postgresql/src/backend/access/nbtree/nbtsearch.c

/*-------------------------------------------------------------------------
 *
 * btsearch.c--
 *    search code for postgres btrees.
 *
 * Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    $Header: /cvsroot/pgsql/src/backend/access/nbtree/nbtsearch.c,v 1.5 1996/10/30 06:08:01 scrappy Exp $
 *
 *-------------------------------------------------------------------------
 */

#include <time.h>

#include "postgres.h"

#include "catalog/pg_attribute.h"
#include "access/attnum.h"
#include "nodes/pg_list.h"
#include "access/tupdesc.h"
#include "storage/fd.h"
#include "catalog/pg_am.h"
#include "catalog/pg_class.h"
#include "nodes/nodes.h"
#include "rewrite/prs2lock.h"
#include "access/skey.h"
#include "access/strat.h"
#include "utils/rel.h"

#include "storage/block.h"
#include "storage/off.h"
#include "storage/itemptr.h"
#include "access/itup.h"
#include "access/funcindex.h"
#include "storage/itemid.h"
#include "storage/item.h"
#include "storage/buf.h"
#include "storage/bufpage.h"
#include "storage/bufmgr.h"
#include "utils/nabstime.h"
#include "access/htup.h"
#include "utils/tqual.h"
#include "utils/palloc.h"
#include "access/relscan.h"
#include "access/sdir.h"
#include "access/nbtree.h"
#include "access/genam.h"

#include "fmgr.h"

static BTStack _bt_searchr(Relation rel, int keysz, ScanKey scankey, Buffer *bufP, BTStack stack_in);
static OffsetNumber _bt_firsteq(Relation rel, TupleDesc itupdesc, Page page, Size keysz, ScanKey scankey, OffsetNumber offnum);
static int _bt_compare(Relation rel, TupleDesc itupdesc, Page page, int keysz, ScanKey scankey, OffsetNumber offnum);
static bool _bt_twostep(IndexScanDesc scan, Buffer *bufP, ScanDirection dir);
static RetrieveIndexResult _bt_endpoint(IndexScanDesc scan, ScanDirection dir);

/*
 *  _bt_search() -- Search for a scan key in the index.
 *
 *	This routine is actually just a helper that sets things up and
 *	calls a recursive-descent search routine on the tree.
 */
BTStack
_bt_search(Relation rel, int keysz, ScanKey scankey, Buffer *bufP)
{
    *bufP = _bt_getroot(rel, BT_READ);
    return (_bt_searchr(rel, keysz, scankey, bufP, (BTStack) NULL));
}

/*
 *  _bt_searchr() -- Search the tree recursively for a particular scankey.
 */
static BTStack
_bt_searchr(Relation rel,
	    int keysz,
	    ScanKey scankey,
	    Buffer *bufP,
	    BTStack stack_in)
{
    BTStack stack;
    OffsetNumber offnum;
    Page page;
    BTPageOpaque opaque;
    BlockNumber par_blkno;
    BlockNumber blkno;
    ItemId itemid;
    BTItem btitem;
    BTItem item_save;
    int item_nbytes;
    IndexTuple itup;
    
    /* if this is a leaf page, we're done */
    page = BufferGetPage(*bufP);
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    if (opaque->btpo_flags & BTP_LEAF)
	return (stack_in);
    
    /*
     *  Find the appropriate item on the internal page, and get the child
     *  page that it points to.
     */
    
    par_blkno = BufferGetBlockNumber(*bufP);
    offnum = _bt_binsrch(rel, *bufP, keysz, scankey, BT_DESCENT);
    itemid = PageGetItemId(page, offnum);
    btitem = (BTItem) PageGetItem(page, itemid);
    itup = &(btitem->bti_itup);
    blkno = ItemPointerGetBlockNumber(&(itup->t_tid));
    
    /*
     *  We need to save the bit image of the index entry we chose in the
     *  parent page on a stack.  In case we split the tree, we'll use this
     *  bit image to figure out what our real parent page is, in case the
     *  parent splits while we're working lower in the tree.  See the paper
     *  by Lehman and Yao for how this is detected and handled.  (We use
     *  unique OIDs to disambiguate duplicate keys in the index -- Lehman
     *  and Yao disallow duplicate keys).
     */
    
    item_nbytes = ItemIdGetLength(itemid);
    item_save = (BTItem) palloc(item_nbytes);
    memmove((char *) item_save, (char *) btitem, item_nbytes);
    stack = (BTStack) palloc(sizeof(BTStackData));
    stack->bts_blkno = par_blkno;
    stack->bts_offset = offnum;
    stack->bts_btitem = item_save;
    stack->bts_parent = stack_in;
    
    /* drop the read lock on the parent page and acquire one on the child */
    _bt_relbuf(rel, *bufP, BT_READ);
    *bufP = _bt_getbuf(rel, blkno, BT_READ);
    
