next vertex and edge if edge is degenerated */
  10.662 -      if (lat1 == lat2 && lon1 == lon2) continue;
  10.663 -      /* otherwise test if point can be projected onto edge of polygon */
  10.664 -      s = (
  10.665 -        ((lat0-lat1) * (lat2-lat1) + (lon0-lon1) * (lon2-lon1)) /
  10.666 -        ((lat2-lat1) * (lat2-lat1) + (lon2-lon1) * (lon2-lon1))
  10.667 -      );
  10.668 -      /* go to next vertex and edge if point cannot be projected */
  10.669 -      if (!(s > 0 && s < 1)) continue;
  10.670 -      /* calculate distance from original point to projected point */
  10.671 -      dist = pgl_distance(
  10.672 -        lat0, lon0,
  10.673 -        lat1 + s * (lat2-lat1),
  10.674 -        lon1 + s * (lon2-lon1)
  10.675 -      );
  10.676 -      /* store calculated distance if smallest */
  10.677 -      if (dist < min_dist) min_dist = dist;
  10.678 -    }
  10.679 -  }
  10.680 -  /* return minimum distance */
  10.681 -  return min_dist;
  10.682 -}
  10.683 -
  10.684 -/* estimator function for distance between box and point */
  10.685 -/* allowed to return smaller values than actually correct */
  10.686 -static double pgl_estimate_point_box_distance(pgl_point *point, pgl_box *box) {
  10.687 -  double dlon;  /* longitude range of box (delta longitude) */
  10.688 -  double h;     /* half of distance along meridian */
  10.689 -  double d;     /* distance between both southern or both northern points */
  10.690 -  double cur_dist;  /* calculated distance */
  10.691 -  double min_dist;  /* minimum distance calculated */
  10.692 -  /* return infinity if bounding box is empty */
  10.693 -  if (box->lat_min > box->lat_max) return INFINITY;
  10.694 -  /* return zero if point is inside bounding box */
  10.695 -  if (pgl_point_in_box(point, box)) return 0;
  10.696 -  /* calculate delta longitude */
  10.697 -  dlon = box->lon_max - box->lon_min;
  10.698 -  if (dlon < 0) dlon += 360;  /* 180th meridian crossed */
  10.699 -  /* if delta longitude is greater than 180 degrees, perform safe fall-back */
  10.700 -  if (dlon > 180) return 0;
  10.701 -  /* calculate half of distance along meridian */
  10.702 -  h = pgl_distance(box->lat_min, 0, box->lat_max, 0) / 2;
  10.703 -  /* calculate full distance between southern points */
  10.704 -  d = pgl_distance(box->lat_min, 0, box->lat_min, dlon);
  10.705 -  /* calculate maximum of full distance and half distance */
  10.706 -  if (h > d) d = h;
  10.707 -  /* calculate distance from point to first southern vertex and substract
  10.708 -     maximum error */
  10.709 -  min_dist = pgl_distance(
  10.710 -    point->lat, point->lon, box->lat_min, box->lon_min
  10.711 -  ) - d;
  10.712 -  /* return zero if estimated distance is smaller than zero */
  10.713 -  if (min_dist <= 0) return 0;
  10.714 -  /* repeat procedure with second southern vertex */
  10.715 -  cur_dist = pgl_distance(
  10.716 -    point->lat, point->lon, box->lat_min, box->lon_max
  10.717 -  ) - d;
  10.718 -  if (cur_dist <= 0) return 0;
  10.719 -  if (cur_dist < min_dist) min_dist = cur_dist;
  10.720 -  /* calculate full distance between northern points */
  10.721 -  d = pgl_distance(box->lat_max, 0, box->lat_max, dlon);
  10.722 -  /* calculate maximum of full distance and half distance */
  10.723 -  if (h > d) d = h;
  10.724 -  /* repeat procedure with northern vertices */
  10.725 -  cur_dist = pgl_distance(
  10.726 -    point->lat, point->lon, box->lat_max, box->lon_max
  10.727 -  ) - d;
  10.728 -  if (cur_dist <= 0) return 0;
  10.729 -  if (cur_dist < min_dist) min_dist = cur_dist;
  10.730 -  cur_dist = pgl_distance(
  10.731 -    point->lat, point->lon, box->lat_max, box->lon_min
  10.732 -  ) - d;
  10.733 -  if (cur_dist <= 0) return 0;
  10.734 -  if (cur_dist < min_dist) min_dist = cur_dist;
  10.735 -  /* return smallest value (unless already returned zero) */
  10.736 -  return min_dist;
  10.737 -}
  10.738 -
  10.739 -
  10.740 -/*----------------------------*
  10.741 - *  fractal geographic index  *
  10.742 - *----------------------------*/
  10.743 -
  10.744 -/* number of bytes used for geographic (center) position in keys */
  10.745 -#define PGL_KEY_LATLON_BYTELEN 7
  10.746 -
  10.747 -/* maximum reference value for logarithmic size of geographic objects */
  10.748 -#define PGL_AREAKEY_REFOBJSIZE (PGL_DIAMETER/3.0)  /* can be tweaked */
  10.749 -
  10.750 -/* safety margin to avoid floating point errors in distance estimation */
  10.751 -#define PGL_FPE_SAFETY (1.0+1e-14)  /* slightly greater than 1.0 */
  10.752 -
  10.753 -/* pointer to index key (either pgl_pointkey or pgl_areakey) */
  10.754 -typedef unsigned char *pgl_keyptr;
  10.755 -
  10.756 -/* index key for points (objects with zero area) on the spheroid */
  10.757 -/* bit  0..55: interspersed bits of latitude and longitude,
  10.758 -   bit 56..57: always zero,
  10.759 -   bit 58..63: node depth in hypothetic (full) tree from 0 to 56 (incl.) */
  10.760 -typedef unsigned char pgl_pointkey[PGL_KEY_LATLON_BYTELEN+1];
  10.761 -
  10.762 -/* index key for geographic objects on spheroid with area greater than zero */
  10.763 -/* bit  0..55: interspersed bits of latitude and longitude of center point,
  10.764 -   bit     56: always set to 1,
  10.765 -   bit 57..63: node depth in hypothetic (full) tree from 0 to (2*56)+1 (incl.),
  10.766 -   bit 64..71: logarithmic object size from 0 to 56+1 = 57 (incl.), but set to
  10.767 -               PGL_KEY_OBJSIZE_EMPTY (with interspersed bits = 0 and node depth
  10.768 -               = 113) for empty objects, and set to PGL_KEY_OBJSIZE_UNIVERSAL
  10.769 -               (with interspersed bits = 0 and node depth = 0) for keys which
  10.770 -               cover both empty and non-empty objects */
  10.771 -
  10.772 -typedef unsigned char pgl_areakey[PGL_KEY_LATLON_BYTELEN+2];
  10.773 -
  10.774 -/* helper macros for reading/writing index keys */
  10.775 -#define PGL_KEY_NODEDEPTH_OFFSET  PGL_KEY_LATLON_BYTELEN
  10.776 -#define PGL_KEY_OBJSIZE_OFFSET    (PGL_KEY_NODEDEPTH_OFFSET+1)
  10.777 -#define PGL_POINTKEY_MAXDEPTH     (PGL_KEY_LATLON_BYTELEN*8)
  10.778 -#define PGL_AREAKEY_MAXDEPTH      (2*PGL_POINTKEY_MAXDEPTH+1)
  10.779 -#define PGL_AREAKEY_MAXOBJSIZE    (PGL_POINTKEY_MAXDEPTH+1)
  10.780 -#define PGL_AREAKEY_TYPEMASK      0x80
  10.781 -#define PGL_KEY_LATLONBIT(key, n) ((key)[(n)/8] & (0x80 >> ((n)%8)))
  10.782 -#define PGL_KEY_LATLONBIT_DIFF(key1, key2, n) \
  10.783 -                                  ( PGL_KEY_LATLONBIT(key1, n) ^ \
  10.784 -                                    PGL_KEY_LATLONBIT(key2, n) )
  10.785 -#define PGL_KEY_IS_AREAKEY(key)   ((key)[PGL_KEY_NODEDEPTH_OFFSET] & \
  10.786 -                                    PGL_AREAKEY_TYPEMASK)
  10.787 -#define PGL_KEY_NODEDEPTH(key)    ((key)[PGL_KEY_NODEDEPTH_OFFSET] & \
  10.788 -                                    (PGL_AREAKEY_TYPEMASK-1))
  10.789 -#define PGL_KEY_OBJSIZE(key)      ((key)[PGL_KEY_OBJSIZE_OFFSET])
  10.790 -#define PGL_KEY_OBJSIZE_EMPTY     126
  10.791 -#define PGL_KEY_OBJSIZE_UNIVERSAL 127
  10.792 -#define PGL_KEY_IS_EMPTY(key)     ( PGL_KEY_IS_AREAKEY(key) && \
  10.793 -                                    (key)[PGL_KEY_OBJSIZE_OFFSET] == \
  10.794 -                                    PGL_KEY_OBJSIZE_EMPTY )
  10.795 -#define PGL_KEY_IS_UNIVERSAL(key) ( PGL_KEY_IS_AREAKEY(key) && \
  10.796 -                                    (key)[PGL_KEY_OBJSIZE_OFFSET] == \
  10.797 -                                    PGL_KEY_OBJSIZE_UNIVERSAL )
  10.798 -
  10.799 -/* set area key to match empty objects only */
  10.800 -static void pgl_key_set_empty(pgl_keyptr key) {
  10.801 -  memset(key, 0, sizeof(pgl_areakey));
  10.802 -  /* Note: setting node depth to maximum is required for picksplit function */
  10.803 -  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK | PGL_AREAKEY_MAXDEPTH;
  10.804 -  key[PGL_KEY_OBJSIZE_OFFSET] = PGL_KEY_OBJSIZE_EMPTY;
  10.805 -}
  10.806 -
  10.807 -/* set area key to match any object (including empty objects) */
  10.808 -static void pgl_key_set_universal(pgl_keyptr key) {
  10.809 -  memset(key, 0, sizeof(pgl_areakey));
  10.810 -  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK;
  10.811 -  key[PGL_KEY_OBJSIZE_OFFSET] = PGL_KEY_OBJSIZE_UNIVERSAL;
  10.812 -}
  10.813 -
  10.814 -/* convert a point on earth into a max-depth key to be used in index */
  10.815 -static void pgl_point_to_key(pgl_point *point, pgl_keyptr key) {
  10.816 -  double lat = point->lat;
  10.817 -  double lon = point->lon;
  10.818 -  int i;
  10.819 -  /* clear latitude and longitude bits */
  10.820 -  memset(key, 0, PGL_KEY_LATLON_BYTELEN);
  10.821 -  /* set node depth to maximum and type bit to zero */
  10.822 -  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_POINTKEY_MAXDEPTH;
  10.823 -  /* iterate over all latitude/longitude bit pairs */
  10.824 -  for (i=0; i<PGL_POINTKEY_MAXDEPTH/2; i++) {
  10.825 -    /* determine latitude bit */
  10.826 -    if (lat >= 0) {
  10.827 -      key[i/4] |= 0x80 >> (2*(i%4));
  10.828 -      lat *= 2; lat -= 90;
  10.829 -    } else {
  10.830 -      lat *= 2; lat += 90;
  10.831 -    }
  10.832 -    /* determine longitude bit */
  10.833 -    if (lon >= 0) {
  10.834 -      key[i/4] |= 0x80 >> (2*(i%4)+1);
  10.835 -      lon *= 2; lon -= 180;
  10.836 -    } else {
  10.837 -      lon *= 2; lon += 180;
  10.838 -    }
  10.839 -  }
  10.840 -}
  10.841 -
  10.842 -/* convert a circle on earth into a max-depth key to be used in an index */
  10.843 -static void pgl_circle_to_key(pgl_circle *circle, pgl_keyptr key) {
  10.844 -  /* handle special case of empty circle */
  10.845 -  if (circle->radius < 0) {
  10.846 -    pgl_key_set_empty(key);
  10.847 -    return;
  10.848 -  }
  10.849 -  /* perform same action as for point keys */
  10.850 -  pgl_point_to_key(&(circle->center), key);
  10.851 -  /* but overwrite type and node depth to fit area index key */
  10.852 -  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK | PGL_AREAKEY_MAXDEPTH;
  10.853 -  /* check if radius is greater than (or equal to) reference size */
  10.854 -  /* (treat equal values as greater values for numerical safety) */
  10.855 -  if (circle->radius >= PGL_AREAKEY_REFOBJSIZE) {
  10.856 -    /* if yes, set logarithmic size to zero */
  10.857 -    key[PGL_KEY_OBJSIZE_OFFSET] = 0;
  10.858 -  } else {
  10.859 -    /* otherwise, determine logarithmic size iteratively */
  10.860 -    /* (one step is equivalent to a factor of sqrt(2)) */
  10.861 -    double reference = PGL_AREAKEY_REFOBJSIZE / M_SQRT2;
  10.862 -    int objsize = 1;
  10.863 -    while (objsize < PGL_AREAKEY_MAXOBJSIZE) {
  10.864 -      /* stop when radius is greater than (or equal to) adjusted reference */
  10.865 -      /* (treat equal values as greater values for numerical safety) */
  10.866 -      if (circle->radius >= reference) break;
  10.867 -      reference /= M_SQRT2;
  10.868 -      objsize++;
  10.869 -    }
  10.870 -    /* set logarithmic size to determined value */
  10.871 -    key[PGL_KEY_OBJSIZE_OFFSET] = objsize;
  10.872 -  }
  10.873 -}
  10.874 -
  10.875 -/* check if one key is subkey of another key or vice versa */
  10.876 -static bool pgl_keys_overlap(pgl_keyptr key1, pgl_keyptr key2) {
  10.877 -  int i;  /* key bit offset (includes both lat/lon and log. obj. size bits) */
  10.878 -  /* determine smallest depth */
  10.879 -  int depth1 = PGL_KEY_NODEDEPTH(key1);
  10.880 -  int depth2 = PGL_KEY_NODEDEPTH(key2);
  10.881 -  int depth = (depth1 < depth2) ? depth1 : depth2;
  10.882 -  /* check if keys are area keys (assuming that both keys have same type) */
  10.883 -  if (PGL_KEY_IS_AREAKEY(key1)) {
  10.884 -    int j = 0;  /* bit offset for logarithmic object size bits */
  10.885 -    int k = 0;  /* bit offset for latitude and longitude */
  10.886 -    /* fetch logarithmic object size information */
  10.887 -    int objsize1 = PGL_KEY_OBJSIZE(key1);
  10.888 -    int objsize2 = PGL_KEY_OBJSIZE(key2);
  10.889 -    /* handle special cases for empty objects (universal and empty keys) */
  10.890 -    if (
  10.891 -      objsize1 == PGL_KEY_OBJSIZE_UNIVERSAL ||
  10.892 -      objsize2 == PGL_KEY_OBJSIZE_UNIVERSAL
  10.893 -    ) return true;
  10.894 -    if (
  10.895 -      objsize1 == PGL_KEY_OBJSIZE_EMPTY ||
  10.896 -      objsize2 == PGL_KEY_OBJSIZE_EMPTY
  10.897 -    ) return objsize1 == objsize2;
  10.898 -    /* iterate through key bits */
  10.899 -    for (i=0; i<depth; i++) {
  10.900 -      /* every second bit is a bit describing the object size */
  10.901 -      if (i%2 == 0) {
  10.902 -        /* check if object size bit is different in both keys (objsize1 and
  10.903 -           objsize2 describe the minimum index when object size bit is set) */
  10.904 -        if (
  10.905 -          (objsize1 <= j && objsize2 > j) ||
  10.906 -          (objsize2 <= j && objsize1 > j)
  10.907 -        ) {
