Add support for nearest-neighbor (KNN) searches to SP-GiST

Currently, KNN searches were supported only by GiST.  SP-GiST also capable to
support them.  This commit implements that support.  SP-GiST scan stack is
replaced with queue, which serves as stack if no ordering is specified.  KNN
support is provided for three SP-GIST opclasses: quad_point_ops, kd_point_ops
and poly_ops (catversion is bumped).  Some common parts between GiST and SP-GiST
KNNs are extracted into separate functions.

Discussion: https://postgr.es/m/570825e8-47d0-4732-2bf6-88d67d2d51c8%40postgrespro.ru
Author: Nikita Glukhov, Alexander Korotkov based on GSoC work by Vlad Sterzhanov
Review: Andrey Borodin, Alexander Korotkov

doc/src/sgml/indices.sgml

@@ -281,6 +281,13 @@ SELECT * FROM places ORDER BY location <-> point '(101,456)' LIMIT 10;
    For more information see <xref linkend="spgist"/>.
   </para>
 
+  <para>
+   Like GiST, SP-GiST supports <quote>nearest-neighbor</quote> searches.
+   For SP-GiST operator classes that support distance ordering, the 
+   corresponding operator is specified in the <quote>Ordering Operators</quote>
+   column in <xref linkend="spgist-builtin-opclasses-table"/>.
+  </para>
+
   <para>
    <indexterm>
     <primary>index</primary>

doc/src/sgml/spgist.sgml

@@ -64,12 +64,13 @@
 
   <table id="spgist-builtin-opclasses-table">
    <title>Built-in <acronym>SP-GiST</acronym> Operator Classes</title>
-   <tgroup cols="3">
+   <tgroup cols="4">
     <thead>
      <row>
       <entry>Name</entry>
       <entry>Indexed Data Type</entry>
       <entry>Indexable Operators</entry>
+      <entry>Ordering Operators</entry>
      </row>
     </thead>
     <tbody>
@@ -84,6 +85,9 @@
        <literal>&gt;^</literal>
        <literal>~=</literal>
       </entry>
+      <entry>
+       <literal>&lt;-&gt;</literal>
+      </entry>
      </row>
      <row>
       <entry><literal>quad_point_ops</literal></entry>
@@ -96,6 +100,9 @@
        <literal>&gt;^</literal>
        <literal>~=</literal>
       </entry>
+      <entry>
+       <literal>&lt;-&gt;</literal>
+      </entry>
      </row>
      <row>
       <entry><literal>range_ops</literal></entry>
@@ -111,6 +118,8 @@
        <literal>&gt;&gt;</literal>
        <literal>@&gt;</literal>
       </entry>
+      <entry>
+      </entry>
      </row>
      <row>
       <entry><literal>box_ops</literal></entry>
@@ -129,6 +138,8 @@
        <literal>|&gt;&gt;</literal>
        <literal>|&amp;&gt;</literal>
       </entry>
+      <entry>
+      </entry>
      </row>
      <row>
       <entry><literal>poly_ops</literal></entry>
@@ -147,6 +158,9 @@
        <literal>|&gt;&gt;</literal>
        <literal>|&amp;&gt;</literal>
       </entry>
+      <entry>
+        <literal>&lt;-&gt;</literal>
+      </entry>      
      </row>
      <row>
       <entry><literal>text_ops</literal></entry>
@@ -163,6 +177,8 @@
        <literal>~&gt;~</literal>
        <literal>^@</literal>
       </entry>
+      <entry>
+      </entry>
      </row>
      <row>
       <entry><literal>inet_ops</literal></entry>
@@ -180,6 +196,8 @@
        <literal>&lt;=</literal>
        <literal>=</literal>
       </entry>
+      <entry>
+      </entry>
      </row>
     </tbody>
    </tgroup>
@@ -191,6 +209,12 @@
   supports the same operators but uses a different index data structure which
   may offer better performance in some applications.
  </para>
+ <para>
+  The <literal>quad_point_ops</literal>, <literal>kd_point_ops</literal> and
+  <literal>poly_ops</literal> operator classes support the <literal>&lt;-&gt;</literal>
+  ordering operator, which enables the k-nearest neighbor (<literal>k-NN</literal>)
+  search over indexed point or polygon datasets.
+ </para>
 
 </sect1>
 
@@ -630,7 +654,10 @@ CREATE FUNCTION my_inner_consistent(internal, internal) RETURNS void ...
 typedef struct spgInnerConsistentIn
 {
     ScanKey     scankeys;       /* array of operators and comparison values */
-    int         nkeys;          /* length of array */
+    ScanKey     orderbys;       /* array of ordering operators and comparison
+                                 * values */
+    int         nkeys;          /* length of scankeys array */
+    int         norderbys;      /* length of orderbys array */
 
     Datum       reconstructedValue;     /* value reconstructed at parent */
     void       *traversalValue; /* opclass-specific traverse value */
@@ -653,6 +680,7 @@ typedef struct spgInnerConsistentOut
     int        *levelAdds;      /* increment level by this much for each */
     Datum      *reconstructedValues;    /* associated reconstructed values */
     void      **traversalValues;        /* opclass-specific traverse values */
+    double    **distances;              /* associated distances */
 } spgInnerConsistentOut;
 </programlisting>
 
@@ -667,6 +695,8 @@ typedef struct spgInnerConsistentOut
        In particular it is not necessary to check <structfield>sk_flags</structfield> to
        see if the comparison value is NULL, because the SP-GiST core code
        will filter out such conditions.
+       The array <structfield>orderbys</structfield>, of length <structfield>norderbys</structfield>,
+       describes ordering operators (if any) in the same manner.
        <structfield>reconstructedValue</structfield> is the value reconstructed for the
        parent tuple; it is <literal>(Datum) 0</literal> at the root level or if the
        <function>inner_consistent</function> function did not provide a value at the
@@ -709,6 +739,10 @@ typedef struct spgInnerConsistentOut
        of <structname>spgConfigOut</structname>.<structfield>leafType</structfield> type
        reconstructed for each child node to be visited; otherwise, leave
        <structfield>reconstructedValues</structfield> as NULL.
+       If ordered search is performed, set <structfield>distances</structfield>
+       to an array of distance values according to <structfield>orderbys</structfield>
+       array (nodes with lowest distances will be processed first).  Leave it
+       NULL otherwise.
        If it is desired to pass down additional out-of-band information
        (<quote>traverse values</quote>) to lower levels of the tree search,
        set <structfield>traversalValues</structfield> to an array of the appropriate
@@ -717,6 +751,7 @@ typedef struct spgInnerConsistentOut
        Note that the <function>inner_consistent</function> function is
        responsible for palloc'ing the
        <structfield>nodeNumbers</structfield>, <structfield>levelAdds</structfield>,
+       <structfield>distances</structfield>,
        <structfield>reconstructedValues</structfield>, and
        <structfield>traversalValues</structfield> arrays in the current memory context.
        However, any output traverse values pointed to by
@@ -747,7 +782,10 @@ CREATE FUNCTION my_leaf_consistent(internal, internal) RETURNS bool ...
 typedef struct spgLeafConsistentIn
 {
     ScanKey     scankeys;       /* array of operators and comparison values */
-    int         nkeys;          /* length of array */
+    ScanKey     orderbys;       /* array of ordering operators and comparison
+                                 * values */
+    int         nkeys;          /* length of scankeys array */
+    int         norderbys;      /* length of orderbys array */
 
     Datum       reconstructedValue;     /* value reconstructed at parent */
     void       *traversalValue; /* opclass-specific traverse value */
@@ -759,8 +797,10 @@ typedef struct spgLeafConsistentIn
 
 typedef struct spgLeafConsistentOut
 {
-    Datum       leafValue;      /* reconstructed original data, if any */
-    bool        recheck;        /* set true if operator must be rechecked */
+    Datum       leafValue;        /* reconstructed original data, if any */
+    bool        recheck;          /* set true if operator must be rechecked */
+    bool        recheckDistances; /* set true if distances must be rechecked */
+    double     *distances;        /* associated distances */
 } spgLeafConsistentOut;
 </programlisting>
 
@@ -775,6 +815,8 @@ typedef struct spgLeafConsistentOut
        In particular it is not necessary to check <structfield>sk_flags</structfield> to
        see if the comparison value is NULL, because the SP-GiST core code
        will filter out such conditions.
+       The array <structfield>orderbys</structfield>, of length <structfield>norderbys</structfield>,
+       describes the ordering operators in the same manner.
        <structfield>reconstructedValue</structfield> is the value reconstructed for the
        parent tuple; it is <literal>(Datum) 0</literal> at the root level or if the
        <function>inner_consistent</function> function did not provide a value at the
@@ -803,6 +845,12 @@ typedef struct spgLeafConsistentOut
        <structfield>recheck</structfield> may be set to <literal>true</literal> if the match
        is uncertain and so the operator(s) must be re-applied to the actual
        heap tuple to verify the match.
+       If ordered search is performed, set <structfield>distances</structfield>
+       to an array of distance values according to <structfield>orderbys</structfield>
+       array.  Leave it NULL otherwise.  If at least one of returned distances
+       is not exact, set <structfield>recheckDistances</structfield> to true.
+       In this case, the executor will calculate the exact distances after
+       fetching the tuple from the heap, and will reorder the tuples if needed.
       </para>
      </listitem>
     </varlistentry>

doc/src/sgml/xindex.sgml

@@ -1242,7 +1242,7 @@ SELECT sum(x) OVER (ORDER BY x RANGE BETWEEN 5 PRECEDING AND 10 FOLLOWING)
   <title>Ordering Operators</title>
 
   <para>
-   Some index access methods (currently, only GiST) support the concept of
+   Some index access methods (currently, only GiST and SP-GiST) support the concept of
    <firstterm>ordering operators</firstterm>.  What we have been discussing so far
    are <firstterm>search operators</firstterm>.  A search operator is one for which
    the index can be searched to find all rows satisfying

src/backend/access/gist/gistget.c

@@ -14,9 +14,9 @@
  */
 #include "postgres.h"
 
+#include "access/genam.h"
 #include "access/gist_private.h"
 #include "access/relscan.h"
-#include "catalog/pg_type.h"
 #include "miscadmin.h"
 #include "storage/lmgr.h"
 #include "storage/predicate.h"
@@ -543,7 +543,6 @@ getNextNearest(IndexScanDesc scan)
 {
 	GISTScanOpaque so = (GISTScanOpaque) scan->opaque;
 	bool		res = false;
-	int			i;
 
 	if (scan->xs_hitup)
 	{
@@ -564,45 +563,10 @@ getNextNearest(IndexScanDesc scan)
 			/* found a heap item at currently minimal distance */
 			scan->xs_ctup.t_self = item->data.heap.heapPtr;
 			scan->xs_recheck = item->data.heap.recheck;
-			scan->xs_recheckorderby = item->data.heap.recheckDistances;
-			for (i = 0; i < scan->numberOfOrderBys; i++)
-			{
-				if (so->orderByTypes[i] == FLOAT8OID)
-				{
-#ifndef USE_FLOAT8_BYVAL
-					/* must free any old value to avoid memory leakage */
-					if (!scan->xs_orderbynulls[i])
-						pfree(DatumGetPointer(scan->xs_orderbyvals[i]));
-#endif
-					scan->xs_orderbyvals[i] = Float8GetDatum(item->distances[i]);
-					scan->xs_orderbynulls[i] = false;
-				}
-				else if (so->orderByTypes[i] == FLOAT4OID)
-				{
-					/* convert distance function's result to ORDER BY type */
-#ifndef USE_FLOAT4_BYVAL
-					/* must free any old value to avoid memory leakage */
-					if (!scan->xs_orderbynulls[i])
-						pfree(DatumGetPointer(scan->xs_orderbyvals[i]));
-#endif
-					scan->xs_orderbyvals[i] = Float4GetDatum((float4) item->distances[i]);
-					scan->xs_orderbynulls[i] = false;
-				}
-				else
-				{
-					/*
-					 * If the ordering operator's return value is anything
-					 * else, we don't know how to convert the float8 bound
-					 * calculated by the distance function to that.  The
-					 * executor won't actually need the order by values we
-					 * return here, if there are no lossy results, so only
-					 * insist on converting if the *recheck flag is set.
-					 */
-					if (scan->xs_recheckorderby)
-						elog(ERROR, "GiST operator family's FOR ORDER BY operator must return float8 or float4 if the distance function is lossy");
-					scan->xs_orderbynulls[i] = true;
-				}
-			}
+
+			index_store_float8_orderby_distances(scan, so->orderByTypes,
+												 item->distances,
+												 item->data.heap.recheckDistances);
 
 			/* in an index-only scan, also return the reconstructed tuple. */
 			if (scan->xs_want_itup)

src/backend/access/gist/gistutil.c

@@ -23,6 +23,7 @@
 #include "storage/lmgr.h"
 #include "utils/float.h"
 #include "utils/syscache.h"
+#include "utils/lsyscache.h"
 
 
 /*
@@ -871,12 +872,6 @@ gistproperty(Oid index_oid, int attno,
 			 IndexAMProperty prop, const char *propname,
 			 bool *res, bool *isnull)
 {
-	HeapTuple	tuple;
-	Form_pg_index rd_index PG_USED_FOR_ASSERTS_ONLY;
-	Form_pg_opclass rd_opclass;
-	Datum		datum;
-	bool		disnull;
-	oidvector  *indclass;
 	Oid			opclass,
 				opfamily,
 				opcintype;
@@ -910,41 +905,19 @@ gistproperty(Oid index_oid, int attno,
 	}
 
 	/* First we need to know the column's opclass. */
-
-	tuple = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(index_oid));
-	if (!HeapTupleIsValid(tuple))
+	opclass = get_index_column_opclass(index_oid, attno);
+	if (!OidIsValid(opclass))
 	{
 		*isnull = true;
 		return true;
 	}
-	rd_index = (Form_pg_index) GETSTRUCT(tuple);
-
-	/* caller is supposed to guarantee this */
-	Assert(attno > 0 && attno <= rd_index->indnatts);
-
-	datum = SysCacheGetAttr(INDEXRELID, tuple,
-							Anum_pg_index_indclass, &disnull);
-	Assert(!disnull);
-
-	indclass = ((oidvector *) DatumGetPointer(datum));
-	opclass = indclass->values[attno - 1];
-
-	ReleaseSysCache(tuple);
 