    /*
     *  Race -- the page we just grabbed may have split since we read its
     *  pointer in the parent.  If it has, we may need to move right to its
     *  new sibling.  Do that.
     */
    
    *bufP = _bt_moveright(rel, *bufP, keysz, scankey, BT_READ);
    
    /* okay, all set to move down a level */
    return (_bt_searchr(rel, keysz, scankey, bufP, stack));
}

/*
 *  _bt_moveright() -- move right in the btree if necessary.
 *
 *	When we drop and reacquire a pointer to a page, it is possible that
 *	the page has changed in the meanwhile.  If this happens, we're
 *	guaranteed that the page has "split right" -- that is, that any
 *	data that appeared on the page originally is either on the page
 *	or strictly to the right of it.
 *
 *	This routine decides whether or not we need to move right in the
 *	tree by examining the high key entry on the page.  If that entry
 *	is strictly less than one we expect to be on the page, then our
 *	picture of the page is incorrect and we need to move right.
 *
 *	On entry, we have the buffer pinned and a lock of the proper type.
 *	If we move right, we release the buffer and lock and acquire the
 *	same on the right sibling.
 */
Buffer
_bt_moveright(Relation rel,
	      Buffer buf,
	      int keysz,
	      ScanKey scankey,
	      int access)
{
    Page page;
    BTPageOpaque opaque;
    ItemId hikey;
    ItemId itemid;
    BlockNumber rblkno;
    
    page = BufferGetPage(buf);
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    
    /* if we're on a rightmost page, we don't need to move right */
    if (P_RIGHTMOST(opaque))
	return (buf);
    
    /* by convention, item 0 on non-rightmost pages is the high key */
    hikey = PageGetItemId(page, P_HIKEY);
    
    /*
     *  If the scan key that brought us to this page is >= the high key
     *  stored on the page, then the page has split and we need to move
     *  right.
     */
    
    if (_bt_skeycmp(rel, keysz, scankey, page, hikey,
		    BTGreaterEqualStrategyNumber)) {
	
	/* move right as long as we need to */
	do {
	    /*
	     *  If this page consists of all duplicate keys (hikey and first
	     *  key on the page have the same value), then we don't need to
	     *  step right.
	     */
	    if (PageGetMaxOffsetNumber(page) > P_HIKEY) {
		itemid = PageGetItemId(page, P_FIRSTKEY);
		if (_bt_skeycmp(rel, keysz, scankey, page, itemid,
				BTEqualStrategyNumber)) {
		    /* break is for the "move right" while loop */
		    break;
		}
	    }
	    
	    /* step right one page */
	    rblkno = opaque->btpo_next;
	    _bt_relbuf(rel, buf, access);
	    buf = _bt_getbuf(rel, rblkno, access);
	    page = BufferGetPage(buf);
	    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	    hikey = PageGetItemId(page, P_HIKEY);
	    
	} while (! P_RIGHTMOST(opaque)
		 && _bt_skeycmp(rel, keysz, scankey, page, hikey,
				BTGreaterEqualStrategyNumber));
    }
    return (buf);
}

/*
 *  _bt_skeycmp() -- compare a scan key to a particular item on a page using
 *		     a requested strategy (<, <=, =, >=, >).
 *
 *	We ignore the unique OIDs stored in the btree item here.  Those
 *	numbers are intended for use internally only, in repositioning a
 *	scan after a page split.  They do not impose any meaningful ordering.
 *
 *	The comparison is A <op> B, where A is the scan key and B is the
 *	tuple pointed at by itemid on page.
 */
bool
_bt_skeycmp(Relation rel,
	    Size keysz,
	    ScanKey scankey,
	    Page page,
	    ItemId itemid,
	    StrategyNumber strat)
{
    BTItem item;
    IndexTuple indexTuple;
    TupleDesc tupDes;
    ScanKey entry;
    int i;
    Datum attrDatum;
    Datum keyDatum;
    bool compare;
    bool isNull;
    
    item = (BTItem) PageGetItem(page, itemid);
    indexTuple = &(item->bti_itup);
    
    tupDes = RelationGetTupleDescriptor(rel);
    
    /* see if the comparison is true for all of the key attributes */
    for (i=1; i <= keysz; i++) {
	
	entry = &scankey[i-1];
	attrDatum = index_getattr(indexTuple,
				  entry->sk_attno,
				  tupDes,
				  &isNull);
	keyDatum  = entry->sk_argument;
	