  10.908 -          /* bit differs, therefore keys are in separate branches */
  10.909 -          return false;
  10.910 -        }
  10.911 -        /* increase bit counter for object size bits */
  10.912 -        j++;
  10.913 -      }
  10.914 -      /* all other bits describe latitude and longitude */
  10.915 -      else {
  10.916 -        /* check if bit differs in both keys */
  10.917 -        if (PGL_KEY_LATLONBIT_DIFF(key1, key2, k)) {
  10.918 -          /* bit differs, therefore keys are in separate branches */
  10.919 -          return false;
  10.920 -        }
  10.921 -        /* increase bit counter for latitude/longitude bits */
  10.922 -        k++;
  10.923 -      }
  10.924 -    }
  10.925 -  }
  10.926 -  /* if not, keys are point keys */
  10.927 -  else {
  10.928 -    /* iterate through key bits */
  10.929 -    for (i=0; i<depth; i++) {
  10.930 -      /* check if bit differs in both keys */
  10.931 -      if (PGL_KEY_LATLONBIT_DIFF(key1, key2, i)) {
  10.932 -        /* bit differs, therefore keys are in separate branches */
  10.933 -        return false;
  10.934 -      }
  10.935 -    }
  10.936 -  }
  10.937 -  /* return true because keys are in the same branch */
  10.938 -  return true;
  10.939 -}
  10.940 -
  10.941 -/* combine two keys into new key which covers both original keys */
  10.942 -/* (result stored in first argument) */
  10.943 -static void pgl_unite_keys(pgl_keyptr dst, pgl_keyptr src) {
  10.944 -  int i;  /* key bit offset (includes both lat/lon and log. obj. size bits) */
  10.945 -  /* determine smallest depth */
  10.946 -  int depth1 = PGL_KEY_NODEDEPTH(dst);
  10.947 -  int depth2 = PGL_KEY_NODEDEPTH(src);
  10.948 -  int depth = (depth1 < depth2) ? depth1 : depth2;
  10.949 -  /* check if keys are area keys (assuming that both keys have same type) */
  10.950 -  if (PGL_KEY_IS_AREAKEY(dst)) {
  10.951 -    pgl_areakey dstbuf = { 0, };  /* destination buffer (cleared) */
  10.952 -    int j = 0;  /* bit offset for logarithmic object size bits */
  10.953 -    int k = 0;  /* bit offset for latitude and longitude */
  10.954 -    /* fetch logarithmic object size information */
  10.955 -    int objsize1 = PGL_KEY_OBJSIZE(dst);
  10.956 -    int objsize2 = PGL_KEY_OBJSIZE(src);
  10.957 -    /* handle special cases for empty objects (universal and empty keys) */
  10.958 -    if (
  10.959 -      objsize1 > PGL_AREAKEY_MAXOBJSIZE ||
  10.960 -      objsize2 > PGL_AREAKEY_MAXOBJSIZE
  10.961 -    ) {
  10.962 -      if (
  10.963 -        objsize1 == PGL_KEY_OBJSIZE_EMPTY &&
  10.964 -        objsize2 == PGL_KEY_OBJSIZE_EMPTY
  10.965 -      ) pgl_key_set_empty(dst);
  10.966 -      else pgl_key_set_universal(dst);
  10.967 -      return;
  10.968 -    }
  10.969 -    /* iterate through key bits */
  10.970 -    for (i=0; i<depth; i++) {
  10.971 -      /* every second bit is a bit describing the object size */
  10.972 -      if (i%2 == 0) {
  10.973 -        /* increase bit counter for object size bits first */
  10.974 -        /* (handy when setting objsize variable) */
  10.975 -        j++;
  10.976 -        /* check if object size bit is set in neither key */
  10.977 -        if (objsize1 >= j && objsize2 >= j) {
  10.978 -          /* set objsize in destination buffer to indicate that size bit is
  10.979 -             unset in destination buffer at the current bit position */
  10.980 -          dstbuf[PGL_KEY_OBJSIZE_OFFSET] = j;
  10.981 -        }
  10.982 -        /* break if object size bit is set in one key only */
  10.983 -        else if (objsize1 >= j || objsize2 >= j) break;
  10.984 -      }
  10.985 -      /* all other bits describe latitude and longitude */
  10.986 -      else {
  10.987 -        /* break if bit differs in both keys */
  10.988 -        if (PGL_KEY_LATLONBIT(dst, k)) {
  10.989 -          if (!PGL_KEY_LATLONBIT(src, k)) break;
  10.990 -          /* but set bit in destination buffer if bit is set in both keys */
  10.991 -          dstbuf[k/8] |= 0x80 >> (k%8);
  10.992 -        } else if (PGL_KEY_LATLONBIT(src, k)) break;
  10.993 -        /* increase bit counter for latitude/longitude bits */
  10.994 -        k++;
  10.995 -      }
  10.996 -    }
  10.997 -    /* set common node depth and type bit (type bit = 1) */
  10.998 -    dstbuf[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK | i;
  10.999 -    /* copy contents of destination buffer to first key */
 10.1000 -    memcpy(dst, dstbuf, sizeof(pgl_areakey));
 10.1001 -  }
 10.1002 -  /* if not, keys are point keys */
 10.1003 -  else {
 10.1004 -    pgl_pointkey dstbuf = { 0, };  /* destination buffer (cleared) */
 10.1005 -    /* iterate through key bits */
 10.1006 -    for (i=0; i<depth; i++) {
 10.1007 -      /* break if bit differs in both keys */
 10.1008 -      if (PGL_KEY_LATLONBIT(dst, i)) {
 10.1009 -        if (!PGL_KEY_LATLONBIT(src, i)) break;
 10.1010 -        /* but set bit in destination buffer if bit is set in both keys */
 10.1011 -        dstbuf[i/8] |= 0x80 >> (i%8);
 10.1012 -      } else if (PGL_KEY_LATLONBIT(src, i)) break;
 10.1013 -    }
 10.1014 -    /* set common node depth (type bit = 0) */
 10.1015 -    dstbuf[PGL_KEY_NODEDEPTH_OFFSET] = i;
 10.1016 -    /* copy contents of destination buffer to first key */
 10.1017 -    memcpy(dst, dstbuf, sizeof(pgl_pointkey));
 10.1018 -  }
 10.1019 -}
 10.1020 -
 10.1021 -/* determine center(!) boundaries and radius estimation of index key */
 10.1022 -static double pgl_key_to_box(pgl_keyptr key, pgl_box *box) {
 10.1023 -  int i;
 10.1024 -  /* determine node depth */
 10.1025 -  int depth = PGL_KEY_NODEDEPTH(key);
 10.1026 -  /* center point of possible result */
 10.1027 -  double lat = 0;
 10.1028 -  double lon = 0;
 10.1029 -  /* maximum distance of real center point from key center */
 10.1030 -  double dlat = 90;
 10.1031 -  double dlon = 180;
 10.1032 -  /* maximum radius of contained objects */
 10.1033 -  double radius = 0;  /* always return zero for point index keys */
 10.1034 -  /* check if key is area key */
 10.1035 -  if (PGL_KEY_IS_AREAKEY(key)) {
 10.1036 -    /* get logarithmic object size */
 10.1037 -    int objsize = PGL_KEY_OBJSIZE(key);
 10.1038 -    /* handle special cases for empty objects (universal and empty keys) */
 10.1039 -    if (objsize == PGL_KEY_OBJSIZE_EMPTY) {
 10.1040 -      pgl_box_set_empty(box);
 10.1041 -      return 0;
 10.1042 -    } else if (objsize == PGL_KEY_OBJSIZE_UNIVERSAL) {
 10.1043 -      box->lat_min = -90;
 10.1044 -      box->lat_max =  90;
 10.1045 -      box->lon_min = -180;
 10.1046 -      box->lon_max =  180;
 10.1047 -      return 0;  /* any value >= 0 would do */
 10.1048 -    }
 10.1049 -    /* calculate maximum possible radius of objects covered by the given key */
 10.1050 -    if (objsize == 0) radius = INFINITY;
 10.1051 -    else {
 10.1052 -      radius = PGL_AREAKEY_REFOBJSIZE;
 10.1053 -      while (--objsize) radius /= M_SQRT2;
 10.1054 -    }
 10.1055 -    /* iterate over latitude and longitude bits in key */
 10.1056 -    /* (every second bit is a latitude or longitude bit) */
 10.1057 -    for (i=0; i<depth/2; i++) {
 10.1058 -      /* check if latitude bit */
 10.1059 -      if (i%2 == 0) {
 10.1060 -        /* cut latitude dimension in half */
 10.1061 -        dlat /= 2;
 10.1062 -        /* increase center latitude if bit is 1, otherwise decrease */
 10.1063 -        if (PGL_KEY_LATLONBIT(key, i)) lat += dlat;
 10.1064 -        else lat -= dlat;
 10.1065 -      }
 10.1066 -      /* otherwise longitude bit */
 10.1067 -      else {
 10.1068 -        /* cut longitude dimension in half */
 10.1069 -        dlon /= 2;
 10.1070 -        /* increase center longitude if bit is 1, otherwise decrease */
 10.1071 -        if (PGL_KEY_LATLONBIT(key, i)) lon += dlon;
 10.1072 -        else lon -= dlon;
 10.1073 -      }
 10.1074 -    }
 10.1075 -  }
 10.1076 -  /* if not, keys are point keys */
 10.1077 -  else {
 10.1078 -    /* iterate over all bits in key */
 10.1079 -    for (i=0; i<depth; i++) {
 10.1080 -      /* check if latitude bit */
 10.1081 -      if (i%2 == 0) {
 10.1082 -        /* cut latitude dimension in half */
 10.1083 -        dlat /= 2;
 10.1084 -        /* increase center latitude if bit is 1, otherwise decrease */
 10.1085 -        if (PGL_KEY_LATLONBIT(key, i)) lat += dlat;
 10.1086 -        else lat -= dlat;
 10.1087 -      }
 10.1088 -      /* otherwise longitude bit */
 10.1089 -      else {
 10.1090 -        /* cut longitude dimension in half */
 10.1091 -        dlon /= 2;
 10.1092 -        /* increase center longitude if bit is 1, otherwise decrease */
 10.1093 -        if (PGL_KEY_LATLONBIT(key, i)) lon += dlon;
 10.1094 -        else lon -= dlon;
 10.1095 -      }
 10.1096 -    }
 10.1097 -  }
 10.1098 -  /* calculate boundaries from center point and remaining dlat and dlon */
 10.1099 -  /* (return values through pointer to box) */
 10.1100 -  box->lat_min = lat - dlat;
 10.1101 -  box->lat_max = lat + dlat;
 10.1102 -  box->lon_min = lon - dlon;
 10.1103 -  box->lon_max = lon + dlon;
 10.1104 -  /* return radius (as a function return value) */
 10.1105 -  return radius;
 10.1106 -}
 10.1107 -
 10.1108 -/* estimator function for distance between point and index key */
 10.1109 -/* allowed to return smaller values than actually correct */
 10.1110 -static double pgl_estimate_key_distance(pgl_keyptr key, pgl_point *point) {
 10.1111 -  pgl_box box;  /* center(!) bounding box of area index key */
 10.1112 -  /* calculate center(!) bounding box and maximum radius of objects covered
 10.1113 -     by area index key (radius is zero for point index keys) */
 10.1114 -  double distance = pgl_key_to_box(key, &box);
 10.1115 -  /* calculate estimated distance between bounding box of center point of
 10.1116 -     indexed object and point passed as second argument, then substract maximum
 10.1117 -     radius of objects covered by index key */
 10.1118 -  /* (use PGL_FPE_SAFETY factor to cope with minor floating point errors) */
 10.1119 -  distance = (
 10.1120 -    pgl_estimate_point_box_distance(point, &box) / PGL_FPE_SAFETY -
 10.1121 -    distance * PGL_FPE_SAFETY
 10.1122 -  );
 10.1123 -  /* truncate negative results to zero */
 10.1124 -  if (distance <= 0) distance = 0;
 10.1125 -  /* return result */
 10.1126 -  return distance;
 10.1127 -}
 10.1128 -
 10.1129 -
 10.1130 -/*---------------------------------*
 10.1131 - *  helper functions for text I/O  *
 10.1132 - *---------------------------------*/
 10.1133 -
 10.1134 -#define PGL_NUMBUFLEN 64  /* buffer size for number to string conversion */
 10.1135 -
 10.1136 -/* convert floating point number to string (round-trip safe) */
 10.1137 -static void pgl_print_float(char *buf, double flt) {
 10.1138 -  /* check if number is integral */
 10.1139 -  if (trunc(flt) == flt) {
 10.1140 -    /* for integral floats use maximum precision */
 10.1141 -    snprintf(buf, PGL_NUMBUFLEN, "%.17g", flt);
 10.1142 -  } else {
 10.1143 -    /* otherwise check if 15, 16, or 17 digits needed (round-trip safety) */
 10.1144 -    snprintf(buf, PGL_NUMBUFLEN, "%.15g", flt);
 10.1145 -    if (strtod(buf, NULL) != flt) snprintf(buf, PGL_NUMBUFLEN, "%.16g", flt);
 10.1146 -    if (strtod(buf, NULL) != flt) snprintf(buf, PGL_NUMBUFLEN, "%.17g", flt);
 10.1147 -  }
 10.1148 -}
 10.1149 -
 10.1150 -/* convert latitude floating point number (in degrees) to string */
 10.1151 -static void pgl_print_lat(char *buf, double lat) {
 10.1152 -  if (signbit(lat)) {
 10.1153 -    /* treat negative latitudes (including -0) as south */
 10.1154 -    snprintf(buf, PGL_NUMBUFLEN, "S%015.12f", -lat);
 10.1155 -  } else {
 10.1156 -    /* treat positive latitudes (including +0) as north */
 10.1157 -    snprintf(buf, PGL_NUMBUFLEN, "N%015.12f", lat);
 10.1158 -  }
 10.1159 -}
 10.1160 -
 10.1161 -/* convert longitude floating point number (in degrees) to string */
 10.1162 -static void pgl_print_lon(char *buf, double lon) {
 10.1163 -  if (signbit(lon)) {
 10.1164 -    /* treat negative longitudes (including -0) as west */
 10.1165 -    snprintf(buf, PGL_NUMBUFLEN, "W%016.12f", -lon);
 10.1166 -  } else {
 10.1167 -    /* treat positive longitudes (including +0) as east */
 10.1168 -    snprintf(buf, PGL_NUMBUFLEN, "E%016.12f", lon);
 10.1169 -  }
 10.1170 -}
 10.1171 -
 10.1172 -/* bit masks used as return value of pgl_scan() function */
 10.1173 -#define PGL_SCAN_NONE 0      /* no value has been parsed */
 10.1174 -#define PGL_SCAN_LAT (1<<0)  /* latitude has been parsed */
 10.1175 -#define PGL_SCAN_LON (1<<1)  /* longitude has been parsed */
 10.1176 -#define PGL_SCAN_LATLON (PGL_SCAN_LAT | PGL_SCAN_LON)  /* bitwise OR of both */
 10.1177 -
 10.1178 -/* parse a coordinate (can be latitude or longitude) */
 10.1179 -static int pgl_scan(char **str, double *lat, double *lon) {
 10.1180 -  double val;
 10.1181 -  int len;
 10.1182 -  if (
 10.1183 -    sscanf(*str, " N %lf %n", &val, &len) ||
