/*-------------------------------------------------------------------------
 *
 * multixact.c
 *		PostgreSQL multi-transaction-log manager
 *
 * The pg_multixact manager is a pg_clog-like manager that stores an array
 * of TransactionIds for each MultiXactId.  It is a fundamental part of the
 * shared-row-lock implementation.  A share-locked tuple stores a
 * MultiXactId in its Xmax, and a transaction that needs to wait for the
 * tuple to be unlocked can sleep on the potentially-several TransactionIds
 * that compose the MultiXactId.
 *
 * We use two SLRU areas, one for storing the offsets on which the data
 * starts for each MultiXactId in the other one.  This trick allows us to
 * store variable length arrays of TransactionIds.  (We could alternatively
 * use one area containing counts and TransactionIds, with valid MultiXactId
 * values pointing at slots containing counts; but that way seems less robust
 * since it would get completely confused if someone inquired about a bogus
 * MultiXactId that pointed to an intermediate slot containing an XID.)
 *
 * This code is based on subtrans.c; see it for additional discussion.
 * Like the subtransaction manager, we only need to remember multixact
 * information for currently-open transactions.  Thus, there is
 * no need to preserve data over a crash and restart.
 *
 * The only XLOG interaction we need to take care of is that generated
 * MultiXactId values must continue to increase across a system crash.
 * Thus we log groups of MultiXactIds acquisition in the same fashion we do
 * for Oids (see XLogPutNextMultiXactId).
 *
 * Portions Copyright (c) 1996-2005, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * $PostgreSQL: pgsql/src/backend/access/transam/multixact.c,v 1.4 2005/05/19 21:35:45 tgl Exp $
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/multixact.h"
#include "access/slru.h"
#include "access/xact.h"
#include "miscadmin.h"
#include "utils/memutils.h"
#include "storage/backendid.h"
#include "storage/lmgr.h"
#include "storage/procarray.h"


/*
 * Defines for MultiXactOffset page sizes.  A page is the same BLCKSZ as is
 * used everywhere else in Postgres.
 *
 * Note: because both uint32 and TransactionIds are 32 bits and wrap around at
 * 0xFFFFFFFF, MultiXact page numbering also wraps around at
 * 0xFFFFFFFF/MULTIXACT_*_PER_PAGE, and segment numbering at
 * 0xFFFFFFFF/MULTIXACT_*_PER_PAGE/SLRU_SEGMENTS_PER_PAGE.  We need take no
 * explicit notice of that fact in this module, except when comparing segment
 * and page numbers in TruncateMultiXact
 * (see MultiXact{Offset,Member}PagePrecedes).
 */

/* We need four bytes per offset and also four bytes per member */
#define MULTIXACT_OFFSETS_PER_PAGE (BLCKSZ / sizeof(uint32))
#define MULTIXACT_MEMBERS_PER_PAGE (BLCKSZ / sizeof(TransactionId))

#define MultiXactIdToOffsetPage(xid) \
	((xid) / (uint32) MULTIXACT_OFFSETS_PER_PAGE)
#define MultiXactIdToOffsetEntry(xid) \
	((xid) % (uint32) MULTIXACT_OFFSETS_PER_PAGE)

#define MXOffsetToMemberPage(xid) \
	((xid) / (TransactionId) MULTIXACT_MEMBERS_PER_PAGE)
#define MXOffsetToMemberEntry(xid) \
	((xid) % (TransactionId) MULTIXACT_MEMBERS_PER_PAGE)

/* Arbitrary number of MultiXactIds to allocate at each XLog call */
#define MXACT_PREFETCH	8192

/*
 * Links to shared-memory data structures for MultiXact control
 */
static SlruCtlData MultiXactOffsetCtlData;
static SlruCtlData MultiXactMemberCtlData;

#define MultiXactOffsetCtl  (&MultiXactOffsetCtlData)
#define MultiXactMemberCtl  (&MultiXactMemberCtlData)

/*
 * MultiXact state shared across all backends.  All this state is protected
 * by MultiXactGenLock.  (We also use MultiXactOffsetControlLock and
 * MultiXactMemberControlLock to guard accesses to the two sets of SLRU
 * buffers.  For concurrency's sake, we avoid holding more than one of these
 * locks at a time.)
 */
typedef struct MultiXactStateData
{
	/* next-to-be-assigned MultiXactId */
	MultiXactId		nextMXact;

	/* MultiXactIds we have left before logging more */
	uint32			mXactCount;

	/* next-to-be-assigned offset */
	uint32			nextOffset;

	/* the Offset SLRU area was last truncated at this MultiXactId */
	MultiXactId		lastTruncationPoint;

