Add amcheck extension to contrib.

This is the beginning of a collection of SQL-callable functions to
verify the integrity of data files.  For now it only contains code to
verify B-Tree indexes.

This adds two SQL-callable functions, validating B-Tree consistency to
a varying degree.  Check the, extensive, docs for details.

The goal is to later extend the coverage of the module to further
access methods, possibly including the heap.  Once checks for
additional access methods exist, we'll likely add some "dispatch"
functions that cover multiple access methods.

Author: Peter Geoghegan, editorialized by Andres Freund
Reviewed-By: Andres Freund, Tomas Vondra, Thomas Munro,
   Anastasia Lubennikova, Robert Haas, Amit Langote
Discussion: CAM3SWZQzLMhMwmBqjzK+pRKXrNUZ4w90wYMUWfkeV8mZ3Debvw@mail.gmail.com

9 files changed, 1451 insertions, 0 deletions

diff --git a/contrib/Makefile b/contrib/Makefile
index 9a74e1b99f..e84eb67008 100644
--- a/contrib/Makefile
+++ b/contrib/Makefile
@@ -6,6 +6,7 @@ include $(top_builddir)/src/Makefile.global
 
 SUBDIRS = \
 		adminpack	\
+		amcheck		\
 		auth_delay	\
 		auto_explain	\
 		bloom		\
diff --git a/contrib/amcheck/Makefile b/contrib/amcheck/Makefile
new file mode 100644
index 0000000000..43bed919ae
--- /dev/null
+++ b/contrib/amcheck/Makefile
@@ -0,0 +1,21 @@
+# contrib/amcheck/Makefile
+
+MODULE_big	= amcheck
+OBJS		= verify_nbtree.o $(WIN32RES)
+
+EXTENSION = amcheck
+DATA = amcheck--1.0.sql
+PGFILEDESC = "amcheck - function for verifying relation integrity"
+
+REGRESS = check check_btree
+
+ifdef USE_PGXS
+PG_CONFIG = pg_config
+PGXS := $(shell $(PG_CONFIG) --pgxs)
+include $(PGXS)
+else
+subdir = contrib/amcheck
+top_builddir = ../..
+include $(top_builddir)/src/Makefile.global
+include $(top_srcdir)/contrib/contrib-global.mk
+endif
diff --git a/contrib/amcheck/amcheck--1.0.sql b/contrib/amcheck/amcheck--1.0.sql
new file mode 100644
index 0000000000..a6612d130c
--- /dev/null
+++ b/contrib/amcheck/amcheck--1.0.sql
@@ -0,0 +1,24 @@
+/* contrib/amcheck/amcheck--1.0.sql */
+
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "CREATE EXTENSION amcheck" to load this file. \quit
+
+--
+-- bt_index_check()
+--
+CREATE FUNCTION bt_index_check(index regclass)
+RETURNS VOID
+AS 'MODULE_PATHNAME', 'bt_index_check'
+LANGUAGE C STRICT PARALLEL RESTRICTED;
+
+--
+-- bt_index_parent_check()
+--
+CREATE FUNCTION bt_index_parent_check(index regclass)
+RETURNS VOID
+AS 'MODULE_PATHNAME', 'bt_index_parent_check'
+LANGUAGE C STRICT PARALLEL RESTRICTED;
+
+-- Don't want these to be available to public
+REVOKE ALL ON FUNCTION bt_index_check(regclass) FROM PUBLIC;
+REVOKE ALL ON FUNCTION bt_index_parent_check(regclass) FROM PUBLIC;
diff --git a/contrib/amcheck/amcheck.control b/contrib/amcheck/amcheck.control
new file mode 100644
index 0000000000..05e2861d7a
--- /dev/null
+++ b/contrib/amcheck/amcheck.control
@@ -0,0 +1,5 @@
+# amcheck extension
+comment = 'functions for verifying relation integrity'
+default_version = '1.0'
+module_pathname = '$libdir/amcheck'
+relocatable = true
diff --git a/contrib/amcheck/expected/check.out b/contrib/amcheck/expected/check.out
new file mode 100644
index 0000000000..5b3e6d530c
--- /dev/null
+++ b/contrib/amcheck/expected/check.out
@@ -0,0 +1 @@
+CREATE EXTENSION amcheck;
diff --git a/contrib/amcheck/expected/check_btree.out b/contrib/amcheck/expected/check_btree.out
new file mode 100644
index 0000000000..612ce7799d
--- /dev/null
+++ b/contrib/amcheck/expected/check_btree.out
@@ -0,0 +1,90 @@
+-- minimal test, basically just verifying that amcheck
+CREATE TABLE bttest_a(id int8);
+CREATE TABLE bttest_b(id int8);
+INSERT INTO bttest_a SELECT * FROM generate_series(1, 100000);
+INSERT INTO bttest_b SELECT * FROM generate_series(100000, 1, -1);
+CREATE INDEX bttest_a_idx ON bttest_a USING btree (id);
+CREATE INDEX bttest_b_idx ON bttest_b USING btree (id);
+CREATE ROLE bttest_role;
+-- verify permissions are checked (error due to function not callable)
+SET ROLE bttest_role;
+SELECT bt_index_check('bttest_a_idx'::regclass);
+ERROR:  permission denied for function bt_index_check
+SELECT bt_index_parent_check('bttest_a_idx'::regclass);
+ERROR:  permission denied for function bt_index_parent_check
+RESET ROLE;
+-- we, intentionally, don't check relation permissions - it's useful
+-- to run this cluster-wide with a restricted account, and as tested
+-- above explicit permission has to be granted for that.
+GRANT EXECUTE ON FUNCTION bt_index_check(regclass) TO bttest_role;
+GRANT EXECUTE ON FUNCTION bt_index_parent_check(regclass) TO bttest_role;
+SET ROLE bttest_role;
+SELECT bt_index_check('bttest_a_idx');
+ bt_index_check 
+----------------
+ 
+(1 row)
+
+SELECT bt_index_parent_check('bttest_a_idx');
+ bt_index_parent_check 
+-----------------------
+ 
+(1 row)
+
+RESET ROLE;
+-- verify plain tables are rejected (error)
+SELECT bt_index_check('bttest_a');
+ERROR:  "bttest_a" is not an index
+SELECT bt_index_parent_check('bttest_a');
+ERROR:  "bttest_a" is not an index
+-- verify non-existing indexes are rejected (error)
+SELECT bt_index_check(17);
+ERROR:  could not open relation with OID 17
+SELECT bt_index_parent_check(17);
+ERROR:  could not open relation with OID 17
+-- verify wrong index types are rejected (error)
+BEGIN;
+CREATE INDEX bttest_a_brin_idx ON bttest_a USING brin(id);
+SELECT bt_index_parent_check('bttest_a_brin_idx');
+ERROR:  only B-Tree indexes are supported as targets for verification
+DETAIL:  Relation "bttest_a_brin_idx" is not a B-Tree index.