 10.1184 -    sscanf(*str, " n %lf %n", &val, &len)
 10.1185 -  ) {
 10.1186 -    *str += len; *lat = val; return PGL_SCAN_LAT;
 10.1187 -  }
 10.1188 -  if (
 10.1189 -    sscanf(*str, " S %lf %n", &val, &len) ||
 10.1190 -    sscanf(*str, " s %lf %n", &val, &len)
 10.1191 -  ) {
 10.1192 -    *str += len; *lat = -val; return PGL_SCAN_LAT;
 10.1193 -  }
 10.1194 -  if (
 10.1195 -    sscanf(*str, " E %lf %n", &val, &len) ||
 10.1196 -    sscanf(*str, " e %lf %n", &val, &len)
 10.1197 -  ) {
 10.1198 -    *str += len; *lon = val; return PGL_SCAN_LON;
 10.1199 -  }
 10.1200 -  if (
 10.1201 -    sscanf(*str, " W %lf %n", &val, &len) ||
 10.1202 -    sscanf(*str, " w %lf %n", &val, &len)
 10.1203 -  ) {
 10.1204 -    *str += len; *lon = -val; return PGL_SCAN_LON;
 10.1205 -  }
 10.1206 -  return PGL_SCAN_NONE;
 10.1207 -}
 10.1208 -
 10.1209 -
 10.1210 -/*-----------------*
 10.1211 - *  SQL functions  *
 10.1212 - *-----------------*/
 10.1213 -
 10.1214 -/* Note: These function names use "epoint", "ebox", etc. notation here instead
 10.1215 -   of "point", "box", etc. in order to distinguish them from any previously
 10.1216 -   defined functions. */
 10.1217 -
 10.1218 -/* function needed for dummy types and/or not implemented features */
 10.1219 -PG_FUNCTION_INFO_V1(pgl_notimpl);
 10.1220 -Datum pgl_notimpl(PG_FUNCTION_ARGS) {
 10.1221 -  ereport(ERROR, (errmsg("not implemented by pgLatLon")));
 10.1222 -}
 10.1223 -
 10.1224 -/* set point to latitude and longitude (including checks) */
 10.1225 -static void pgl_epoint_set_latlon(pgl_point *point, double lat, double lon) {
 10.1226 -  /* reject infinite or NaN values */
 10.1227 -  if (!isfinite(lat) || !isfinite(lon)) {
 10.1228 -    ereport(ERROR, (
 10.1229 -      errcode(ERRCODE_DATA_EXCEPTION),
 10.1230 -      errmsg("epoint requires finite coordinates")
 10.1231 -    ));
 10.1232 -  }
 10.1233 -  /* check latitude bounds */
 10.1234 -  if (lat < -90) {
 10.1235 -    ereport(WARNING, (errmsg("latitude exceeds south pole")));
 10.1236 -    lat = -90;
 10.1237 -  } else if (lat > 90) {
 10.1238 -    ereport(WARNING, (errmsg("latitude exceeds north pole")));
 10.1239 -    lat = 90;
 10.1240 -  }
 10.1241 -  /* check longitude bounds */
 10.1242 -  if (lon < -180) {
 10.1243 -    ereport(NOTICE, (errmsg("longitude west of 180th meridian normalized")));
 10.1244 -    lon += 360 - trunc(lon / 360) * 360;
 10.1245 -  } else if (lon > 180) {
 10.1246 -    ereport(NOTICE, (errmsg("longitude east of 180th meridian normalized")));
 10.1247 -    lon -= 360 + trunc(lon / 360) * 360;
 10.1248 -  }
 10.1249 -  /* store rounded latitude/longitude values for round-trip safety */
 10.1250 -  point->lat = pgl_round(lat);
 10.1251 -  point->lon = pgl_round(lon);
 10.1252 -}
 10.1253 -
 10.1254 -/* create point ("epoint" in SQL) from latitude and longitude */
 10.1255 -PG_FUNCTION_INFO_V1(pgl_create_epoint);
 10.1256 -Datum pgl_create_epoint(PG_FUNCTION_ARGS) {
 10.1257 -  pgl_point *point = (pgl_point *)palloc(sizeof(pgl_point));
 10.1258 -  pgl_epoint_set_latlon(point, PG_GETARG_FLOAT8(0), PG_GETARG_FLOAT8(1));
 10.1259 -  PG_RETURN_POINTER(point);
 10.1260 -}
 10.1261 -
 10.1262 -/* parse point ("epoint" in SQL) */
 10.1263 -/* format: '[NS]<float> [EW]<float>' */
 10.1264 -PG_FUNCTION_INFO_V1(pgl_epoint_in);
 10.1265 -Datum pgl_epoint_in(PG_FUNCTION_ARGS) {
 10.1266 -  char *str = PG_GETARG_CSTRING(0);  /* input string */
 10.1267 -  char *strptr = str;  /* current position within string */
 10.1268 -  int done = 0;        /* bit mask storing if latitude or longitude was read */
 10.1269 -  double lat, lon;     /* parsed values as double precision floats */
 10.1270 -  pgl_point *point;    /* return value (to be palloc'ed) */
 10.1271 -  /* parse two floats (each latitude or longitude) separated by white-space */
 10.1272 -  done |= pgl_scan(&strptr, &lat, &lon);
 10.1273 -  if (strptr != str && isspace(strptr[-1])) {
 10.1274 -    done |= pgl_scan(&strptr, &lat, &lon);
 10.1275 -  }
 10.1276 -  /* require end of string, and latitude and longitude parsed successfully */
 10.1277 -  if (strptr[0] || done != PGL_SCAN_LATLON) {
 10.1278 -    ereport(ERROR, (
 10.1279 -      errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 10.1280 -      errmsg("invalid input syntax for type epoint: \"%s\"", str)
 10.1281 -    ));
 10.1282 -  }
 10.1283 -  /* allocate memory for result */
 10.1284 -  point = (pgl_point *)palloc(sizeof(pgl_point));
 10.1285 -  /* set latitude and longitude (and perform checks) */
 10.1286 -  pgl_epoint_set_latlon(point, lat, lon);
 10.1287 -  /* return result */
 10.1288 -  PG_RETURN_POINTER(point);
 10.1289 -}
 10.1290 -
 10.1291 -/* create box ("ebox" in SQL) that is empty */
 10.1292 -PG_FUNCTION_INFO_V1(pgl_create_empty_ebox);
 10.1293 -Datum pgl_create_empty_ebox(PG_FUNCTION_ARGS) {
 10.1294 -  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
 10.1295 -  pgl_box_set_empty(box);
 10.1296 -  PG_RETURN_POINTER(box);
 10.1297 -}
 10.1298 -
 10.1299 -/* set box to given boundaries (including checks) */
 10.1300 -static void pgl_ebox_set_boundaries(
 10.1301 -  pgl_box *box,
 10.1302 -  double lat_min, double lat_max, double lon_min, double lon_max
 10.1303 -) {
 10.1304 -  /* if minimum latitude is greater than maximum latitude, return empty box */
 10.1305 -  if (lat_min > lat_max) {
 10.1306 -    pgl_box_set_empty(box);
 10.1307 -    return;
 10.1308 -  }
 10.1309 -  /* otherwise reject infinite or NaN values */
 10.1310 -  if (
 10.1311 -    !isfinite(lat_min) || !isfinite(lat_max) ||
 10.1312 -    !isfinite(lon_min) || !isfinite(lon_max)
 10.1313 -  ) {
 10.1314 -    ereport(ERROR, (
 10.1315 -      errcode(ERRCODE_DATA_EXCEPTION),
 10.1316 -      errmsg("ebox requires finite coordinates")
 10.1317 -    ));
 10.1318 -  }
 10.1319 -  /* check latitude bounds */
 10.1320 -  if (lat_max < -90) {
 10.1321 -    ereport(WARNING, (errmsg("northern latitude exceeds south pole")));
 10.1322 -    lat_max = -90;
 10.1323 -  } else if (lat_max > 90) {
 10.1324 -    ereport(WARNING, (errmsg("northern latitude exceeds north pole")));
 10.1325 -    lat_max = 90;
 10.1326 -  }
 10.1327 -  if (lat_min < -90) {
 10.1328 -    ereport(WARNING, (errmsg("southern latitude exceeds south pole")));
 10.1329 -    lat_min = -90;
 10.1330 -  } else if (lat_min > 90) {
 10.1331 -    ereport(WARNING, (errmsg("southern latitude exceeds north pole")));
 10.1332 -    lat_min = 90;
 10.1333 -  }
 10.1334 -  /* check if all longitudes are included */
 10.1335 -  if (lon_max - lon_min >= 360) {
 10.1336 -    if (lon_max - lon_min > 360) ereport(WARNING, (
 10.1337 -      errmsg("longitude coverage greater than 360 degrees")
 10.1338 -    ));
 10.1339 -    lon_min = -180;
 10.1340 -    lon_max = 180;
 10.1341 -  } else {
 10.1342 -    /* normalize longitude bounds */
 10.1343 -    if      (lon_min < -180) lon_min += 360 - trunc(lon_min / 360) * 360;
 10.1344 -    else if (lon_min >  180) lon_min -= 360 + trunc(lon_min / 360) * 360;
 10.1345 -    if      (lon_max < -180) lon_max += 360 - trunc(lon_max / 360) * 360;
 10.1346 -    else if (lon_max >  180) lon_max -= 360 + trunc(lon_max / 360) * 360;
 10.1347 -  }
 10.1348 -  /* store rounded latitude/longitude values for round-trip safety */
 10.1349 -  box->lat_min = pgl_round(lat_min);
 10.1350 -  box->lat_max = pgl_round(lat_max);
 10.1351 -  box->lon_min = pgl_round(lon_min);
 10.1352 -  box->lon_max = pgl_round(lon_max);
 10.1353 -  /* ensure that rounding does not change orientation */
 10.1354 -  if (lon_min > lon_max && box->lon_min == box->lon_max) {
 10.1355 -    box->lon_min = -180;
 10.1356 -    box->lon_max = 180;
 10.1357 -  }
 10.1358 -}
 10.1359 -
 10.1360 -/* create box ("ebox" in SQL) from min/max latitude and min/max longitude */
 10.1361 -PG_FUNCTION_INFO_V1(pgl_create_ebox);
 10.1362 -Datum pgl_create_ebox(PG_FUNCTION_ARGS) {
 10.1363 -  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
 10.1364 -  pgl_ebox_set_boundaries(
 10.1365 -    box,
 10.1366 -    PG_GETARG_FLOAT8(0), PG_GETARG_FLOAT8(1),
 10.1367 -    PG_GETARG_FLOAT8(2), PG_GETARG_FLOAT8(3)
 10.1368 -  );
 10.1369 -  PG_RETURN_POINTER(box);
 10.1370 -}
 10.1371 -
 10.1372 -/* create box ("ebox" in SQL) from two points ("epoint"s) */
 10.1373 -/* (can not be used to cover a longitude range of more than 120 degrees) */
 10.1374 -PG_FUNCTION_INFO_V1(pgl_create_ebox_from_epoints);
 10.1375 -Datum pgl_create_ebox_from_epoints(PG_FUNCTION_ARGS) {
 10.1376 -  pgl_point *point1 = (pgl_point *)PG_GETARG_POINTER(0);
 10.1377 -  pgl_point *point2 = (pgl_point *)PG_GETARG_POINTER(1);
 10.1378 -  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
 10.1379 -  double lat_min, lat_max, lon_min, lon_max;
 10.1380 -  double dlon;  /* longitude range (delta longitude) */
 10.1381 -  /* order latitude and longitude boundaries */
 10.1382 -  if (point2->lat < point1->lat) {
 10.1383 -    lat_min = point2->lat;
 10.1384 -    lat_max = point1->lat;
 10.1385 -  } else {
 10.1386 -    lat_min = point1->lat;
 10.1387 -    lat_max = point2->lat;
 10.1388 -  }
 10.1389 -  if (point2->lon < point1->lon) {
 10.1390 -    lon_min = point2->lon;
 10.1391 -    lon_max = point1->lon;
 10.1392 -  } else {
 10.1393 -    lon_min = point1->lon;
 10.1394 -    lon_max = point2->lon;
 10.1395 -  }
 10.1396 -  /* calculate longitude range (round to avoid floating point errors) */
 10.1397 -  dlon = pgl_round(lon_max - lon_min);
 10.1398 -  /* determine east-west direction */
 10.1399 -  if (dlon >= 240) {
 10.1400 -    /* assume that 180th meridian is crossed and swap min/max longitude */
 10.1401 -    double swap = lon_min; lon_min = lon_max; lon_max = swap;
 10.1402 -  } else if (dlon > 120) {
 10.1403 -    /* unclear orientation since delta longitude > 120 */
 10.1404 -    ereport(ERROR, (
 10.1405 -      errcode(ERRCODE_DATA_EXCEPTION),
 10.1406 -      errmsg("can not determine east/west orientation for ebox")
 10.1407 -    ));
 10.1408 -  }
 10.1409 -  /* use boundaries to setup box (and perform checks) */
 10.1410 -  pgl_ebox_set_boundaries(box, lat_min, lat_max, lon_min, lon_max);
 10.1411 -  /* return result */
 10.1412 -  PG_RETURN_POINTER(box);
 10.1413 -}
 10.1414 -
 10.1415 -/* parse box ("ebox" in SQL) */
 10.1416 -/* format: '[NS]<float> [EW]<float> [NS]<float> [EW]<float>'
 10.1417 -       or: '[NS]<float> [NS]<float> [EW]<float> [EW]<float>' */
 10.1418 -PG_FUNCTION_INFO_V1(pgl_ebox_in);
 10.1419 -Datum pgl_ebox_in(PG_FUNCTION_ARGS) {
 10.1420 -  char *str = PG_GETARG_CSTRING(0);  /* input string */
 10.1421 -  char *str_lower;     /* lower case version of input string */
 10.1422 -  char *strptr;        /* current position within string */
 10.1423 -  int valid;           /* number of valid chars */
 10.1424 -  int done;            /* specifies if latitude or longitude was read */
 10.1425 -  double val;          /* temporary variable */
 10.1426 -  int lat_count = 0;   /* count of latitude values parsed */
 10.1427 -  int lon_count = 0;   /* count of longitufde values parsed */
 10.1428 -  double lat_min, lat_max, lon_min, lon_max;  /* see pgl_box struct */
 10.1429 -  pgl_box *box;        /* return value (to be palloc'ed) */
 10.1430 -  /* lowercase input */
 10.1431 -  str_lower = psprintf("%s", str);
 10.1432 -  for (strptr=str_lower; *strptr; strptr++) {
 10.1433 -    if (*strptr >= 'A' && *strptr <= 'Z') *strptr += 'a' - 'A';
 10.1434 -  }
 10.1435 -  /* reset reading position to start of (lowercase) string */
 10.1436 -  strptr = str_lower;
 10.1437 -  /* check if empty box */
 10.1438 -  valid = 0;
 10.1439 -  sscanf(strptr, " empty %n", &valid);
 10.1440 -  if (valid && strptr[valid] == 0) {
 10.1441 -    /* allocate and return empty box */
 10.1442 -    box = (pgl_box *)palloc(sizeof(pgl_box));
 10.1443 -    pgl_box_set_empty(box);
 10.1444 -    PG_RETURN_POINTER(box);
 10.1445 -  }
 10.1446 -  /* demand four blocks separated by whitespace */
 10.1447 -  valid = 0;
 10.1448 -  sscanf(strptr, " %*s %*s %*s %*s %n", &valid);
 10.1449 -  /* if four blocks separated by whitespace exist, parse those blocks */
 10.1450 -  if (strptr[valid] == 0) while (strptr[0]) {
 10.1451 -    /* parse either latitude or longitude (whichever found in input string) */
 10.1452 -    done = pgl_scan(&strptr, &val, &val);
 10.1453 -    /* store latitude or longitude in lat_min, lat_max, lon_min, or lon_max */
 10.1454 -    if (done == PGL_SCAN_LAT) {
 10.1455 -      if (!lat_count) lat_min = val; else lat_max = val;
 10.1456 -      lat_count++;
 10.1457 -    } else if (done == PGL_SCAN_LON) {
 10.1458 -      if (!lon_count) lon_min = val; else lon_max = val;
 10.1459 -      lon_count++;
 10.1460 -    } else {
 10.1461 -      break;
 10.1462 -    }
 10.1463 -  }
 10.1464 -  /* require end of string, and two latitude and two longitude values */
 10.1465 -  if (strptr[0] || lat_count != 2 || lon_count != 2) {
 10.1466 -    ereport(ERROR, (
 10.1467 -      errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 10.1468 -      errmsg("invalid input syntax for type ebox: \"%s\"", str)