	/*
	 * This may happen in a nested loop if an attribute used
	 * as scan key is null.			DZ 29-10-1996
	 */
	if ((entry->sk_flags & SK_ISNULL) || (isNull)) {
	    if ((entry->sk_flags & SK_ISNULL) && (isNull)) {
		return (true);
	    } else {
		return (false);
	    }
	}

	compare = _bt_invokestrat(rel, i, strat, keyDatum, attrDatum);
	if (!compare)
	    return (false);
    }
    
    return (true);
}

/*
 *  _bt_binsrch() -- Do a binary search for a key on a particular page.
 *
 *	The scankey we get has the compare function stored in the procedure
 *	entry of each data struct.  We invoke this regproc to do the
 *	comparison for every key in the scankey.  _bt_binsrch() returns
 *	the OffsetNumber of the first matching key on the page, or the
 *	OffsetNumber at which the matching key would appear if it were
 *	on this page.
 *
 *	By the time this procedure is called, we're sure we're looking
 *	at the right page -- don't need to walk right.  _bt_binsrch() has
 *	no lock or refcount side effects on the buffer.
 */
OffsetNumber
_bt_binsrch(Relation rel,
	    Buffer buf,
	    int keysz,
	    ScanKey scankey,
	    int srchtype)
{
    TupleDesc itupdesc;
    Page page;
    BTPageOpaque opaque;
    OffsetNumber low, mid, high;
    int result;
    
    page = BufferGetPage(buf);
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    
    /* by convention, item 0 on any non-rightmost page is the high key */
    low = mid = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
    
    high = PageGetMaxOffsetNumber(page);
    
    /*
     *  Since for non-rightmost pages, the zeroeth item on the page is the
     *  high key, there are two notions of emptiness.  One is if nothing
     *  appears on the page.  The other is if nothing but the high key does.
     *  The reason we test high <= low, rather than high == low, is that
     *  after vacuuming there may be nothing *but* the high key on a page.
     *  In that case, given the scheme above, low = 1 and high = 0.
     */
    
    if (PageIsEmpty(page) || (! P_RIGHTMOST(opaque) && high <= low))
	return (low);
    
    itupdesc = RelationGetTupleDescriptor(rel);
    
    while ((high - low) > 1) {
	mid = low + ((high - low) / 2);
	result = _bt_compare(rel, itupdesc, page, keysz, scankey, mid);
	
	if (result > 0)
	    low = mid;
	else if (result < 0)
	    high = mid - 1;
	else
	return (_bt_firsteq(rel, itupdesc, page, keysz, scankey, mid));
    }
	
	/*
	 *  We terminated because the endpoints got too close together.  There
	 *  are two cases to take care of.
	 *
	 *  For non-insertion searches on internal pages, we want to point at
	 *  the last key <, or first key =, the scankey on the page.  This
	 *  guarantees that we'll descend the tree correctly.
	 *
	 *  For all other cases, we want to point at the first key >=
	 *  the scankey on the page.  This guarantees that scans and
	 *  insertions will happen correctly.
	 */
	
	opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	if (!(opaque->btpo_flags & BTP_LEAF) && srchtype == BT_DESCENT) {
	    
	    /*
	     *  We want the last key <, or first key ==, the scan key.
	     */
	    
	    result = _bt_compare(rel, itupdesc, page, keysz, scankey, high);
	    
	    if (result == 0) {
		return (_bt_firsteq(rel, itupdesc, page, keysz, scankey, high));
	    } else if (result > 0) {
		return (high);
	    } else {
		return (low);
	    }
	} else {
	    
	    /* we want the first key >= the scan key */
	    result = _bt_compare(rel, itupdesc, page, keysz, scankey, low);
	    if (result <= 0) {
		return (low);
	    } else {
		if (low == high)
		    return (OffsetNumberNext(low));
		
		result = _bt_compare(rel, itupdesc, page, keysz, scankey, high);
		if (result <= 0)
		    return (high);
		else
		    return (OffsetNumberNext(high));
	    }
	}
}

static OffsetNumber
_bt_firsteq(Relation rel,
	    TupleDesc itupdesc,
	    Page page,
	    Size keysz,
	    ScanKey scankey,
	    OffsetNumber offnum)
{
    BTPageOpaque opaque;
    OffsetNumber limit;
    
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    
    /* skip the high key, if any */
    limit = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
    
    /* walk backwards looking for the first key in the chain of duplicates */
    while (offnum > limit
	   && _bt_compare(rel, itupdesc, page,
			  keysz, scankey, OffsetNumberPrev(offnum)) == 0) {
	offnum = OffsetNumberPrev(offnum);
    }
    
    return (offnum);
}

/*
 *  _bt_compare() -- Compare scankey to a particular tuple on the page.
 *
 *	This routine returns:
 *	    -1 if scankey < tuple at offnum;
 *	     0 if scankey == tuple at offnum;
 *	    +1 if scankey > tuple at offnum.
 *
 *	In order to avoid having to propagate changes up the tree any time
 *	a new minimal key is inserted, the leftmost entry on the leftmost
 *	page is less than all possible keys, by definition.
 */
static int
_bt_compare(Relation rel,
	    TupleDesc itupdesc,
	    Page page,
	    int keysz,
	    ScanKey scankey,
	    OffsetNumber offnum)
{
    Datum datum;
    BTItem btitem;
    ItemId itemid;
    IndexTuple itup;
    BTPageOpaque opaque;
    ScanKey entry;
    AttrNumber attno;
    int result;
    int i;
    bool null;
    
