/*-------------------------------------------------------------------------
 *
 * nbtutils.c
 *	  Utility code for Postgres btree implementation.
 *
 * Portions Copyright (c) 1996-2014, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  src/backend/access/nbtree/nbtutils.c
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#include <time.h>

#include "access/nbtree.h"
#include "access/reloptions.h"
#include "access/relscan.h"
#include "miscadmin.h"
#include "utils/array.h"
#include "utils/lsyscache.h"
#include "utils/memutils.h"
#include "utils/rel.h"


typedef struct BTSortArrayContext
{
	FmgrInfo	flinfo;
	Oid			collation;
	bool		reverse;
} BTSortArrayContext;

static Datum _bt_find_extreme_element(IndexScanDesc scan, ScanKey skey,
						 StrategyNumber strat,
						 Datum *elems, int nelems);
static int _bt_sort_array_elements(IndexScanDesc scan, ScanKey skey,
						bool reverse,
						Datum *elems, int nelems);
static int	_bt_compare_array_elements(const void *a, const void *b, void *arg);
static bool _bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
						 ScanKey leftarg, ScanKey rightarg,
						 bool *result);
static bool _bt_fix_scankey_strategy(ScanKey skey, int16 *indoption);
static void _bt_mark_scankey_required(ScanKey skey);
static bool _bt_check_rowcompare(ScanKey skey,
					 IndexTuple tuple, TupleDesc tupdesc,
					 ScanDirection dir, bool *continuescan);


/*
 * _bt_mkscankey
 *		Build an insertion scan key that contains comparison data from itup
 *		as well as comparator routines appropriate to the key datatypes.
 *
 *		The result is intended for use with _bt_compare().
 */
ScanKey
_bt_mkscankey(Relation rel, IndexTuple itup)
{
	ScanKey		skey;
	TupleDesc	itupdesc;
	int			natts;
	int16	   *indoption;
	int			i;

	itupdesc = RelationGetDescr(rel);
	natts = RelationGetNumberOfAttributes(rel);
	indoption = rel->rd_indoption;

	skey = (ScanKey) palloc(natts * sizeof(ScanKeyData));

	for (i = 0; i < natts; i++)
	{
		FmgrInfo   *procinfo;
		Datum		arg;
		bool		null;
		int			flags;

		/*
		 * We can use the cached (default) support procs since no cross-type
		 * comparison can be needed.
		 */
		procinfo = index_getprocinfo(rel, i + 1, BTORDER_PROC);
		arg = index_getattr(itup, i + 1, itupdesc, &null);
		flags = (null ? SK_ISNULL : 0) | (indoption[i] << SK_BT_INDOPTION_SHIFT);
		ScanKeyEntryInitializeWithInfo(&skey[i],
									   flags,
									   (AttrNumber) (i + 1),
									   InvalidStrategy,
									   InvalidOid,
									   rel->rd_indcollation[i],
									   procinfo,
									   arg);
	}

	return skey;
}

/*
 * _bt_mkscankey_nodata
 *		Build an insertion scan key that contains 3-way comparator routines
 *		appropriate to the key datatypes, but no comparison data.  The
 *		comparison data ultimately used must match the key datatypes.
 *
 *		The result cannot be used with _bt_compare(), unless comparison
 *		data is first stored into the key entries.  Currently this
 *		routine is only called by nbtsort.c and tuplesort.c, which have
 *		their own comparison routines.
 */
ScanKey
_bt_mkscankey_nodata(Relation rel)
{
	ScanKey		skey;
	int			natts;
	int16	   *indoption;
	int			i;

	natts = RelationGetNumberOfAttributes(rel);
	indoption = rel->rd_indoption;

	skey = (ScanKey) palloc(natts * sizeof(ScanKeyData));

	for (i = 0; i < natts; i++)
	{
		FmgrInfo   *procinfo;
		int			flags;

		/*
		 * We can use the cached (default) support procs since no cross-type
		 * comparison can be needed.
		 */
		procinfo = index_getprocinfo(rel, i + 1, BTORDER_PROC);
		flags = SK_ISNULL | (indoption[i] << SK_BT_INDOPTION_SHIFT);
		ScanKeyEntryInitializeWithInfo(&skey[i],
									   flags,
									   (AttrNumber) (i + 1),
									   InvalidStrategy,
									   InvalidOid,
									   rel->rd_indcollation[i],
									   procinfo,
									   (Datum) 0);
	}

	return skey;
}

/*
 * free a scan key made by either _bt_mkscankey or _bt_mkscankey_nodata.
 */
void
_bt_freeskey(ScanKey skey)
{
	pfree(skey);
}

/*
 * free a retracement stack made by _bt_search.
 */
void
_bt_freestack(BTStack stack)
{
	BTStack		ostack;

	while (stack != NULL)
	{
		ostack = stack;
		stack = stack->bts_parent;
		pfree(ostack);
	}
}


/*
 *	_bt_preprocess_array_keys() -- Preprocess SK_SEARCHARRAY scan keys
 *
 * If there are any SK_SEARCHARRAY scan keys, deconstruct the array(s) and
 * set up BTArrayKeyInfo info for each one that is an equality-type key.
 * Prepare modified scan keys in so->arrayKeyData, which will hold the current
 * array elements during each primitive indexscan operation.  For inequality
 * array keys, it's sufficient to find the extreme element value and replace
 * the whole array with that scalar value.
 *
 * Note: the reason we need so->arrayKeyData, rather than just scribbling
 * on scan->keyData, is that callers are permitted to call btrescan without
 * supplying a new set of scankey data.
 */
void
_bt_preprocess_array_keys(IndexScanDesc scan)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	int			numberOfKeys = scan->numberOfKeys;
	int16	   *indoption = scan->indexRelation->rd_indoption;
	int			numArrayKeys;
	ScanKey		cur;
	int			i;
	MemoryContext oldContext;

	/* Quick check to see if there are any array keys */
	numArrayKeys = 0;
	for (i = 0; i < numberOfKeys; i++)
	{
		cur = &scan->keyData[i];
		if (cur->sk_flags & SK_SEARCHARRAY)
		{
			numArrayKeys++;
			Assert(!(cur->sk_flags & (SK_ROW_HEADER | SK_SEARCHNULL | SK_SEARCHNOTNULL)));
			/* If any arrays are null as a whole, we can quit right now. */
			if (cur->sk_flags & SK_ISNULL)
			{
				so->numArrayKeys = -1;
				so->arrayKeyData = NULL;
				return;
			}
		}
	}

	/* Quit if nothing to do. */
	if (numArrayKeys == 0)
	{
		so->numArrayKeys = 0;
		so->arrayKeyData = NULL;
		return;
	}

	/*
	 * Make a scan-lifespan context to hold array-associated data, or reset it
	 * if we already have one from a previous rescan cycle.
	 */
	if (so->arrayContext == NULL)
		so->arrayContext = AllocSetContextCreate(CurrentMemoryContext,
												 "BTree Array Context",
												 ALLOCSET_SMALL_MINSIZE,
												 ALLOCSET_SMALL_INITSIZE,
												 ALLOCSET_SMALL_MAXSIZE);
	else
		MemoryContextReset(so->arrayContext);

	oldContext = MemoryContextSwitchTo(so->arrayContext);

	/* Create modifiable copy of scan->keyData in the workspace context */
	so->arrayKeyData = (ScanKey) palloc(scan->numberOfKeys * sizeof(ScanKeyData));
	memcpy(so->arrayKeyData,
		   scan->keyData,
		   scan->numberOfKeys * sizeof(ScanKeyData));

	/* Allocate space for per-array data in the workspace context */
	so->arrayKeys = (BTArrayKeyInfo *) palloc0(numArrayKeys * sizeof(BTArrayKeyInfo));

	/* Now process each array key */
	numArrayKeys = 0;
	for (i = 0; i < numberOfKeys; i++)
	{
		ArrayType  *arrayval;
		int16		elmlen;
		bool		elmbyval;
		char		elmalign;
		int			num_elems;
		Datum	   *elem_values;
		bool	   *elem_nulls;
		int			num_nonnulls;
		int			j;

		cur = &so->arrayKeyData[i];
		if (!(cur->sk_flags & SK_SEARCHARRAY))
			continue;