 10.1469 -    ));
 10.1470 -  }
 10.1471 -  /* free lower case string */
 10.1472 -  pfree(str_lower);
 10.1473 -  /* order boundaries (maximum greater than minimum) */
 10.1474 -  if (lat_min > lat_max) { val = lat_min; lat_min = lat_max; lat_max = val; }
 10.1475 -  if (lon_min > lon_max) { val = lon_min; lon_min = lon_max; lon_max = val; }
 10.1476 -  /* allocate memory for result */
 10.1477 -  box = (pgl_box *)palloc(sizeof(pgl_box));
 10.1478 -  /* set boundaries (and perform checks) */
 10.1479 -  pgl_ebox_set_boundaries(box, lat_min, lat_max, lon_min, lon_max);
 10.1480 -  /* return result */
 10.1481 -  PG_RETURN_POINTER(box);
 10.1482 -}
 10.1483 -
 10.1484 -/* set circle to given latitude, longitude, and radius (including checks) */
 10.1485 -static void pgl_ecircle_set_latlon_radius(
 10.1486 -  pgl_circle *circle, double lat, double lon, double radius
 10.1487 -) {
 10.1488 -  /* set center point (including checks) */
 10.1489 -  pgl_epoint_set_latlon(&(circle->center), lat, lon);
 10.1490 -  /* handle non-positive radius */
 10.1491 -  if (isnan(radius)) {
 10.1492 -    ereport(ERROR, (
 10.1493 -      errcode(ERRCODE_DATA_EXCEPTION),
 10.1494 -      errmsg("invalid radius for ecircle")
 10.1495 -    ));
 10.1496 -  }
 10.1497 -  if (radius == 0) radius = 0;  /* avoids -0 */
 10.1498 -  else if (radius < 0) {
 10.1499 -    if (isfinite(radius)) {
 10.1500 -      ereport(NOTICE, (errmsg("negative radius converted to minus infinity")));
 10.1501 -    }
 10.1502 -    radius = -INFINITY;
 10.1503 -  }
 10.1504 -  /* store radius (round-trip safety is ensured by pgl_print_float) */
 10.1505 -  circle->radius = radius;
 10.1506 -}
 10.1507 -
 10.1508 -/* create circle ("ecircle" in SQL) from latitude, longitude, and radius */
 10.1509 -PG_FUNCTION_INFO_V1(pgl_create_ecircle);
 10.1510 -Datum pgl_create_ecircle(PG_FUNCTION_ARGS) {
 10.1511 -  pgl_circle *circle = (pgl_circle *)palloc(sizeof(pgl_circle));
 10.1512 -  pgl_ecircle_set_latlon_radius(
 10.1513 -    circle, PG_GETARG_FLOAT8(0), PG_GETARG_FLOAT8(1), PG_GETARG_FLOAT8(2)
 10.1514 -  );
 10.1515 -  PG_RETURN_POINTER(circle);
 10.1516 -}
 10.1517 -
 10.1518 -/* create circle ("ecircle" in SQL) from point ("epoint"), and radius */
 10.1519 -PG_FUNCTION_INFO_V1(pgl_create_ecircle_from_epoint);
 10.1520 -Datum pgl_create_ecircle_from_epoint(PG_FUNCTION_ARGS) {
 10.1521 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.1522 -  double radius = PG_GETARG_FLOAT8(1);
 10.1523 -  pgl_circle *circle = (pgl_circle *)palloc(sizeof(pgl_circle));
 10.1524 -  /* set latitude, longitude, radius (and perform checks) */
 10.1525 -  pgl_ecircle_set_latlon_radius(circle, point->lat, point->lon, radius);
 10.1526 -  /* return result */
 10.1527 -  PG_RETURN_POINTER(circle);
 10.1528 -}
 10.1529 -
 10.1530 -/* parse circle ("ecircle" in SQL) */
 10.1531 -/* format: '[NS]<float> [EW]<float> <float>' */
 10.1532 -PG_FUNCTION_INFO_V1(pgl_ecircle_in);
 10.1533 -Datum pgl_ecircle_in(PG_FUNCTION_ARGS) {
 10.1534 -  char *str = PG_GETARG_CSTRING(0);  /* input string */
 10.1535 -  char *strptr = str;       /* current position within string */
 10.1536 -  double lat, lon, radius;  /* parsed values as double precision flaots */
 10.1537 -  int valid = 0;            /* number of valid chars */
 10.1538 -  int done = 0;             /* stores if latitude and/or longitude was read */
 10.1539 -  pgl_circle *circle;       /* return value (to be palloc'ed) */
 10.1540 -  /* demand three blocks separated by whitespace */
 10.1541 -  sscanf(strptr, " %*s %*s %*s %n", &valid);
 10.1542 -  /* if three blocks separated by whitespace exist, parse those blocks */
 10.1543 -  if (strptr[valid] == 0) {
 10.1544 -    /* parse latitude and longitude */
 10.1545 -    done |= pgl_scan(&strptr, &lat, &lon);
 10.1546 -    done |= pgl_scan(&strptr, &lat, &lon);
 10.1547 -    /* parse radius (while incrementing strptr by number of bytes parsed) */
 10.1548 -    valid = 0;
 10.1549 -    if (sscanf(strptr, " %lf %n", &radius, &valid) == 1) strptr += valid;
 10.1550 -  }
 10.1551 -  /* require end of string and both latitude and longitude being parsed */
 10.1552 -  if (strptr[0] || done != PGL_SCAN_LATLON) {
 10.1553 -    ereport(ERROR, (
 10.1554 -      errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 10.1555 -      errmsg("invalid input syntax for type ecircle: \"%s\"", str)
 10.1556 -    ));
 10.1557 -  }
 10.1558 -  /* allocate memory for result */
 10.1559 -  circle = (pgl_circle *)palloc(sizeof(pgl_circle));
 10.1560 -  /* set latitude, longitude, radius (and perform checks) */
 10.1561 -  pgl_ecircle_set_latlon_radius(circle, lat, lon, radius);
 10.1562 -  /* return result */
 10.1563 -  PG_RETURN_POINTER(circle);
 10.1564 -}
 10.1565 -
 10.1566 -/* parse cluster ("ecluster" in SQL) */
 10.1567 -PG_FUNCTION_INFO_V1(pgl_ecluster_in);
 10.1568 -Datum pgl_ecluster_in(PG_FUNCTION_ARGS) {
 10.1569 -  int i;
 10.1570 -  char *str = PG_GETARG_CSTRING(0);  /* input string */
 10.1571 -  char *str_lower;         /* lower case version of input string */
 10.1572 -  char *strptr;            /* pointer to current reading position of input */
 10.1573 -  int npoints_total = 0;   /* total number of points in cluster */
 10.1574 -  int nentries = 0;        /* total number of entries */
 10.1575 -  pgl_newentry *entries;   /* array of pgl_newentry to create pgl_cluster */
 10.1576 -  int entries_buflen = 4;  /* maximum number of elements in entries array */
 10.1577 -  int valid;               /* number of valid chars processed */
 10.1578 -  double lat, lon;         /* latitude and longitude of parsed point */
 10.1579 -  int entrytype;           /* current entry type */
 10.1580 -  int npoints;             /* number of points in current entry */
 10.1581 -  pgl_point *points;       /* array of pgl_point for pgl_newentry */
 10.1582 -  int points_buflen;       /* maximum number of elements in points array */
 10.1583 -  int done;                /* return value of pgl_scan function */
 10.1584 -  pgl_cluster *cluster;    /* created cluster */
 10.1585 -  /* lowercase input */
 10.1586 -  str_lower = psprintf("%s", str);
 10.1587 -  for (strptr=str_lower; *strptr; strptr++) {
 10.1588 -    if (*strptr >= 'A' && *strptr <= 'Z') *strptr += 'a' - 'A';
 10.1589 -  }
 10.1590 -  /* reset reading position to start of (lowercase) string */
 10.1591 -  strptr = str_lower;
 10.1592 -  /* allocate initial buffer for entries */
 10.1593 -  entries = palloc(entries_buflen * sizeof(pgl_newentry));
 10.1594 -  /* parse until end of string */
 10.1595 -  while (strptr[0]) {
 10.1596 -    /* require previous white-space or closing parenthesis before next token */
 10.1597 -    if (strptr != str_lower && !isspace(strptr[-1]) && strptr[-1] != ')') {
 10.1598 -      goto pgl_ecluster_in_error;
 10.1599 -    }
 10.1600 -    /* ignore token "empty" */
 10.1601 -    valid = 0; sscanf(strptr, " empty %n", &valid);
 10.1602 -    if (valid) { strptr += valid; continue; }
 10.1603 -    /* test for "point" token */
 10.1604 -    valid = 0; sscanf(strptr, " point ( %n", &valid);
 10.1605 -    if (valid) {
 10.1606 -      strptr += valid;
 10.1607 -      entrytype = PGL_ENTRY_POINT;
 10.1608 -      goto pgl_ecluster_in_type_ok;
 10.1609 -    }
 10.1610 -    /* test for "path" token */
 10.1611 -    valid = 0; sscanf(strptr, " path ( %n", &valid);
 10.1612 -    if (valid) {
 10.1613 -      strptr += valid;
 10.1614 -      entrytype = PGL_ENTRY_PATH;
 10.1615 -      goto pgl_ecluster_in_type_ok;
 10.1616 -    }
 10.1617 -    /* test for "outline" token */
 10.1618 -    valid = 0; sscanf(strptr, " outline ( %n", &valid);
 10.1619 -    if (valid) {
 10.1620 -      strptr += valid;
 10.1621 -      entrytype = PGL_ENTRY_OUTLINE;
 10.1622 -      goto pgl_ecluster_in_type_ok;
 10.1623 -    }
 10.1624 -    /* test for "polygon" token */
 10.1625 -    valid = 0; sscanf(strptr, " polygon ( %n", &valid);
 10.1626 -    if (valid) {
 10.1627 -      strptr += valid;
 10.1628 -      entrytype = PGL_ENTRY_POLYGON;
 10.1629 -      goto pgl_ecluster_in_type_ok;
 10.1630 -    }
 10.1631 -    /* error if no valid token found */
 10.1632 -    goto pgl_ecluster_in_error;
 10.1633 -    pgl_ecluster_in_type_ok:
 10.1634 -    /* check if pgl_newentry array needs to grow */
 10.1635 -    if (nentries == entries_buflen) {
 10.1636 -      pgl_newentry *newbuf;
 10.1637 -      entries_buflen *= 2;
 10.1638 -      newbuf = palloc(entries_buflen * sizeof(pgl_newentry));
 10.1639 -      memcpy(newbuf, entries, nentries * sizeof(pgl_newentry));
 10.1640 -      pfree(entries);
 10.1641 -      entries = newbuf;
 10.1642 -    }
 10.1643 -    /* reset number of points for current entry */
 10.1644 -    npoints = 0;
 10.1645 -    /* allocate array for points */
 10.1646 -    points_buflen = 4;
 10.1647 -    points = palloc(points_buflen * sizeof(pgl_point));
 10.1648 -    /* parse until closing parenthesis */
 10.1649 -    while (strptr[0] != ')') {
 10.1650 -      /* error on unexpected end of string */
 10.1651 -      if (strptr[0] == 0) goto pgl_ecluster_in_error;
 10.1652 -      /* mark neither latitude nor longitude as read */
 10.1653 -      done = PGL_SCAN_NONE;
 10.1654 -      /* require white-space before second, third, etc. point */
 10.1655 -      if (npoints != 0 && !isspace(strptr[-1])) goto pgl_ecluster_in_error;
 10.1656 -      /* scan latitude (or longitude) */
 10.1657 -      done |= pgl_scan(&strptr, &lat, &lon);
 10.1658 -      /* require white-space before second coordinate */
 10.1659 -      if (strptr != str && !isspace(strptr[-1])) goto pgl_ecluster_in_error;
 10.1660 -      /* scan longitude (or latitude) */
 10.1661 -      done |= pgl_scan(&strptr, &lat, &lon);
 10.1662 -      /* error unless both latitude and longitude were parsed */
 10.1663 -      if (done != PGL_SCAN_LATLON) goto pgl_ecluster_in_error;
 10.1664 -      /* throw error if number of points is too high */
 10.1665 -      if (npoints_total == PGL_CLUSTER_MAXPOINTS) {
 10.1666 -        ereport(ERROR, (
 10.1667 -          errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 10.1668 -          errmsg(
 10.1669 -            "too many points for ecluster entry (maximum %i)",
 10.1670 -            PGL_CLUSTER_MAXPOINTS
 10.1671 -          )
 10.1672 -        ));
 10.1673 -      }
 10.1674 -      /* check if pgl_point array needs to grow */
 10.1675 -      if (npoints == points_buflen) {
 10.1676 -        pgl_point *newbuf;
 10.1677 -        points_buflen *= 2;
 10.1678 -        newbuf = palloc(points_buflen * sizeof(pgl_point));
 10.1679 -        memcpy(newbuf, points, npoints * sizeof(pgl_point));
 10.1680 -        pfree(points);
 10.1681 -        points = newbuf;
 10.1682 -      }
 10.1683 -      /* append point to pgl_point array (includes checks) */
 10.1684 -      pgl_epoint_set_latlon(&(points[npoints++]), lat, lon);
 10.1685 -      /* increase total number of points */
 10.1686 -      npoints_total++;
 10.1687 -    }
 10.1688 -    /* error if entry has no points */
 10.1689 -    if (!npoints) goto pgl_ecluster_in_error;
 10.1690 -    /* entries with one point are automatically of type "point" */
 10.1691 -    if (npoints == 1) entrytype = PGL_ENTRY_POINT;
 10.1692 -    /* if entries have more than one point */
 10.1693 -    else {
 10.1694 -      /* throw error if entry type is "point" */
 10.1695 -      if (entrytype == PGL_ENTRY_POINT) {
 10.1696 -        ereport(ERROR, (
 10.1697 -          errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 10.1698 -          errmsg("invalid input syntax for type ecluster (point entry with more than one point)")
 10.1699 -        ));
 10.1700 -      }
 10.1701 -      /* coerce outlines and polygons with more than 2 points to be a path */
 10.1702 -      if (npoints == 2) entrytype = PGL_ENTRY_PATH;
 10.1703 -    }
 10.1704 -    /* append entry to pgl_newentry array */
 10.1705 -    entries[nentries].entrytype = entrytype;
 10.1706 -    entries[nentries].npoints = npoints;
 10.1707 -    entries[nentries].points = points;
 10.1708 -    nentries++;
 10.1709 -    /* consume closing parenthesis */
 10.1710 -    strptr++;
 10.1711 -    /* consume white-space */
 10.1712 -    while (isspace(strptr[0])) strptr++;
 10.1713 -  }
 10.1714 -  /* free lower case string */
 10.1715 -  pfree(str_lower);
 10.1716 -  /* create cluster from pgl_newentry array */
 10.1717 -  cluster = pgl_new_cluster(nentries, entries);
 10.1718 -  /* free pgl_newentry array */
 10.1719 -  for (i=0; i<nentries; i++) pfree(entries[i].points);
 10.1720 -  pfree(entries);
 10.1721 -  /* set bounding circle of cluster and check east/west orientation */
 10.1722 -  if (!pgl_finalize_cluster(cluster)) {
 10.1723 -    ereport(ERROR, (
 10.1724 -      errcode(ERRCODE_DATA_EXCEPTION),
 10.1725 -      errmsg("can not determine east/west orientation for ecluster"),
 10.1726 -      errhint("Ensure that each entry has a longitude span of less than 180 degrees.")
