When starts_with() and the equivalent ^@ operator were added, they
were plugged into the planner in only a rather half-baked way.
Selectivity estimation got taught about the operator, but the
other infrastructure associated with LIKE/regex matching wasn't
updated.  This causes these operators to be planned more stupidly
than a functionally-equivalent LIKE/regex pattern [1].

With the (admittedly later) introduction of planner support functions,
it's really quite easy to do better.  The attached patch adds a planner
support function for starts_with(), with these benefits:

* A condition such as "textcol ^@ constant" can now use a regular
btree index, not only an SP-GiST index, so long as the index's
collation is C.  (This works just like "textcol LIKE 'foo%'".)

* "starts_with(textcol, constant)" can be optimized the same as
"textcol ^@ constant".

I also rejiggered match_pattern_prefix() a bit, with the effect
that fixed-prefix LIKE and regex patterns are now more like
starts_with() in another way: if you apply one to an SPGiST-indexed
column, you'll get an index condition using ^@ rather than two
index conditions with >= and <.  That should be more efficient
at runtime, though I didn't try to do any performance testing.

                        regards, tom lane

[1] 
https://www.postgresql.org/message-id/CADT4RqB13KQHOJqqQ%2BWXmYtJrukS2UiFdtfTvT-XA3qYLyB6Cw%40mail.gmail.com
diff --git a/src/backend/utils/adt/like_support.c b/src/backend/utils/adt/like_support.c
index 241e6f0f59..988568825e 100644
--- a/src/backend/utils/adt/like_support.c
+++ b/src/backend/utils/adt/like_support.c
@@ -143,6 +143,14 @@ texticregexeq_support(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Regex_IC));
 }
 
+Datum
+text_starts_with_support(PG_FUNCTION_ARGS)
+{
+	Node	   *rawreq = (Node *) PG_GETARG_POINTER(0);
+
+	PG_RETURN_POINTER(like_regex_support(rawreq, Pattern_Type_Prefix));
+}
+
 /* Common code for the above */
 static Node *
 like_regex_support(Node *rawreq, Pattern_Type ptype)
@@ -246,6 +254,7 @@ match_pattern_prefix(Node *leftop,
 	Oid			eqopr;
 	Oid			ltopr;
 	Oid			geopr;
+	Oid			preopr = InvalidOid;
 	bool		collation_aware;
 	Expr	   *expr;
 	FmgrInfo	ltproc;
@@ -302,12 +311,20 @@ match_pattern_prefix(Node *leftop,
 	switch (ldatatype)
 	{
 		case TEXTOID:
-			if (opfamily == TEXT_PATTERN_BTREE_FAM_OID ||
-				opfamily == TEXT_SPGIST_FAM_OID)
+			if (opfamily == TEXT_PATTERN_BTREE_FAM_OID)
+			{
+				eqopr = TextEqualOperator;
+				ltopr = TextPatternLessOperator;
+				geopr = TextPatternGreaterEqualOperator;
+				collation_aware = false;
+			}
+			else if (opfamily == TEXT_SPGIST_FAM_OID)
 			{
 				eqopr = TextEqualOperator;
 				ltopr = TextPatternLessOperator;
 				geopr = TextPatternGreaterEqualOperator;
+				/* This opfamily has direct support for prefixing */
+				preopr = TextPrefixOperator;
 				collation_aware = false;
 			}
 			else
@@ -360,20 +377,6 @@ match_pattern_prefix(Node *leftop,
 			return NIL;
 	}
 
-	/*
-	 * If necessary, verify that the index's collation behavior is compatible.
-	 * For an exact-match case, we don't have to be picky.  Otherwise, insist
-	 * that the index collation be "C".  Note that here we are looking at the
-	 * index's collation, not the expression's collation -- this test is *not*
-	 * dependent on the LIKE/regex operator's collation.
-	 */
-	if (collation_aware)
-	{
-		if (!(pstatus == Pattern_Prefix_Exact ||
-			  lc_collate_is_c(indexcollation)))
-			return NIL;
-	}
-
 	/*
 	 * If necessary, coerce the prefix constant to the right type.  The given
 	 * prefix constant is either text or bytea type, therefore the only case
@@ -409,8 +412,31 @@ match_pattern_prefix(Node *leftop,
 	}
 