	/*
	 * Per-backend data starts here.  We have two arrays stored in
	 * the area immediately following the MultiXactStateData struct.
	 * Each is indexed by BackendId.  (Note: valid BackendIds run from 1 to
	 * MaxBackends; element zero of each array is never used.)
	 *
	 * OldestMemberMXactId[k] is the oldest MultiXactId each backend's
	 * current transaction(s) could possibly be a member of, or
	 * InvalidMultiXactId when the backend has no live transaction that
	 * could possibly be a member of a MultiXact.  Each backend sets its
	 * entry to the current nextMXact counter just before first acquiring a
	 * shared lock in a given transaction, and clears it at transaction end.
	 * (This works because only during or after acquiring a shared lock
	 * could an XID possibly become a member of a MultiXact, and that
	 * MultiXact would have to be created during or after the lock
	 * acquisition.)
	 *
	 * OldestVisibleMXactId[k] is the oldest MultiXactId each backend's
	 * current transaction(s) think is potentially live, or InvalidMultiXactId
	 * when not in a transaction or not in a transaction that's paid any
	 * attention to MultiXacts yet.  This is computed when first needed in
	 * a given transaction, and cleared at transaction end.  We can compute
	 * it as the minimum of the valid OldestMemberMXactId[] entries at the
	 * time we compute it (using nextMXact if none are valid).  Each backend
	 * is required not to attempt to access any SLRU data for MultiXactIds
	 * older than its own OldestVisibleMXactId[] setting; this is necessary
	 * because the checkpointer could truncate away such data at any instant.
	 *
	 * The checkpointer can compute the safe truncation point as the oldest
	 * valid value among all the OldestMemberMXactId[] and
	 * OldestVisibleMXactId[] entries, or nextMXact if none are valid.
	 * Clearly, it is not possible for any later-computed OldestVisibleMXactId
	 * value to be older than this, and so there is no risk of truncating
	 * data that is still needed.
	 */
	MultiXactId	   perBackendXactIds[1];	/* VARIABLE LENGTH ARRAY */
} MultiXactStateData;

/* Pointers to the state data in shared memory */
static MultiXactStateData *MultiXactState;
static MultiXactId *OldestMemberMXactId;
static MultiXactId *OldestVisibleMXactId;


/*
 * Definitions for the backend-local MultiXactId cache.
 *
 * We use this cache to store known MultiXacts, so we don't need to go to
 * SLRU areas everytime.
 *
 * The cache lasts for the duration of a single transaction, the rationale
 * for this being that most entries will contain our own TransactionId and
 * so they will be uninteresting by the time our next transaction starts.
 * (XXX not clear that this is correct --- other members of the MultiXact
 * could hang around longer than we did.)
 *
 * We allocate the cache entries in a memory context that is deleted at
 * transaction end, so we don't need to do retail freeing of entries.
 */
typedef struct mXactCacheEnt
{
	struct mXactCacheEnt *next;
	MultiXactId		multi;
	int				nxids;
	TransactionId	xids[1];	/* VARIABLE LENGTH ARRAY */
} mXactCacheEnt;

static mXactCacheEnt   *MXactCache = NULL;
static MemoryContext	MXactContext = NULL;


#ifdef MULTIXACT_DEBUG
#define debug_elog2(a,b) elog(a,b)
#define debug_elog3(a,b,c) elog(a,b,c)
#define debug_elog4(a,b,c,d) elog(a,b,c,d)
#define debug_elog5(a,b,c,d,e) elog(a,b,c,d,e)
#else
#define debug_elog2(a,b)
#define debug_elog3(a,b,c)
#define debug_elog4(a,b,c,d)
#define debug_elog5(a,b,c,d,e)
#endif

/* internal MultiXactId management */
static void MultiXactIdSetOldestVisible(void);
static MultiXactId CreateMultiXactId(int nxids, TransactionId *xids);
static int GetMultiXactIdMembers(MultiXactId multi, TransactionId **xids);
static MultiXactId GetNewMultiXactId(int nxids, uint32 *offset);

/* MultiXact cache management */
static MultiXactId mXactCacheGetBySet(int nxids, TransactionId *xids);
static int mXactCacheGetById(MultiXactId multi, TransactionId **xids);
static void mXactCachePut(MultiXactId multi, int nxids, TransactionId *xids);
static int xidComparator(const void *arg1, const void *arg2);
#ifdef MULTIXACT_DEBUG
static char *mxid_to_string(MultiXactId multi, int nxids, TransactionId *xids);
#endif

/* management of SLRU infrastructure */
static int	ZeroMultiXactOffsetPage(int pageno);
static int	ZeroMultiXactMemberPage(int pageno);
static bool MultiXactOffsetPagePrecedes(int page1, int page2);
static bool MultiXactMemberPagePrecedes(int page1, int page2);
static bool MultiXactIdPrecedes(MultiXactId multi1, MultiXactId multi2);
static bool MultiXactOffsetPrecedes(uint32 offset1, uint32 offset2);
static void ExtendMultiXactOffset(MultiXactId multi);
static void ExtendMultiXactMember(uint32 offset);
static void TruncateMultiXact(void);


/*
 * MultiXactIdCreate
 *		Construct a MultiXactId representing two TransactionIds.
 *
 * The two XIDs must be different.
 *
 * NB - we don't worry about our local MultiXactId cache here, because that
 * is handled by the lower-level routines.
 */
MultiXactId
MultiXactIdCreate(TransactionId xid1, TransactionId xid2)
{
	MultiXactId		newMulti;
	TransactionId	xids[2];

	AssertArg(TransactionIdIsValid(xid1));
	AssertArg(TransactionIdIsValid(xid2));

	Assert(!TransactionIdEquals(xid1, xid2));