		/*
		 * First, deconstruct the array into elements.  Anything allocated
		 * here (including a possibly detoasted array value) is in the
		 * workspace context.
		 */
		arrayval = DatumGetArrayTypeP(cur->sk_argument);
		/* We could cache this data, but not clear it's worth it */
		get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
							 &elmlen, &elmbyval, &elmalign);
		deconstruct_array(arrayval,
						  ARR_ELEMTYPE(arrayval),
						  elmlen, elmbyval, elmalign,
						  &elem_values, &elem_nulls, &num_elems);

		/*
		 * Compress out any null elements.  We can ignore them since we assume
		 * all btree operators are strict.
		 */
		num_nonnulls = 0;
		for (j = 0; j < num_elems; j++)
		{
			if (!elem_nulls[j])
				elem_values[num_nonnulls++] = elem_values[j];
		}

		/* We could pfree(elem_nulls) now, but not worth the cycles */

		/* If there's no non-nulls, the scan qual is unsatisfiable */
		if (num_nonnulls == 0)
		{
			numArrayKeys = -1;
			break;
		}

		/*
		 * If the comparison operator is not equality, then the array qual
		 * degenerates to a simple comparison against the smallest or largest
		 * non-null array element, as appropriate.
		 */
		switch (cur->sk_strategy)
		{
			case BTLessStrategyNumber:
			case BTLessEqualStrategyNumber:
				cur->sk_argument =
					_bt_find_extreme_element(scan, cur,
											 BTGreaterStrategyNumber,
											 elem_values, num_nonnulls);
				continue;
			case BTEqualStrategyNumber:
				/* proceed with rest of loop */
				break;
			case BTGreaterEqualStrategyNumber:
			case BTGreaterStrategyNumber:
				cur->sk_argument =
					_bt_find_extreme_element(scan, cur,
											 BTLessStrategyNumber,
											 elem_values, num_nonnulls);
				continue;
			default:
				elog(ERROR, "unrecognized StrategyNumber: %d",
					 (int) cur->sk_strategy);
				break;
		}

		/*
		 * Sort the non-null elements and eliminate any duplicates.  We must
		 * sort in the same ordering used by the index column, so that the
		 * successive primitive indexscans produce data in index order.
		 */
		num_elems = _bt_sort_array_elements(scan, cur,
						(indoption[cur->sk_attno - 1] & INDOPTION_DESC) != 0,
											elem_values, num_nonnulls);

		/*
		 * And set up the BTArrayKeyInfo data.
		 */
		so->arrayKeys[numArrayKeys].scan_key = i;
		so->arrayKeys[numArrayKeys].num_elems = num_elems;
		so->arrayKeys[numArrayKeys].elem_values = elem_values;
		numArrayKeys++;
	}

	so->numArrayKeys = numArrayKeys;

	MemoryContextSwitchTo(oldContext);
}

/*
 * _bt_find_extreme_element() -- get least or greatest array element
 *
 * scan and skey identify the index column, whose opfamily determines the
 * comparison semantics.  strat should be BTLessStrategyNumber to get the
 * least element, or BTGreaterStrategyNumber to get the greatest.
 */
static Datum
_bt_find_extreme_element(IndexScanDesc scan, ScanKey skey,
						 StrategyNumber strat,
						 Datum *elems, int nelems)
{
	Relation	rel = scan->indexRelation;
	Oid			elemtype,
				cmp_op;
	RegProcedure cmp_proc;
	FmgrInfo	flinfo;
	Datum		result;
	int			i;

	/*
	 * Determine the nominal datatype of the array elements.  We have to
	 * support the convention that sk_subtype == InvalidOid means the opclass
	 * input type; this is a hack to simplify life for ScanKeyInit().
	 */
	elemtype = skey->sk_subtype;
	if (elemtype == InvalidOid)
		elemtype = rel->rd_opcintype[skey->sk_attno - 1];

	/*
	 * Look up the appropriate comparison operator in the opfamily.
	 *
	 * Note: it's possible that this would fail, if the opfamily is
	 * incomplete, but it seems quite unlikely that an opfamily would omit
	 * non-cross-type comparison operators for any datatype that it supports
	 * at all.
	 */
	cmp_op = get_opfamily_member(rel->rd_opfamily[skey->sk_attno - 1],
								 elemtype,
								 elemtype,
								 strat);
	if (!OidIsValid(cmp_op))
		elog(ERROR, "missing operator %d(%u,%u) in opfamily %u",
			 strat, elemtype, elemtype,
			 rel->rd_opfamily[skey->sk_attno - 1]);
	cmp_proc = get_opcode(cmp_op);
	if (!RegProcedureIsValid(cmp_proc))
		elog(ERROR, "missing oprcode for operator %u", cmp_op);

	fmgr_info(cmp_proc, &flinfo);

	Assert(nelems > 0);
	result = elems[0];
	for (i = 1; i < nelems; i++)
	{
		if (DatumGetBool(FunctionCall2Coll(&flinfo,
										   skey->sk_collation,
										   elems[i],
										   result)))
			result = elems[i];
	}

	return result;
}

/*
 * _bt_sort_array_elements() -- sort and de-dup array elements
 *
 * The array elements are sorted in-place, and the new number of elements
 * after duplicate removal is returned.
 *
 * scan and skey identify the index column, whose opfamily determines the
 * comparison semantics.  If reverse is true, we sort in descending order.
 */
static int
_bt_sort_array_elements(IndexScanDesc scan, ScanKey skey,
						bool reverse,
						Datum *elems, int nelems)
{
	Relation	rel = scan->indexRelation;
	Oid			elemtype;
	RegProcedure cmp_proc;
	BTSortArrayContext cxt;
	int			last_non_dup;
	int			i;

	if (nelems <= 1)
		return nelems;			/* no work to do */

	/*
	 * Determine the nominal datatype of the array elements.  We have to
	 * support the convention that sk_subtype == InvalidOid means the opclass
	 * input type; this is a hack to simplify life for ScanKeyInit().
	 */
	elemtype = skey->sk_subtype;
	if (elemtype == InvalidOid)
		elemtype = rel->rd_opcintype[skey->sk_attno - 1];

	/*
	 * Look up the appropriate comparison function in the opfamily.
	 *
	 * Note: it's possible that this would fail, if the opfamily is
	 * incomplete, but it seems quite unlikely that an opfamily would omit
	 * non-cross-type support functions for any datatype that it supports at
	 * all.
	 */
	cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
								 elemtype,
								 elemtype,
								 BTORDER_PROC);
	if (!RegProcedureIsValid(cmp_proc))
		elog(ERROR, "missing support function %d(%u,%u) in opfamily %u",
			 BTORDER_PROC, elemtype, elemtype,
			 rel->rd_opfamily[skey->sk_attno - 1]);

	/* Sort the array elements */
	fmgr_info(cmp_proc, &cxt.flinfo);
	cxt.collation = skey->sk_collation;
	cxt.reverse = reverse;
	qsort_arg((void *) elems, nelems, sizeof(Datum),
			  _bt_compare_array_elements, (void *) &cxt);

	/* Now scan the sorted elements and remove duplicates */
	last_non_dup = 0;
	for (i = 1; i < nelems; i++)
	{
		int32		compare;

		compare = DatumGetInt32(FunctionCall2Coll(&cxt.flinfo,
												  cxt.collation,
												  elems[last_non_dup],
												  elems[i]));
		if (compare != 0)
			elems[++last_non_dup] = elems[i];
	}

	return last_non_dup + 1;
}

/*
 * qsort_arg comparator for sorting array elements
 */
static int
_bt_compare_array_elements(const void *a, const void *b, void *arg)
{
	Datum		da = *((const Datum *) a);
	Datum		db = *((const Datum *) b);
	BTSortArrayContext *cxt = (BTSortArrayContext *) arg;
	int32		compare;

	compare = DatumGetInt32(FunctionCall2Coll(&cxt->flinfo,
											  cxt->collation,
											  da, db));
	if (cxt->reverse)
		compare = -compare;
	return compare;
}

/*
 * _bt_start_array_keys() -- Initialize array keys at start of a scan
 *
 * Set up the cur_elem counters and fill in the first sk_argument value for
 * each array scankey.  We can't do this until we know the scan direction.
 */
void
_bt_start_array_keys(IndexScanDesc scan, ScanDirection dir)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	int			i;

	for (i = 0; i < so->numArrayKeys; i++)
	{
		BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
		ScanKey		skey = &so->arrayKeyData[curArrayKey->scan_key];