    /*
     *  If this is a leftmost internal page, and if our comparison is
     *  with the first key on the page, then the item at that position is
     *  by definition less than the scan key.
     */
    
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    if (!(opaque->btpo_flags & BTP_LEAF)
	&& P_LEFTMOST(opaque)
	&& offnum == P_HIKEY) {
	itemid = PageGetItemId(page, offnum);
	
	/*
	 *  we just have to believe that this will only be called with
	 *  offnum == P_HIKEY when P_HIKEY is the OffsetNumber of the
	 *  first actual data key (i.e., this is also a rightmost
	 *  page).  there doesn't seem to be any code that implies
	 *  that the leftmost page is normally missing a high key as
	 *  well as the rightmost page.  but that implies that this
	 *  code path only applies to the root -- which seems
	 *  unlikely..
	 */
	if (! P_RIGHTMOST(opaque)) {
	    elog(WARN, "_bt_compare: invalid comparison to high key");
	}

	/*
	 *  If the item on the page is equal to the scankey, that's
	 *  okay to admit.  We just can't claim that the first key on
	 *  the page is greater than anything.
	 */
	
	if (_bt_skeycmp(rel, keysz, scankey, page, itemid,
			BTEqualStrategyNumber)) {
	    return (0);
	}
	return (1);
    }
    
    btitem = (BTItem) PageGetItem(page, PageGetItemId(page, offnum));
    itup = &(btitem->bti_itup);
    
    /*
     *  The scan key is set up with the attribute number associated with each
     *  term in the key.  It is important that, if the index is multi-key,
     *  the scan contain the first k key attributes, and that they be in
     *  order.  If you think about how multi-key ordering works, you'll
     *  understand why this is.
     *
     *  We don't test for violation of this condition here.
     */
    
    for (i = 1; i <= keysz; i++) {
	long tmpres;
	
	entry = &scankey[i - 1];
	attno = entry->sk_attno;
	datum = index_getattr(itup, attno, itupdesc, &null);

	/*
	 * This may happen in a nested loop if an attribute used
	 * as scan key is null.			DZ 29-10-1996
	 */
	if ((entry->sk_flags & SK_ISNULL) || (null)) {
	    if ((entry->sk_flags & SK_ISNULL) && (null)) {
		return (0);
	    } else {
		return (null ? +1 : -1);
	    }
	}

	tmpres = (long) FMGR_PTR2(entry->sk_func, entry->sk_procedure,
				  entry->sk_argument, datum);
	result = tmpres;
	
	/* if the keys are unequal, return the difference */
	if (result != 0)
	    return (result);
    }
    
    /* by here, the keys are equal */
    return (0);
}

/*
 *  _bt_next() -- Get the next item in a scan.
 *
 *	On entry, we have a valid currentItemData in the scan, and a
 *	read lock on the page that contains that item.  We do not have
 *	the page pinned.  We return the next item in the scan.  On
 *	exit, we have the page containing the next item locked but not
 *	pinned.
 */
RetrieveIndexResult
_bt_next(IndexScanDesc scan, ScanDirection dir)
{
    Relation rel;
    Buffer buf;
    Page page;
    OffsetNumber offnum;
    RetrieveIndexResult res;
    BlockNumber blkno;
    ItemPointer current;
    ItemPointer iptr;
    BTItem btitem;
    IndexTuple itup;
    BTScanOpaque so;
    
    rel = scan->relation;
    so = (BTScanOpaque) scan->opaque;
    current = &(scan->currentItemData);
    
    /*
     *  XXX 10 may 91:  somewhere there's a bug in our management of the
     *  cached buffer for this scan.  wei discovered it.  the following
     *  is a workaround so he can work until i figure out what's going on.
     */
    
    if (!BufferIsValid(so->btso_curbuf))
	so->btso_curbuf = _bt_getbuf(rel, ItemPointerGetBlockNumber(current),
				     BT_READ);
    
    /* we still have the buffer pinned and locked */
    buf = so->btso_curbuf;
    blkno = BufferGetBlockNumber(buf);
    
    /* step one tuple in the appropriate direction */
    if (!_bt_step(scan, &buf, dir))
	return ((RetrieveIndexResult) NULL);
    
    /* by here, current is the tuple we want to return */
    offnum = ItemPointerGetOffsetNumber(current);
    page = BufferGetPage(buf);
    btitem = (BTItem) PageGetItem(page, PageGetItemId(page, offnum));
    itup = &btitem->bti_itup;
    
    if (_bt_checkqual(scan, itup)) {
	iptr = (ItemPointer) palloc(sizeof(ItemPointerData));
	memmove((char *) iptr, (char *) &(itup->t_tid),
		sizeof(ItemPointerData));
	res = FormRetrieveIndexResult(current, iptr);
	