+ROLLBACK;
+-- normal check outside of xact
+SELECT bt_index_check('bttest_a_idx');
+ bt_index_check 
+----------------
+ 
+(1 row)
+
+-- more expansive test
+SELECT bt_index_parent_check('bttest_b_idx');
+ bt_index_parent_check 
+-----------------------
+ 
+(1 row)
+
+BEGIN;
+SELECT bt_index_check('bttest_a_idx');
+ bt_index_check 
+----------------
+ 
+(1 row)
+
+SELECT bt_index_parent_check('bttest_b_idx');
+ bt_index_parent_check 
+-----------------------
+ 
+(1 row)
+
+-- make sure we don't have any leftover locks
+SELECT * FROM pg_locks WHERE relation IN ('bttest_a_idx'::regclass, 'bttest_b_idx'::regclass);
+ locktype | database | relation | page | tuple | virtualxid | transactionid | classid | objid | objsubid | virtualtransaction | pid | mode | granted | fastpath 
+----------+----------+----------+------+-------+------------+---------------+---------+-------+----------+--------------------+-----+------+---------+----------
+(0 rows)
+
+COMMIT;
+-- cleanup
+DROP TABLE bttest_a;
+DROP TABLE bttest_b;
+DROP OWNED BY bttest_role; -- permissions
+DROP ROLE bttest_role;
diff --git a/contrib/amcheck/sql/check.sql b/contrib/amcheck/sql/check.sql
new file mode 100644
index 0000000000..5b3e6d530c
--- /dev/null
+++ b/contrib/amcheck/sql/check.sql
@@ -0,0 +1 @@
+CREATE EXTENSION amcheck;
diff --git a/contrib/amcheck/sql/check_btree.sql b/contrib/amcheck/sql/check_btree.sql
new file mode 100644
index 0000000000..783fb635e7
--- /dev/null
+++ b/contrib/amcheck/sql/check_btree.sql
@@ -0,0 +1,59 @@
+-- minimal test, basically just verifying that amcheck
+CREATE TABLE bttest_a(id int8);
+CREATE TABLE bttest_b(id int8);
+
+INSERT INTO bttest_a SELECT * FROM generate_series(1, 100000);
+INSERT INTO bttest_b SELECT * FROM generate_series(100000, 1, -1);
+
+CREATE INDEX bttest_a_idx ON bttest_a USING btree (id);
+CREATE INDEX bttest_b_idx ON bttest_b USING btree (id);
+
+CREATE ROLE bttest_role;
+
+-- verify permissions are checked (error due to function not callable)
+SET ROLE bttest_role;
+SELECT bt_index_check('bttest_a_idx'::regclass);
+SELECT bt_index_parent_check('bttest_a_idx'::regclass);
+RESET ROLE;
+
+-- we, intentionally, don't check relation permissions - it's useful
+-- to run this cluster-wide with a restricted account, and as tested
+-- above explicit permission has to be granted for that.
+GRANT EXECUTE ON FUNCTION bt_index_check(regclass) TO bttest_role;
+GRANT EXECUTE ON FUNCTION bt_index_parent_check(regclass) TO bttest_role;
+SET ROLE bttest_role;
+SELECT bt_index_check('bttest_a_idx');
+SELECT bt_index_parent_check('bttest_a_idx');
+RESET ROLE;
+
+-- verify plain tables are rejected (error)
+SELECT bt_index_check('bttest_a');
+SELECT bt_index_parent_check('bttest_a');
+
+-- verify non-existing indexes are rejected (error)
+SELECT bt_index_check(17);
+SELECT bt_index_parent_check(17);
+
+-- verify wrong index types are rejected (error)
+BEGIN;
+CREATE INDEX bttest_a_brin_idx ON bttest_a USING brin(id);
+SELECT bt_index_parent_check('bttest_a_brin_idx');
+ROLLBACK;
+
+-- normal check outside of xact
+SELECT bt_index_check('bttest_a_idx');
+-- more expansive test
+SELECT bt_index_parent_check('bttest_b_idx');
+
+BEGIN;
+SELECT bt_index_check('bttest_a_idx');
+SELECT bt_index_parent_check('bttest_b_idx');
+-- make sure we don't have any leftover locks
+SELECT * FROM pg_locks WHERE relation IN ('bttest_a_idx'::regclass, 'bttest_b_idx'::regclass);
+COMMIT;
+
+-- cleanup
+DROP TABLE bttest_a;
+DROP TABLE bttest_b;
+DROP OWNED BY bttest_role; -- permissions
+DROP ROLE bttest_role;
diff --git a/contrib/amcheck/verify_nbtree.c b/contrib/amcheck/verify_nbtree.c
new file mode 100644
index 0000000000..5724aa6be3
--- /dev/null
+++ b/contrib/amcheck/verify_nbtree.c
@@ -0,0 +1,1249 @@
+/*-------------------------------------------------------------------------
+ *
+ * verify_nbtree.c
+ *		Verifies the integrity of nbtree indexes based on invariants.
+ *
+ * For B-Tree indexes, verification includes checking that each page in the
+ * target index has items in logical order as reported by an insertion scankey
+ * (the insertion scankey sort-wise NULL semantics are needed for
+ * verification).
+ *
+ *
+ * Copyright (c) 2017, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ *	  contrib/amcheck/verify_nbtree.c
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include "access/nbtree.h"
+#include "access/transam.h"
+#include "catalog/index.h"
+#include "catalog/pg_am.h"
+#include "commands/tablecmds.h"
+#include "miscadmin.h"
+#include "storage/lmgr.h"
+#include "utils/memutils.h"
+#include "utils/snapmgr.h"
+
+
+PG_MODULE_MAGIC;
+
+/*
+ * A B-Tree cannot possibly have this many levels, since there must be one
+ * block per level, which is bound by the range of BlockNumber:
+ */
+#define InvalidBtreeLevel	((uint32) InvalidBlockNumber)
+
+/*
+ * State associated with verifying a B-Tree index
+ *
+ * target is the point of reference for a verification operation.
+ *
+ * Other B-Tree pages may be allocated, but those are always auxiliary (e.g.,
+ * they are current target's child pages). Conceptually, problems are only
+ * ever found in the current target page. Each page found by verification's
+ * left/right, top/bottom scan becomes the target exactly once.
+ */
+typedef struct BtreeCheckState
+{
+	/*
+	 * Unchanging state, established at start of verification:
+	 */
+
+	/* B-Tree Index Relation */
+	Relation	rel;
+	/* ExclusiveLock held? */
+	bool		exclusivelylocked;
+	/* Per-page context */
+	MemoryContext targetcontext;
+	/* Buffer access strategy */
+	BufferAccessStrategy checkstrategy;
+
+	/*
+	 * Mutable state, for verification of particular page:
+	 */
+
+	/* Current target page */
+	Page		target;
+	/* Target block number */
+	BlockNumber targetblock;
+	/* Target page's LSN */
+	XLogRecPtr	targetlsn;
+} BtreeCheckState;
+
+/*
+ * Starting point for verifying an entire B-Tree index level
+ */
+typedef struct BtreeLevel
+{
+	/* Level number (0 is leaf page level). */
+	uint32		level;
+
+	/* Left most block on level.  Scan of level begins here. */
+	BlockNumber leftmost;
+
+	/* Is this level reported as "true" root level by meta page? */
+	bool		istruerootlevel;
+} BtreeLevel;
+
+PG_FUNCTION_INFO_V1(bt_index_check);
+PG_FUNCTION_INFO_V1(bt_index_parent_check);
+
+static void bt_index_check_internal(Oid indrelid, bool parentcheck);
+static inline void btree_index_checkable(Relation rel);
+static void bt_check_every_level(Relation rel, bool exclusivelylocked);
+static BtreeLevel bt_check_level_from_leftmost(BtreeCheckState *state,
+							 BtreeLevel level);
+static void bt_target_page_check(BtreeCheckState *state);
+static ScanKey bt_right_page_check_scankey(BtreeCheckState *state);
+static void bt_downlink_check(BtreeCheckState *state, BlockNumber childblock,
+				  ScanKey targetkey);
+static inline bool offset_is_negative_infinity(BTPageOpaque opaque,
+							OffsetNumber offset);
+static inline bool invariant_leq_offset(BtreeCheckState *state,
+					 ScanKey key,
+					 OffsetNumber upperbound);
+static inline bool invariant_geq_offset(BtreeCheckState *state,
+					 ScanKey key,
+					 OffsetNumber lowerbound);
+static inline bool invariant_leq_nontarget_offset(BtreeCheckState *state,
+							   Page other,
+							   ScanKey key,
+							   OffsetNumber upperbound);
+static Page palloc_btree_page(BtreeCheckState *state, BlockNumber blocknum);
+
+/*
+ * bt_index_check(index regclass)
+ *
+ * Verify integrity of B-Tree index.