 10.1727 -    ));
 10.1728 -  }
 10.1729 -  /* return cluster */
 10.1730 -  PG_RETURN_POINTER(cluster);
 10.1731 -  /* code to throw error */
 10.1732 -  pgl_ecluster_in_error:
 10.1733 -  ereport(ERROR, (
 10.1734 -    errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 10.1735 -    errmsg("invalid input syntax for type ecluster: \"%s\"", str)
 10.1736 -  ));
 10.1737 -}
 10.1738 -
 10.1739 -/* convert point ("epoint") to string representation */
 10.1740 -PG_FUNCTION_INFO_V1(pgl_epoint_out);
 10.1741 -Datum pgl_epoint_out(PG_FUNCTION_ARGS) {
 10.1742 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.1743 -  char latstr[PGL_NUMBUFLEN];
 10.1744 -  char lonstr[PGL_NUMBUFLEN];
 10.1745 -  pgl_print_lat(latstr, point->lat);
 10.1746 -  pgl_print_lon(lonstr, point->lon);
 10.1747 -  PG_RETURN_CSTRING(psprintf("%s %s", latstr, lonstr));
 10.1748 -}
 10.1749 -
 10.1750 -/* convert box ("ebox") to string representation */
 10.1751 -PG_FUNCTION_INFO_V1(pgl_ebox_out);
 10.1752 -Datum pgl_ebox_out(PG_FUNCTION_ARGS) {
 10.1753 -  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
 10.1754 -  double lon_min = box->lon_min;
 10.1755 -  double lon_max = box->lon_max;
 10.1756 -  char lat_min_str[PGL_NUMBUFLEN];
 10.1757 -  char lat_max_str[PGL_NUMBUFLEN];
 10.1758 -  char lon_min_str[PGL_NUMBUFLEN];
 10.1759 -  char lon_max_str[PGL_NUMBUFLEN];
 10.1760 -  /* return string "empty" if box is set to be empty */
 10.1761 -  if (box->lat_min > box->lat_max) PG_RETURN_CSTRING("empty");
 10.1762 -  /* use boundaries exceeding W180 or E180 if 180th meridian is enclosed */
 10.1763 -  /* (required since pgl_box_in orders the longitude boundaries) */
 10.1764 -  if (lon_min > lon_max) {
 10.1765 -    if (lon_min + lon_max >= 0) lon_min -= 360;
 10.1766 -    else lon_max += 360;
 10.1767 -  }
 10.1768 -  /* format and return result */
 10.1769 -  pgl_print_lat(lat_min_str, box->lat_min);
 10.1770 -  pgl_print_lat(lat_max_str, box->lat_max);
 10.1771 -  pgl_print_lon(lon_min_str, lon_min);
 10.1772 -  pgl_print_lon(lon_max_str, lon_max);
 10.1773 -  PG_RETURN_CSTRING(psprintf(
 10.1774 -    "%s %s %s %s",
 10.1775 -    lat_min_str, lon_min_str, lat_max_str, lon_max_str
 10.1776 -  ));
 10.1777 -}
 10.1778 -
 10.1779 -/* convert circle ("ecircle") to string representation */
 10.1780 -PG_FUNCTION_INFO_V1(pgl_ecircle_out);
 10.1781 -Datum pgl_ecircle_out(PG_FUNCTION_ARGS) {
 10.1782 -  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
 10.1783 -  char latstr[PGL_NUMBUFLEN];
 10.1784 -  char lonstr[PGL_NUMBUFLEN];
 10.1785 -  char radstr[PGL_NUMBUFLEN];
 10.1786 -  pgl_print_lat(latstr, circle->center.lat);
 10.1787 -  pgl_print_lon(lonstr, circle->center.lon);
 10.1788 -  pgl_print_float(radstr, circle->radius);
 10.1789 -  PG_RETURN_CSTRING(psprintf("%s %s %s", latstr, lonstr, radstr));
 10.1790 -}
 10.1791 -
 10.1792 -/* convert cluster ("ecluster") to string representation */
 10.1793 -PG_FUNCTION_INFO_V1(pgl_ecluster_out);
 10.1794 -Datum pgl_ecluster_out(PG_FUNCTION_ARGS) {
 10.1795 -  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0));
 10.1796 -  char latstr[PGL_NUMBUFLEN];  /* string buffer for latitude */
 10.1797 -  char lonstr[PGL_NUMBUFLEN];  /* string buffer for longitude */
 10.1798 -  char ***strings;     /* array of array of strings */
 10.1799 -  char *string;        /* string of current token */
 10.1800 -  char *res, *resptr;  /* result and pointer to current write position */
 10.1801 -  size_t reslen = 1;   /* length of result (init with 1 for terminator) */
 10.1802 -  int npoints;         /* number of points of current entry */
 10.1803 -  int i, j;            /* i: entry, j: point in entry */
 10.1804 -  /* handle empty clusters */
 10.1805 -  if (cluster->nentries == 0) {
 10.1806 -    /* free detoasted cluster (if copy) */
 10.1807 -    PG_FREE_IF_COPY(cluster, 0);
 10.1808 -    /* return static result */
 10.1809 -    PG_RETURN_CSTRING("empty");
 10.1810 -  }
 10.1811 -  /* allocate array of array of strings */
 10.1812 -  strings = palloc(cluster->nentries * sizeof(char **));
 10.1813 -  /* iterate over all entries in cluster */
 10.1814 -  for (i=0; i<cluster->nentries; i++) {
 10.1815 -    /* get number of points in entry */
 10.1816 -    npoints = cluster->entries[i].npoints;
 10.1817 -    /* allocate array of strings (one string for each point plus two extra) */
 10.1818 -    strings[i] = palloc((2 + npoints) * sizeof(char *));
 10.1819 -    /* determine opening string */
 10.1820 -    switch (cluster->entries[i].entrytype) {
 10.1821 -      case PGL_ENTRY_POINT:   string = (i==0)?"point ("  :" point (";   break;
 10.1822 -      case PGL_ENTRY_PATH:    string = (i==0)?"path ("   :" path (";    break;
 10.1823 -      case PGL_ENTRY_OUTLINE: string = (i==0)?"outline (":" outline ("; break;
 10.1824 -      case PGL_ENTRY_POLYGON: string = (i==0)?"polygon (":" polygon ("; break;
 10.1825 -      default:                string = (i==0)?"unknown"  :" unknown";
 10.1826 -    }
 10.1827 -    /* use opening string as first string in array */
 10.1828 -    strings[i][0] = string;
 10.1829 -    /* update result length (for allocating result string later) */
 10.1830 -    reslen += strlen(string);
 10.1831 -    /* iterate over all points */
 10.1832 -    for (j=0; j<npoints; j++) {
 10.1833 -      /* create string representation of point */
 10.1834 -      pgl_print_lat(latstr, PGL_ENTRY_POINTS(cluster, i)[j].lat);
 10.1835 -      pgl_print_lon(lonstr, PGL_ENTRY_POINTS(cluster, i)[j].lon);
 10.1836 -      string = psprintf((j == 0) ? "%s %s" : " %s %s", latstr, lonstr);
 10.1837 -      /* copy string pointer to string array */
 10.1838 -      strings[i][j+1] = string;
 10.1839 -      /* update result length (for allocating result string later) */
 10.1840 -      reslen += strlen(string);
 10.1841 -    }
 10.1842 -    /* use closing parenthesis as last string in array */
 10.1843 -    strings[i][npoints+1] = ")";
 10.1844 -    /* update result length (for allocating result string later) */
 10.1845 -    reslen++;
 10.1846 -  }
 10.1847 -  /* allocate result string */
 10.1848 -  res = palloc(reslen);
 10.1849 -  /* set write pointer to begin of result string */
 10.1850 -  resptr = res;
 10.1851 -  /* copy strings into result string */
 10.1852 -  for (i=0; i<cluster->nentries; i++) {
 10.1853 -    npoints = cluster->entries[i].npoints;
 10.1854 -    for (j=0; j<npoints+2; j++) {
 10.1855 -      string = strings[i][j];
 10.1856 -      strcpy(resptr, string);
 10.1857 -      resptr += strlen(string);
 10.1858 -      /* free strings allocated by psprintf */
 10.1859 -      if (j != 0 && j != npoints+1) pfree(string);
 10.1860 -    }
 10.1861 -    /* free array of strings */
 10.1862 -    pfree(strings[i]);
 10.1863 -  }
 10.1864 -  /* free array of array of strings */
 10.1865 -  pfree(strings);
 10.1866 -  /* free detoasted cluster (if copy) */
 10.1867 -  PG_FREE_IF_COPY(cluster, 0);
 10.1868 -  /* return result */
 10.1869 -  PG_RETURN_CSTRING(res);
 10.1870 -}
 10.1871 -
 10.1872 -/* binary input function for point ("epoint") */
 10.1873 -PG_FUNCTION_INFO_V1(pgl_epoint_recv);
 10.1874 -Datum pgl_epoint_recv(PG_FUNCTION_ARGS) {
 10.1875 -  StringInfo buf = (StringInfo)PG_GETARG_POINTER(0);
 10.1876 -  pgl_point *point = (pgl_point *)palloc(sizeof(pgl_point));
 10.1877 -  point->lat = pq_getmsgfloat8(buf);
 10.1878 -  point->lon = pq_getmsgfloat8(buf);
 10.1879 -  PG_RETURN_POINTER(point);
 10.1880 -}
 10.1881 -
 10.1882 -/* binary input function for box ("ebox") */
 10.1883 -PG_FUNCTION_INFO_V1(pgl_ebox_recv);
 10.1884 -Datum pgl_ebox_recv(PG_FUNCTION_ARGS) {
 10.1885 -  StringInfo buf = (StringInfo)PG_GETARG_POINTER(0);
 10.1886 -  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
 10.1887 -  box->lat_min = pq_getmsgfloat8(buf);
 10.1888 -  box->lat_max = pq_getmsgfloat8(buf);
 10.1889 -  box->lon_min = pq_getmsgfloat8(buf);
 10.1890 -  box->lon_max = pq_getmsgfloat8(buf);
 10.1891 -  PG_RETURN_POINTER(box);
 10.1892 -}
 10.1893 -
 10.1894 -/* binary input function for circle ("ecircle") */
 10.1895 -PG_FUNCTION_INFO_V1(pgl_ecircle_recv);
 10.1896 -Datum pgl_ecircle_recv(PG_FUNCTION_ARGS) {
 10.1897 -  StringInfo buf = (StringInfo)PG_GETARG_POINTER(0);
 10.1898 -  pgl_circle *circle = (pgl_circle *)palloc(sizeof(pgl_circle));
 10.1899 -  circle->center.lat = pq_getmsgfloat8(buf);
 10.1900 -  circle->center.lon = pq_getmsgfloat8(buf);
 10.1901 -  circle->radius = pq_getmsgfloat8(buf);
 10.1902 -  PG_RETURN_POINTER(circle);
 10.1903 -}
 10.1904 -
 10.1905 -/* TODO: binary receive function for cluster */
 10.1906 -
 10.1907 -/* binary output function for point ("epoint") */
 10.1908 -PG_FUNCTION_INFO_V1(pgl_epoint_send);
 10.1909 -Datum pgl_epoint_send(PG_FUNCTION_ARGS) {
 10.1910 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.1911 -  StringInfoData buf;
 10.1912 -  pq_begintypsend(&buf);
 10.1913 -  pq_sendfloat8(&buf, point->lat);
 10.1914 -  pq_sendfloat8(&buf, point->lon);
 10.1915 -  PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
 10.1916 -}
 10.1917 -
 10.1918 -/* binary output function for box ("ebox") */
 10.1919 -PG_FUNCTION_INFO_V1(pgl_ebox_send);
 10.1920 -Datum pgl_ebox_send(PG_FUNCTION_ARGS) {
 10.1921 -  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
 10.1922 -  StringInfoData buf;
 10.1923 -  pq_begintypsend(&buf);
 10.1924 -  pq_sendfloat8(&buf, box->lat_min);
 10.1925 -  pq_sendfloat8(&buf, box->lat_max);
 10.1926 -  pq_sendfloat8(&buf, box->lon_min);
 10.1927 -  pq_sendfloat8(&buf, box->lon_max);
 10.1928 -  PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
 10.1929 -}
 10.1930 -
 10.1931 -/* binary output function for circle ("ecircle") */
 10.1932 -PG_FUNCTION_INFO_V1(pgl_ecircle_send);
 10.1933 -Datum pgl_ecircle_send(PG_FUNCTION_ARGS) {
 10.1934 -  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
 10.1935 -  StringInfoData buf;
 10.1936 -  pq_begintypsend(&buf);
 10.1937 -  pq_sendfloat8(&buf, circle->center.lat);
 10.1938 -  pq_sendfloat8(&buf, circle->center.lon);
 10.1939 -  pq_sendfloat8(&buf, circle->radius);
 10.1940 -  PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
 10.1941 -}
 10.1942 -
 10.1943 -/* TODO: binary send functions for cluster */
 10.1944 -
 10.1945 -/* cast point ("epoint") to box ("ebox") */
 10.1946 -PG_FUNCTION_INFO_V1(pgl_epoint_to_ebox);
 10.1947 -Datum pgl_epoint_to_ebox(PG_FUNCTION_ARGS) {
 10.1948 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.1949 -  pgl_box *box = palloc(sizeof(pgl_box));
 10.1950 -  box->lat_min = point->lat;
 10.1951 -  box->lat_max = point->lat;
 10.1952 -  box->lon_min = point->lon;
 10.1953 -  box->lon_max = point->lon;
 10.1954 -  PG_RETURN_POINTER(box);
 10.1955 -}
 10.1956 -
 10.1957 -/* cast point ("epoint") to circle ("ecircle") */
 10.1958 -PG_FUNCTION_INFO_V1(pgl_epoint_to_ecircle);
 10.1959 -Datum pgl_epoint_to_ecircle(PG_FUNCTION_ARGS) {
 10.1960 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.1961 -  pgl_circle *circle = palloc(sizeof(pgl_box));
 10.1962 -  circle->center = *point;
 10.1963 -  circle->radius = 0;
 10.1964 -  PG_RETURN_POINTER(circle);
 10.1965 -}
 10.1966 -
 10.1967 -/* cast point ("epoint") to cluster ("ecluster") */
 10.1968 -PG_FUNCTION_INFO_V1(pgl_epoint_to_ecluster);
 10.1969 -Datum pgl_epoint_to_ecluster(PG_FUNCTION_ARGS) {
 10.1970 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.1971 -  pgl_newentry entry;
 10.1972 -  entry.entrytype = PGL_ENTRY_POINT;
 10.1973 -  entry.npoints = 1;
 10.1974 -  entry.points = point;
 10.1975 -  PG_RETURN_POINTER(pgl_new_cluster(1, &entry));
 10.1976 -}
 10.1977 -
 10.1978 -/* cast box ("ebox") to cluster ("ecluster") */
 10.1979 -#define pgl_ebox_to_ecluster_macro(i, a, b) \
 10.1980 -  entries[i].entrytype = PGL_ENTRY_POLYGON; \
 10.1981 -  entries[i].npoints = 4; \
 10.1982 -  entries[i].points = points[i]; \
 10.1983 -  points[i][0].lat = box->lat_min; \
 10.1984 -  points[i][0].lon = (a); \
 10.1985 -  points[i][1].lat = box->lat_min; \
 10.1986 -  points[i][1].lon = (b); \
 10.1987 -  points[i][2].lat = box->lat_max; \
 10.1988 -  points[i][2].lon = (b); \