	/* remember which buffer we have pinned and locked */
	so->btso_curbuf = buf;
    } else {
	ItemPointerSetInvalid(current);
	so->btso_curbuf = InvalidBuffer;
	_bt_relbuf(rel, buf, BT_READ);
	res = (RetrieveIndexResult) NULL;
    }
    
    return (res);
}

/*
 *  _bt_first() -- Find the first item in a scan.
 *
 *	We need to be clever about the type of scan, the operation it's
 *	performing, and the tree ordering.  We return the RetrieveIndexResult
 *	of the first item in the tree that satisfies the qualification
 *	associated with the scan descriptor.  On exit, the page containing
 *	the current index tuple is read locked and pinned, and the scan's
 *	opaque data entry is updated to include the buffer.
 */
RetrieveIndexResult
_bt_first(IndexScanDesc scan, ScanDirection dir)
{
    Relation rel;
    TupleDesc itupdesc;
    Buffer buf;
    Page page;
    BTStack stack;
    OffsetNumber offnum, maxoff;
    BTItem btitem;
    IndexTuple itup;
    ItemPointer current;
    ItemPointer iptr;
    BlockNumber blkno;
    StrategyNumber strat;
    RetrieveIndexResult res;
    RegProcedure proc;
    int result;
    BTScanOpaque so;
    ScanKeyData skdata;
    
    so = (BTScanOpaque) scan->opaque;
    if ( so->qual_ok == 0 )		/* may be set by _bt_orderkeys */
    	return ((RetrieveIndexResult) NULL);
    
    /* if we just need to walk down one edge of the tree, do that */
    if (scan->scanFromEnd)
	return (_bt_endpoint(scan, dir));
    
    rel = scan->relation;
    itupdesc = RelationGetTupleDescriptor(scan->relation);
    current = &(scan->currentItemData);
    
    /*
     *  Okay, we want something more complicated.  What we'll do is use
     *  the first item in the scan key passed in (which has been correctly
     *  ordered to take advantage of index ordering) to position ourselves
     *  at the right place in the scan.
     */
    
    /*
     *  XXX -- The attribute number stored in the scan key is the attno
     *	       in the heap relation.  We need to transmogrify this into
     *         the index relation attno here.  For the moment, we have
     *	       hardwired attno == 1.
     */
    proc = index_getprocid(rel, 1, BTORDER_PROC);
    ScanKeyEntryInitialize(&skdata, so->keyData[0].sk_flags, 1, proc,
			   so->keyData[0].sk_argument);
    
    stack = _bt_search(rel, 1, &skdata, &buf);
    _bt_freestack(stack);
    
    /* find the nearest match to the manufactured scan key on the page */
    offnum = _bt_binsrch(rel, buf, 1, &skdata, BT_DESCENT);
    page = BufferGetPage(buf);
    
    /*
     *  This will happen if the tree we're searching is entirely empty,
     *  or if we're doing a search for a key that would appear on an
     *  entirely empty internal page.  In either case, there are no
     *  matching tuples in the index.
     */
    
    if (PageIsEmpty(page)) {
	ItemPointerSetInvalid(current);
	so->btso_curbuf = InvalidBuffer;
	_bt_relbuf(rel, buf, BT_READ);
	return ((RetrieveIndexResult) NULL);
    }
    
    maxoff = PageGetMaxOffsetNumber(page);
    
    if (offnum > maxoff)
	offnum = maxoff;
    
    blkno = BufferGetBlockNumber(buf);
    ItemPointerSet(current, blkno, offnum);
    
    /*
     *  Now find the right place to start the scan.  Result is the
     *  value we're looking for minus the value we're looking at
     *  in the index.
     */
    
    result = _bt_compare(rel, itupdesc, page, 1, &skdata, offnum);
    strat = _bt_getstrat(rel, 1, so->keyData[0].sk_procedure);
    
    switch (strat) {
    case BTLessStrategyNumber:
	if (result <= 0) {
	    do {
		if (!_bt_twostep(scan, &buf, BackwardScanDirection))
		    break;
		
		offnum = ItemPointerGetOffsetNumber(current);
		page = BufferGetPage(buf);
		result = _bt_compare(rel, itupdesc, page, 1, &skdata, offnum);
	    } while (result <= 0);
	    
	    /* if this is true, the key we just looked at is gone */
	    if (result > 0)
		(void) _bt_twostep(scan, &buf, ForwardScanDirection);
	}
	break;
	
    case BTLessEqualStrategyNumber:
	if (result >= 0) {
	    do {
		if (!_bt_twostep(scan, &buf, ForwardScanDirection))
		    break;
		
		offnum = ItemPointerGetOffsetNumber(current);
		page = BufferGetPage(buf);
		result = _bt_compare(rel, itupdesc, page, 1, &skdata, offnum);
	    } while (result >= 0);
	    
	    if (result < 0)
		(void) _bt_twostep(scan, &buf, BackwardScanDirection);
	}
	break;
	