+ *
+ * Acquires AccessShareLock on heap & index relations.  Does not consider
+ * invariants that exist between parent/child pages.
+ */
+Datum
+bt_index_check(PG_FUNCTION_ARGS)
+{
+	Oid			indrelid = PG_GETARG_OID(0);
+
+	bt_index_check_internal(indrelid, false);
+
+	PG_RETURN_VOID();
+}
+
+/*
+ * bt_index_parent_check(index regclass)
+ *
+ * Verify integrity of B-Tree index.
+ *
+ * Acquires ShareLock on heap & index relations.  Verifies that downlinks in
+ * parent pages are valid lower bounds on child pages.
+ */
+Datum
+bt_index_parent_check(PG_FUNCTION_ARGS)
+{
+	Oid			indrelid = PG_GETARG_OID(0);
+
+	bt_index_check_internal(indrelid, true);
+
+	PG_RETURN_VOID();
+}
+
+/*
+ * Helper for bt_index_[parent_]check, coordinating the bulk of the work.
+ */
+static void
+bt_index_check_internal(Oid indrelid, bool parentcheck)
+{
+	Oid			heapid;
+	Relation	indrel;
+	Relation	heaprel;
+	LOCKMODE	lockmode;
+
+	if (parentcheck)
+		lockmode = ShareLock;
+	else
+		lockmode = AccessShareLock;
+
+	/*
+	 * We must lock table before index to avoid deadlocks.  However, if the
+	 * passed indrelid isn't an index then IndexGetRelation() will fail.
+	 * Rather than emitting a not-very-helpful error message, postpone
+	 * complaining, expecting that the is-it-an-index test below will fail.
+	 *
+	 * In hot standby mode this will raise an error when parentcheck is true.
+	 */
+	heapid = IndexGetRelation(indrelid, true);
+	if (OidIsValid(heapid))
+		heaprel = heap_open(heapid, lockmode);
+	else
+		heaprel = NULL;
+
+	/*
+	 * Open the target index relations separately (like relation_openrv(), but
+	 * with heap relation locked first to prevent deadlocking).  In hot
+	 * standby mode this will raise an error when parentcheck is true.
+	 */
+	indrel = index_open(indrelid, lockmode);
+
+	/*
+	 * Since we did the IndexGetRelation call above without any lock, it's
+	 * barely possible that a race against an index drop/recreation could have
+	 * netted us the wrong table.  Although the table itself won't actually be
+	 * examined during verification currently, a recheck still seems like a
+	 * good idea.
+	 */
+	if (heaprel == NULL || heapid != IndexGetRelation(indrelid, false))
+		ereport(ERROR,
+				(errcode(ERRCODE_UNDEFINED_TABLE),
+				 errmsg("could not open parent table of index %s",
+						RelationGetRelationName(indrel))));
+
+	/* Relation suitable for checking as B-Tree? */
+	btree_index_checkable(indrel);
+
+	/* Check index */
+	bt_check_every_level(indrel, parentcheck);
+
+	/*
+	 * Release locks early. That's ok here because nothing in the called
+	 * routines will trigger shared cache invalidations to be sent, so we can
+	 * relax the usual pattern of only releasing locks after commit.
+	 */
+	index_close(indrel, lockmode);
+	if (heaprel)
+		heap_close(heaprel, lockmode);
+}
+
+/*
+ * Basic checks about the suitability of a relation for checking as a B-Tree
+ * index.
+ *
+ * NB: Intentionally not checking permissions, the function is normally not
+ * callable by non-superusers. If granted, it's useful to be able to check a
+ * whole cluster.
+ */
+static inline void
+btree_index_checkable(Relation rel)
+{
+	if (rel->rd_rel->relkind != RELKIND_INDEX ||
+		rel->rd_rel->relam != BTREE_AM_OID)
+		ereport(ERROR,
+				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				 errmsg("only B-Tree indexes are supported as targets for verification"),
+				 errdetail("Relation \"%s\" is not a B-Tree index.",
+						   RelationGetRelationName(rel))));
+
+	if (RELATION_IS_OTHER_TEMP(rel))
+		ereport(ERROR,
+				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				 errmsg("cannot access temporary tables of other sessions"),
+			 errdetail("Index \"%s\" is associated with temporary relation.",
+					   RelationGetRelationName(rel))));
+
+	if (!IndexIsValid(rel->rd_index))
+		ereport(ERROR,
+				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				 errmsg("cannot check index \"%s\"",
+						RelationGetRelationName(rel)),
+				 errdetail("Index is not valid")));
+}
+
+/*
+ * Main entry point for B-Tree SQL-callable functions. Walks the B-Tree in
+ * logical order, verifying invariants as it goes.
+ *
+ * It is the caller's responsibility to acquire appropriate heavyweight lock on
+ * the index relation, and advise us if extra checks are safe when an
+ * ExclusiveLock is held.
+ *
+ * An ExclusiveLock is generally assumed to prevent any kind of physical
+ * modification to the index structure, including modifications that VACUUM may
+ * make.  This does not include setting of the LP_DEAD bit by concurrent index
+ * scans, although that is just metadata that is not able to directly affect
+ * any check performed here.  Any concurrent process that might act on the
+ * LP_DEAD bit being set (recycle space) requires a heavyweight lock that
+ * cannot be held while we hold an ExclusiveLock.  (Besides, even if that could
+ * happen, the ad-hoc recycling when a page might otherwise split is performed
+ * per-page, and requires an exclusive buffer lock, which wouldn't cause us
+ * trouble.  _bt_delitems_vacuum() may only delete leaf items, and so the extra
+ * parent/child check cannot be affected.)
+ */
+static void
+bt_check_every_level(Relation rel, bool exclusivelylocked)
+{
+	BtreeCheckState *state;
+	Page		metapage;
+	BTMetaPageData *metad;
+	uint32		previouslevel;
+	BtreeLevel	current;
+
+	/*
+	 * RecentGlobalXmin assertion matches index_getnext_tid().  See note on
+	 * RecentGlobalXmin/B-Tree page deletion.
+	 */
+	Assert(TransactionIdIsValid(RecentGlobalXmin));
+
+	/*
+	 * Initialize state for entire verification operation
+	 */
+	state = palloc(sizeof(BtreeCheckState));
+	state->rel = rel;
+	state->exclusivelylocked = exclusivelylocked;
+	/* Create context for page */
+	state->targetcontext = AllocSetContextCreate(CurrentMemoryContext,
+												 "amcheck context",
+												 ALLOCSET_DEFAULT_MINSIZE,
+												 ALLOCSET_DEFAULT_INITSIZE,
+												 ALLOCSET_DEFAULT_MAXSIZE);
+	state->checkstrategy = GetAccessStrategy(BAS_BULKREAD);
+
+	/* Get true root block from meta-page */
+	metapage = palloc_btree_page(state, BTREE_METAPAGE);
+	metad = BTPageGetMeta(metapage);
+
+	/*
+	 * Certain deletion patterns can result in "skinny" B-Tree indexes, where
+	 * the fast root and true root differ.
