1.1 --- a/GNUmakefile	Fri Sep 02 14:32:38 2016 +0200
     1.2 +++ b/GNUmakefile	Sat Sep 03 16:00:22 2016 +0200
     1.3 @@ -1,6 +1,6 @@
     1.4  EXTENSION = latlon
     1.5 -DATA = latlon--0.1--0.2.sql latlon--0.2--0.3.sql latlon--0.3.sql
     1.6 -MODULES = latlon-v0003
     1.7 +DATA = latlon--0.1--0.2.sql latlon--0.2--0.3.sql latlon--0.3.sql latlon--0.4.sql
     1.8 +MODULES = latlon-v0003 latlon-v0004
     1.9  
    1.10  PG_CONFIG = pg_config
    1.11  PGXS := $(shell $(PG_CONFIG) --pgxs)

     2.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.2 +++ b/latlon--0.4.sql	Sat Sep 03 16:00:22 2016 +0200
     2.3 @@ -0,0 +1,1335 @@
     2.4 +
     2.5 +----------------------------------------
     2.6 +-- forward declarations (shell types) --
     2.7 +----------------------------------------
     2.8 +
     2.9 +CREATE TYPE epoint;
    2.10 +CREATE TYPE ebox;
    2.11 +CREATE TYPE ecircle;
    2.12 +CREATE TYPE ecluster;
    2.13 +
    2.14 +
    2.15 +------------------------------------------------------------
    2.16 +-- dummy input/output functions for dummy index key types --
    2.17 +------------------------------------------------------------
    2.18 +
    2.19 +CREATE FUNCTION ekey_point_in_dummy(cstring)
    2.20 +  RETURNS ekey_point
    2.21 +  LANGUAGE C IMMUTABLE STRICT
    2.22 +  AS '$libdir/latlon-v0004', 'pgl_notimpl';
    2.23 +
    2.24 +CREATE FUNCTION ekey_point_out_dummy(ekey_point)
    2.25 +  RETURNS cstring
    2.26 +  LANGUAGE C IMMUTABLE STRICT
    2.27 +  AS '$libdir/latlon-v0004', 'pgl_notimpl';
    2.28 +
    2.29 +CREATE FUNCTION ekey_area_in_dummy(cstring)
    2.30 +  RETURNS ekey_area
    2.31 +  LANGUAGE C IMMUTABLE STRICT
    2.32 +  AS '$libdir/latlon-v0004', 'pgl_notimpl';
    2.33 +
    2.34 +CREATE FUNCTION ekey_area_out_dummy(ekey_area)
    2.35 +  RETURNS cstring
    2.36 +  LANGUAGE C IMMUTABLE STRICT
    2.37 +  AS '$libdir/latlon-v0004', 'pgl_notimpl';
    2.38 +
    2.39 +
    2.40 +--------------------------
    2.41 +-- text input functions --
    2.42 +--------------------------
    2.43 +
    2.44 +CREATE FUNCTION epoint_in(cstring)
    2.45 +  RETURNS epoint
    2.46 +  LANGUAGE C IMMUTABLE STRICT
    2.47 +  AS '$libdir/latlon-v0004', 'pgl_epoint_in';
    2.48 +
    2.49 +CREATE FUNCTION ebox_in(cstring)
    2.50 +  RETURNS ebox
    2.51 +  LANGUAGE C IMMUTABLE STRICT
    2.52 +  AS '$libdir/latlon-v0004', 'pgl_ebox_in';
    2.53 +
    2.54 +CREATE FUNCTION ecircle_in(cstring)
    2.55 +  RETURNS ecircle
    2.56 +  LANGUAGE C IMMUTABLE STRICT
    2.57 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_in';
    2.58 +
    2.59 +CREATE FUNCTION ecluster_in(cstring)
    2.60 +  RETURNS ecluster
    2.61 +  LANGUAGE C IMMUTABLE STRICT
    2.62 +  AS '$libdir/latlon-v0004', 'pgl_ecluster_in';
    2.63 +
    2.64 +
    2.65 +---------------------------
    2.66 +-- text output functions --
    2.67 +---------------------------
    2.68 +
    2.69 +CREATE FUNCTION epoint_out(epoint)
    2.70 +  RETURNS cstring
    2.71 +  LANGUAGE C IMMUTABLE STRICT
    2.72 +  AS '$libdir/latlon-v0004', 'pgl_epoint_out';
    2.73 +
    2.74 +CREATE FUNCTION ebox_out(ebox)
    2.75 +  RETURNS cstring
    2.76 +  LANGUAGE C IMMUTABLE STRICT
    2.77 +  AS '$libdir/latlon-v0004', 'pgl_ebox_out';
    2.78 +
    2.79 +CREATE FUNCTION ecircle_out(ecircle)
    2.80 +  RETURNS cstring
    2.81 +  LANGUAGE C IMMUTABLE STRICT
    2.82 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_out';
    2.83 +
    2.84 +CREATE FUNCTION ecluster_out(ecluster)
    2.85 +  RETURNS cstring
    2.86 +  LANGUAGE C IMMUTABLE STRICT
    2.87 +  AS '$libdir/latlon-v0004', 'pgl_ecluster_out';
    2.88 +
    2.89 +
    2.90 +--------------------------
    2.91 +-- binary I/O functions --
    2.92 +--------------------------
    2.93 +
    2.94 +CREATE FUNCTION epoint_recv(internal)
    2.95 +  RETURNS epoint
    2.96 +  LANGUAGE C IMMUTABLE STRICT
    2.97 +  AS '$libdir/latlon-v0004', 'pgl_epoint_recv';
    2.98 +
    2.99 +CREATE FUNCTION ebox_recv(internal)
   2.100 +  RETURNS ebox
   2.101 +  LANGUAGE C IMMUTABLE STRICT
   2.102 +  AS '$libdir/latlon-v0004', 'pgl_ebox_recv';
   2.103 +
   2.104 +CREATE FUNCTION ecircle_recv(internal)
   2.105 +  RETURNS ecircle
   2.106 +  LANGUAGE C IMMUTABLE STRICT
   2.107 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_recv';
   2.108 +
   2.109 +CREATE FUNCTION epoint_send(epoint)
   2.110 +  RETURNS bytea
   2.111 +  LANGUAGE C IMMUTABLE STRICT
   2.112 +  AS '$libdir/latlon-v0004', 'pgl_epoint_send';
   2.113 +
   2.114 +CREATE FUNCTION ebox_send(ebox)
   2.115 +  RETURNS bytea
   2.116 +  LANGUAGE C IMMUTABLE STRICT
   2.117 +  AS '$libdir/latlon-v0004', 'pgl_ebox_send';
   2.118 +
   2.119 +CREATE FUNCTION ecircle_send(ecircle)
   2.120 +  RETURNS bytea
   2.121 +  LANGUAGE C IMMUTABLE STRICT
   2.122 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_send';
   2.123 +
   2.124 +
   2.125 +-----------------------------------------------
   2.126 +-- type definitions of dummy index key types --
   2.127 +-----------------------------------------------
   2.128 +
   2.129 +CREATE TYPE ekey_point (
   2.130 +  internallength = 8,
   2.131 +  input = ekey_point_in_dummy,
   2.132 +  output = ekey_point_out_dummy,
   2.133 +  alignment = char );
   2.134 +
   2.135 +CREATE TYPE ekey_area (
   2.136 +  internallength = 9,
   2.137 +  input = ekey_area_in_dummy,
   2.138 +  output = ekey_area_out_dummy,
   2.139 +  alignment = char );
   2.140 +
   2.141 +
   2.142 +------------------------------------------
   2.143 +-- definitions of geographic data types --
   2.144 +------------------------------------------
   2.145 +
   2.146 +CREATE TYPE epoint (
   2.147 +  internallength = 16,
   2.148 +  input = epoint_in,
   2.149 +  output = epoint_out,
   2.150 +  receive = epoint_recv,
   2.151 +  send = epoint_send,
   2.152 +  alignment = double );
   2.153 +
   2.154 +CREATE TYPE ebox (
   2.155 +  internallength = 32,
   2.156 +  input = ebox_in,
   2.157 +  output = ebox_out,
   2.158 +  receive = ebox_recv,
   2.159 +  send = ebox_send,
   2.160 +  alignment = double );
   2.161 +
   2.162 +CREATE TYPE ecircle (
   2.163 +  internallength = 24,
   2.164 +  input = ecircle_in,
   2.165 +  output = ecircle_out,
   2.166 +  receive = ecircle_recv,
   2.167 +  send = ecircle_send,
   2.168 +  alignment = double );
   2.169 +
   2.170 +CREATE TYPE ecluster (
   2.171 +  internallength = VARIABLE,
   2.172 +  input = ecluster_in,
   2.173 +  output = ecluster_out,
   2.174 +  alignment = double,
   2.175 +  storage = external );
   2.176 +
   2.177 +
   2.178 +--------------------
   2.179 +-- B-tree support --
   2.180 +--------------------
   2.181 +
   2.182 +-- begin of B-tree support for epoint
   2.183 +
   2.184 +CREATE FUNCTION epoint_btree_lt(epoint, epoint)
   2.185 +  RETURNS boolean
   2.186 +  LANGUAGE C IMMUTABLE STRICT
   2.187 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_lt';
   2.188 +
   2.189 +CREATE FUNCTION epoint_btree_le(epoint, epoint)
   2.190 +  RETURNS boolean
   2.191 +  LANGUAGE C IMMUTABLE STRICT
   2.192 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_le';
   2.193 +
   2.194 +CREATE FUNCTION epoint_btree_eq(epoint, epoint)
   2.195 +  RETURNS boolean
   2.196 +  LANGUAGE C IMMUTABLE STRICT
   2.197 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_eq';
   2.198 +
   2.199 +CREATE FUNCTION epoint_btree_ne(epoint, epoint)
   2.200 +  RETURNS boolean
   2.201 +  LANGUAGE C IMMUTABLE STRICT
   2.202 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_ne';
   2.203 +
   2.204 +CREATE FUNCTION epoint_btree_ge(epoint, epoint)
   2.205 +  RETURNS boolean
   2.206 +  LANGUAGE C IMMUTABLE STRICT
   2.207 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_ge';
   2.208 +
   2.209 +CREATE FUNCTION epoint_btree_gt(epoint, epoint)
   2.210 +  RETURNS boolean
   2.211 +  LANGUAGE C IMMUTABLE STRICT
   2.212 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_gt';
   2.213 +
   2.214 +CREATE OPERATOR <<< (
   2.215 +  leftarg = epoint,
   2.216 +  rightarg = epoint,
   2.217 +  procedure = epoint_btree_lt,
   2.218 +  commutator = >>>,
   2.219 +  negator = >>>=,
   2.220 +  restrict = scalarltsel,
   2.221 +  join = scalarltjoinsel
   2.222 +);
   2.223 +
   2.224 +CREATE OPERATOR <<<= (
   2.225 +  leftarg = epoint,
   2.226 +  rightarg = epoint,
   2.227 +  procedure = epoint_btree_le,
   2.228 +  commutator = >>>=,
   2.229 +  negator = >>>,
   2.230 +  restrict = scalarltsel,
   2.231 +  join = scalarltjoinsel
   2.232 +);
   2.233 +
   2.234 +CREATE OPERATOR = (
   2.235 +  leftarg = epoint,
   2.236 +  rightarg = epoint,
   2.237 +  procedure = epoint_btree_eq,
   2.238 +  commutator = =,
   2.239 +  negator = <>,
   2.240 +  restrict = eqsel,
   2.241 +  join = eqjoinsel,
   2.242 +  merges
   2.243 +);
   2.244 +
   2.245 +CREATE OPERATOR <> (
   2.246 +  leftarg = epoint,
   2.247 +  rightarg = epoint,
   2.248 +  procedure = epoint_btree_eq,
   2.249 +  commutator = <>,
   2.250 +  negator = =,
   2.251 +  restrict = neqsel,
   2.252 +  join = neqjoinsel
   2.253 +);
   2.254 +
   2.255 +CREATE OPERATOR >>>= (
   2.256 +  leftarg = epoint,
   2.257 +  rightarg = epoint,
   2.258 +  procedure = epoint_btree_ge,
   2.259 +  commutator = <<<=,
   2.260 +  negator = <<<,
   2.261 +  restrict = scalargtsel,
   2.262 +  join = scalargtjoinsel
   2.263 +);
   2.264 +
   2.265 +CREATE OPERATOR >>> (
   2.266 +  leftarg = epoint,
   2.267 +  rightarg = epoint,
   2.268 +  procedure = epoint_btree_gt,
   2.269 +  commutator = <<<,
   2.270 +  negator = <<<=,
   2.271 +  restrict = scalargtsel,
   2.272 +  join = scalargtjoinsel
   2.273 +);
   2.274 +
   2.275 +CREATE FUNCTION epoint_btree_cmp(epoint, epoint)
   2.276 +  RETURNS int4
   2.277 +  LANGUAGE C IMMUTABLE STRICT
   2.278 +  AS '$libdir/latlon-v0004', 'pgl_btree_epoint_cmp';
   2.279 +
   2.280 +CREATE OPERATOR CLASS epoint_btree_ops
   2.281 +  DEFAULT FOR TYPE epoint USING btree AS
   2.282 +  OPERATOR 1 <<< ,
   2.283 +  OPERATOR 2 <<<= ,
   2.284 +  OPERATOR 3 = ,
   2.285 +  OPERATOR 4 >>>= ,
   2.286 +  OPERATOR 5 >>> ,
   2.287 +  FUNCTION 1 epoint_btree_cmp(epoint, epoint);
   2.288 +
   2.289 +-- end of B-tree support for epoint
   2.290 +
   2.291 +-- begin of B-tree support for ebox
   2.292 +
   2.293 +CREATE FUNCTION ebox_btree_lt(ebox, ebox)
   2.294 +  RETURNS boolean
   2.295 +  LANGUAGE C IMMUTABLE STRICT
   2.296 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_lt';
   2.297 +
   2.298 +CREATE FUNCTION ebox_btree_le(ebox, ebox)
   2.299 +  RETURNS boolean
   2.300 +  LANGUAGE C IMMUTABLE STRICT
   2.301 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_le';
   2.302 +
   2.303 +CREATE FUNCTION ebox_btree_eq(ebox, ebox)
   2.304 +  RETURNS boolean
   2.305 +  LANGUAGE C IMMUTABLE STRICT
   2.306 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_eq';
   2.307 +
   2.308 +CREATE FUNCTION ebox_btree_ne(ebox, ebox)
   2.309 +  RETURNS boolean
   2.310 +  LANGUAGE C IMMUTABLE STRICT
   2.311 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_ne';
   2.312 +
   2.313 +CREATE FUNCTION ebox_btree_ge(ebox, ebox)
   2.314 +  RETURNS boolean
   2.315 +  LANGUAGE C IMMUTABLE STRICT
   2.316 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_ge';
   2.317 +
   2.318 +CREATE FUNCTION ebox_btree_gt(ebox, ebox)
   2.319 +  RETURNS boolean
   2.320 +  LANGUAGE C IMMUTABLE STRICT
   2.321 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_gt';
   2.322 +
   2.323 +CREATE OPERATOR <<< (
   2.324 +  leftarg = ebox,
   2.325 +  rightarg = ebox,
   2.326 +  procedure = ebox_btree_lt,
   2.327 +  commutator = >>>,
   2.328 +  negator = >>>=,
   2.329 +  restrict = scalarltsel,
   2.330 +  join = scalarltjoinsel
   2.331 +);
   2.332 +
   2.333 +CREATE OPERATOR <<<= (
   2.334 +  leftarg = ebox,
   2.335 +  rightarg = ebox,
   2.336 +  procedure = ebox_btree_le,
   2.337 +  commutator = >>>=,
   2.338 +  negator = >>>,
   2.339 +  restrict = scalarltsel,
   2.340 +  join = scalarltjoinsel
   2.341 +);
   2.342 +
   2.343 +CREATE OPERATOR = (
   2.344 +  leftarg = ebox,
   2.345 +  rightarg = ebox,
   2.346 +  procedure = ebox_btree_eq,
   2.347 +  commutator = =,
   2.348 +  negator = <>,
   2.349 +  restrict = eqsel,
   2.350 +  join = eqjoinsel,
   2.351 +  merges
   2.352 +);
   2.353 +
   2.354 +CREATE OPERATOR <> (
   2.355 +  leftarg = ebox,
   2.356 +  rightarg = ebox,
   2.357 +  procedure = ebox_btree_eq,
   2.358 +  commutator = <>,
   2.359 +  negator = =,
   2.360 +  restrict = neqsel,
   2.361 +  join = neqjoinsel
   2.362 +);
   2.363 +
   2.364 +CREATE OPERATOR >>>= (
   2.365 +  leftarg = ebox,
   2.366 +  rightarg = ebox,
   2.367 +  procedure = ebox_btree_ge,
   2.368 +  commutator = <<<=,
   2.369 +  negator = <<<,
   2.370 +  restrict = scalargtsel,
   2.371 +  join = scalargtjoinsel
   2.372 +);
   2.373 +
   2.374 +CREATE OPERATOR >>> (
   2.375 +  leftarg = ebox,
   2.376 +  rightarg = ebox,
   2.377 +  procedure = ebox_btree_gt,
   2.378 +  commutator = <<<,
   2.379 +  negator = <<<=,
   2.380 +  restrict = scalargtsel,
   2.381 +  join = scalargtjoinsel
   2.382 +);
   2.383 +
   2.384 +CREATE FUNCTION ebox_btree_cmp(ebox, ebox)
   2.385 +  RETURNS int4
   2.386 +  LANGUAGE C IMMUTABLE STRICT
   2.387 +  AS '$libdir/latlon-v0004', 'pgl_btree_ebox_cmp';
   2.388 +
   2.389 +CREATE OPERATOR CLASS ebox_btree_ops
   2.390 +  DEFAULT FOR TYPE ebox USING btree AS
   2.391 +  OPERATOR 1 <<< ,
   2.392 +  OPERATOR 2 <<<= ,
   2.393 +  OPERATOR 3 = ,
   2.394 +  OPERATOR 4 >>>= ,
   2.395 +  OPERATOR 5 >>> ,
   2.396 +  FUNCTION 1 ebox_btree_cmp(ebox, ebox);
   2.397 +
   2.398 +-- end of B-tree support for ebox
   2.399 +
   2.400 +-- begin of B-tree support for ecircle
   2.401 +
   2.402 +CREATE FUNCTION ecircle_btree_lt(ecircle, ecircle)
   2.403 +  RETURNS boolean
   2.404 +  LANGUAGE C IMMUTABLE STRICT
   2.405 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_lt';
   2.406 +
   2.407 +CREATE FUNCTION ecircle_btree_le(ecircle, ecircle)
   2.408 +  RETURNS boolean
   2.409 +  LANGUAGE C IMMUTABLE STRICT
   2.410 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_le';
   2.411 +
   2.412 +CREATE FUNCTION ecircle_btree_eq(ecircle, ecircle)
   2.413 +  RETURNS boolean
   2.414 +  LANGUAGE C IMMUTABLE STRICT
   2.415 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_eq';
   2.416 +
   2.417 +CREATE FUNCTION ecircle_btree_ne(ecircle, ecircle)
   2.418 +  RETURNS boolean
   2.419 +  LANGUAGE C IMMUTABLE STRICT
   2.420 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_ne';
   2.421 +
   2.422 +CREATE FUNCTION ecircle_btree_ge(ecircle, ecircle)
   2.423 +  RETURNS boolean
   2.424 +  LANGUAGE C IMMUTABLE STRICT
   2.425 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_ge';
   2.426 +
   2.427 +CREATE FUNCTION ecircle_btree_gt(ecircle, ecircle)
   2.428 +  RETURNS boolean
   2.429 +  LANGUAGE C IMMUTABLE STRICT
   2.430 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_gt';
   2.431 +
   2.432 +CREATE OPERATOR <<< (
   2.433 +  leftarg = ecircle,
   2.434 +  rightarg = ecircle,
   2.435 +  procedure = ecircle_btree_lt,
   2.436 +  commutator = >>>,
   2.437 +  negator = >>>=,
   2.438 +  restrict = scalarltsel,
   2.439 +  join = scalarltjoinsel
   2.440 +);
   2.441 +
   2.442 +CREATE OPERATOR <<<= (
   2.443 +  leftarg = ecircle,
   2.444 +  rightarg = ecircle,
   2.445 +  procedure = ecircle_btree_le,
   2.446 +  commutator = >>>=,
   2.447 +  negator = >>>,
   2.448 +  restrict = scalarltsel,
   2.449 +  join = scalarltjoinsel
   2.450 +);
   2.451 +
   2.452 +CREATE OPERATOR = (
   2.453 +  leftarg = ecircle,
   2.454 +  rightarg = ecircle,
   2.455 +  procedure = ecircle_btree_eq,
   2.456 +  commutator = =,
   2.457 +  negator = <>,
   2.458 +  restrict = eqsel,
   2.459 +  join = eqjoinsel,
   2.460 +  merges
   2.461 +);
   2.462 +
   2.463 +CREATE OPERATOR <> (
   2.464 +  leftarg = ecircle,
   2.465 +  rightarg = ecircle,
   2.466 +  procedure = ecircle_btree_eq,
   2.467 +  commutator = <>,
   2.468 +  negator = =,
   2.469 +  restrict = neqsel,
   2.470 +  join = neqjoinsel
   2.471 +);
   2.472 +
   2.473 +CREATE OPERATOR >>>= (
   2.474 +  leftarg = ecircle,
   2.475 +  rightarg = ecircle,
   2.476 +  procedure = ecircle_btree_ge,
   2.477 +  commutator = <<<=,
   2.478 +  negator = <<<,
   2.479 +  restrict = scalargtsel,
   2.480 +  join = scalargtjoinsel
   2.481 +);
   2.482 +
   2.483 +CREATE OPERATOR >>> (
   2.484 +  leftarg = ecircle,
   2.485 +  rightarg = ecircle,
   2.486 +  procedure = ecircle_btree_gt,
   2.487 +  commutator = <<<,
   2.488 +  negator = <<<=,
   2.489 +  restrict = scalargtsel,
   2.490 +  join = scalargtjoinsel
   2.491 +);
   2.492 +
   2.493 +CREATE FUNCTION ecircle_btree_cmp(ecircle, ecircle)
   2.494 +  RETURNS int4
   2.495 +  LANGUAGE C IMMUTABLE STRICT
   2.496 +  AS '$libdir/latlon-v0004', 'pgl_btree_ecircle_cmp';
   2.497 +
   2.498 +CREATE OPERATOR CLASS ecircle_btree_ops
   2.499 +  DEFAULT FOR TYPE ecircle USING btree AS
   2.500 +  OPERATOR 1 <<< ,
   2.501 +  OPERATOR 2 <<<= ,
   2.502 +  OPERATOR 3 = ,
   2.503 +  OPERATOR 4 >>>= ,
   2.504 +  OPERATOR 5 >>> ,
   2.505 +  FUNCTION 1 ecircle_btree_cmp(ecircle, ecircle);
   2.506 +
   2.507 +-- end of B-tree support for ecircle
   2.508 +
   2.509 +
   2.510 +----------------
   2.511 +-- type casts --
   2.512 +----------------
   2.513 +
   2.514 +CREATE FUNCTION cast_epoint_to_ebox(epoint)
   2.515 +  RETURNS ebox
   2.516 +  LANGUAGE C IMMUTABLE STRICT
   2.517 +  AS '$libdir/latlon-v0004', 'pgl_epoint_to_ebox';
   2.518 +
   2.519 +CREATE CAST (epoint AS ebox) WITH FUNCTION cast_epoint_to_ebox(epoint);
   2.520 +
   2.521 +CREATE FUNCTION cast_epoint_to_ecircle(epoint)
   2.522 +  RETURNS ecircle
   2.523 +  LANGUAGE C IMMUTABLE STRICT
   2.524 +  AS '$libdir/latlon-v0004', 'pgl_epoint_to_ecircle';
   2.525 +
   2.526 +CREATE CAST (epoint AS ecircle) WITH FUNCTION cast_epoint_to_ecircle(epoint);
   2.527 +
   2.528 +CREATE FUNCTION cast_epoint_to_ecluster(epoint)
   2.529 +  RETURNS ecluster
   2.530 +  LANGUAGE C IMMUTABLE STRICT
   2.531 +  AS '$libdir/latlon-v0004', 'pgl_epoint_to_ecluster';
   2.532 +
   2.533 +CREATE CAST (epoint AS ecluster) WITH FUNCTION cast_epoint_to_ecluster(epoint);
   2.534 +
   2.535 +CREATE FUNCTION cast_ebox_to_ecluster(ebox)
   2.536 +  RETURNS ecluster
   2.537 +  LANGUAGE C IMMUTABLE STRICT
   2.538 +  AS '$libdir/latlon-v0004', 'pgl_ebox_to_ecluster';
   2.539 +
   2.540 +CREATE CAST (ebox AS ecluster) WITH FUNCTION cast_ebox_to_ecluster(ebox);
   2.541 +
   2.542 +
   2.543 +---------------------------
   2.544 +-- constructor functions --
   2.545 +---------------------------
   2.546 +
   2.547 +CREATE FUNCTION epoint(float8, float8)
   2.548 +  RETURNS epoint
   2.549 +  LANGUAGE C IMMUTABLE STRICT
   2.550 +  AS '$libdir/latlon-v0004', 'pgl_create_epoint';
   2.551 +
   2.552 +CREATE FUNCTION epoint_latlon(float8, float8)
   2.553 +  RETURNS epoint
   2.554 +  LANGUAGE SQL IMMUTABLE STRICT AS $$
   2.555 +    SELECT epoint($1, $2)
   2.556 +  $$;
   2.557 +
   2.558 +CREATE FUNCTION epoint_lonlat(float8, float8)
   2.559 +  RETURNS epoint
   2.560 +  LANGUAGE SQL IMMUTABLE STRICT AS $$
   2.561 +    SELECT epoint($2, $1)
   2.562 +  $$;
   2.563 +
   2.564 +CREATE FUNCTION empty_ebox()
   2.565 +  RETURNS ebox
   2.566 +  LANGUAGE C IMMUTABLE STRICT
   2.567 +  AS '$libdir/latlon-v0004', 'pgl_create_empty_ebox';
   2.568 +
   2.569 +CREATE FUNCTION ebox(float8, float8, float8, float8)
   2.570 +  RETURNS ebox
   2.571 +  LANGUAGE C IMMUTABLE STRICT
   2.572 +  AS '$libdir/latlon-v0004', 'pgl_create_ebox';
   2.573 +
   2.574 +CREATE FUNCTION ebox(epoint, epoint)
   2.575 +  RETURNS ebox
   2.576 +  LANGUAGE C IMMUTABLE STRICT
   2.577 +  AS '$libdir/latlon-v0004', 'pgl_create_ebox_from_epoints';
   2.578 +
   2.579 +CREATE FUNCTION ecircle(float8, float8, float8)
   2.580 +  RETURNS ecircle
   2.581 +  LANGUAGE C IMMUTABLE STRICT
   2.582 +  AS '$libdir/latlon-v0004', 'pgl_create_ecircle';
   2.583 +
   2.584 +CREATE FUNCTION ecircle(epoint, float8)
   2.585 +  RETURNS ecircle
   2.586 +  LANGUAGE C IMMUTABLE STRICT
   2.587 +  AS '$libdir/latlon-v0004', 'pgl_create_ecircle_from_epoint';
   2.588 +
   2.589 +CREATE FUNCTION ecluster_concat(ecluster[])
   2.590 +  RETURNS ecluster
   2.591 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.592 +    SELECT array_to_string($1, ' ')::ecluster
   2.593 +  $$;
   2.594 +
   2.595 +CREATE FUNCTION ecluster_concat(ecluster, ecluster)
   2.596 +  RETURNS ecluster
   2.597 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.598 +    SELECT ($1::text || ' ' || $2::text)::ecluster
   2.599 +  $$;
   2.600 +
   2.601 +CREATE FUNCTION ecluster_create_multipoint(epoint[])
   2.602 +  RETURNS ecluster
   2.603 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.604 +    SELECT
   2.605 +      array_to_string(array_agg('point (' || unnest || ')'), ' ')::ecluster
   2.606 +    FROM unnest($1)
   2.607 +  $$;
   2.608 +
   2.609 +CREATE FUNCTION ecluster_create_path(epoint[])
   2.610 +  RETURNS ecluster
   2.611 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.612 +    SELECT CASE WHEN "str" = '' THEN 'empty'::ecluster ELSE
   2.613 +      ('path (' || array_to_string($1, ' ') || ')')::ecluster
   2.614 +    END
   2.615 +    FROM array_to_string($1, ' ') AS "str"
   2.616 +  $$;
   2.617 +
   2.618 +CREATE FUNCTION ecluster_create_outline(epoint[])
   2.619 +  RETURNS ecluster
   2.620 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.621 +    SELECT CASE WHEN "str" = '' THEN 'empty'::ecluster ELSE
   2.622 +      ('outline (' || array_to_string($1, ' ') || ')')::ecluster
   2.623 +    END
   2.624 +    FROM array_to_string($1, ' ') AS "str"
   2.625 +  $$;
   2.626 +
   2.627 +CREATE FUNCTION ecluster_create_polygon(epoint[])
   2.628 +  RETURNS ecluster
   2.629 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.630 +    SELECT CASE WHEN "str" = '' THEN 'empty'::ecluster ELSE
   2.631 +      ('polygon (' || array_to_string($1, ' ') || ')')::ecluster
   2.632 +    END
   2.633 +    FROM array_to_string($1, ' ') AS "str"
   2.634 +  $$;
   2.635 +
   2.636 +
   2.637 +----------------------
   2.638 +-- getter functions --
   2.639 +----------------------
   2.640 +
   2.641 +CREATE FUNCTION latitude(epoint)
   2.642 +  RETURNS float8
   2.643 +  LANGUAGE C IMMUTABLE STRICT
   2.644 +  AS '$libdir/latlon-v0004', 'pgl_epoint_lat';
   2.645 +
   2.646 +CREATE FUNCTION longitude(epoint)
   2.647 +  RETURNS float8
   2.648 +  LANGUAGE C IMMUTABLE STRICT