    case BTEqualStrategyNumber:
	if (result != 0) {
	    _bt_relbuf(scan->relation, buf, BT_READ);
	    so->btso_curbuf = InvalidBuffer;
	    ItemPointerSetInvalid(&(scan->currentItemData));
	    return ((RetrieveIndexResult) NULL);
	}
	break;
	
    case BTGreaterEqualStrategyNumber:
	if (result < 0) {
	    do {
		if (!_bt_twostep(scan, &buf, BackwardScanDirection))
		    break;
		
		page = BufferGetPage(buf);
		offnum = ItemPointerGetOffsetNumber(current);
		result = _bt_compare(rel, itupdesc, page, 1, &skdata, offnum);
	    } while (result < 0);
	    
	    if (result > 0)
		(void) _bt_twostep(scan, &buf, ForwardScanDirection);
	}
	break;
	
    case BTGreaterStrategyNumber:
	if (result >= 0) {
	    do {
		if (!_bt_twostep(scan, &buf, ForwardScanDirection))
		    break;
		
		offnum = ItemPointerGetOffsetNumber(current);
		page = BufferGetPage(buf);
		result = _bt_compare(rel, itupdesc, page, 1, &skdata, offnum);
	    } while (result >= 0);
	}
	break;
    }
    
    /* okay, current item pointer for the scan is right */
    offnum = ItemPointerGetOffsetNumber(current);
    page = BufferGetPage(buf);
    btitem = (BTItem) PageGetItem(page, PageGetItemId(page, offnum));
    itup = &btitem->bti_itup;
    
    if (_bt_checkqual(scan, itup)) {
	iptr = (ItemPointer) palloc(sizeof(ItemPointerData));
	memmove((char *) iptr, (char *) &(itup->t_tid),
		sizeof(ItemPointerData));
	res = FormRetrieveIndexResult(current, iptr);
	pfree(iptr);
	
	/* remember which buffer we have pinned */
	so->btso_curbuf = buf;
    } else {
	ItemPointerSetInvalid(current);
	so->btso_curbuf = InvalidBuffer;
	_bt_relbuf(rel, buf, BT_READ);
	res = (RetrieveIndexResult) NULL;
    }
    
    return (res);
}

/*
 *  _bt_step() -- Step one item in the requested direction in a scan on
 *		  the tree.
 *
 *	If no adjacent record exists in the requested direction, return
 *	false.  Else, return true and set the currentItemData for the
 *	scan to the right thing.
 */
bool
_bt_step(IndexScanDesc scan, Buffer *bufP, ScanDirection dir)
{
    Page page;
    BTPageOpaque opaque;
    OffsetNumber offnum, maxoff;
    OffsetNumber start;
    BlockNumber blkno;
    BlockNumber obknum;
    BTScanOpaque so;
    ItemPointer current;
    Relation rel;
    
    rel = scan->relation;
    current = &(scan->currentItemData);
    offnum = ItemPointerGetOffsetNumber(current);
    page = BufferGetPage(*bufP);
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    so = (BTScanOpaque) scan->opaque;
    maxoff = PageGetMaxOffsetNumber(page);
    
    /* get the next tuple */
    if (ScanDirectionIsForward(dir)) {
	if (!PageIsEmpty(page) && offnum < maxoff) {
	    offnum = OffsetNumberNext(offnum);
	} else {
	    
	    /* if we're at end of scan, release the buffer and return */
	    blkno = opaque->btpo_next;
	    if (P_RIGHTMOST(opaque)) {
		_bt_relbuf(rel, *bufP, BT_READ);
		ItemPointerSetInvalid(current);
		*bufP = so->btso_curbuf = InvalidBuffer;
		return (false);
	    } else {
		
		/* walk right to the next page with data */
		_bt_relbuf(rel, *bufP, BT_READ);
		for (;;) {
		    *bufP = _bt_getbuf(rel, blkno, BT_READ);
		    page = BufferGetPage(*bufP);
		    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
		    maxoff = PageGetMaxOffsetNumber(page);
		    start = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
		    
		    if (!PageIsEmpty(page) && start <= maxoff) {
			break;
		    } else {
			blkno = opaque->btpo_next;
			_bt_relbuf(rel, *bufP, BT_READ);
			if (blkno == P_NONE) {
			    *bufP = so->btso_curbuf = InvalidBuffer;
			    ItemPointerSetInvalid(current);
			    return (false);
			}
		    }
		}
		offnum = start;
	    }
	}
    } else if (ScanDirectionIsBackward(dir)) {
	
	/* remember that high key is item zero on non-rightmost pages */
	start = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;

	if (offnum > start) {
	    offnum = OffsetNumberPrev(offnum);
	} else {
	    
	    /* if we're at end of scan, release the buffer and return */
	    blkno = opaque->btpo_prev;
	    if (P_LEFTMOST(opaque)) {
		_bt_relbuf(rel, *bufP, BT_READ);
		*bufP = so->btso_curbuf = InvalidBuffer;
		ItemPointerSetInvalid(current);
		return (false);
	    } else {
		
		obknum = BufferGetBlockNumber(*bufP);
		