+	 *
+	 * Start from the true root, not the fast root, unlike conventional index
+	 * scans.  This approach is more thorough, and removes the risk of
+	 * following a stale fast root from the meta page.
+	 */
+	if (metad->btm_fastroot != metad->btm_root)
+		ereport(DEBUG1,
+				(errcode(ERRCODE_NO_DATA),
+				 errmsg("harmless fast root mismatch in index %s",
+						RelationGetRelationName(rel)),
+				 errdetail_internal("Fast root block %u (level %u) differs from true root block %u (level %u).",
+									metad->btm_fastroot, metad->btm_fastlevel,
+									metad->btm_root, metad->btm_level)));
+
+	/*
+	 * Starting at the root, verify every level.  Move left to right, top to
+	 * bottom.  Note that there may be no pages other than the meta page (meta
+	 * page can indicate that root is P_NONE when the index is totally empty).
+	 */
+	previouslevel = InvalidBtreeLevel;
+	current.level = metad->btm_level;
+	current.leftmost = metad->btm_root;
+	current.istruerootlevel = true;
+	while (current.leftmost != P_NONE)
+	{
+		/*
+		 * Verify this level, and get left most page for next level down, if
+		 * not at leaf level
+		 */
+		current = bt_check_level_from_leftmost(state, current);
+
+		if (current.leftmost == InvalidBlockNumber)
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("index \"%s\" has no valid pages on level below %u or first level",
+							RelationGetRelationName(rel), previouslevel)));
+
+		previouslevel = current.level;
+	}
+
+	/* Be tidy: */
+	MemoryContextDelete(state->targetcontext);
+}
+
+/*
+ * Given a left-most block at some level, move right, verifying each page
+ * individually (with more verification across pages for "exclusivelylocked"
+ * callers).  Caller should pass the true root page as the leftmost initially,
+ * working their way down by passing what is returned for the last call here
+ * until level 0 (leaf page level) was reached.
+ *
+ * Returns state for next call, if any.  This includes left-most block number
+ * one level lower that should be passed on next level/call, which is set to
+ * P_NONE on last call here (when leaf level is verified).  Level numbers
+ * follow the nbtree convention: higher levels have higher numbers, because new
+ * levels are added only due to a root page split.  Note that prior to the
+ * first root page split, the root is also a leaf page, so there is always a
+ * level 0 (leaf level), and it's always the last level processed.
+ *
+ * Note on memory management:  State's per-page context is reset here, between
+ * each call to bt_target_page_check().
+ */
+static BtreeLevel
+bt_check_level_from_leftmost(BtreeCheckState *state, BtreeLevel level)
+{
+	/* State to establish early, concerning entire level */
+	BTPageOpaque opaque;
+	MemoryContext oldcontext;
+	BtreeLevel	nextleveldown;
+
+	/* Variables for iterating across level using right links */
+	BlockNumber leftcurrent = P_NONE;
+	BlockNumber current = level.leftmost;
+
+	/* Initialize return state */
+	nextleveldown.leftmost = InvalidBlockNumber;
+	nextleveldown.level = InvalidBtreeLevel;
+	nextleveldown.istruerootlevel = false;
+
+	/* Use page-level context for duration of this call */
+	oldcontext = MemoryContextSwitchTo(state->targetcontext);
+
+	elog(DEBUG2, "verifying level %u%s", level.level,
+		 level.istruerootlevel ?
+		 " (true root level)" : level.level == 0 ? " (leaf level)" : "");
+
+	do
+	{
+		/* Don't rely on CHECK_FOR_INTERRUPTS() calls at lower level */
+		CHECK_FOR_INTERRUPTS();
+
+		/* Initialize state for this iteration */
+		state->targetblock = current;
+		state->target = palloc_btree_page(state, state->targetblock);
+		state->targetlsn = PageGetLSN(state->target);
+
+		opaque = (BTPageOpaque) PageGetSpecialPointer(state->target);
+
+		if (P_IGNORE(opaque))
+		{
+			if (P_RIGHTMOST(opaque))
+				ereport(ERROR,
+						(errcode(ERRCODE_INDEX_CORRUPTED),
+						 errmsg("block %u fell off the end of index \"%s\"",
+							 current, RelationGetRelationName(state->rel))));
+			else
+				ereport(DEBUG1,
+						(errcode(ERRCODE_NO_DATA),
+						 errmsg("block %u of index \"%s\" ignored",
+							 current, RelationGetRelationName(state->rel))));
+			goto nextpage;
+		}
+		else if (nextleveldown.leftmost == InvalidBlockNumber)
+		{
+			/*
+			 * A concurrent page split could make the caller supplied leftmost
+			 * block no longer contain the leftmost page, or no longer be the
+			 * true root, but where that isn't possible due to heavyweight
+			 * locking, check that the first valid page meets caller's
+			 * expectations.
+			 */
+			if (state->exclusivelylocked)
+			{
+				if (!P_LEFTMOST(opaque))
+					ereport(ERROR,
+							(errcode(ERRCODE_INDEX_CORRUPTED),
+						   errmsg("block %u is not leftmost in index \"%s\"",
+							 current, RelationGetRelationName(state->rel))));
+
+				if (level.istruerootlevel && !P_ISROOT(opaque))
+					ereport(ERROR,
+							(errcode(ERRCODE_INDEX_CORRUPTED),
+						  errmsg("block %u is not true root in index \"%s\"",
+							 current, RelationGetRelationName(state->rel))));
+			}
+
+			/*
+			 * Before beginning any non-trivial examination of level, prepare
+			 * state for next bt_check_level_from_leftmost() invocation for
+			 * the next level for the next level down (if any).
+			 *
+			 * There should be at least one non-ignorable page per level,
+			 * unless this is the leaf level, which is assumed by caller to be
+			 * final level.
+			 */
+			if (!P_ISLEAF(opaque))
+			{
+				IndexTuple	itup;
+				ItemId		itemid;
+
+				/* Internal page -- downlink gets leftmost on next level */
+				itemid = PageGetItemId(state->target, P_FIRSTDATAKEY(opaque));
+				itup = (IndexTuple) PageGetItem(state->target, itemid);
+				nextleveldown.leftmost = ItemPointerGetBlockNumber(&(itup->t_tid));
+				nextleveldown.level = opaque->btpo.level - 1;
+			}
+			else
+			{
+				/*
+				 * Leaf page -- final level caller must process.
+				 *
+				 * Note that this could also be the root page, if there has
+				 * been no root page split yet.
+				 */
+				nextleveldown.leftmost = P_NONE;
+				nextleveldown.level = InvalidBtreeLevel;
+			}
+
+			/*
+			 * Finished setting up state for this call/level.  Control will
+			 * never end up back here in any future loop iteration for this
+			 * level.