   2.649 +  AS '$libdir/latlon-v0004', 'pgl_epoint_lon';
   2.650 +
   2.651 +CREATE FUNCTION min_latitude(ebox)
   2.652 +  RETURNS float8
   2.653 +  LANGUAGE C IMMUTABLE STRICT
   2.654 +  AS '$libdir/latlon-v0004', 'pgl_ebox_lat_min';
   2.655 +
   2.656 +CREATE FUNCTION max_latitude(ebox)
   2.657 +  RETURNS float8
   2.658 +  LANGUAGE C IMMUTABLE STRICT
   2.659 +  AS '$libdir/latlon-v0004', 'pgl_ebox_lat_max';
   2.660 +
   2.661 +CREATE FUNCTION min_longitude(ebox)
   2.662 +  RETURNS float8
   2.663 +  LANGUAGE C IMMUTABLE STRICT
   2.664 +  AS '$libdir/latlon-v0004', 'pgl_ebox_lon_min';
   2.665 +
   2.666 +CREATE FUNCTION max_longitude(ebox)
   2.667 +  RETURNS float8
   2.668 +  LANGUAGE C IMMUTABLE STRICT
   2.669 +  AS '$libdir/latlon-v0004', 'pgl_ebox_lon_max';
   2.670 +
   2.671 +CREATE FUNCTION center(ecircle)
   2.672 +  RETURNS epoint
   2.673 +  LANGUAGE C IMMUTABLE STRICT
   2.674 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_center';
   2.675 +
   2.676 +CREATE FUNCTION radius(ecircle)
   2.677 +  RETURNS float8
   2.678 +  LANGUAGE C IMMUTABLE STRICT
   2.679 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_radius';
   2.680 +
   2.681 +CREATE FUNCTION ecluster_extract_points(ecluster)
   2.682 +  RETURNS SETOF epoint
   2.683 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.684 +    SELECT "match"[2]::epoint
   2.685 +    FROM regexp_matches($1::text, e'(^| )point \\(([^)]+)\\)', 'g') AS "match"
   2.686 +  $$;
   2.687 +
   2.688 +CREATE FUNCTION ecluster_extract_paths(ecluster)
   2.689 +  RETURNS SETOF epoint[]
   2.690 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.691 +    SELECT (
   2.692 +      SELECT array_agg("m2"[1]::epoint)
   2.693 +      FROM regexp_matches("m1"[2], e'[^ ]+ [^ ]+', 'g') AS "m2"
   2.694 +    )
   2.695 +    FROM regexp_matches($1::text, e'(^| )path \\(([^)]+)\\)', 'g') AS "m1"
   2.696 +  $$;
   2.697 +
   2.698 +CREATE FUNCTION ecluster_extract_outlines(ecluster)
   2.699 +  RETURNS SETOF epoint[]
   2.700 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.701 +    SELECT (
   2.702 +      SELECT array_agg("m2"[1]::epoint)
   2.703 +      FROM regexp_matches("m1"[2], e'[^ ]+ [^ ]+', 'g') AS "m2"
   2.704 +    )
   2.705 +    FROM regexp_matches($1::text, e'(^| )outline \\(([^)]+)\\)', 'g') AS "m1"
   2.706 +  $$;
   2.707 +
   2.708 +CREATE FUNCTION ecluster_extract_polygons(ecluster)
   2.709 +  RETURNS SETOF epoint[]
   2.710 +  LANGUAGE sql IMMUTABLE STRICT AS $$
   2.711 +    SELECT (
   2.712 +      SELECT array_agg("m2"[1]::epoint)
   2.713 +      FROM regexp_matches("m1"[2], e'[^ ]+ [^ ]+', 'g') AS "m2"
   2.714 +    )
   2.715 +    FROM regexp_matches($1::text, e'(^| )polygon \\(([^)]+)\\)', 'g') AS "m1"
   2.716 +  $$;
   2.717 +
   2.718 +
   2.719 +---------------
   2.720 +-- operators --
   2.721 +---------------
   2.722 +
   2.723 +CREATE FUNCTION epoint_ebox_overlap_proc(epoint, ebox)
   2.724 +  RETURNS boolean
   2.725 +  LANGUAGE C IMMUTABLE STRICT
   2.726 +  AS '$libdir/latlon-v0004', 'pgl_epoint_ebox_overlap';
   2.727 +
   2.728 +CREATE FUNCTION epoint_ecircle_overlap_proc(epoint, ecircle)
   2.729 +  RETURNS boolean
   2.730 +  LANGUAGE C IMMUTABLE STRICT
   2.731 +  AS '$libdir/latlon-v0004', 'pgl_epoint_ecircle_overlap';
   2.732 +
   2.733 +CREATE FUNCTION epoint_ecluster_overlap_proc(epoint, ecluster)
   2.734 +  RETURNS boolean
   2.735 +  LANGUAGE C IMMUTABLE STRICT
   2.736 +  AS '$libdir/latlon-v0004', 'pgl_epoint_ecluster_overlap';
   2.737 +
   2.738 +CREATE FUNCTION epoint_ecluster_may_overlap_proc(epoint, ecluster)
   2.739 +  RETURNS boolean
   2.740 +  LANGUAGE C IMMUTABLE STRICT
   2.741 +  AS '$libdir/latlon-v0004', 'pgl_epoint_ecluster_may_overlap';
   2.742 +
   2.743 +CREATE FUNCTION ebox_overlap_proc(ebox, ebox)
   2.744 +  RETURNS boolean
   2.745 +  LANGUAGE C IMMUTABLE STRICT
   2.746 +  AS '$libdir/latlon-v0004', 'pgl_ebox_overlap';
   2.747 +
   2.748 +CREATE FUNCTION ebox_ecircle_may_overlap_proc(ebox, ecircle)
   2.749 +  RETURNS boolean
   2.750 +  LANGUAGE C IMMUTABLE STRICT
   2.751 +  AS '$libdir/latlon-v0004', 'pgl_ebox_ecircle_may_overlap';
   2.752 +
   2.753 +CREATE FUNCTION ebox_ecluster_may_overlap_proc(ebox, ecluster)
   2.754 +  RETURNS boolean
   2.755 +  LANGUAGE C IMMUTABLE STRICT
   2.756 +  AS '$libdir/latlon-v0004', 'pgl_ebox_ecluster_may_overlap';
   2.757 +
   2.758 +CREATE FUNCTION ecircle_overlap_proc(ecircle, ecircle)
   2.759 +  RETURNS boolean
   2.760 +  LANGUAGE C IMMUTABLE STRICT
   2.761 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_overlap';
   2.762 +
   2.763 +CREATE FUNCTION ecircle_ecluster_overlap_proc(ecircle, ecluster)
   2.764 +  RETURNS boolean
   2.765 +  LANGUAGE C IMMUTABLE STRICT
   2.766 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_ecluster_overlap';
   2.767 +
   2.768 +CREATE FUNCTION ecircle_ecluster_may_overlap_proc(ecircle, ecluster)
   2.769 +  RETURNS boolean
   2.770 +  LANGUAGE C IMMUTABLE STRICT
   2.771 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_ecluster_may_overlap';
   2.772 +
   2.773 +CREATE FUNCTION ecluster_may_overlap_proc(ecluster, ecluster)
   2.774 +  RETURNS boolean
   2.775 +  LANGUAGE C IMMUTABLE STRICT
   2.776 +  AS '$libdir/latlon-v0004', 'pgl_ecluster_may_overlap';
   2.777 +
   2.778 +CREATE FUNCTION epoint_distance_proc(epoint, epoint)
   2.779 +  RETURNS float8
   2.780 +  LANGUAGE C IMMUTABLE STRICT
   2.781 +  AS '$libdir/latlon-v0004', 'pgl_epoint_distance';
   2.782 +
   2.783 +CREATE FUNCTION epoint_ecircle_distance_proc(epoint, ecircle)
   2.784 +  RETURNS float8
   2.785 +  LANGUAGE C IMMUTABLE STRICT
   2.786 +  AS '$libdir/latlon-v0004', 'pgl_epoint_ecircle_distance';
   2.787 +
   2.788 +CREATE FUNCTION epoint_ecluster_distance_proc(epoint, ecluster)
   2.789 +  RETURNS float8
   2.790 +  LANGUAGE C IMMUTABLE STRICT
   2.791 +  AS '$libdir/latlon-v0004', 'pgl_epoint_ecluster_distance';
   2.792 +
   2.793 +CREATE FUNCTION ecircle_distance_proc(ecircle, ecircle)
   2.794 +  RETURNS float8
   2.795 +  LANGUAGE C IMMUTABLE STRICT
   2.796 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_distance';
   2.797 +
   2.798 +CREATE FUNCTION ecircle_ecluster_distance_proc(ecircle, ecluster)
   2.799 +  RETURNS float8
   2.800 +  LANGUAGE C IMMUTABLE STRICT
   2.801 +  AS '$libdir/latlon-v0004', 'pgl_ecircle_ecluster_distance';
   2.802 +
   2.803 +CREATE OPERATOR && (
   2.804 +  leftarg = epoint,
   2.805 +  rightarg = ebox,
   2.806 +  procedure = epoint_ebox_overlap_proc,
   2.807 +  commutator = &&,
   2.808 +  restrict = areasel,
   2.809 +  join = areajoinsel
   2.810 +);
   2.811 +
   2.812 +CREATE FUNCTION epoint_ebox_overlap_commutator(ebox, epoint)
   2.813 +  RETURNS boolean
   2.814 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   2.815 +
   2.816 +CREATE OPERATOR && (
   2.817 +  leftarg = ebox,
   2.818 +  rightarg = epoint,
   2.819 +  procedure = epoint_ebox_overlap_commutator,
   2.820 +  commutator = &&,
   2.821 +  restrict = areasel,
   2.822 +  join = areajoinsel
   2.823 +);
   2.824 +
   2.825 +CREATE OPERATOR && (
   2.826 +  leftarg = epoint,
   2.827 +  rightarg = ecircle,
   2.828 +  procedure = epoint_ecircle_overlap_proc,
   2.829 +  commutator = &&,
   2.830 +  restrict = areasel,
   2.831 +  join = areajoinsel
   2.832 +);
   2.833 +
   2.834 +CREATE FUNCTION epoint_ecircle_overlap_commutator(ecircle, epoint)
   2.835 +  RETURNS boolean
   2.836 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   2.837 +
   2.838 +CREATE OPERATOR && (
   2.839 +  leftarg = ecircle,
   2.840 +  rightarg = epoint,
   2.841 +  procedure = epoint_ecircle_overlap_commutator,
   2.842 +  commutator = &&,
   2.843 +  restrict = areasel,
   2.844 +  join = areajoinsel
   2.845 +);
   2.846 +
   2.847 +CREATE OPERATOR && (
   2.848 +  leftarg = epoint,
   2.849 +  rightarg = ecluster,
   2.850 +  procedure = epoint_ecluster_overlap_proc,
   2.851 +  commutator = &&,
   2.852 +  restrict = areasel,
   2.853 +  join = areajoinsel
   2.854 +);
   2.855 +
   2.856 +CREATE FUNCTION epoint_ecluster_overlap_commutator(ecluster, epoint)
   2.857 +  RETURNS boolean
   2.858 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   2.859 +
   2.860 +CREATE OPERATOR && (
   2.861 +  leftarg = ecluster,
   2.862 +  rightarg = epoint,
   2.863 +  procedure = epoint_ecluster_overlap_commutator,
   2.864 +  commutator = &&,
   2.865 +  restrict = areasel,
   2.866 +  join = areajoinsel
   2.867 +);
   2.868 +
   2.869 +CREATE OPERATOR && (
   2.870 +  leftarg = ebox,
   2.871 +  rightarg = ebox,
   2.872 +  procedure = ebox_overlap_proc,
   2.873 +  commutator = &&,
   2.874 +  restrict = areasel,
   2.875 +  join = areajoinsel
   2.876 +);
   2.877 +
   2.878 +CREATE OPERATOR && (
   2.879 +  leftarg = ecircle,
   2.880 +  rightarg = ecircle,
   2.881 +  procedure = ecircle_overlap_proc,
   2.882 +  commutator = &&,
   2.883 +  restrict = areasel,
   2.884 +  join = areajoinsel
   2.885 +);
   2.886 +
   2.887 +CREATE OPERATOR && (
   2.888 +  leftarg = ecircle,
   2.889 +  rightarg = ecluster,
   2.890 +  procedure = ecircle_ecluster_overlap_proc,
   2.891 +  commutator = &&,
   2.892 +  restrict = areasel,
   2.893 +  join = areajoinsel
   2.894 +);
   2.895 +
   2.896 +CREATE FUNCTION ecircle_ecluster_overlap_commutator(ecluster, ecircle)
   2.897 +  RETURNS boolean
   2.898 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 && $1';
   2.899 +
   2.900 +CREATE OPERATOR && (
   2.901 +  leftarg = ecluster,
   2.902 +  rightarg = ecircle,
   2.903 +  procedure = ecircle_ecluster_overlap_commutator,
   2.904 +  commutator = &&,
   2.905 +  restrict = areasel,
   2.906 +  join = areajoinsel
   2.907 +);
   2.908 +
   2.909 +CREATE OPERATOR &&+ (
   2.910 +  leftarg = epoint,
   2.911 +  rightarg = ecluster,
   2.912 +  procedure = epoint_ecluster_may_overlap_proc,
   2.913 +  commutator = &&+,
   2.914 +  restrict = areasel,
   2.915 +  join = areajoinsel
   2.916 +);
   2.917 +
   2.918 +CREATE FUNCTION epoint_ecluster_may_overlap_commutator(ecluster, epoint)
   2.919 +  RETURNS boolean
   2.920 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 &&+ $1';
   2.921 +
   2.922 +CREATE OPERATOR &&+ (
   2.923 +  leftarg = ecluster,
   2.924 +  rightarg = epoint,
   2.925 +  procedure = epoint_ecluster_may_overlap_commutator,
   2.926 +  commutator = &&+,
   2.927 +  restrict = areasel,
   2.928 +  join = areajoinsel
   2.929 +);
   2.930 +
   2.931 +CREATE OPERATOR &&+ (
   2.932 +  leftarg = ebox,
   2.933 +  rightarg = ecircle,
   2.934 +  procedure = ebox_ecircle_may_overlap_proc,
   2.935 +  commutator = &&+,
   2.936 +  restrict = areasel,
   2.937 +  join = areajoinsel
   2.938 +);
   2.939 +
   2.940 +CREATE FUNCTION ebox_ecircle_may_overlap_commutator(ecircle, ebox)
   2.941 +  RETURNS boolean
   2.942 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 &&+ $1';
   2.943 +
   2.944 +CREATE OPERATOR &&+ (
   2.945 +  leftarg = ecircle,
   2.946 +  rightarg = ebox,
   2.947 +  procedure = ebox_ecircle_may_overlap_commutator,
   2.948 +  commutator = &&+,
   2.949 +  restrict = areasel,
   2.950 +  join = areajoinsel
   2.951 +);
   2.952 +
   2.953 +CREATE OPERATOR &&+ (
   2.954 +  leftarg = ebox,
   2.955 +  rightarg = ecluster,
   2.956 +  procedure = ebox_ecluster_may_overlap_proc,
   2.957 +  commutator = &&+,
   2.958 +  restrict = areasel,
   2.959 +  join = areajoinsel
   2.960 +);
   2.961 +
   2.962 +CREATE FUNCTION ebox_ecluster_may_overlap_commutator(ecluster, ebox)
   2.963 +  RETURNS boolean
   2.964 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 &&+ $1';
   2.965 +
   2.966 +CREATE OPERATOR &&+ (
   2.967 +  leftarg = ecluster,
   2.968 +  rightarg = ebox,
   2.969 +  procedure = ebox_ecluster_may_overlap_commutator,
   2.970 +  commutator = &&+,
   2.971 +  restrict = areasel,
   2.972 +  join = areajoinsel
   2.973 +);
   2.974 +
   2.975 +CREATE OPERATOR &&+ (
   2.976 +  leftarg = ecircle,
   2.977 +  rightarg = ecluster,
   2.978 +  procedure = ecircle_ecluster_may_overlap_proc,
   2.979 +  commutator = &&+,
   2.980 +  restrict = areasel,
   2.981 +  join = areajoinsel
   2.982 +);
   2.983 +
   2.984 +CREATE FUNCTION ecircle_ecluster_may_overlap_commutator(ecluster, ecircle)
   2.985 +  RETURNS boolean
   2.986 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 &&+ $1';
   2.987 +
   2.988 +CREATE OPERATOR &&+ (
   2.989 +  leftarg = ecluster,
   2.990 +  rightarg = ecircle,
   2.991 +  procedure = ecircle_ecluster_may_overlap_commutator,
   2.992 +  commutator = &&+,
   2.993 +  restrict = areasel,
   2.994 +  join = areajoinsel
   2.995 +);
   2.996 +
   2.997 +CREATE OPERATOR &&+ (
   2.998 +  leftarg = ecluster,
   2.999 +  rightarg = ecluster,
  2.1000 +  procedure = ecluster_may_overlap_proc,
  2.1001 +  commutator = &&+,
  2.1002 +  restrict = areasel,
  2.1003 +  join = areajoinsel
  2.1004 +);
  2.1005 +
  2.1006 +CREATE OPERATOR <-> (
  2.1007 +  leftarg = epoint,
  2.1008 +  rightarg = epoint,
  2.1009 +  procedure = epoint_distance_proc,
  2.1010 +  commutator = <->
  2.1011 +);
  2.1012 +
  2.1013 +CREATE OPERATOR <-> (
  2.1014 +  leftarg = epoint,
  2.1015 +  rightarg = ecircle,
  2.1016 +  procedure = epoint_ecircle_distance_proc,
  2.1017 +  commutator = <->
  2.1018 +);
  2.1019 +
  2.1020 +CREATE FUNCTION epoint_ecircle_distance_commutator(ecircle, epoint)
  2.1021 +  RETURNS float8
  2.1022 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 <-> $1';
  2.1023 +
  2.1024 +CREATE OPERATOR <-> (
  2.1025 +  leftarg = ecircle,
  2.1026 +  rightarg = epoint,
  2.1027 +  procedure = epoint_ecircle_distance_commutator,
  2.1028 +  commutator = <->
  2.1029 +);
  2.1030 +
  2.1031 +CREATE OPERATOR <-> (
  2.1032 +  leftarg = epoint,
  2.1033 +  rightarg = ecluster,
  2.1034 +  procedure = epoint_ecluster_distance_proc,
  2.1035 +  commutator = <->
  2.1036 +);
  2.1037 +
  2.1038 +CREATE FUNCTION epoint_ecluster_distance_commutator(ecluster, epoint)
  2.1039 +  RETURNS float8
  2.1040 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 <-> $1';
  2.1041 +
  2.1042 +CREATE OPERATOR <-> (
  2.1043 +  leftarg = ecluster,
  2.1044 +  rightarg = epoint,
  2.1045 +  procedure = epoint_ecluster_distance_commutator,
  2.1046 +  commutator = <->
  2.1047 +);
  2.1048 +
  2.1049 +CREATE OPERATOR <-> (
  2.1050 +  leftarg = ecircle,
  2.1051 +  rightarg = ecircle,
  2.1052 +  procedure = ecircle_distance_proc,
  2.1053 +  commutator = <->
  2.1054 +);
  2.1055 +
  2.1056 +CREATE OPERATOR <-> (
  2.1057 +  leftarg = ecircle,
  2.1058 +  rightarg = ecluster,
  2.1059 +  procedure = ecircle_ecluster_distance_proc,
  2.1060 +  commutator = <->
  2.1061 +);
  2.1062 +
  2.1063 +CREATE FUNCTION ecircle_ecluster_distance_commutator(ecluster, ecircle)
  2.1064 +  RETURNS float8
  2.1065 +  LANGUAGE sql IMMUTABLE AS 'SELECT $2 <-> $1';
  2.1066 +
  2.1067 +CREATE OPERATOR <-> (
  2.1068 +  leftarg = ecluster,
  2.1069 +  rightarg = ecircle,
  2.1070 +  procedure = ecircle_ecluster_distance_commutator,
  2.1071 +  commutator = <->
  2.1072 +);
  2.1073 +
  2.1074 +
  2.1075 +----------------
  2.1076 +-- GiST index --
  2.1077 +----------------
  2.1078 +
  2.1079 +CREATE FUNCTION pgl_gist_consistent(internal, internal, smallint, oid, internal)
  2.1080 +  RETURNS boolean
  2.1081 +  LANGUAGE C STRICT
  2.1082 +  AS '$libdir/latlon-v0004', 'pgl_gist_consistent';
  2.1083 +
  2.1084 +CREATE FUNCTION pgl_gist_union(internal, internal)
  2.1085 +  RETURNS internal
  2.1086 +  LANGUAGE C STRICT
  2.1087 +  AS '$libdir/latlon-v0004', 'pgl_gist_union';
  2.1088 +
  2.1089 +CREATE FUNCTION pgl_gist_compress_epoint(internal)
  2.1090 +  RETURNS internal
  2.1091 +  LANGUAGE C STRICT
  2.1092 +  AS '$libdir/latlon-v0004', 'pgl_gist_compress_epoint';
  2.1093 +
  2.1094 +CREATE FUNCTION pgl_gist_compress_ecircle(internal)
  2.1095 +  RETURNS internal
  2.1096 +  LANGUAGE C STRICT
  2.1097 +  AS '$libdir/latlon-v0004', 'pgl_gist_compress_ecircle';
  2.1098 +
  2.1099 +CREATE FUNCTION pgl_gist_compress_ecluster(internal)
  2.1100 +  RETURNS internal
  2.1101 +  LANGUAGE C STRICT
  2.1102 +  AS '$libdir/latlon-v0004', 'pgl_gist_compress_ecluster';
  2.1103 +
  2.1104 +CREATE FUNCTION pgl_gist_decompress(internal)
  2.1105 +  RETURNS internal
  2.1106 +  LANGUAGE C STRICT
  2.1107 +  AS '$libdir/latlon-v0004', 'pgl_gist_decompress';
  2.1108 +
  2.1109 +CREATE FUNCTION pgl_gist_penalty(internal, internal, internal)
  2.1110 +  RETURNS internal
  2.1111 +  LANGUAGE C STRICT
  2.1112 +  AS '$libdir/latlon-v0004', 'pgl_gist_penalty';
  2.1113 +
  2.1114 +CREATE FUNCTION pgl_gist_picksplit(internal, internal)
  2.1115 +  RETURNS internal
  2.1116 +  LANGUAGE C STRICT
  2.1117 +  AS '$libdir/latlon-v0004', 'pgl_gist_picksplit';
  2.1118 +
  2.1119 +CREATE FUNCTION pgl_gist_same(internal, internal, internal)
  2.1120 +  RETURNS internal
  2.1121 +  LANGUAGE C STRICT
  2.1122 +  AS '$libdir/latlon-v0004', 'pgl_gist_same';
  2.1123 +
  2.1124 +CREATE FUNCTION pgl_gist_distance(internal, internal, smallint, oid)
  2.1125 +  RETURNS internal
  2.1126 +  LANGUAGE C STRICT
  2.1127 +  AS '$libdir/latlon-v0004', 'pgl_gist_distance';
  2.1128 +
  2.1129 +CREATE OPERATOR CLASS epoint_ops
  2.1130 +  DEFAULT FOR TYPE epoint USING gist AS
  2.1131 +  OPERATOR  11 = ,
  2.1132 +  OPERATOR  22 &&  (epoint, ebox),
  2.1133 +  OPERATOR  23 &&  (epoint, ecircle),
  2.1134 +  OPERATOR  24 &&  (epoint, ecluster),
  2.1135 +  OPERATOR 124 &&+ (epoint, ecluster),
  2.1136 +  OPERATOR  31 <-> (epoint, epoint) FOR ORDER BY float_ops,
  2.1137 +  OPERATOR  33 <-> (epoint, ecircle) FOR ORDER BY float_ops,
  2.1138 +  OPERATOR  34 <-> (epoint, ecluster) FOR ORDER BY float_ops,
  2.1139 +  FUNCTION 1 pgl_gist_consistent(internal, internal, smallint, oid, internal),
  2.1140 +  FUNCTION 2 pgl_gist_union(internal, internal),
  2.1141 +  FUNCTION 3 pgl_gist_compress_epoint(internal),
  2.1142 +  FUNCTION 4 pgl_gist_decompress(internal),
  2.1143 +  FUNCTION 5 pgl_gist_penalty(internal, internal, internal),
  2.1144 +  FUNCTION 6 pgl_gist_picksplit(internal, internal),
  2.1145 +  FUNCTION 7 pgl_gist_same(internal, internal, internal),
  2.1146 +  FUNCTION 8 pgl_gist_distance(internal, internal, smallint, oid),
  2.1147 +  STORAGE ekey_point;
  2.1148 +
  2.1149 +CREATE OPERATOR CLASS ecircle_ops
  2.1150 +  DEFAULT FOR TYPE ecircle USING gist AS
  2.1151 +  OPERATOR  13 = ,
  2.1152 +  OPERATOR  21 &&  (ecircle, epoint),
  2.1153 +  OPERATOR 122 &&+ (ecircle, ebox),
  2.1154 +  OPERATOR  23 &&  (ecircle, ecircle),
  2.1155 +  OPERATOR  24 &&  (ecircle, ecluster),
  2.1156 +  OPERATOR 124 &&+ (ecircle, ecluster),
  2.1157 +  OPERATOR  31 <-> (ecircle, epoint) FOR ORDER BY float_ops,
  2.1158 +  OPERATOR  33 <-> (ecircle, ecircle) FOR ORDER BY float_ops,
  2.1159 +  OPERATOR  34 <-> (ecircle, ecluster) FOR ORDER BY float_ops,
  2.1160 +  FUNCTION 1 pgl_gist_consistent(internal, internal, smallint, oid, internal),
  2.1161 +  FUNCTION 2 pgl_gist_union(internal, internal),
  2.1162 +  FUNCTION 3 pgl_gist_compress_ecircle(internal),
  2.1163 +  FUNCTION 4 pgl_gist_decompress(internal),
  2.1164 +  FUNCTION 5 pgl_gist_penalty(internal, internal, internal),
  2.1165 +  FUNCTION 6 pgl_gist_picksplit(internal, internal),
  2.1166 +  FUNCTION 7 pgl_gist_same(internal, internal, internal),
  2.1167 +  FUNCTION 8 pgl_gist_distance(internal, internal, smallint, oid),
  2.1168 +  STORAGE ekey_area;
  2.1169 +
  2.1170 +CREATE OPERATOR CLASS ecluster_ops
  2.1171 +  DEFAULT FOR TYPE ecluster USING gist AS
  2.1172 +  OPERATOR  21 &&  (ecluster, epoint),
  2.1173 +  OPERATOR 121 &&+ (ecluster, epoint),
  2.1174 +  OPERATOR 122 &&+ (ecluster, ebox),
  2.1175 +  OPERATOR  23 &&  (ecluster, ecircle),
  2.1176 +  OPERATOR 123 &&+ (ecluster, ecircle),
  2.1177 +  OPERATOR 124 &&+ (ecluster, ecluster),
  2.1178 +  FUNCTION 1 pgl_gist_consistent(internal, internal, smallint, oid, internal),
  2.1179 +  FUNCTION 2 pgl_gist_union(internal, internal),
  2.1180 +  FUNCTION 3 pgl_gist_compress_ecluster(internal),
  2.1181 +  FUNCTION 4 pgl_gist_decompress(internal),
  2.1182 +  FUNCTION 5 pgl_gist_penalty(internal, internal, internal),
  2.1183 +  FUNCTION 6 pgl_gist_picksplit(internal, internal),
  2.1184 +  FUNCTION 7 pgl_gist_same(internal, internal, internal),
  2.1185 +  FUNCTION 8 pgl_gist_distance(internal, internal, smallint, oid),
  2.1186 +  STORAGE ekey_area;
  2.1187 +
  2.1188 +
  2.1189 +---------------------
  2.1190 +-- alias functions --
  2.1191 +---------------------
  2.1192 +
  2.1193 +CREATE FUNCTION distance(epoint, epoint)
  2.1194 +  RETURNS float8
  2.1195 +  LANGUAGE sql IMMUTABLE AS 'SELECT $1 <-> $2';
  2.1196 +
  2.1197 +CREATE FUNCTION distance(ecluster, epoint)
  2.1198 +  RETURNS float8
  2.1199 +  LANGUAGE sql IMMUTABLE AS 'SELECT $1 <-> $2';
  2.1200 +
  2.1201 +CREATE FUNCTION distance_within(epoint, epoint, float8)
  2.1202 +  RETURNS boolean
  2.1203 +  LANGUAGE sql IMMUTABLE AS 'SELECT $1 && ecircle($2, $3)';
  2.1204 +
  2.1205 +CREATE FUNCTION distance_within(ecluster, epoint, float8)
  2.1206 +  RETURNS boolean
  2.1207 +  LANGUAGE sql IMMUTABLE AS 'SELECT $1 && ecircle($2, $3)';
  2.1208 +
  2.1209 +
  2.1210 +--------------------------------
  2.1211 +-- other data storage formats --
  2.1212 +--------------------------------
  2.1213 +
  2.1214 +CREATE FUNCTION coords_to_epoint(float8, float8, text = 'epoint_lonlat')
  2.1215 +  RETURNS epoint
  2.1216 +  LANGUAGE plpgsql IMMUTABLE STRICT AS $$
  2.1217 +    DECLARE
  2.1218 +      "result" epoint;
  2.1219 +    BEGIN
  2.1220 +      IF $3 = 'epoint_lonlat' THEN
  2.1221 +        -- avoid dynamic command execution for better performance
  2.1222 +        RETURN epoint($2, $1);
  2.1223 +      END IF;
  2.1224 +      IF $3 = 'epoint' OR $3 = 'epoint_latlon' THEN
  2.1225 +        -- avoid dynamic command execution for better performance
  2.1226 +        RETURN epoint($1, $2);
  2.1227 +      END IF;
  2.1228 +      EXECUTE 'SELECT ' || $3 || '($1, $2)' INTO STRICT "result" USING $1, $2;
  2.1229 +      RETURN "result";
  2.1230 +    END;
  2.1231 +  $$;
  2.1232 +
  2.1233 +CREATE FUNCTION GeoJSON_to_epoint(jsonb, text = 'epoint_lonlat')
  2.1234 +  RETURNS epoint
  2.1235 +  LANGUAGE sql IMMUTABLE STRICT AS $$
  2.1236 +    SELECT CASE
  2.1237 +    WHEN $1->>'type' = 'Point' THEN
  2.1238 +      coords_to_epoint(
  2.1239 +        ($1->'coordinates'->>1)::float8,
  2.1240 +        ($1->'coordinates'->>0)::float8,
  2.1241 +        $2
  2.1242 +      )
  2.1243 +    WHEN $1->>'type' = 'Feature' THEN
  2.1244 +      GeoJSON_to_epoint($1->'geometry', $2)