		/* walk right to the next page with data */
		_bt_relbuf(rel, *bufP, BT_READ);
		for (;;) {
		    *bufP = _bt_getbuf(rel, blkno, BT_READ);
		    page = BufferGetPage(*bufP);
		    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
		    maxoff = PageGetMaxOffsetNumber(page);
		    
		    /*
		     *  If the adjacent page just split, then we may have the
		     *  wrong block.  Handle this case.  Because pages only
		     *  split right, we don't have to worry about this failing
		     *  to terminate.
		     */
		    
		    while (opaque->btpo_next != obknum) {
			blkno = opaque->btpo_next;
			_bt_relbuf(rel, *bufP, BT_READ);
			*bufP = _bt_getbuf(rel, blkno, BT_READ);
			page = BufferGetPage(*bufP);
			opaque = (BTPageOpaque) PageGetSpecialPointer(page);
			maxoff = PageGetMaxOffsetNumber(page);
		    }
		    
		    /* don't consider the high key */
		    start = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
		    
		    /* anything to look at here? */
		    if (!PageIsEmpty(page) && maxoff >= start) {
			break;
		    } else {
			blkno = opaque->btpo_prev;
			obknum = BufferGetBlockNumber(*bufP);
			_bt_relbuf(rel, *bufP, BT_READ);
			if (blkno == P_NONE) {
			    *bufP = so->btso_curbuf = InvalidBuffer;
			    ItemPointerSetInvalid(current);
			    return (false);
			}
		    }
		}
		offnum = maxoff;	/* XXX PageIsEmpty? */
	    }
	}
    }
    blkno = BufferGetBlockNumber(*bufP);
    so->btso_curbuf = *bufP;
    ItemPointerSet(current, blkno, offnum);
    
    return (true);
}

/*
 *  _bt_twostep() -- Move to an adjacent record in a scan on the tree,
 *		     if an adjacent record exists.
 *
 *	This is like _bt_step, except that if no adjacent record exists
 *	it restores us to where we were before trying the step.  This is
 *	only hairy when you cross page boundaries, since the page you cross
 *	from could have records inserted or deleted, or could even split.
 *	This is unlikely, but we try to handle it correctly here anyway.
 *
 *	This routine contains the only case in which our changes to Lehman
 *	and Yao's algorithm.
 *
 *	Like step, this routine leaves the scan's currentItemData in the
 *	proper state and acquires a lock and pin on *bufP.  If the twostep
 *	succeeded, we return true; otherwise, we return false.
 */
static bool
_bt_twostep(IndexScanDesc scan, Buffer *bufP, ScanDirection dir)
{
    Page page;
    BTPageOpaque opaque;
    OffsetNumber offnum, maxoff;
    OffsetNumber start;
    ItemPointer current;
    ItemId itemid;
    int itemsz;
    BTItem btitem;
    BTItem svitem;
    BlockNumber blkno;
    
    blkno = BufferGetBlockNumber(*bufP);
    page = BufferGetPage(*bufP);
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    maxoff = PageGetMaxOffsetNumber(page);
    current = &(scan->currentItemData);
    offnum = ItemPointerGetOffsetNumber(current);
    
    start = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
    
    /* if we're safe, just do it */
    if (ScanDirectionIsForward(dir) && offnum < maxoff) { /* XXX PageIsEmpty? */
	ItemPointerSet(current, blkno, OffsetNumberNext(offnum));
	return (true);
    } else if (ScanDirectionIsBackward(dir) && offnum > start) {
	ItemPointerSet(current, blkno, OffsetNumberPrev(offnum));
	return (true);
    }
    
    /* if we've hit end of scan we don't have to do any work */
    if (ScanDirectionIsForward(dir) && P_RIGHTMOST(opaque)) {
	return (false);
    } else if (ScanDirectionIsBackward(dir) && P_LEFTMOST(opaque)) {
	return (false);
    }
    
    /*
     *  Okay, it's off the page; let _bt_step() do the hard work, and we'll
     *  try to remember where we were.  This is not guaranteed to work; this
     *  is the only place in the code where concurrency can screw us up,
     *  and it's because we want to be able to move in two directions in
     *  the scan.
     */
    
    itemid = PageGetItemId(page, offnum);
    itemsz = ItemIdGetLength(itemid);
    btitem = (BTItem) PageGetItem(page, itemid);
    svitem = (BTItem) palloc(itemsz);
    memmove((char *) svitem, (char *) btitem, itemsz);
    
    if (_bt_step(scan, bufP, dir)) {
	pfree(svitem);
	return (true);
    }
    
    /* try to find our place again */
    *bufP = _bt_getbuf(scan->relation, blkno, BT_READ);
    page = BufferGetPage(*bufP);
    maxoff = PageGetMaxOffsetNumber(page);
    
    while (offnum <= maxoff) {
	itemid = PageGetItemId(page, offnum);
	btitem = (BTItem) PageGetItem(page, itemid);
	if (btitem->bti_oid == svitem->bti_oid) {
	    pfree(svitem);
	    ItemPointerSet(current, blkno, offnum);
	    return (false);
	}
    }
    