		Assert(curArrayKey->num_elems > 0);
		if (ScanDirectionIsBackward(dir))
			curArrayKey->cur_elem = curArrayKey->num_elems - 1;
		else
			curArrayKey->cur_elem = 0;
		skey->sk_argument = curArrayKey->elem_values[curArrayKey->cur_elem];
	}
}

/*
 * _bt_advance_array_keys() -- Advance to next set of array elements
 *
 * Returns TRUE if there is another set of values to consider, FALSE if not.
 * On TRUE result, the scankeys are initialized with the next set of values.
 */
bool
_bt_advance_array_keys(IndexScanDesc scan, ScanDirection dir)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	bool		found = false;
	int			i;

	/*
	 * We must advance the last array key most quickly, since it will
	 * correspond to the lowest-order index column among the available
	 * qualifications. This is necessary to ensure correct ordering of output
	 * when there are multiple array keys.
	 */
	for (i = so->numArrayKeys - 1; i >= 0; i--)
	{
		BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
		ScanKey		skey = &so->arrayKeyData[curArrayKey->scan_key];
		int			cur_elem = curArrayKey->cur_elem;
		int			num_elems = curArrayKey->num_elems;

		if (ScanDirectionIsBackward(dir))
		{
			if (--cur_elem < 0)
			{
				cur_elem = num_elems - 1;
				found = false;	/* need to advance next array key */
			}
			else
				found = true;
		}
		else
		{
			if (++cur_elem >= num_elems)
			{
				cur_elem = 0;
				found = false;	/* need to advance next array key */
			}
			else
				found = true;
		}

		curArrayKey->cur_elem = cur_elem;
		skey->sk_argument = curArrayKey->elem_values[cur_elem];
		if (found)
			break;
	}

	return found;
}

/*
 * _bt_mark_array_keys() -- Handle array keys during btmarkpos
 *
 * Save the current state of the array keys as the "mark" position.
 */
void
_bt_mark_array_keys(IndexScanDesc scan)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	int			i;

	for (i = 0; i < so->numArrayKeys; i++)
	{
		BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];

		curArrayKey->mark_elem = curArrayKey->cur_elem;
	}
}

/*
 * _bt_restore_array_keys() -- Handle array keys during btrestrpos
 *
 * Restore the array keys to where they were when the mark was set.
 */
void
_bt_restore_array_keys(IndexScanDesc scan)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	bool		changed = false;
	int			i;

	/* Restore each array key to its position when the mark was set */
	for (i = 0; i < so->numArrayKeys; i++)
	{
		BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
		ScanKey		skey = &so->arrayKeyData[curArrayKey->scan_key];
		int			mark_elem = curArrayKey->mark_elem;

		if (curArrayKey->cur_elem != mark_elem)
		{
			curArrayKey->cur_elem = mark_elem;
			skey->sk_argument = curArrayKey->elem_values[mark_elem];
			changed = true;
		}
	}

	/*
	 * If we changed any keys, we must redo _bt_preprocess_keys.  That might
	 * sound like overkill, but in cases with multiple keys per index column
	 * it seems necessary to do the full set of pushups.
	 */
	if (changed)
	{
		_bt_preprocess_keys(scan);
		/* The mark should have been set on a consistent set of keys... */
		Assert(so->qual_ok);
	}
}


/*
 *	_bt_preprocess_keys() -- Preprocess scan keys
 *
 * The given search-type keys (in scan->keyData[] or so->arrayKeyData[])
 * are copied to so->keyData[] with possible transformation.
 * scan->numberOfKeys is the number of input keys, so->numberOfKeys gets
 * the number of output keys (possibly less, never greater).
 *
 * The output keys are marked with additional sk_flag bits beyond the
 * system-standard bits supplied by the caller.  The DESC and NULLS_FIRST
 * indoption bits for the relevant index attribute are copied into the flags.
 * Also, for a DESC column, we commute (flip) all the sk_strategy numbers
 * so that the index sorts in the desired direction.
 *
 * One key purpose of this routine is to discover which scan keys must be
 * satisfied to continue the scan.  It also attempts to eliminate redundant
 * keys and detect contradictory keys.  (If the index opfamily provides
 * incomplete sets of cross-type operators, we may fail to detect redundant
 * or contradictory keys, but we can survive that.)
 *
 * The output keys must be sorted by index attribute.  Presently we expect
 * (but verify) that the input keys are already so sorted --- this is done
 * by match_clauses_to_index() in indxpath.c.  Some reordering of the keys
 * within each attribute may be done as a byproduct of the processing here,
 * but no other code depends on that.
 *
 * The output keys are marked with flags SK_BT_REQFWD and/or SK_BT_REQBKWD
 * if they must be satisfied in order to continue the scan forward or backward
 * respectively.  _bt_checkkeys uses these flags.  For example, if the quals
 * are "x = 1 AND y < 4 AND z < 5", then _bt_checkkeys will reject a tuple
 * (1,2,7), but we must continue the scan in case there are tuples (1,3,z).
 * But once we reach tuples like (1,4,z) we can stop scanning because no
 * later tuples could match.  This is reflected by marking the x and y keys,
 * but not the z key, with SK_BT_REQFWD.  In general, the keys for leading
 * attributes with "=" keys are marked both SK_BT_REQFWD and SK_BT_REQBKWD.
 * For the first attribute without an "=" key, any "<" and "<=" keys are
 * marked SK_BT_REQFWD while any ">" and ">=" keys are marked SK_BT_REQBKWD.
 * This can be seen to be correct by considering the above example.  Note
 * in particular that if there are no keys for a given attribute, the keys for
 * subsequent attributes can never be required; for instance "WHERE y = 4"
 * requires a full-index scan.
 *
 * If possible, redundant keys are eliminated: we keep only the tightest
 * >/>= bound and the tightest </<= bound, and if there's an = key then
 * that's the only one returned.  (So, we return either a single = key,
 * or one or two boundary-condition keys for each attr.)  However, if we
 * cannot compare two keys for lack of a suitable cross-type operator,
 * we cannot eliminate either.  If there are two such keys of the same
 * operator strategy, the second one is just pushed into the output array
 * without further processing here.  We may also emit both >/>= or both
 * </<= keys if we can't compare them.  The logic about required keys still
 * works if we don't eliminate redundant keys.
 *
 * Note that one reason we need direction-sensitive required-key flags is
 * precisely that we may not be able to eliminate redundant keys.  Suppose
 * we have "x > 4::int AND x > 10::bigint", and we are unable to determine
 * which key is more restrictive for lack of a suitable cross-type operator.
 * _bt_first will arbitrarily pick one of the keys to do the initial
 * positioning with.  If it picks x > 4, then the x > 10 condition will fail
 * until we reach index entries > 10; but we can't stop the scan just because
 * x > 10 is failing.  On the other hand, if we are scanning backwards, then
 * failure of either key is indeed enough to stop the scan.  (In general, when
 * inequality keys are present, the initial-positioning code only promises to
 * position before the first possible match, not exactly at the first match,
 * for a forward scan; or after the last match for a backward scan.)
 *
 * As a byproduct of this work, we can detect contradictory quals such
 * as "x = 1 AND x > 2".  If we see that, we return so->qual_ok = FALSE,
 * indicating the scan need not be run at all since no tuples can match.
 * (In this case we do not bother completing the output key array!)
 * Again, missing cross-type operators might cause us to fail to prove the
 * quals contradictory when they really are, but the scan will work correctly.
 *
 * Row comparison keys are currently also treated without any smarts:
 * we just transfer them into the preprocessed array without any
 * editorialization.  We can treat them the same as an ordinary inequality
 * comparison on the row's first index column, for the purposes of the logic
 * about required keys.
 *
 * Note: the reason we have to copy the preprocessed scan keys into private
 * storage is that we are modifying the array based on comparisons of the
 * key argument values, which could change on a rescan or after moving to
 * new elements of array keys.  Therefore we can't overwrite the source data.
 */
void
_bt_preprocess_keys(IndexScanDesc scan)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	int			numberOfKeys = scan->numberOfKeys;
	int16	   *indoption = scan->indexRelation->rd_indoption;
	int			new_numberOfKeys;
	int			numberOfEqualCols;
	ScanKey		inkeys;
	ScanKey		outkeys;
	ScanKey		cur;
	ScanKey		xform[BTMaxStrategyNumber];
	bool		test_result;
	int			i,
				j;
	AttrNumber	attno;