 	/* Now look up the opclass family and input datatype. */
-
-	tuple = SearchSysCache1(CLAOID, ObjectIdGetDatum(opclass));
-	if (!HeapTupleIsValid(tuple))
+	if (!get_opclass_opfamily_and_input_type(opclass, &opfamily, &opcintype))
 	{
 		*isnull = true;
 		return true;
 	}
-	rd_opclass = (Form_pg_opclass) GETSTRUCT(tuple);
-
-	opfamily = rd_opclass->opcfamily;
-	opcintype = rd_opclass->opcintype;
-
-	ReleaseSysCache(tuple);
 
 	/* And now we can check whether the function is provided. */
 
@@ -967,6 +940,8 @@ gistproperty(Oid index_oid, int attno,
 									  Int16GetDatum(GIST_COMPRESS_PROC));
 	}
 
+	*isnull = false;
+
 	return true;
 }
 

src/backend/access/index/indexam.c

@@ -74,6 +74,7 @@
 #include "access/transam.h"
 #include "access/xlog.h"
 #include "catalog/index.h"
+#include "catalog/pg_type.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
@@ -897,3 +898,72 @@ index_getprocinfo(Relation irel,
 
 	return locinfo;
 }
+
+/* ----------------
+ *		index_store_float8_orderby_distances
+ *
+ *		Convert AM distance function's results (that can be inexact)
+ *		to ORDER BY types and save them into xs_orderbyvals/xs_orderbynulls
+ *		for a possible recheck.
+ * ----------------
+ */
+void
+index_store_float8_orderby_distances(IndexScanDesc scan, Oid *orderByTypes,
+									 double *distances, bool recheckOrderBy)
+{
+	int			i;
+
+	scan->xs_recheckorderby = recheckOrderBy;
+
+	if (!distances)
+	{
+		Assert(!scan->xs_recheckorderby);
+
+		for (i = 0; i < scan->numberOfOrderBys; i++)
+		{
+			scan->xs_orderbyvals[i] = (Datum) 0;
+			scan->xs_orderbynulls[i] = true;
+		}
+
+		return;
+	}
+
+	for (i = 0; i < scan->numberOfOrderBys; i++)
+	{
+		if (orderByTypes[i] == FLOAT8OID)
+		{
+#ifndef USE_FLOAT8_BYVAL
+			/* must free any old value to avoid memory leakage */
+			if (!scan->xs_orderbynulls[i])
+				pfree(DatumGetPointer(scan->xs_orderbyvals[i]));
+#endif
+			scan->xs_orderbyvals[i] = Float8GetDatum(distances[i]);
+			scan->xs_orderbynulls[i] = false;
+		}
+		else if (orderByTypes[i] == FLOAT4OID)
+		{
+			/* convert distance function's result to ORDER BY type */
+#ifndef USE_FLOAT4_BYVAL
+			/* must free any old value to avoid memory leakage */
+			if (!scan->xs_orderbynulls[i])
+				pfree(DatumGetPointer(scan->xs_orderbyvals[i]));
+#endif
+			scan->xs_orderbyvals[i] = Float4GetDatum((float4) distances[i]);
+			scan->xs_orderbynulls[i] = false;
+		}
+		else
+		{
+			/*
+			 * If the ordering operator's return value is anything else, we
+			 * don't know how to convert the float8 bound calculated by the
+			 * distance function to that.  The executor won't actually need
+			 * the order by values we return here, if there are no lossy
+			 * results, so only insist on converting if the *recheck flag is
+			 * set.
+			 */
+			if (scan->xs_recheckorderby)
+				elog(ERROR, "ORDER BY operator must return float8 or float4 if the distance function is lossy");
+			scan->xs_orderbynulls[i] = true;
+		}
+	}
+}

src/backend/access/spgist/Makefile

@@ -14,6 +14,7 @@ include $(top_builddir)/src/Makefile.global
 
 OBJS = spgutils.o spginsert.o spgscan.o spgvacuum.o spgvalidate.o \
 	spgdoinsert.o spgxlog.o \
-	spgtextproc.o spgquadtreeproc.o spgkdtreeproc.o
+	spgtextproc.o spgquadtreeproc.o spgkdtreeproc.o \
+	spgproc.o
 
 include $(top_srcdir)/src/backend/common.mk

src/backend/access/spgist/README

@@ -41,7 +41,11 @@ contain exactly one inner tuple.
 
 When the search traversal algorithm reaches an inner tuple, it chooses a set
 of nodes to continue tree traverse in depth.  If it reaches a leaf page it
-scans a list of leaf tuples to find the ones that match the query.
+scans a list of leaf tuples to find the ones that match the query. SP-GiST
+also supports ordered (nearest-neighbor) searches - that is during scan pending
+nodes are put into priority queue, so traversal is performed by the
+closest-first model.
+
 
 The insertion algorithm descends the tree similarly, except it must choose
 just one node to descend to from each inner tuple.  Insertion might also have

src/backend/access/spgist/spgkdtreeproc.c

@@ -16,9 +16,11 @@
 #include "postgres.h"
 
 #include "access/spgist.h"
+#include "access/spgist_private.h"
 #include "access/stratnum.h"
 #include "catalog/pg_type.h"
 #include "utils/builtins.h"
+#include "utils/float.h"
 #include "utils/geo_decls.h"
 
 
@@ -162,6 +164,7 @@ spg_kd_inner_consistent(PG_FUNCTION_ARGS)
 	double		coord;
 	int			which;
 	int			i;
+	BOX			bboxes[2];
 
 	Assert(in->hasPrefix);
 	coord = DatumGetFloat8(in->prefixDatum);
@@ -248,12 +251,87 @@ spg_kd_inner_consistent(PG_FUNCTION_ARGS)
 	}
 
 	/* We must descend into the children identified by which */
-	out->nodeNumbers = (int *) palloc(sizeof(int) * 2);
 	out->nNodes = 0;
+
+	/* Fast-path for no matching children */
+	if (!which)
+		PG_RETURN_VOID();
+
+	out->nodeNumbers = (int *) palloc(sizeof(int) * 2);
+
+	/*
+	 * When ordering scan keys are specified, we've to calculate distance for
+	 * them.  In order to do that, we need calculate bounding boxes for both
+	 * children nodes.  Calculation of those bounding boxes on non-zero level
+	 * require knowledge of bounding box of upper node.  So, we save bounding
+	 * boxes to traversalValues.
+	 */
+	if (in->norderbys > 0)
+	{
+		BOX			infArea;
+		BOX		   *area;
+
+		out->distances = (double **) palloc(sizeof(double *) * in->nNodes);
+		out->traversalValues = (void **) palloc(sizeof(void *) * in->nNodes);
+
+		if (in->level == 0)
+		{
+			float8		inf = get_float8_infinity();
+
+			infArea.high.x = inf;
+			infArea.high.y = inf;
+			infArea.low.x = -inf;
+			infArea.low.y = -inf;
+			area = &infArea;
+		}
+		else
+		{
+			area = (BOX *) in->traversalValue;
+			Assert(area);
+		}
+
+		bboxes[0].low = area->low;
+		bboxes[1].high = area->high;
+
+		if (in->level % 2)
+		{
+			/* split box by x */
+			bboxes[0].high.x = bboxes[1].low.x = coord;
+			bboxes[0].high.y = area->high.y;
+			bboxes[1].low.y = area->low.y;
+		}
+		else
+		{
+			/* split box by y */
+			bboxes[0].high.y = bboxes[1].low.y = coord;
+			bboxes[0].high.x = area->high.x;
+			bboxes[1].low.x = area->low.x;
+		}
+	}
+
 	for (i = 1; i <= 2; i++)
 	{
 		if (which & (1 << i))
-			out->nodeNumbers[out->nNodes++] = i - 1;
+		{
+			out->nodeNumbers[out->nNodes] = i - 1;
+
+			if (in->norderbys > 0)
+			{
+				MemoryContext oldCtx = MemoryContextSwitchTo(
+															 in->traversalMemoryContext);
+				BOX		   *box = box_copy(&bboxes[i - 1]);
+
+				MemoryContextSwitchTo(oldCtx);
+
+				out->traversalValues[out->nNodes] = box;
+
+				out->distances[out->nNodes] = spg_key_orderbys_distances(
+																		 BoxPGetDatum(box), false,
+																		 in->orderbys, in->norderbys);
+			}
+
+			out->nNodes++;
+		}
 	}
 
 	/* Set up level increments, too */

src/backend/access/spgist/spgproc.c

+/*-------------------------------------------------------------------------
+ *
+ * spgproc.c
+ *	  Common supporting procedures for SP-GiST opclasses.
+ *
+ *
+ * Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1994, Regents of the University of California
+ *
+ * IDENTIFICATION
+ *			src/backend/access/spgist/spgproc.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "postgres.h"
+
+#include <math.h>
+
+#include "access/spgist_private.h"
+#include "utils/builtins.h"
+#include "utils/float.h"
+#include "utils/geo_decls.h"
+
+#define point_point_distance(p1,p2) \
+	DatumGetFloat8(DirectFunctionCall2(point_distance, \
+									   PointPGetDatum(p1), PointPGetDatum(p2)))
+
+/* Point-box distance in the assumption that box is aligned by axis */
+static double
+point_box_distance(Point *point, BOX *box)
+{
+	double		dx,
+				dy;
+
+	if (isnan(point->x) || isnan(box->low.x) ||
+		isnan(point->y) || isnan(box->low.y))
+		return get_float8_nan();
+
+	if (point->x < box->low.x)
+		dx = box->low.x - point->x;
+	else if (point->x > box->high.x)
+		dx = point->x - box->high.x;
+	else
+		dx = 0.0;
+
+	if (point->y < box->low.y)
+		dy = box->low.y - point->y;
+	else if (point->y > box->high.y)
+		dy = point->y - box->high.y;
+	else
+		dy = 0.0;
+
+	return HYPOT(dx, dy);
+}
+
+/*
+ * Returns distances from given key to array of ordering scan keys.  Leaf key
+ * is expected to be point, non-leaf key is expected to be box.  Scan key
+ * arguments are expected to be points.
+ */
+double *
+spg_key_orderbys_distances(Datum key, bool isLeaf,
+						   ScanKey orderbys, int norderbys)
+{
+	int			sk_num;
+	double	   *distances = (double *) palloc(norderbys * sizeof(double)),
+			   *distance = distances;
+
+	for (sk_num = 0; sk_num < norderbys; ++sk_num, ++orderbys, ++distance)
+	{
+		Point	   *point = DatumGetPointP(orderbys->sk_argument);
+
+		*distance = isLeaf ? point_point_distance(point, DatumGetPointP(key))
+			: point_box_distance(point, DatumGetBoxP(key));
+	}
+
+	return distances;
+}
+
+BOX *
+box_copy(BOX *orig)
+{
+	BOX		   *result = palloc(sizeof(BOX));
+
+	*result = *orig;
+	return result;
+}

src/backend/access/spgist/spgquadtreeproc.c

@@ -17,8 +17,10 @@
 
 #include "access/spgist.h"
 #include "access/stratnum.h"
+#include "access/spgist_private.h"
 #include "catalog/pg_type.h"
 #include "utils/builtins.h"
+#include "utils/float.h"
 #include "utils/geo_decls.h"
 
 
@@ -77,6 +79,38 @@ getQuadrant(Point *centroid, Point *tst)
 	return 0;
 }
 
+/* Returns bounding box of a given quadrant inside given bounding box */
+static BOX *
+getQuadrantArea(BOX *bbox, Point *centroid, int quadrant)
+{
+	BOX		   *result = (BOX *) palloc(sizeof(BOX));
+
+	switch (quadrant)
+	{
+		case 1:
+			result->high = bbox->high;
+			result->low = *centroid;
+			break;
+		case 2:
+			result->high.x = bbox->high.x;
+			result->high.y = centroid->y;
+			result->low.x = centroid->x;
+			result->low.y = bbox->low.y;
+			break;
+		case 3:
+			result->high = *centroid;
+			result->low = bbox->low;
+			break;
+		case 4:
+			result->high.x = centroid->x;
+			result->high.y = bbox->high.y;
+			result->low.x = bbox->low.x;
+			result->low.y = centroid->y;
+			break;
+	}
+
+	return result;
+}
 
 Datum
 spg_quad_choose(PG_FUNCTION_ARGS)
@@ -196,19 +230,68 @@ spg_quad_inner_consistent(PG_FUNCTION_ARGS)
 	spgInnerConsistentIn *in = (spgInnerConsistentIn *) PG_GETARG_POINTER(0);
 	spgInnerConsistentOut *out = (spgInnerConsistentOut *) PG_GETARG_POINTER(1);
 	Point	   *centroid;
+	BOX			infbbox;
+	BOX		   *bbox = NULL;
 	int			which;
 	int			i;
 
 	Assert(in->hasPrefix);
 	centroid = DatumGetPointP(in->prefixDatum);
 
+	/*
+	 * When ordering scan keys are specified, we've to calculate distance for
+	 * them.  In order to do that, we need calculate bounding boxes for all
+	 * children nodes.  Calculation of those bounding boxes on non-zero level
+	 * require knowledge of bounding box of upper node.  So, we save bounding
+	 * boxes to traversalValues.
+	 */
+	if (in->norderbys > 0)
+	{
+		out->distances = (double **) palloc(sizeof(double *) * in->nNodes);
+		out->traversalValues = (void **) palloc(sizeof(void *) * in->nNodes);
+
+		if (in->level == 0)
+		{
+			double		inf = get_float8_infinity();
+
+			infbbox.high.x = inf;
+			infbbox.high.y = inf;
+			infbbox.low.x = -inf;
+			infbbox.low.y = -inf;
+			bbox = &infbbox;
+		}
+		else
+		{
+			bbox = in->traversalValue;
+			Assert(bbox);
+		}
+	}
+
 	if (in->allTheSame)
 	{
 		/* Report that all nodes should be visited */
 		out->nNodes = in->nNodes;
 		out->nodeNumbers = (int *) palloc(sizeof(int) * in->nNodes);
 		for (i = 0; i < in->nNodes; i++)
+		{
 			out->nodeNumbers[i] = i;
+
+			if (in->norderbys > 0)
+			{
+				MemoryContext oldCtx = MemoryContextSwitchTo(
+															 in->traversalMemoryContext);
+
+				/* Use parent quadrant box as traversalValue */
+				BOX		   *quadrant = box_copy(bbox);
+
+				MemoryContextSwitchTo(oldCtx);
+
+				out->traversalValues[i] = quadrant;
+				out->distances[i] = spg_key_orderbys_distances(
+															   BoxPGetDatum(quadrant), false,
+															   in->orderbys, in->norderbys);
+			}
+		}
 		PG_RETURN_VOID();
 	}
 