 10.1989 -  points[i][3].lat = box->lat_max; \
 10.1990 -  points[i][3].lon = (a);
 10.1991 -PG_FUNCTION_INFO_V1(pgl_ebox_to_ecluster);
 10.1992 -Datum pgl_ebox_to_ecluster(PG_FUNCTION_ARGS) {
 10.1993 -  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
 10.1994 -  double lon, dlon;
 10.1995 -  int nentries;
 10.1996 -  pgl_newentry entries[3];
 10.1997 -  pgl_point points[3][4];
 10.1998 -  if (box->lat_min > box->lat_max) {
 10.1999 -    nentries = 0;
 10.2000 -  } else if (box->lon_min > box->lon_max) {
 10.2001 -    if (box->lon_min < 0) {
 10.2002 -      lon = pgl_round((box->lon_min + 180) / 2.0);
 10.2003 -      nentries = 3;
 10.2004 -      pgl_ebox_to_ecluster_macro(0, box->lon_min, lon);
 10.2005 -      pgl_ebox_to_ecluster_macro(1, lon, 180);
 10.2006 -      pgl_ebox_to_ecluster_macro(2, -180, box->lon_max);
 10.2007 -    } else if (box->lon_max > 0) {
 10.2008 -      lon = pgl_round((box->lon_max - 180) / 2.0);
 10.2009 -      nentries = 3;
 10.2010 -      pgl_ebox_to_ecluster_macro(0, box->lon_min, 180);
 10.2011 -      pgl_ebox_to_ecluster_macro(1, -180, lon);
 10.2012 -      pgl_ebox_to_ecluster_macro(2, lon, box->lon_max);
 10.2013 -    } else {
 10.2014 -      nentries = 2;
 10.2015 -      pgl_ebox_to_ecluster_macro(0, box->lon_min, 180);
 10.2016 -      pgl_ebox_to_ecluster_macro(1, -180, box->lon_max);
 10.2017 -    }
 10.2018 -  } else {
 10.2019 -    dlon = pgl_round(box->lon_max - box->lon_min);
 10.2020 -    if (dlon < 180) {
 10.2021 -      nentries = 1;
 10.2022 -      pgl_ebox_to_ecluster_macro(0, box->lon_min, box->lon_max);
 10.2023 -    } else {
 10.2024 -      lon = pgl_round((box->lon_min + box->lon_max) / 2.0);
 10.2025 -      if (
 10.2026 -        pgl_round(lon - box->lon_min) < 180 &&
 10.2027 -        pgl_round(box->lon_max - lon) < 180
 10.2028 -      ) {
 10.2029 -        nentries = 2;
 10.2030 -        pgl_ebox_to_ecluster_macro(0, box->lon_min, lon);
 10.2031 -        pgl_ebox_to_ecluster_macro(1, lon, box->lon_max);
 10.2032 -      } else {
 10.2033 -        nentries = 3;
 10.2034 -        pgl_ebox_to_ecluster_macro(0, box->lon_min, -60);
 10.2035 -        pgl_ebox_to_ecluster_macro(1, -60, 60);
 10.2036 -        pgl_ebox_to_ecluster_macro(2, 60, box->lon_max);
 10.2037 -      }
 10.2038 -    }
 10.2039 -  }
 10.2040 -  PG_RETURN_POINTER(pgl_new_cluster(nentries, entries));
 10.2041 -}
 10.2042 -
 10.2043 -/* extract latitude from point ("epoint") */
 10.2044 -PG_FUNCTION_INFO_V1(pgl_epoint_lat);
 10.2045 -Datum pgl_epoint_lat(PG_FUNCTION_ARGS) {
 10.2046 -  PG_RETURN_FLOAT8(((pgl_point *)PG_GETARG_POINTER(0))->lat);
 10.2047 -}
 10.2048 -
 10.2049 -/* extract longitude from point ("epoint") */
 10.2050 -PG_FUNCTION_INFO_V1(pgl_epoint_lon);
 10.2051 -Datum pgl_epoint_lon(PG_FUNCTION_ARGS) {
 10.2052 -  PG_RETURN_FLOAT8(((pgl_point *)PG_GETARG_POINTER(0))->lon);
 10.2053 -}
 10.2054 -
 10.2055 -/* extract minimum latitude from box ("ebox") */
 10.2056 -PG_FUNCTION_INFO_V1(pgl_ebox_lat_min);
 10.2057 -Datum pgl_ebox_lat_min(PG_FUNCTION_ARGS) {
 10.2058 -  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lat_min);
 10.2059 -}
 10.2060 -
 10.2061 -/* extract maximum latitude from box ("ebox") */
 10.2062 -PG_FUNCTION_INFO_V1(pgl_ebox_lat_max);
 10.2063 -Datum pgl_ebox_lat_max(PG_FUNCTION_ARGS) {
 10.2064 -  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lat_max);
 10.2065 -}
 10.2066 -
 10.2067 -/* extract minimum longitude from box ("ebox") */
 10.2068 -PG_FUNCTION_INFO_V1(pgl_ebox_lon_min);
 10.2069 -Datum pgl_ebox_lon_min(PG_FUNCTION_ARGS) {
 10.2070 -  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lon_min);
 10.2071 -}
 10.2072 -
 10.2073 -/* extract maximum longitude from box ("ebox") */
 10.2074 -PG_FUNCTION_INFO_V1(pgl_ebox_lon_max);
 10.2075 -Datum pgl_ebox_lon_max(PG_FUNCTION_ARGS) {
 10.2076 -  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lon_max);
 10.2077 -}
 10.2078 -
 10.2079 -/* extract center point from circle ("ecircle") */
 10.2080 -PG_FUNCTION_INFO_V1(pgl_ecircle_center);
 10.2081 -Datum pgl_ecircle_center(PG_FUNCTION_ARGS) {
 10.2082 -  PG_RETURN_POINTER(&(((pgl_circle *)PG_GETARG_POINTER(0))->center));
 10.2083 -}
 10.2084 -
 10.2085 -/* extract radius from circle ("ecircle") */
 10.2086 -PG_FUNCTION_INFO_V1(pgl_ecircle_radius);
 10.2087 -Datum pgl_ecircle_radius(PG_FUNCTION_ARGS) {
 10.2088 -  PG_RETURN_FLOAT8(((pgl_circle *)PG_GETARG_POINTER(0))->radius);
 10.2089 -}
 10.2090 -
 10.2091 -/* check if point is inside box (overlap operator "&&") in SQL */
 10.2092 -PG_FUNCTION_INFO_V1(pgl_epoint_ebox_overlap);
 10.2093 -Datum pgl_epoint_ebox_overlap(PG_FUNCTION_ARGS) {
 10.2094 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.2095 -  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(1);
 10.2096 -  PG_RETURN_BOOL(pgl_point_in_box(point, box));
 10.2097 -}
 10.2098 -
 10.2099 -/* check if point is inside circle (overlap operator "&&") in SQL */
 10.2100 -PG_FUNCTION_INFO_V1(pgl_epoint_ecircle_overlap);
 10.2101 -Datum pgl_epoint_ecircle_overlap(PG_FUNCTION_ARGS) {
 10.2102 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.2103 -  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2104 -  PG_RETURN_BOOL(
 10.2105 -    pgl_distance(
 10.2106 -      point->lat, point->lon,
 10.2107 -      circle->center.lat, circle->center.lon
 10.2108 -    ) <= circle->radius
 10.2109 -  );
 10.2110 -}
 10.2111 -
 10.2112 -/* check if point is inside cluster (overlap operator "&&") in SQL */
 10.2113 -PG_FUNCTION_INFO_V1(pgl_epoint_ecluster_overlap);
 10.2114 -Datum pgl_epoint_ecluster_overlap(PG_FUNCTION_ARGS) {
 10.2115 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.2116 -  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
 10.2117 -  bool retval = pgl_point_in_cluster(point, cluster);
 10.2118 -  PG_FREE_IF_COPY(cluster, 1);
 10.2119 -  PG_RETURN_BOOL(retval);
 10.2120 -}
 10.2121 -
 10.2122 -/* check if two boxes overlap (overlap operator "&&") in SQL */
 10.2123 -PG_FUNCTION_INFO_V1(pgl_ebox_overlap);
 10.2124 -Datum pgl_ebox_overlap(PG_FUNCTION_ARGS) {
 10.2125 -  pgl_box *box1 = (pgl_box *)PG_GETARG_POINTER(0);
 10.2126 -  pgl_box *box2 = (pgl_box *)PG_GETARG_POINTER(1);
 10.2127 -  PG_RETURN_BOOL(pgl_boxes_overlap(box1, box2));
 10.2128 -}
 10.2129 -
 10.2130 -/* check if two circles overlap (overlap operator "&&") in SQL */
 10.2131 -PG_FUNCTION_INFO_V1(pgl_ecircle_overlap);
 10.2132 -Datum pgl_ecircle_overlap(PG_FUNCTION_ARGS) {
 10.2133 -  pgl_circle *circle1 = (pgl_circle *)PG_GETARG_POINTER(0);
 10.2134 -  pgl_circle *circle2 = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2135 -  PG_RETURN_BOOL(
 10.2136 -    pgl_distance(
 10.2137 -      circle1->center.lat, circle1->center.lon,
 10.2138 -      circle2->center.lat, circle2->center.lon
 10.2139 -    ) <= circle1->radius + circle2->radius
 10.2140 -  );
 10.2141 -}
 10.2142 -
 10.2143 -/* check if circle and cluster overlap (overlap operator "&&") in SQL */
 10.2144 -PG_FUNCTION_INFO_V1(pgl_ecircle_ecluster_overlap);
 10.2145 -Datum pgl_ecircle_ecluster_overlap(PG_FUNCTION_ARGS) {
 10.2146 -  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
 10.2147 -  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
 10.2148 -  bool retval = (
 10.2149 -    pgl_point_cluster_distance(&(circle->center), cluster) <= circle->radius
 10.2150 -  );
 10.2151 -  PG_FREE_IF_COPY(cluster, 1);
 10.2152 -  PG_RETURN_BOOL(retval);
 10.2153 -}
 10.2154 -
 10.2155 -/* calculate distance between two points ("<->" operator) in SQL */
 10.2156 -PG_FUNCTION_INFO_V1(pgl_epoint_distance);
 10.2157 -Datum pgl_epoint_distance(PG_FUNCTION_ARGS) {
 10.2158 -  pgl_point *point1 = (pgl_point *)PG_GETARG_POINTER(0);
 10.2159 -  pgl_point *point2 = (pgl_point *)PG_GETARG_POINTER(1);
 10.2160 -  PG_RETURN_FLOAT8(pgl_distance(
 10.2161 -    point1->lat, point1->lon, point2->lat, point2->lon
 10.2162 -  ));
 10.2163 -}
 10.2164 -
 10.2165 -/* calculate point to circle distance ("<->" operator) in SQL */
 10.2166 -PG_FUNCTION_INFO_V1(pgl_epoint_ecircle_distance);
 10.2167 -Datum pgl_epoint_ecircle_distance(PG_FUNCTION_ARGS) {
 10.2168 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.2169 -  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2170 -  double distance = pgl_distance(
 10.2171 -    point->lat, point->lon, circle->center.lat, circle->center.lon
 10.2172 -  ) - circle->radius;
 10.2173 -  PG_RETURN_FLOAT8((distance <= 0) ? 0 : distance);
 10.2174 -}
 10.2175 -
 10.2176 -/* calculate point to cluster distance ("<->" operator) in SQL */
 10.2177 -PG_FUNCTION_INFO_V1(pgl_epoint_ecluster_distance);
 10.2178 -Datum pgl_epoint_ecluster_distance(PG_FUNCTION_ARGS) {
 10.2179 -  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
 10.2180 -  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
 10.2181 -  double distance = pgl_point_cluster_distance(point, cluster);
 10.2182 -  PG_FREE_IF_COPY(cluster, 1);
 10.2183 -  PG_RETURN_FLOAT8(distance);
 10.2184 -}
 10.2185 -
 10.2186 -/* calculate distance between two circles ("<->" operator) in SQL */
 10.2187 -PG_FUNCTION_INFO_V1(pgl_ecircle_distance);
 10.2188 -Datum pgl_ecircle_distance(PG_FUNCTION_ARGS) {
 10.2189 -  pgl_circle *circle1 = (pgl_circle *)PG_GETARG_POINTER(0);
 10.2190 -  pgl_circle *circle2 = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2191 -  double distance = pgl_distance(
 10.2192 -    circle1->center.lat, circle1->center.lon,
 10.2193 -    circle2->center.lat, circle2->center.lon
 10.2194 -  ) - (circle1->radius + circle2->radius);
 10.2195 -  PG_RETURN_FLOAT8((distance <= 0) ? 0 : distance);
 10.2196 -}
 10.2197 -
 10.2198 -/* calculate circle to cluster distance ("<->" operator) in SQL */
 10.2199 -PG_FUNCTION_INFO_V1(pgl_ecircle_ecluster_distance);
 10.2200 -Datum pgl_ecircle_ecluster_distance(PG_FUNCTION_ARGS) {
 10.2201 -  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
 10.2202 -  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
 10.2203 -  double distance = (
 10.2204 -    pgl_point_cluster_distance(&(circle->center), cluster) - circle->radius
 10.2205 -  );
 10.2206 -  PG_FREE_IF_COPY(cluster, 1);
 10.2207 -  PG_RETURN_FLOAT8((distance <= 0) ? 0 : distance);
 10.2208 -}
 10.2209 -
 10.2210 -
 10.2211 -/*-----------------------------------------------------------*
 10.2212 - *  B-tree comparison operators and index support functions  *
 10.2213 - *-----------------------------------------------------------*/
 10.2214 -
 10.2215 -/* macro for a B-tree operator (without detoasting) */
 10.2216 -#define PGL_BTREE_OPER(func, type, cmpfunc, oper) \
 10.2217 -  PG_FUNCTION_INFO_V1(func); \
 10.2218 -  Datum func(PG_FUNCTION_ARGS) { \
 10.2219 -    type *a = (type *)PG_GETARG_POINTER(0); \
 10.2220 -    type *b = (type *)PG_GETARG_POINTER(1); \
 10.2221 -    PG_RETURN_BOOL(cmpfunc(a, b) oper 0); \
 10.2222 -  }
 10.2223 -
 10.2224 -/* macro for a B-tree comparison function (without detoasting) */
 10.2225 -#define PGL_BTREE_CMP(func, type, cmpfunc) \
 10.2226 -  PG_FUNCTION_INFO_V1(func); \
 10.2227 -  Datum func(PG_FUNCTION_ARGS) { \
 10.2228 -    type *a = (type *)PG_GETARG_POINTER(0); \
 10.2229 -    type *b = (type *)PG_GETARG_POINTER(1); \
 10.2230 -    PG_RETURN_INT32(cmpfunc(a, b)); \
 10.2231 -  }
 10.2232 -
 10.2233 -/* macro for a B-tree operator (with detoasting) */
 10.2234 -#define PGL_BTREE_OPER_DETOAST(func, type, cmpfunc, oper) \
 10.2235 -  PG_FUNCTION_INFO_V1(func); \
 10.2236 -  Datum func(PG_FUNCTION_ARGS) { \
 10.2237 -    bool res; \
 10.2238 -    type *a = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0)); \
 10.2239 -    type *b = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1)); \
 10.2240 -    res = cmpfunc(a, b) oper 0; \
 10.2241 -    PG_FREE_IF_COPY(a, 0); \
 10.2242 -    PG_FREE_IF_COPY(b, 1); \
 10.2243 -    PG_RETURN_BOOL(res); \
 10.2244 -  }
 10.2245 -
 10.2246 -/* macro for a B-tree comparison function (with detoasting) */
 10.2247 -#define PGL_BTREE_CMP_DETOAST(func, type, cmpfunc) \
 10.2248 -  PG_FUNCTION_INFO_V1(func); \
 10.2249 -  Datum func(PG_FUNCTION_ARGS) { \
 10.2250 -    int32_t res; \