	/* initialize result variables */
	so->qual_ok = true;
	so->numberOfKeys = 0;

	if (numberOfKeys < 1)
		return;					/* done if qual-less scan */

	/*
	 * Read so->arrayKeyData if array keys are present, else scan->keyData
	 */
	if (so->arrayKeyData != NULL)
		inkeys = so->arrayKeyData;
	else
		inkeys = scan->keyData;

	outkeys = so->keyData;
	cur = &inkeys[0];
	/* we check that input keys are correctly ordered */
	if (cur->sk_attno < 1)
		elog(ERROR, "btree index keys must be ordered by attribute");

	/* We can short-circuit most of the work if there's just one key */
	if (numberOfKeys == 1)
	{
		/* Apply indoption to scankey (might change sk_strategy!) */
		if (!_bt_fix_scankey_strategy(cur, indoption))
			so->qual_ok = false;
		memcpy(outkeys, cur, sizeof(ScanKeyData));
		so->numberOfKeys = 1;
		/* We can mark the qual as required if it's for first index col */
		if (cur->sk_attno == 1)
			_bt_mark_scankey_required(outkeys);
		return;
	}

	/*
	 * Otherwise, do the full set of pushups.
	 */
	new_numberOfKeys = 0;
	numberOfEqualCols = 0;

	/*
	 * Initialize for processing of keys for attr 1.
	 *
	 * xform[i] points to the currently best scan key of strategy type i+1; it
	 * is NULL if we haven't yet found such a key for this attr.
	 */
	attno = 1;
	memset(xform, 0, sizeof(xform));

	/*
	 * Loop iterates from 0 to numberOfKeys inclusive; we use the last pass to
	 * handle after-last-key processing.  Actual exit from the loop is at the
	 * "break" statement below.
	 */
	for (i = 0;; cur++, i++)
	{
		if (i < numberOfKeys)
		{
			/* Apply indoption to scankey (might change sk_strategy!) */
			if (!_bt_fix_scankey_strategy(cur, indoption))
			{
				/* NULL can't be matched, so give up */
				so->qual_ok = false;
				return;
			}
		}

		/*
		 * If we are at the end of the keys for a particular attr, finish up
		 * processing and emit the cleaned-up keys.
		 */
		if (i == numberOfKeys || cur->sk_attno != attno)
		{
			int			priorNumberOfEqualCols = numberOfEqualCols;

			/* check input keys are correctly ordered */
			if (i < numberOfKeys && cur->sk_attno < attno)
				elog(ERROR, "btree index keys must be ordered by attribute");

			/*
			 * If = has been specified, all other keys can be eliminated as
			 * redundant.  If we have a case like key = 1 AND key > 2, we can
			 * set qual_ok to false and abandon further processing.
			 *
			 * We also have to deal with the case of "key IS NULL", which is
			 * unsatisfiable in combination with any other index condition. By
			 * the time we get here, that's been classified as an equality
			 * check, and we've rejected any combination of it with a regular
			 * equality condition; but not with other types of conditions.
			 */
			if (xform[BTEqualStrategyNumber - 1])
			{
				ScanKey		eq = xform[BTEqualStrategyNumber - 1];

				for (j = BTMaxStrategyNumber; --j >= 0;)
				{
					ScanKey		chk = xform[j];

					if (!chk || j == (BTEqualStrategyNumber - 1))
						continue;

					if (eq->sk_flags & SK_SEARCHNULL)
					{
						/* IS NULL is contradictory to anything else */
						so->qual_ok = false;
						return;
					}

					if (_bt_compare_scankey_args(scan, chk, eq, chk,
												 &test_result))
					{
						if (!test_result)
						{
							/* keys proven mutually contradictory */
							so->qual_ok = false;
							return;
						}
						/* else discard the redundant non-equality key */
						xform[j] = NULL;
					}
					/* else, cannot determine redundancy, keep both keys */
				}
				/* track number of attrs for which we have "=" keys */
				numberOfEqualCols++;
			}

			/* try to keep only one of <, <= */
			if (xform[BTLessStrategyNumber - 1]
				&& xform[BTLessEqualStrategyNumber - 1])
			{
				ScanKey		lt = xform[BTLessStrategyNumber - 1];
				ScanKey		le = xform[BTLessEqualStrategyNumber - 1];

				if (_bt_compare_scankey_args(scan, le, lt, le,
											 &test_result))
				{
					if (test_result)
						xform[BTLessEqualStrategyNumber - 1] = NULL;
					else
						xform[BTLessStrategyNumber - 1] = NULL;
				}
			}

			/* try to keep only one of >, >= */
			if (xform[BTGreaterStrategyNumber - 1]
				&& xform[BTGreaterEqualStrategyNumber - 1])
			{
				ScanKey		gt = xform[BTGreaterStrategyNumber - 1];
				ScanKey		ge = xform[BTGreaterEqualStrategyNumber - 1];

				if (_bt_compare_scankey_args(scan, ge, gt, ge,
											 &test_result))
				{
					if (test_result)
						xform[BTGreaterEqualStrategyNumber - 1] = NULL;
					else
						xform[BTGreaterStrategyNumber - 1] = NULL;
				}
			}

			/*
			 * Emit the cleaned-up keys into the outkeys[] array, and then
			 * mark them if they are required.  They are required (possibly
			 * only in one direction) if all attrs before this one had "=".
			 */
			for (j = BTMaxStrategyNumber; --j >= 0;)
			{
				if (xform[j])
				{
					ScanKey		outkey = &outkeys[new_numberOfKeys++];

					memcpy(outkey, xform[j], sizeof(ScanKeyData));
					if (priorNumberOfEqualCols == attno - 1)
						_bt_mark_scankey_required(outkey);
				}
			}

			/*
			 * Exit loop here if done.
			 */
			if (i == numberOfKeys)
				break;

			/* Re-initialize for new attno */
			attno = cur->sk_attno;
			memset(xform, 0, sizeof(xform));
		}

		/* check strategy this key's operator corresponds to */
		j = cur->sk_strategy - 1;

		/* if row comparison, push it directly to the output array */
		if (cur->sk_flags & SK_ROW_HEADER)
		{
			ScanKey		outkey = &outkeys[new_numberOfKeys++];

			memcpy(outkey, cur, sizeof(ScanKeyData));
			if (numberOfEqualCols == attno - 1)
				_bt_mark_scankey_required(outkey);

			/*
			 * We don't support RowCompare using equality; such a qual would
			 * mess up the numberOfEqualCols tracking.
			 */
			Assert(j != (BTEqualStrategyNumber - 1));
			continue;
		}

		/* have we seen one of these before? */
		if (xform[j] == NULL)
		{
			/* nope, so remember this scankey */
			xform[j] = cur;
		}
		else
		{
			/* yup, keep only the more restrictive key */
			if (_bt_compare_scankey_args(scan, cur, cur, xform[j],
										 &test_result))
			{
				if (test_result)
					xform[j] = cur;
				else if (j == (BTEqualStrategyNumber - 1))
				{
					/* key == a && key == b, but a != b */
					so->qual_ok = false;
					return;
				}
				/* else old key is more restrictive, keep it */
			}
			else
			{
				/*
				 * We can't determine which key is more restrictive.  Keep the
				 * previous one in xform[j] and push this one directly to the
				 * output array.
				 */
				ScanKey		outkey = &outkeys[new_numberOfKeys++];

				memcpy(outkey, cur, sizeof(ScanKeyData));
				if (numberOfEqualCols == attno - 1)
					_bt_mark_scankey_required(outkey);
			}
		}
	}

	so->numberOfKeys = new_numberOfKeys;
}

/*
 * Compare two scankey values using a specified operator.
 *
 * The test we want to perform is logically "leftarg op rightarg", where
 * leftarg and rightarg are the sk_argument values in those ScanKeys, and
 * the comparison operator is the one in the op ScanKey.  However, in
 * cross-data-type situations we may need to look up the correct operator in
 * the index's opfamily: it is the one having amopstrategy = op->sk_strategy
 * and amoplefttype/amoprighttype equal to the two argument datatypes.
 *
 * If the opfamily doesn't supply a complete set of cross-type operators we
 * may not be able to make the comparison.  If we can make the comparison
 * we store the operator result in *result and return TRUE.  We return FALSE
 * if the comparison could not be made.
 *
 * Note: op always points at the same ScanKey as either leftarg or rightarg.
 * Since we don't scribble on the scankeys, this aliasing should cause no
 * trouble.
 *
 * Note: this routine needs to be insensitive to any DESC option applied
 * to the index column.  For example, "x < 4" is a tighter constraint than
 * "x < 5" regardless of which way the index is sorted.
 */
static bool
_bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
						 ScanKey leftarg, ScanKey rightarg,
						 bool *result)
{
	Relation	rel = scan->indexRelation;
	Oid			lefttype,
				righttype,
				optype,
				opcintype,
				cmp_op;
	StrategyNumber strat;