 	/*
-	 * Otherwise, we have a nonempty required prefix of the values.
-	 *
+	 * Otherwise, we have a nonempty required prefix of the values.  Some
+	 * opclasses support prefix checks directly, otherwise we'll try to
+	 * generate a range constraint.
+	 */
+	if (OidIsValid(preopr) && op_in_opfamily(preopr, opfamily))
+	{
+		expr = make_opclause(preopr, BOOLOID, false,
+							 (Expr *) leftop, (Expr *) prefix,
+							 InvalidOid, indexcollation);
+		result = list_make1(expr);
+		return result;
+	}
+
+	/*
+	 * Since we need a range constraint, it's only going to work reliably if
+	 * the index is collation-insensitive or has "C" collation.  Note that
+	 * here we are looking at the index's collation, not the expression's
+	 * collation -- this test is *not* dependent on the LIKE/regex operator's
+	 * collation.
+	 */
+	if (collation_aware &&
+		!lc_collate_is_c(indexcollation))
+		return NIL;
+
+	/*
 	 * We can always say "x >= prefix".
 	 */
 	if (!op_in_opfamily(geopr, opfamily))
@@ -1165,7 +1191,6 @@ pattern_fixed_prefix(Const *patt, Pattern_Type ptype, Oid collation,
 		case Pattern_Type_Prefix:
 			/* Prefix type work is trivial.  */
 			result = Pattern_Prefix_Partial;
-			*rest_selec = 1.0;	/* all */
 			*prefix = makeConst(patt->consttype,
 								patt->consttypmod,
 								patt->constcollid,
@@ -1175,6 +1200,8 @@ pattern_fixed_prefix(Const *patt, Pattern_Type ptype, Oid collation,
 										  patt->constlen),
 								patt->constisnull,
 								patt->constbyval);
+			if (rest_selec != NULL)
+				*rest_selec = 1.0;	/* all */
 			break;
 		default:
 			elog(ERROR, "unrecognized ptype: %d", (int) ptype);
diff --git a/src/include/catalog/pg_operator.dat b/src/include/catalog/pg_operator.dat
index 89c73acd68..0075a02f32 100644
--- a/src/include/catalog/pg_operator.dat
+++ b/src/include/catalog/pg_operator.dat
@@ -102,7 +102,7 @@
   oprright => 'text', oprresult => 'bool', oprcom => '=(text,text)',
   oprnegate => '<>(text,text)', oprcode => 'texteq', oprrest => 'eqsel',
   oprjoin => 'eqjoinsel' },
-{ oid => '3877', descr => 'starts with',
+{ oid => '3877', oid_symbol => 'TextPrefixOperator', descr => 'starts with',
   oprname => '^@', oprleft => 'text', oprright => 'text', oprresult => 'bool',
   oprcode => 'starts_with', oprrest => 'prefixsel',
   oprjoin => 'prefixjoinsel' },
diff --git a/src/include/catalog/pg_proc.dat b/src/include/catalog/pg_proc.dat
index d068d6532e..6412f369f1 100644
--- a/src/include/catalog/pg_proc.dat
+++ b/src/include/catalog/pg_proc.dat
@@ -167,8 +167,12 @@
   proname => 'texteq', proleakproof => 't', prorettype => 'bool',
   proargtypes => 'text text', prosrc => 'texteq' },
 { oid => '3696',
-  proname => 'starts_with', proleakproof => 't', prorettype => 'bool',
-  proargtypes => 'text text', prosrc => 'text_starts_with' },
+  proname => 'starts_with', prosupport => 'text_starts_with_support',
+  proleakproof => 't', prorettype => 'bool', proargtypes => 'text text',
+  prosrc => 'text_starts_with' },
+{ oid => '8923', descr => 'planner support for text_starts_with',
+  proname => 'text_starts_with_support', prorettype => 'internal',
+  proargtypes => 'internal', prosrc => 'text_starts_with_support' },
 { oid => '68',
   proname => 'xideq', proleakproof => 't', prorettype => 'bool',
   proargtypes => 'xid xid', prosrc => 'xideq' },
diff --git a/src/test/regress/expected/create_index_spgist.out b/src/test/regress/expected/create_index_spgist.out
index f4fb08a289..5c04df9c01 100644
--- a/src/test/regress/expected/create_index_spgist.out
+++ b/src/test/regress/expected/create_index_spgist.out
@@ -804,6 +804,22 @@ SELECT count(*) FROM radix_text_tbl WHERE t ^@	 'Worth';
      2
 (1 row)
 
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+                         QUERY PLAN                         
+------------------------------------------------------------
+ Aggregate
+   ->  Index Only Scan using sp_radix_ind on radix_text_tbl
+         Index Cond: (t ^@ 'Worth'::text)
+         Filter: starts_with(t, 'Worth'::text)
+(4 rows)
+
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+ count 
+-------
+     2
+(1 row)
+
 -- Now check the results from bitmap indexscan
 SET enable_seqscan = OFF;
 SET enable_indexscan = OFF;
@@ -1333,6 +1349,23 @@ SELECT count(*) FROM radix_text_tbl WHERE t ^@	 'Worth';
      2
 (1 row)
 
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+                   QUERY PLAN                   
+------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on radix_text_tbl
+         Filter: starts_with(t, 'Worth'::text)
+         ->  Bitmap Index Scan on sp_radix_ind
+               Index Cond: (t ^@ 'Worth'::text)
+(5 rows)
+
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+ count 
+-------
+     2
+(1 row)
+
 RESET enable_seqscan;
 RESET enable_indexscan;
 RESET enable_bitmapscan;
diff --git a/src/test/regress/sql/create_index_spgist.sql b/src/test/regress/sql/create_index_spgist.sql
index b126dae629..660bfc6193 100644
--- a/src/test/regress/sql/create_index_spgist.sql
+++ b/src/test/regress/sql/create_index_spgist.sql
@@ -295,6 +295,10 @@ EXPLAIN (COSTS OFF)
 SELECT count(*) FROM radix_text_tbl WHERE t ^@	 'Worth';
 SELECT count(*) FROM radix_text_tbl WHERE t ^@	 'Worth';
 
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+
 -- Now check the results from bitmap indexscan
 SET enable_seqscan = OFF;
 SET enable_indexscan = OFF;
@@ -424,6 +428,10 @@ EXPLAIN (COSTS OFF)
 SELECT count(*) FROM radix_text_tbl WHERE t ^@	 'Worth';
 SELECT count(*) FROM radix_text_tbl WHERE t ^@	 'Worth';
 
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+SELECT count(*) FROM radix_text_tbl WHERE starts_with(t, 'Worth');
+
 RESET enable_seqscan;
 RESET enable_indexscan;
 RESET enable_bitmapscan;

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