	/*
	 * Note: unlike MultiXactIdExpand, we don't bother to check that both
	 * XIDs are still running.  In typical usage, xid2 will be our own XID
	 * and the caller just did a check on xid1, so it'd be wasted effort.
	 */

	xids[0] = xid1;
	xids[1] = xid2;

	newMulti = CreateMultiXactId(2, xids);

	debug_elog5(DEBUG2, "Create: returning %u for %u, %u",
				newMulti, xid1, xid2);

	return newMulti;
}

/*
 * MultiXactIdExpand
 *		Add a TransactionId to a pre-existing MultiXactId.
 *
 * If the TransactionId is already a member of the passed MultiXactId,
 * just return it as-is.
 *
 * Note that we do NOT actually modify the membership of a pre-existing
 * MultiXactId; instead we create a new one.  This is necessary to avoid
 * a race condition against MultiXactIdWait (see notes there).
 *
 * NB - we don't worry about our local MultiXactId cache here, because that
 * is handled by the lower-level routines.
 */
MultiXactId
MultiXactIdExpand(MultiXactId multi, TransactionId xid)
{
	MultiXactId		newMulti;
	TransactionId  *members;
	TransactionId  *newMembers;
	int				nmembers;
	int				i;
	int				j;

	AssertArg(MultiXactIdIsValid(multi));
	AssertArg(TransactionIdIsValid(xid));

	debug_elog4(DEBUG2, "Expand: received multi %u, xid %u",
				multi, xid);

	nmembers = GetMultiXactIdMembers(multi, &members);

	if (nmembers < 0)
	{
		/*
		 * The MultiXactId is obsolete.  This can only happen if all the
		 * MultiXactId members stop running between the caller checking and
		 * passing it to us.  It would be better to return that fact to the
		 * caller, but it would complicate the API and it's unlikely to happen
		 * too often, so just deal with it by creating a singleton MultiXact.
		 */
		newMulti = CreateMultiXactId(1, &xid);

		debug_elog4(DEBUG2, "Expand: %u has no members, create singleton %u",
					multi, newMulti);
		return newMulti;
	}

	/*
	 * If the TransactionId is already a member of the MultiXactId,
	 * just return the existing MultiXactId.
	 */
	for (i = 0; i < nmembers; i++)
	{
		if (TransactionIdEquals(members[i], xid))
		{
			debug_elog4(DEBUG2, "Expand: %u is already a member of %u",
						xid, multi);
			pfree(members);
			return multi;
		}
	}

	/*
	 * Determine which of the members of the MultiXactId are still running,
	 * and use them to create a new one.  (Removing dead members is just
	 * an optimization, but a useful one.  Note we have the same race
	 * condition here as above: j could be 0 at the end of the loop.)
	 */
	newMembers = (TransactionId *)
		palloc(sizeof(TransactionId) * (nmembers + 1));

	for (i = 0, j = 0; i < nmembers; i++)
	{
		if (TransactionIdIsInProgress(members[i]))
			newMembers[j++] = members[i];
	}

	newMembers[j++] = xid;
	newMulti = CreateMultiXactId(j, newMembers);

	pfree(members);
	pfree(newMembers);

	debug_elog3(DEBUG2, "Expand: returning new multi %u", newMulti);

	return newMulti;
}

/*
 * MultiXactIdIsRunning
 * 		Returns whether a MultiXactId is "running".
 *
 * We return true if at least one member of the given MultiXactId is still
 * running.  Note that a "false" result is certain not to change,
 * because it is not legal to add members to an existing MultiXactId.
 */
bool
MultiXactIdIsRunning(MultiXactId multi)
{
	TransactionId *members;
	TransactionId  myXid;
	int		nmembers;
	int		i;

	debug_elog3(DEBUG2, "IsRunning %u?", multi);

	nmembers = GetMultiXactIdMembers(multi, &members);

	if (nmembers < 0)
	{
		debug_elog2(DEBUG2, "IsRunning: no members");
		return false;
	}

	/* checking for myself is cheap */
	myXid = GetTopTransactionId();

	for (i = 0; i < nmembers; i++)
	{
		if (TransactionIdEquals(members[i], myXid))
		{
			debug_elog3(DEBUG2, "IsRunning: I (%d) am running!", i);
			pfree(members);
			return true;
		}
	}

	/*
	 * This could be made faster by having another entry point in procarray.c,
	 * walking the PGPROC array only once for all the members.  But in most
	 * cases nmembers should be small enough that it doesn't much matter.
	 */
	for (i = 0; i < nmembers; i++)
	{
		if (TransactionIdIsInProgress(members[i]))
		{
			debug_elog4(DEBUG2, "IsRunning: member %d (%u) is running",
						i, members[i]);
			pfree(members);
			return true;
		}
	}

	pfree(members);

	debug_elog3(DEBUG2, "IsRunning: %u is not running", multi);

	return false;
}

/*
 * MultiXactIdSetOldestMember
 *		Save the oldest MultiXactId this transaction could be a member of.
 *
 * We set the OldestMemberMXactId for a given transaction the first time
 * it's going to acquire a shared lock.  We need to do this even if we end
 * up using a TransactionId instead of a MultiXactId, because there is a
 * chance that another transaction would add our XID to a MultiXactId.
 *
 * The value to set is the next-to-be-assigned MultiXactId, so this is meant
 * to be called just before acquiring a shared lock.
 */
void
MultiXactIdSetOldestMember(void)
{
	if (!MultiXactIdIsValid(OldestMemberMXactId[MyBackendId]))
	{
		MultiXactId nextMXact;