@@ -286,13 +369,37 @@ spg_quad_inner_consistent(PG_FUNCTION_ARGS)
 			break;				/* no need to consider remaining conditions */
 	}
 
+	out->levelAdds = palloc(sizeof(int) * 4);
+	for (i = 0; i < 4; ++i)
+		out->levelAdds[i] = 1;
+
 	/* We must descend into the quadrant(s) identified by which */
 	out->nodeNumbers = (int *) palloc(sizeof(int) * 4);
 	out->nNodes = 0;
+
 	for (i = 1; i <= 4; i++)
 	{
 		if (which & (1 << i))
-			out->nodeNumbers[out->nNodes++] = i - 1;
+		{
+			out->nodeNumbers[out->nNodes] = i - 1;
+
+			if (in->norderbys > 0)
+			{
+				MemoryContext oldCtx = MemoryContextSwitchTo(
+															 in->traversalMemoryContext);
+				BOX		   *quadrant = getQuadrantArea(bbox, centroid, i);
+
+				MemoryContextSwitchTo(oldCtx);
+
+				out->traversalValues[out->nNodes] = quadrant;
+
+				out->distances[out->nNodes] = spg_key_orderbys_distances(
+																		 BoxPGetDatum(quadrant), false,
+																		 in->orderbys, in->norderbys);
+			}
+
+			out->nNodes++;
+		}
 	}
 
 	PG_RETURN_VOID();
@@ -356,5 +463,11 @@ spg_quad_leaf_consistent(PG_FUNCTION_ARGS)
 			break;
 	}
 
+	if (res && in->norderbys > 0)
+		/* ok, it passes -> let's compute the distances */
+		out->distances = spg_key_orderbys_distances(
+													BoxPGetDatum(in->leafDatum), true,
+													in->orderbys, in->norderbys);
+
 	PG_RETURN_BOOL(res);
 }

src/backend/access/spgist/spgscan.c

@@ -15,64 +15,136 @@
 
 #include "postgres.h"
 
+#include "access/genam.h"
 #include "access/relscan.h"
 #include "access/spgist_private.h"
 #include "miscadmin.h"
 #include "storage/bufmgr.h"
 #include "utils/datum.h"
+#include "utils/float.h"
+#include "utils/lsyscache.h"
 #include "utils/memutils.h"
 #include "utils/rel.h"
 
-
 typedef void (*storeRes_func) (SpGistScanOpaque so, ItemPointer heapPtr,
-							   Datum leafValue, bool isnull, bool recheck);
+							   Datum leafValue, bool isNull, bool recheck,
+							   bool recheckDistances, double *distances);
 
-typedef struct ScanStackEntry
+/*
+ * Pairing heap comparison function for the SpGistSearchItem queue.
+ * KNN-searches currently only support NULLS LAST.  So, preserve this logic
+ * here.
+ */
+static int
+pairingheap_SpGistSearchItem_cmp(const pairingheap_node *a,
+								 const pairingheap_node *b, void *arg)
 {
-	Datum		reconstructedValue; /* value reconstructed from parent */
-	void	   *traversalValue; /* opclass-specific traverse value */
-	int			level;			/* level of items on this page */
-	ItemPointerData ptr;		/* block and offset to scan from */
-} ScanStackEntry;
+	const		SpGistSearchItem *sa = (const SpGistSearchItem *) a;
+	const		SpGistSearchItem *sb = (const SpGistSearchItem *) b;
+	SpGistScanOpaque so = (SpGistScanOpaque) arg;
+	int			i;
+
+	if (sa->isNull)
+	{
+		if (!sb->isNull)
+			return -1;
+	}
+	else if (sb->isNull)
+	{
+		return 1;
+	}
+	else
+	{
+		/* Order according to distance comparison */
+		for (i = 0; i < so->numberOfOrderBys; i++)
+		{
+			if (isnan(sa->distances[i]) && isnan(sb->distances[i]))
+				continue;		/* NaN == NaN */
+			if (isnan(sa->distances[i]))
+				return -1;		/* NaN > number */
+			if (isnan(sb->distances[i]))
+				return 1;		/* number < NaN */
+			if (sa->distances[i] != sb->distances[i])
+				return (sa->distances[i] < sb->distances[i]) ? 1 : -1;
+		}
+	}
 
+	/* Leaf items go before inner pages, to ensure a depth-first search */
+	if (sa->isLeaf && !sb->isLeaf)
+		return 1;
+	if (!sa->isLeaf && sb->isLeaf)
+		return -1;
+
+	return 0;
+}
 
-/* Free a ScanStackEntry */
 static void
-freeScanStackEntry(SpGistScanOpaque so, ScanStackEntry *stackEntry)
+spgFreeSearchItem(SpGistScanOpaque so, SpGistSearchItem * item)
 {
 	if (!so->state.attLeafType.attbyval &&
-		DatumGetPointer(stackEntry->reconstructedValue) != NULL)
-		pfree(DatumGetPointer(stackEntry->reconstructedValue));
-	if (stackEntry->traversalValue)
-		pfree(stackEntry->traversalValue);
+		DatumGetPointer(item->value) != NULL)
+		pfree(DatumGetPointer(item->value));
 
-	pfree(stackEntry);
+	if (item->traversalValue)
+		pfree(item->traversalValue);
+
+	pfree(item);
 }
 
-/* Free the entire stack */
+/*
+ * Add SpGistSearchItem to queue
+ *
+ * Called in queue context
+ */
 static void
-freeScanStack(SpGistScanOpaque so)
+spgAddSearchItemToQueue(SpGistScanOpaque so, SpGistSearchItem * item)
 {
-	ListCell   *lc;
+	pairingheap_add(so->scanQueue, &item->phNode);
+}
 
-	foreach(lc, so->scanStack)
-	{
-		freeScanStackEntry(so, (ScanStackEntry *) lfirst(lc));
-	}
-	list_free(so->scanStack);
-	so->scanStack = NIL;
+static SpGistSearchItem *
+spgAllocSearchItem(SpGistScanOpaque so, bool isnull, double *distances)
+{
+	/* allocate distance array only for non-NULL items */
+	SpGistSearchItem *item =
+	palloc(SizeOfSpGistSearchItem(isnull ? 0 : so->numberOfOrderBys));
+
+	item->isNull = isnull;
+
+	if (!isnull && so->numberOfOrderBys > 0)
+		memcpy(item->distances, distances,
+			   so->numberOfOrderBys * sizeof(double));
+
+	return item;
+}
+
+static void
+spgAddStartItem(SpGistScanOpaque so, bool isnull)
+{
+	SpGistSearchItem *startEntry =
+	spgAllocSearchItem(so, isnull, so->zeroDistances);
+
+	ItemPointerSet(&startEntry->heapPtr,
+				   isnull ? SPGIST_NULL_BLKNO : SPGIST_ROOT_BLKNO,
+				   FirstOffsetNumber);
+	startEntry->isLeaf = false;
+	startEntry->level = 0;
+	startEntry->value = (Datum) 0;
+	startEntry->traversalValue = NULL;
+	startEntry->recheck = false;
+	startEntry->recheckDistances = false;
+
+	spgAddSearchItemToQueue(so, startEntry);
 }
 
 /*
- * Initialize scanStack to search the root page, resetting
+ * Initialize queue to search the root page, resetting
  * any previously active scan
  */
 static void
 resetSpGistScanOpaque(SpGistScanOpaque so)
 {
-	ScanStackEntry *startEntry;
-
-	freeScanStack(so);
+	MemoryContext oldCtx;
 
 	/*
 	 * clear traversal context before proceeding to the next scan; this must
@@ -81,20 +153,29 @@ resetSpGistScanOpaque(SpGistScanOpaque so)
 	 */
 	MemoryContextReset(so->traversalCxt);
 
+	oldCtx = MemoryContextSwitchTo(so->traversalCxt);
+
+	/* initialize queue only for distance-ordered scans */
+	so->scanQueue = pairingheap_allocate(pairingheap_SpGistSearchItem_cmp, so);
+
 	if (so->searchNulls)
-	{
-		/* Stack a work item to scan the null index entries */
-		startEntry = (ScanStackEntry *) palloc0(sizeof(ScanStackEntry));
-		ItemPointerSet(&startEntry->ptr, SPGIST_NULL_BLKNO, FirstOffsetNumber);
-		so->scanStack = lappend(so->scanStack, startEntry);
-	}
+		/* Add a work item to scan the null index entries */
+		spgAddStartItem(so, true);
 
 	if (so->searchNonNulls)
+		/* Add a work item to scan the non-null index entries */
+		spgAddStartItem(so, false);
+
+	MemoryContextSwitchTo(oldCtx);
+
+	if (so->numberOfOrderBys > 0)
 	{
-		/* Stack a work item to scan the non-null index entries */
-		startEntry = (ScanStackEntry *) palloc0(sizeof(ScanStackEntry));
-		ItemPointerSet(&startEntry->ptr, SPGIST_ROOT_BLKNO, FirstOffsetNumber);
-		so->scanStack = lappend(so->scanStack, startEntry);
+		/* Must pfree distances to avoid memory leak */
+		int			i;
+
+		for (i = 0; i < so->nPtrs; i++)
+			if (so->distances[i])
+				pfree(so->distances[i]);
 	}
 
 	if (so->want_itup)
@@ -129,6 +210,9 @@ spgPrepareScanKeys(IndexScanDesc scan)
 	int			nkeys;
 	int			i;
 
+	so->numberOfOrderBys = scan->numberOfOrderBys;
+	so->orderByData = scan->orderByData;
+
 	if (scan->numberOfKeys <= 0)
 	{
 		/* If no quals, whole-index scan is required */
@@ -189,8 +273,9 @@ spgbeginscan(Relation rel, int keysz, int orderbysz)
 {
 	IndexScanDesc scan;
 	SpGistScanOpaque so;
+	int			i;
 
-	scan = RelationGetIndexScan(rel, keysz, 0);
+	scan = RelationGetIndexScan(rel, keysz, orderbysz);
 
 	so = (SpGistScanOpaque) palloc0(sizeof(SpGistScanOpaqueData));
 	if (keysz > 0)
@@ -198,6 +283,7 @@ spgbeginscan(Relation rel, int keysz, int orderbysz)
 	else
 		so->keyData = NULL;
 	initSpGistState(&so->state, scan->indexRelation);
+
 	so->tempCxt = AllocSetContextCreate(CurrentMemoryContext,
 										"SP-GiST search temporary context",
 										ALLOCSET_DEFAULT_SIZES);
@@ -208,6 +294,32 @@ spgbeginscan(Relation rel, int keysz, int orderbysz)
 	/* Set up indexTupDesc and xs_hitupdesc in case it's an index-only scan */
 	so->indexTupDesc = scan->xs_hitupdesc = RelationGetDescr(rel);
 
+	if (scan->numberOfOrderBys > 0)
+	{
+		so->zeroDistances = palloc(sizeof(double) * scan->numberOfOrderBys);
+		so->infDistances = palloc(sizeof(double) * scan->numberOfOrderBys);
+
+		for (i = 0; i < scan->numberOfOrderBys; i++)
+		{
+			so->zeroDistances[i] = 0.0;
+			so->infDistances[i] = get_float8_infinity();
+		}
+
+		scan->xs_orderbyvals = palloc0(sizeof(Datum) * scan->numberOfOrderBys);
+		scan->xs_orderbynulls = palloc(sizeof(bool) * scan->numberOfOrderBys);
+		memset(scan->xs_orderbynulls, true, sizeof(bool) * scan->numberOfOrderBys);
+	}
+
+	fmgr_info_copy(&so->innerConsistentFn,
+				   index_getprocinfo(rel, 1, SPGIST_INNER_CONSISTENT_PROC),
+				   CurrentMemoryContext);
+
+	fmgr_info_copy(&so->leafConsistentFn,
+				   index_getprocinfo(rel, 1, SPGIST_LEAF_CONSISTENT_PROC),
+				   CurrentMemoryContext);
+
+	so->indexCollation = rel->rd_indcollation[0];
+
 	scan->opaque = so;
 
 	return scan;
@@ -221,15 +333,42 @@ spgrescan(IndexScanDesc scan, ScanKey scankey, int nscankeys,
 
 	/* copy scankeys into local storage */
 	if (scankey && scan->numberOfKeys > 0)
-	{
 		memmove(scan->keyData, scankey,
 				scan->numberOfKeys * sizeof(ScanKeyData));
+
+	if (orderbys && scan->numberOfOrderBys > 0)
+	{
+		int			i;
+
+		memmove(scan->orderByData, orderbys,
+				scan->numberOfOrderBys * sizeof(ScanKeyData));
+
+		so->orderByTypes = (Oid *) palloc(sizeof(Oid) * scan->numberOfOrderBys);
+
+		for (i = 0; i < scan->numberOfOrderBys; i++)
+		{
+			ScanKey		skey = &scan->orderByData[i];
+
+			/*
+			 * Look up the datatype returned by the original ordering
+			 * operator. SP-GiST always uses a float8 for the distance
+			 * function, but the ordering operator could be anything else.
+			 *
+			 * XXX: The distance function is only allowed to be lossy if the
+			 * ordering operator's result type is float4 or float8.  Otherwise
+			 * we don't know how to return the distance to the executor.  But
+			 * we cannot check that here, as we won't know if the distance
+			 * function is lossy until it returns *recheck = true for the
+			 * first time.
+			 */
+			so->orderByTypes[i] = get_func_rettype(skey->sk_func.fn_oid);
+		}
 	}
 