  2.1245 +    ELSE
  2.1246 +      NULL
  2.1247 +    END
  2.1248 +  $$;
  2.1249 +
  2.1250 +CREATE FUNCTION GeoJSON_to_ecluster(jsonb, text = 'epoint_lonlat')
  2.1251 +  RETURNS ecluster
  2.1252 +  LANGUAGE sql IMMUTABLE STRICT AS $$
  2.1253 +    SELECT CASE $1->>'type'
  2.1254 +    WHEN 'Point' THEN
  2.1255 +      coords_to_epoint(
  2.1256 +        ($1->'coordinates'->>1)::float8,
  2.1257 +        ($1->'coordinates'->>0)::float8,
  2.1258 +        $2
  2.1259 +      )::ecluster
  2.1260 +    WHEN 'MultiPoint' THEN
  2.1261 +      ( SELECT ecluster_create_multipoint(array_agg(
  2.1262 +          coords_to_epoint(
  2.1263 +            ("coord"->>1)::float8,
  2.1264 +            ("coord"->>0)::float8,
  2.1265 +            $2
  2.1266 +          )
  2.1267 +        ))
  2.1268 +        FROM jsonb_array_elements($1->'coordinates') AS "coord"
  2.1269 +      )
  2.1270 +    WHEN 'LineString' THEN
  2.1271 +      ( SELECT ecluster_create_path(array_agg(
  2.1272 +          coords_to_epoint(
  2.1273 +            ("coord"->>1)::float8,
  2.1274 +            ("coord"->>0)::float8,
  2.1275 +            $2
  2.1276 +          )
  2.1277 +        ))
  2.1278 +        FROM jsonb_array_elements($1->'coordinates') AS "coord"
  2.1279 +      )
  2.1280 +    WHEN 'MultiLineString' THEN
  2.1281 +      ( SELECT ecluster_concat(array_agg(
  2.1282 +          ( SELECT ecluster_create_path(array_agg(
  2.1283 +              coords_to_epoint(
  2.1284 +                ("coord"->>1)::float8,
  2.1285 +                ("coord"->>0)::float8,
  2.1286 +                $2
  2.1287 +              )
  2.1288 +            ))
  2.1289 +            FROM jsonb_array_elements("coord_array") AS "coord"
  2.1290 +          )
  2.1291 +        ))
  2.1292 +        FROM jsonb_array_elements($1->'coordinates') AS "coord_array"
  2.1293 +      )
  2.1294 +    WHEN 'Polygon' THEN
  2.1295 +      ( SELECT ecluster_concat(array_agg(
  2.1296 +          ( SELECT ecluster_create_polygon(array_agg(
  2.1297 +              coords_to_epoint(
  2.1298 +                ("coord"->>1)::float8,
  2.1299 +                ("coord"->>0)::float8,
  2.1300 +                $2
  2.1301 +              )
  2.1302 +            ))
  2.1303 +            FROM jsonb_array_elements("coord_array") AS "coord"
  2.1304 +          )
  2.1305 +        ))
  2.1306 +        FROM jsonb_array_elements($1->'coordinates') AS "coord_array"
  2.1307 +      )
  2.1308 +    WHEN 'MultiPolygon' THEN
  2.1309 +      ( SELECT ecluster_concat(array_agg(
  2.1310 +          ( SELECT ecluster_concat(array_agg(
  2.1311 +              ( SELECT ecluster_create_polygon(array_agg(
  2.1312 +                  coords_to_epoint(
  2.1313 +                    ("coord"->>1)::float8,
  2.1314 +                    ("coord"->>0)::float8,
  2.1315 +                    $2
  2.1316 +                  )
  2.1317 +                ))
  2.1318 +                FROM jsonb_array_elements("coord_array") AS "coord"
  2.1319 +              )
  2.1320 +            ))
  2.1321 +            FROM jsonb_array_elements("coord_array_array") AS "coord_array"
  2.1322 +          )
  2.1323 +        ))
  2.1324 +        FROM jsonb_array_elements($1->'coordinates') AS "coord_array_array"
  2.1325 +      )
  2.1326 +    WHEN 'Feature' THEN
  2.1327 +      GeoJSON_to_ecluster($1->'geometry', $2)
  2.1328 +    WHEN 'FeatureCollection' THEN
  2.1329 +      ( SELECT ecluster_concat(array_agg(
  2.1330 +          GeoJSON_to_ecluster("feature", $2)
  2.1331 +        ))
  2.1332 +        FROM jsonb_array_elements($1->'features') AS "feature"
  2.1333 +      )
  2.1334 +    ELSE
  2.1335 +      NULL
  2.1336 +    END
  2.1337 +  $$;
  2.1338 +

     3.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.2 +++ b/latlon-v0004.c	Sat Sep 03 16:00:22 2016 +0200
     3.3 @@ -0,0 +1,2768 @@
     3.4 +
     3.5 +/*-------------*
     3.6 + *  C prelude  *
     3.7 + *-------------*/
     3.8 +
     3.9 +#include "postgres.h"
    3.10 +#include "fmgr.h"
    3.11 +#include "libpq/pqformat.h"
    3.12 +#include "access/gist.h"
    3.13 +#include "access/stratnum.h"
    3.14 +#include "utils/array.h"
    3.15 +#include <math.h>
    3.16 +
    3.17 +#ifdef PG_MODULE_MAGIC
    3.18 +PG_MODULE_MAGIC;
    3.19 +#endif
    3.20 +
    3.21 +#if INT_MAX < 2147483647
    3.22 +#error Expected int type to be at least 32 bit wide
    3.23 +#endif
    3.24 +
    3.25 +
    3.26 +/*---------------------------------*
    3.27 + *  distance calculation on earth  *
    3.28 + *  (using WGS-84 spheroid)        *
    3.29 + *---------------------------------*/
    3.30 +
    3.31 +/*  WGS-84 spheroid with following parameters:
    3.32 +    semi-major axis  a = 6378137
    3.33 +    semi-minor axis  b = a * (1 - 1/298.257223563)
    3.34 +    estimated diameter = 2 * (2*a+b)/3
    3.35 +*/
    3.36 +#define PGL_SPHEROID_A 6378137.0            /* semi major axis */
    3.37 +#define PGL_SPHEROID_F (1.0/298.257223563)  /* flattening */
    3.38 +#define PGL_SPHEROID_B (PGL_SPHEROID_A * (1.0-PGL_SPHEROID_F))
    3.39 +#define PGL_EPS2       ( ( PGL_SPHEROID_A * PGL_SPHEROID_A - \
    3.40 +                           PGL_SPHEROID_B * PGL_SPHEROID_B ) / \
    3.41 +                         ( PGL_SPHEROID_A * PGL_SPHEROID_A ) )
    3.42 +#define PGL_SUBEPS2    (1.0-PGL_EPS2)
    3.43 +#define PGL_DIAMETER   ((4.0*PGL_SPHEROID_A + 2.0*PGL_SPHEROID_B) / 3.0)
    3.44 +#define PGL_SCALE      (PGL_SPHEROID_A / PGL_DIAMETER)  /* semi-major ref. */
    3.45 +#define PGL_FADELIMIT  (PGL_DIAMETER * M_PI / 6.0)      /* 1/6 circumference */
    3.46 +#define PGL_MAXDIST    (PGL_DIAMETER * M_PI / 2.0)      /* maximum distance */
    3.47 +
    3.48 +/* calculate distance between two points on earth (given in degrees) */
    3.49 +static inline double pgl_distance(
    3.50 +  double lat1, double lon1, double lat2, double lon2
    3.51 +) {
    3.52 +  float8 lat1cos, lat1sin, lat2cos, lat2sin, lon2cos, lon2sin;
    3.53 +  float8 nphi1, nphi2, x1, z1, x2, y2, z2, g, s, t;
    3.54 +  /* normalize delta longitude (lon2 > 0 && lon1 = 0) */
    3.55 +  /* lon1 = 0 (not used anymore) */
    3.56 +  lon2 = fabs(lon2-lon1);
    3.57 +  /* convert to radians (first divide, then multiply) */
    3.58 +  lat1 = (lat1 / 180.0) * M_PI;
    3.59 +  lat2 = (lat2 / 180.0) * M_PI;
    3.60 +  lon2 = (lon2 / 180.0) * M_PI;
    3.61 +  /* make lat2 >= lat1 to ensure reversal-symmetry despite floating point
    3.62 +     operations (lon2 >= lon1 is already ensured in a previous step) */
    3.63 +  if (lat2 < lat1) { float8 swap = lat1; lat1 = lat2; lat2 = swap; }
    3.64 +  /* calculate 3d coordinates on scaled ellipsoid which has an average diameter
    3.65 +     of 1.0 */
    3.66 +  lat1cos = cos(lat1); lat1sin = sin(lat1);
    3.67 +  lat2cos = cos(lat2); lat2sin = sin(lat2);
    3.68 +  lon2cos = cos(lon2); lon2sin = sin(lon2);
    3.69 +  nphi1 = PGL_SCALE / sqrt(1 - PGL_EPS2 * lat1sin * lat1sin);
    3.70 +  nphi2 = PGL_SCALE / sqrt(1 - PGL_EPS2 * lat2sin * lat2sin);
    3.71 +  x1 = nphi1 * lat1cos;
    3.72 +  z1 = nphi1 * PGL_SUBEPS2 * lat1sin;
    3.73 +  x2 = nphi2 * lat2cos * lon2cos;
    3.74 +  y2 = nphi2 * lat2cos * lon2sin;
    3.75 +  z2 = nphi2 * PGL_SUBEPS2 * lat2sin;
    3.76 +  /* calculate tunnel distance through scaled (diameter 1.0) ellipsoid */
    3.77 +  g = sqrt((x2-x1)*(x2-x1) + y2*y2 + (z2-z1)*(z2-z1));
    3.78 +  /* convert tunnel distance through scaled ellipsoid to approximated surface
    3.79 +     distance on original ellipsoid */
    3.80 +  if (g > 1.0) g = 1.0;
    3.81 +  s = PGL_DIAMETER * asin(g);
    3.82 +  /* return result only if small enough to be precise (less than 1/3 of
    3.83 +     maximum possible distance) */
    3.84 +  if (s <= PGL_FADELIMIT) return s;
    3.85 +  /* calculate tunnel distance to antipodal point through scaled ellipsoid */
    3.86 +  g = sqrt((x2+x1)*(x2+x1) + y2*y2 + (z2+z1)*(z2+z1));
    3.87 +  /* convert tunnel distance to antipodal point through scaled ellipsoid to
    3.88 +     approximated surface distance to antipodal point on original ellipsoid */
    3.89 +  if (g > 1.0) g = 1.0;
    3.90 +  t = PGL_DIAMETER * asin(g);
    3.91 +  /* surface distance between original points can now be approximated by
    3.92 +     substracting antipodal distance from maximum possible distance;
    3.93 +     return result only if small enough (less than 1/3 of maximum possible
    3.94 +     distance) */
    3.95 +  if (t <= PGL_FADELIMIT) return PGL_MAXDIST-t;
    3.96 +  /* otherwise crossfade direct and antipodal result to ensure monotonicity */
    3.97 +  return (
    3.98 +    (s * (t-PGL_FADELIMIT) + (PGL_MAXDIST-t) * (s-PGL_FADELIMIT)) /
    3.99 +    (s + t - 2*PGL_FADELIMIT)
   3.100 +  );
   3.101 +}
   3.102 +
   3.103 +/* finite distance that can not be reached on earth */
   3.104 +#define PGL_ULTRA_DISTANCE (3 * PGL_MAXDIST)
   3.105 +
   3.106 +
   3.107 +/*--------------------------------*
   3.108 + *  simple geographic data types  *
   3.109 + *--------------------------------*/
   3.110 +
   3.111 +/* point on earth given by latitude and longitude in degrees */
   3.112 +/* (type "epoint" in SQL) */
   3.113 +typedef struct {
   3.114 +  double lat;  /* between  -90 and  90 (both inclusive) */
   3.115 +  double lon;  /* between -180 and 180 (both inclusive) */
   3.116 +} pgl_point;
   3.117 +
   3.118 +/* box delimited by two parallels and two meridians (all in degrees) */
   3.119 +/* (type "ebox" in SQL) */
   3.120 +typedef struct {
   3.121 +  double lat_min;  /* between  -90 and  90 (both inclusive) */
   3.122 +  double lat_max;  /* between  -90 and  90 (both inclusive) */
   3.123 +  double lon_min;  /* between -180 and 180 (both inclusive) */
   3.124 +  double lon_max;  /* between -180 and 180 (both inclusive) */
   3.125 +  /* if lat_min > lat_max, then box is empty */
   3.126 +  /* if lon_min > lon_max, then 180th meridian is crossed */
   3.127 +} pgl_box;
   3.128 +
   3.129 +/* circle on earth surface (for radial searches with fixed radius) */
   3.130 +/* (type "ecircle" in SQL) */
   3.131 +typedef struct {
   3.132 +  pgl_point center;
   3.133 +  double radius; /* positive (including +0 but excluding -0), or -INFINITY */
   3.134 +  /* A negative radius (i.e. -INFINITY) denotes nothing (i.e. no point),
   3.135 +     zero radius (0) denotes a single point,
   3.136 +     a finite radius (0 < radius < INFINITY) denotes a filled circle, and
   3.137 +     a radius of INFINITY is valid and means complete coverage of earth. */
   3.138 +} pgl_circle;
   3.139 +
   3.140 +
   3.141 +/*----------------------------------*
   3.142 + *  geographic "cluster" data type  *
   3.143 + *----------------------------------*/
   3.144 +
   3.145 +/* A cluster is a collection of points, paths, outlines, and polygons. If two
   3.146 +   polygons in a cluster overlap, the area covered by both polygons does not
   3.147 +   belong to the cluster. This way, a cluster can be used to describe complex
   3.148 +   shapes like polygons with holes. Outlines are non-filled polygons. Paths are
   3.149 +   open by default (i.e. the last point in the list is not connected with the
   3.150 +   first point in the list). Note that each outline or polygon in a cluster
   3.151 +   must cover a longitude range of less than 180 degrees to avoid ambiguities.
   3.152 +   Areas which are larger may be split into multiple polygons. */
   3.153 +
   3.154 +/* maximum number of points in a cluster */
   3.155 +/* (limited to avoid integer overflows, e.g. when allocating memory) */
   3.156 +#define PGL_CLUSTER_MAXPOINTS 16777216
   3.157 +
   3.158 +/* types of cluster entries */
   3.159 +#define PGL_ENTRY_POINT   1  /* a point */
   3.160 +#define PGL_ENTRY_PATH    2  /* a path from first point to last point */
   3.161 +#define PGL_ENTRY_OUTLINE 3  /* a non-filled polygon with given vertices */
   3.162 +#define PGL_ENTRY_POLYGON 4  /* a filled polygon with given vertices */
   3.163 +
   3.164 +/* Entries of a cluster are described by two different structs: pgl_newentry
   3.165 +   and pgl_entry. The first is used only during construction of a cluster, the
   3.166 +   second is used in all other cases (e.g. when reading clusters from the
   3.167 +   database, performing operations, etc). */
   3.168 +
   3.169 +/* entry for new geographic cluster during construction of that cluster */
   3.170 +typedef struct {
   3.171 +  int32_t entrytype;
   3.172 +  int32_t npoints;
   3.173 +  pgl_point *points;  /* pointer to an array of points (pgl_point) */
   3.174 +} pgl_newentry;
   3.175 +
   3.176 +/* entry of geographic cluster */
   3.177 +typedef struct {
   3.178 +  int32_t entrytype;  /* type of entry: point, path, outline, polygon */
   3.179 +  int32_t npoints;    /* number of stored points (set to 1 for point entry) */
   3.180 +  int32_t offset;     /* offset of pgl_point array from cluster base address */
   3.181 +  /* use macro PGL_ENTRY_POINTS to obtain a pointer to the array of points */
   3.182 +} pgl_entry;
   3.183 +
   3.184 +/* geographic cluster which is a collection of points, (open) paths, polygons,
   3.185 +   and outlines (non-filled polygons) */
   3.186 +typedef struct {
   3.187 +  char header[VARHDRSZ];  /* PostgreSQL header for variable size data types */
   3.188 +  int32_t nentries;       /* number of stored points */
   3.189 +  pgl_circle bounding;    /* bounding circle */
   3.190 +  /* Note: bounding circle ensures alignment of pgl_cluster for points */
   3.191 +  pgl_entry entries[FLEXIBLE_ARRAY_MEMBER];  /* var-length data */
   3.192 +} pgl_cluster;
   3.193 +
   3.194 +/* macro to determine memory alignment of points */
   3.195 +/* (needed to store pgl_point array after entries in pgl_cluster) */
   3.196 +typedef struct { char dummy; pgl_point aligned; } pgl_point_alignment;
   3.197 +#define PGL_POINT_ALIGNMENT offsetof(pgl_point_alignment, aligned)
   3.198 +
   3.199 +/* macro to extract a pointer to the array of points of a cluster entry */
   3.200 +#define PGL_ENTRY_POINTS(cluster, idx) \
   3.201 +  ((pgl_point *)(((intptr_t)cluster)+(cluster)->entries[idx].offset))
   3.202 +
   3.203 +/* convert pgl_newentry array to pgl_cluster */
   3.204 +static pgl_cluster *pgl_new_cluster(int nentries, pgl_newentry *entries) {
   3.205 +  int i;              /* index of current entry */
   3.206 +  int npoints = 0;    /* number of points in whole cluster */
   3.207 +  int entry_npoints;  /* number of points in current entry */
   3.208 +  int points_offset = PGL_POINT_ALIGNMENT * (
   3.209 +    ( offsetof(pgl_cluster, entries) +
   3.210 +      nentries * sizeof(pgl_entry) +
   3.211 +      PGL_POINT_ALIGNMENT - 1
   3.212 +    ) / PGL_POINT_ALIGNMENT
   3.213 +  );  /* offset of pgl_point array from base address (considering alignment) */
   3.214 +  pgl_cluster *cluster;  /* new cluster to be returned */
   3.215 +  /* determine total number of points */
   3.216 +  for (i=0; i<nentries; i++) npoints += entries[i].npoints;
   3.217 +  /* allocate memory for cluster (including entries and points) */
   3.218 +  cluster = palloc(points_offset + npoints * sizeof(pgl_point));
   3.219 +  /* re-count total number of points to determine offset for each entry */
   3.220 +  npoints = 0;
   3.221 +  /* copy entries and points */
   3.222 +  for (i=0; i<nentries; i++) {
   3.223 +    /* determine number of points in entry */
   3.224 +    entry_npoints = entries[i].npoints;
   3.225 +    /* copy entry */
   3.226 +    cluster->entries[i].entrytype = entries[i].entrytype;
   3.227 +    cluster->entries[i].npoints = entry_npoints;
   3.228 +    /* calculate offset (in bytes) of pgl_point array */
   3.229 +    cluster->entries[i].offset = points_offset + npoints * sizeof(pgl_point);
   3.230 +    /* copy points */
   3.231 +    memcpy(
   3.232 +      PGL_ENTRY_POINTS(cluster, i),
   3.233 +      entries[i].points,
   3.234 +      entry_npoints * sizeof(pgl_point)
   3.235 +    );
   3.236 +    /* update total number of points processed */
   3.237 +    npoints += entry_npoints;
   3.238 +  }
   3.239 +  /* set number of entries in cluster */
   3.240 +  cluster->nentries = nentries;
   3.241 +  /* set PostgreSQL header for variable sized data */
   3.242 +  SET_VARSIZE(cluster, points_offset + npoints * sizeof(pgl_point));
   3.243 +  /* return newly created cluster */
   3.244 +  return cluster;
   3.245 +}
   3.246 +
   3.247 +
   3.248 +/*----------------------------------------*
   3.249 + *  C functions on geographic data types  *
   3.250 + *----------------------------------------*/
   3.251 +
   3.252 +/* round latitude or longitude to 12 digits after decimal point */
   3.253 +static inline double pgl_round(double val) {
   3.254 +  return round(val * 1e12) / 1e12;
   3.255 +}
   3.256 +
   3.257 +/* compare two points */
   3.258 +/* (equality when same point on earth is described, otherwise an arbitrary
   3.259 +   linear order) */
   3.260 +static int pgl_point_cmp(pgl_point *point1, pgl_point *point2) {
   3.261 +  double lon1, lon2;  /* modified longitudes for special cases */
   3.262 +  /* use latitude as first ordering criterion */
   3.263 +  if (point1->lat < point2->lat) return -1;
   3.264 +  if (point1->lat > point2->lat) return 1;
   3.265 +  /* determine modified longitudes (considering special case of poles and
   3.266 +     180th meridian which can be described as W180 or E180) */
   3.267 +  if (point1->lat == -90 || point1->lat == 90) lon1 = 0;
   3.268 +  else if (point1->lon == 180) lon1 = -180;
   3.269 +  else lon1 = point1->lon;
   3.270 +  if (point2->lat == -90 || point2->lat == 90) lon2 = 0;
   3.271 +  else if (point2->lon == 180) lon2 = -180;
   3.272 +  else lon2 = point2->lon;
   3.273 +  /* use (modified) longitude as secondary ordering criterion */
   3.274 +  if (lon1 < lon2) return -1;
   3.275 +  if (lon1 > lon2) return 1;
   3.276 +  /* no difference found, points are equal */
   3.277 +  return 0;
   3.278 +}
   3.279 +
   3.280 +/* compare two boxes */
   3.281 +/* (equality when same box on earth is described, otherwise an arbitrary linear
   3.282 +   order) */
   3.283 +static int pgl_box_cmp(pgl_box *box1, pgl_box *box2) {
   3.284 +  /* two empty boxes are equal, and an empty box is always considered "less
   3.285 +     than" a non-empty box */
   3.286 +  if (box1->lat_min> box1->lat_max && box2->lat_min<=box2->lat_max) return -1;
   3.287 +  if (box1->lat_min> box1->lat_max && box2->lat_min> box2->lat_max) return 0;
   3.288 +  if (box1->lat_min<=box1->lat_max && box2->lat_min> box2->lat_max) return 1;
   3.289 +  /* use southern border as first ordering criterion */
   3.290 +  if (box1->lat_min < box2->lat_min) return -1;
   3.291 +  if (box1->lat_min > box2->lat_min) return 1;
   3.292 +  /* use northern border as second ordering criterion */
   3.293 +  if (box1->lat_max < box2->lat_max) return -1;
   3.294 +  if (box1->lat_max > box2->lat_max) return 1;
   3.295 +  /* use western border as third ordering criterion */
   3.296 +  if (box1->lon_min < box2->lon_min) return -1;
   3.297 +  if (box1->lon_min > box2->lon_min) return 1;
   3.298 +  /* use eastern border as fourth ordering criterion */
   3.299 +  if (box1->lon_max < box2->lon_max) return -1;
   3.300 +  if (box1->lon_max > box2->lon_max) return 1;
   3.301 +  /* no difference found, boxes are equal */
   3.302 +  return 0;
   3.303 +}
   3.304 +
   3.305 +/* compare two circles */
   3.306 +/* (equality when same circle on earth is described, otherwise an arbitrary
   3.307 +   linear order) */
   3.308 +static int pgl_circle_cmp(pgl_circle *circle1, pgl_circle *circle2) {
   3.309 +  /* two circles with same infinite radius (positive or negative infinity) are
   3.310 +     considered equal independently of center point */
   3.311 +  if (
   3.312 +    !isfinite(circle1->radius) && !isfinite(circle2->radius) &&
   3.313 +    circle1->radius == circle2->radius
   3.314 +  ) return 0;
   3.315 +  /* use radius as first ordering criterion */
   3.316 +  if (circle1->radius < circle2->radius) return -1;
   3.317 +  if (circle1->radius > circle2->radius) return 1;
   3.318 +  /* use center point as secondary ordering criterion */
   3.319 +  return pgl_point_cmp(&(circle1->center), &(circle2->center));
   3.320 +}
   3.321 +
   3.322 +/* set box to empty box*/
   3.323 +static void pgl_box_set_empty(pgl_box *box) {
   3.324 +  box->lat_min = INFINITY;
   3.325 +  box->lat_max = -INFINITY;
   3.326 +  box->lon_min = 0;
   3.327 +  box->lon_max = 0;
   3.328 +}
   3.329 +
   3.330 +/* check if point is inside a box */
   3.331 +static bool pgl_point_in_box(pgl_point *point, pgl_box *box) {
   3.332 +  return (
   3.333 +    point->lat >= box->lat_min && point->lat <= box->lat_max && (
   3.334 +      (box->lon_min > box->lon_max) ? (
   3.335 +        /* box crosses 180th meridian */
   3.336 +        point->lon >= box->lon_min || point->lon <= box->lon_max
   3.337 +      ) : (
   3.338 +        /* box does not cross the 180th meridian */
   3.339 +        point->lon >= box->lon_min && point->lon <= box->lon_max
   3.340 +      )
   3.341 +    )
   3.342 +  );
   3.343 +}
   3.344 +
   3.345 +/* check if two boxes overlap */
   3.346 +static bool pgl_boxes_overlap(pgl_box *box1, pgl_box *box2) {
   3.347 +  return (
   3.348 +    box2->lat_max >= box2->lat_min &&  /* ensure box2 is not empty */
   3.349 +    ( box2->lat_min >= box1->lat_min || box2->lat_max >= box1->lat_min ) &&
   3.350 +    ( box2->lat_min <= box1->lat_max || box2->lat_max <= box1->lat_max ) && (
   3.351 +      (
   3.352 +        /* check if one and only one box crosses the 180th meridian */
   3.353 +        ((box1->lon_min > box1->lon_max) ? 1 : 0) ^
   3.354 +        ((box2->lon_min > box2->lon_max) ? 1 : 0)
   3.355 +      ) ? (
   3.356 +        /* exactly one box crosses the 180th meridian */
   3.357 +        box2->lon_min >= box1->lon_min || box2->lon_max >= box1->lon_min ||
   3.358 +        box2->lon_min <= box1->lon_max || box2->lon_max <= box1->lon_max
   3.359 +      ) : (
   3.360 +        /* no box or both boxes cross the 180th meridian */
   3.361 +        (
   3.362 +          (box2->lon_min >= box1->lon_min || box2->lon_max >= box1->lon_min) &&
   3.363 +          (box2->lon_min <= box1->lon_max || box2->lon_max <= box1->lon_max)
   3.364 +        ) ||
   3.365 +        /* handle W180 == E180 */
   3.366 +        ( box1->lon_min == -180 && box2->lon_max == 180 ) ||
   3.367 +        ( box2->lon_min == -180 && box1->lon_max == 180 )
   3.368 +      )
   3.369 +    )
   3.370 +  );
   3.371 +}
   3.372 +