    /*
     *  XXX crash and burn -- can't find our place.  We can be a little
     *  smarter -- walk to the next page to the right, for example, since
     *  that's the only direction that splits happen in.  Deletions screw
     *  us up less often since they're only done by the vacuum daemon.
     */
    
    elog(WARN, "btree synchronization error:  concurrent update botched scan");
    
    return (false);
}

/*
 *  _bt_endpoint() -- Find the first or last key in the index.
 */
static RetrieveIndexResult
_bt_endpoint(IndexScanDesc scan, ScanDirection dir)
{
    Relation rel;
    Buffer buf;
    Page page;
    BTPageOpaque opaque;
    ItemPointer current;
    ItemPointer iptr;
    OffsetNumber offnum, maxoff;
    OffsetNumber start = 0;
    BlockNumber blkno;
    BTItem btitem;
    IndexTuple itup;
    BTScanOpaque so;
    RetrieveIndexResult res;
    
    rel = scan->relation;
    current = &(scan->currentItemData);
    
    buf = _bt_getroot(rel, BT_READ);
    blkno = BufferGetBlockNumber(buf);
    page = BufferGetPage(buf);
    opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    
    for (;;) {
	if (opaque->btpo_flags & BTP_LEAF)
	    break;
	
	if (ScanDirectionIsForward(dir)) {
	    offnum = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
	} else {
	    offnum = PageGetMaxOffsetNumber(page);
	}
	
	btitem = (BTItem) PageGetItem(page, PageGetItemId(page, offnum));
	itup = &(btitem->bti_itup);
	
	blkno = ItemPointerGetBlockNumber(&(itup->t_tid));
	
	_bt_relbuf(rel, buf, BT_READ);
	buf = _bt_getbuf(rel, blkno, BT_READ);
	page = BufferGetPage(buf);
	opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	
	/*
	 *  Race condition: If the child page we just stepped onto is
	 *  in the process of being split, we need to make sure we're
	 *  all the way at the right edge of the tree.  See the paper
	 *  by Lehman and Yao.
	 */
	
	if (ScanDirectionIsBackward(dir) && ! P_RIGHTMOST(opaque)) {
	    do {
		blkno = opaque->btpo_next;
		_bt_relbuf(rel, buf, BT_READ);
		buf = _bt_getbuf(rel, blkno, BT_READ);
		page = BufferGetPage(buf);
		opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	    } while (! P_RIGHTMOST(opaque));
	}
    }
    
    /* okay, we've got the {left,right}-most page in the tree */
    maxoff = PageGetMaxOffsetNumber(page);
    
    if (ScanDirectionIsForward(dir)) {
	if (PageIsEmpty(page)) {
	    maxoff = FirstOffsetNumber;
	} else {
	    maxoff = PageGetMaxOffsetNumber(page);
	}
	start = P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY;
	
	if (PageIsEmpty(page) || start > maxoff) {
	    ItemPointerSet(current, blkno, maxoff);
	    if (!_bt_step(scan, &buf, BackwardScanDirection))
		return ((RetrieveIndexResult) NULL);
	    
	    start = ItemPointerGetOffsetNumber(current);
	    page = BufferGetPage(buf);
	} else {
	    ItemPointerSet(current, blkno, start);
	}
    } else if (ScanDirectionIsBackward(dir)) {
	if (PageIsEmpty(page)) {
	    ItemPointerSet(current, blkno, FirstOffsetNumber);
	    if (!_bt_step(scan, &buf, ForwardScanDirection))
		return ((RetrieveIndexResult) NULL);
	    
	    start = ItemPointerGetOffsetNumber(current);
	    page = BufferGetPage(buf);
	} else {
	    start = PageGetMaxOffsetNumber(page);
	    ItemPointerSet(current, blkno, start);
	}
    } else {
	elog(WARN, "Illegal scan direction %d", dir);
    }
    
    btitem = (BTItem) PageGetItem(page, PageGetItemId(page, start));
    itup = &(btitem->bti_itup);
    
    /* see if we picked a winner */
    if (_bt_checkqual(scan, itup)) {
	iptr = (ItemPointer) palloc(sizeof(ItemPointerData));
	memmove((char *) iptr, (char *) &(itup->t_tid),
		sizeof(ItemPointerData));
	res = FormRetrieveIndexResult(current, iptr);
	
	/* remember which buffer we have pinned */
	so = (BTScanOpaque) scan->opaque;
	so->btso_curbuf = buf;
    } else {
	_bt_relbuf(rel, buf, BT_READ);
	res = (RetrieveIndexResult) NULL;
    }
    
    return (res);
}