 	/* preprocess scankeys, set up the representation in *so */
 	spgPrepareScanKeys(scan);
 
-	/* set up starting stack entries */
+	/* set up starting queue entries */
 	resetSpGistScanOpaque(so);
 }
 
@@ -240,65 +379,332 @@ spgendscan(IndexScanDesc scan)
 
 	MemoryContextDelete(so->tempCxt);
 	MemoryContextDelete(so->traversalCxt);
+
+	if (scan->numberOfOrderBys > 0)
+	{
+		pfree(so->zeroDistances);
+		pfree(so->infDistances);
+	}
+}
+
+/*
+ * Leaf SpGistSearchItem constructor, called in queue context
+ */
+static SpGistSearchItem *
+spgNewHeapItem(SpGistScanOpaque so, int level, ItemPointer heapPtr,
+			   Datum leafValue, bool recheck, bool recheckDistances,
+			   bool isnull, double *distances)
+{
+	SpGistSearchItem *item = spgAllocSearchItem(so, isnull, distances);
+
+	item->level = level;
+	item->heapPtr = *heapPtr;
+	/* copy value to queue cxt out of tmp cxt */
+	item->value = isnull ? (Datum) 0 :
+		datumCopy(leafValue, so->state.attLeafType.attbyval,
+				  so->state.attLeafType.attlen);
+	item->traversalValue = NULL;
+	item->isLeaf = true;
+	item->recheck = recheck;
+	item->recheckDistances = recheckDistances;
+
+	return item;
 }
 
 /*
  * Test whether a leaf tuple satisfies all the scan keys
  *
- * *leafValue is set to the reconstructed datum, if provided
- * *recheck is set true if any of the operators are lossy
+ * *reportedSome is set to true if:
+ *		the scan is not ordered AND the item satisfies the scankeys
  */
 static bool
-spgLeafTest(Relation index, SpGistScanOpaque so,
+spgLeafTest(SpGistScanOpaque so, SpGistSearchItem * item,
 			SpGistLeafTuple leafTuple, bool isnull,
-			int level, Datum reconstructedValue,
-			void *traversalValue,
-			Datum *leafValue, bool *recheck)
+			bool *reportedSome, storeRes_func storeRes)
 {
+	Datum		leafValue;
+	double	   *distances;
 	bool		result;
-	Datum		leafDatum;
-	spgLeafConsistentIn in;
-	spgLeafConsistentOut out;
-	FmgrInfo   *procinfo;
-	MemoryContext oldCtx;
+	bool		recheck;
+	bool		recheckDistances;
 
 	if (isnull)
 	{
 		/* Should not have arrived on a nulls page unless nulls are wanted */
 		Assert(so->searchNulls);
-		*leafValue = (Datum) 0;
-		*recheck = false;
-		return true;
+		leafValue = (Datum) 0;
+		distances = NULL;
+		recheck = false;
+		recheckDistances = false;
+		result = true;
+	}
+	else
+	{
+		spgLeafConsistentIn in;
+		spgLeafConsistentOut out;
+
+		/* use temp context for calling leaf_consistent */
+		MemoryContext oldCxt = MemoryContextSwitchTo(so->tempCxt);
+
+		in.scankeys = so->keyData;
+		in.nkeys = so->numberOfKeys;
+		in.orderbys = so->orderByData;
+		in.norderbys = so->numberOfOrderBys;
+		in.reconstructedValue = item->value;
+		in.traversalValue = item->traversalValue;
+		in.level = item->level;
+		in.returnData = so->want_itup;
+		in.leafDatum = SGLTDATUM(leafTuple, &so->state);
+
+		out.leafValue = (Datum) 0;
+		out.recheck = false;
+		out.distances = NULL;
+		out.recheckDistances = false;
+
+		result = DatumGetBool(FunctionCall2Coll(&so->leafConsistentFn,
+												so->indexCollation,
+												PointerGetDatum(&in),
+												PointerGetDatum(&out)));
+		recheck = out.recheck;
+		recheckDistances = out.recheckDistances;
+		leafValue = out.leafValue;
+		distances = out.distances;
+
+		MemoryContextSwitchTo(oldCxt);
 	}
 
-	leafDatum = SGLTDATUM(leafTuple, &so->state);
+	if (result)
+	{
+		/* item passes the scankeys */
+		if (so->numberOfOrderBys > 0)
+		{
+			/* the scan is ordered -> add the item to the queue */
+			MemoryContext oldCxt = MemoryContextSwitchTo(so->traversalCxt);
+			SpGistSearchItem *heapItem = spgNewHeapItem(so, item->level,
+														&leafTuple->heapPtr,
+														leafValue,
+														recheck,
+														recheckDistances,
+														isnull,
+														distances);
+
+			spgAddSearchItemToQueue(so, heapItem);
+
+			MemoryContextSwitchTo(oldCxt);
+		}
+		else
+		{
+			/* non-ordered scan, so report the item right away */
+			Assert(!recheckDistances);
+			storeRes(so, &leafTuple->heapPtr, leafValue, isnull,
+					 recheck, false, NULL);
+			*reportedSome = true;
+		}
+	}
 
-	/* use temp context for calling leaf_consistent */
-	oldCtx = MemoryContextSwitchTo(so->tempCxt);
+	return result;
+}
 
-	in.scankeys = so->keyData;
-	in.nkeys = so->numberOfKeys;
-	in.reconstructedValue = reconstructedValue;
-	in.traversalValue = traversalValue;
-	in.level = level;
-	in.returnData = so->want_itup;
-	in.leafDatum = leafDatum;
+/* A bundle initializer for inner_consistent methods */
+static void
+spgInitInnerConsistentIn(spgInnerConsistentIn *in,
+						 SpGistScanOpaque so,
+						 SpGistSearchItem * item,
+						 SpGistInnerTuple innerTuple)
+{
+	in->scankeys = so->keyData;
+	in->orderbys = so->orderByData;
+	in->nkeys = so->numberOfKeys;
+	in->norderbys = so->numberOfOrderBys;
+	in->reconstructedValue = item->value;
+	in->traversalMemoryContext = so->traversalCxt;
+	in->traversalValue = item->traversalValue;
+	in->level = item->level;
+	in->returnData = so->want_itup;
+	in->allTheSame = innerTuple->allTheSame;
+	in->hasPrefix = (innerTuple->prefixSize > 0);
+	in->prefixDatum = SGITDATUM(innerTuple, &so->state);
+	in->nNodes = innerTuple->nNodes;
+	in->nodeLabels = spgExtractNodeLabels(&so->state, innerTuple);
+}
 
-	out.leafValue = (Datum) 0;
-	out.recheck = false;
+static SpGistSearchItem *
+spgMakeInnerItem(SpGistScanOpaque so,
+				 SpGistSearchItem * parentItem,
+				 SpGistNodeTuple tuple,
+				 spgInnerConsistentOut *out, int i, bool isnull,
+				 double *distances)
+{
+	SpGistSearchItem *item = spgAllocSearchItem(so, isnull, distances);
 
-	procinfo = index_getprocinfo(index, 1, SPGIST_LEAF_CONSISTENT_PROC);
-	result = DatumGetBool(FunctionCall2Coll(procinfo,
-											index->rd_indcollation[0],
-											PointerGetDatum(&in),
-											PointerGetDatum(&out)));
+	item->heapPtr = tuple->t_tid;
+	item->level = out->levelAdds ? parentItem->level + out->levelAdds[i]
+		: parentItem->level;
 
-	*leafValue = out.leafValue;
-	*recheck = out.recheck;
+	/* Must copy value out of temp context */
+	item->value = out->reconstructedValues
+		? datumCopy(out->reconstructedValues[i],
+					so->state.attLeafType.attbyval,
+					so->state.attLeafType.attlen)
+		: (Datum) 0;
 
-	MemoryContextSwitchTo(oldCtx);
+	/*
+	 * Elements of out.traversalValues should be allocated in
+	 * in.traversalMemoryContext, which is actually a long lived context of
+	 * index scan.
+	 */
+	item->traversalValue =
+		out->traversalValues ? out->traversalValues[i] : NULL;
 
-	return result;
+	item->isLeaf = false;
+	item->recheck = false;
+	item->recheckDistances = false;
+
+	return item;
+}
+
+static void
+spgInnerTest(SpGistScanOpaque so, SpGistSearchItem * item,
+			 SpGistInnerTuple innerTuple, bool isnull)
+{
+	MemoryContext oldCxt = MemoryContextSwitchTo(so->tempCxt);
+	spgInnerConsistentOut out;
+	int			nNodes = innerTuple->nNodes;
+	int			i;
+
+	memset(&out, 0, sizeof(out));
+
+	if (!isnull)
+	{
+		spgInnerConsistentIn in;
+
+		spgInitInnerConsistentIn(&in, so, item, innerTuple);
+
+		/* use user-defined inner consistent method */
+		FunctionCall2Coll(&so->innerConsistentFn,
+						  so->indexCollation,
+						  PointerGetDatum(&in),
+						  PointerGetDatum(&out));
+	}
+	else
+	{
+		/* force all children to be visited */
+		out.nNodes = nNodes;
+		out.nodeNumbers = (int *) palloc(sizeof(int) * nNodes);
+		for (i = 0; i < nNodes; i++)
+			out.nodeNumbers[i] = i;
+	}
+
+	/* If allTheSame, they should all or none of them match */
+	if (innerTuple->allTheSame && out.nNodes != 0 && out.nNodes != nNodes)
+		elog(ERROR, "inconsistent inner_consistent results for allTheSame inner tuple");
+
+	if (out.nNodes)
+	{
+		/* collect node pointers */
+		SpGistNodeTuple node;
+		SpGistNodeTuple *nodes = (SpGistNodeTuple *) palloc(
+															sizeof(SpGistNodeTuple) * nNodes);
+
+		SGITITERATE(innerTuple, i, node)
+		{
+			nodes[i] = node;
+		}
+
+		MemoryContextSwitchTo(so->traversalCxt);
+
+		for (i = 0; i < out.nNodes; i++)
+		{
+			int			nodeN = out.nodeNumbers[i];
+			SpGistSearchItem *innerItem;
+			double	   *distances;
+
+			Assert(nodeN >= 0 && nodeN < nNodes);
+
+			node = nodes[nodeN];
+
+			if (!ItemPointerIsValid(&node->t_tid))
+				continue;
+
+			/*
+			 * Use infinity distances if innerConsistent() failed to return
+			 * them or if is a NULL item (their distances are really unused).
+			 */
+			distances = out.distances ? out.distances[i] : so->infDistances;
+
+			innerItem = spgMakeInnerItem(so, item, node, &out, i, isnull,
+										 distances);
+
+			spgAddSearchItemToQueue(so, innerItem);
+		}
+	}
+
+	MemoryContextSwitchTo(oldCxt);
+}
+
+/* Returns a next item in an (ordered) scan or null if the index is exhausted */
+static SpGistSearchItem *
+spgGetNextQueueItem(SpGistScanOpaque so)
+{
+	if (pairingheap_is_empty(so->scanQueue))
+		return NULL;			/* Done when both heaps are empty */
+
+	/* Return item; caller is responsible to pfree it */
+	return (SpGistSearchItem *) pairingheap_remove_first(so->scanQueue);
+}
+
+enum SpGistSpecialOffsetNumbers
+{
+	SpGistBreakOffsetNumber = InvalidOffsetNumber,
+	SpGistRedirectOffsetNumber = MaxOffsetNumber + 1,
+	SpGistErrorOffsetNumber = MaxOffsetNumber + 2
+};
+
+static OffsetNumber
+spgTestLeafTuple(SpGistScanOpaque so,
+				 SpGistSearchItem * item,
+				 Page page, OffsetNumber offset,
+				 bool isnull, bool isroot,
+				 bool *reportedSome,
+				 storeRes_func storeRes)
+{
+	SpGistLeafTuple leafTuple = (SpGistLeafTuple)
+	PageGetItem(page, PageGetItemId(page, offset));
+
+	if (leafTuple->tupstate != SPGIST_LIVE)
+	{
+		if (!isroot)			/* all tuples on root should be live */
+		{
+			if (leafTuple->tupstate == SPGIST_REDIRECT)
+			{
+				/* redirection tuple should be first in chain */
+				Assert(offset == ItemPointerGetOffsetNumber(&item->heapPtr));
+				/* transfer attention to redirect point */
+				item->heapPtr = ((SpGistDeadTuple) leafTuple)->pointer;
+				Assert(ItemPointerGetBlockNumber(&item->heapPtr) != SPGIST_METAPAGE_BLKNO);
+				return SpGistRedirectOffsetNumber;
+			}
+
+			if (leafTuple->tupstate == SPGIST_DEAD)
+			{
+				/* dead tuple should be first in chain */
+				Assert(offset == ItemPointerGetOffsetNumber(&item->heapPtr));
+				/* No live entries on this page */
+				Assert(leafTuple->nextOffset == InvalidOffsetNumber);
+				return SpGistBreakOffsetNumber;
+			}
+		}
+
+		/* We should not arrive at a placeholder */
+		elog(ERROR, "unexpected SPGiST tuple state: %d", leafTuple->tupstate);
+		return SpGistErrorOffsetNumber;
+	}
+
+	Assert(ItemPointerIsValid(&leafTuple->heapPtr));
+
+	spgLeafTest(so, item, leafTuple, isnull, reportedSome, storeRes);
+
+	return leafTuple->nextOffset;
 }
 
 /*
@@ -317,247 +723,101 @@ spgWalk(Relation index, SpGistScanOpaque so, bool scanWholeIndex,
 
 	while (scanWholeIndex || !reportedSome)
 	{
-		ScanStackEntry *stackEntry;
-		BlockNumber blkno;
-		OffsetNumber offset;
-		Page		page;
-		bool		isnull;
-
-		/* Pull next to-do item from the list */
-		if (so->scanStack == NIL)
-			break;				/* there are no more pages to scan */
+		SpGistSearchItem *item = spgGetNextQueueItem(so);
 