   3.373 +/* check unambiguousness of east/west orientation of cluster entries and set
   3.374 +   bounding circle of cluster */
   3.375 +static bool pgl_finalize_cluster(pgl_cluster *cluster) {
   3.376 +  int i, j;                 /* i: index of entry, j: index of point in entry */
   3.377 +  int npoints;              /* number of points in entry */
   3.378 +  int total_npoints = 0;    /* total number of points in cluster */
   3.379 +  pgl_point *points;        /* points in entry */
   3.380 +  int lon_dir;              /* first point of entry west (-1) or east (+1) */
   3.381 +  double lon_break = 0;     /* antipodal longitude of first point in entry */
   3.382 +  double lon_min, lon_max;  /* covered longitude range of entry */
   3.383 +  double value;             /* temporary variable */
   3.384 +  /* reset bounding circle center to empty circle at 0/0 coordinates */
   3.385 +  cluster->bounding.center.lat = 0;
   3.386 +  cluster->bounding.center.lon = 0;
   3.387 +  cluster->bounding.radius = -INFINITY;
   3.388 +  /* if cluster is not empty */
   3.389 +  if (cluster->nentries != 0) {
   3.390 +    /* iterate over all cluster entries and ensure they each cover a longitude
   3.391 +       range less than 180 degrees */
   3.392 +    for (i=0; i<cluster->nentries; i++) {
   3.393 +      /* get properties of entry */
   3.394 +      npoints = cluster->entries[i].npoints;
   3.395 +      points = PGL_ENTRY_POINTS(cluster, i);
   3.396 +      /* get longitude of first point of entry */
   3.397 +      value = points[0].lon;
   3.398 +      /* initialize lon_min and lon_max with longitude of first point */
   3.399 +      lon_min = value;
   3.400 +      lon_max = value;
   3.401 +      /* determine east/west orientation of first point and calculate antipodal
   3.402 +         longitude (Note: rounding required here) */
   3.403 +      if      (value < 0) { lon_dir = -1; lon_break = pgl_round(value + 180); }
   3.404 +      else if (value > 0) { lon_dir =  1; lon_break = pgl_round(value - 180); }
   3.405 +      else lon_dir = 0;
   3.406 +      /* iterate over all other points in entry */
   3.407 +      for (j=1; j<npoints; j++) {
   3.408 +        /* consider longitude wrap-around */
   3.409 +        value = points[j].lon;
   3.410 +        if      (lon_dir<0 && value>lon_break) value = pgl_round(value - 360);
   3.411 +        else if (lon_dir>0 && value<lon_break) value = pgl_round(value + 360);
   3.412 +        /* update lon_min and lon_max */
   3.413 +        if      (value < lon_min) lon_min = value;
   3.414 +        else if (value > lon_max) lon_max = value;
   3.415 +        /* return false if 180 degrees or more are covered */
   3.416 +        if (lon_max - lon_min >= 180) return false;
   3.417 +      }
   3.418 +    }
   3.419 +    /* iterate over all points of all entries and calculate arbitrary center
   3.420 +       point for bounding circle (best if center point minimizes the radius,
   3.421 +       but some error is allowed here) */
   3.422 +    for (i=0; i<cluster->nentries; i++) {
   3.423 +      /* get properties of entry */
   3.424 +      npoints = cluster->entries[i].npoints;
   3.425 +      points = PGL_ENTRY_POINTS(cluster, i);
   3.426 +      /* check if first entry */
   3.427 +      if (i==0) {
   3.428 +        /* get longitude of first point of first entry in whole cluster */
   3.429 +        value = points[0].lon;
   3.430 +        /* initialize lon_min and lon_max with longitude of first point of
   3.431 +           first entry in whole cluster (used to determine if whole cluster
   3.432 +           covers a longitude range of 180 degrees or more) */
   3.433 +        lon_min = value;
   3.434 +        lon_max = value;
   3.435 +        /* determine east/west orientation of first point and calculate
   3.436 +           antipodal longitude (Note: rounding not necessary here) */
   3.437 +        if      (value < 0) { lon_dir = -1; lon_break = value + 180; }
   3.438 +        else if (value > 0) { lon_dir =  1; lon_break = value - 180; }
   3.439 +        else lon_dir = 0;
   3.440 +      }
   3.441 +      /* iterate over all points in entry */
   3.442 +      for (j=0; j<npoints; j++) {
   3.443 +        /* longitude wrap-around (Note: rounding not necessary here) */
   3.444 +        value = points[j].lon;
   3.445 +        if      (lon_dir < 0 && value > lon_break) value -= 360;
   3.446 +        else if (lon_dir > 0 && value < lon_break) value += 360;
   3.447 +        if      (value < lon_min) lon_min = value;
   3.448 +        else if (value > lon_max) lon_max = value;
   3.449 +        /* set bounding circle to cover whole earth if more than 180 degrees
   3.450 +           are covered */
   3.451 +        if (lon_max - lon_min >= 180) {
   3.452 +          cluster->bounding.center.lat = 0;
   3.453 +          cluster->bounding.center.lon = 0;
   3.454 +          cluster->bounding.radius = INFINITY;
   3.455 +          return true;
   3.456 +        }
   3.457 +        /* add point to bounding circle center (for average calculation) */
   3.458 +        cluster->bounding.center.lat += points[j].lat;
   3.459 +        cluster->bounding.center.lon += value;
   3.460 +      }
   3.461 +      /* count total number of points */
   3.462 +      total_npoints += npoints;
   3.463 +    }
   3.464 +    /* determine average latitude and longitude of cluster */
   3.465 +    cluster->bounding.center.lat /= total_npoints;
   3.466 +    cluster->bounding.center.lon /= total_npoints;
   3.467 +    /* normalize longitude of center of cluster bounding circle */
   3.468 +    if (cluster->bounding.center.lon < -180) {
   3.469 +      cluster->bounding.center.lon += 360;
   3.470 +    }
   3.471 +    else if (cluster->bounding.center.lon > 180) {
   3.472 +      cluster->bounding.center.lon -= 360;
   3.473 +    }
   3.474 +    /* round bounding circle center (useful if it is used by other functions) */
   3.475 +    cluster->bounding.center.lat = pgl_round(cluster->bounding.center.lat);
   3.476 +    cluster->bounding.center.lon = pgl_round(cluster->bounding.center.lon);
   3.477 +    /* calculate radius of bounding circle */
   3.478 +    for (i=0; i<cluster->nentries; i++) {
   3.479 +      npoints = cluster->entries[i].npoints;
   3.480 +      points = PGL_ENTRY_POINTS(cluster, i);
   3.481 +      for (j=0; j<npoints; j++) {
   3.482 +        value = pgl_distance(
   3.483 +          cluster->bounding.center.lat, cluster->bounding.center.lon,
   3.484 +          points[j].lat, points[j].lon
   3.485 +        );
   3.486 +        if (value > cluster->bounding.radius) cluster->bounding.radius = value;
   3.487 +      }
   3.488 +    }
   3.489 +  }
   3.490 +  /* return true (east/west orientation is unambiguous) */
   3.491 +  return true;
   3.492 +}
   3.493 +
   3.494 +/* check if point is inside cluster */
   3.495 +static bool pgl_point_in_cluster(pgl_point *point, pgl_cluster *cluster) {
   3.496 +  int i, j, k;  /* i: entry, j: point in entry, k: next point in entry */
   3.497 +  int entrytype;         /* type of entry */
   3.498 +  int npoints;           /* number of points in entry */
   3.499 +  pgl_point *points;     /* array of points in entry */
   3.500 +  int lon_dir = 0;       /* first vertex west (-1) or east (+1) */
   3.501 +  double lon_break = 0;  /* antipodal longitude of first vertex */
   3.502 +  double lat0 = point->lat;  /* latitude of point */
   3.503 +  double lon0;           /* (adjusted) longitude of point */
   3.504 +  double lat1, lon1;     /* latitude and (adjusted) longitude of vertex */
   3.505 +  double lat2, lon2;     /* latitude and (adjusted) longitude of next vertex */
   3.506 +  double lon;            /* longitude of intersection */
   3.507 +  int counter = 0;       /* counter for intersections east of point */
   3.508 +  /* points outside bounding circle are always assumed to be non-overlapping */
   3.509 +  /* (necessary for consistent table and index scans) */
   3.510 +  if (
   3.511 +    pgl_distance(
   3.512 +      point->lat, point->lon,
   3.513 +      cluster->bounding.center.lat, cluster->bounding.center.lon
   3.514 +    ) > cluster->bounding.radius
   3.515 +  ) return false;
   3.516 +  /* iterate over all entries */
   3.517 +  for (i=0; i<cluster->nentries; i++) {
   3.518 +    /* get properties of entry */
   3.519 +    entrytype = cluster->entries[i].entrytype;
   3.520 +    npoints = cluster->entries[i].npoints;
   3.521 +    points = PGL_ENTRY_POINTS(cluster, i);
   3.522 +    /* determine east/west orientation of first point of entry and calculate
   3.523 +       antipodal longitude */
   3.524 +    lon_break = points[0].lon;
   3.525 +    if      (lon_break < 0) { lon_dir = -1; lon_break += 180; }
   3.526 +    else if (lon_break > 0) { lon_dir =  1; lon_break -= 180; }
   3.527 +    else lon_dir = 0;
   3.528 +    /* get longitude of point */
   3.529 +    lon0 = point->lon;
   3.530 +    /* consider longitude wrap-around for point */
   3.531 +    if      (lon_dir < 0 && lon0 > lon_break) lon0 = pgl_round(lon0 - 360);
   3.532 +    else if (lon_dir > 0 && lon0 < lon_break) lon0 = pgl_round(lon0 + 360);
   3.533 +    /* iterate over all edges and vertices */
   3.534 +    for (j=0; j<npoints; j++) {
   3.535 +      /* return true if point is on vertex of polygon */
   3.536 +      if (pgl_point_cmp(point, &(points[j])) == 0) return true;
   3.537 +      /* calculate index of next vertex */
   3.538 +      k = (j+1) % npoints;
   3.539 +      /* skip last edge unless entry is (closed) outline or polygon */
   3.540 +      if (
   3.541 +        k == 0 &&
   3.542 +        entrytype != PGL_ENTRY_OUTLINE &&
   3.543 +        entrytype != PGL_ENTRY_POLYGON
   3.544 +      ) continue;
   3.545 +      /* get latitude and longitude values of edge */
   3.546 +      lat1 = points[j].lat;
   3.547 +      lat2 = points[k].lat;
   3.548 +      lon1 = points[j].lon;
   3.549 +      lon2 = points[k].lon;
   3.550 +      /* consider longitude wrap-around for edge */
   3.551 +      if      (lon_dir < 0 && lon1 > lon_break) lon1 = pgl_round(lon1 - 360);
   3.552 +      else if (lon_dir > 0 && lon1 < lon_break) lon1 = pgl_round(lon1 + 360);
   3.553 +      if      (lon_dir < 0 && lon2 > lon_break) lon2 = pgl_round(lon2 - 360);
   3.554 +      else if (lon_dir > 0 && lon2 < lon_break) lon2 = pgl_round(lon2 + 360);
   3.555 +      /* return true if point is on horizontal (west to east) edge of polygon */
   3.556 +      if (
   3.557 +        lat0 == lat1 && lat0 == lat2 &&
   3.558 +        ( (lon0 >= lon1 && lon0 <= lon2) || (lon0 >= lon2 && lon0 <= lon1) )
   3.559 +      ) return true;
   3.560 +      /* check if edge crosses east/west line of point */
   3.561 +      if ((lat1 < lat0 && lat2 >= lat0) || (lat2 < lat0 && lat1 >= lat0)) {
   3.562 +        /* calculate longitude of intersection */
   3.563 +        lon = (lon1 * (lat2-lat0) + lon2 * (lat0-lat1)) / (lat2-lat1);
   3.564 +        /* return true if intersection goes (approximately) through point */
   3.565 +        if (pgl_round(lon) == lon0) return true;
   3.566 +        /* count intersection if east of point and entry is polygon*/
   3.567 +        if (entrytype == PGL_ENTRY_POLYGON && lon > lon0) counter++;
   3.568 +      }
   3.569 +    }
   3.570 +  }
   3.571 +  /* return true if number of intersections is odd */
   3.572 +  return counter & 1;
   3.573 +}
   3.574 +
   3.575 +/* calculate (approximate) distance between point and cluster */
   3.576 +static double pgl_point_cluster_distance(pgl_point *point, pgl_cluster *cluster) {
   3.577 +  int i, j, k;  /* i: entry, j: point in entry, k: next point in entry */
   3.578 +  int entrytype;         /* type of entry */
   3.579 +  int npoints;           /* number of points in entry */
   3.580 +  pgl_point *points;     /* array of points in entry */
   3.581 +  int lon_dir = 0;       /* first vertex west (-1) or east (+1) */
   3.582 +  double lon_break = 0;  /* antipodal longitude of first vertex */
   3.583 +  double lon_min = 0;    /* minimum (adjusted) longitude of entry vertices */
   3.584 +  double lon_max = 0;    /* maximum (adjusted) longitude of entry vertices */
   3.585 +  double lat0 = point->lat;  /* latitude of point */
   3.586 +  double lon0;           /* (adjusted) longitude of point */
   3.587 +  double lat1, lon1;     /* latitude and (adjusted) longitude of vertex */
   3.588 +  double lat2, lon2;     /* latitude and (adjusted) longitude of next vertex */
   3.589 +  double s;              /* scalar for vector calculations */
   3.590 +  double dist;           /* distance calculated in one step */
   3.591 +  double min_dist = INFINITY;   /* minimum distance */
   3.592 +  /* distance is zero if point is contained in cluster */
   3.593 +  if (pgl_point_in_cluster(point, cluster)) return 0;
   3.594 +  /* iterate over all entries */
   3.595 +  for (i=0; i<cluster->nentries; i++) {
   3.596 +    /* get properties of entry */
   3.597 +    entrytype = cluster->entries[i].entrytype;
   3.598 +    npoints = cluster->entries[i].npoints;
   3.599 +    points = PGL_ENTRY_POINTS(cluster, i);
   3.600 +    /* determine east/west orientation of first point of entry and calculate
   3.601 +       antipodal longitude */
   3.602 +    lon_break = points[0].lon;
   3.603 +    if      (lon_break < 0) { lon_dir = -1; lon_break += 180; }
   3.604 +    else if (lon_break > 0) { lon_dir =  1; lon_break -= 180; }
   3.605 +    else lon_dir = 0;
   3.606 +    /* determine covered longitude range */
   3.607 +    for (j=0; j<npoints; j++) {
   3.608 +      /* get longitude of vertex */
   3.609 +      lon1 = points[j].lon;
   3.610 +      /* adjust longitude to fix potential wrap-around */
   3.611 +      if      (lon_dir < 0 && lon1 > lon_break) lon1 -= 360;
   3.612 +      else if (lon_dir > 0 && lon1 < lon_break) lon1 += 360;
   3.613 +      /* update minimum and maximum longitude of polygon */
   3.614 +      if (j == 0 || lon1 < lon_min) lon_min = lon1;
   3.615 +      if (j == 0 || lon1 > lon_max) lon_max = lon1;
   3.616 +    }
   3.617 +    /* adjust longitude wrap-around according to full longitude range */
   3.618 +    lon_break = (lon_max + lon_min) / 2;
   3.619 +    if      (lon_break < 0) { lon_dir = -1; lon_break += 180; }
   3.620 +    else if (lon_break > 0) { lon_dir =  1; lon_break -= 180; }
   3.621 +    /* get longitude of point */
   3.622 +    lon0 = point->lon;
   3.623 +    /* consider longitude wrap-around for point */
   3.624 +    if      (lon_dir < 0 && lon0 > lon_break) lon0 -= 360;
   3.625 +    else if (lon_dir > 0 && lon0 < lon_break) lon0 += 360;
   3.626 +    /* iterate over all edges and vertices */
   3.627 +    for (j=0; j<npoints; j++) {
   3.628 +      /* get latitude and longitude values of current point */
   3.629 +      lat1 = points[j].lat;
   3.630 +      lon1 = points[j].lon;
   3.631 +      /* consider longitude wrap-around for current point */
   3.632 +      if      (lon_dir < 0 && lon1 > lon_break) lon1 -= 360;
   3.633 +      else if (lon_dir > 0 && lon1 < lon_break) lon1 += 360;
   3.634 +      /* calculate distance to vertex */
   3.635 +      dist = pgl_distance(lat0, lon0, lat1, lon1);
   3.636 +      /* store calculated distance if smallest */
   3.637 +      if (dist < min_dist) min_dist = dist;
   3.638 +      /* calculate index of next vertex */
   3.639 +      k = (j+1) % npoints;
   3.640 +      /* skip last edge unless entry is (closed) outline or polygon */
   3.641 +      if (
   3.642 +        k == 0 &&
   3.643 +        entrytype != PGL_ENTRY_OUTLINE &&
   3.644 +        entrytype != PGL_ENTRY_POLYGON
   3.645 +      ) continue;
   3.646 +      /* get latitude and longitude values of next point */
   3.647 +      lat2 = points[k].lat;
   3.648 +      lon2 = points[k].lon;
   3.649 +      /* consider longitude wrap-around for next point */
   3.650 +      if      (lon_dir < 0 && lon2 > lon_break) lon2 -= 360;
   3.651 +      else if (lon_dir > 0 && lon2 < lon_break) lon2 += 360;
   3.652 +      /* go to next vertex and edge if edge is degenerated */
   3.653 +      if (lat1 == lat2 && lon1 == lon2) continue;
   3.654 +      /* otherwise test if point can be projected onto edge of polygon */
   3.655 +      s = (
   3.656 +        ((lat0-lat1) * (lat2-lat1) + (lon0-lon1) * (lon2-lon1)) /
   3.657 +        ((lat2-lat1) * (lat2-lat1) + (lon2-lon1) * (lon2-lon1))
   3.658 +      );
   3.659 +      /* go to next vertex and edge if point cannot be projected */
   3.660 +      if (!(s > 0 && s < 1)) continue;
   3.661 +      /* calculate distance from original point to projected point */
   3.662 +      dist = pgl_distance(
   3.663 +        lat0, lon0,
   3.664 +        lat1 + s * (lat2-lat1),
   3.665 +        lon1 + s * (lon2-lon1)
   3.666 +      );
   3.667 +      /* store calculated distance if smallest */
   3.668 +      if (dist < min_dist) min_dist = dist;
   3.669 +    }
   3.670 +  }
   3.671 +  /* return minimum distance */
   3.672 +  return min_dist;
   3.673 +}
   3.674 +
   3.675 +/* estimator function for distance between box and point */
   3.676 +/* allowed to return smaller values than actually correct */
   3.677 +static double pgl_estimate_point_box_distance(pgl_point *point, pgl_box *box) {
   3.678 +  double dlon;  /* longitude range of box (delta longitude) */
   3.679 +  double h;     /* half of distance along meridian */
   3.680 +  double d;     /* distance between both southern or both northern points */
   3.681 +  double cur_dist;  /* calculated distance */
   3.682 +  double min_dist;  /* minimum distance calculated */
   3.683 +  /* return infinity if bounding box is empty */
   3.684 +  if (box->lat_min > box->lat_max) return INFINITY;
   3.685 +  /* return zero if point is inside bounding box */
   3.686 +  if (pgl_point_in_box(point, box)) return 0;
   3.687 +  /* calculate delta longitude */
   3.688 +  dlon = box->lon_max - box->lon_min;
   3.689 +  if (dlon < 0) dlon += 360;  /* 180th meridian crossed */
   3.690 +  /* if delta longitude is greater than 180 degrees, perform safe fall-back */
   3.691 +  if (dlon > 180) return 0;
   3.692 +  /* calculate half of distance along meridian */
   3.693 +  h = pgl_distance(box->lat_min, 0, box->lat_max, 0) / 2;
   3.694 +  /* calculate full distance between southern points */
   3.695 +  d = pgl_distance(box->lat_min, 0, box->lat_min, dlon);
   3.696 +  /* calculate maximum of full distance and half distance */
   3.697 +  if (h > d) d = h;
   3.698 +  /* calculate distance from point to first southern vertex and substract
   3.699 +     maximum error */
   3.700 +  min_dist = pgl_distance(
   3.701 +    point->lat, point->lon, box->lat_min, box->lon_min
   3.702 +  ) - d;
   3.703 +  /* return zero if estimated distance is smaller than zero */
   3.704 +  if (min_dist <= 0) return 0;
   3.705 +  /* repeat procedure with second southern vertex */
   3.706 +  cur_dist = pgl_distance(
   3.707 +    point->lat, point->lon, box->lat_min, box->lon_max
   3.708 +  ) - d;
   3.709 +  if (cur_dist <= 0) return 0;
   3.710 +  if (cur_dist < min_dist) min_dist = cur_dist;
   3.711 +  /* calculate full distance between northern points */
   3.712 +  d = pgl_distance(box->lat_max, 0, box->lat_max, dlon);
   3.713 +  /* calculate maximum of full distance and half distance */
   3.714 +  if (h > d) d = h;
   3.715 +  /* repeat procedure with northern vertices */
   3.716 +  cur_dist = pgl_distance(
   3.717 +    point->lat, point->lon, box->lat_max, box->lon_max
   3.718 +  ) - d;
   3.719 +  if (cur_dist <= 0) return 0;
   3.720 +  if (cur_dist < min_dist) min_dist = cur_dist;
   3.721 +  cur_dist = pgl_distance(
   3.722 +    point->lat, point->lon, box->lat_max, box->lon_min
   3.723 +  ) - d;
   3.724 +  if (cur_dist <= 0) return 0;
   3.725 +  if (cur_dist < min_dist) min_dist = cur_dist;
   3.726 +  /* return smallest value (unless already returned zero) */
   3.727 +  return min_dist;
   3.728 +}
   3.729 +
   3.730 +
   3.731 +/*----------------------------*
   3.732 + *  fractal geographic index  *
   3.733 + *----------------------------*/
   3.734 +
   3.735 +/* number of bytes used for geographic (center) position in keys */
   3.736 +#define PGL_KEY_LATLON_BYTELEN 7
   3.737 +
   3.738 +/* maximum reference value for logarithmic size of geographic objects */
   3.739 +#define PGL_AREAKEY_REFOBJSIZE (PGL_DIAMETER/3.0)  /* can be tweaked */
   3.740 +
   3.741 +/* safety margin to avoid floating point errors in distance estimation */
   3.742 +#define PGL_FPE_SAFETY (1.0+1e-14)  /* slightly greater than 1.0 */
   3.743 +
   3.744 +/* pointer to index key (either pgl_pointkey or pgl_areakey) */
   3.745 +typedef unsigned char *pgl_keyptr;
   3.746 +
   3.747 +/* index key for points (objects with zero area) on the spheroid */
   3.748 +/* bit  0..55: interspersed bits of latitude and longitude,
   3.749 +   bit 56..57: always zero,
   3.750 +   bit 58..63: node depth in hypothetic (full) tree from 0 to 56 (incl.) */
   3.751 +typedef unsigned char pgl_pointkey[PGL_KEY_LATLON_BYTELEN+1];
   3.752 +
   3.753 +/* index key for geographic objects on spheroid with area greater than zero */
   3.754 +/* bit  0..55: interspersed bits of latitude and longitude of center point,
   3.755 +   bit     56: always set to 1,
   3.756 +   bit 57..63: node depth in hypothetic (full) tree from 0 to (2*56)+1 (incl.),
   3.757 +   bit 64..71: logarithmic object size from 0 to 56+1 = 57 (incl.), but set to
   3.758 +               PGL_KEY_OBJSIZE_EMPTY (with interspersed bits = 0 and node depth
   3.759 +               = 113) for empty objects, and set to PGL_KEY_OBJSIZE_UNIVERSAL
   3.760 +               (with interspersed bits = 0 and node depth = 0) for keys which
   3.761 +               cover both empty and non-empty objects */
   3.762 +
   3.763 +typedef unsigned char pgl_areakey[PGL_KEY_LATLON_BYTELEN+2];
   3.764 +
   3.765 +/* helper macros for reading/writing index keys */
   3.766 +#define PGL_KEY_NODEDEPTH_OFFSET  PGL_KEY_LATLON_BYTELEN
   3.767 +#define PGL_KEY_OBJSIZE_OFFSET    (PGL_KEY_NODEDEPTH_OFFSET+1)
   3.768 +#define PGL_POINTKEY_MAXDEPTH     (PGL_KEY_LATLON_BYTELEN*8)
   3.769 +#define PGL_AREAKEY_MAXDEPTH      (2*PGL_POINTKEY_MAXDEPTH+1)
   3.770 +#define PGL_AREAKEY_MAXOBJSIZE    (PGL_POINTKEY_MAXDEPTH+1)
   3.771 +#define PGL_AREAKEY_TYPEMASK      0x80
   3.772 +#define PGL_KEY_LATLONBIT(key, n) ((key)[(n)/8] & (0x80 >> ((n)%8)))
   3.773 +#define PGL_KEY_LATLONBIT_DIFF(key1, key2, n) \
   3.774 +                                  ( PGL_KEY_LATLONBIT(key1, n) ^ \