+			 */
+		}
+
+		if (state->exclusivelylocked && opaque->btpo_prev != leftcurrent)
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("left link/right link pair in index \"%s\" not in agreement",
+							RelationGetRelationName(state->rel)),
+					 errdetail_internal("Block=%u left block=%u left link from block=%u.",
+								  current, leftcurrent, opaque->btpo_prev)));
+
+		/* Check level, which must be valid for non-ignorable page */
+		if (level.level != opaque->btpo.level)
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("leftmost down link for level points to block in index \"%s\" whose level is not one level down",
+							RelationGetRelationName(state->rel)),
+					 errdetail_internal("Block pointed to=%u expected level=%u level in pointed to block=%u.",
+								 current, level.level, opaque->btpo.level)));
+
+		/* Verify invariants for page -- all important checks occur here */
+		bt_target_page_check(state);
+
+nextpage:
+
+		/* Try to detect circular links */
+		if (current == leftcurrent || current == opaque->btpo_prev)
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+			  errmsg("circular link chain found in block %u of index \"%s\"",
+					 current, RelationGetRelationName(state->rel))));
+
+		leftcurrent = current;
+		current = opaque->btpo_next;
+
+		/* Free page and associated memory for this iteration */
+		MemoryContextReset(state->targetcontext);
+	}
+	while (current != P_NONE);
+
+	/* Don't change context for caller */
+	MemoryContextSwitchTo(oldcontext);
+
+	return nextleveldown;
+}
+
+/*
+ * Function performs the following checks on target page, or pages ancillary to
+ * target page:
+ *
+ * - That every "real" data item is less than or equal to the high key, which
+ *	 is an upper bound on the items on the pages (where there is a high key at
+ *	 all -- pages that are rightmost lack one).
+ *
+ * - That within the page, every "real" item is less than or equal to the item
+ *	 immediately to its right, if any (i.e., that the items are in order within
+ *	 the page, so that the binary searches performed by index scans are sane).
+ *
+ * - That the last item stored on the page is less than or equal to the first
+ *	 "real" data item on the page to the right (if such a first item is
+ *	 available).
+ *
+ * Furthermore, when state passed shows ExclusiveLock held, and target page is
+ * internal page, function also checks:
+ *
+ * - That all child pages respect downlinks lower bound.
+ *
+ * Note:  Memory allocated in this routine is expected to be released by caller
+ * resetting state->targetcontext.
+ */
+static void
+bt_target_page_check(BtreeCheckState *state)
+{
+	OffsetNumber offset;
+	OffsetNumber max;
+	BTPageOpaque topaque;
+
+	topaque = (BTPageOpaque) PageGetSpecialPointer(state->target);
+	max = PageGetMaxOffsetNumber(state->target);
+
+	elog(DEBUG2, "verifying %u items on %s block %u", max,
+		 P_ISLEAF(topaque) ? "leaf" : "internal", state->targetblock);
+
+	/*
+	 * Loop over page items, starting from first non-highkey item, not high
+	 * key (if any).  Also, immediately skip "negative infinity" real item (if
+	 * any).
+	 */
+	for (offset = P_FIRSTDATAKEY(topaque);
+		 offset <= max;
+		 offset = OffsetNumberNext(offset))
+	{
+		ItemId		itemid;
+		IndexTuple	itup;
+		ScanKey		skey;
+
+		CHECK_FOR_INTERRUPTS();
+
+		/*
+		 * Don't try to generate scankey using "negative infinity" garbage
+		 * data
+		 */
+		if (offset_is_negative_infinity(topaque, offset))
+			continue;
+
+		/* Build insertion scankey for current page offset */
+		itemid = PageGetItemId(state->target, offset);
+		itup = (IndexTuple) PageGetItem(state->target, itemid);
+		skey = _bt_mkscankey(state->rel, itup);
+
+		/*
+		 * * High key check *
+		 *
+		 * If there is a high key (if this is not the rightmost page on its
+		 * entire level), check that high key actually is upper bound on all
+		 * page items.
+		 *
+		 * We prefer to check all items against high key rather than checking
+		 * just the first and trusting that the operator class obeys the
+		 * transitive law (which implies that all subsequent items also
+		 * respected the high key invariant if they pass the item order
+		 * check).
+		 *
+		 * Ideally, we'd compare every item in the index against every other
+		 * item in the index, and not trust opclass obedience of the
+		 * transitive law to bridge the gap between children and their
+		 * grandparents (as well as great-grandparents, and so on).  We don't
+		 * go to those lengths because that would be prohibitively expensive,
+		 * and probably not markedly more effective in practice.
+		 */
+		if (!P_RIGHTMOST(topaque) &&
+			!invariant_leq_offset(state, skey, P_HIKEY))
+		{
+			char	   *itid,
+					   *htid;
+
+			itid = psprintf("(%u,%u)", state->targetblock, offset);
+			htid = psprintf("(%u,%u)",
+							ItemPointerGetBlockNumber(&(itup->t_tid)),
+							ItemPointerGetOffsetNumber(&(itup->t_tid)));
+
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("high key invariant violated for index \"%s\"",
+							RelationGetRelationName(state->rel)),
+					 errdetail_internal("Index tid=%s points to %s tid=%s page lsn=%X/%X.",
+										itid,
+										P_ISLEAF(topaque) ? "heap" : "index",
+										htid,
+										(uint32) (state->targetlsn >> 32),
+										(uint32) state->targetlsn)));
+		}
+
+		/*
+		 * * Item order check *
+		 *
+		 * Check that items are stored on page in logical order, by checking
+		 * current item is less than or equal to next item (if any).
+		 */
+		if (OffsetNumberNext(offset) <= max &&
+			!invariant_leq_offset(state, skey,
+								  OffsetNumberNext(offset)))
+		{
+			char	   *itid,
+					   *htid,
+					   *nitid,
+					   *nhtid;
+
+			itid = psprintf("(%u,%u)", state->targetblock, offset);
+			htid = psprintf("(%u,%u)",
+							ItemPointerGetBlockNumber(&(itup->t_tid)),
+							ItemPointerGetOffsetNumber(&(itup->t_tid)));
+			nitid = psprintf("(%u,%u)", state->targetblock,
+							 OffsetNumberNext(offset));
+
+			/* Reuse itup to get pointed-to heap location of second item */
+			itemid = PageGetItemId(state->target, OffsetNumberNext(offset));
+			itup = (IndexTuple) PageGetItem(state->target, itemid);
+			nhtid = psprintf("(%u,%u)",
+							 ItemPointerGetBlockNumber(&(itup->t_tid)),
+							 ItemPointerGetOffsetNumber(&(itup->t_tid)));
+
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("item order invariant violated for index \"%s\"",
+							RelationGetRelationName(state->rel)),
+			   errdetail_internal("Lower index tid=%s (points to %s tid=%s) "
+								  "higher index tid=%s (points to %s tid=%s) "
+								  "page lsn=%X/%X.",
+								  itid,
+								  P_ISLEAF(topaque) ? "heap" : "index",
+								  htid,
+								  nitid,
+								  P_ISLEAF(topaque) ? "heap" : "index",
+								  nhtid,
+								  (uint32) (state->targetlsn >> 32),
+								  (uint32) state->targetlsn)));
+		}
+
+		/*
+		 * * Last item check *
+		 *
+		 * Check last item against next/right page's first data item's when
+		 * last item on page is reached.  This additional check can detect
+		 * transposed pages.
+		 *
+		 * This check is similar to the item order check that will have
+		 * already been performed for every other "real" item on target page
+		 * when last item is checked.  The difference is that the next item
+		 * (the item that is compared to target's last item) needs to come
+		 * from the next/sibling page.  There may not be such an item
+		 * available from sibling for various reasons, though (e.g., target is
+		 * the rightmost page on level).