	/*
	 * First, deal with cases where one or both args are NULL.  This should
	 * only happen when the scankeys represent IS NULL/NOT NULL conditions.
	 */
	if ((leftarg->sk_flags | rightarg->sk_flags) & SK_ISNULL)
	{
		bool		leftnull,
					rightnull;

		if (leftarg->sk_flags & SK_ISNULL)
		{
			Assert(leftarg->sk_flags & (SK_SEARCHNULL | SK_SEARCHNOTNULL));
			leftnull = true;
		}
		else
			leftnull = false;
		if (rightarg->sk_flags & SK_ISNULL)
		{
			Assert(rightarg->sk_flags & (SK_SEARCHNULL | SK_SEARCHNOTNULL));
			rightnull = true;
		}
		else
			rightnull = false;

		/*
		 * We treat NULL as either greater than or less than all other values.
		 * Since true > false, the tests below work correctly for NULLS LAST
		 * logic.  If the index is NULLS FIRST, we need to flip the strategy.
		 */
		strat = op->sk_strategy;
		if (op->sk_flags & SK_BT_NULLS_FIRST)
			strat = BTCommuteStrategyNumber(strat);

		switch (strat)
		{
			case BTLessStrategyNumber:
				*result = (leftnull < rightnull);
				break;
			case BTLessEqualStrategyNumber:
				*result = (leftnull <= rightnull);
				break;
			case BTEqualStrategyNumber:
				*result = (leftnull == rightnull);
				break;
			case BTGreaterEqualStrategyNumber:
				*result = (leftnull >= rightnull);
				break;
			case BTGreaterStrategyNumber:
				*result = (leftnull > rightnull);
				break;
			default:
				elog(ERROR, "unrecognized StrategyNumber: %d", (int) strat);
				*result = false;	/* keep compiler quiet */
				break;
		}
		return true;
	}

	/*
	 * The opfamily we need to worry about is identified by the index column.
	 */
	Assert(leftarg->sk_attno == rightarg->sk_attno);

	opcintype = rel->rd_opcintype[leftarg->sk_attno - 1];

	/*
	 * Determine the actual datatypes of the ScanKey arguments.  We have to
	 * support the convention that sk_subtype == InvalidOid means the opclass
	 * input type; this is a hack to simplify life for ScanKeyInit().
	 */
	lefttype = leftarg->sk_subtype;
	if (lefttype == InvalidOid)
		lefttype = opcintype;
	righttype = rightarg->sk_subtype;
	if (righttype == InvalidOid)
		righttype = opcintype;
	optype = op->sk_subtype;
	if (optype == InvalidOid)
		optype = opcintype;

	/*
	 * If leftarg and rightarg match the types expected for the "op" scankey,
	 * we can use its already-looked-up comparison function.
	 */
	if (lefttype == opcintype && righttype == optype)
	{
		*result = DatumGetBool(FunctionCall2Coll(&op->sk_func,
												 op->sk_collation,
												 leftarg->sk_argument,
												 rightarg->sk_argument));
		return true;
	}

	/*
	 * Otherwise, we need to go to the syscache to find the appropriate
	 * operator.  (This cannot result in infinite recursion, since no
	 * indexscan initiated by syscache lookup will use cross-data-type
	 * operators.)
	 *
	 * If the sk_strategy was flipped by _bt_fix_scankey_strategy, we have to
	 * un-flip it to get the correct opfamily member.
	 */
	strat = op->sk_strategy;
	if (op->sk_flags & SK_BT_DESC)
		strat = BTCommuteStrategyNumber(strat);

	cmp_op = get_opfamily_member(rel->rd_opfamily[leftarg->sk_attno - 1],
								 lefttype,
								 righttype,
								 strat);
	if (OidIsValid(cmp_op))
	{
		RegProcedure cmp_proc = get_opcode(cmp_op);

		if (RegProcedureIsValid(cmp_proc))
		{
			*result = DatumGetBool(OidFunctionCall2Coll(cmp_proc,
														op->sk_collation,
														leftarg->sk_argument,
													 rightarg->sk_argument));
			return true;
		}
	}

	/* Can't make the comparison */
	*result = false;			/* suppress compiler warnings */
	return false;
}

/*
 * Adjust a scankey's strategy and flags setting as needed for indoptions.
 *
 * We copy the appropriate indoption value into the scankey sk_flags
 * (shifting to avoid clobbering system-defined flag bits).  Also, if
 * the DESC option is set, commute (flip) the operator strategy number.
 *
 * A secondary purpose is to check for IS NULL/NOT NULL scankeys and set up
 * the strategy field correctly for them.
 *
 * Lastly, for ordinary scankeys (not IS NULL/NOT NULL), we check for a
 * NULL comparison value.  Since all btree operators are assumed strict,
 * a NULL means that the qual cannot be satisfied.  We return TRUE if the
 * comparison value isn't NULL, or FALSE if the scan should be abandoned.
 *
 * This function is applied to the *input* scankey structure; therefore
 * on a rescan we will be looking at already-processed scankeys.  Hence
 * we have to be careful not to re-commute the strategy if we already did it.
 * It's a bit ugly to modify the caller's copy of the scankey but in practice
 * there shouldn't be any problem, since the index's indoptions are certainly
 * not going to change while the scankey survives.
 */
static bool
_bt_fix_scankey_strategy(ScanKey skey, int16 *indoption)
{
	int			addflags;

	addflags = indoption[skey->sk_attno - 1] << SK_BT_INDOPTION_SHIFT;

	/*
	 * We treat all btree operators as strict (even if they're not so marked
	 * in pg_proc). This means that it is impossible for an operator condition
	 * with a NULL comparison constant to succeed, and we can reject it right
	 * away.
	 *
	 * However, we now also support "x IS NULL" clauses as search conditions,
	 * so in that case keep going. The planner has not filled in any
	 * particular strategy in this case, so set it to BTEqualStrategyNumber
	 * --- we can treat IS NULL as an equality operator for purposes of search
	 * strategy.
	 *
	 * Likewise, "x IS NOT NULL" is supported.  We treat that as either "less
	 * than NULL" in a NULLS LAST index, or "greater than NULL" in a NULLS
	 * FIRST index.
	 *
	 * Note: someday we might have to fill in sk_collation from the index
	 * column's collation.  At the moment this is a non-issue because we'll
	 * never actually call the comparison operator on a NULL.
	 */
	if (skey->sk_flags & SK_ISNULL)
	{
		/* SK_ISNULL shouldn't be set in a row header scankey */
		Assert(!(skey->sk_flags & SK_ROW_HEADER));

		/* Set indoption flags in scankey (might be done already) */
		skey->sk_flags |= addflags;

		/* Set correct strategy for IS NULL or NOT NULL search */
		if (skey->sk_flags & SK_SEARCHNULL)
		{
			skey->sk_strategy = BTEqualStrategyNumber;
			skey->sk_subtype = InvalidOid;
			skey->sk_collation = InvalidOid;
		}
		else if (skey->sk_flags & SK_SEARCHNOTNULL)
		{
			if (skey->sk_flags & SK_BT_NULLS_FIRST)
				skey->sk_strategy = BTGreaterStrategyNumber;
			else
				skey->sk_strategy = BTLessStrategyNumber;
			skey->sk_subtype = InvalidOid;
			skey->sk_collation = InvalidOid;
		}
		else
		{
			/* regular qual, so it cannot be satisfied */
			return false;
		}

		/* Needn't do the rest */
		return true;
	}

	/* Adjust strategy for DESC, if we didn't already */
	if ((addflags & SK_BT_DESC) && !(skey->sk_flags & SK_BT_DESC))
		skey->sk_strategy = BTCommuteStrategyNumber(skey->sk_strategy);
	skey->sk_flags |= addflags;