-		stackEntry = (ScanStackEntry *) linitial(so->scanStack);
-		so->scanStack = list_delete_first(so->scanStack);
+		if (item == NULL)
+			break;				/* No more items in queue -> done */
 
 redirect:
 		/* Check for interrupts, just in case of infinite loop */
 		CHECK_FOR_INTERRUPTS();
 
-		blkno = ItemPointerGetBlockNumber(&stackEntry->ptr);
-		offset = ItemPointerGetOffsetNumber(&stackEntry->ptr);
-
-		if (buffer == InvalidBuffer)
+		if (item->isLeaf)
 		{
-			buffer = ReadBuffer(index, blkno);
-			LockBuffer(buffer, BUFFER_LOCK_SHARE);
+			/* We store heap items in the queue only in case of ordered search */
+			Assert(so->numberOfOrderBys > 0);
+			storeRes(so, &item->heapPtr, item->value, item->isNull,
+					 item->recheck, item->recheckDistances, item->distances);
+			reportedSome = true;
 		}
-		else if (blkno != BufferGetBlockNumber(buffer))
+		else
 		{
-			UnlockReleaseBuffer(buffer);
-			buffer = ReadBuffer(index, blkno);
-			LockBuffer(buffer, BUFFER_LOCK_SHARE);
-		}
-		/* else new pointer points to the same page, no work needed */
+			BlockNumber blkno = ItemPointerGetBlockNumber(&item->heapPtr);
+			OffsetNumber offset = ItemPointerGetOffsetNumber(&item->heapPtr);
+			Page		page;
+			bool		isnull;
 
-		page = BufferGetPage(buffer);
-		TestForOldSnapshot(snapshot, index, page);
+			if (buffer == InvalidBuffer)
+			{
+				buffer = ReadBuffer(index, blkno);
+				LockBuffer(buffer, BUFFER_LOCK_SHARE);
+			}
+			else if (blkno != BufferGetBlockNumber(buffer))
+			{
+				UnlockReleaseBuffer(buffer);
+				buffer = ReadBuffer(index, blkno);
+				LockBuffer(buffer, BUFFER_LOCK_SHARE);
+			}
 
-		isnull = SpGistPageStoresNulls(page) ? true : false;
+			/* else new pointer points to the same page, no work needed */
 
-		if (SpGistPageIsLeaf(page))
-		{
-			SpGistLeafTuple leafTuple;
-			OffsetNumber max = PageGetMaxOffsetNumber(page);
-			Datum		leafValue = (Datum) 0;
-			bool		recheck = false;
+			page = BufferGetPage(buffer);
+			TestForOldSnapshot(snapshot, index, page);
+
+			isnull = SpGistPageStoresNulls(page) ? true : false;
 
-			if (SpGistBlockIsRoot(blkno))
+			if (SpGistPageIsLeaf(page))
 			{
-				/* When root is a leaf, examine all its tuples */
-				for (offset = FirstOffsetNumber; offset <= max; offset++)
-				{
-					leafTuple = (SpGistLeafTuple)
-						PageGetItem(page, PageGetItemId(page, offset));
-					if (leafTuple->tupstate != SPGIST_LIVE)
-					{
-						/* all tuples on root should be live */
-						elog(ERROR, "unexpected SPGiST tuple state: %d",
-							 leafTuple->tupstate);
-					}
+				/* Page is a leaf - that is, all it's tuples are heap items */
+				OffsetNumber max = PageGetMaxOffsetNumber(page);
 
-					Assert(ItemPointerIsValid(&leafTuple->heapPtr));
-					if (spgLeafTest(index, so,
-									leafTuple, isnull,
-									stackEntry->level,
-									stackEntry->reconstructedValue,
-									stackEntry->traversalValue,
-									&leafValue,
-									&recheck))
-					{
-						storeRes(so, &leafTuple->heapPtr,
-								 leafValue, isnull, recheck);
-						reportedSome = true;
-					}
+				if (SpGistBlockIsRoot(blkno))
+				{
+					/* When root is a leaf, examine all its tuples */
+					for (offset = FirstOffsetNumber; offset <= max; offset++)
+						(void) spgTestLeafTuple(so, item, page, offset,
+												isnull, true,
+												&reportedSome, storeRes);
 				}
-			}
-			else
-			{
-				/* Normal case: just examine the chain we arrived at */
-				while (offset != InvalidOffsetNumber)
+				else
 				{
-					Assert(offset >= FirstOffsetNumber && offset <= max);
-					leafTuple = (SpGistLeafTuple)
-						PageGetItem(page, PageGetItemId(page, offset));
-					if (leafTuple->tupstate != SPGIST_LIVE)
+					/* Normal case: just examine the chain we arrived at */
+					while (offset != InvalidOffsetNumber)
 					{
-						if (leafTuple->tupstate == SPGIST_REDIRECT)
-						{
-							/* redirection tuple should be first in chain */
-							Assert(offset == ItemPointerGetOffsetNumber(&stackEntry->ptr));
-							/* transfer attention to redirect point */
-							stackEntry->ptr = ((SpGistDeadTuple) leafTuple)->pointer;
-							Assert(ItemPointerGetBlockNumber(&stackEntry->ptr) != SPGIST_METAPAGE_BLKNO);
+						Assert(offset >= FirstOffsetNumber && offset <= max);
+						offset = spgTestLeafTuple(so, item, page, offset,
+												  isnull, false,
+												  &reportedSome, storeRes);
+						if (offset == SpGistRedirectOffsetNumber)
 							goto redirect;
-						}
-						if (leafTuple->tupstate == SPGIST_DEAD)
-						{
-							/* dead tuple should be first in chain */
-							Assert(offset == ItemPointerGetOffsetNumber(&stackEntry->ptr));
-							/* No live entries on this page */
-							Assert(leafTuple->nextOffset == InvalidOffsetNumber);
-							break;
-						}
-						/* We should not arrive at a placeholder */
-						elog(ERROR, "unexpected SPGiST tuple state: %d",
-							 leafTuple->tupstate);
-					}
-
-					Assert(ItemPointerIsValid(&leafTuple->heapPtr));
-					if (spgLeafTest(index, so,
-									leafTuple, isnull,
-									stackEntry->level,
-									stackEntry->reconstructedValue,
-									stackEntry->traversalValue,
-									&leafValue,
-									&recheck))
-					{
-						storeRes(so, &leafTuple->heapPtr,
-								 leafValue, isnull, recheck);
-						reportedSome = true;
 					}
-
-					offset = leafTuple->nextOffset;
-				}
-			}
-		}
-		else					/* page is inner */
-		{
-			SpGistInnerTuple innerTuple;
-			spgInnerConsistentIn in;
-			spgInnerConsistentOut out;
-			FmgrInfo   *procinfo;
-			SpGistNodeTuple *nodes;
-			SpGistNodeTuple node;
-			int			i;
-			MemoryContext oldCtx;
-
-			innerTuple = (SpGistInnerTuple) PageGetItem(page,
-														PageGetItemId(page, offset));
-
-			if (innerTuple->tupstate != SPGIST_LIVE)
-			{
-				if (innerTuple->tupstate == SPGIST_REDIRECT)
-				{
-					/* transfer attention to redirect point */
-					stackEntry->ptr = ((SpGistDeadTuple) innerTuple)->pointer;
-					Assert(ItemPointerGetBlockNumber(&stackEntry->ptr) != SPGIST_METAPAGE_BLKNO);
-					goto redirect;
 				}
-				elog(ERROR, "unexpected SPGiST tuple state: %d",
-					 innerTuple->tupstate);
-			}
-
-			/* use temp context for calling inner_consistent */
-			oldCtx = MemoryContextSwitchTo(so->tempCxt);
-
-			in.scankeys = so->keyData;
-			in.nkeys = so->numberOfKeys;
-			in.reconstructedValue = stackEntry->reconstructedValue;
-			in.traversalMemoryContext = so->traversalCxt;
-			in.traversalValue = stackEntry->traversalValue;
-			in.level = stackEntry->level;
-			in.returnData = so->want_itup;
-			in.allTheSame = innerTuple->allTheSame;
-			in.hasPrefix = (innerTuple->prefixSize > 0);
-			in.prefixDatum = SGITDATUM(innerTuple, &so->state);
-			in.nNodes = innerTuple->nNodes;
-			in.nodeLabels = spgExtractNodeLabels(&so->state, innerTuple);
-
-			/* collect node pointers */
-			nodes = (SpGistNodeTuple *) palloc(sizeof(SpGistNodeTuple) * in.nNodes);
-			SGITITERATE(innerTuple, i, node)
-			{
-				nodes[i] = node;
-			}
-
-			memset(&out, 0, sizeof(out));
-
-			if (!isnull)
-			{
-				/* use user-defined inner consistent method */
-				procinfo = index_getprocinfo(index, 1, SPGIST_INNER_CONSISTENT_PROC);
-				FunctionCall2Coll(procinfo,
-								  index->rd_indcollation[0],
-								  PointerGetDatum(&in),
-								  PointerGetDatum(&out));
-			}
-			else
-			{
-				/* force all children to be visited */
-				out.nNodes = in.nNodes;
-				out.nodeNumbers = (int *) palloc(sizeof(int) * in.nNodes);
-				for (i = 0; i < in.nNodes; i++)
-					out.nodeNumbers[i] = i;
 			}
-
-			MemoryContextSwitchTo(oldCtx);
-
-			/* If allTheSame, they should all or none of 'em match */
-			if (innerTuple->allTheSame)
-				if (out.nNodes != 0 && out.nNodes != in.nNodes)
-					elog(ERROR, "inconsistent inner_consistent results for allTheSame inner tuple");
-
-			for (i = 0; i < out.nNodes; i++)
+			else				/* page is inner */
 			{
-				int			nodeN = out.nodeNumbers[i];
+				SpGistInnerTuple innerTuple = (SpGistInnerTuple)
+				PageGetItem(page, PageGetItemId(page, offset));
 
-				Assert(nodeN >= 0 && nodeN < in.nNodes);
-				if (ItemPointerIsValid(&nodes[nodeN]->t_tid))
+				if (innerTuple->tupstate != SPGIST_LIVE)
 				{
-					ScanStackEntry *newEntry;
-
-					/* Create new work item for this node */
-					newEntry = palloc(sizeof(ScanStackEntry));
-					newEntry->ptr = nodes[nodeN]->t_tid;
-					if (out.levelAdds)
-						newEntry->level = stackEntry->level + out.levelAdds[i];
-					else
-						newEntry->level = stackEntry->level;
-					/* Must copy value out of temp context */
-					if (out.reconstructedValues)
-						newEntry->reconstructedValue =
-							datumCopy(out.reconstructedValues[i],
-									  so->state.attLeafType.attbyval,
-									  so->state.attLeafType.attlen);
-					else
-						newEntry->reconstructedValue = (Datum) 0;
-
-					/*
-					 * Elements of out.traversalValues should be allocated in
-					 * in.traversalMemoryContext, which is actually a long
-					 * lived context of index scan.
-					 */
-					newEntry->traversalValue = (out.traversalValues) ?
-						out.traversalValues[i] : NULL;
-
-					so->scanStack = lcons(newEntry, so->scanStack);
+					if (innerTuple->tupstate == SPGIST_REDIRECT)
+					{
+						/* transfer attention to redirect point */
+						item->heapPtr = ((SpGistDeadTuple) innerTuple)->pointer;
+						Assert(ItemPointerGetBlockNumber(&item->heapPtr) !=
+							   SPGIST_METAPAGE_BLKNO);
+						goto redirect;
+					}
+					elog(ERROR, "unexpected SPGiST tuple state: %d",
+						 innerTuple->tupstate);
 				}
+
+				spgInnerTest(so, item, innerTuple, isnull);
 			}
 		}
 
-		/* done with this scan stack entry */
-		freeScanStackEntry(so, stackEntry);
+		/* done with this scan item */
+		spgFreeSearchItem(so, item);
 		/* clear temp context before proceeding to the next one */
 		MemoryContextReset(so->tempCxt);
 	}
@@ -566,11 +826,14 @@ redirect:
 		UnlockReleaseBuffer(buffer);
 }
 
+
 /* storeRes subroutine for getbitmap case */
 static void
 storeBitmap(SpGistScanOpaque so, ItemPointer heapPtr,
-			Datum leafValue, bool isnull, bool recheck)
+			Datum leafValue, bool isnull, bool recheck, bool recheckDistances,
+			double *distances)
 {
+	Assert(!recheckDistances && !distances);
 	tbm_add_tuples(so->tbm, heapPtr, 1, recheck);
 	so->ntids++;
 }
@@ -594,11 +857,26 @@ spggetbitmap(IndexScanDesc scan, TIDBitmap *tbm)
 /* storeRes subroutine for gettuple case */
 static void
 storeGettuple(SpGistScanOpaque so, ItemPointer heapPtr,
-			  Datum leafValue, bool isnull, bool recheck)
+			  Datum leafValue, bool isnull, bool recheck, bool recheckDistances,
+			  double *distances)
 {
 	Assert(so->nPtrs < MaxIndexTuplesPerPage);
 	so->heapPtrs[so->nPtrs] = *heapPtr;
 	so->recheck[so->nPtrs] = recheck;
+	so->recheckDistances[so->nPtrs] = recheckDistances;
+
+	if (so->numberOfOrderBys > 0)
+	{
+		if (isnull)
+			so->distances[so->nPtrs] = NULL;
+		else
+		{
+			Size		size = sizeof(double) * so->numberOfOrderBys;
+
+			so->distances[so->nPtrs] = memcpy(palloc(size), distances, size);
+		}
+	}
+
 	if (so->want_itup)
 	{
 		/*
@@ -627,14 +905,29 @@ spggettuple(IndexScanDesc scan, ScanDirection dir)
 	{
 		if (so->iPtr < so->nPtrs)
 		{
-			/* continuing to return tuples from a leaf page */
+			/* continuing to return reported tuples */
 			scan->xs_ctup.t_self = so->heapPtrs[so->iPtr];
 			scan->xs_recheck = so->recheck[so->iPtr];
 			scan->xs_hitup = so->reconTups[so->iPtr];
+
+			if (so->numberOfOrderBys > 0)
+				index_store_float8_orderby_distances(scan, so->orderByTypes,
+													 so->distances[so->iPtr],
+													 so->recheckDistances[so->iPtr]);
 			so->iPtr++;
 			return true;
 		}
 