   3.775 +                                    PGL_KEY_LATLONBIT(key2, n) )
   3.776 +#define PGL_KEY_IS_AREAKEY(key)   ((key)[PGL_KEY_NODEDEPTH_OFFSET] & \
   3.777 +                                    PGL_AREAKEY_TYPEMASK)
   3.778 +#define PGL_KEY_NODEDEPTH(key)    ((key)[PGL_KEY_NODEDEPTH_OFFSET] & \
   3.779 +                                    (PGL_AREAKEY_TYPEMASK-1))
   3.780 +#define PGL_KEY_OBJSIZE(key)      ((key)[PGL_KEY_OBJSIZE_OFFSET])
   3.781 +#define PGL_KEY_OBJSIZE_EMPTY     126
   3.782 +#define PGL_KEY_OBJSIZE_UNIVERSAL 127
   3.783 +#define PGL_KEY_IS_EMPTY(key)     ( PGL_KEY_IS_AREAKEY(key) && \
   3.784 +                                    (key)[PGL_KEY_OBJSIZE_OFFSET] == \
   3.785 +                                    PGL_KEY_OBJSIZE_EMPTY )
   3.786 +#define PGL_KEY_IS_UNIVERSAL(key) ( PGL_KEY_IS_AREAKEY(key) && \
   3.787 +                                    (key)[PGL_KEY_OBJSIZE_OFFSET] == \
   3.788 +                                    PGL_KEY_OBJSIZE_UNIVERSAL )
   3.789 +
   3.790 +/* set area key to match empty objects only */
   3.791 +static void pgl_key_set_empty(pgl_keyptr key) {
   3.792 +  memset(key, 0, sizeof(pgl_areakey));
   3.793 +  /* Note: setting node depth to maximum is required for picksplit function */
   3.794 +  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK | PGL_AREAKEY_MAXDEPTH;
   3.795 +  key[PGL_KEY_OBJSIZE_OFFSET] = PGL_KEY_OBJSIZE_EMPTY;
   3.796 +}
   3.797 +
   3.798 +/* set area key to match any object (including empty objects) */
   3.799 +static void pgl_key_set_universal(pgl_keyptr key) {
   3.800 +  memset(key, 0, sizeof(pgl_areakey));
   3.801 +  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK;
   3.802 +  key[PGL_KEY_OBJSIZE_OFFSET] = PGL_KEY_OBJSIZE_UNIVERSAL;
   3.803 +}
   3.804 +
   3.805 +/* convert a point on earth into a max-depth key to be used in index */
   3.806 +static void pgl_point_to_key(pgl_point *point, pgl_keyptr key) {
   3.807 +  double lat = point->lat;
   3.808 +  double lon = point->lon;
   3.809 +  int i;
   3.810 +  /* clear latitude and longitude bits */
   3.811 +  memset(key, 0, PGL_KEY_LATLON_BYTELEN);
   3.812 +  /* set node depth to maximum and type bit to zero */
   3.813 +  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_POINTKEY_MAXDEPTH;
   3.814 +  /* iterate over all latitude/longitude bit pairs */
   3.815 +  for (i=0; i<PGL_POINTKEY_MAXDEPTH/2; i++) {
   3.816 +    /* determine latitude bit */
   3.817 +    if (lat >= 0) {
   3.818 +      key[i/4] |= 0x80 >> (2*(i%4));
   3.819 +      lat *= 2; lat -= 90;
   3.820 +    } else {
   3.821 +      lat *= 2; lat += 90;
   3.822 +    }
   3.823 +    /* determine longitude bit */
   3.824 +    if (lon >= 0) {
   3.825 +      key[i/4] |= 0x80 >> (2*(i%4)+1);
   3.826 +      lon *= 2; lon -= 180;
   3.827 +    } else {
   3.828 +      lon *= 2; lon += 180;
   3.829 +    }
   3.830 +  }
   3.831 +}
   3.832 +
   3.833 +/* convert a circle on earth into a max-depth key to be used in an index */
   3.834 +static void pgl_circle_to_key(pgl_circle *circle, pgl_keyptr key) {
   3.835 +  /* handle special case of empty circle */
   3.836 +  if (circle->radius < 0) {
   3.837 +    pgl_key_set_empty(key);
   3.838 +    return;
   3.839 +  }
   3.840 +  /* perform same action as for point keys */
   3.841 +  pgl_point_to_key(&(circle->center), key);
   3.842 +  /* but overwrite type and node depth to fit area index key */
   3.843 +  key[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK | PGL_AREAKEY_MAXDEPTH;
   3.844 +  /* check if radius is greater than (or equal to) reference size */
   3.845 +  /* (treat equal values as greater values for numerical safety) */
   3.846 +  if (circle->radius >= PGL_AREAKEY_REFOBJSIZE) {
   3.847 +    /* if yes, set logarithmic size to zero */
   3.848 +    key[PGL_KEY_OBJSIZE_OFFSET] = 0;
   3.849 +  } else {
   3.850 +    /* otherwise, determine logarithmic size iteratively */
   3.851 +    /* (one step is equivalent to a factor of sqrt(2)) */
   3.852 +    double reference = PGL_AREAKEY_REFOBJSIZE / M_SQRT2;
   3.853 +    int objsize = 1;
   3.854 +    while (objsize < PGL_AREAKEY_MAXOBJSIZE) {
   3.855 +      /* stop when radius is greater than (or equal to) adjusted reference */
   3.856 +      /* (treat equal values as greater values for numerical safety) */
   3.857 +      if (circle->radius >= reference) break;
   3.858 +      reference /= M_SQRT2;
   3.859 +      objsize++;
   3.860 +    }
   3.861 +    /* set logarithmic size to determined value */
   3.862 +    key[PGL_KEY_OBJSIZE_OFFSET] = objsize;
   3.863 +  }
   3.864 +}
   3.865 +
   3.866 +/* check if one key is subkey of another key or vice versa */
   3.867 +static bool pgl_keys_overlap(pgl_keyptr key1, pgl_keyptr key2) {
   3.868 +  int i;  /* key bit offset (includes both lat/lon and log. obj. size bits) */
   3.869 +  /* determine smallest depth */
   3.870 +  int depth1 = PGL_KEY_NODEDEPTH(key1);
   3.871 +  int depth2 = PGL_KEY_NODEDEPTH(key2);
   3.872 +  int depth = (depth1 < depth2) ? depth1 : depth2;
   3.873 +  /* check if keys are area keys (assuming that both keys have same type) */
   3.874 +  if (PGL_KEY_IS_AREAKEY(key1)) {
   3.875 +    int j = 0;  /* bit offset for logarithmic object size bits */
   3.876 +    int k = 0;  /* bit offset for latitude and longitude */
   3.877 +    /* fetch logarithmic object size information */
   3.878 +    int objsize1 = PGL_KEY_OBJSIZE(key1);
   3.879 +    int objsize2 = PGL_KEY_OBJSIZE(key2);
   3.880 +    /* handle special cases for empty objects (universal and empty keys) */
   3.881 +    if (
   3.882 +      objsize1 == PGL_KEY_OBJSIZE_UNIVERSAL ||
   3.883 +      objsize2 == PGL_KEY_OBJSIZE_UNIVERSAL
   3.884 +    ) return true;
   3.885 +    if (
   3.886 +      objsize1 == PGL_KEY_OBJSIZE_EMPTY ||
   3.887 +      objsize2 == PGL_KEY_OBJSIZE_EMPTY
   3.888 +    ) return objsize1 == objsize2;
   3.889 +    /* iterate through key bits */
   3.890 +    for (i=0; i<depth; i++) {
   3.891 +      /* every second bit is a bit describing the object size */
   3.892 +      if (i%2 == 0) {
   3.893 +        /* check if object size bit is different in both keys (objsize1 and
   3.894 +           objsize2 describe the minimum index when object size bit is set) */
   3.895 +        if (
   3.896 +          (objsize1 <= j && objsize2 > j) ||
   3.897 +          (objsize2 <= j && objsize1 > j)
   3.898 +        ) {
   3.899 +          /* bit differs, therefore keys are in separate branches */
   3.900 +          return false;
   3.901 +        }
   3.902 +        /* increase bit counter for object size bits */
   3.903 +        j++;
   3.904 +      }
   3.905 +      /* all other bits describe latitude and longitude */
   3.906 +      else {
   3.907 +        /* check if bit differs in both keys */
   3.908 +        if (PGL_KEY_LATLONBIT_DIFF(key1, key2, k)) {
   3.909 +          /* bit differs, therefore keys are in separate branches */
   3.910 +          return false;
   3.911 +        }
   3.912 +        /* increase bit counter for latitude/longitude bits */
   3.913 +        k++;
   3.914 +      }
   3.915 +    }
   3.916 +  }
   3.917 +  /* if not, keys are point keys */
   3.918 +  else {
   3.919 +    /* iterate through key bits */
   3.920 +    for (i=0; i<depth; i++) {
   3.921 +      /* check if bit differs in both keys */
   3.922 +      if (PGL_KEY_LATLONBIT_DIFF(key1, key2, i)) {
   3.923 +        /* bit differs, therefore keys are in separate branches */
   3.924 +        return false;
   3.925 +      }
   3.926 +    }
   3.927 +  }
   3.928 +  /* return true because keys are in the same branch */
   3.929 +  return true;
   3.930 +}
   3.931 +
   3.932 +/* combine two keys into new key which covers both original keys */
   3.933 +/* (result stored in first argument) */
   3.934 +static void pgl_unite_keys(pgl_keyptr dst, pgl_keyptr src) {
   3.935 +  int i;  /* key bit offset (includes both lat/lon and log. obj. size bits) */
   3.936 +  /* determine smallest depth */
   3.937 +  int depth1 = PGL_KEY_NODEDEPTH(dst);
   3.938 +  int depth2 = PGL_KEY_NODEDEPTH(src);
   3.939 +  int depth = (depth1 < depth2) ? depth1 : depth2;
   3.940 +  /* check if keys are area keys (assuming that both keys have same type) */
   3.941 +  if (PGL_KEY_IS_AREAKEY(dst)) {
   3.942 +    pgl_areakey dstbuf = { 0, };  /* destination buffer (cleared) */
   3.943 +    int j = 0;  /* bit offset for logarithmic object size bits */
   3.944 +    int k = 0;  /* bit offset for latitude and longitude */
   3.945 +    /* fetch logarithmic object size information */
   3.946 +    int objsize1 = PGL_KEY_OBJSIZE(dst);
   3.947 +    int objsize2 = PGL_KEY_OBJSIZE(src);
   3.948 +    /* handle special cases for empty objects (universal and empty keys) */
   3.949 +    if (
   3.950 +      objsize1 > PGL_AREAKEY_MAXOBJSIZE ||
   3.951 +      objsize2 > PGL_AREAKEY_MAXOBJSIZE
   3.952 +    ) {
   3.953 +      if (
   3.954 +        objsize1 == PGL_KEY_OBJSIZE_EMPTY &&
   3.955 +        objsize2 == PGL_KEY_OBJSIZE_EMPTY
   3.956 +      ) pgl_key_set_empty(dst);
   3.957 +      else pgl_key_set_universal(dst);
   3.958 +      return;
   3.959 +    }
   3.960 +    /* iterate through key bits */
   3.961 +    for (i=0; i<depth; i++) {
   3.962 +      /* every second bit is a bit describing the object size */
   3.963 +      if (i%2 == 0) {
   3.964 +        /* increase bit counter for object size bits first */
   3.965 +        /* (handy when setting objsize variable) */
   3.966 +        j++;
   3.967 +        /* check if object size bit is set in neither key */
   3.968 +        if (objsize1 >= j && objsize2 >= j) {
   3.969 +          /* set objsize in destination buffer to indicate that size bit is
   3.970 +             unset in destination buffer at the current bit position */
   3.971 +          dstbuf[PGL_KEY_OBJSIZE_OFFSET] = j;
   3.972 +        }
   3.973 +        /* break if object size bit is set in one key only */
   3.974 +        else if (objsize1 >= j || objsize2 >= j) break;
   3.975 +      }
   3.976 +      /* all other bits describe latitude and longitude */
   3.977 +      else {
   3.978 +        /* break if bit differs in both keys */
   3.979 +        if (PGL_KEY_LATLONBIT(dst, k)) {
   3.980 +          if (!PGL_KEY_LATLONBIT(src, k)) break;
   3.981 +          /* but set bit in destination buffer if bit is set in both keys */
   3.982 +          dstbuf[k/8] |= 0x80 >> (k%8);
   3.983 +        } else if (PGL_KEY_LATLONBIT(src, k)) break;
   3.984 +        /* increase bit counter for latitude/longitude bits */
   3.985 +        k++;
   3.986 +      }
   3.987 +    }
   3.988 +    /* set common node depth and type bit (type bit = 1) */
   3.989 +    dstbuf[PGL_KEY_NODEDEPTH_OFFSET] = PGL_AREAKEY_TYPEMASK | i;
   3.990 +    /* copy contents of destination buffer to first key */
   3.991 +    memcpy(dst, dstbuf, sizeof(pgl_areakey));
   3.992 +  }
   3.993 +  /* if not, keys are point keys */
   3.994 +  else {
   3.995 +    pgl_pointkey dstbuf = { 0, };  /* destination buffer (cleared) */
   3.996 +    /* iterate through key bits */
   3.997 +    for (i=0; i<depth; i++) {
   3.998 +      /* break if bit differs in both keys */
   3.999 +      if (PGL_KEY_LATLONBIT(dst, i)) {
  3.1000 +        if (!PGL_KEY_LATLONBIT(src, i)) break;
  3.1001 +        /* but set bit in destination buffer if bit is set in both keys */
  3.1002 +        dstbuf[i/8] |= 0x80 >> (i%8);
  3.1003 +      } else if (PGL_KEY_LATLONBIT(src, i)) break;
  3.1004 +    }
  3.1005 +    /* set common node depth (type bit = 0) */
  3.1006 +    dstbuf[PGL_KEY_NODEDEPTH_OFFSET] = i;
  3.1007 +    /* copy contents of destination buffer to first key */
  3.1008 +    memcpy(dst, dstbuf, sizeof(pgl_pointkey));
  3.1009 +  }
  3.1010 +}
  3.1011 +
  3.1012 +/* determine center(!) boundaries and radius estimation of index key */
  3.1013 +static double pgl_key_to_box(pgl_keyptr key, pgl_box *box) {
  3.1014 +  int i;
  3.1015 +  /* determine node depth */
  3.1016 +  int depth = PGL_KEY_NODEDEPTH(key);
  3.1017 +  /* center point of possible result */
  3.1018 +  double lat = 0;
  3.1019 +  double lon = 0;
  3.1020 +  /* maximum distance of real center point from key center */
  3.1021 +  double dlat = 90;
  3.1022 +  double dlon = 180;
  3.1023 +  /* maximum radius of contained objects */
  3.1024 +  double radius = 0;  /* always return zero for point index keys */
  3.1025 +  /* check if key is area key */
  3.1026 +  if (PGL_KEY_IS_AREAKEY(key)) {
  3.1027 +    /* get logarithmic object size */
  3.1028 +    int objsize = PGL_KEY_OBJSIZE(key);
  3.1029 +    /* handle special cases for empty objects (universal and empty keys) */
  3.1030 +    if (objsize == PGL_KEY_OBJSIZE_EMPTY) {
  3.1031 +      pgl_box_set_empty(box);
  3.1032 +      return 0;
  3.1033 +    } else if (objsize == PGL_KEY_OBJSIZE_UNIVERSAL) {
  3.1034 +      box->lat_min = -90;
  3.1035 +      box->lat_max =  90;
  3.1036 +      box->lon_min = -180;
  3.1037 +      box->lon_max =  180;
  3.1038 +      return 0;  /* any value >= 0 would do */
  3.1039 +    }
  3.1040 +    /* calculate maximum possible radius of objects covered by the given key */
  3.1041 +    if (objsize == 0) radius = INFINITY;
  3.1042 +    else {
  3.1043 +      radius = PGL_AREAKEY_REFOBJSIZE;
  3.1044 +      while (--objsize) radius /= M_SQRT2;
  3.1045 +    }
  3.1046 +    /* iterate over latitude and longitude bits in key */
  3.1047 +    /* (every second bit is a latitude or longitude bit) */
  3.1048 +    for (i=0; i<depth/2; i++) {
  3.1049 +      /* check if latitude bit */
  3.1050 +      if (i%2 == 0) {
  3.1051 +        /* cut latitude dimension in half */
  3.1052 +        dlat /= 2;
  3.1053 +        /* increase center latitude if bit is 1, otherwise decrease */
  3.1054 +        if (PGL_KEY_LATLONBIT(key, i)) lat += dlat;
  3.1055 +        else lat -= dlat;
  3.1056 +      }
  3.1057 +      /* otherwise longitude bit */
  3.1058 +      else {
  3.1059 +        /* cut longitude dimension in half */
  3.1060 +        dlon /= 2;
  3.1061 +        /* increase center longitude if bit is 1, otherwise decrease */
  3.1062 +        if (PGL_KEY_LATLONBIT(key, i)) lon += dlon;
  3.1063 +        else lon -= dlon;
  3.1064 +      }
  3.1065 +    }
  3.1066 +  }
  3.1067 +  /* if not, keys are point keys */
  3.1068 +  else {
  3.1069 +    /* iterate over all bits in key */
  3.1070 +    for (i=0; i<depth; i++) {
  3.1071 +      /* check if latitude bit */
  3.1072 +      if (i%2 == 0) {
  3.1073 +        /* cut latitude dimension in half */
  3.1074 +        dlat /= 2;
  3.1075 +        /* increase center latitude if bit is 1, otherwise decrease */
  3.1076 +        if (PGL_KEY_LATLONBIT(key, i)) lat += dlat;
  3.1077 +        else lat -= dlat;
  3.1078 +      }
  3.1079 +      /* otherwise longitude bit */
  3.1080 +      else {
  3.1081 +        /* cut longitude dimension in half */
  3.1082 +        dlon /= 2;
  3.1083 +        /* increase center longitude if bit is 1, otherwise decrease */
  3.1084 +        if (PGL_KEY_LATLONBIT(key, i)) lon += dlon;
  3.1085 +        else lon -= dlon;
  3.1086 +      }
  3.1087 +    }
  3.1088 +  }
  3.1089 +  /* calculate boundaries from center point and remaining dlat and dlon */
  3.1090 +  /* (return values through pointer to box) */
  3.1091 +  box->lat_min = lat - dlat;
  3.1092 +  box->lat_max = lat + dlat;
  3.1093 +  box->lon_min = lon - dlon;
  3.1094 +  box->lon_max = lon + dlon;
  3.1095 +  /* return radius (as a function return value) */
  3.1096 +  return radius;
  3.1097 +}
  3.1098 +
  3.1099 +/* estimator function for distance between point and index key */
  3.1100 +/* allowed to return smaller values than actually correct */
  3.1101 +static double pgl_estimate_key_distance(pgl_keyptr key, pgl_point *point) {
  3.1102 +  pgl_box box;  /* center(!) bounding box of area index key */
  3.1103 +  /* calculate center(!) bounding box and maximum radius of objects covered
  3.1104 +     by area index key (radius is zero for point index keys) */
  3.1105 +  double distance = pgl_key_to_box(key, &box);
  3.1106 +  /* calculate estimated distance between bounding box of center point of
  3.1107 +     indexed object and point passed as second argument, then substract maximum
  3.1108 +     radius of objects covered by index key */
  3.1109 +  /* (use PGL_FPE_SAFETY factor to cope with minor floating point errors) */
  3.1110 +  distance = (
  3.1111 +    pgl_estimate_point_box_distance(point, &box) / PGL_FPE_SAFETY -
  3.1112 +    distance * PGL_FPE_SAFETY
  3.1113 +  );
  3.1114 +  /* truncate negative results to zero */
  3.1115 +  if (distance <= 0) distance = 0;
  3.1116 +  /* return result */
  3.1117 +  return distance;
  3.1118 +}
  3.1119 +
  3.1120 +
  3.1121 +/*---------------------------------*
  3.1122 + *  helper functions for text I/O  *
  3.1123 + *---------------------------------*/
  3.1124 +
  3.1125 +#define PGL_NUMBUFLEN 64  /* buffer size for number to string conversion */
  3.1126 +
  3.1127 +/* convert floating point number to string (round-trip safe) */
  3.1128 +static void pgl_print_float(char *buf, double flt) {
  3.1129 +  /* check if number is integral */
  3.1130 +  if (trunc(flt) == flt) {
  3.1131 +    /* for integral floats use maximum precision */
  3.1132 +    snprintf(buf, PGL_NUMBUFLEN, "%.17g", flt);
  3.1133 +  } else {
  3.1134 +    /* otherwise check if 15, 16, or 17 digits needed (round-trip safety) */
  3.1135 +    snprintf(buf, PGL_NUMBUFLEN, "%.15g", flt);
  3.1136 +    if (strtod(buf, NULL) != flt) snprintf(buf, PGL_NUMBUFLEN, "%.16g", flt);
  3.1137 +    if (strtod(buf, NULL) != flt) snprintf(buf, PGL_NUMBUFLEN, "%.17g", flt);
  3.1138 +  }
  3.1139 +}
  3.1140 +
  3.1141 +/* convert latitude floating point number (in degrees) to string */
  3.1142 +static void pgl_print_lat(char *buf, double lat) {
  3.1143 +  if (signbit(lat)) {
  3.1144 +    /* treat negative latitudes (including -0) as south */
  3.1145 +    snprintf(buf, PGL_NUMBUFLEN, "S%015.12f", -lat);
  3.1146 +  } else {
  3.1147 +    /* treat positive latitudes (including +0) as north */
  3.1148 +    snprintf(buf, PGL_NUMBUFLEN, "N%015.12f", lat);
  3.1149 +  }
  3.1150 +}
  3.1151 +
  3.1152 +/* convert longitude floating point number (in degrees) to string */
  3.1153 +static void pgl_print_lon(char *buf, double lon) {
  3.1154 +  if (signbit(lon)) {
  3.1155 +    /* treat negative longitudes (including -0) as west */
  3.1156 +    snprintf(buf, PGL_NUMBUFLEN, "W%016.12f", -lon);
  3.1157 +  } else {
  3.1158 +    /* treat positive longitudes (including +0) as east */
  3.1159 +    snprintf(buf, PGL_NUMBUFLEN, "E%016.12f", lon);
  3.1160 +  }
  3.1161 +}
  3.1162 +
  3.1163 +/* bit masks used as return value of pgl_scan() function */
  3.1164 +#define PGL_SCAN_NONE 0      /* no value has been parsed */
  3.1165 +#define PGL_SCAN_LAT (1<<0)  /* latitude has been parsed */
  3.1166 +#define PGL_SCAN_LON (1<<1)  /* longitude has been parsed */
  3.1167 +#define PGL_SCAN_LATLON (PGL_SCAN_LAT | PGL_SCAN_LON)  /* bitwise OR of both */
  3.1168 +
  3.1169 +/* parse a coordinate (can be latitude or longitude) */
  3.1170 +static int pgl_scan(char **str, double *lat, double *lon) {
  3.1171 +  double val;
  3.1172 +  int len;
  3.1173 +  if (
  3.1174 +    sscanf(*str, " N %lf %n", &val, &len) ||
  3.1175 +    sscanf(*str, " n %lf %n", &val, &len)
  3.1176 +  ) {
  3.1177 +    *str += len; *lat = val; return PGL_SCAN_LAT;
  3.1178 +  }
  3.1179 +  if (
  3.1180 +    sscanf(*str, " S %lf %n", &val, &len) ||
  3.1181 +    sscanf(*str, " s %lf %n", &val, &len)
  3.1182 +  ) {
  3.1183 +    *str += len; *lat = -val; return PGL_SCAN_LAT;
  3.1184 +  }
  3.1185 +  if (
  3.1186 +    sscanf(*str, " E %lf %n", &val, &len) ||
  3.1187 +    sscanf(*str, " e %lf %n", &val, &len)
  3.1188 +  ) {
  3.1189 +    *str += len; *lon = val; return PGL_SCAN_LON;
  3.1190 +  }
  3.1191 +  if (
  3.1192 +    sscanf(*str, " W %lf %n", &val, &len) ||
  3.1193 +    sscanf(*str, " w %lf %n", &val, &len)
  3.1194 +  ) {
  3.1195 +    *str += len; *lon = -val; return PGL_SCAN_LON;
  3.1196 +  }
  3.1197 +  return PGL_SCAN_NONE;
  3.1198 +}
  3.1199 +
  3.1200 +
  3.1201 +/*-----------------*
  3.1202 + *  SQL functions  *
  3.1203 + *-----------------*/
  3.1204 +
  3.1205 +/* Note: These function names use "epoint", "ebox", etc. notation here instead
  3.1206 +   of "point", "box", etc. in order to distinguish them from any previously
  3.1207 +   defined functions. */
  3.1208 +
  3.1209 +/* function needed for dummy types and/or not implemented features */
  3.1210 +PG_FUNCTION_INFO_V1(pgl_notimpl);
  3.1211 +Datum pgl_notimpl(PG_FUNCTION_ARGS) {
  3.1212 +  ereport(ERROR, (errmsg("not implemented by pgLatLon")));
  3.1213 +}
  3.1214 +
  3.1215 +/* set point to latitude and longitude (including checks) */
  3.1216 +static void pgl_epoint_set_latlon(pgl_point *point, double lat, double lon) {
  3.1217 +  /* reject infinite or NaN values */
  3.1218 +  if (!isfinite(lat) || !isfinite(lon)) {
  3.1219 +    ereport(ERROR, (
  3.1220 +      errcode(ERRCODE_DATA_EXCEPTION),
  3.1221 +      errmsg("epoint requires finite coordinates")
  3.1222 +    ));
  3.1223 +  }
  3.1224 +  /* check latitude bounds */
  3.1225 +  if (lat < -90) {
  3.1226 +    ereport(WARNING, (errmsg("latitude exceeds south pole")));
  3.1227 +    lat = -90;
  3.1228 +  } else if (lat > 90) {
  3.1229 +    ereport(WARNING, (errmsg("latitude exceeds north pole")));
  3.1230 +    lat = 90;
  3.1231 +  }
  3.1232 +  /* check longitude bounds */
  3.1233 +  if (lon < -180) {
  3.1234 +    ereport(NOTICE, (errmsg("longitude west of 180th meridian normalized")));
  3.1235 +    lon += 360 - trunc(lon / 360) * 360;
  3.1236 +  } else if (lon > 180) {
  3.1237 +    ereport(NOTICE, (errmsg("longitude east of 180th meridian normalized")));
  3.1238 +    lon -= 360 + trunc(lon / 360) * 360;
  3.1239 +  }
  3.1240 +  /* store rounded latitude/longitude values for round-trip safety */
  3.1241 +  point->lat = pgl_round(lat);
  3.1242 +  point->lon = pgl_round(lon);
  3.1243 +}
  3.1244 +
  3.1245 +/* create point ("epoint" in SQL) from latitude and longitude */
  3.1246 +PG_FUNCTION_INFO_V1(pgl_create_epoint);
  3.1247 +Datum pgl_create_epoint(PG_FUNCTION_ARGS) {
  3.1248 +  pgl_point *point = (pgl_point *)palloc(sizeof(pgl_point));
  3.1249 +  pgl_epoint_set_latlon(point, PG_GETARG_FLOAT8(0), PG_GETARG_FLOAT8(1));
  3.1250 +  PG_RETURN_POINTER(point);
  3.1251 +}
  3.1252 +
  3.1253 +/* parse point ("epoint" in SQL) */
  3.1254 +/* format: '[NS]<float> [EW]<float>' */
  3.1255 +PG_FUNCTION_INFO_V1(pgl_epoint_in);