	/* If it's a row header, fix row member flags and strategies similarly */
	if (skey->sk_flags & SK_ROW_HEADER)
	{
		ScanKey		subkey = (ScanKey) DatumGetPointer(skey->sk_argument);

		for (;;)
		{
			Assert(subkey->sk_flags & SK_ROW_MEMBER);
			addflags = indoption[subkey->sk_attno - 1] << SK_BT_INDOPTION_SHIFT;
			if ((addflags & SK_BT_DESC) && !(subkey->sk_flags & SK_BT_DESC))
				subkey->sk_strategy = BTCommuteStrategyNumber(subkey->sk_strategy);
			subkey->sk_flags |= addflags;
			if (subkey->sk_flags & SK_ROW_END)
				break;
			subkey++;
		}
	}

	return true;
}

/*
 * Mark a scankey as "required to continue the scan".
 *
 * Depending on the operator type, the key may be required for both scan
 * directions or just one.  Also, if the key is a row comparison header,
 * we have to mark the appropriate subsidiary ScanKeys as required.  In
 * such cases, the first subsidiary key is required, but subsequent ones
 * are required only as long as they correspond to successive index columns
 * and match the leading column as to sort direction.
 * Otherwise the row comparison ordering is different from the index ordering
 * and so we can't stop the scan on the basis of those lower-order columns.
 *
 * Note: when we set required-key flag bits in a subsidiary scankey, we are
 * scribbling on a data structure belonging to the index AM's caller, not on
 * our private copy.  This should be OK because the marking will not change
 * from scan to scan within a query, and so we'd just re-mark the same way
 * anyway on a rescan.  Something to keep an eye on though.
 */
static void
_bt_mark_scankey_required(ScanKey skey)
{
	int			addflags;

	switch (skey->sk_strategy)
	{
		case BTLessStrategyNumber:
		case BTLessEqualStrategyNumber:
			addflags = SK_BT_REQFWD;
			break;
		case BTEqualStrategyNumber:
			addflags = SK_BT_REQFWD | SK_BT_REQBKWD;
			break;
		case BTGreaterEqualStrategyNumber:
		case BTGreaterStrategyNumber:
			addflags = SK_BT_REQBKWD;
			break;
		default:
			elog(ERROR, "unrecognized StrategyNumber: %d",
				 (int) skey->sk_strategy);
			addflags = 0;		/* keep compiler quiet */
			break;
	}

	skey->sk_flags |= addflags;

	if (skey->sk_flags & SK_ROW_HEADER)
	{
		ScanKey		subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
		AttrNumber	attno = skey->sk_attno;

		/* First subkey should be same as the header says */
		Assert(subkey->sk_attno == attno);

		for (;;)
		{
			Assert(subkey->sk_flags & SK_ROW_MEMBER);
			if (subkey->sk_attno != attno)
				break;			/* non-adjacent key, so not required */
			if (subkey->sk_strategy != skey->sk_strategy)
				break;			/* wrong direction, so not required */
			subkey->sk_flags |= addflags;
			if (subkey->sk_flags & SK_ROW_END)
				break;
			subkey++;
			attno++;
		}
	}
}

/*
 * Test whether an indextuple satisfies all the scankey conditions.
 *
 * If so, return the address of the index tuple on the index page.
 * If not, return NULL.
 *
 * If the tuple fails to pass the qual, we also determine whether there's
 * any need to continue the scan beyond this tuple, and set *continuescan
 * accordingly.  See comments for _bt_preprocess_keys(), above, about how
 * this is done.
 *
 * scan: index scan descriptor (containing a search-type scankey)
 * page: buffer page containing index tuple
 * offnum: offset number of index tuple (must be a valid item!)
 * dir: direction we are scanning in
 * continuescan: output parameter (will be set correctly in all cases)
 *
 * Caller must hold pin and lock on the index page.
 */
IndexTuple
_bt_checkkeys(IndexScanDesc scan,
			  Page page, OffsetNumber offnum,
			  ScanDirection dir, bool *continuescan)
{
	ItemId		iid = PageGetItemId(page, offnum);
	bool		tuple_alive;
	IndexTuple	tuple;
	TupleDesc	tupdesc;
	BTScanOpaque so;
	int			keysz;
	int			ikey;
	ScanKey		key;

	*continuescan = true;		/* default assumption */

	/*
	 * If the scan specifies not to return killed tuples, then we treat a
	 * killed tuple as not passing the qual.  Most of the time, it's a win to
	 * not bother examining the tuple's index keys, but just return
	 * immediately with continuescan = true to proceed to the next tuple.
	 * However, if this is the last tuple on the page, we should check the
	 * index keys to prevent uselessly advancing to the next page.
	 */
	if (scan->ignore_killed_tuples && ItemIdIsDead(iid))
	{
		/* return immediately if there are more tuples on the page */
		if (ScanDirectionIsForward(dir))
		{
			if (offnum < PageGetMaxOffsetNumber(page))
				return NULL;
		}
		else
		{
			BTPageOpaque opaque = (BTPageOpaque) PageGetSpecialPointer(page);

			if (offnum > P_FIRSTDATAKEY(opaque))
				return NULL;
		}

		/*
		 * OK, we want to check the keys so we can set continuescan correctly,
		 * but we'll return NULL even if the tuple passes the key tests.
		 */
		tuple_alive = false;
	}
	else
		tuple_alive = true;

	tuple = (IndexTuple) PageGetItem(page, iid);

	tupdesc = RelationGetDescr(scan->indexRelation);
	so = (BTScanOpaque) scan->opaque;
	keysz = so->numberOfKeys;

	for (key = so->keyData, ikey = 0; ikey < keysz; key++, ikey++)
	{
		Datum		datum;
		bool		isNull;
		Datum		test;

		/*
		 * If the scan key has already matched we can skip this key, as
		 * long as the index tuple does not contain NULL values.
		 */
		if (key->sk_flags & SK_BT_MATCHED && !IndexTupleHasNulls(tuple))
			continue;

		/* row-comparison keys need special processing */
		if (key->sk_flags & SK_ROW_HEADER)
		{
			if (_bt_check_rowcompare(key, tuple, tupdesc, dir, continuescan))
				continue;
			return NULL;
		}

		datum = index_getattr(tuple,
							  key->sk_attno,
							  tupdesc,
							  &isNull);

		if (key->sk_flags & SK_ISNULL)
		{
			/* Handle IS NULL/NOT NULL tests */
			if (key->sk_flags & SK_SEARCHNULL)
			{
				if (isNull)
					continue;	/* tuple satisfies this qual */
			}
			else
			{
				Assert(key->sk_flags & SK_SEARCHNOTNULL);
				if (!isNull)
					continue;	/* tuple satisfies this qual */
			}

			/*
			 * Tuple fails this qual.  If it's a required qual for the current
			 * scan direction, then we can conclude no further tuples will
			 * pass, either.
			 */
			if ((key->sk_flags & SK_BT_REQFWD) &&
				ScanDirectionIsForward(dir))
				*continuescan = false;
			else if ((key->sk_flags & SK_BT_REQBKWD) &&
					 ScanDirectionIsBackward(dir))
				*continuescan = false;

			/*
			 * In any case, this indextuple doesn't match the qual.
			 */
			return NULL;
		}

		if (isNull)
		{
			if (key->sk_flags & SK_BT_NULLS_FIRST)
			{
				/*
				 * Since NULLs are sorted before non-NULLs, we know we have
				 * reached the lower limit of the range of values for this
				 * index attr.  On a backward scan, we can stop if this qual
				 * is one of the "must match" subset.  We can stop regardless
				 * of whether the qual is > or <, so long as it's required,
				 * because it's not possible for any future tuples to pass. On
				 * a forward scan, however, we must keep going, because we may
				 * have initially positioned to the start of the index.
				 */
				if ((key->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
					ScanDirectionIsBackward(dir))
					*continuescan = false;
			}
			else
			{
				/*
				 * Since NULLs are sorted after non-NULLs, we know we have
				 * reached the upper limit of the range of values for this
				 * index attr.  On a forward scan, we can stop if this qual is
				 * one of the "must match" subset.  We can stop regardless of
				 * whether the qual is > or <, so long as it's required,
				 * because it's not possible for any future tuples to pass. On
				 * a backward scan, however, we must keep going, because we
				 * may have initially positioned to the end of the index.
				 */
				if ((key->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
					ScanDirectionIsForward(dir))
					*continuescan = false;
			}