+		if (so->numberOfOrderBys > 0)
+		{
+			/* Must pfree distances to avoid memory leak */
+			int			i;
+
+			for (i = 0; i < so->nPtrs; i++)
+				if (so->distances[i])
+					pfree(so->distances[i]);
+		}
+
 		if (so->want_itup)
 		{
 			/* Must pfree reconstructed tuples to avoid memory leak */

src/backend/access/spgist/spgutils.c

@@ -15,17 +15,26 @@
 
 #include "postgres.h"
 
+#include "access/amvalidate.h"
+#include "access/htup_details.h"
 #include "access/reloptions.h"
 #include "access/spgist_private.h"
 #include "access/transam.h"
 #include "access/xact.h"
+#include "catalog/pg_amop.h"
+#include "optimizer/paths.h"
 #include "storage/bufmgr.h"
 #include "storage/indexfsm.h"
 #include "storage/lmgr.h"
 #include "utils/builtins.h"
+#include "utils/catcache.h"
 #include "utils/index_selfuncs.h"
 #include "utils/lsyscache.h"
+#include "utils/syscache.h"
 
+extern Expr *spgcanorderbyop(IndexOptInfo *index,
+				PathKey *pathkey, int pathkeyno,
+				Expr *orderby_clause, int *indexcol_p);
 
 /*
  * SP-GiST handler function: return IndexAmRoutine with access method parameters
@@ -39,7 +48,7 @@ spghandler(PG_FUNCTION_ARGS)
 	amroutine->amstrategies = 0;
 	amroutine->amsupport = SPGISTNProc;
 	amroutine->amcanorder = false;
-	amroutine->amcanorderbyop = false;
+	amroutine->amcanorderbyop = true;
 	amroutine->amcanbackward = false;
 	amroutine->amcanunique = false;
 	amroutine->amcanmulticol = false;
@@ -61,7 +70,7 @@ spghandler(PG_FUNCTION_ARGS)
 	amroutine->amcanreturn = spgcanreturn;
 	amroutine->amcostestimate = spgcostestimate;
 	amroutine->amoptions = spgoptions;
-	amroutine->amproperty = NULL;
+	amroutine->amproperty = spgproperty;
 	amroutine->amvalidate = spgvalidate;
 	amroutine->ambeginscan = spgbeginscan;
 	amroutine->amrescan = spgrescan;
@@ -949,3 +958,82 @@ SpGistPageAddNewItem(SpGistState *state, Page page, Item item, Size size,
 
 	return offnum;
 }
+
+/*
+ *	spgproperty() -- Check boolean properties of indexes.
+ *
+ * This is optional for most AMs, but is required for SP-GiST because the core
+ * property code doesn't support AMPROP_DISTANCE_ORDERABLE.
+ */
+bool
+spgproperty(Oid index_oid, int attno,
+			IndexAMProperty prop, const char *propname,
+			bool *res, bool *isnull)
+{
+	Oid			opclass,
+				opfamily,
+				opcintype;
+	CatCList   *catlist;
+	int			i;
+
+	/* Only answer column-level inquiries */
+	if (attno == 0)
+		return false;
+
+	switch (prop)
+	{
+		case AMPROP_DISTANCE_ORDERABLE:
+			break;
+		default:
+			return false;
+	}
+
+	/*
+	 * Currently, SP-GiST distance-ordered scans require that there be a
+	 * distance operator in the opclass with the default types. So we assume
+	 * that if such a operator exists, then there's a reason for it.
+	 */
+
+	/* First we need to know the column's opclass. */
+	opclass = get_index_column_opclass(index_oid, attno);
+	if (!OidIsValid(opclass))
+	{
+		*isnull = true;
+		return true;
+	}
+
+	/* Now look up the opclass family and input datatype. */
+	if (!get_opclass_opfamily_and_input_type(opclass, &opfamily, &opcintype))
+	{
+		*isnull = true;
+		return true;
+	}
+
+	/* And now we can check whether the operator is provided. */
+	catlist = SearchSysCacheList1(AMOPSTRATEGY,
+								  ObjectIdGetDatum(opfamily));
+
+	*res = false;
+
+	for (i = 0; i < catlist->n_members; i++)
+	{
+		HeapTuple	amoptup = &catlist->members[i]->tuple;
+		Form_pg_amop amopform = (Form_pg_amop) GETSTRUCT(amoptup);
+
+		if (amopform->amoppurpose == AMOP_ORDER &&
+			(amopform->amoplefttype == opcintype ||
+			 amopform->amoprighttype == opcintype) &&
+			opfamily_can_sort_type(amopform->amopsortfamily,
+								   get_op_rettype(amopform->amopopr)))
+		{
+			*res = true;
+			break;
+		}
+	}
+
+	ReleaseSysCacheList(catlist);
+
+	*isnull = false;
+
+	return true;
+}

src/backend/access/spgist/spgvalidate.c

@@ -187,6 +187,7 @@ spgvalidate(Oid opclassoid)
 	{
 		HeapTuple	oprtup = &oprlist->members[i]->tuple;
 		Form_pg_amop oprform = (Form_pg_amop) GETSTRUCT(oprtup);
+		Oid			op_rettype;
 
 		/* TODO: Check that only allowed strategy numbers exist */
 		if (oprform->amopstrategy < 1 || oprform->amopstrategy > 63)
@@ -200,20 +201,26 @@ spgvalidate(Oid opclassoid)
 			result = false;
 		}
 
-		/* spgist doesn't support ORDER BY operators */
-		if (oprform->amoppurpose != AMOP_SEARCH ||
-			OidIsValid(oprform->amopsortfamily))
+		/* spgist supports ORDER BY operators */
+		if (oprform->amoppurpose != AMOP_SEARCH)
 		{
-			ereport(INFO,
-					(errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
-					 errmsg("operator family \"%s\" of access method %s contains invalid ORDER BY specification for operator %s",
-							opfamilyname, "spgist",
-							format_operator(oprform->amopopr))));
-			result = false;
+			/* ... and operator result must match the claimed btree opfamily */
+			op_rettype = get_op_rettype(oprform->amopopr);
+			if (!opfamily_can_sort_type(oprform->amopsortfamily, op_rettype))
+			{
+				ereport(INFO,
+						(errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
+						 errmsg("operator family \"%s\" of access method %s contains invalid ORDER BY specification for operator %s",
+								opfamilyname, "spgist",
+								format_operator(oprform->amopopr))));
+				result = false;
+			}
 		}
+		else
+			op_rettype = BOOLOID;
 
 		/* Check operator signature --- same for all spgist strategies */
-		if (!check_amop_signature(oprform->amopopr, BOOLOID,
+		if (!check_amop_signature(oprform->amopopr, op_rettype,
 								  oprform->amoplefttype,
 								  oprform->amoprighttype))
 		{

src/backend/utils/adt/geo_spgist.c

@@ -74,9 +74,11 @@
 #include "postgres.h"
 
 #include "access/spgist.h"
+#include "access/spgist_private.h"
 #include "access/stratnum.h"
 #include "catalog/pg_type.h"
 #include "utils/float.h"
+#include "utils/fmgroids.h"
 #include "utils/fmgrprotos.h"
 #include "utils/geo_decls.h"
 
@@ -367,6 +369,31 @@ overAbove4D(RectBox *rect_box, RangeBox *query)
 	return overHigher2D(&rect_box->range_box_y, &query->right);
 }
 
+/* Lower bound for the distance between point and rect_box */
+static double
+pointToRectBoxDistance(Point *point, RectBox *rect_box)
+{
+	double		dx;
+	double		dy;
+
+	if (point->x < rect_box->range_box_x.left.low)
+		dx = rect_box->range_box_x.left.low - point->x;
+	else if (point->x > rect_box->range_box_x.right.high)
+		dx = point->x - rect_box->range_box_x.right.high;
+	else
+		dx = 0;
+
+	if (point->y < rect_box->range_box_y.left.low)
+		dy = rect_box->range_box_y.left.low - point->y;
+	else if (point->y > rect_box->range_box_y.right.high)
+		dy = point->y - rect_box->range_box_y.right.high;
+	else
+		dy = 0;
+
+	return HYPOT(dx, dy);
+}
+
+
 /*
  * SP-GiST config function
  */
@@ -534,6 +561,15 @@ spg_box_quad_inner_consistent(PG_FUNCTION_ARGS)
 	RangeBox   *centroid,
 			  **queries;
 
+	/*
+	 * We are saving the traversal value or initialize it an unbounded one, if
+	 * we have just begun to walk the tree.
+	 */
+	if (in->traversalValue)
+		rect_box = in->traversalValue;
+	else
+		rect_box = initRectBox();
+
 	if (in->allTheSame)
 	{
 		/* Report that all nodes should be visited */
@@ -542,18 +578,32 @@ spg_box_quad_inner_consistent(PG_FUNCTION_ARGS)
 		for (i = 0; i < in->nNodes; i++)
 			out->nodeNumbers[i] = i;
 
+		if (in->norderbys > 0 && in->nNodes > 0)
+		{
+			double	   *distances = palloc(sizeof(double) * in->norderbys);
+			int			j;
+
+			for (j = 0; j < in->norderbys; j++)
+			{
+				Point	   *pt = DatumGetPointP(in->orderbys[j].sk_argument);
+
+				distances[j] = pointToRectBoxDistance(pt, rect_box);
+			}
+
+			out->distances = (double **) palloc(sizeof(double *) * in->nNodes);
+			out->distances[0] = distances;
+
+			for (i = 1; i < in->nNodes; i++)
+			{
+				out->distances[i] = palloc(sizeof(double) * in->norderbys);
+				memcpy(out->distances[i], distances,
+					   sizeof(double) * in->norderbys);
+			}
+		}
+
 		PG_RETURN_VOID();
 	}
 
-	/*
-	 * We are saving the traversal value or initialize it an unbounded one, if
-	 * we have just begun to walk the tree.
-	 */
-	if (in->traversalValue)
-		rect_box = in->traversalValue;
-	else
-		rect_box = initRectBox();
-
 	/*
 	 * We are casting the prefix and queries to RangeBoxes for ease of the
 	 * following operations.
@@ -571,6 +621,8 @@ spg_box_quad_inner_consistent(PG_FUNCTION_ARGS)
 	out->nNodes = 0;
 	out->nodeNumbers = (int *) palloc(sizeof(int) * in->nNodes);
 	out->traversalValues = (void **) palloc(sizeof(void *) * in->nNodes);
+	if (in->norderbys > 0)
+		out->distances = (double **) palloc(sizeof(double *) * in->nNodes);
 
 	/*
 	 * We switch memory context, because we want to allocate memory for new
@@ -648,6 +700,22 @@ spg_box_quad_inner_consistent(PG_FUNCTION_ARGS)
 		{
 			out->traversalValues[out->nNodes] = next_rect_box;
 			out->nodeNumbers[out->nNodes] = quadrant;
+
+			if (in->norderbys > 0)
+			{
+				double	   *distances = palloc(sizeof(double) * in->norderbys);
+				int			j;
+
+				out->distances[out->nNodes] = distances;
+
+				for (j = 0; j < in->norderbys; j++)
+				{
+					Point	   *pt = DatumGetPointP(in->orderbys[j].sk_argument);
+
+					distances[j] = pointToRectBoxDistance(pt, next_rect_box);
+				}
+			}
+
 			out->nNodes++;
 		}
 		else
@@ -763,6 +831,17 @@ spg_box_quad_leaf_consistent(PG_FUNCTION_ARGS)
 			break;
 	}
 
+	if (flag && in->norderbys > 0)
+	{
+		Oid			distfnoid = in->orderbys[0].sk_func.fn_oid;
+
+		out->distances = spg_key_orderbys_distances(leaf, false,
+													in->orderbys, in->norderbys);
+
+		/* Recheck is necessary when computing distance to polygon */
+		out->recheckDistances = distfnoid == F_DIST_POLYP;
+	}
+
 	PG_RETURN_BOOL(flag);
 }
 

src/backend/utils/cache/lsyscache.c

@@ -1067,6 +1067,32 @@ get_opclass_input_type(Oid opclass)
 	return result;
 }
 
+/*
+ * get_opclass_family_and_input_type
+ *
+ *		Returns the OID of the operator family the opclass belongs to,
+ *				the OID of the datatype the opclass indexes
+ */
+bool
+get_opclass_opfamily_and_input_type(Oid opclass, Oid *opfamily, Oid *opcintype)
+{
+	HeapTuple	tp;
+	Form_pg_opclass cla_tup;
+
+	tp = SearchSysCache1(CLAOID, ObjectIdGetDatum(opclass));
+	if (!HeapTupleIsValid(tp))
+		return false;
+
+	cla_tup = (Form_pg_opclass) GETSTRUCT(tp);
+
+	*opfamily = cla_tup->opcfamily;
+	*opcintype = cla_tup->opcintype;
+
+	ReleaseSysCache(tp);
+
+	return true;
+}
+
 /*				---------- OPERATOR CACHE ----------					 */
 
 /*
@@ -3106,3 +3132,45 @@ get_range_subtype(Oid rangeOid)
 	else
 		return InvalidOid;
 }
+
+/*				---------- PG_INDEX CACHE ----------				 */
+
+/*
+ * get_index_column_opclass
+ *
+ *		Given the index OID and column number,
+ *		return opclass of the index column
+ *			or InvalidOid if the index was not found.
+ */
+Oid
+get_index_column_opclass(Oid index_oid, int attno)
+{
+	HeapTuple	tuple;
+	Form_pg_index rd_index PG_USED_FOR_ASSERTS_ONLY;
+	Datum		datum;
+	bool		isnull;
+	oidvector  *indclass;
+	Oid			opclass;
+
+	/* First we need to know the column's opclass. */
+
+	tuple = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(index_oid));
+	if (!HeapTupleIsValid(tuple))
+		return InvalidOid;
+
+	rd_index = (Form_pg_index) GETSTRUCT(tuple);
+
+	/* caller is supposed to guarantee this */
+	Assert(attno > 0 && attno <= rd_index->indnatts);
+
+	datum = SysCacheGetAttr(INDEXRELID, tuple,
+							Anum_pg_index_indclass, &isnull);
+	Assert(!isnull);
+
+	indclass = ((oidvector *) DatumGetPointer(datum));
+	opclass = indclass->values[attno - 1];
+
+	ReleaseSysCache(tuple);
+
+	return opclass;
+}

src/include/access/genam.h

@@ -174,6 +174,9 @@ extern RegProcedure index_getprocid(Relation irel, AttrNumber attnum,
 				uint16 procnum);
 extern FmgrInfo *index_getprocinfo(Relation irel, AttrNumber attnum,
 				  uint16 procnum);
+extern void index_store_float8_orderby_distances(IndexScanDesc scan,
+									 Oid *orderByTypes, double *distances,
+									 bool recheckOrderBy);
 