+		 */
+		else if (offset == max)
+		{
+			ScanKey		rightkey;
+
+			/* Get item in next/right page */
+			rightkey = bt_right_page_check_scankey(state);
+
+			if (rightkey &&
+				!invariant_geq_offset(state, rightkey, max))
+			{
+				/*
+				 * As explained at length in bt_right_page_check_scankey(),
+				 * there is a known !exclusivelylocked race that could account
+				 * for apparent violation of invariant, which we must check
+				 * for before actually proceeding with raising error.  Our
+				 * canary condition is that target page was deleted.
+				 */
+				if (!state->exclusivelylocked)
+				{
+					/* Get fresh copy of target page */
+					state->target = palloc_btree_page(state, state->targetblock);
+					/* Note that we deliberately do not update target LSN */
+					topaque = (BTPageOpaque) PageGetSpecialPointer(state->target);
+
+					/*
+					 * All !exclusivelylocked checks now performed; just
+					 * return
+					 */
+					if (P_IGNORE(topaque))
+						return;
+				}
+
+				ereport(ERROR,
+						(errcode(ERRCODE_INDEX_CORRUPTED),
+						 errmsg("cross page item order invariant violated for index \"%s\"",
+								RelationGetRelationName(state->rel)),
+						 errdetail_internal("Last item on page tid=(%u,%u) page lsn=%X/%X.",
+											state->targetblock, offset,
+											(uint32) (state->targetlsn >> 32),
+											(uint32) state->targetlsn)));
+			}
+		}
+
+		/*
+		 * * Downlink check *
+		 *
+		 * Additional check of child items iff this is an internal page and
+		 * caller holds an ExclusiveLock.  This happens for every downlink
+		 * (item) in target excluding the negative-infinity downlink (again,
+		 * this is because it has no useful value to compare).
+		 */
+		if (!P_ISLEAF(topaque) && state->exclusivelylocked)
+		{
+			BlockNumber childblock = ItemPointerGetBlockNumber(&(itup->t_tid));
+
+			bt_downlink_check(state, childblock, skey);
+		}
+	}
+}
+
+/*
+ * Return a scankey for an item on page to right of current target (or the
+ * first non-ignorable page), sufficient to check ordering invariant on last
+ * item in current target page.  Returned scankey relies on local memory
+ * allocated for the child page, which caller cannot pfree().  Caller's memory
+ * context should be reset between calls here.
+ *
+ * This is the first data item, and so all adjacent items are checked against
+ * their immediate sibling item (which may be on a sibling page, or even a
+ * "cousin" page at parent boundaries where target's rightlink points to page
+ * with different parent page).  If no such valid item is available, return
+ * NULL instead.
+ *
+ * Note that !exclusivelylocked callers must reverify that target page has not
+ * been concurrently deleted.
+ */
+static ScanKey
+bt_right_page_check_scankey(BtreeCheckState *state)
+{
+	BTPageOpaque opaque;
+	ItemId		rightitem;
+	BlockNumber targetnext;
+	Page		rightpage;
+	OffsetNumber nline;
+
+	/* Determine target's next block number */
+	opaque = (BTPageOpaque) PageGetSpecialPointer(state->target);
+
+	/* If target is already rightmost, no right sibling; nothing to do here */
+	if (P_RIGHTMOST(opaque))
+		return NULL;
+
+	/*
+	 * General notes on concurrent page splits and page deletion:
+	 *
+	 * Routines like _bt_search() don't require *any* page split interlock
+	 * when descending the tree, including something very light like a buffer
+	 * pin. That's why it's okay that we don't either.  This avoidance of any
+	 * need to "couple" buffer locks is the raison d' etre of the Lehman & Yao
+	 * algorithm, in fact.
+	 *
+	 * That leaves deletion.  A deleted page won't actually be recycled by
+	 * VACUUM early enough for us to fail to at least follow its right link
+	 * (or left link, or downlink) and find its sibling, because recycling
+	 * does not occur until no possible index scan could land on the page.
+	 * Index scans can follow links with nothing more than their snapshot as
+	 * an interlock and be sure of at least that much.  (See page
+	 * recycling/RecentGlobalXmin notes in nbtree README.)
+	 *
+	 * Furthermore, it's okay if we follow a rightlink and find a half-dead or
+	 * dead (ignorable) page one or more times.  There will either be a
+	 * further right link to follow that leads to a live page before too long
+	 * (before passing by parent's rightmost child), or we will find the end
+	 * of the entire level instead (possible when parent page is itself the
+	 * rightmost on its level).
+	 */
+	targetnext = opaque->btpo_next;
+	for (;;)
+	{
+		CHECK_FOR_INTERRUPTS();
+
+		rightpage = palloc_btree_page(state, targetnext);
+		opaque = (BTPageOpaque) PageGetSpecialPointer(rightpage);
+
+		if (!P_IGNORE(opaque) || P_RIGHTMOST(opaque))
+			break;
+
+		/* We landed on a deleted page, so step right to find a live page */
+		targetnext = opaque->btpo_next;
+		ereport(DEBUG1,
+				(errcode(ERRCODE_NO_DATA),
+				 errmsg("level %u leftmost page of index \"%s\" was found deleted or half dead",
+					opaque->btpo.level, RelationGetRelationName(state->rel)),
+				 errdetail_internal("Deleted page found when building scankey from right sibling.")));
+
+		/* Be slightly more pro-active in freeing this memory, just in case */
+		pfree(rightpage);
+	}
+
+	/*
+	 * No ExclusiveLock held case -- why it's safe to proceed.
+	 *
+	 * Problem:
+	 *
+	 * We must avoid false positive reports of corruption when caller treats
+	 * item returned here as an upper bound on target's last item.  In
+	 * general, false positives are disallowed.  Avoiding them here when
+	 * caller is !exclusivelylocked is subtle.
+	 *
+	 * A concurrent page deletion by VACUUM of the target page can result in
+	 * the insertion of items on to this right sibling page that would
+	 * previously have been inserted on our target page.  There might have
+	 * been insertions that followed the target's downlink after it was made
+	 * to point to right sibling instead of target by page deletion's first
+	 * phase. The inserters insert items that would belong on target page.
+	 * This race is very tight, but it's possible.  This is our only problem.
+	 *
+	 * Non-problems:
+	 *
+	 * We are not hindered by a concurrent page split of the target; we'll
+	 * never land on the second half of the page anyway.  A concurrent split
+	 * of the right page will also not matter, because the first data item
+	 * remains the same within the left half, which we'll reliably land on. If
+	 * we had to skip over ignorable/deleted pages, it cannot matter because
+	 * their key space has already been atomically merged with the first
+	 * non-ignorable page we eventually find (doesn't matter whether the page
+	 * we eventually find is a true sibling or a cousin of target, which we go
+	 * into below).
+	 *
+	 * Solution:
+	 *
+	 * Caller knows that it should reverify that target is not ignorable
+	 * (half-dead or deleted) when cross-page sibling item comparison appears
+	 * to indicate corruption (invariant fails).  This detects the single race
+	 * condition that exists for caller.  This is correct because the
+	 * continued existence of target block as non-ignorable (not half-dead or
+	 * deleted) implies that target page was not merged into from the right by
+	 * deletion; the key space at or after target never moved left.  Target's
+	 * parent either has the same downlink to target as before, or a <=
+	 * downlink due to deletion at the left of target.  Target either has the
+	 * same highkey as before, or a highkey <= before when there is a page
+	 * split. (The rightmost concurrently-split-from-target-page page will
+	 * still have the same highkey as target was originally found to have,
+	 * which for our purposes is equivalent to target's highkey itself never
+	 * changing, since we reliably skip over
+	 * concurrently-split-from-target-page pages.)