			/*
			 * In any case, this indextuple doesn't match the qual.
			 */
			return NULL;
		}

		test = FunctionCall2Coll(&key->sk_func, key->sk_collation,
								 datum, key->sk_argument);

		if (!DatumGetBool(test))
		{
			/*
			 * Tuple fails this qual.  If it's a required qual for the current
			 * scan direction, then we can conclude no further tuples will
			 * pass, either.
			 *
			 * Note: because we stop the scan as soon as any required equality
			 * qual fails, it is critical that equality quals be used for the
			 * initial positioning in _bt_first() when they are available. See
			 * comments in _bt_first().
			 */
			if ((key->sk_flags & SK_BT_REQFWD) &&
				ScanDirectionIsForward(dir))
				*continuescan = false;
			else if ((key->sk_flags & SK_BT_REQBKWD) &&
					 ScanDirectionIsBackward(dir))
				*continuescan = false;

			/*
			 * In any case, this indextuple doesn't match the qual.
			 */
			return NULL;
		}
	}

	/* Check for failure due to it being a killed tuple. */
	if (!tuple_alive)
		return NULL;

	/* If we get here, the tuple passes all index quals. */
	return tuple;
}

/*
 * Test whether an indextuple satisfies a row-comparison scan condition.
 *
 * Return true if so, false if not.  If not, also clear *continuescan if
 * it's not possible for any future tuples in the current scan direction
 * to pass the qual.
 *
 * This is a subroutine for _bt_checkkeys, which see for more info.
 */
static bool
_bt_check_rowcompare(ScanKey skey, IndexTuple tuple, TupleDesc tupdesc,
					 ScanDirection dir, bool *continuescan)
{
	ScanKey		subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
	int32		cmpresult = 0;
	bool		result;

	/* First subkey should be same as the header says */
	Assert(subkey->sk_attno == skey->sk_attno);

	/* Loop over columns of the row condition */
	for (;;)
	{
		Datum		datum;
		bool		isNull;

		Assert(subkey->sk_flags & SK_ROW_MEMBER);

		datum = index_getattr(tuple,
							  subkey->sk_attno,
							  tupdesc,
							  &isNull);

		if (isNull)
		{
			if (subkey->sk_flags & SK_BT_NULLS_FIRST)
			{
				/*
				 * Since NULLs are sorted before non-NULLs, we know we have
				 * reached the lower limit of the range of values for this
				 * index attr.  On a backward scan, we can stop if this qual
				 * is one of the "must match" subset.  We can stop regardless
				 * of whether the qual is > or <, so long as it's required,
				 * because it's not possible for any future tuples to pass. On
				 * a forward scan, however, we must keep going, because we may
				 * have initially positioned to the start of the index.
				 */
				if ((subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
					ScanDirectionIsBackward(dir))
					*continuescan = false;
			}
			else
			{
				/*
				 * Since NULLs are sorted after non-NULLs, we know we have
				 * reached the upper limit of the range of values for this
				 * index attr.  On a forward scan, we can stop if this qual is
				 * one of the "must match" subset.  We can stop regardless of
				 * whether the qual is > or <, so long as it's required,
				 * because it's not possible for any future tuples to pass. On
				 * a backward scan, however, we must keep going, because we
				 * may have initially positioned to the end of the index.
				 */
				if ((subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
					ScanDirectionIsForward(dir))
					*continuescan = false;
			}

			/*
			 * In any case, this indextuple doesn't match the qual.
			 */
			return false;
		}

		if (subkey->sk_flags & SK_ISNULL)
		{
			/*
			 * Unlike the simple-scankey case, this isn't a disallowed case.
			 * But it can never match.  If all the earlier row comparison
			 * columns are required for the scan direction, we can stop the
			 * scan, because there can't be another tuple that will succeed.
			 */
			if (subkey != (ScanKey) DatumGetPointer(skey->sk_argument))
				subkey--;
			if ((subkey->sk_flags & SK_BT_REQFWD) &&
				ScanDirectionIsForward(dir))
				*continuescan = false;
			else if ((subkey->sk_flags & SK_BT_REQBKWD) &&
					 ScanDirectionIsBackward(dir))
				*continuescan = false;
			return false;
		}

		/* Perform the test --- three-way comparison not bool operator */
		cmpresult = DatumGetInt32(FunctionCall2Coll(&subkey->sk_func,
													subkey->sk_collation,
													datum,
													subkey->sk_argument));

		if (subkey->sk_flags & SK_BT_DESC)
			cmpresult = -cmpresult;

		/* Done comparing if unequal, else advance to next column */
		if (cmpresult != 0)
			break;

		if (subkey->sk_flags & SK_ROW_END)
			break;
		subkey++;
	}

	/*
	 * At this point cmpresult indicates the overall result of the row
	 * comparison, and subkey points to the deciding column (or the last
	 * column if the result is "=").
	 */
	switch (subkey->sk_strategy)
	{
			/* EQ and NE cases aren't allowed here */
		case BTLessStrategyNumber:
			result = (cmpresult < 0);
			break;
		case BTLessEqualStrategyNumber:
			result = (cmpresult <= 0);
			break;
		case BTGreaterEqualStrategyNumber:
			result = (cmpresult >= 0);
			break;
		case BTGreaterStrategyNumber:
			result = (cmpresult > 0);
			break;
		default:
			elog(ERROR, "unrecognized RowCompareType: %d",
				 (int) subkey->sk_strategy);
			result = 0;			/* keep compiler quiet */
			break;
	}

	if (!result)
	{
		/*
		 * Tuple fails this qual.  If it's a required qual for the current
		 * scan direction, then we can conclude no further tuples will pass,
		 * either.  Note we have to look at the deciding column, not
		 * necessarily the first or last column of the row condition.
		 */
		if ((subkey->sk_flags & SK_BT_REQFWD) &&
			ScanDirectionIsForward(dir))
			*continuescan = false;
		else if ((subkey->sk_flags & SK_BT_REQBKWD) &&
				 ScanDirectionIsBackward(dir))
			*continuescan = false;
	}

	return result;
}

/*
 * _bt_killitems - set LP_DEAD state for items an indexscan caller has
 * told us were killed
 *
 * scan->so contains information about the current page and killed tuples
 * thereon (generally, this should only be called if so->numKilled > 0).
 *
 * The caller must have pin on so->currPos.buf, but may or may not have
 * read-lock, as indicated by haveLock.  Note that we assume read-lock
 * is sufficient for setting LP_DEAD status (which is only a hint).
 *
 * We match items by heap TID before assuming they are the right ones to
 * delete.  We cope with cases where items have moved right due to insertions.
 * If an item has moved off the current page due to a split, we'll fail to
 * find it and do nothing (this is not an error case --- we assume the item
 * will eventually get marked in a future indexscan).  Note that because we
 * hold pin on the target page continuously from initially reading the items
 * until applying this function, VACUUM cannot have deleted any items from
 * the page, and so there is no need to search left from the recorded offset.
 * (This observation also guarantees that the item is still the right one
 * to delete, which might otherwise be questionable since heap TIDs can get
 * recycled.)
 */
void
_bt_killitems(IndexScanDesc scan, bool haveLock)
{
	BTScanOpaque so = (BTScanOpaque) scan->opaque;
	Page		page;
	BTPageOpaque opaque;
	OffsetNumber minoff;
	OffsetNumber maxoff;
	int			i;
	bool		killedsomething = false;

	Assert(BufferIsValid(so->currPos.buf));

	if (!haveLock)
		LockBuffer(so->currPos.buf, BT_READ);

	page = BufferGetPage(so->currPos.buf);
	opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	minoff = P_FIRSTDATAKEY(opaque);
	maxoff = PageGetMaxOffsetNumber(page);

	for (i = 0; i < so->numKilled; i++)
	{
		int			itemIndex = so->killedItems[i];
		BTScanPosItem *kitem = &so->currPos.items[itemIndex];
		OffsetNumber offnum = kitem->indexOffset;

		Assert(itemIndex >= so->currPos.firstItem &&
			   itemIndex <= so->currPos.lastItem);
		if (offnum < minoff)
			continue;			/* pure paranoia */
		while (offnum <= maxoff)
		{
			ItemId		iid = PageGetItemId(page, offnum);
			IndexTuple	ituple = (IndexTuple) PageGetItem(page, iid);

			if (ItemPointerEquals(&ituple->t_tid, &kitem->heapTid))
			{
				/* found the item */
				ItemIdMarkDead(iid);
				killedsomething = true;
				break;			/* out of inner search loop */
			}
			offnum = OffsetNumberNext(offnum);
		}
	}