 /*
  * index access method support routines (in genam.c)

src/include/access/spgist.h

@@ -136,7 +136,10 @@ typedef struct spgPickSplitOut
 typedef struct spgInnerConsistentIn
 {
 	ScanKey		scankeys;		/* array of operators and comparison values */
-	int			nkeys;			/* length of array */
+	ScanKey		orderbys;		/* array of ordering operators and comparison
+								 * values */
+	int			nkeys;			/* length of scankeys array */
+	int			norderbys;		/* length of orderbys array */
 
 	Datum		reconstructedValue; /* value reconstructed at parent */
 	void	   *traversalValue; /* opclass-specific traverse value */
@@ -159,6 +162,7 @@ typedef struct spgInnerConsistentOut
 	int		   *levelAdds;		/* increment level by this much for each */
 	Datum	   *reconstructedValues;	/* associated reconstructed values */
 	void	  **traversalValues;	/* opclass-specific traverse values */
+	double	  **distances;		/* associated distances */
 } spgInnerConsistentOut;
 
 /*
@@ -167,7 +171,10 @@ typedef struct spgInnerConsistentOut
 typedef struct spgLeafConsistentIn
 {
 	ScanKey		scankeys;		/* array of operators and comparison values */
-	int			nkeys;			/* length of array */
+	ScanKey		orderbys;		/* array of ordering operators and comparison
+								 * values */
+	int			nkeys;			/* length of scankeys array */
+	int			norderbys;		/* length of orderbys array */
 
 	Datum		reconstructedValue; /* value reconstructed at parent */
 	void	   *traversalValue; /* opclass-specific traverse value */
@@ -181,6 +188,8 @@ typedef struct spgLeafConsistentOut
 {
 	Datum		leafValue;		/* reconstructed original data, if any */
 	bool		recheck;		/* set true if operator must be rechecked */
+	bool		recheckDistances;	/* set true if distances must be rechecked */
+	double	   *distances;		/* associated distances */
 } spgLeafConsistentOut;
 
 

src/include/access/spgist_private.h

@@ -18,6 +18,7 @@
 #include "access/spgist.h"
 #include "nodes/tidbitmap.h"
 #include "storage/buf.h"
+#include "utils/geo_decls.h"
 #include "utils/relcache.h"
 
 
@@ -130,14 +131,35 @@ typedef struct SpGistState
 	bool		isBuild;		/* true if doing index build */
 } SpGistState;
 
+typedef struct SpGistSearchItem
+{
+	pairingheap_node phNode;	/* pairing heap node */
+	Datum		value;			/* value reconstructed from parent or
+								 * leafValue if heaptuple */
+	void	   *traversalValue; /* opclass-specific traverse value */
+	int			level;			/* level of items on this page */
+	ItemPointerData heapPtr;	/* heap info, if heap tuple */
+	bool		isNull;			/* SearchItem is NULL item */
+	bool		isLeaf;			/* SearchItem is heap item */
+	bool		recheck;		/* qual recheck is needed */
+	bool		recheckDistances;	/* distance recheck is needed */
+
+	/* array with numberOfOrderBys entries */
+	double		distances[FLEXIBLE_ARRAY_MEMBER];
+}			SpGistSearchItem;
+
+#define SizeOfSpGistSearchItem(n_distances) \
+	(offsetof(SpGistSearchItem, distances) + sizeof(double) * (n_distances))
+
 /*
  * Private state of an index scan
  */
 typedef struct SpGistScanOpaqueData
 {
 	SpGistState state;			/* see above */
+	pairingheap *scanQueue;		/* queue of to be visited items */
 	MemoryContext tempCxt;		/* short-lived memory context */
-	MemoryContext traversalCxt; /* memory context for traversalValues */
+	MemoryContext traversalCxt; /* single scan lifetime memory context */
 
 	/* Control flags showing whether to search nulls and/or non-nulls */
 	bool		searchNulls;	/* scan matches (all) null entries */
@@ -146,9 +168,18 @@ typedef struct SpGistScanOpaqueData
 	/* Index quals to be passed to opclass (null-related quals removed) */
 	int			numberOfKeys;	/* number of index qualifier conditions */
 	ScanKey		keyData;		/* array of index qualifier descriptors */
+	int			numberOfOrderBys;	/* number of ordering operators */
+	ScanKey		orderByData;	/* array of ordering op descriptors */
+	Oid		   *orderByTypes;	/* array of ordering op return types */
+	Oid			indexCollation; /* collation of index column */
 
-	/* Stack of yet-to-be-visited pages */
-	List	   *scanStack;		/* List of ScanStackEntrys */
+	/* Opclass defined functions: */
+	FmgrInfo	innerConsistentFn;
+	FmgrInfo	leafConsistentFn;
+
+	/* Pre-allocated workspace arrays: */
+	double	   *zeroDistances;
+	double	   *infDistances;
 
 	/* These fields are only used in amgetbitmap scans: */
 	TIDBitmap  *tbm;			/* bitmap being filled */
@@ -161,7 +192,10 @@ typedef struct SpGistScanOpaqueData
 	int			iPtr;			/* index for scanning through same */
 	ItemPointerData heapPtrs[MaxIndexTuplesPerPage];	/* TIDs from cur page */
 	bool		recheck[MaxIndexTuplesPerPage]; /* their recheck flags */
+	bool		recheckDistances[MaxIndexTuplesPerPage];	/* distance recheck
+															 * flags */
 	HeapTuple	reconTups[MaxIndexTuplesPerPage];	/* reconstructed tuples */
+	double	   *distances[MaxIndexTuplesPerPage];	/* distances (for recheck) */
 
 	/*
 	 * Note: using MaxIndexTuplesPerPage above is a bit hokey since
@@ -410,6 +444,9 @@ extern OffsetNumber SpGistPageAddNewItem(SpGistState *state, Page page,
 					 Item item, Size size,
 					 OffsetNumber *startOffset,
 					 bool errorOK);
+extern bool spgproperty(Oid index_oid, int attno,
+			IndexAMProperty prop, const char *propname,
+			bool *res, bool *isnull);
 
 /* spgdoinsert.c */
 extern void spgUpdateNodeLink(SpGistInnerTuple tup, int nodeN,
@@ -421,4 +458,9 @@ extern void spgPageIndexMultiDelete(SpGistState *state, Page page,
 extern bool spgdoinsert(Relation index, SpGistState *state,
 			ItemPointer heapPtr, Datum datum, bool isnull);
 
+/* spgproc.c */
+extern double *spg_key_orderbys_distances(Datum key, bool isLeaf,
+						   ScanKey orderbys, int norderbys);
+extern BOX *box_copy(BOX *orig);
+
 #endif							/* SPGIST_PRIVATE_H */

src/include/catalog/catversion.h

@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	201809181
+#define CATALOG_VERSION_NO	201809191
 
 #endif

src/include/catalog/pg_amop.dat

@@ -1401,6 +1401,10 @@
 { amopfamily => 'spgist/quad_point_ops', amoplefttype => 'point',
   amoprighttype => 'box', amopstrategy => '8', amopopr => '<@(point,box)',
   amopmethod => 'spgist' },
+{ amopfamily => 'spgist/quad_point_ops', amoplefttype => 'point',
+  amoprighttype => 'point', amopstrategy => '15', amopopr => '<->(point,point)',
+  amopmethod => 'spgist', amoppurpose => 'o',
+  amopsortfamily => 'btree/float_ops' },
 
 # SP-GiST kd_point_ops
 { amopfamily => 'spgist/kd_point_ops', amoplefttype => 'point',
@@ -1421,6 +1425,10 @@
 { amopfamily => 'spgist/kd_point_ops', amoplefttype => 'point',
   amoprighttype => 'box', amopstrategy => '8', amopopr => '<@(point,box)',
   amopmethod => 'spgist' },
+{ amopfamily => 'spgist/kd_point_ops', amoplefttype => 'point',
+  amoprighttype => 'point', amopstrategy => '15', amopopr => '<->(point,point)',
+  amopmethod => 'spgist', amoppurpose => 'o',
+  amopsortfamily => 'btree/float_ops' },
 
 # SP-GiST text_ops
 { amopfamily => 'spgist/text_ops', amoplefttype => 'text',
@@ -1590,6 +1598,10 @@
 { amopfamily => 'spgist/poly_ops', amoplefttype => 'polygon',
   amoprighttype => 'polygon', amopstrategy => '12',
   amopopr => '|&>(polygon,polygon)', amopmethod => 'spgist' },
+{ amopfamily => 'spgist/poly_ops', amoplefttype => 'polygon',
+  amoprighttype => 'point', amopstrategy => '15',
+  amopopr => '<->(polygon,point)', amoppurpose => 'o', amopmethod => 'spgist',
+  amopsortfamily => 'btree/float_ops' },
 
 # GiST inet_ops
 { amopfamily => 'gist/network_ops', amoplefttype => 'inet',

src/include/utils/lsyscache.h

@@ -95,6 +95,8 @@ extern char *get_constraint_name(Oid conoid);
 extern char *get_language_name(Oid langoid, bool missing_ok);
 extern Oid	get_opclass_family(Oid opclass);
 extern Oid	get_opclass_input_type(Oid opclass);
+extern bool get_opclass_opfamily_and_input_type(Oid opclass,
+									Oid *opfamily, Oid *opcintype);
 extern RegProcedure get_opcode(Oid opno);
 extern char *get_opname(Oid opno);
 extern Oid	get_op_rettype(Oid opno);
@@ -176,6 +178,7 @@ extern void free_attstatsslot(AttStatsSlot *sslot);
 extern char *get_namespace_name(Oid nspid);
 extern char *get_namespace_name_or_temp(Oid nspid);
 extern Oid	get_range_subtype(Oid rangeOid);
+extern Oid	get_index_column_opclass(Oid index_oid, int attno);
 
 #define type_is_array(typid)  (get_element_type(typid) != InvalidOid)
 /* type_is_array_domain accepts both plain arrays and domains over arrays */

src/test/regress/expected/amutils.out

@@ -83,7 +83,8 @@ select prop,
        pg_index_column_has_property('onek_hundred'::regclass, 1, prop) as btree,
        pg_index_column_has_property('hash_i4_index'::regclass, 1, prop) as hash,
        pg_index_column_has_property('gcircleind'::regclass, 1, prop) as gist,
-       pg_index_column_has_property('sp_radix_ind'::regclass, 1, prop) as spgist,
+       pg_index_column_has_property('sp_radix_ind'::regclass, 1, prop) as spgist_radix,
+       pg_index_column_has_property('sp_quad_ind'::regclass, 1, prop) as spgist_quad,
        pg_index_column_has_property('botharrayidx'::regclass, 1, prop) as gin,
        pg_index_column_has_property('brinidx'::regclass, 1, prop) as brin
   from unnest(array['asc', 'desc', 'nulls_first', 'nulls_last',
@@ -92,18 +93,18 @@ select prop,
                     'bogus']::text[])
          with ordinality as u(prop,ord)
  order by ord;
-        prop        | btree | hash | gist | spgist | gin | brin 
---------------------+-------+------+------+--------+-----+------
- asc                | t     | f    | f    | f      | f   | f
- desc               | f     | f    | f    | f      | f   | f
- nulls_first        | f     | f    | f    | f      | f   | f
- nulls_last         | t     | f    | f    | f      | f   | f
- orderable          | t     | f    | f    | f      | f   | f
- distance_orderable | f     | f    | t    | f      | f   | f
- returnable         | t     | f    | f    | t      | f   | f
- search_array       | t     | f    | f    | f      | f   | f
- search_nulls       | t     | f    | t    | t      | f   | t
- bogus              |       |      |      |        |     | 
+        prop        | btree | hash | gist | spgist_radix | spgist_quad | gin | brin 
+--------------------+-------+------+------+--------------+-------------+-----+------
+ asc                | t     | f    | f    | f            | f           | f   | f
+ desc               | f     | f    | f    | f            | f           | f   | f
+ nulls_first        | f     | f    | f    | f            | f           | f   | f
+ nulls_last         | t     | f    | f    | f            | f           | f   | f
+ orderable          | t     | f    | f    | f            | f           | f   | f
+ distance_orderable | f     | f    | t    | f            | t           | f   | f
+ returnable         | t     | f    | f    | t            | t           | f   | f
+ search_array       | t     | f    | f    | f            | f           | f   | f
+ search_nulls       | t     | f    | t    | t            | t           | f   | t
+ bogus              |       |      |      |              |             |     | 
 (10 rows)
 
 select prop,

src/test/regress/expected/create_index.out

@@ -294,6 +294,15 @@ SELECT count(*) FROM quad_point_tbl WHERE p ~= '(4585, 365)';
      1
 (1 row)
 
+CREATE TEMP TABLE quad_point_tbl_ord_seq1 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl;
+CREATE TEMP TABLE quad_point_tbl_ord_seq2 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+CREATE TEMP TABLE quad_point_tbl_ord_seq3 AS
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM quad_point_tbl WHERE p IS NOT NULL;
 SELECT count(*) FROM radix_text_tbl WHERE t = 'P0123456789abcdef';
  count 
 -------
@@ -888,6 +897,71 @@ SELECT count(*) FROM quad_point_tbl WHERE p ~= '(4585, 365)';
      1
 (1 row)
 