+	 *
+	 * In simpler terms, we allow that the key space of the target may expand
+	 * left (the key space can move left on the left side of target only), but
+	 * the target key space cannot expand right and get ahead of us without
+	 * our detecting it.  The key space of the target cannot shrink, unless it
+	 * shrinks to zero due to the deletion of the original page, our canary
+	 * condition.  (To be very precise, we're a bit stricter than that because
+	 * it might just have been that the target page split and only the
+	 * original target page was deleted.  We can be more strict, just not more
+	 * lax.)
+	 *
+	 * Top level tree walk caller moves on to next page (makes it the new
+	 * target) following recovery from this race.  (cf.  The rationale for
+	 * child/downlink verification needing an ExclusiveLock within
+	 * bt_downlink_check(), where page deletion is also the main source of
+	 * trouble.)
+	 *
+	 * Note that it doesn't matter if right sibling page here is actually a
+	 * cousin page, because in order for the key space to be readjusted in a
+	 * way that causes us issues in next level up (guiding problematic
+	 * concurrent insertions to the cousin from the grandparent rather than to
+	 * the sibling from the parent), there'd have to be page deletion of
+	 * target's parent page (affecting target's parent's downlink in target's
+	 * grandparent page).  Internal page deletion only occurs when there are
+	 * no child pages (they were all fully deleted), and caller is checking
+	 * that the target's parent has at least one non-deleted (so
+	 * non-ignorable) child: the target page.  (Note that the first phase of
+	 * deletion atomically marks the page to be deleted half-dead/ignorable at
+	 * the same time downlink in its parent is removed, so caller will
+	 * definitely not fail to detect that this happened.)
+	 *
+	 * This trick is inspired by the method backward scans use for dealing
+	 * with concurrent page splits; concurrent page deletion is a problem that
+	 * similarly receives special consideration sometimes (it's possible that
+	 * the backwards scan will re-read its "original" block after failing to
+	 * find a right-link to it, having already moved in the opposite direction
+	 * (right/"forwards") a few times to try to locate one).  Just like us,
+	 * that happens only to determine if there was a concurrent page deletion
+	 * of a reference page, and just like us if there was a page deletion of
+	 * that reference page it means we can move on from caring about the
+	 * reference page.  See the nbtree README for a full description of how
+	 * that works.
+	 */
+	nline = PageGetMaxOffsetNumber(rightpage);
+
+	/*
+	 * Get first data item, if any
+	 */
+	if (P_ISLEAF(opaque) && nline >= P_FIRSTDATAKEY(opaque))
+	{
+		/* Return first data item (if any) */
+		rightitem = PageGetItemId(rightpage, P_FIRSTDATAKEY(opaque));
+	}
+	else if (!P_ISLEAF(opaque) &&
+			 nline >= OffsetNumberNext(P_FIRSTDATAKEY(opaque)))
+	{
+		/*
+		 * Return first item after the internal page's "negative infinity"
+		 * item
+		 */
+		rightitem = PageGetItemId(rightpage,
+								  OffsetNumberNext(P_FIRSTDATAKEY(opaque)));
+	}
+	else
+	{
+		/*
+		 * No first item.  Page is probably empty leaf page, but it's also
+		 * possible that it's an internal page with only a negative infinity
+		 * item.
+		 */
+		ereport(DEBUG1,
+				(errcode(ERRCODE_NO_DATA),
+				 errmsg("%s block %u of index \"%s\" has no first data item",
+						P_ISLEAF(opaque) ? "leaf" : "internal", targetnext,
+						RelationGetRelationName(state->rel))));
+		return NULL;
+	}
+
+	/*
+	 * Return first real item scankey.  Note that this relies on right page
+	 * memory remaining allocated.
+	 */
+	return _bt_mkscankey(state->rel,
+						 (IndexTuple) PageGetItem(rightpage, rightitem));
+}
+
+/*
+ * Checks one of target's downlink against its child page.
+ *
+ * Conceptually, the target page continues to be what is checked here.  The
+ * target block is still blamed in the event of finding an invariant violation.
+ * The downlink insertion into the target is probably where any problem raised
+ * here arises, and there is no such thing as a parent link, so doing the
+ * verification this way around is much more practical.
+ */
+static void
+bt_downlink_check(BtreeCheckState *state, BlockNumber childblock,
+				  ScanKey targetkey)
+{
+	OffsetNumber offset;
+	OffsetNumber maxoffset;
+	Page		child;
+	BTPageOpaque copaque;
+
+	/*
+	 * Caller must have ExclusiveLock on target relation, because of
+	 * considerations around page deletion by VACUUM.
+	 *
+	 * NB: In general, page deletion deletes the right sibling's downlink, not
+	 * the downlink of the page being deleted; the deleted page's downlink is
+	 * reused for its sibling.  The key space is thereby consolidated between
+	 * the deleted page and its right sibling.  (We cannot delete a parent
+	 * page's rightmost child unless it is the last child page, and we intend
+	 * to also delete the parent itself.)
+	 *
+	 * If this verification happened without an ExclusiveLock, the following
+	 * race condition could cause false positives:
+	 *
+	 * In general, concurrent page deletion might occur, including deletion of
+	 * the left sibling of the child page that is examined here.  If such a
+	 * page deletion were to occur, closely followed by an insertion into the
+	 * newly expanded key space of the child, a window for the false positive
+	 * opens up: the stale parent/target downlink originally followed to get
+	 * to the child legitimately ceases to be a lower bound on all items in
+	 * the page, since the key space was concurrently expanded "left".
+	 * (Insertion followed the "new" downlink for the child, not our now-stale
+	 * downlink, which was concurrently physically removed in target/parent as
+	 * part of deletion's first phase.)
+	 *
+	 * Note that while the cross-page-same-level last item check uses a trick
+	 * that allows it to perform verification for !exclusivelylocked callers,
+	 * a similar trick seems difficult here.  The trick that that other check
+	 * uses is, in essence, to lock down race conditions to those that occur
+	 * due to concurrent page deletion of the target; that's a race that can
+	 * be reliably detected before actually reporting corruption.
+	 *
+	 * On the other hand, we'd need to lock down race conditions involving
+	 * deletion of child's left page, for long enough to read the child page
+	 * into memory (in other words, a scheme with concurrently held buffer
+	 * locks on both child and left-of-child pages).  That's unacceptable for
+	 * amcheck functions on general principle, though.
+	 */
+	Assert(state->exclusivelylocked);
+
+	/*
+	 * Verify child page has the downlink key from target page (its parent) as
+	 * a lower bound.
+	 *
+	 * Check all items, rather than checking just the first and trusting that
+	 * the operator class obeys the transitive law.
+	 */
+	child = palloc_btree_page(state, childblock);
+	copaque = (BTPageOpaque) PageGetSpecialPointer(child);
+	maxoffset = PageGetMaxOffsetNumber(child);
+
+	for (offset = P_FIRSTDATAKEY(copaque);
+		 offset <= maxoffset;
+		 offset = OffsetNumberNext(offset))
+	{
+		/*
+		 * Skip comparison of target page key against "negative infinity"
+		 * item, if any.  Checking it would indicate that it's not an upper
+		 * bound, but that's only because of the hard-coding within
+		 * _bt_compare().