	/*
	 * Since this can be redone later if needed, mark as dirty hint.
	 *
	 * Whenever we mark anything LP_DEAD, we also set the page's
	 * BTP_HAS_GARBAGE flag, which is likewise just a hint.
	 */
	if (killedsomething)
	{
		opaque->btpo_flags |= BTP_HAS_GARBAGE;
		MarkBufferDirtyHint(so->currPos.buf, true);
	}

	if (!haveLock)
		LockBuffer(so->currPos.buf, BUFFER_LOCK_UNLOCK);

	/*
	 * Always reset the scan state, so we don't look for same items on other
	 * pages.
	 */
	so->numKilled = 0;
}


/*
 * The following routines manage a shared-memory area in which we track
 * assignment of "vacuum cycle IDs" to currently-active btree vacuuming
 * operations.  There is a single counter which increments each time we
 * start a vacuum to assign it a cycle ID.  Since multiple vacuums could
 * be active concurrently, we have to track the cycle ID for each active
 * vacuum; this requires at most MaxBackends entries (usually far fewer).
 * We assume at most one vacuum can be active for a given index.
 *
 * Access to the shared memory area is controlled by BtreeVacuumLock.
 * In principle we could use a separate lmgr locktag for each index,
 * but a single LWLock is much cheaper, and given the short time that
 * the lock is ever held, the concurrency hit should be minimal.
 */

typedef struct BTOneVacInfo
{
	LockRelId	relid;			/* global identifier of an index */
	BTCycleId	cycleid;		/* cycle ID for its active VACUUM */
} BTOneVacInfo;

typedef struct BTVacInfo
{
	BTCycleId	cycle_ctr;		/* cycle ID most recently assigned */
	int			num_vacuums;	/* number of currently active VACUUMs */
	int			max_vacuums;	/* allocated length of vacuums[] array */
	BTOneVacInfo vacuums[1];	/* VARIABLE LENGTH ARRAY */
} BTVacInfo;

static BTVacInfo *btvacinfo;


/*
 * _bt_vacuum_cycleid --- get the active vacuum cycle ID for an index,
 *		or zero if there is no active VACUUM
 *
 * Note: for correct interlocking, the caller must already hold pin and
 * exclusive lock on each buffer it will store the cycle ID into.  This
 * ensures that even if a VACUUM starts immediately afterwards, it cannot
 * process those pages until the page split is complete.
 */
BTCycleId
_bt_vacuum_cycleid(Relation rel)
{
	BTCycleId	result = 0;
	int			i;

	/* Share lock is enough since this is a read-only operation */
	LWLockAcquire(BtreeVacuumLock, LW_SHARED);

	for (i = 0; i < btvacinfo->num_vacuums; i++)
	{
		BTOneVacInfo *vac = &btvacinfo->vacuums[i];

		if (vac->relid.relId == rel->rd_lockInfo.lockRelId.relId &&
			vac->relid.dbId == rel->rd_lockInfo.lockRelId.dbId)
		{
			result = vac->cycleid;
			break;
		}
	}

	LWLockRelease(BtreeVacuumLock);
	return result;
}

/*
 * _bt_start_vacuum --- assign a cycle ID to a just-starting VACUUM operation
 *
 * Note: the caller must guarantee that it will eventually call
 * _bt_end_vacuum, else we'll permanently leak an array slot.  To ensure
 * that this happens even in elog(FATAL) scenarios, the appropriate coding
 * is not just a PG_TRY, but
 *		PG_ENSURE_ERROR_CLEANUP(_bt_end_vacuum_callback, PointerGetDatum(rel))
 */
BTCycleId
_bt_start_vacuum(Relation rel)
{
	BTCycleId	result;
	int			i;
	BTOneVacInfo *vac;

	LWLockAcquire(BtreeVacuumLock, LW_EXCLUSIVE);

	/*
	 * Assign the next cycle ID, being careful to avoid zero as well as the
	 * reserved high values.
	 */
	result = ++(btvacinfo->cycle_ctr);
	if (result == 0 || result > MAX_BT_CYCLE_ID)
		result = btvacinfo->cycle_ctr = 1;

	/* Let's just make sure there's no entry already for this index */
	for (i = 0; i < btvacinfo->num_vacuums; i++)
	{
		vac = &btvacinfo->vacuums[i];
		if (vac->relid.relId == rel->rd_lockInfo.lockRelId.relId &&
			vac->relid.dbId == rel->rd_lockInfo.lockRelId.dbId)
		{
			/*
			 * Unlike most places in the backend, we have to explicitly
			 * release our LWLock before throwing an error.  This is because
			 * we expect _bt_end_vacuum() to be called before transaction
			 * abort cleanup can run to release LWLocks.
			 */
			LWLockRelease(BtreeVacuumLock);
			elog(ERROR, "multiple active vacuums for index \"%s\"",
				 RelationGetRelationName(rel));
		}
	}

	/* OK, add an entry */
	if (btvacinfo->num_vacuums >= btvacinfo->max_vacuums)
	{
		LWLockRelease(BtreeVacuumLock);
		elog(ERROR, "out of btvacinfo slots");
	}
	vac = &btvacinfo->vacuums[btvacinfo->num_vacuums];
	vac->relid = rel->rd_lockInfo.lockRelId;
	vac->cycleid = result;
	btvacinfo->num_vacuums++;

	LWLockRelease(BtreeVacuumLock);
	return result;
}

/*
 * _bt_end_vacuum --- mark a btree VACUUM operation as done
 *
 * Note: this is deliberately coded not to complain if no entry is found;
 * this allows the caller to put PG_TRY around the start_vacuum operation.
 */
void
_bt_end_vacuum(Relation rel)
{
	int			i;

	LWLockAcquire(BtreeVacuumLock, LW_EXCLUSIVE);

	/* Find the array entry */
	for (i = 0; i < btvacinfo->num_vacuums; i++)
	{
		BTOneVacInfo *vac = &btvacinfo->vacuums[i];

		if (vac->relid.relId == rel->rd_lockInfo.lockRelId.relId &&
			vac->relid.dbId == rel->rd_lockInfo.lockRelId.dbId)
		{
			/* Remove it by shifting down the last entry */
			*vac = btvacinfo->vacuums[btvacinfo->num_vacuums - 1];
			btvacinfo->num_vacuums--;
			break;
		}
	}

	LWLockRelease(BtreeVacuumLock);
}

/*
 * _bt_end_vacuum wrapped as an on_shmem_exit callback function
 */
void
_bt_end_vacuum_callback(int code, Datum arg)
{
	_bt_end_vacuum((Relation) DatumGetPointer(arg));
}

/*
 * BTreeShmemSize --- report amount of shared memory space needed
 */
Size
BTreeShmemSize(void)
{
	Size		size;

	size = offsetof(BTVacInfo, vacuums[0]);
	size = add_size(size, mul_size(MaxBackends, sizeof(BTOneVacInfo)));
	return size;
}

/*
 * BTreeShmemInit --- initialize this module's shared memory
 */
void
BTreeShmemInit(void)
{
	bool		found;

	btvacinfo = (BTVacInfo *) ShmemInitStruct("BTree Vacuum State",
											  BTreeShmemSize(),
											  &found);

	if (!IsUnderPostmaster)
	{
		/* Initialize shared memory area */
		Assert(!found);

		/*
		 * It doesn't really matter what the cycle counter starts at, but
		 * having it always start the same doesn't seem good.  Seed with
		 * low-order bits of time() instead.
		 */
		btvacinfo->cycle_ctr = (BTCycleId) time(NULL);

		btvacinfo->num_vacuums = 0;
		btvacinfo->max_vacuums = MaxBackends;
	}
	else
		Assert(found);
}

Datum
btoptions(PG_FUNCTION_ARGS)
{
	Datum		reloptions = PG_GETARG_DATUM(0);
	bool		validate = PG_GETARG_BOOL(1);
	bytea	   *result;

	result = default_reloptions(reloptions, validate, RELOPT_KIND_BTREE);
	if (result)
		PG_RETURN_BYTEA_P(result);
	PG_RETURN_NULL();
}