  3.1256 +Datum pgl_epoint_in(PG_FUNCTION_ARGS) {
  3.1257 +  char *str = PG_GETARG_CSTRING(0);  /* input string */
  3.1258 +  char *strptr = str;  /* current position within string */
  3.1259 +  int done = 0;        /* bit mask storing if latitude or longitude was read */
  3.1260 +  double lat, lon;     /* parsed values as double precision floats */
  3.1261 +  pgl_point *point;    /* return value (to be palloc'ed) */
  3.1262 +  /* parse two floats (each latitude or longitude) separated by white-space */
  3.1263 +  done |= pgl_scan(&strptr, &lat, &lon);
  3.1264 +  if (strptr != str && isspace(strptr[-1])) {
  3.1265 +    done |= pgl_scan(&strptr, &lat, &lon);
  3.1266 +  }
  3.1267 +  /* require end of string, and latitude and longitude parsed successfully */
  3.1268 +  if (strptr[0] || done != PGL_SCAN_LATLON) {
  3.1269 +    ereport(ERROR, (
  3.1270 +      errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
  3.1271 +      errmsg("invalid input syntax for type epoint: \"%s\"", str)
  3.1272 +    ));
  3.1273 +  }
  3.1274 +  /* allocate memory for result */
  3.1275 +  point = (pgl_point *)palloc(sizeof(pgl_point));
  3.1276 +  /* set latitude and longitude (and perform checks) */
  3.1277 +  pgl_epoint_set_latlon(point, lat, lon);
  3.1278 +  /* return result */
  3.1279 +  PG_RETURN_POINTER(point);
  3.1280 +}
  3.1281 +
  3.1282 +/* create box ("ebox" in SQL) that is empty */
  3.1283 +PG_FUNCTION_INFO_V1(pgl_create_empty_ebox);
  3.1284 +Datum pgl_create_empty_ebox(PG_FUNCTION_ARGS) {
  3.1285 +  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
  3.1286 +  pgl_box_set_empty(box);
  3.1287 +  PG_RETURN_POINTER(box);
  3.1288 +}
  3.1289 +
  3.1290 +/* set box to given boundaries (including checks) */
  3.1291 +static void pgl_ebox_set_boundaries(
  3.1292 +  pgl_box *box,
  3.1293 +  double lat_min, double lat_max, double lon_min, double lon_max
  3.1294 +) {
  3.1295 +  /* if minimum latitude is greater than maximum latitude, return empty box */
  3.1296 +  if (lat_min > lat_max) {
  3.1297 +    pgl_box_set_empty(box);
  3.1298 +    return;
  3.1299 +  }
  3.1300 +  /* otherwise reject infinite or NaN values */
  3.1301 +  if (
  3.1302 +    !isfinite(lat_min) || !isfinite(lat_max) ||
  3.1303 +    !isfinite(lon_min) || !isfinite(lon_max)
  3.1304 +  ) {
  3.1305 +    ereport(ERROR, (
  3.1306 +      errcode(ERRCODE_DATA_EXCEPTION),
  3.1307 +      errmsg("ebox requires finite coordinates")
  3.1308 +    ));
  3.1309 +  }
  3.1310 +  /* check latitude bounds */
  3.1311 +  if (lat_max < -90) {
  3.1312 +    ereport(WARNING, (errmsg("northern latitude exceeds south pole")));
  3.1313 +    lat_max = -90;
  3.1314 +  } else if (lat_max > 90) {
  3.1315 +    ereport(WARNING, (errmsg("northern latitude exceeds north pole")));
  3.1316 +    lat_max = 90;
  3.1317 +  }
  3.1318 +  if (lat_min < -90) {
  3.1319 +    ereport(WARNING, (errmsg("southern latitude exceeds south pole")));
  3.1320 +    lat_min = -90;
  3.1321 +  } else if (lat_min > 90) {
  3.1322 +    ereport(WARNING, (errmsg("southern latitude exceeds north pole")));
  3.1323 +    lat_min = 90;
  3.1324 +  }
  3.1325 +  /* check if all longitudes are included */
  3.1326 +  if (lon_max - lon_min >= 360) {
  3.1327 +    if (lon_max - lon_min > 360) ereport(WARNING, (
  3.1328 +      errmsg("longitude coverage greater than 360 degrees")
  3.1329 +    ));
  3.1330 +    lon_min = -180;
  3.1331 +    lon_max = 180;
  3.1332 +  } else {
  3.1333 +    /* normalize longitude bounds */
  3.1334 +    if      (lon_min < -180) lon_min += 360 - trunc(lon_min / 360) * 360;
  3.1335 +    else if (lon_min >  180) lon_min -= 360 + trunc(lon_min / 360) * 360;
  3.1336 +    if      (lon_max < -180) lon_max += 360 - trunc(lon_max / 360) * 360;
  3.1337 +    else if (lon_max >  180) lon_max -= 360 + trunc(lon_max / 360) * 360;
  3.1338 +  }
  3.1339 +  /* store rounded latitude/longitude values for round-trip safety */
  3.1340 +  box->lat_min = pgl_round(lat_min);
  3.1341 +  box->lat_max = pgl_round(lat_max);
  3.1342 +  box->lon_min = pgl_round(lon_min);
  3.1343 +  box->lon_max = pgl_round(lon_max);
  3.1344 +  /* ensure that rounding does not change orientation */
  3.1345 +  if (lon_min > lon_max && box->lon_min == box->lon_max) {
  3.1346 +    box->lon_min = -180;
  3.1347 +    box->lon_max = 180;
  3.1348 +  }
  3.1349 +}
  3.1350 +
  3.1351 +/* create box ("ebox" in SQL) from min/max latitude and min/max longitude */
  3.1352 +PG_FUNCTION_INFO_V1(pgl_create_ebox);
  3.1353 +Datum pgl_create_ebox(PG_FUNCTION_ARGS) {
  3.1354 +  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
  3.1355 +  pgl_ebox_set_boundaries(
  3.1356 +    box,
  3.1357 +    PG_GETARG_FLOAT8(0), PG_GETARG_FLOAT8(1),
  3.1358 +    PG_GETARG_FLOAT8(2), PG_GETARG_FLOAT8(3)
  3.1359 +  );
  3.1360 +  PG_RETURN_POINTER(box);
  3.1361 +}
  3.1362 +
  3.1363 +/* create box ("ebox" in SQL) from two points ("epoint"s) */
  3.1364 +/* (can not be used to cover a longitude range of more than 120 degrees) */
  3.1365 +PG_FUNCTION_INFO_V1(pgl_create_ebox_from_epoints);
  3.1366 +Datum pgl_create_ebox_from_epoints(PG_FUNCTION_ARGS) {
  3.1367 +  pgl_point *point1 = (pgl_point *)PG_GETARG_POINTER(0);
  3.1368 +  pgl_point *point2 = (pgl_point *)PG_GETARG_POINTER(1);
  3.1369 +  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
  3.1370 +  double lat_min, lat_max, lon_min, lon_max;
  3.1371 +  double dlon;  /* longitude range (delta longitude) */
  3.1372 +  /* order latitude and longitude boundaries */
  3.1373 +  if (point2->lat < point1->lat) {
  3.1374 +    lat_min = point2->lat;
  3.1375 +    lat_max = point1->lat;
  3.1376 +  } else {
  3.1377 +    lat_min = point1->lat;
  3.1378 +    lat_max = point2->lat;
  3.1379 +  }
  3.1380 +  if (point2->lon < point1->lon) {
  3.1381 +    lon_min = point2->lon;
  3.1382 +    lon_max = point1->lon;
  3.1383 +  } else {
  3.1384 +    lon_min = point1->lon;
  3.1385 +    lon_max = point2->lon;
  3.1386 +  }
  3.1387 +  /* calculate longitude range (round to avoid floating point errors) */
  3.1388 +  dlon = pgl_round(lon_max - lon_min);
  3.1389 +  /* determine east-west direction */
  3.1390 +  if (dlon >= 240) {
  3.1391 +    /* assume that 180th meridian is crossed and swap min/max longitude */
  3.1392 +    double swap = lon_min; lon_min = lon_max; lon_max = swap;
  3.1393 +  } else if (dlon > 120) {
  3.1394 +    /* unclear orientation since delta longitude > 120 */
  3.1395 +    ereport(ERROR, (
  3.1396 +      errcode(ERRCODE_DATA_EXCEPTION),
  3.1397 +      errmsg("can not determine east/west orientation for ebox")
  3.1398 +    ));
  3.1399 +  }
  3.1400 +  /* use boundaries to setup box (and perform checks) */
  3.1401 +  pgl_ebox_set_boundaries(box, lat_min, lat_max, lon_min, lon_max);
  3.1402 +  /* return result */
  3.1403 +  PG_RETURN_POINTER(box);
  3.1404 +}
  3.1405 +
  3.1406 +/* parse box ("ebox" in SQL) */
  3.1407 +/* format: '[NS]<float> [EW]<float> [NS]<float> [EW]<float>'
  3.1408 +       or: '[NS]<float> [NS]<float> [EW]<float> [EW]<float>' */
  3.1409 +PG_FUNCTION_INFO_V1(pgl_ebox_in);
  3.1410 +Datum pgl_ebox_in(PG_FUNCTION_ARGS) {
  3.1411 +  char *str = PG_GETARG_CSTRING(0);  /* input string */
  3.1412 +  char *str_lower;     /* lower case version of input string */
  3.1413 +  char *strptr;        /* current position within string */
  3.1414 +  int valid;           /* number of valid chars */
  3.1415 +  int done;            /* specifies if latitude or longitude was read */
  3.1416 +  double val;          /* temporary variable */
  3.1417 +  int lat_count = 0;   /* count of latitude values parsed */
  3.1418 +  int lon_count = 0;   /* count of longitufde values parsed */
  3.1419 +  double lat_min, lat_max, lon_min, lon_max;  /* see pgl_box struct */
  3.1420 +  pgl_box *box;        /* return value (to be palloc'ed) */
  3.1421 +  /* lowercase input */
  3.1422 +  str_lower = psprintf("%s", str);
  3.1423 +  for (strptr=str_lower; *strptr; strptr++) {
  3.1424 +    if (*strptr >= 'A' && *strptr <= 'Z') *strptr += 'a' - 'A';
  3.1425 +  }
  3.1426 +  /* reset reading position to start of (lowercase) string */
  3.1427 +  strptr = str_lower;
  3.1428 +  /* check if empty box */
  3.1429 +  valid = 0;
  3.1430 +  sscanf(strptr, " empty %n", &valid);
  3.1431 +  if (valid && strptr[valid] == 0) {
  3.1432 +    /* allocate and return empty box */
  3.1433 +    box = (pgl_box *)palloc(sizeof(pgl_box));
  3.1434 +    pgl_box_set_empty(box);
  3.1435 +    PG_RETURN_POINTER(box);
  3.1436 +  }
  3.1437 +  /* demand four blocks separated by whitespace */
  3.1438 +  valid = 0;
  3.1439 +  sscanf(strptr, " %*s %*s %*s %*s %n", &valid);
  3.1440 +  /* if four blocks separated by whitespace exist, parse those blocks */
  3.1441 +  if (strptr[valid] == 0) while (strptr[0]) {
  3.1442 +    /* parse either latitude or longitude (whichever found in input string) */
  3.1443 +    done = pgl_scan(&strptr, &val, &val);
  3.1444 +    /* store latitude or longitude in lat_min, lat_max, lon_min, or lon_max */
  3.1445 +    if (done == PGL_SCAN_LAT) {
  3.1446 +      if (!lat_count) lat_min = val; else lat_max = val;
  3.1447 +      lat_count++;
  3.1448 +    } else if (done == PGL_SCAN_LON) {
  3.1449 +      if (!lon_count) lon_min = val; else lon_max = val;
  3.1450 +      lon_count++;
  3.1451 +    } else {
  3.1452 +      break;
  3.1453 +    }
  3.1454 +  }
  3.1455 +  /* require end of string, and two latitude and two longitude values */
  3.1456 +  if (strptr[0] || lat_count != 2 || lon_count != 2) {
  3.1457 +    ereport(ERROR, (
  3.1458 +      errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
  3.1459 +      errmsg("invalid input syntax for type ebox: \"%s\"", str)
  3.1460 +    ));
  3.1461 +  }
  3.1462 +  /* free lower case string */
  3.1463 +  pfree(str_lower);
  3.1464 +  /* order boundaries (maximum greater than minimum) */
  3.1465 +  if (lat_min > lat_max) { val = lat_min; lat_min = lat_max; lat_max = val; }
  3.1466 +  if (lon_min > lon_max) { val = lon_min; lon_min = lon_max; lon_max = val; }
  3.1467 +  /* allocate memory for result */
  3.1468 +  box = (pgl_box *)palloc(sizeof(pgl_box));
  3.1469 +  /* set boundaries (and perform checks) */
  3.1470 +  pgl_ebox_set_boundaries(box, lat_min, lat_max, lon_min, lon_max);
  3.1471 +  /* return result */
  3.1472 +  PG_RETURN_POINTER(box);
  3.1473 +}
  3.1474 +
  3.1475 +/* set circle to given latitude, longitude, and radius (including checks) */
  3.1476 +static void pgl_ecircle_set_latlon_radius(
  3.1477 +  pgl_circle *circle, double lat, double lon, double radius
  3.1478 +) {
  3.1479 +  /* set center point (including checks) */
  3.1480 +  pgl_epoint_set_latlon(&(circle->center), lat, lon);
  3.1481 +  /* handle non-positive radius */
  3.1482 +  if (isnan(radius)) {
  3.1483 +    ereport(ERROR, (
  3.1484 +      errcode(ERRCODE_DATA_EXCEPTION),
  3.1485 +      errmsg("invalid radius for ecircle")
  3.1486 +    ));
  3.1487 +  }
  3.1488 +  if (radius == 0) radius = 0;  /* avoids -0 */
  3.1489 +  else if (radius < 0) {
  3.1490 +    if (isfinite(radius)) {
  3.1491 +      ereport(NOTICE, (errmsg("negative radius converted to minus infinity")));
  3.1492 +    }
  3.1493 +    radius = -INFINITY;
  3.1494 +  }
  3.1495 +  /* store radius (round-trip safety is ensured by pgl_print_float) */
  3.1496 +  circle->radius = radius;
  3.1497 +}
  3.1498 +
  3.1499 +/* create circle ("ecircle" in SQL) from latitude, longitude, and radius */
  3.1500 +PG_FUNCTION_INFO_V1(pgl_create_ecircle);
  3.1501 +Datum pgl_create_ecircle(PG_FUNCTION_ARGS) {
  3.1502 +  pgl_circle *circle = (pgl_circle *)palloc(sizeof(pgl_circle));
  3.1503 +  pgl_ecircle_set_latlon_radius(
  3.1504 +    circle, PG_GETARG_FLOAT8(0), PG_GETARG_FLOAT8(1), PG_GETARG_FLOAT8(2)
  3.1505 +  );
  3.1506 +  PG_RETURN_POINTER(circle);
  3.1507 +}
  3.1508 +
  3.1509 +/* create circle ("ecircle" in SQL) from point ("epoint"), and radius */
  3.1510 +PG_FUNCTION_INFO_V1(pgl_create_ecircle_from_epoint);
  3.1511 +Datum pgl_create_ecircle_from_epoint(PG_FUNCTION_ARGS) {
  3.1512 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.1513 +  double radius = PG_GETARG_FLOAT8(1);
  3.1514 +  pgl_circle *circle = (pgl_circle *)palloc(sizeof(pgl_circle));
  3.1515 +  /* set latitude, longitude, radius (and perform checks) */
  3.1516 +  pgl_ecircle_set_latlon_radius(circle, point->lat, point->lon, radius);
  3.1517 +  /* return result */
  3.1518 +  PG_RETURN_POINTER(circle);
  3.1519 +}
  3.1520 +
  3.1521 +/* parse circle ("ecircle" in SQL) */
  3.1522 +/* format: '[NS]<float> [EW]<float> <float>' */
  3.1523 +PG_FUNCTION_INFO_V1(pgl_ecircle_in);
  3.1524 +Datum pgl_ecircle_in(PG_FUNCTION_ARGS) {
  3.1525 +  char *str = PG_GETARG_CSTRING(0);  /* input string */
  3.1526 +  char *strptr = str;       /* current position within string */
  3.1527 +  double lat, lon, radius;  /* parsed values as double precision flaots */
  3.1528 +  int valid = 0;            /* number of valid chars */
  3.1529 +  int done = 0;             /* stores if latitude and/or longitude was read */
  3.1530 +  pgl_circle *circle;       /* return value (to be palloc'ed) */
  3.1531 +  /* demand three blocks separated by whitespace */
  3.1532 +  sscanf(strptr, " %*s %*s %*s %n", &valid);
  3.1533 +  /* if three blocks separated by whitespace exist, parse those blocks */
  3.1534 +  if (strptr[valid] == 0) {
  3.1535 +    /* parse latitude and longitude */
  3.1536 +    done |= pgl_scan(&strptr, &lat, &lon);
  3.1537 +    done |= pgl_scan(&strptr, &lat, &lon);
  3.1538 +    /* parse radius (while incrementing strptr by number of bytes parsed) */
  3.1539 +    valid = 0;
  3.1540 +    if (sscanf(strptr, " %lf %n", &radius, &valid) == 1) strptr += valid;
  3.1541 +  }
  3.1542 +  /* require end of string and both latitude and longitude being parsed */
  3.1543 +  if (strptr[0] || done != PGL_SCAN_LATLON) {
  3.1544 +    ereport(ERROR, (
  3.1545 +      errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
  3.1546 +      errmsg("invalid input syntax for type ecircle: \"%s\"", str)
  3.1547 +    ));
  3.1548 +  }
  3.1549 +  /* allocate memory for result */
  3.1550 +  circle = (pgl_circle *)palloc(sizeof(pgl_circle));
  3.1551 +  /* set latitude, longitude, radius (and perform checks) */
  3.1552 +  pgl_ecircle_set_latlon_radius(circle, lat, lon, radius);
  3.1553 +  /* return result */
  3.1554 +  PG_RETURN_POINTER(circle);
  3.1555 +}
  3.1556 +
  3.1557 +/* parse cluster ("ecluster" in SQL) */
  3.1558 +PG_FUNCTION_INFO_V1(pgl_ecluster_in);
  3.1559 +Datum pgl_ecluster_in(PG_FUNCTION_ARGS) {
  3.1560 +  int i;
  3.1561 +  char *str = PG_GETARG_CSTRING(0);  /* input string */
  3.1562 +  char *str_lower;         /* lower case version of input string */
  3.1563 +  char *strptr;            /* pointer to current reading position of input */
  3.1564 +  int npoints_total = 0;   /* total number of points in cluster */
  3.1565 +  int nentries = 0;        /* total number of entries */
  3.1566 +  pgl_newentry *entries;   /* array of pgl_newentry to create pgl_cluster */
  3.1567 +  int entries_buflen = 4;  /* maximum number of elements in entries array */
  3.1568 +  int valid;               /* number of valid chars processed */
  3.1569 +  double lat, lon;         /* latitude and longitude of parsed point */
  3.1570 +  int entrytype;           /* current entry type */
  3.1571 +  int npoints;             /* number of points in current entry */
  3.1572 +  pgl_point *points;       /* array of pgl_point for pgl_newentry */
  3.1573 +  int points_buflen;       /* maximum number of elements in points array */
  3.1574 +  int done;                /* return value of pgl_scan function */
  3.1575 +  pgl_cluster *cluster;    /* created cluster */
  3.1576 +  /* lowercase input */
  3.1577 +  str_lower = psprintf("%s", str);
  3.1578 +  for (strptr=str_lower; *strptr; strptr++) {
  3.1579 +    if (*strptr >= 'A' && *strptr <= 'Z') *strptr += 'a' - 'A';
  3.1580 +  }
  3.1581 +  /* reset reading position to start of (lowercase) string */
  3.1582 +  strptr = str_lower;
  3.1583 +  /* allocate initial buffer for entries */
  3.1584 +  entries = palloc(entries_buflen * sizeof(pgl_newentry));
  3.1585 +  /* parse until end of string */
  3.1586 +  while (strptr[0]) {
  3.1587 +    /* require previous white-space or closing parenthesis before next token */
  3.1588 +    if (strptr != str_lower && !isspace(strptr[-1]) && strptr[-1] != ')') {
  3.1589 +      goto pgl_ecluster_in_error;
  3.1590 +    }
  3.1591 +    /* ignore token "empty" */
  3.1592 +    valid = 0; sscanf(strptr, " empty %n", &valid);
  3.1593 +    if (valid) { strptr += valid; continue; }
  3.1594 +    /* test for "point" token */
  3.1595 +    valid = 0; sscanf(strptr, " point ( %n", &valid);
  3.1596 +    if (valid) {
  3.1597 +      strptr += valid;
  3.1598 +      entrytype = PGL_ENTRY_POINT;
  3.1599 +      goto pgl_ecluster_in_type_ok;
  3.1600 +    }
  3.1601 +    /* test for "path" token */
  3.1602 +    valid = 0; sscanf(strptr, " path ( %n", &valid);
  3.1603 +    if (valid) {
  3.1604 +      strptr += valid;
  3.1605 +      entrytype = PGL_ENTRY_PATH;
  3.1606 +      goto pgl_ecluster_in_type_ok;
  3.1607 +    }
  3.1608 +    /* test for "outline" token */
  3.1609 +    valid = 0; sscanf(strptr, " outline ( %n", &valid);
  3.1610 +    if (valid) {
  3.1611 +      strptr += valid;
  3.1612 +      entrytype = PGL_ENTRY_OUTLINE;
  3.1613 +      goto pgl_ecluster_in_type_ok;
  3.1614 +    }
  3.1615 +    /* test for "polygon" token */
  3.1616 +    valid = 0; sscanf(strptr, " polygon ( %n", &valid);
  3.1617 +    if (valid) {
  3.1618 +      strptr += valid;
  3.1619 +      entrytype = PGL_ENTRY_POLYGON;
  3.1620 +      goto pgl_ecluster_in_type_ok;
  3.1621 +    }
  3.1622 +    /* error if no valid token found */
  3.1623 +    goto pgl_ecluster_in_error;
  3.1624 +    pgl_ecluster_in_type_ok:
  3.1625 +    /* check if pgl_newentry array needs to grow */
  3.1626 +    if (nentries == entries_buflen) {
  3.1627 +      pgl_newentry *newbuf;
  3.1628 +      entries_buflen *= 2;
  3.1629 +      newbuf = palloc(entries_buflen * sizeof(pgl_newentry));
  3.1630 +      memcpy(newbuf, entries, nentries * sizeof(pgl_newentry));
  3.1631 +      pfree(entries);
  3.1632 +      entries = newbuf;
  3.1633 +    }
  3.1634 +    /* reset number of points for current entry */
  3.1635 +    npoints = 0;
  3.1636 +    /* allocate array for points */
  3.1637 +    points_buflen = 4;
  3.1638 +    points = palloc(points_buflen * sizeof(pgl_point));
  3.1639 +    /* parse until closing parenthesis */
  3.1640 +    while (strptr[0] != ')') {
  3.1641 +      /* error on unexpected end of string */
  3.1642 +      if (strptr[0] == 0) goto pgl_ecluster_in_error;
  3.1643 +      /* mark neither latitude nor longitude as read */
  3.1644 +      done = PGL_SCAN_NONE;
  3.1645 +      /* require white-space before second, third, etc. point */
  3.1646 +      if (npoints != 0 && !isspace(strptr[-1])) goto pgl_ecluster_in_error;
  3.1647 +      /* scan latitude (or longitude) */
  3.1648 +      done |= pgl_scan(&strptr, &lat, &lon);
  3.1649 +      /* require white-space before second coordinate */
  3.1650 +      if (strptr != str && !isspace(strptr[-1])) goto pgl_ecluster_in_error;
  3.1651 +      /* scan longitude (or latitude) */
  3.1652 +      done |= pgl_scan(&strptr, &lat, &lon);
  3.1653 +      /* error unless both latitude and longitude were parsed */
  3.1654 +      if (done != PGL_SCAN_LATLON) goto pgl_ecluster_in_error;
  3.1655 +      /* throw error if number of points is too high */
  3.1656 +      if (npoints_total == PGL_CLUSTER_MAXPOINTS) {
  3.1657 +        ereport(ERROR, (
  3.1658 +          errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
  3.1659 +          errmsg(
  3.1660 +            "too many points for ecluster entry (maximum %i)",
  3.1661 +            PGL_CLUSTER_MAXPOINTS
  3.1662 +          )
  3.1663 +        ));
  3.1664 +      }
  3.1665 +      /* check if pgl_point array needs to grow */
  3.1666 +      if (npoints == points_buflen) {
  3.1667 +        pgl_point *newbuf;
  3.1668 +        points_buflen *= 2;
  3.1669 +        newbuf = palloc(points_buflen * sizeof(pgl_point));
  3.1670 +        memcpy(newbuf, points, npoints * sizeof(pgl_point));
  3.1671 +        pfree(points);
  3.1672 +        points = newbuf;
  3.1673 +      }
  3.1674 +      /* append point to pgl_point array (includes checks) */
  3.1675 +      pgl_epoint_set_latlon(&(points[npoints++]), lat, lon);
  3.1676 +      /* increase total number of points */
  3.1677 +      npoints_total++;
  3.1678 +    }
  3.1679 +    /* error if entry has no points */
  3.1680 +    if (!npoints) goto pgl_ecluster_in_error;
  3.1681 +    /* entries with one point are automatically of type "point" */
  3.1682 +    if (npoints == 1) entrytype = PGL_ENTRY_POINT;
  3.1683 +    /* if entries have more than one point */
  3.1684 +    else {
  3.1685 +      /* throw error if entry type is "point" */
  3.1686 +      if (entrytype == PGL_ENTRY_POINT) {
  3.1687 +        ereport(ERROR, (
  3.1688 +          errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
  3.1689 +          errmsg("invalid input syntax for type ecluster (point entry with more than one point)")
  3.1690 +        ));
  3.1691 +      }
  3.1692 +      /* coerce outlines and polygons with more than 2 points to be a path */
  3.1693 +      if (npoints == 2) entrytype = PGL_ENTRY_PATH;
  3.1694 +    }
  3.1695 +    /* append entry to pgl_newentry array */
  3.1696 +    entries[nentries].entrytype = entrytype;
  3.1697 +    entries[nentries].npoints = npoints;
  3.1698 +    entries[nentries].points = points;
  3.1699 +    nentries++;
  3.1700 +    /* consume closing parenthesis */
  3.1701 +    strptr++;
  3.1702 +    /* consume white-space */
  3.1703 +    while (isspace(strptr[0])) strptr++;
  3.1704 +  }
  3.1705 +  /* free lower case string */
  3.1706 +  pfree(str_lower);
  3.1707 +  /* create cluster from pgl_newentry array */
  3.1708 +  cluster = pgl_new_cluster(nentries, entries);
  3.1709 +  /* free pgl_newentry array */
  3.1710 +  for (i=0; i<nentries; i++) pfree(entries[i].points);
  3.1711 +  pfree(entries);
  3.1712 +  /* set bounding circle of cluster and check east/west orientation */
  3.1713 +  if (!pgl_finalize_cluster(cluster)) {
  3.1714 +    ereport(ERROR, (
  3.1715 +      errcode(ERRCODE_DATA_EXCEPTION),
  3.1716 +      errmsg("can not determine east/west orientation for ecluster"),
  3.1717 +      errhint("Ensure that each entry has a longitude span of less than 180 degrees.")