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl;
+                        QUERY PLAN                         
+-----------------------------------------------------------
+ WindowAgg
+   ->  Index Only Scan using sp_quad_ind on quad_point_tbl
+         Order By: (p <-> '(0,0)'::point)
+(3 rows)
+
+CREATE TEMP TABLE quad_point_tbl_ord_idx1 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl;
+SELECT * FROM quad_point_tbl_ord_seq1 seq FULL JOIN quad_point_tbl_ord_idx1 idx
+ON seq.n = idx.n
+AND (seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+ n | dist | p | n | dist | p 
+---+------+---+---+------+---
+(0 rows)
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+                        QUERY PLAN                         
+-----------------------------------------------------------
+ WindowAgg
+   ->  Index Only Scan using sp_quad_ind on quad_point_tbl
+         Index Cond: (p <@ '(1000,1000),(200,200)'::box)
+         Order By: (p <-> '(0,0)'::point)
+(4 rows)
+
+CREATE TEMP TABLE quad_point_tbl_ord_idx2 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+SELECT * FROM quad_point_tbl_ord_seq2 seq FULL JOIN quad_point_tbl_ord_idx2 idx
+ON seq.n = idx.n
+AND (seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+ n | dist | p | n | dist | p 
+---+------+---+---+------+---
+(0 rows)
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM quad_point_tbl WHERE p IS NOT NULL;
+                        QUERY PLAN                         
+-----------------------------------------------------------
+ WindowAgg
+   ->  Index Only Scan using sp_quad_ind on quad_point_tbl
+         Index Cond: (p IS NOT NULL)
+         Order By: (p <-> '(333,400)'::point)
+(4 rows)
+
+CREATE TEMP TABLE quad_point_tbl_ord_idx3 AS
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM quad_point_tbl WHERE p IS NOT NULL;
+SELECT * FROM quad_point_tbl_ord_seq3 seq FULL JOIN quad_point_tbl_ord_idx3 idx
+ON seq.n = idx.n
+AND (seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+ n | dist | p | n | dist | p 
+---+------+---+---+------+---
+(0 rows)
+
 EXPLAIN (COSTS OFF)
 SELECT count(*) FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
                        QUERY PLAN                        
@@ -993,6 +1067,71 @@ SELECT count(*) FROM kd_point_tbl WHERE p ~= '(4585, 365)';
      1
 (1 row)
 
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl;
+                      QUERY PLAN                       
+-------------------------------------------------------
+ WindowAgg
+   ->  Index Only Scan using sp_kd_ind on kd_point_tbl
+         Order By: (p <-> '(0,0)'::point)
+(3 rows)
+
+CREATE TEMP TABLE kd_point_tbl_ord_idx1 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl;
+SELECT * FROM quad_point_tbl_ord_seq1 seq FULL JOIN kd_point_tbl_ord_idx1 idx
+ON seq.n = idx.n AND
+(seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+ n | dist | p | n | dist | p 
+---+------+---+---+------+---
+(0 rows)
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+                       QUERY PLAN                        
+---------------------------------------------------------
+ WindowAgg
+   ->  Index Only Scan using sp_kd_ind on kd_point_tbl
+         Index Cond: (p <@ '(1000,1000),(200,200)'::box)
+         Order By: (p <-> '(0,0)'::point)
+(4 rows)
+
+CREATE TEMP TABLE kd_point_tbl_ord_idx2 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+SELECT * FROM quad_point_tbl_ord_seq2 seq FULL JOIN kd_point_tbl_ord_idx2 idx
+ON seq.n = idx.n AND
+(seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+ n | dist | p | n | dist | p 
+---+------+---+---+------+---
+(0 rows)
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM kd_point_tbl WHERE p IS NOT NULL;
+                      QUERY PLAN                       
+-------------------------------------------------------
+ WindowAgg
+   ->  Index Only Scan using sp_kd_ind on kd_point_tbl
+         Index Cond: (p IS NOT NULL)
+         Order By: (p <-> '(333,400)'::point)
+(4 rows)
+
+CREATE TEMP TABLE kd_point_tbl_ord_idx3 AS
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM kd_point_tbl WHERE p IS NOT NULL;
+SELECT * FROM quad_point_tbl_ord_seq3 seq FULL JOIN kd_point_tbl_ord_idx3 idx
+ON seq.n = idx.n AND
+(seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+ n | dist | p | n | dist | p 
+---+------+---+---+------+---
+(0 rows)
+
 EXPLAIN (COSTS OFF)
 SELECT count(*) FROM radix_text_tbl WHERE t = 'P0123456789abcdef';
                          QUERY PLAN                         

src/test/regress/expected/opr_sanity.out

@@ -1911,6 +1911,7 @@ ORDER BY 1, 2, 3;
        4000 |           12 | <=
        4000 |           12 | |&>
        4000 |           14 | >=
+       4000 |           15 | <->
        4000 |           15 | >
        4000 |           16 | @>
        4000 |           18 | =
@@ -1924,7 +1925,7 @@ ORDER BY 1, 2, 3;
        4000 |           26 | >>
        4000 |           27 | >>=
        4000 |           28 | ^@
-(122 rows)
+(123 rows)
 
 -- Check that all opclass search operators have selectivity estimators.
 -- This is not absolutely required, but it seems a reasonable thing

src/test/regress/expected/polygon.out

@@ -462,6 +462,54 @@ SELECT count(*) FROM quad_poly_tbl WHERE p ~= polygon '((200, 300),(210, 310),(2
   1000
 (1 row)
 
+-- test ORDER BY distance
+SET enable_indexscan = ON;
+SET enable_bitmapscan = OFF;
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl;
+                        QUERY PLAN                         
+-----------------------------------------------------------
+ WindowAgg
+   ->  Index Scan using quad_poly_tbl_idx on quad_poly_tbl
+         Order By: (p <-> '(123,456)'::point)
+(3 rows)
+
+CREATE TEMP TABLE quad_poly_tbl_ord_idx1 AS
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl;
+SELECT *
+FROM quad_poly_tbl_ord_seq1 seq FULL JOIN quad_poly_tbl_ord_idx1 idx
+	ON seq.n = idx.n AND seq.id = idx.id AND
+		(seq.dist = idx.dist OR seq.dist IS NULL AND idx.dist IS NULL)
+WHERE seq.id IS NULL OR idx.id IS NULL;
+ n | dist | id | n | dist | id 
+---+------+----+---+------+----
+(0 rows)
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl WHERE p <@ polygon '((300,300),(400,600),(600,500),(700,200))';
+                                   QUERY PLAN                                    
+---------------------------------------------------------------------------------
+ WindowAgg
+   ->  Index Scan using quad_poly_tbl_idx on quad_poly_tbl
+         Index Cond: (p <@ '((300,300),(400,600),(600,500),(700,200))'::polygon)
+         Order By: (p <-> '(123,456)'::point)
+(4 rows)
+
+CREATE TEMP TABLE quad_poly_tbl_ord_idx2 AS
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl WHERE p <@ polygon '((300,300),(400,600),(600,500),(700,200))';
+SELECT *
+FROM quad_poly_tbl_ord_seq2 seq FULL JOIN quad_poly_tbl_ord_idx2 idx
+	ON seq.n = idx.n AND seq.id = idx.id AND
+		(seq.dist = idx.dist OR seq.dist IS NULL AND idx.dist IS NULL)
+WHERE seq.id IS NULL OR idx.id IS NULL;
+ n | dist | id | n | dist | id 
+---+------+----+---+------+----
+(0 rows)
+
 RESET enable_seqscan;
 RESET enable_indexscan;
 RESET enable_bitmapscan;

src/test/regress/sql/amutils.sql

@@ -40,7 +40,8 @@ select prop,
        pg_index_column_has_property('onek_hundred'::regclass, 1, prop) as btree,
        pg_index_column_has_property('hash_i4_index'::regclass, 1, prop) as hash,
        pg_index_column_has_property('gcircleind'::regclass, 1, prop) as gist,
-       pg_index_column_has_property('sp_radix_ind'::regclass, 1, prop) as spgist,
+       pg_index_column_has_property('sp_radix_ind'::regclass, 1, prop) as spgist_radix,
+       pg_index_column_has_property('sp_quad_ind'::regclass, 1, prop) as spgist_quad,
        pg_index_column_has_property('botharrayidx'::regclass, 1, prop) as gin,
        pg_index_column_has_property('brinidx'::regclass, 1, prop) as brin
   from unnest(array['asc', 'desc', 'nulls_first', 'nulls_last',

src/test/regress/sql/create_index.sql

@@ -198,6 +198,18 @@ SELECT count(*) FROM quad_point_tbl WHERE p >^ '(5000, 4000)';
 
 SELECT count(*) FROM quad_point_tbl WHERE p ~= '(4585, 365)';
 
+CREATE TEMP TABLE quad_point_tbl_ord_seq1 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl;
+
+CREATE TEMP TABLE quad_point_tbl_ord_seq2 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+
+CREATE TEMP TABLE quad_point_tbl_ord_seq3 AS
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM quad_point_tbl WHERE p IS NOT NULL;
+
 SELECT count(*) FROM radix_text_tbl WHERE t = 'P0123456789abcdef';
 
 SELECT count(*) FROM radix_text_tbl WHERE t = 'P0123456789abcde';
@@ -363,6 +375,39 @@ EXPLAIN (COSTS OFF)
 SELECT count(*) FROM quad_point_tbl WHERE p ~= '(4585, 365)';
 SELECT count(*) FROM quad_point_tbl WHERE p ~= '(4585, 365)';
 
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl;
+CREATE TEMP TABLE quad_point_tbl_ord_idx1 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl;
+SELECT * FROM quad_point_tbl_ord_seq1 seq FULL JOIN quad_point_tbl_ord_idx1 idx
+ON seq.n = idx.n
+AND (seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+CREATE TEMP TABLE quad_point_tbl_ord_idx2 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM quad_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+SELECT * FROM quad_point_tbl_ord_seq2 seq FULL JOIN quad_point_tbl_ord_idx2 idx
+ON seq.n = idx.n
+AND (seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM quad_point_tbl WHERE p IS NOT NULL;
+CREATE TEMP TABLE quad_point_tbl_ord_idx3 AS
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM quad_point_tbl WHERE p IS NOT NULL;
+SELECT * FROM quad_point_tbl_ord_seq3 seq FULL JOIN quad_point_tbl_ord_idx3 idx
+ON seq.n = idx.n
+AND (seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+
 EXPLAIN (COSTS OFF)
 SELECT count(*) FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
 SELECT count(*) FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
@@ -391,6 +436,39 @@ EXPLAIN (COSTS OFF)
 SELECT count(*) FROM kd_point_tbl WHERE p ~= '(4585, 365)';
 SELECT count(*) FROM kd_point_tbl WHERE p ~= '(4585, 365)';
 
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl;
+CREATE TEMP TABLE kd_point_tbl_ord_idx1 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl;
+SELECT * FROM quad_point_tbl_ord_seq1 seq FULL JOIN kd_point_tbl_ord_idx1 idx
+ON seq.n = idx.n AND
+(seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+CREATE TEMP TABLE kd_point_tbl_ord_idx2 AS
+SELECT rank() OVER (ORDER BY p <-> '0,0') n, p <-> '0,0' dist, p
+FROM kd_point_tbl WHERE p <@ box '(200,200,1000,1000)';
+SELECT * FROM quad_point_tbl_ord_seq2 seq FULL JOIN kd_point_tbl_ord_idx2 idx
+ON seq.n = idx.n AND
+(seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM kd_point_tbl WHERE p IS NOT NULL;
+CREATE TEMP TABLE kd_point_tbl_ord_idx3 AS
+SELECT rank() OVER (ORDER BY p <-> '333,400') n, p <-> '333,400' dist, p
+FROM kd_point_tbl WHERE p IS NOT NULL;
+SELECT * FROM quad_point_tbl_ord_seq3 seq FULL JOIN kd_point_tbl_ord_idx3 idx
+ON seq.n = idx.n AND
+(seq.dist = idx.dist AND seq.p ~= idx.p OR seq.p IS NULL AND idx.p IS NULL)
+WHERE seq.n IS NULL OR idx.n IS NULL;
+
 EXPLAIN (COSTS OFF)
 SELECT count(*) FROM radix_text_tbl WHERE t = 'P0123456789abcdef';
 SELECT count(*) FROM radix_text_tbl WHERE t = 'P0123456789abcdef';

src/test/regress/sql/polygon.sql

@@ -206,6 +206,39 @@ EXPLAIN (COSTS OFF)
 SELECT count(*) FROM quad_poly_tbl WHERE p ~= polygon '((200, 300),(210, 310),(230, 290))';
 SELECT count(*) FROM quad_poly_tbl WHERE p ~= polygon '((200, 300),(210, 310),(230, 290))';
 
+-- test ORDER BY distance
+SET enable_indexscan = ON;
+SET enable_bitmapscan = OFF;
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl;
+
+CREATE TEMP TABLE quad_poly_tbl_ord_idx1 AS
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl;
+
+SELECT *
+FROM quad_poly_tbl_ord_seq1 seq FULL JOIN quad_poly_tbl_ord_idx1 idx
+	ON seq.n = idx.n AND seq.id = idx.id AND
+		(seq.dist = idx.dist OR seq.dist IS NULL AND idx.dist IS NULL)
+WHERE seq.id IS NULL OR idx.id IS NULL;
+
+
+EXPLAIN (COSTS OFF)
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl WHERE p <@ polygon '((300,300),(400,600),(600,500),(700,200))';
+
+CREATE TEMP TABLE quad_poly_tbl_ord_idx2 AS
+SELECT rank() OVER (ORDER BY p <-> point '123,456') n, p <-> point '123,456' dist, id
+FROM quad_poly_tbl WHERE p <@ polygon '((300,300),(400,600),(600,500),(700,200))';
+
+SELECT *
+FROM quad_poly_tbl_ord_seq2 seq FULL JOIN quad_poly_tbl_ord_idx2 idx
+	ON seq.n = idx.n AND seq.id = idx.id AND
+		(seq.dist = idx.dist OR seq.dist IS NULL AND idx.dist IS NULL)
+WHERE seq.id IS NULL OR idx.id IS NULL;
+
 RESET enable_seqscan;
 RESET enable_indexscan;
 RESET enable_bitmapscan;