 10.2251 -    type *a = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0)); \
 10.2252 -    type *b = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1)); \
 10.2253 -    res = cmpfunc(a, b); \
 10.2254 -    PG_FREE_IF_COPY(a, 0); \
 10.2255 -    PG_FREE_IF_COPY(b, 1); \
 10.2256 -    PG_RETURN_INT32(res); \
 10.2257 -  }
 10.2258 -
 10.2259 -/* B-tree operators and comparison function for point */
 10.2260 -PGL_BTREE_OPER(pgl_btree_epoint_lt, pgl_point, pgl_point_cmp, <)
 10.2261 -PGL_BTREE_OPER(pgl_btree_epoint_le, pgl_point, pgl_point_cmp, <=)
 10.2262 -PGL_BTREE_OPER(pgl_btree_epoint_eq, pgl_point, pgl_point_cmp, ==)
 10.2263 -PGL_BTREE_OPER(pgl_btree_epoint_ne, pgl_point, pgl_point_cmp, !=)
 10.2264 -PGL_BTREE_OPER(pgl_btree_epoint_ge, pgl_point, pgl_point_cmp, >=)
 10.2265 -PGL_BTREE_OPER(pgl_btree_epoint_gt, pgl_point, pgl_point_cmp, >)
 10.2266 -PGL_BTREE_CMP(pgl_btree_epoint_cmp, pgl_point, pgl_point_cmp)
 10.2267 -
 10.2268 -/* B-tree operators and comparison function for box */
 10.2269 -PGL_BTREE_OPER(pgl_btree_ebox_lt, pgl_box, pgl_box_cmp, <)
 10.2270 -PGL_BTREE_OPER(pgl_btree_ebox_le, pgl_box, pgl_box_cmp, <=)
 10.2271 -PGL_BTREE_OPER(pgl_btree_ebox_eq, pgl_box, pgl_box_cmp, ==)
 10.2272 -PGL_BTREE_OPER(pgl_btree_ebox_ne, pgl_box, pgl_box_cmp, !=)
 10.2273 -PGL_BTREE_OPER(pgl_btree_ebox_ge, pgl_box, pgl_box_cmp, >=)
 10.2274 -PGL_BTREE_OPER(pgl_btree_ebox_gt, pgl_box, pgl_box_cmp, >)
 10.2275 -PGL_BTREE_CMP(pgl_btree_ebox_cmp, pgl_box, pgl_box_cmp)
 10.2276 -
 10.2277 -/* B-tree operators and comparison function for circle */
 10.2278 -PGL_BTREE_OPER(pgl_btree_ecircle_lt, pgl_circle, pgl_circle_cmp, <)
 10.2279 -PGL_BTREE_OPER(pgl_btree_ecircle_le, pgl_circle, pgl_circle_cmp, <=)
 10.2280 -PGL_BTREE_OPER(pgl_btree_ecircle_eq, pgl_circle, pgl_circle_cmp, ==)
 10.2281 -PGL_BTREE_OPER(pgl_btree_ecircle_ne, pgl_circle, pgl_circle_cmp, !=)
 10.2282 -PGL_BTREE_OPER(pgl_btree_ecircle_ge, pgl_circle, pgl_circle_cmp, >=)
 10.2283 -PGL_BTREE_OPER(pgl_btree_ecircle_gt, pgl_circle, pgl_circle_cmp, >)
 10.2284 -PGL_BTREE_CMP(pgl_btree_ecircle_cmp, pgl_circle, pgl_circle_cmp)
 10.2285 -
 10.2286 -
 10.2287 -/*--------------------------------*
 10.2288 - *  GiST index support functions  *
 10.2289 - *--------------------------------*/
 10.2290 -
 10.2291 -/* GiST "consistent" support function */
 10.2292 -PG_FUNCTION_INFO_V1(pgl_gist_consistent);
 10.2293 -Datum pgl_gist_consistent(PG_FUNCTION_ARGS) {
 10.2294 -  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
 10.2295 -  pgl_keyptr key = (pgl_keyptr)DatumGetPointer(entry->key);
 10.2296 -  StrategyNumber strategy = (StrategyNumber)PG_GETARG_UINT16(2);
 10.2297 -  bool *recheck = (bool *)PG_GETARG_POINTER(4);
 10.2298 -  /* demand recheck because index and query methods are lossy */
 10.2299 -  *recheck = true;
 10.2300 -  /* strategy number 11: equality of two points */
 10.2301 -  if (strategy == 11) {
 10.2302 -    /* query datum is another point */
 10.2303 -    pgl_point *query = (pgl_point *)PG_GETARG_POINTER(1);
 10.2304 -    /* convert other point to key */
 10.2305 -    pgl_pointkey querykey;
 10.2306 -    pgl_point_to_key(query, querykey);
 10.2307 -    /* return true if both keys overlap */
 10.2308 -    PG_RETURN_BOOL(pgl_keys_overlap(key, querykey));
 10.2309 -  }
 10.2310 -  /* strategy number 13: equality of two circles */
 10.2311 -  if (strategy == 13) {
 10.2312 -    /* query datum is another circle */
 10.2313 -    pgl_circle *query = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2314 -    /* convert other circle to key */
 10.2315 -    pgl_areakey querykey;
 10.2316 -    pgl_circle_to_key(query, querykey);
 10.2317 -    /* return true if both keys overlap */
 10.2318 -    PG_RETURN_BOOL(pgl_keys_overlap(key, querykey));
 10.2319 -  }
 10.2320 -  /* for all remaining strategies, keys on empty objects produce no match */
 10.2321 -  /* (check necessary because query radius may be infinite) */
 10.2322 -  if (PGL_KEY_IS_EMPTY(key)) PG_RETURN_BOOL(false);
 10.2323 -  /* strategy number 21: overlapping with point */
 10.2324 -  if (strategy == 21) {
 10.2325 -    /* query datum is a point */
 10.2326 -    pgl_point *query = (pgl_point *)PG_GETARG_POINTER(1);
 10.2327 -    /* return true if estimated distance (allowed to be smaller than real
 10.2328 -       distance) between index key and point is zero */
 10.2329 -    PG_RETURN_BOOL(pgl_estimate_key_distance(key, query) == 0);
 10.2330 -  }
 10.2331 -  /* strategy number 22: (point) overlapping with box */
 10.2332 -  if (strategy == 22) {
 10.2333 -    /* query datum is a box */
 10.2334 -    pgl_box *query = (pgl_box *)PG_GETARG_POINTER(1);
 10.2335 -    /* determine bounding box of indexed key */
 10.2336 -    pgl_box keybox;
 10.2337 -    pgl_key_to_box(key, &keybox);
 10.2338 -    /* return true if query box overlaps with bounding box of indexed key */
 10.2339 -    PG_RETURN_BOOL(pgl_boxes_overlap(query, &keybox));
 10.2340 -  }
 10.2341 -  /* strategy number 23: overlapping with circle */
 10.2342 -  if (strategy == 23) {
 10.2343 -    /* query datum is a circle */
 10.2344 -    pgl_circle *query = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2345 -    /* return true if estimated distance (allowed to be smaller than real
 10.2346 -       distance) between index key and circle center is smaller than radius */
 10.2347 -    PG_RETURN_BOOL(
 10.2348 -      pgl_estimate_key_distance(key, &(query->center)) <= query->radius
 10.2349 -    );
 10.2350 -  }
 10.2351 -  /* strategy number 24: overlapping with cluster */
 10.2352 -  if (strategy == 24) {
 10.2353 -    bool retval;  /* return value */
 10.2354 -    /* query datum is a cluster */
 10.2355 -    pgl_cluster *query = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
 10.2356 -    /* return true if estimated distance (allowed to be smaller than real
 10.2357 -       distance) between index key and circle center is smaller than radius */
 10.2358 -    retval = (
 10.2359 -      pgl_estimate_key_distance(key, &(query->bounding.center)) <=
 10.2360 -      query->bounding.radius
 10.2361 -    );
 10.2362 -    PG_FREE_IF_COPY(query, 1);  /* free detoasted cluster (if copy) */
 10.2363 -    PG_RETURN_BOOL(retval);
 10.2364 -  }
 10.2365 -  /* throw error for any unknown strategy number */
 10.2366 -  elog(ERROR, "unrecognized strategy number: %d", strategy);
 10.2367 -}
 10.2368 -
 10.2369 -/* GiST "union" support function */
 10.2370 -PG_FUNCTION_INFO_V1(pgl_gist_union);
 10.2371 -Datum pgl_gist_union(PG_FUNCTION_ARGS) {
 10.2372 -  GistEntryVector *entryvec = (GistEntryVector *)PG_GETARG_POINTER(0);
 10.2373 -  pgl_keyptr out;  /* return value (to be palloc'ed) */
 10.2374 -  int i;
 10.2375 -  /* determine key size */
 10.2376 -  size_t keysize = PGL_KEY_IS_AREAKEY(
 10.2377 -    (pgl_keyptr)DatumGetPointer(entryvec->vector[0].key)
 10.2378 -  ) ? sizeof (pgl_areakey) : sizeof(pgl_pointkey);
 10.2379 -  /* begin with first key as result */
 10.2380 -  out = palloc(keysize);
 10.2381 -  memcpy(out, (pgl_keyptr)DatumGetPointer(entryvec->vector[0].key), keysize);
 10.2382 -  /* unite current result with second, third, etc. key */
 10.2383 -  for (i=1; i<entryvec->n; i++) {
 10.2384 -    pgl_unite_keys(out, (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key));
 10.2385 -  }
 10.2386 -  /* return result */
 10.2387 -  PG_RETURN_POINTER(out);
 10.2388 -}
 10.2389 -
 10.2390 -/* GiST "compress" support function for indicis on points */
 10.2391 -PG_FUNCTION_INFO_V1(pgl_gist_compress_epoint);
 10.2392 -Datum pgl_gist_compress_epoint(PG_FUNCTION_ARGS) {
 10.2393 -  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
 10.2394 -  GISTENTRY *retval;  /* return value (to be palloc'ed unless set to entry) */
 10.2395 -  /* only transform new leaves */
 10.2396 -  if (entry->leafkey) {
 10.2397 -    /* get point to be transformed */
 10.2398 -    pgl_point *point = (pgl_point *)DatumGetPointer(entry->key);
 10.2399 -    /* allocate memory for key */
 10.2400 -    pgl_keyptr key = palloc(sizeof(pgl_pointkey));
 10.2401 -    /* transform point to key */
 10.2402 -    pgl_point_to_key(point, key);
 10.2403 -    /* create new GISTENTRY structure as return value */
 10.2404 -    retval = palloc(sizeof(GISTENTRY));
 10.2405 -    gistentryinit(
 10.2406 -      *retval, PointerGetDatum(key),
 10.2407 -      entry->rel, entry->page, entry->offset, FALSE
 10.2408 -    );
 10.2409 -  } else {
 10.2410 -    /* inner nodes have already been transformed */
 10.2411 -    retval = entry;
 10.2412 -  }
 10.2413 -  /* return pointer to old or new GISTENTRY structure */
 10.2414 -  PG_RETURN_POINTER(retval);
 10.2415 -}
 10.2416 -
 10.2417 -/* GiST "compress" support function for indicis on circles */
 10.2418 -PG_FUNCTION_INFO_V1(pgl_gist_compress_ecircle);
 10.2419 -Datum pgl_gist_compress_ecircle(PG_FUNCTION_ARGS) {
 10.2420 -  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
 10.2421 -  GISTENTRY *retval;  /* return value (to be palloc'ed unless set to entry) */
 10.2422 -  /* only transform new leaves */
 10.2423 -  if (entry->leafkey) {
 10.2424 -    /* get circle to be transformed */
 10.2425 -    pgl_circle *circle = (pgl_circle *)DatumGetPointer(entry->key);
 10.2426 -    /* allocate memory for key */
 10.2427 -    pgl_keyptr key = palloc(sizeof(pgl_areakey));
 10.2428 -    /* transform circle to key */
 10.2429 -    pgl_circle_to_key(circle, key);
 10.2430 -    /* create new GISTENTRY structure as return value */
 10.2431 -    retval = palloc(sizeof(GISTENTRY));
 10.2432 -    gistentryinit(
 10.2433 -      *retval, PointerGetDatum(key),
 10.2434 -      entry->rel, entry->page, entry->offset, FALSE
 10.2435 -    );
 10.2436 -  } else {
 10.2437 -    /* inner nodes have already been transformed */
 10.2438 -    retval = entry;
 10.2439 -  }
 10.2440 -  /* return pointer to old or new GISTENTRY structure */
 10.2441 -  PG_RETURN_POINTER(retval);
 10.2442 -}
 10.2443 -
 10.2444 -/* GiST "compress" support function for indices on clusters */
 10.2445 -PG_FUNCTION_INFO_V1(pgl_gist_compress_ecluster);
 10.2446 -Datum pgl_gist_compress_ecluster(PG_FUNCTION_ARGS) {
 10.2447 -  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
 10.2448 -  GISTENTRY *retval;  /* return value (to be palloc'ed unless set to entry) */
 10.2449 -  /* only transform new leaves */
 10.2450 -  if (entry->leafkey) {
 10.2451 -    /* get cluster to be transformed (detoasting necessary!) */
 10.2452 -    pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(entry->key);
 10.2453 -    /* allocate memory for key */
 10.2454 -    pgl_keyptr key = palloc(sizeof(pgl_areakey));
 10.2455 -    /* transform cluster to key */
 10.2456 -    pgl_circle_to_key(&(cluster->bounding), key);
 10.2457 -    /* create new GISTENTRY structure as return value */
 10.2458 -    retval = palloc(sizeof(GISTENTRY));
 10.2459 -    gistentryinit(
 10.2460 -      *retval, PointerGetDatum(key),
 10.2461 -      entry->rel, entry->page, entry->offset, FALSE
 10.2462 -    );
 10.2463 -    /* free detoasted datum */
 10.2464 -    if ((void *)cluster != (void *)DatumGetPointer(entry->key)) pfree(cluster);
 10.2465 -  } else {
 10.2466 -    /* inner nodes have already been transformed */
 10.2467 -    retval = entry;
 10.2468 -  }
 10.2469 -  /* return pointer to old or new GISTENTRY structure */
 10.2470 -  PG_RETURN_POINTER(retval);
 10.2471 -}
 10.2472 -
 10.2473 -/* GiST "decompress" support function for indices */
 10.2474 -PG_FUNCTION_INFO_V1(pgl_gist_decompress);
 10.2475 -Datum pgl_gist_decompress(PG_FUNCTION_ARGS) {
 10.2476 -  /* return passed pointer without transformation */
 10.2477 -  PG_RETURN_POINTER(PG_GETARG_POINTER(0));
 10.2478 -}
 10.2479 -
 10.2480 -/* GiST "penalty" support function */
 10.2481 -PG_FUNCTION_INFO_V1(pgl_gist_penalty);
 10.2482 -Datum pgl_gist_penalty(PG_FUNCTION_ARGS) {
 10.2483 -  GISTENTRY *origentry = (GISTENTRY *)PG_GETARG_POINTER(0);
 10.2484 -  GISTENTRY *newentry = (GISTENTRY *)PG_GETARG_POINTER(1);
 10.2485 -  float *penalty = (float *)PG_GETARG_POINTER(2);
 10.2486 -  /* get original key and key to insert */