  3.1718 +    ));
  3.1719 +  }
  3.1720 +  /* return cluster */
  3.1721 +  PG_RETURN_POINTER(cluster);
  3.1722 +  /* code to throw error */
  3.1723 +  pgl_ecluster_in_error:
  3.1724 +  ereport(ERROR, (
  3.1725 +    errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
  3.1726 +    errmsg("invalid input syntax for type ecluster: \"%s\"", str)
  3.1727 +  ));
  3.1728 +}
  3.1729 +
  3.1730 +/* convert point ("epoint") to string representation */
  3.1731 +PG_FUNCTION_INFO_V1(pgl_epoint_out);
  3.1732 +Datum pgl_epoint_out(PG_FUNCTION_ARGS) {
  3.1733 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.1734 +  char latstr[PGL_NUMBUFLEN];
  3.1735 +  char lonstr[PGL_NUMBUFLEN];
  3.1736 +  pgl_print_lat(latstr, point->lat);
  3.1737 +  pgl_print_lon(lonstr, point->lon);
  3.1738 +  PG_RETURN_CSTRING(psprintf("%s %s", latstr, lonstr));
  3.1739 +}
  3.1740 +
  3.1741 +/* convert box ("ebox") to string representation */
  3.1742 +PG_FUNCTION_INFO_V1(pgl_ebox_out);
  3.1743 +Datum pgl_ebox_out(PG_FUNCTION_ARGS) {
  3.1744 +  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
  3.1745 +  double lon_min = box->lon_min;
  3.1746 +  double lon_max = box->lon_max;
  3.1747 +  char lat_min_str[PGL_NUMBUFLEN];
  3.1748 +  char lat_max_str[PGL_NUMBUFLEN];
  3.1749 +  char lon_min_str[PGL_NUMBUFLEN];
  3.1750 +  char lon_max_str[PGL_NUMBUFLEN];
  3.1751 +  /* return string "empty" if box is set to be empty */
  3.1752 +  if (box->lat_min > box->lat_max) PG_RETURN_CSTRING("empty");
  3.1753 +  /* use boundaries exceeding W180 or E180 if 180th meridian is enclosed */
  3.1754 +  /* (required since pgl_box_in orders the longitude boundaries) */
  3.1755 +  if (lon_min > lon_max) {
  3.1756 +    if (lon_min + lon_max >= 0) lon_min -= 360;
  3.1757 +    else lon_max += 360;
  3.1758 +  }
  3.1759 +  /* format and return result */
  3.1760 +  pgl_print_lat(lat_min_str, box->lat_min);
  3.1761 +  pgl_print_lat(lat_max_str, box->lat_max);
  3.1762 +  pgl_print_lon(lon_min_str, lon_min);
  3.1763 +  pgl_print_lon(lon_max_str, lon_max);
  3.1764 +  PG_RETURN_CSTRING(psprintf(
  3.1765 +    "%s %s %s %s",
  3.1766 +    lat_min_str, lon_min_str, lat_max_str, lon_max_str
  3.1767 +  ));
  3.1768 +}
  3.1769 +
  3.1770 +/* convert circle ("ecircle") to string representation */
  3.1771 +PG_FUNCTION_INFO_V1(pgl_ecircle_out);
  3.1772 +Datum pgl_ecircle_out(PG_FUNCTION_ARGS) {
  3.1773 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
  3.1774 +  char latstr[PGL_NUMBUFLEN];
  3.1775 +  char lonstr[PGL_NUMBUFLEN];
  3.1776 +  char radstr[PGL_NUMBUFLEN];
  3.1777 +  pgl_print_lat(latstr, circle->center.lat);
  3.1778 +  pgl_print_lon(lonstr, circle->center.lon);
  3.1779 +  pgl_print_float(radstr, circle->radius);
  3.1780 +  PG_RETURN_CSTRING(psprintf("%s %s %s", latstr, lonstr, radstr));
  3.1781 +}
  3.1782 +
  3.1783 +/* convert cluster ("ecluster") to string representation */
  3.1784 +PG_FUNCTION_INFO_V1(pgl_ecluster_out);
  3.1785 +Datum pgl_ecluster_out(PG_FUNCTION_ARGS) {
  3.1786 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0));
  3.1787 +  char latstr[PGL_NUMBUFLEN];  /* string buffer for latitude */
  3.1788 +  char lonstr[PGL_NUMBUFLEN];  /* string buffer for longitude */
  3.1789 +  char ***strings;     /* array of array of strings */
  3.1790 +  char *string;        /* string of current token */
  3.1791 +  char *res, *resptr;  /* result and pointer to current write position */
  3.1792 +  size_t reslen = 1;   /* length of result (init with 1 for terminator) */
  3.1793 +  int npoints;         /* number of points of current entry */
  3.1794 +  int i, j;            /* i: entry, j: point in entry */
  3.1795 +  /* handle empty clusters */
  3.1796 +  if (cluster->nentries == 0) {
  3.1797 +    /* free detoasted cluster (if copy) */
  3.1798 +    PG_FREE_IF_COPY(cluster, 0);
  3.1799 +    /* return static result */
  3.1800 +    PG_RETURN_CSTRING("empty");
  3.1801 +  }
  3.1802 +  /* allocate array of array of strings */
  3.1803 +  strings = palloc(cluster->nentries * sizeof(char **));
  3.1804 +  /* iterate over all entries in cluster */
  3.1805 +  for (i=0; i<cluster->nentries; i++) {
  3.1806 +    /* get number of points in entry */
  3.1807 +    npoints = cluster->entries[i].npoints;
  3.1808 +    /* allocate array of strings (one string for each point plus two extra) */
  3.1809 +    strings[i] = palloc((2 + npoints) * sizeof(char *));
  3.1810 +    /* determine opening string */
  3.1811 +    switch (cluster->entries[i].entrytype) {
  3.1812 +      case PGL_ENTRY_POINT:   string = (i==0)?"point ("  :" point (";   break;
  3.1813 +      case PGL_ENTRY_PATH:    string = (i==0)?"path ("   :" path (";    break;
  3.1814 +      case PGL_ENTRY_OUTLINE: string = (i==0)?"outline (":" outline ("; break;
  3.1815 +      case PGL_ENTRY_POLYGON: string = (i==0)?"polygon (":" polygon ("; break;
  3.1816 +      default:                string = (i==0)?"unknown"  :" unknown";
  3.1817 +    }
  3.1818 +    /* use opening string as first string in array */
  3.1819 +    strings[i][0] = string;
  3.1820 +    /* update result length (for allocating result string later) */
  3.1821 +    reslen += strlen(string);
  3.1822 +    /* iterate over all points */
  3.1823 +    for (j=0; j<npoints; j++) {
  3.1824 +      /* create string representation of point */
  3.1825 +      pgl_print_lat(latstr, PGL_ENTRY_POINTS(cluster, i)[j].lat);
  3.1826 +      pgl_print_lon(lonstr, PGL_ENTRY_POINTS(cluster, i)[j].lon);
  3.1827 +      string = psprintf((j == 0) ? "%s %s" : " %s %s", latstr, lonstr);
  3.1828 +      /* copy string pointer to string array */
  3.1829 +      strings[i][j+1] = string;
  3.1830 +      /* update result length (for allocating result string later) */
  3.1831 +      reslen += strlen(string);
  3.1832 +    }
  3.1833 +    /* use closing parenthesis as last string in array */
  3.1834 +    strings[i][npoints+1] = ")";
  3.1835 +    /* update result length (for allocating result string later) */
  3.1836 +    reslen++;
  3.1837 +  }
  3.1838 +  /* allocate result string */
  3.1839 +  res = palloc(reslen);
  3.1840 +  /* set write pointer to begin of result string */
  3.1841 +  resptr = res;
  3.1842 +  /* copy strings into result string */
  3.1843 +  for (i=0; i<cluster->nentries; i++) {
  3.1844 +    npoints = cluster->entries[i].npoints;
  3.1845 +    for (j=0; j<npoints+2; j++) {
  3.1846 +      string = strings[i][j];
  3.1847 +      strcpy(resptr, string);
  3.1848 +      resptr += strlen(string);
  3.1849 +      /* free strings allocated by psprintf */
  3.1850 +      if (j != 0 && j != npoints+1) pfree(string);
  3.1851 +    }
  3.1852 +    /* free array of strings */
  3.1853 +    pfree(strings[i]);
  3.1854 +  }
  3.1855 +  /* free array of array of strings */
  3.1856 +  pfree(strings);
  3.1857 +  /* free detoasted cluster (if copy) */
  3.1858 +  PG_FREE_IF_COPY(cluster, 0);
  3.1859 +  /* return result */
  3.1860 +  PG_RETURN_CSTRING(res);
  3.1861 +}
  3.1862 +
  3.1863 +/* binary input function for point ("epoint") */
  3.1864 +PG_FUNCTION_INFO_V1(pgl_epoint_recv);
  3.1865 +Datum pgl_epoint_recv(PG_FUNCTION_ARGS) {
  3.1866 +  StringInfo buf = (StringInfo)PG_GETARG_POINTER(0);
  3.1867 +  pgl_point *point = (pgl_point *)palloc(sizeof(pgl_point));
  3.1868 +  point->lat = pq_getmsgfloat8(buf);
  3.1869 +  point->lon = pq_getmsgfloat8(buf);
  3.1870 +  PG_RETURN_POINTER(point);
  3.1871 +}
  3.1872 +
  3.1873 +/* binary input function for box ("ebox") */
  3.1874 +PG_FUNCTION_INFO_V1(pgl_ebox_recv);
  3.1875 +Datum pgl_ebox_recv(PG_FUNCTION_ARGS) {
  3.1876 +  StringInfo buf = (StringInfo)PG_GETARG_POINTER(0);
  3.1877 +  pgl_box *box = (pgl_box *)palloc(sizeof(pgl_box));
  3.1878 +  box->lat_min = pq_getmsgfloat8(buf);
  3.1879 +  box->lat_max = pq_getmsgfloat8(buf);
  3.1880 +  box->lon_min = pq_getmsgfloat8(buf);
  3.1881 +  box->lon_max = pq_getmsgfloat8(buf);
  3.1882 +  PG_RETURN_POINTER(box);
  3.1883 +}
  3.1884 +
  3.1885 +/* binary input function for circle ("ecircle") */
  3.1886 +PG_FUNCTION_INFO_V1(pgl_ecircle_recv);
  3.1887 +Datum pgl_ecircle_recv(PG_FUNCTION_ARGS) {
  3.1888 +  StringInfo buf = (StringInfo)PG_GETARG_POINTER(0);
  3.1889 +  pgl_circle *circle = (pgl_circle *)palloc(sizeof(pgl_circle));
  3.1890 +  circle->center.lat = pq_getmsgfloat8(buf);
  3.1891 +  circle->center.lon = pq_getmsgfloat8(buf);
  3.1892 +  circle->radius = pq_getmsgfloat8(buf);
  3.1893 +  PG_RETURN_POINTER(circle);
  3.1894 +}
  3.1895 +
  3.1896 +/* TODO: binary receive function for cluster */
  3.1897 +
  3.1898 +/* binary output function for point ("epoint") */
  3.1899 +PG_FUNCTION_INFO_V1(pgl_epoint_send);
  3.1900 +Datum pgl_epoint_send(PG_FUNCTION_ARGS) {
  3.1901 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.1902 +  StringInfoData buf;
  3.1903 +  pq_begintypsend(&buf);
  3.1904 +  pq_sendfloat8(&buf, point->lat);
  3.1905 +  pq_sendfloat8(&buf, point->lon);
  3.1906 +  PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
  3.1907 +}
  3.1908 +
  3.1909 +/* binary output function for box ("ebox") */
  3.1910 +PG_FUNCTION_INFO_V1(pgl_ebox_send);
  3.1911 +Datum pgl_ebox_send(PG_FUNCTION_ARGS) {
  3.1912 +  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
  3.1913 +  StringInfoData buf;
  3.1914 +  pq_begintypsend(&buf);
  3.1915 +  pq_sendfloat8(&buf, box->lat_min);
  3.1916 +  pq_sendfloat8(&buf, box->lat_max);
  3.1917 +  pq_sendfloat8(&buf, box->lon_min);
  3.1918 +  pq_sendfloat8(&buf, box->lon_max);
  3.1919 +  PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
  3.1920 +}
  3.1921 +
  3.1922 +/* binary output function for circle ("ecircle") */
  3.1923 +PG_FUNCTION_INFO_V1(pgl_ecircle_send);
  3.1924 +Datum pgl_ecircle_send(PG_FUNCTION_ARGS) {
  3.1925 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
  3.1926 +  StringInfoData buf;
  3.1927 +  pq_begintypsend(&buf);
  3.1928 +  pq_sendfloat8(&buf, circle->center.lat);
  3.1929 +  pq_sendfloat8(&buf, circle->center.lon);
  3.1930 +  pq_sendfloat8(&buf, circle->radius);
  3.1931 +  PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
  3.1932 +}
  3.1933 +
  3.1934 +/* TODO: binary send functions for cluster */
  3.1935 +
  3.1936 +/* cast point ("epoint") to box ("ebox") */
  3.1937 +PG_FUNCTION_INFO_V1(pgl_epoint_to_ebox);
  3.1938 +Datum pgl_epoint_to_ebox(PG_FUNCTION_ARGS) {
  3.1939 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.1940 +  pgl_box *box = palloc(sizeof(pgl_box));
  3.1941 +  box->lat_min = point->lat;
  3.1942 +  box->lat_max = point->lat;
  3.1943 +  box->lon_min = point->lon;
  3.1944 +  box->lon_max = point->lon;
  3.1945 +  PG_RETURN_POINTER(box);
  3.1946 +}
  3.1947 +
  3.1948 +/* cast point ("epoint") to circle ("ecircle") */
  3.1949 +PG_FUNCTION_INFO_V1(pgl_epoint_to_ecircle);
  3.1950 +Datum pgl_epoint_to_ecircle(PG_FUNCTION_ARGS) {
  3.1951 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.1952 +  pgl_circle *circle = palloc(sizeof(pgl_box));
  3.1953 +  circle->center = *point;
  3.1954 +  circle->radius = 0;
  3.1955 +  PG_RETURN_POINTER(circle);
  3.1956 +}
  3.1957 +
  3.1958 +/* cast point ("epoint") to cluster ("ecluster") */
  3.1959 +PG_FUNCTION_INFO_V1(pgl_epoint_to_ecluster);
  3.1960 +Datum pgl_epoint_to_ecluster(PG_FUNCTION_ARGS) {
  3.1961 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.1962 +  pgl_newentry entry;
  3.1963 +  entry.entrytype = PGL_ENTRY_POINT;
  3.1964 +  entry.npoints = 1;
  3.1965 +  entry.points = point;
  3.1966 +  PG_RETURN_POINTER(pgl_new_cluster(1, &entry));
  3.1967 +}
  3.1968 +
  3.1969 +/* cast box ("ebox") to cluster ("ecluster") */
  3.1970 +#define pgl_ebox_to_ecluster_macro(i, a, b) \
  3.1971 +  entries[i].entrytype = PGL_ENTRY_POLYGON; \
  3.1972 +  entries[i].npoints = 4; \
  3.1973 +  entries[i].points = points[i]; \
  3.1974 +  points[i][0].lat = box->lat_min; \
  3.1975 +  points[i][0].lon = (a); \
  3.1976 +  points[i][1].lat = box->lat_min; \
  3.1977 +  points[i][1].lon = (b); \
  3.1978 +  points[i][2].lat = box->lat_max; \
  3.1979 +  points[i][2].lon = (b); \
  3.1980 +  points[i][3].lat = box->lat_max; \
  3.1981 +  points[i][3].lon = (a);
  3.1982 +PG_FUNCTION_INFO_V1(pgl_ebox_to_ecluster);
  3.1983 +Datum pgl_ebox_to_ecluster(PG_FUNCTION_ARGS) {
  3.1984 +  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
  3.1985 +  double lon, dlon;
  3.1986 +  int nentries;
  3.1987 +  pgl_newentry entries[3];
  3.1988 +  pgl_point points[3][4];
  3.1989 +  if (box->lat_min > box->lat_max) {
  3.1990 +    nentries = 0;
  3.1991 +  } else if (box->lon_min > box->lon_max) {
  3.1992 +    if (box->lon_min < 0) {
  3.1993 +      lon = pgl_round((box->lon_min + 180) / 2.0);
  3.1994 +      nentries = 3;
  3.1995 +      pgl_ebox_to_ecluster_macro(0, box->lon_min, lon);
  3.1996 +      pgl_ebox_to_ecluster_macro(1, lon, 180);
  3.1997 +      pgl_ebox_to_ecluster_macro(2, -180, box->lon_max);
  3.1998 +    } else if (box->lon_max > 0) {
  3.1999 +      lon = pgl_round((box->lon_max - 180) / 2.0);
  3.2000 +      nentries = 3;
  3.2001 +      pgl_ebox_to_ecluster_macro(0, box->lon_min, 180);
  3.2002 +      pgl_ebox_to_ecluster_macro(1, -180, lon);
  3.2003 +      pgl_ebox_to_ecluster_macro(2, lon, box->lon_max);
  3.2004 +    } else {
  3.2005 +      nentries = 2;
  3.2006 +      pgl_ebox_to_ecluster_macro(0, box->lon_min, 180);
  3.2007 +      pgl_ebox_to_ecluster_macro(1, -180, box->lon_max);
  3.2008 +    }
  3.2009 +  } else {
  3.2010 +    dlon = pgl_round(box->lon_max - box->lon_min);
  3.2011 +    if (dlon < 180) {
  3.2012 +      nentries = 1;
  3.2013 +      pgl_ebox_to_ecluster_macro(0, box->lon_min, box->lon_max);
  3.2014 +    } else {
  3.2015 +      lon = pgl_round((box->lon_min + box->lon_max) / 2.0);
  3.2016 +      if (
  3.2017 +        pgl_round(lon - box->lon_min) < 180 &&
  3.2018 +        pgl_round(box->lon_max - lon) < 180
  3.2019 +      ) {
  3.2020 +        nentries = 2;
  3.2021 +        pgl_ebox_to_ecluster_macro(0, box->lon_min, lon);
  3.2022 +        pgl_ebox_to_ecluster_macro(1, lon, box->lon_max);
  3.2023 +      } else {
  3.2024 +        nentries = 3;
  3.2025 +        pgl_ebox_to_ecluster_macro(0, box->lon_min, -60);
  3.2026 +        pgl_ebox_to_ecluster_macro(1, -60, 60);
  3.2027 +        pgl_ebox_to_ecluster_macro(2, 60, box->lon_max);
  3.2028 +      }
  3.2029 +    }
  3.2030 +  }
  3.2031 +  PG_RETURN_POINTER(pgl_new_cluster(nentries, entries));
  3.2032 +}
  3.2033 +
  3.2034 +/* extract latitude from point ("epoint") */
  3.2035 +PG_FUNCTION_INFO_V1(pgl_epoint_lat);
  3.2036 +Datum pgl_epoint_lat(PG_FUNCTION_ARGS) {
  3.2037 +  PG_RETURN_FLOAT8(((pgl_point *)PG_GETARG_POINTER(0))->lat);
  3.2038 +}
  3.2039 +
  3.2040 +/* extract longitude from point ("epoint") */
  3.2041 +PG_FUNCTION_INFO_V1(pgl_epoint_lon);
  3.2042 +Datum pgl_epoint_lon(PG_FUNCTION_ARGS) {
  3.2043 +  PG_RETURN_FLOAT8(((pgl_point *)PG_GETARG_POINTER(0))->lon);
  3.2044 +}
  3.2045 +
  3.2046 +/* extract minimum latitude from box ("ebox") */
  3.2047 +PG_FUNCTION_INFO_V1(pgl_ebox_lat_min);
  3.2048 +Datum pgl_ebox_lat_min(PG_FUNCTION_ARGS) {
  3.2049 +  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lat_min);
  3.2050 +}
  3.2051 +
  3.2052 +/* extract maximum latitude from box ("ebox") */
  3.2053 +PG_FUNCTION_INFO_V1(pgl_ebox_lat_max);
  3.2054 +Datum pgl_ebox_lat_max(PG_FUNCTION_ARGS) {
  3.2055 +  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lat_max);
  3.2056 +}
  3.2057 +
  3.2058 +/* extract minimum longitude from box ("ebox") */
  3.2059 +PG_FUNCTION_INFO_V1(pgl_ebox_lon_min);
  3.2060 +Datum pgl_ebox_lon_min(PG_FUNCTION_ARGS) {
  3.2061 +  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lon_min);
  3.2062 +}
  3.2063 +
  3.2064 +/* extract maximum longitude from box ("ebox") */
  3.2065 +PG_FUNCTION_INFO_V1(pgl_ebox_lon_max);
  3.2066 +Datum pgl_ebox_lon_max(PG_FUNCTION_ARGS) {
  3.2067 +  PG_RETURN_FLOAT8(((pgl_box *)PG_GETARG_POINTER(0))->lon_max);
  3.2068 +}
  3.2069 +
  3.2070 +/* extract center point from circle ("ecircle") */
  3.2071 +PG_FUNCTION_INFO_V1(pgl_ecircle_center);
  3.2072 +Datum pgl_ecircle_center(PG_FUNCTION_ARGS) {
  3.2073 +  PG_RETURN_POINTER(&(((pgl_circle *)PG_GETARG_POINTER(0))->center));
  3.2074 +}
  3.2075 +
  3.2076 +/* extract radius from circle ("ecircle") */
  3.2077 +PG_FUNCTION_INFO_V1(pgl_ecircle_radius);
  3.2078 +Datum pgl_ecircle_radius(PG_FUNCTION_ARGS) {
  3.2079 +  PG_RETURN_FLOAT8(((pgl_circle *)PG_GETARG_POINTER(0))->radius);
  3.2080 +}
  3.2081 +
  3.2082 +/* check if point is inside box (overlap operator "&&") in SQL */
  3.2083 +PG_FUNCTION_INFO_V1(pgl_epoint_ebox_overlap);
  3.2084 +Datum pgl_epoint_ebox_overlap(PG_FUNCTION_ARGS) {
  3.2085 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.2086 +  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(1);
  3.2087 +  PG_RETURN_BOOL(pgl_point_in_box(point, box));
  3.2088 +}
  3.2089 +
  3.2090 +/* check if point is inside circle (overlap operator "&&") in SQL */
  3.2091 +PG_FUNCTION_INFO_V1(pgl_epoint_ecircle_overlap);
  3.2092 +Datum pgl_epoint_ecircle_overlap(PG_FUNCTION_ARGS) {
  3.2093 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.2094 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2095 +  PG_RETURN_BOOL(
  3.2096 +    pgl_distance(
  3.2097 +      point->lat, point->lon,
  3.2098 +      circle->center.lat, circle->center.lon
  3.2099 +    ) <= circle->radius
  3.2100 +  );
  3.2101 +}
  3.2102 +
  3.2103 +/* check if point is inside cluster (overlap operator "&&") in SQL */
  3.2104 +PG_FUNCTION_INFO_V1(pgl_epoint_ecluster_overlap);
  3.2105 +Datum pgl_epoint_ecluster_overlap(PG_FUNCTION_ARGS) {
  3.2106 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.2107 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2108 +  bool retval = pgl_point_in_cluster(point, cluster);
  3.2109 +  PG_FREE_IF_COPY(cluster, 1);
  3.2110 +  PG_RETURN_BOOL(retval);
  3.2111 +}
  3.2112 +
  3.2113 +/* check if point may be inside cluster (lossy overl. operator "&&+") in SQL */
  3.2114 +PG_FUNCTION_INFO_V1(pgl_epoint_ecluster_may_overlap);
  3.2115 +Datum pgl_epoint_ecluster_may_overlap(PG_FUNCTION_ARGS) {
  3.2116 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.2117 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2118 +  bool retval = pgl_distance(
  3.2119 +    point->lat, point->lon,
  3.2120 +    cluster->bounding.center.lat, cluster->bounding.center.lon
  3.2121 +  ) <= cluster->bounding.radius;
  3.2122 +  PG_FREE_IF_COPY(cluster, 1);
  3.2123 +  PG_RETURN_BOOL(retval);
  3.2124 +}
  3.2125 +
  3.2126 +/* check if two boxes overlap (overlap operator "&&") in SQL */
  3.2127 +PG_FUNCTION_INFO_V1(pgl_ebox_overlap);
  3.2128 +Datum pgl_ebox_overlap(PG_FUNCTION_ARGS) {
  3.2129 +  pgl_box *box1 = (pgl_box *)PG_GETARG_POINTER(0);
  3.2130 +  pgl_box *box2 = (pgl_box *)PG_GETARG_POINTER(1);
  3.2131 +  PG_RETURN_BOOL(pgl_boxes_overlap(box1, box2));
  3.2132 +}
  3.2133 +
  3.2134 +/* check if box and circle may overlap (lossy overl. operator "&&+") in SQL */
  3.2135 +PG_FUNCTION_INFO_V1(pgl_ebox_ecircle_may_overlap);
  3.2136 +Datum pgl_ebox_ecircle_may_overlap(PG_FUNCTION_ARGS) {
  3.2137 +  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
  3.2138 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2139 +  PG_RETURN_BOOL(
  3.2140 +    pgl_estimate_point_box_distance(&circle->center, box) <= circle->radius
  3.2141 +  );
  3.2142 +}
  3.2143 +
  3.2144 +/* check if box and cluster may overlap (lossy overl. operator "&&+") in SQL */
  3.2145 +PG_FUNCTION_INFO_V1(pgl_ebox_ecluster_may_overlap);
  3.2146 +Datum pgl_ebox_ecluster_may_overlap(PG_FUNCTION_ARGS) {
  3.2147 +  pgl_box *box = (pgl_box *)PG_GETARG_POINTER(0);
  3.2148 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2149 +  bool retval = pgl_estimate_point_box_distance(
  3.2150 +    &cluster->bounding.center,
  3.2151 +    box
  3.2152 +  ) <= cluster->bounding.radius;
  3.2153 +  PG_FREE_IF_COPY(cluster, 1);
  3.2154 +  PG_RETURN_BOOL(retval);
  3.2155 +}
  3.2156 +
  3.2157 +/* check if two circles overlap (overlap operator "&&") in SQL */
  3.2158 +PG_FUNCTION_INFO_V1(pgl_ecircle_overlap);
  3.2159 +Datum pgl_ecircle_overlap(PG_FUNCTION_ARGS) {
  3.2160 +  pgl_circle *circle1 = (pgl_circle *)PG_GETARG_POINTER(0);
  3.2161 +  pgl_circle *circle2 = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2162 +  PG_RETURN_BOOL(
  3.2163 +    pgl_distance(
  3.2164 +      circle1->center.lat, circle1->center.lon,
  3.2165 +      circle2->center.lat, circle2->center.lon
  3.2166 +    ) <= circle1->radius + circle2->radius
  3.2167 +  );
  3.2168 +}
  3.2169 +
  3.2170 +/* check if circle and cluster overlap (overlap operator "&&") in SQL */
  3.2171 +PG_FUNCTION_INFO_V1(pgl_ecircle_ecluster_overlap);
  3.2172 +Datum pgl_ecircle_ecluster_overlap(PG_FUNCTION_ARGS) {
  3.2173 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
  3.2174 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2175 +  bool retval = (
  3.2176 +    pgl_point_cluster_distance(&(circle->center), cluster) <= circle->radius
  3.2177 +  );
  3.2178 +  PG_FREE_IF_COPY(cluster, 1);
  3.2179 +  PG_RETURN_BOOL(retval);
  3.2180 +}
  3.2181 +
  3.2182 +/* check if circle and cluster may be overlap (l. ov. operator "&&+") in SQL */
  3.2183 +PG_FUNCTION_INFO_V1(pgl_ecircle_ecluster_may_overlap);
  3.2184 +Datum pgl_ecircle_ecluster_may_overlap(PG_FUNCTION_ARGS) {
  3.2185 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
  3.2186 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2187 +  bool retval = pgl_distance(
  3.2188 +    circle->center.lat, circle->center.lon,
  3.2189 +    cluster->bounding.center.lat, cluster->bounding.center.lon
  3.2190 +  ) <= circle->radius + cluster->bounding.radius;
  3.2191 +  PG_FREE_IF_COPY(cluster, 1);
  3.2192 +  PG_RETURN_BOOL(retval);
  3.2193 +}
  3.2194 +
  3.2195 +/* check if two clusters may overlap (lossy overlap operator "&&+") in SQL */
  3.2196 +PG_FUNCTION_INFO_V1(pgl_ecluster_may_overlap);
  3.2197 +Datum pgl_ecluster_may_overlap(PG_FUNCTION_ARGS) {
  3.2198 +  pgl_cluster *cluster1 = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0));
  3.2199 +  pgl_cluster *cluster2 = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2200 +  bool retval = pgl_distance(
  3.2201 +    cluster1->bounding.center.lat, cluster1->bounding.center.lon,
  3.2202 +    cluster2->bounding.center.lat, cluster2->bounding.center.lon
  3.2203 +  ) <= cluster1->bounding.radius + cluster2->bounding.radius;
  3.2204 +  PG_FREE_IF_COPY(cluster1, 0);
  3.2205 +  PG_FREE_IF_COPY(cluster2, 1);
  3.2206 +  PG_RETURN_BOOL(retval);
  3.2207 +}
  3.2208 +
  3.2209 +/* calculate distance between two points ("<->" operator) in SQL */
  3.2210 +PG_FUNCTION_INFO_V1(pgl_epoint_distance);
  3.2211 +Datum pgl_epoint_distance(PG_FUNCTION_ARGS) {
  3.2212 +  pgl_point *point1 = (pgl_point *)PG_GETARG_POINTER(0);
  3.2213 +  pgl_point *point2 = (pgl_point *)PG_GETARG_POINTER(1);
  3.2214 +  PG_RETURN_FLOAT8(pgl_distance(
  3.2215 +    point1->lat, point1->lon, point2->lat, point2->lon
  3.2216 +  ));
  3.2217 +}
  3.2218 +
  3.2219 +/* calculate point to circle distance ("<->" operator) in SQL */
  3.2220 +PG_FUNCTION_INFO_V1(pgl_epoint_ecircle_distance);
  3.2221 +Datum pgl_epoint_ecircle_distance(PG_FUNCTION_ARGS) {
  3.2222 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.2223 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2224 +  double distance = pgl_distance(
  3.2225 +    point->lat, point->lon, circle->center.lat, circle->center.lon
  3.2226 +  ) - circle->radius;
  3.2227 +  PG_RETURN_FLOAT8((distance <= 0) ? 0 : distance);
  3.2228 +}
  3.2229 +
  3.2230 +/* calculate point to cluster distance ("<->" operator) in SQL */
  3.2231 +PG_FUNCTION_INFO_V1(pgl_epoint_ecluster_distance);
  3.2232 +Datum pgl_epoint_ecluster_distance(PG_FUNCTION_ARGS) {
  3.2233 +  pgl_point *point = (pgl_point *)PG_GETARG_POINTER(0);
  3.2234 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2235 +  double distance = pgl_point_cluster_distance(point, cluster);
  3.2236 +  PG_FREE_IF_COPY(cluster, 1);
  3.2237 +  PG_RETURN_FLOAT8(distance);
  3.2238 +}
  3.2239 +
  3.2240 +/* calculate distance between two circles ("<->" operator) in SQL */
  3.2241 +PG_FUNCTION_INFO_V1(pgl_ecircle_distance);
  3.2242 +Datum pgl_ecircle_distance(PG_FUNCTION_ARGS) {
  3.2243 +  pgl_circle *circle1 = (pgl_circle *)PG_GETARG_POINTER(0);
  3.2244 +  pgl_circle *circle2 = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2245 +  double distance = pgl_distance(
  3.2246 +    circle1->center.lat, circle1->center.lon,
  3.2247 +    circle2->center.lat, circle2->center.lon
  3.2248 +  ) - (circle1->radius + circle2->radius);
  3.2249 +  PG_RETURN_FLOAT8((distance <= 0) ? 0 : distance);
  3.2250 +}
  3.2251 +
  3.2252 +/* calculate circle to cluster distance ("<->" operator) in SQL */
  3.2253 +PG_FUNCTION_INFO_V1(pgl_ecircle_ecluster_distance);
  3.2254 +Datum pgl_ecircle_ecluster_distance(PG_FUNCTION_ARGS) {
  3.2255 +  pgl_circle *circle = (pgl_circle *)PG_GETARG_POINTER(0);
  3.2256 +  pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2257 +  double distance = (
  3.2258 +    pgl_point_cluster_distance(&(circle->center), cluster) - circle->radius
  3.2259 +  );
  3.2260 +  PG_FREE_IF_COPY(cluster, 1);
  3.2261 +  PG_RETURN_FLOAT8((distance <= 0) ? 0 : distance);
  3.2262 +}