		/*
		 * You might think we don't need to acquire a lock here, since
		 * fetching and storing of TransactionIds is probably atomic,
		 * but in fact we do: suppose we pick up nextMXact and then
		 * lose the CPU for a long time.  Someone else could advance
		 * nextMXact, and then another someone else could compute an
		 * OldestVisibleMXactId that would be after the value we are
		 * going to store when we get control back.  Which would be wrong.
		 */
		LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);

		/*
		 * We have to beware of the possibility that nextMXact is in the
		 * wrapped-around state.  We don't fix the counter itself here,
		 * but we must be sure to store a valid value in our array entry.
		 */
		nextMXact = MultiXactState->nextMXact;
		if (nextMXact < FirstMultiXactId)
			nextMXact = FirstMultiXactId;

		OldestMemberMXactId[MyBackendId] = nextMXact;

		LWLockRelease(MultiXactGenLock);

		debug_elog4(DEBUG2, "MultiXact: setting OldestMember[%d] = %u",
					MyBackendId, nextMXact);
	}
}

/*
 * MultiXactIdSetOldestVisible
 *		Save the oldest MultiXactId this transaction considers possibly live.
 *
 * We set the OldestVisibleMXactId for a given transaction the first time
 * it's going to inspect any MultiXactId.  Once we have set this, we are
 * guaranteed that the checkpointer won't truncate off SLRU data for
 * MultiXactIds at or after our OldestVisibleMXactId.
 *
 * The value to set is the oldest of nextMXact and all the valid per-backend
 * OldestMemberMXactId[] entries.  Because of the locking we do, we can be
 * certain that no subsequent call to MultiXactIdSetOldestMember can set
 * an OldestMemberMXactId[] entry older than what we compute here.  Therefore
 * there is no live transaction, now or later, that can be a member of any
 * MultiXactId older than the OldestVisibleMXactId we compute here.
 */
static void
MultiXactIdSetOldestVisible(void)
{
	if (!MultiXactIdIsValid(OldestVisibleMXactId[MyBackendId]))
	{
		MultiXactId oldestMXact;
		int		i;

		LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);

		/*
		 * We have to beware of the possibility that nextMXact is in the
		 * wrapped-around state.  We don't fix the counter itself here,
		 * but we must be sure to store a valid value in our array entry.
		 */
		oldestMXact = MultiXactState->nextMXact;
		if (oldestMXact < FirstMultiXactId)
			oldestMXact = FirstMultiXactId;

		for (i = 1; i <= MaxBackends; i++)
		{
			MultiXactId thisoldest = OldestMemberMXactId[i];

			if (MultiXactIdIsValid(thisoldest) &&
				MultiXactIdPrecedes(thisoldest, oldestMXact))
				oldestMXact = thisoldest;
		}

		OldestVisibleMXactId[MyBackendId] = oldestMXact;

		LWLockRelease(MultiXactGenLock);

		debug_elog4(DEBUG2, "MultiXact: setting OldestVisible[%d] = %u",
					MyBackendId, oldestMXact);
	}
}

/*
 * MultiXactIdWait
 *		Sleep on a MultiXactId.
 *
 * We do this by sleeping on each member using XactLockTableWait.  Any
 * members that belong to the current backend are *not* waited for, however;
 * this would not merely be useless but would lead to Assert failure inside
 * XactLockTableWait.  By the time this returns, it is certain that all
 * transactions *of other backends* that were members of the MultiXactId
 * are dead (and no new ones can have been added, since it is not legal
 * to add members to an existing MultiXactId).
 *
 * But by the time we finish sleeping, someone else may have changed the Xmax
 * of the containing tuple, so the caller needs to iterate on us somehow.
 */
void
MultiXactIdWait(MultiXactId multi)
{
	TransactionId *members;
	int		nmembers;

	nmembers = GetMultiXactIdMembers(multi, &members);

	if (nmembers >= 0)
	{
		int		i;

		for (i = 0; i < nmembers; i++)
		{
			TransactionId	member = members[i];

			debug_elog4(DEBUG2, "MultiXactIdWait: waiting for %d (%u)",
						i, member);
			if (!TransactionIdIsCurrentTransactionId(member))
				XactLockTableWait(member);
		}

		pfree(members);
	}
}

/*
 * CreateMultiXactId
 * 		Make a new MultiXactId
 *
 * Make SLRU and cache entries for a new MultiXactId, recording the given
 * TransactionIds as members.  Returns the newly created MultiXactId.
 *
 * NB: the passed xids[] array will be sorted in-place.
 */
static MultiXactId
CreateMultiXactId(int nxids, TransactionId *xids)
{
	MultiXactId	multi;
	int			pageno;
	int			prev_pageno;
	int			entryno;
	int			slotno;
	uint32	   *offptr;
	uint32		offset;
	int			i;

	debug_elog3(DEBUG2, "Create: %s",
				mxid_to_string(InvalidMultiXactId, nxids, xids));