 10.2487 -  pgl_keyptr orig = (pgl_keyptr)DatumGetPointer(origentry->key);
 10.2488 -  pgl_keyptr new = (pgl_keyptr)DatumGetPointer(newentry->key);
 10.2489 -  /* copy original key */
 10.2490 -  union { pgl_pointkey pointkey; pgl_areakey areakey; } union_key;
 10.2491 -  if (PGL_KEY_IS_AREAKEY(orig)) {
 10.2492 -    memcpy(union_key.areakey, orig, sizeof(union_key.areakey));
 10.2493 -  } else {
 10.2494 -    memcpy(union_key.pointkey, orig, sizeof(union_key.pointkey));
 10.2495 -  }
 10.2496 -  /* calculate union of both keys */
 10.2497 -  pgl_unite_keys((pgl_keyptr)&union_key, new);
 10.2498 -  /* penalty equal to reduction of key length (logarithm of added area) */
 10.2499 -  /* (return value by setting referenced value and returning pointer) */
 10.2500 -  *penalty = (
 10.2501 -    PGL_KEY_NODEDEPTH(orig) - PGL_KEY_NODEDEPTH((pgl_keyptr)&union_key)
 10.2502 -  );
 10.2503 -  PG_RETURN_POINTER(penalty);
 10.2504 -}
 10.2505 -
 10.2506 -/* GiST "picksplit" support function */
 10.2507 -PG_FUNCTION_INFO_V1(pgl_gist_picksplit);
 10.2508 -Datum pgl_gist_picksplit(PG_FUNCTION_ARGS) {
 10.2509 -  GistEntryVector *entryvec = (GistEntryVector *)PG_GETARG_POINTER(0);
 10.2510 -  GIST_SPLITVEC *v = (GIST_SPLITVEC *)PG_GETARG_POINTER(1);
 10.2511 -  OffsetNumber i;  /* between FirstOffsetNumber and entryvec->n (inclusive) */
 10.2512 -  union {
 10.2513 -    pgl_pointkey pointkey;
 10.2514 -    pgl_areakey areakey;
 10.2515 -  } union_all;  /* union of all keys (to be calculated from scratch)
 10.2516 -                   (later cut in half) */
 10.2517 -  int is_areakey = PGL_KEY_IS_AREAKEY(
 10.2518 -    (pgl_keyptr)DatumGetPointer(entryvec->vector[FirstOffsetNumber].key)
 10.2519 -  );
 10.2520 -  int keysize = is_areakey ? sizeof(pgl_areakey) : sizeof(pgl_pointkey);
 10.2521 -  pgl_keyptr unionL = palloc(keysize);  /* union of keys that go left */
 10.2522 -  pgl_keyptr unionR = palloc(keysize);  /* union of keys that go right */
 10.2523 -  pgl_keyptr key;  /* current key to be processed */
 10.2524 -  /* allocate memory for array of left and right keys, set counts to zero */
 10.2525 -  v->spl_left = (OffsetNumber *)palloc(entryvec->n * sizeof(OffsetNumber));
 10.2526 -  v->spl_nleft = 0;
 10.2527 -  v->spl_right = (OffsetNumber *)palloc(entryvec->n * sizeof(OffsetNumber));
 10.2528 -  v->spl_nright = 0;
 10.2529 -  /* calculate union of all keys from scratch */
 10.2530 -  memcpy(
 10.2531 -    (pgl_keyptr)&union_all,
 10.2532 -    (pgl_keyptr)DatumGetPointer(entryvec->vector[FirstOffsetNumber].key),
 10.2533 -    keysize
 10.2534 -  );
 10.2535 -  for (i=FirstOffsetNumber+1; i<entryvec->n; i=OffsetNumberNext(i)) {
 10.2536 -    pgl_unite_keys(
 10.2537 -      (pgl_keyptr)&union_all,
 10.2538 -      (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key)
 10.2539 -    );
 10.2540 -  }
 10.2541 -  /* check if trivial split is necessary due to exhausted key length */
 10.2542 -  /* (Note: keys for empty objects must have node depth set to maximum) */
 10.2543 -  if (PGL_KEY_NODEDEPTH((pgl_keyptr)&union_all) == (
 10.2544 -    is_areakey ? PGL_AREAKEY_MAXDEPTH : PGL_POINTKEY_MAXDEPTH
 10.2545 -  )) {
 10.2546 -    /* half of all keys go left */
 10.2547 -    for (
 10.2548 -      i=FirstOffsetNumber;
 10.2549 -      i<FirstOffsetNumber+(entryvec->n - FirstOffsetNumber)/2;
 10.2550 -      i=OffsetNumberNext(i)
 10.2551 -    ) {
 10.2552 -      /* pointer to current key */
 10.2553 -      key = (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key);
 10.2554 -      /* update unionL */
 10.2555 -      /* check if key is first key that goes left */
 10.2556 -      if (!v->spl_nleft) {
 10.2557 -        /* first key that goes left is just copied to unionL */
 10.2558 -        memcpy(unionL, key, keysize);
 10.2559 -      } else {
 10.2560 -        /* unite current value and next key */
 10.2561 -        pgl_unite_keys(unionL, key);
 10.2562 -      }
 10.2563 -      /* append offset number to list of keys that go left */
 10.2564 -      v->spl_left[v->spl_nleft++] = i;
 10.2565 -    }
 10.2566 -    /* other half goes right */
 10.2567 -    for (
 10.2568 -      i=FirstOffsetNumber+(entryvec->n - FirstOffsetNumber)/2;
 10.2569 -      i<entryvec->n;
 10.2570 -      i=OffsetNumberNext(i)
 10.2571 -    ) {
 10.2572 -      /* pointer to current key */
 10.2573 -      key = (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key);
 10.2574 -      /* update unionR */
 10.2575 -      /* check if key is first key that goes right */
 10.2576 -      if (!v->spl_nright) {
 10.2577 -        /* first key that goes right is just copied to unionR */
 10.2578 -        memcpy(unionR, key, keysize);
 10.2579 -      } else {
 10.2580 -        /* unite current value and next key */
 10.2581 -        pgl_unite_keys(unionR, key);
 10.2582 -      }
 10.2583 -      /* append offset number to list of keys that go right */
 10.2584 -      v->spl_right[v->spl_nright++] = i;
 10.2585 -    }
 10.2586 -  }
 10.2587 -  /* otherwise, a non-trivial split is possible */
 10.2588 -  else {
 10.2589 -    /* cut covered area in half */
 10.2590 -    /* (union_all then refers to area of keys that go left) */
 10.2591 -    /* check if union of all keys covers empty and non-empty objects */
 10.2592 -    if (PGL_KEY_IS_UNIVERSAL((pgl_keyptr)&union_all)) {
 10.2593 -      /* if yes, split into empty and non-empty objects */
 10.2594 -      pgl_key_set_empty((pgl_keyptr)&union_all);
 10.2595 -    } else {
 10.2596 -      /* otherwise split by next bit */
 10.2597 -      ((pgl_keyptr)&union_all)[PGL_KEY_NODEDEPTH_OFFSET]++;
 10.2598 -      /* NOTE: type bit conserved */
 10.2599 -    }
 10.2600 -    /* determine for each key if it goes left or right */
 10.2601 -    for (i=FirstOffsetNumber; i<entryvec->n; i=OffsetNumberNext(i)) {
 10.2602 -      /* pointer to current key */
 10.2603 -      key = (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key);
 10.2604 -      /* keys within one half of the area go left */
 10.2605 -      if (pgl_keys_overlap((pgl_keyptr)&union_all, key)) {
 10.2606 -        /* update unionL */
 10.2607 -        /* check if key is first key that goes left */
 10.2608 -        if (!v->spl_nleft) {
 10.2609 -          /* first key that goes left is just copied to unionL */
 10.2610 -          memcpy(unionL, key, keysize);
 10.2611 -        } else {
 10.2612 -          /* unite current value of unionL and processed key */
 10.2613 -          pgl_unite_keys(unionL, key);
 10.2614 -        }
 10.2615 -        /* append offset number to list of keys that go left */
 10.2616 -        v->spl_left[v->spl_nleft++] = i;
 10.2617 -      }
 10.2618 -      /* the other keys go right */
 10.2619 -      else {
 10.2620 -        /* update unionR */
 10.2621 -        /* check if key is first key that goes right */
 10.2622 -        if (!v->spl_nright) {
 10.2623 -          /* first key that goes right is just copied to unionR */
 10.2624 -          memcpy(unionR, key, keysize);
 10.2625 -        } else {
 10.2626 -          /* unite current value of unionR and processed key */
 10.2627 -          pgl_unite_keys(unionR, key);
 10.2628 -        }
 10.2629 -        /* append offset number to list of keys that go right */
 10.2630 -        v->spl_right[v->spl_nright++] = i;
 10.2631 -      }
 10.2632 -    }
 10.2633 -  }
 10.2634 -  /* store unions in return value */
 10.2635 -  v->spl_ldatum = PointerGetDatum(unionL);
 10.2636 -  v->spl_rdatum = PointerGetDatum(unionR);
 10.2637 -  /* return all results */
 10.2638 -  PG_RETURN_POINTER(v);
 10.2639 -}
 10.2640 -
 10.2641 -/* GiST "same"/"equal" support function */
 10.2642 -PG_FUNCTION_INFO_V1(pgl_gist_same);
 10.2643 -Datum pgl_gist_same(PG_FUNCTION_ARGS) {
 10.2644 -  pgl_keyptr key1 = (pgl_keyptr)PG_GETARG_POINTER(0);
 10.2645 -  pgl_keyptr key2 = (pgl_keyptr)PG_GETARG_POINTER(1);
 10.2646 -  bool *boolptr = (bool *)PG_GETARG_POINTER(2);
 10.2647 -  /* two keys are equal if they are binary equal */
 10.2648 -  /* (return result by setting referenced boolean and returning pointer) */
 10.2649 -  *boolptr = !memcmp(
 10.2650 -    key1,
 10.2651 -    key2,
 10.2652 -    PGL_KEY_IS_AREAKEY(key1) ? sizeof(pgl_areakey) : sizeof(pgl_pointkey)
 10.2653 -  );
 10.2654 -  PG_RETURN_POINTER(boolptr);
 10.2655 -}
 10.2656 -
 10.2657 -/* GiST "distance" support function */
 10.2658 -PG_FUNCTION_INFO_V1(pgl_gist_distance);
 10.2659 -Datum pgl_gist_distance(PG_FUNCTION_ARGS) {
 10.2660 -  GISTENTRY *entry = (GISTENTRY *)PG_GETARG_POINTER(0);
 10.2661 -  pgl_keyptr key = (pgl_keyptr)DatumGetPointer(entry->key);
 10.2662 -  StrategyNumber strategy = (StrategyNumber)PG_GETARG_UINT16(2);
 10.2663 -  bool *recheck = (bool *)PG_GETARG_POINTER(4);
 10.2664 -  double distance;  /* return value */
 10.2665 -  /* demand recheck because distance is just an estimation */
 10.2666 -  /* (real distance may be bigger) */
 10.2667 -  *recheck = true;
 10.2668 -  /* strategy number 31: distance to point */
 10.2669 -  if (strategy == 31) {
 10.2670 -    /* query datum is a point */
 10.2671 -    pgl_point *query = (pgl_point *)PG_GETARG_POINTER(1);
 10.2672 -    /* use pgl_estimate_pointkey_distance() function to compute result */
 10.2673 -    distance = pgl_estimate_key_distance(key, query);
 10.2674 -    /* avoid infinity (reserved!) */
 10.2675 -    if (!isfinite(distance)) distance = PGL_ULTRA_DISTANCE;
 10.2676 -    /* return result */
 10.2677 -    PG_RETURN_FLOAT8(distance);
 10.2678 -  }
 10.2679 -  /* strategy number 33: distance to circle */
 10.2680 -  if (strategy == 33) {
 10.2681 -    /* query datum is a circle */
 10.2682 -    pgl_circle *query = (pgl_circle *)PG_GETARG_POINTER(1);
 10.2683 -    /* estimate distance to circle center and substract circle radius */
 10.2684 -    distance = (
 10.2685 -      pgl_estimate_key_distance(key, &(query->center)) - query->radius
 10.2686 -    );
 10.2687 -    /* convert non-positive values to zero and avoid infinity (reserved!) */
 10.2688 -    if (distance <= 0) distance = 0;
 10.2689 -    else if (!isfinite(distance)) distance = PGL_ULTRA_DISTANCE;
 10.2690 -    /* return result */
 10.2691 -    PG_RETURN_FLOAT8(distance);
 10.2692 -  }
 10.2693 -  /* strategy number 34: distance to cluster */
 10.2694 -  if (strategy == 34) {
 10.2695 -    /* query datum is a cluster */
 10.2696 -    pgl_cluster *query = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
 10.2697 -    /* estimate distance to bounding center and substract bounding radius */
 10.2698 -    distance = (
 10.2699 -      pgl_estimate_key_distance(key, &(query->bounding.center)) -
 10.2700 -      query->bounding.radius
 10.2701 -    );
 10.2702 -    /* convert non-positive values to zero and avoid infinity (reserved!) */
 10.2703 -    if (distance <= 0) distance = 0;
 10.2704 -    else if (!isfinite(distance)) distance = PGL_ULTRA_DISTANCE;
 10.2705 -    /* free detoasted cluster (if copy) */
 10.2706 -    PG_FREE_IF_COPY(query, 1);
 10.2707 -    /* return result */
 10.2708 -    PG_RETURN_FLOAT8(distance);
 10.2709 -  }
 10.2710 -  /* throw error for any unknown strategy number */
 10.2711 -  elog(ERROR, "unrecognized strategy number: %d", strategy);
 10.2712 -}
 10.2713 -
    11.1 --- a/pgLatLon/latlon.control	Sun Aug 21 16:28:21 2016 +0200
    11.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
    11.3 @@ -1,4 +0,0 @@
    11.4 -# geographical extension
    11.5 -comment = 'geospatial support'
    11.6 -default_version = '0.1'
    11.7 -relocatable = true
    12.1 --- a/pgLatLon/make-doc.sh	Sun Aug 21 16:28:21 2016 +0200
    12.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
    12.3 @@ -1,8 +0,0 @@
    12.4 -#!/bin/sh
    12.5 -#
    12.6 -# This command can be used to update the README.html file after changing the
    12.7 -# README.mkd file.
    12.8 -
    12.9 -echo "<html><head><title>"`grep '[^ \t\r\n][^ \t\r\n]*' README.mkd | head -n 1`"</title></head><body>" > README.html
   12.10 -markdown2 README.mkd >> README.html
   12.11 -echo "</body></html>" >> README.html

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