+		 */
+		if (offset_is_negative_infinity(copaque, offset))
+			continue;
+
+		if (!invariant_leq_nontarget_offset(state, child,
+											targetkey, offset))
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("down-link lower bound invariant violated for index \"%s\"",
+							RelationGetRelationName(state->rel)),
+					 errdetail_internal("Parent block=%u child index tid=(%u,%u) parent page lsn=%X/%X.",
+									  state->targetblock, childblock, offset,
+										(uint32) (state->targetlsn >> 32),
+										(uint32) state->targetlsn)));
+	}
+
+	pfree(child);
+}
+
+/*
+ * Is particular offset within page (whose special state is passed by caller)
+ * the page negative-infinity item?
+ *
+ * As noted in comments above _bt_compare(), there is special handling of the
+ * first data item as a "negative infinity" item.  The hard-coding within
+ * _bt_compare() makes comparing this item for the purposes of verification
+ * pointless at best, since the IndexTuple only contains a valid TID (a
+ * reference TID to child page).
+ */
+static inline bool
+offset_is_negative_infinity(BTPageOpaque opaque, OffsetNumber offset)
+{
+	/*
+	 * For internal pages only, the first item after high key, if any, is
+	 * negative infinity item.  Internal pages always have a negative infinity
+	 * item, whereas leaf pages never have one.  This implies that negative
+	 * infinity item is either first or second line item, or there is none
+	 * within page.
+	 *
+	 * Right-most pages don't have a high key, but could be said to
+	 * conceptually have a "positive infinity" high key.  Thus, there is a
+	 * symmetry between down link items in parent pages, and high keys in
+	 * children.  Together, they represent the part of the key space that
+	 * belongs to each page in the index.  For example, all children of the
+	 * root page will have negative infinity as a lower bound from root
+	 * negative infinity downlink, and positive infinity as an upper bound
+	 * (implicitly, from "imaginary" positive infinity high key in root).
+	 */
+	return !P_ISLEAF(opaque) && offset == P_FIRSTDATAKEY(opaque);
+}
+
+/*
+ * Does the invariant hold that the key is less than or equal to a given upper
+ * bound offset item?
+ *
+ * If this function returns false, convention is that caller throws error due
+ * to corruption.
+ */
+static inline bool
+invariant_leq_offset(BtreeCheckState *state, ScanKey key,
+					 OffsetNumber upperbound)
+{
+	int16		natts = state->rel->rd_rel->relnatts;
+	int32		cmp;
+
+	cmp = _bt_compare(state->rel, natts, key, state->target, upperbound);
+
+	return cmp <= 0;
+}
+
+/*
+ * Does the invariant hold that the key is greater than or equal to a given
+ * lower bound offset item?
+ *
+ * If this function returns false, convention is that caller throws error due
+ * to corruption.
+ */
+static inline bool
+invariant_geq_offset(BtreeCheckState *state, ScanKey key,
+					 OffsetNumber lowerbound)
+{
+	int16		natts = state->rel->rd_rel->relnatts;
+	int32		cmp;
+
+	cmp = _bt_compare(state->rel, natts, key, state->target, lowerbound);
+
+	return cmp >= 0;
+}
+
+/*
+ * Does the invariant hold that the key is less than or equal to a given upper
+ * bound offset item, with the offset relating to a caller-supplied page that
+ * is not the current target page? Caller's non-target page is typically a
+ * child page of the target, checked as part of checking a property of the
+ * target page (i.e. the key comes from the target).
+ *
+ * If this function returns false, convention is that caller throws error due
+ * to corruption.
+ */
+static inline bool
+invariant_leq_nontarget_offset(BtreeCheckState *state,
+							   Page nontarget, ScanKey key,
+							   OffsetNumber upperbound)
+{
+	int16		natts = state->rel->rd_rel->relnatts;
+	int32		cmp;
+
+	cmp = _bt_compare(state->rel, natts, key, nontarget, upperbound);
+
+	return cmp <= 0;
+}
+
+/*
+ * Given a block number of a B-Tree page, return page in palloc()'d memory.
+ * While at it, perform some basic checks of the page.
+ *
+ * There is never an attempt to get a consistent view of multiple pages using
+ * multiple concurrent buffer locks; in general, we only acquire a single pin
+ * and buffer lock at a time, which is often all that the nbtree code requires.
+ *
+ * Operating on a copy of the page is useful because it prevents control
+ * getting stuck in an uninterruptible state when an underlying operator class
+ * misbehaves.
+ */
+static Page
+palloc_btree_page(BtreeCheckState *state, BlockNumber blocknum)
+{
+	Buffer		buffer;
+	Page		page;
+	BTPageOpaque opaque;
+
+	page = palloc(BLCKSZ);
+
+	/*
+	 * We copy the page into local storage to avoid holding pin on the buffer
+	 * longer than we must.
+	 */
+	buffer = ReadBufferExtended(state->rel, MAIN_FORKNUM, blocknum, RBM_NORMAL,
+								state->checkstrategy);
+	LockBuffer(buffer, BT_READ);
+
+	/*
+	 * Perform the same basic sanity checking that nbtree itself performs for
+	 * every page:
+	 */
+	_bt_checkpage(state->rel, buffer);
+
+	/* Only use copy of page in palloc()'d memory */
+	memcpy(page, BufferGetPage(buffer), BLCKSZ);
+	UnlockReleaseBuffer(buffer);
+
+	opaque = (BTPageOpaque) PageGetSpecialPointer(page);
+
+	if (opaque->btpo_flags & BTP_META && blocknum != BTREE_METAPAGE)
+		ereport(ERROR,
+				(errcode(ERRCODE_INDEX_CORRUPTED),
+				 errmsg("invalid meta page found at block %u in index \"%s\"",
+						blocknum, RelationGetRelationName(state->rel))));
+
+	/* Check page from block that ought to be meta page */
+	if (blocknum == BTREE_METAPAGE)
+	{
+		BTMetaPageData *metad = BTPageGetMeta(page);
+
+		if (!(opaque->btpo_flags & BTP_META) ||
+			metad->btm_magic != BTREE_MAGIC)
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("index \"%s\" meta page is corrupt",
+							RelationGetRelationName(state->rel))));
+
+		if (metad->btm_version != BTREE_VERSION)
+			ereport(ERROR,
+					(errcode(ERRCODE_INDEX_CORRUPTED),
+					 errmsg("version mismatch in index \"%s\": file version %d, code version %d",
+							RelationGetRelationName(state->rel),
+							metad->btm_version, BTREE_VERSION)));
+	}
+
+	/*
+	 * Deleted pages have no sane "level" field, so can only check non-deleted
+	 * page level
+	 */
+	if (P_ISLEAF(opaque) && !P_ISDELETED(opaque) && opaque->btpo.level != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_INDEX_CORRUPTED),
+			errmsg("invalid leaf page level %u for block %u in index \"%s\"",
+		opaque->btpo.level, blocknum, RelationGetRelationName(state->rel))));
+
+	if (blocknum != BTREE_METAPAGE && !P_ISLEAF(opaque) &&
+		!P_ISDELETED(opaque) && opaque->btpo.level == 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_INDEX_CORRUPTED),
+		 errmsg("invalid internal page level 0 for block %u in index \"%s\"",
+				opaque->btpo.level, RelationGetRelationName(state->rel))));
+
+	if (!P_ISLEAF(opaque) && P_HAS_GARBAGE(opaque))
+		ereport(ERROR,
+				(errcode(ERRCODE_INDEX_CORRUPTED),
+		   errmsg("internal page block %u in index \"%s\" has garbage items",
+				  blocknum, RelationGetRelationName(state->rel))));
+
+	return page;
+}