	/*
	 * See if the same set of XIDs already exists in our cache; if so, just
	 * re-use that MultiXactId.  (Note: it might seem that looking in our
	 * cache is insufficient, and we ought to search disk to see if a
	 * duplicate definition already exists.  But since we only ever create
	 * MultiXacts containing our own XID, in most cases any such MultiXacts
	 * were in fact created by us, and so will be in our cache.  There are
	 * corner cases where someone else added us to a MultiXact without our
	 * knowledge, but it's not worth checking for.)
	 */
	multi = mXactCacheGetBySet(nxids, xids);
	if (MultiXactIdIsValid(multi))
	{	
		debug_elog2(DEBUG2, "Create: in cache!");
		return multi;
	}

	multi = GetNewMultiXactId(nxids, &offset);

	LWLockAcquire(MultiXactOffsetControlLock, LW_EXCLUSIVE);

	ExtendMultiXactOffset(multi);

	pageno = MultiXactIdToOffsetPage(multi);
	entryno = MultiXactIdToOffsetEntry(multi);

	/*
	 * Note: we pass the MultiXactId to SimpleLruReadPage as the "transaction"
	 * to complain about if there's any I/O error.  This is kinda bogus, but
	 * since the errors will always give the full pathname, it should be
	 * clear enough that a MultiXactId is really involved.  Perhaps someday
	 * we'll take the trouble to generalize the slru.c error reporting code.
	 */
	slotno = SimpleLruReadPage(MultiXactOffsetCtl, pageno, multi);
	offptr = (uint32 *) MultiXactOffsetCtl->shared->page_buffer[slotno];
	offptr += entryno;
	*offptr = offset;

	MultiXactOffsetCtl->shared->page_status[slotno] = SLRU_PAGE_DIRTY;

	/* Exchange our lock */
	LWLockRelease(MultiXactOffsetControlLock);

	debug_elog3(DEBUG2, "Create: got offset %u", offset);

	LWLockAcquire(MultiXactMemberControlLock, LW_EXCLUSIVE);

	prev_pageno = -1;

	for (i = 0; i < nxids; i++, offset++)
	{
		TransactionId *memberptr;

		ExtendMultiXactMember(offset);

		pageno = MXOffsetToMemberPage(offset);
		entryno = MXOffsetToMemberEntry(offset);

		if (pageno != prev_pageno)
		{
			slotno = SimpleLruReadPage(MultiXactMemberCtl, pageno, multi);
			prev_pageno = pageno;
		}

		memberptr = (TransactionId *)
			MultiXactMemberCtl->shared->page_buffer[slotno];
		memberptr += entryno;

		*memberptr = xids[i];
		MultiXactMemberCtl->shared->page_status[slotno] = SLRU_PAGE_DIRTY;
	}

	LWLockRelease(MultiXactMemberControlLock);

	/* Store the new MultiXactId in the local cache, too */
	mXactCachePut(multi, nxids, xids);

	debug_elog2(DEBUG2, "Create: all done");

	return multi;
}

/*
 * GetNewMultiXactId
 *		Get the next MultiXactId.
 *
 * Get the next MultiXactId, XLogging if needed.  Also, reserve the needed
 * amount of space in the "members" area.  The starting offset of the
 * reserved space is returned in *offset.
 */
static MultiXactId
GetNewMultiXactId(int nxids, uint32 *offset)
{
	MultiXactId		result;

	debug_elog3(DEBUG2, "GetNew: for %d xids", nxids);

	/* MultiXactIdSetOldestMember() must have been called already */
	Assert(MultiXactIdIsValid(OldestMemberMXactId[MyBackendId]));

	LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);

	/* Handle wraparound of the nextMXact counter */
	if (MultiXactState->nextMXact < FirstMultiXactId)
	{
		MultiXactState->nextMXact = FirstMultiXactId;
		MultiXactState->mXactCount = 0;
	}

	/* If we run out of logged for use multixacts then we must log more */
	if (MultiXactState->mXactCount == 0)
	{
		XLogPutNextMultiXactId(MultiXactState->nextMXact + MXACT_PREFETCH);
		MultiXactState->mXactCount = MXACT_PREFETCH;
	}

	result = MultiXactState->nextMXact;

	/*
	 * We don't care about MultiXactId wraparound here; it will be handled by
	 * the next iteration.  But note that nextMXact may be InvalidMultiXactId
	 * after this routine exits, so anyone else looking at the variable must
	 * be prepared to deal with that.
	 */
	(MultiXactState->nextMXact)++;
	(MultiXactState->mXactCount)--;

	/*
	 * Reserve the members space.
	 */
	*offset = MultiXactState->nextOffset;
	MultiXactState->nextOffset += nxids;

	LWLockRelease(MultiXactGenLock);

	debug_elog4(DEBUG2, "GetNew: returning %u offset %u", result, *offset);
	return result;
}