  3.2263 +
  3.2264 +
  3.2265 +/*-----------------------------------------------------------*
  3.2266 + *  B-tree comparison operators and index support functions  *
  3.2267 + *-----------------------------------------------------------*/
  3.2268 +
  3.2269 +/* macro for a B-tree operator (without detoasting) */
  3.2270 +#define PGL_BTREE_OPER(func, type, cmpfunc, oper) \
  3.2271 +  PG_FUNCTION_INFO_V1(func); \
  3.2272 +  Datum func(PG_FUNCTION_ARGS) { \
  3.2273 +    type *a = (type *)PG_GETARG_POINTER(0); \
  3.2274 +    type *b = (type *)PG_GETARG_POINTER(1); \
  3.2275 +    PG_RETURN_BOOL(cmpfunc(a, b) oper 0); \
  3.2276 +  }
  3.2277 +
  3.2278 +/* macro for a B-tree comparison function (without detoasting) */
  3.2279 +#define PGL_BTREE_CMP(func, type, cmpfunc) \
  3.2280 +  PG_FUNCTION_INFO_V1(func); \
  3.2281 +  Datum func(PG_FUNCTION_ARGS) { \
  3.2282 +    type *a = (type *)PG_GETARG_POINTER(0); \
  3.2283 +    type *b = (type *)PG_GETARG_POINTER(1); \
  3.2284 +    PG_RETURN_INT32(cmpfunc(a, b)); \
  3.2285 +  }
  3.2286 +
  3.2287 +/* macro for a B-tree operator (with detoasting) */
  3.2288 +#define PGL_BTREE_OPER_DETOAST(func, type, cmpfunc, oper) \
  3.2289 +  PG_FUNCTION_INFO_V1(func); \
  3.2290 +  Datum func(PG_FUNCTION_ARGS) { \
  3.2291 +    bool res; \
  3.2292 +    type *a = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0)); \
  3.2293 +    type *b = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1)); \
  3.2294 +    res = cmpfunc(a, b) oper 0; \
  3.2295 +    PG_FREE_IF_COPY(a, 0); \
  3.2296 +    PG_FREE_IF_COPY(b, 1); \
  3.2297 +    PG_RETURN_BOOL(res); \
  3.2298 +  }
  3.2299 +
  3.2300 +/* macro for a B-tree comparison function (with detoasting) */
  3.2301 +#define PGL_BTREE_CMP_DETOAST(func, type, cmpfunc) \
  3.2302 +  PG_FUNCTION_INFO_V1(func); \
  3.2303 +  Datum func(PG_FUNCTION_ARGS) { \
  3.2304 +    int32_t res; \
  3.2305 +    type *a = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(0)); \
  3.2306 +    type *b = (type *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1)); \
  3.2307 +    res = cmpfunc(a, b); \
  3.2308 +    PG_FREE_IF_COPY(a, 0); \
  3.2309 +    PG_FREE_IF_COPY(b, 1); \
  3.2310 +    PG_RETURN_INT32(res); \
  3.2311 +  }
  3.2312 +
  3.2313 +/* B-tree operators and comparison function for point */
  3.2314 +PGL_BTREE_OPER(pgl_btree_epoint_lt, pgl_point, pgl_point_cmp, <)
  3.2315 +PGL_BTREE_OPER(pgl_btree_epoint_le, pgl_point, pgl_point_cmp, <=)
  3.2316 +PGL_BTREE_OPER(pgl_btree_epoint_eq, pgl_point, pgl_point_cmp, ==)
  3.2317 +PGL_BTREE_OPER(pgl_btree_epoint_ne, pgl_point, pgl_point_cmp, !=)
  3.2318 +PGL_BTREE_OPER(pgl_btree_epoint_ge, pgl_point, pgl_point_cmp, >=)
  3.2319 +PGL_BTREE_OPER(pgl_btree_epoint_gt, pgl_point, pgl_point_cmp, >)
  3.2320 +PGL_BTREE_CMP(pgl_btree_epoint_cmp, pgl_point, pgl_point_cmp)
  3.2321 +
  3.2322 +/* B-tree operators and comparison function for box */
  3.2323 +PGL_BTREE_OPER(pgl_btree_ebox_lt, pgl_box, pgl_box_cmp, <)
  3.2324 +PGL_BTREE_OPER(pgl_btree_ebox_le, pgl_box, pgl_box_cmp, <=)
  3.2325 +PGL_BTREE_OPER(pgl_btree_ebox_eq, pgl_box, pgl_box_cmp, ==)
  3.2326 +PGL_BTREE_OPER(pgl_btree_ebox_ne, pgl_box, pgl_box_cmp, !=)
  3.2327 +PGL_BTREE_OPER(pgl_btree_ebox_ge, pgl_box, pgl_box_cmp, >=)
  3.2328 +PGL_BTREE_OPER(pgl_btree_ebox_gt, pgl_box, pgl_box_cmp, >)
  3.2329 +PGL_BTREE_CMP(pgl_btree_ebox_cmp, pgl_box, pgl_box_cmp)
  3.2330 +
  3.2331 +/* B-tree operators and comparison function for circle */
  3.2332 +PGL_BTREE_OPER(pgl_btree_ecircle_lt, pgl_circle, pgl_circle_cmp, <)
  3.2333 +PGL_BTREE_OPER(pgl_btree_ecircle_le, pgl_circle, pgl_circle_cmp, <=)
  3.2334 +PGL_BTREE_OPER(pgl_btree_ecircle_eq, pgl_circle, pgl_circle_cmp, ==)
  3.2335 +PGL_BTREE_OPER(pgl_btree_ecircle_ne, pgl_circle, pgl_circle_cmp, !=)
  3.2336 +PGL_BTREE_OPER(pgl_btree_ecircle_ge, pgl_circle, pgl_circle_cmp, >=)
  3.2337 +PGL_BTREE_OPER(pgl_btree_ecircle_gt, pgl_circle, pgl_circle_cmp, >)
  3.2338 +PGL_BTREE_CMP(pgl_btree_ecircle_cmp, pgl_circle, pgl_circle_cmp)
  3.2339 +
  3.2340 +
  3.2341 +/*--------------------------------*
  3.2342 + *  GiST index support functions  *
  3.2343 + *--------------------------------*/
  3.2344 +
  3.2345 +/* GiST "consistent" support function */
  3.2346 +PG_FUNCTION_INFO_V1(pgl_gist_consistent);
  3.2347 +Datum pgl_gist_consistent(PG_FUNCTION_ARGS) {
  3.2348 +  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
  3.2349 +  pgl_keyptr key = (pgl_keyptr)DatumGetPointer(entry->key);
  3.2350 +  StrategyNumber strategy = (StrategyNumber)PG_GETARG_UINT16(2);
  3.2351 +  bool *recheck = (bool *)PG_GETARG_POINTER(4);
  3.2352 +  /* demand recheck because index and query methods are lossy */
  3.2353 +  *recheck = true;
  3.2354 +  /* strategy number aliases for different operators using the same strategy */
  3.2355 +  strategy %= 100;
  3.2356 +  /* strategy number 11: equality of two points */
  3.2357 +  if (strategy == 11) {
  3.2358 +    /* query datum is another point */
  3.2359 +    pgl_point *query = (pgl_point *)PG_GETARG_POINTER(1);
  3.2360 +    /* convert other point to key */
  3.2361 +    pgl_pointkey querykey;
  3.2362 +    pgl_point_to_key(query, querykey);
  3.2363 +    /* return true if both keys overlap */
  3.2364 +    PG_RETURN_BOOL(pgl_keys_overlap(key, querykey));
  3.2365 +  }
  3.2366 +  /* strategy number 13: equality of two circles */
  3.2367 +  if (strategy == 13) {
  3.2368 +    /* query datum is another circle */
  3.2369 +    pgl_circle *query = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2370 +    /* convert other circle to key */
  3.2371 +    pgl_areakey querykey;
  3.2372 +    pgl_circle_to_key(query, querykey);
  3.2373 +    /* return true if both keys overlap */
  3.2374 +    PG_RETURN_BOOL(pgl_keys_overlap(key, querykey));
  3.2375 +  }
  3.2376 +  /* for all remaining strategies, keys on empty objects produce no match */
  3.2377 +  /* (check necessary because query radius may be infinite) */
  3.2378 +  if (PGL_KEY_IS_EMPTY(key)) PG_RETURN_BOOL(false);
  3.2379 +  /* strategy number 21: overlapping with point */
  3.2380 +  if (strategy == 21) {
  3.2381 +    /* query datum is a point */
  3.2382 +    pgl_point *query = (pgl_point *)PG_GETARG_POINTER(1);
  3.2383 +    /* return true if estimated distance (allowed to be smaller than real
  3.2384 +       distance) between index key and point is zero */
  3.2385 +    PG_RETURN_BOOL(pgl_estimate_key_distance(key, query) == 0);
  3.2386 +  }
  3.2387 +  /* strategy number 22: (point) overlapping with box */
  3.2388 +  if (strategy == 22) {
  3.2389 +    /* query datum is a box */
  3.2390 +    pgl_box *query = (pgl_box *)PG_GETARG_POINTER(1);
  3.2391 +    /* determine bounding box of indexed key */
  3.2392 +    pgl_box keybox;
  3.2393 +    pgl_key_to_box(key, &keybox);
  3.2394 +    /* return true if query box overlaps with bounding box of indexed key */
  3.2395 +    PG_RETURN_BOOL(pgl_boxes_overlap(query, &keybox));
  3.2396 +  }
  3.2397 +  /* strategy number 23: overlapping with circle */
  3.2398 +  if (strategy == 23) {
  3.2399 +    /* query datum is a circle */
  3.2400 +    pgl_circle *query = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2401 +    /* return true if estimated distance (allowed to be smaller than real
  3.2402 +       distance) between index key and circle center is smaller than radius */
  3.2403 +    PG_RETURN_BOOL(
  3.2404 +      pgl_estimate_key_distance(key, &(query->center)) <= query->radius
  3.2405 +    );
  3.2406 +  }
  3.2407 +  /* strategy number 24: overlapping with cluster */
  3.2408 +  if (strategy == 24) {
  3.2409 +    bool retval;  /* return value */
  3.2410 +    /* query datum is a cluster */
  3.2411 +    pgl_cluster *query = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2412 +    /* return true if estimated distance (allowed to be smaller than real
  3.2413 +       distance) between index key and circle center is smaller than radius */
  3.2414 +    retval = (
  3.2415 +      pgl_estimate_key_distance(key, &(query->bounding.center)) <=
  3.2416 +      query->bounding.radius
  3.2417 +    );
  3.2418 +    PG_FREE_IF_COPY(query, 1);  /* free detoasted cluster (if copy) */
  3.2419 +    PG_RETURN_BOOL(retval);
  3.2420 +  }
  3.2421 +  /* throw error for any unknown strategy number */
  3.2422 +  elog(ERROR, "unrecognized strategy number: %d", strategy);
  3.2423 +}
  3.2424 +
  3.2425 +/* GiST "union" support function */
  3.2426 +PG_FUNCTION_INFO_V1(pgl_gist_union);
  3.2427 +Datum pgl_gist_union(PG_FUNCTION_ARGS) {
  3.2428 +  GistEntryVector *entryvec = (GistEntryVector *)PG_GETARG_POINTER(0);
  3.2429 +  pgl_keyptr out;  /* return value (to be palloc'ed) */
  3.2430 +  int i;
  3.2431 +  /* determine key size */
  3.2432 +  size_t keysize = PGL_KEY_IS_AREAKEY(
  3.2433 +    (pgl_keyptr)DatumGetPointer(entryvec->vector[0].key)
  3.2434 +  ) ? sizeof (pgl_areakey) : sizeof(pgl_pointkey);
  3.2435 +  /* begin with first key as result */
  3.2436 +  out = palloc(keysize);
  3.2437 +  memcpy(out, (pgl_keyptr)DatumGetPointer(entryvec->vector[0].key), keysize);
  3.2438 +  /* unite current result with second, third, etc. key */
  3.2439 +  for (i=1; i<entryvec->n; i++) {
  3.2440 +    pgl_unite_keys(out, (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key));
  3.2441 +  }
  3.2442 +  /* return result */
  3.2443 +  PG_RETURN_POINTER(out);
  3.2444 +}
  3.2445 +
  3.2446 +/* GiST "compress" support function for indicis on points */
  3.2447 +PG_FUNCTION_INFO_V1(pgl_gist_compress_epoint);
  3.2448 +Datum pgl_gist_compress_epoint(PG_FUNCTION_ARGS) {
  3.2449 +  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
  3.2450 +  GISTENTRY *retval;  /* return value (to be palloc'ed unless set to entry) */
  3.2451 +  /* only transform new leaves */
  3.2452 +  if (entry->leafkey) {
  3.2453 +    /* get point to be transformed */
  3.2454 +    pgl_point *point = (pgl_point *)DatumGetPointer(entry->key);
  3.2455 +    /* allocate memory for key */
  3.2456 +    pgl_keyptr key = palloc(sizeof(pgl_pointkey));
  3.2457 +    /* transform point to key */
  3.2458 +    pgl_point_to_key(point, key);
  3.2459 +    /* create new GISTENTRY structure as return value */
  3.2460 +    retval = palloc(sizeof(GISTENTRY));
  3.2461 +    gistentryinit(
  3.2462 +      *retval, PointerGetDatum(key),
  3.2463 +      entry->rel, entry->page, entry->offset, FALSE
  3.2464 +    );
  3.2465 +  } else {
  3.2466 +    /* inner nodes have already been transformed */
  3.2467 +    retval = entry;
  3.2468 +  }
  3.2469 +  /* return pointer to old or new GISTENTRY structure */
  3.2470 +  PG_RETURN_POINTER(retval);
  3.2471 +}
  3.2472 +
  3.2473 +/* GiST "compress" support function for indicis on circles */
  3.2474 +PG_FUNCTION_INFO_V1(pgl_gist_compress_ecircle);
  3.2475 +Datum pgl_gist_compress_ecircle(PG_FUNCTION_ARGS) {
  3.2476 +  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
  3.2477 +  GISTENTRY *retval;  /* return value (to be palloc'ed unless set to entry) */
  3.2478 +  /* only transform new leaves */
  3.2479 +  if (entry->leafkey) {
  3.2480 +    /* get circle to be transformed */
  3.2481 +    pgl_circle *circle = (pgl_circle *)DatumGetPointer(entry->key);
  3.2482 +    /* allocate memory for key */
  3.2483 +    pgl_keyptr key = palloc(sizeof(pgl_areakey));
  3.2484 +    /* transform circle to key */
  3.2485 +    pgl_circle_to_key(circle, key);
  3.2486 +    /* create new GISTENTRY structure as return value */
  3.2487 +    retval = palloc(sizeof(GISTENTRY));
  3.2488 +    gistentryinit(
  3.2489 +      *retval, PointerGetDatum(key),
  3.2490 +      entry->rel, entry->page, entry->offset, FALSE
  3.2491 +    );
  3.2492 +  } else {
  3.2493 +    /* inner nodes have already been transformed */
  3.2494 +    retval = entry;
  3.2495 +  }
  3.2496 +  /* return pointer to old or new GISTENTRY structure */
  3.2497 +  PG_RETURN_POINTER(retval);
  3.2498 +}
  3.2499 +
  3.2500 +/* GiST "compress" support function for indices on clusters */
  3.2501 +PG_FUNCTION_INFO_V1(pgl_gist_compress_ecluster);
  3.2502 +Datum pgl_gist_compress_ecluster(PG_FUNCTION_ARGS) {
  3.2503 +  GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
  3.2504 +  GISTENTRY *retval;  /* return value (to be palloc'ed unless set to entry) */
  3.2505 +  /* only transform new leaves */
  3.2506 +  if (entry->leafkey) {
  3.2507 +    /* get cluster to be transformed (detoasting necessary!) */
  3.2508 +    pgl_cluster *cluster = (pgl_cluster *)PG_DETOAST_DATUM(entry->key);
  3.2509 +    /* allocate memory for key */
  3.2510 +    pgl_keyptr key = palloc(sizeof(pgl_areakey));
  3.2511 +    /* transform cluster to key */
  3.2512 +    pgl_circle_to_key(&(cluster->bounding), key);
  3.2513 +    /* create new GISTENTRY structure as return value */
  3.2514 +    retval = palloc(sizeof(GISTENTRY));
  3.2515 +    gistentryinit(
  3.2516 +      *retval, PointerGetDatum(key),
  3.2517 +      entry->rel, entry->page, entry->offset, FALSE
  3.2518 +    );
  3.2519 +    /* free detoasted datum */
  3.2520 +    if ((void *)cluster != (void *)DatumGetPointer(entry->key)) pfree(cluster);
  3.2521 +  } else {
  3.2522 +    /* inner nodes have already been transformed */
  3.2523 +    retval = entry;
  3.2524 +  }
  3.2525 +  /* return pointer to old or new GISTENTRY structure */
  3.2526 +  PG_RETURN_POINTER(retval);
  3.2527 +}
  3.2528 +
  3.2529 +/* GiST "decompress" support function for indices */
  3.2530 +PG_FUNCTION_INFO_V1(pgl_gist_decompress);
  3.2531 +Datum pgl_gist_decompress(PG_FUNCTION_ARGS) {
  3.2532 +  /* return passed pointer without transformation */
  3.2533 +  PG_RETURN_POINTER(PG_GETARG_POINTER(0));
  3.2534 +}
  3.2535 +
  3.2536 +/* GiST "penalty" support function */
  3.2537 +PG_FUNCTION_INFO_V1(pgl_gist_penalty);
  3.2538 +Datum pgl_gist_penalty(PG_FUNCTION_ARGS) {
  3.2539 +  GISTENTRY *origentry = (GISTENTRY *)PG_GETARG_POINTER(0);
  3.2540 +  GISTENTRY *newentry = (GISTENTRY *)PG_GETARG_POINTER(1);
  3.2541 +  float *penalty = (float *)PG_GETARG_POINTER(2);
  3.2542 +  /* get original key and key to insert */
  3.2543 +  pgl_keyptr orig = (pgl_keyptr)DatumGetPointer(origentry->key);
  3.2544 +  pgl_keyptr new = (pgl_keyptr)DatumGetPointer(newentry->key);
  3.2545 +  /* copy original key */
  3.2546 +  union { pgl_pointkey pointkey; pgl_areakey areakey; } union_key;
  3.2547 +  if (PGL_KEY_IS_AREAKEY(orig)) {
  3.2548 +    memcpy(union_key.areakey, orig, sizeof(union_key.areakey));
  3.2549 +  } else {
  3.2550 +    memcpy(union_key.pointkey, orig, sizeof(union_key.pointkey));
  3.2551 +  }
  3.2552 +  /* calculate union of both keys */
  3.2553 +  pgl_unite_keys((pgl_keyptr)&union_key, new);
  3.2554 +  /* penalty equal to reduction of key length (logarithm of added area) */
  3.2555 +  /* (return value by setting referenced value and returning pointer) */
  3.2556 +  *penalty = (
  3.2557 +    PGL_KEY_NODEDEPTH(orig) - PGL_KEY_NODEDEPTH((pgl_keyptr)&union_key)
  3.2558 +  );
  3.2559 +  PG_RETURN_POINTER(penalty);
  3.2560 +}
  3.2561 +
  3.2562 +/* GiST "picksplit" support function */
  3.2563 +PG_FUNCTION_INFO_V1(pgl_gist_picksplit);
  3.2564 +Datum pgl_gist_picksplit(PG_FUNCTION_ARGS) {
  3.2565 +  GistEntryVector *entryvec = (GistEntryVector *)PG_GETARG_POINTER(0);
  3.2566 +  GIST_SPLITVEC *v = (GIST_SPLITVEC *)PG_GETARG_POINTER(1);
  3.2567 +  OffsetNumber i;  /* between FirstOffsetNumber and entryvec->n (inclusive) */
  3.2568 +  union {
  3.2569 +    pgl_pointkey pointkey;
  3.2570 +    pgl_areakey areakey;
  3.2571 +  } union_all;  /* union of all keys (to be calculated from scratch)
  3.2572 +                   (later cut in half) */
  3.2573 +  int is_areakey = PGL_KEY_IS_AREAKEY(
  3.2574 +    (pgl_keyptr)DatumGetPointer(entryvec->vector[FirstOffsetNumber].key)
  3.2575 +  );
  3.2576 +  int keysize = is_areakey ? sizeof(pgl_areakey) : sizeof(pgl_pointkey);
  3.2577 +  pgl_keyptr unionL = palloc(keysize);  /* union of keys that go left */
  3.2578 +  pgl_keyptr unionR = palloc(keysize);  /* union of keys that go right */
  3.2579 +  pgl_keyptr key;  /* current key to be processed */
  3.2580 +  /* allocate memory for array of left and right keys, set counts to zero */
  3.2581 +  v->spl_left = (OffsetNumber *)palloc(entryvec->n * sizeof(OffsetNumber));
  3.2582 +  v->spl_nleft = 0;
  3.2583 +  v->spl_right = (OffsetNumber *)palloc(entryvec->n * sizeof(OffsetNumber));
  3.2584 +  v->spl_nright = 0;
  3.2585 +  /* calculate union of all keys from scratch */
  3.2586 +  memcpy(
  3.2587 +    (pgl_keyptr)&union_all,
  3.2588 +    (pgl_keyptr)DatumGetPointer(entryvec->vector[FirstOffsetNumber].key),
  3.2589 +    keysize
  3.2590 +  );
  3.2591 +  for (i=FirstOffsetNumber+1; i<entryvec->n; i=OffsetNumberNext(i)) {
  3.2592 +    pgl_unite_keys(
  3.2593 +      (pgl_keyptr)&union_all,
  3.2594 +      (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key)
  3.2595 +    );
  3.2596 +  }
  3.2597 +  /* check if trivial split is necessary due to exhausted key length */
  3.2598 +  /* (Note: keys for empty objects must have node depth set to maximum) */
  3.2599 +  if (PGL_KEY_NODEDEPTH((pgl_keyptr)&union_all) == (
  3.2600 +    is_areakey ? PGL_AREAKEY_MAXDEPTH : PGL_POINTKEY_MAXDEPTH
  3.2601 +  )) {
  3.2602 +    /* half of all keys go left */
  3.2603 +    for (
  3.2604 +      i=FirstOffsetNumber;
  3.2605 +      i<FirstOffsetNumber+(entryvec->n - FirstOffsetNumber)/2;
  3.2606 +      i=OffsetNumberNext(i)
  3.2607 +    ) {
  3.2608 +      /* pointer to current key */
  3.2609 +      key = (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key);
  3.2610 +      /* update unionL */
  3.2611 +      /* check if key is first key that goes left */
  3.2612 +      if (!v->spl_nleft) {
  3.2613 +        /* first key that goes left is just copied to unionL */
  3.2614 +        memcpy(unionL, key, keysize);
  3.2615 +      } else {
  3.2616 +        /* unite current value and next key */
  3.2617 +        pgl_unite_keys(unionL, key);
  3.2618 +      }
  3.2619 +      /* append offset number to list of keys that go left */
  3.2620 +      v->spl_left[v->spl_nleft++] = i;
  3.2621 +    }
  3.2622 +    /* other half goes right */
  3.2623 +    for (
  3.2624 +      i=FirstOffsetNumber+(entryvec->n - FirstOffsetNumber)/2;
  3.2625 +      i<entryvec->n;
  3.2626 +      i=OffsetNumberNext(i)
  3.2627 +    ) {
  3.2628 +      /* pointer to current key */
  3.2629 +      key = (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key);
  3.2630 +      /* update unionR */
  3.2631 +      /* check if key is first key that goes right */
  3.2632 +      if (!v->spl_nright) {
  3.2633 +        /* first key that goes right is just copied to unionR */
  3.2634 +        memcpy(unionR, key, keysize);
  3.2635 +      } else {
  3.2636 +        /* unite current value and next key */
  3.2637 +        pgl_unite_keys(unionR, key);
  3.2638 +      }
  3.2639 +      /* append offset number to list of keys that go right */
  3.2640 +      v->spl_right[v->spl_nright++] = i;
  3.2641 +    }
  3.2642 +  }
  3.2643 +  /* otherwise, a non-trivial split is possible */
  3.2644 +  else {
  3.2645 +    /* cut covered area in half */
  3.2646 +    /* (union_all then refers to area of keys that go left) */
  3.2647 +    /* check if union of all keys covers empty and non-empty objects */
  3.2648 +    if (PGL_KEY_IS_UNIVERSAL((pgl_keyptr)&union_all)) {
  3.2649 +      /* if yes, split into empty and non-empty objects */
  3.2650 +      pgl_key_set_empty((pgl_keyptr)&union_all);
  3.2651 +    } else {
  3.2652 +      /* otherwise split by next bit */
  3.2653 +      ((pgl_keyptr)&union_all)[PGL_KEY_NODEDEPTH_OFFSET]++;
  3.2654 +      /* NOTE: type bit conserved */
  3.2655 +    }
  3.2656 +    /* determine for each key if it goes left or right */
  3.2657 +    for (i=FirstOffsetNumber; i<entryvec->n; i=OffsetNumberNext(i)) {
  3.2658 +      /* pointer to current key */
  3.2659 +      key = (pgl_keyptr)DatumGetPointer(entryvec->vector[i].key);
  3.2660 +      /* keys within one half of the area go left */
  3.2661 +      if (pgl_keys_overlap((pgl_keyptr)&union_all, key)) {
  3.2662 +        /* update unionL */
  3.2663 +        /* check if key is first key that goes left */
  3.2664 +        if (!v->spl_nleft) {
  3.2665 +          /* first key that goes left is just copied to unionL */
  3.2666 +          memcpy(unionL, key, keysize);
  3.2667 +        } else {
  3.2668 +          /* unite current value of unionL and processed key */
  3.2669 +          pgl_unite_keys(unionL, key);
  3.2670 +        }
  3.2671 +        /* append offset number to list of keys that go left */
  3.2672 +        v->spl_left[v->spl_nleft++] = i;
  3.2673 +      }
  3.2674 +      /* the other keys go right */
  3.2675 +      else {
  3.2676 +        /* update unionR */
  3.2677 +        /* check if key is first key that goes right */
  3.2678 +        if (!v->spl_nright) {
  3.2679 +          /* first key that goes right is just copied to unionR */
  3.2680 +          memcpy(unionR, key, keysize);
  3.2681 +        } else {
  3.2682 +          /* unite current value of unionR and processed key */
  3.2683 +          pgl_unite_keys(unionR, key);
  3.2684 +        }
  3.2685 +        /* append offset number to list of keys that go right */
  3.2686 +        v->spl_right[v->spl_nright++] = i;
  3.2687 +      }
  3.2688 +    }
  3.2689 +  }
  3.2690 +  /* store unions in return value */
  3.2691 +  v->spl_ldatum = PointerGetDatum(unionL);
  3.2692 +  v->spl_rdatum = PointerGetDatum(unionR);
  3.2693 +  /* return all results */
  3.2694 +  PG_RETURN_POINTER(v);
  3.2695 +}
  3.2696 +
  3.2697 +/* GiST "same"/"equal" support function */
  3.2698 +PG_FUNCTION_INFO_V1(pgl_gist_same);
  3.2699 +Datum pgl_gist_same(PG_FUNCTION_ARGS) {
  3.2700 +  pgl_keyptr key1 = (pgl_keyptr)PG_GETARG_POINTER(0);
  3.2701 +  pgl_keyptr key2 = (pgl_keyptr)PG_GETARG_POINTER(1);
  3.2702 +  bool *boolptr = (bool *)PG_GETARG_POINTER(2);
  3.2703 +  /* two keys are equal if they are binary equal */
  3.2704 +  /* (return result by setting referenced boolean and returning pointer) */
  3.2705 +  *boolptr = !memcmp(
  3.2706 +    key1,
  3.2707 +    key2,
  3.2708 +    PGL_KEY_IS_AREAKEY(key1) ? sizeof(pgl_areakey) : sizeof(pgl_pointkey)
  3.2709 +  );
  3.2710 +  PG_RETURN_POINTER(boolptr);
  3.2711 +}
  3.2712 +
  3.2713 +/* GiST "distance" support function */
  3.2714 +PG_FUNCTION_INFO_V1(pgl_gist_distance);
  3.2715 +Datum pgl_gist_distance(PG_FUNCTION_ARGS) {
  3.2716 +  GISTENTRY *entry = (GISTENTRY *)PG_GETARG_POINTER(0);
  3.2717 +  pgl_keyptr key = (pgl_keyptr)DatumGetPointer(entry->key);
  3.2718 +  StrategyNumber strategy = (StrategyNumber)PG_GETARG_UINT16(2);
  3.2719 +  bool *recheck = (bool *)PG_GETARG_POINTER(4);
  3.2720 +  double distance;  /* return value */
  3.2721 +  /* demand recheck because distance is just an estimation */
  3.2722 +  /* (real distance may be bigger) */
  3.2723 +  *recheck = true;
  3.2724 +  /* strategy number aliases for different operators using the same strategy */
  3.2725 +  strategy %= 100;
  3.2726 +  /* strategy number 31: distance to point */
  3.2727 +  if (strategy == 31) {
  3.2728 +    /* query datum is a point */
  3.2729 +    pgl_point *query = (pgl_point *)PG_GETARG_POINTER(1);
  3.2730 +    /* use pgl_estimate_pointkey_distance() function to compute result */
  3.2731 +    distance = pgl_estimate_key_distance(key, query);
  3.2732 +    /* avoid infinity (reserved!) */
  3.2733 +    if (!isfinite(distance)) distance = PGL_ULTRA_DISTANCE;
  3.2734 +    /* return result */
  3.2735 +    PG_RETURN_FLOAT8(distance);
  3.2736 +  }
  3.2737 +  /* strategy number 33: distance to circle */
  3.2738 +  if (strategy == 33) {
  3.2739 +    /* query datum is a circle */
  3.2740 +    pgl_circle *query = (pgl_circle *)PG_GETARG_POINTER(1);
  3.2741 +    /* estimate distance to circle center and substract circle radius */
  3.2742 +    distance = (
  3.2743 +      pgl_estimate_key_distance(key, &(query->center)) - query->radius
  3.2744 +    );
  3.2745 +    /* convert non-positive values to zero and avoid infinity (reserved!) */
  3.2746 +    if (distance <= 0) distance = 0;
  3.2747 +    else if (!isfinite(distance)) distance = PGL_ULTRA_DISTANCE;
  3.2748 +    /* return result */
  3.2749 +    PG_RETURN_FLOAT8(distance);
  3.2750 +  }
  3.2751 +  /* strategy number 34: distance to cluster */
  3.2752 +  if (strategy == 34) {
  3.2753 +    /* query datum is a cluster */
  3.2754 +    pgl_cluster *query = (pgl_cluster *)PG_DETOAST_DATUM(PG_GETARG_DATUM(1));
  3.2755 +    /* estimate distance to bounding center and substract bounding radius */
  3.2756 +    distance = (
  3.2757 +      pgl_estimate_key_distance(key, &(query->bounding.center)) -
  3.2758 +      query->bounding.radius
  3.2759 +    );
  3.2760 +    /* convert non-positive values to zero and avoid infinity (reserved!) */
  3.2761 +    if (distance <= 0) distance = 0;
  3.2762 +    else if (!isfinite(distance)) distance = PGL_ULTRA_DISTANCE;
  3.2763 +    /* free detoasted cluster (if copy) */
  3.2764 +    PG_FREE_IF_COPY(query, 1);
  3.2765 +    /* return result */
  3.2766 +    PG_RETURN_FLOAT8(distance);
  3.2767 +  }
  3.2768 +  /* throw error for any unknown strategy number */
  3.2769 +  elog(ERROR, "unrecognized strategy number: %d", strategy);
  3.2770 +}
  3.2771 +