/*
 * GetMultiXactIdMembers
 * 		Returns the set of TransactionIds that make up a MultiXactId
 *
 * We return -1 if the MultiXactId is too old to possibly have any members
 * still running; in that case we have not actually looked them up, and
 * *xids is not set.
 */
static int
GetMultiXactIdMembers(MultiXactId multi, TransactionId **xids)
{
	int			pageno;
	int			prev_pageno;
	int			entryno;
	int			slotno;
	uint32	   *offptr;
	uint32		offset;
	int			length;
	int			i;
	MultiXactId	nextMXact;
	MultiXactId	tmpMXact;
	uint32		nextOffset;
	TransactionId *ptr;

	debug_elog3(DEBUG2, "GetMembers: asked for %u", multi);

	Assert(MultiXactIdIsValid(multi));

	/* See if the MultiXactId is in the local cache */
	length = mXactCacheGetById(multi, xids);
	if (length >= 0)
	{
		debug_elog3(DEBUG2, "GetMembers: found %s in the cache",
					mxid_to_string(multi, length, *xids));
		return length;
	}

	/* Set our OldestVisibleMXactId[] entry if we didn't already */
	MultiXactIdSetOldestVisible();

	/*
	 * We check known limits on MultiXact before resorting to the SLRU area.
	 *
	 * An ID older than our OldestVisibleMXactId[] entry can't possibly still
	 * be running, and we'd run the risk of trying to read already-truncated
	 * SLRU data if we did try to examine it.
	 *
	 * Conversely, an ID >= nextMXact shouldn't ever be seen here; if it is
	 * seen, it implies undetected ID wraparound has occurred.  We just
	 * silently assume that such an ID is no longer running.
	 *
	 * Shared lock is enough here since we aren't modifying any global state.
	 * Also, we can examine our own OldestVisibleMXactId without the lock,
	 * since no one else is allowed to change it.
	 */
	if (MultiXactIdPrecedes(multi, OldestVisibleMXactId[MyBackendId]))
	{
		debug_elog2(DEBUG2, "GetMembers: it's too old");
		*xids = NULL;
		return -1;
	}

	LWLockAcquire(MultiXactGenLock, LW_SHARED);

	if (!MultiXactIdPrecedes(multi, MultiXactState->nextMXact))
	{
		LWLockRelease(MultiXactGenLock);
		debug_elog2(DEBUG2, "GetMembers: it's too new!");
		*xids = NULL;
		return -1;
	}

	/*
	 * Before releasing the lock, save the current counter values, because
	 * the target MultiXactId may be just one less than nextMXact.  We will
	 * need to use nextOffset as the endpoint if so.
	 */
	nextMXact = MultiXactState->nextMXact;
	nextOffset = MultiXactState->nextOffset;

	LWLockRelease(MultiXactGenLock);

	/* Get the offset at which we need to start reading MultiXactMembers */
	LWLockAcquire(MultiXactOffsetControlLock, LW_EXCLUSIVE);

	pageno = MultiXactIdToOffsetPage(multi);
	entryno = MultiXactIdToOffsetEntry(multi);

	slotno = SimpleLruReadPage(MultiXactOffsetCtl, pageno, multi);
	offptr = (uint32 *) MultiXactOffsetCtl->shared->page_buffer[slotno];
	offptr += entryno;
	offset = *offptr;

	/*
	 * How many members do we need to read?  If we are at the end of the
	 * assigned MultiXactIds, use the offset just saved above.  Else we
	 * need to check the MultiXactId following ours.
	 *
	 * Use the same increment rule as GetNewMultiXactId(), that is, don't
	 * handle wraparound explicitly until needed.
	 */
	tmpMXact = multi + 1;

	if (nextMXact == tmpMXact)
		length = nextOffset - offset;
	else
	{
		/* handle wraparound if needed */
		if (tmpMXact < FirstMultiXactId)
			tmpMXact = FirstMultiXactId;

		prev_pageno = pageno;

		pageno = MultiXactIdToOffsetPage(tmpMXact);
		entryno = MultiXactIdToOffsetEntry(tmpMXact);

		if (pageno != prev_pageno)
			slotno = SimpleLruReadPage(MultiXactOffsetCtl, pageno, tmpMXact);

		offptr = (uint32 *) MultiXactOffsetCtl->shared->page_buffer[slotno];
		offptr += entryno;
		length = *offptr - offset;
	}

	LWLockRelease(MultiXactOffsetControlLock);

	ptr = (TransactionId *) palloc(length * sizeof(TransactionId));
	*xids = ptr;

	/* Now get the members themselves. */
	LWLockAcquire(MultiXactMemberControlLock, LW_EXCLUSIVE);

	prev_pageno = -1;
	for (i = 0; i < length; i++, offset++)
	{
		TransactionId *xactptr;

		pageno = MXOffsetToMemberPage(offset);
		entryno = MXOffsetToMemberEntry(offset);

		if (pageno != prev_pageno)
		{
			slotno = SimpleLruReadPage(MultiXactMemberCtl, pageno, multi);
			prev_pageno = pageno;
		}

		xactptr = (TransactionId *)
			MultiXactMemberCtl->shared->page_buffer[slotno];
		xactptr += entryno;

		ptr[i] = *xactptr;
	}

	LWLockRelease(MultiXactMemberControlLock);

	/*
	 * Copy the result into the local cache.
	 */
	mXactCachePut(multi, length, ptr);

	debug_elog3(DEBUG2, "GetMembers: no cache for %s",
				mxid_to_string(multi, length, ptr));
	return length;
}

/*
 * mXactCacheGetBySet
 * 		returns a MultiXactId from the cache based on the set of
 * 		TransactionIds that compose it, or InvalidMultiXactId if
 * 		none matches.
 *
 * This is helpful, for example, if two transactions want to lock a huge
 * table.  By using the cache, the second will use the same MultiXactId
 * for the majority of tuples, thus keeping MultiXactId usage low (saving
 * both I/O and wraparound issues).
 *
 * NB: the passed xids[] array will be sorted in-place.
 */
static MultiXactId
mXactCacheGetBySet(int nxids, TransactionId *xids)
{
	mXactCacheEnt	*entry;

	debug_elog3(DEBUG2, "CacheGet: looking for %s",
				mxid_to_string(InvalidMultiXactId, nxids, xids));

	/* sort the array so comparison is easy */
	qsort(xids, nxids, sizeof(TransactionId), xidComparator);

	for (entry = MXactCache; entry != NULL; entry = entry->next)
	{
		if (entry->nxids != nxids)
			continue;

		/* We assume the cache entries are sorted */
		if (memcmp(xids, entry->xids, nxids * sizeof(TransactionId)) == 0)
		{
			debug_elog3(DEBUG2, "CacheGet: found %u", entry->multi);
			return entry->multi;
		}
	}

	debug_elog2(DEBUG2, "CacheGet: not found :-(");
	return InvalidMultiXactId;
}

/*
 * mXactCacheGetById
 * 		returns the composing TransactionId set from the cache for a
 * 		given MultiXactId, if present.
 *
 * If successful, *xids is set to the address of a palloc'd copy of the
 * TransactionId set.  Return value is number of members, or -1 on failure.
 */
static int
mXactCacheGetById(MultiXactId multi, TransactionId **xids)
{
	mXactCacheEnt	*entry;

	debug_elog3(DEBUG2, "CacheGet: looking for %u", multi);

	for (entry = MXactCache; entry != NULL; entry = entry->next)
	{
		if (entry->multi == multi)
		{
			TransactionId	*ptr;
			Size		size;

			size = sizeof(TransactionId) * entry->nxids;
			ptr = (TransactionId *) palloc(size);
			*xids = ptr;

			memcpy(ptr, entry->xids, size);

			debug_elog3(DEBUG2, "CacheGet: found %s",
					mxid_to_string(multi, entry->nxids, entry->xids));
			return entry->nxids;
		}
	}

	debug_elog2(DEBUG2, "CacheGet: not found");
	return -1;
}

/*
 * mXactCachePut
 * 		Add a new MultiXactId and its composing set into the local cache.
 */
static void
mXactCachePut(MultiXactId multi, int nxids, TransactionId *xids)
{
	mXactCacheEnt  *entry;

	debug_elog3(DEBUG2, "CachePut: storing %s",
				mxid_to_string(multi, nxids, xids));

	if (MXactContext == NULL)
	{
		/* The cache only lives as long as the current transaction */
		debug_elog2(DEBUG2, "CachePut: initializing memory context");
		MXactContext = AllocSetContextCreate(TopTransactionContext,
											 "MultiXact Cache Context",
											 ALLOCSET_SMALL_MINSIZE,
											 ALLOCSET_SMALL_INITSIZE,
											 ALLOCSET_SMALL_MAXSIZE);
	}

	entry = (mXactCacheEnt *)
		MemoryContextAlloc(MXactContext,
						   offsetof(mXactCacheEnt, xids) +
						   nxids * sizeof(TransactionId));

	entry->multi = multi;
	entry->nxids = nxids;
	memcpy(entry->xids, xids, nxids * sizeof(TransactionId));

	/* mXactCacheGetBySet assumes the entries are sorted, so sort them */
	qsort(entry->xids, nxids, sizeof(TransactionId), xidComparator);

	entry->next = MXactCache;
	MXactCache = entry;
}

/*
 * xidComparator
 * 		qsort comparison function for XIDs
 *
 * We don't need to use wraparound comparison for XIDs, and indeed must
 * not do so since that does not respect the triangle inequality!  Any
 * old sort order will do.
 */
static int
xidComparator(const void *arg1, const void *arg2)
{
	TransactionId xid1 = * (const TransactionId *) arg1;
	TransactionId xid2 = * (const TransactionId *) arg2;

	if (xid1 > xid2)
		return 1;
	if (xid1 < xid2)
		return -1;
	return 0;
}

#ifdef MULTIXACT_DEBUG
static char *
mxid_to_string(MultiXactId multi, int nxids, TransactionId *xids)
{
	char *str = palloc(15 * (nxids + 1) + 4);
	int i;
	snprintf(str, 47, "%u %d[%u", multi, nxids, xids[0]);

	for (i = 1; i < nxids; i++)
		snprintf(str + strlen(str), 17, ", %u", xids[i]);

	strcat(str, "]");
	return str;
}
#endif

/*
 * AtEOXact_MultiXact
 *		Handle transaction end for MultiXact
 *
 * This is called at top transaction commit or abort (we don't care which).
 */
void
AtEOXact_MultiXact(void)
{
	/*
	 * Reset our OldestMemberMXactId and OldestVisibleMXactId values,
	 * both of which should only be valid while within a transaction.
	 *
	 * We assume that storing a MultiXactId is atomic and so we need
	 * not take MultiXactGenLock to do this.
	 */
	OldestMemberMXactId[MyBackendId] = InvalidMultiXactId;
	OldestVisibleMXactId[MyBackendId] = InvalidMultiXactId;

	/*
	 * Discard the local MultiXactId cache.  Since MXactContext was created
	 * as a child of TopTransactionContext, we needn't delete it explicitly.
	 */
	MXactContext = NULL;
	MXactCache = NULL;
}

/*
 * Initialization of shared memory for MultiXact.  We use two SLRU areas,
 * thus double memory.  Also, reserve space for the shared MultiXactState
 * struct and the per-backend MultiXactId arrays (two of those, too).
 */
int
MultiXactShmemSize(void)
{
#define SHARED_MULTIXACT_STATE_SIZE \
	(sizeof(MultiXactStateData) + sizeof(MultiXactId) * 2 * MaxBackends)

	return (SimpleLruShmemSize() * 2 + SHARED_MULTIXACT_STATE_SIZE);
}

void
MultiXactShmemInit(void)
{
	bool	found;

	debug_elog2(DEBUG2, "Shared Memory Init for MultiXact");

	MultiXactOffsetCtl->PagePrecedes = MultiXactOffsetPagePrecedes;
	MultiXactMemberCtl->PagePrecedes = MultiXactMemberPagePrecedes;

	SimpleLruInit(MultiXactOffsetCtl, "MultiXactOffset Ctl",
				  MultiXactOffsetControlLock, "pg_multixact/offsets");
	SimpleLruInit(MultiXactMemberCtl, "MultiXactMember Ctl",
				  MultiXactMemberControlLock, "pg_multixact/members");

	/* Override default assumption that writes should be fsync'd */
	MultiXactOffsetCtl->do_fsync = false;
	MultiXactMemberCtl->do_fsync = false;

	/* Initialize our shared state struct */
	MultiXactState = ShmemInitStruct("Shared MultiXact State",
									 SHARED_MULTIXACT_STATE_SIZE,
									 &found);
	if (!IsUnderPostmaster)
	{
		Assert(!found);

		/* Make sure we zero out the per-backend state */
		MemSet(MultiXactState, 0, SHARED_MULTIXACT_STATE_SIZE);
	}
	else
		Assert(found);

	/*
	 * Set up array pointers.  Note that perBackendXactIds[0] is wasted
	 * space since we only use indexes 1..MaxBackends in each array.
	 */
	OldestMemberMXactId = MultiXactState->perBackendXactIds;
	OldestVisibleMXactId = OldestMemberMXactId + MaxBackends;
}

/*
 * This func must be called ONCE on system install.  It creates the initial
 * MultiXact segments.  (The MultiXacts directories are assumed to have been
 * created by initdb, and MultiXactShmemInit must have been called already.)
 *
 * Note: it's not really necessary to create the initial segments now,
 * since slru.c would create 'em on first write anyway.	But we may as well
 * do it to be sure the directories are set up correctly.
 */
void
BootStrapMultiXact(void)
{
	int			slotno;

	LWLockAcquire(MultiXactOffsetControlLock, LW_EXCLUSIVE);

	/* Offsets first page */
	slotno = ZeroMultiXactOffsetPage(0);
	SimpleLruWritePage(MultiXactOffsetCtl, slotno, NULL);
	Assert(MultiXactOffsetCtl->shared->page_status[slotno] == SLRU_PAGE_CLEAN);

	LWLockRelease(MultiXactOffsetControlLock);

	LWLockAcquire(MultiXactMemberControlLock, LW_EXCLUSIVE);

	/* Members first page */
	slotno = ZeroMultiXactMemberPage(0);
	SimpleLruWritePage(MultiXactMemberCtl, slotno, NULL);
	Assert(MultiXactMemberCtl->shared->page_status[slotno] == SLRU_PAGE_CLEAN);

	LWLockRelease(MultiXactMemberControlLock);
}

/*
 * Initialize (or reinitialize) a page of MultiXactOffset to zeroes.
 *
 * The page is not actually written, just set up in shared memory.
 * The slot number of the new page is returned.
 *
 * Control lock must be held at entry, and will be held at exit.
 */
static int
ZeroMultiXactOffsetPage(int pageno)
{
	return SimpleLruZeroPage(MultiXactOffsetCtl, pageno);
}

/*
 * Ditto, for MultiXactMember
 */
static int
ZeroMultiXactMemberPage(int pageno)
{
	return SimpleLruZeroPage(MultiXactMemberCtl, pageno);
}

/*
 * This must be called ONCE during postmaster or standalone-backend startup.
 *
 * StartupXLOG has already established nextMXact by calling
 * MultiXactSetNextMXact and/or MultiXactAdvanceNextMXact.
 *
 * We don't need any locks here, really; the SLRU locks are taken
 * only because slru.c expects to be called with locks held.
 */
void
StartupMultiXact(void)
{
	int			startPage;
	int			cutoffPage;
	uint32		offset;

	/*
	 * We start nextOffset at zero after every reboot; there is no need to
	 * avoid offset values that were used in the previous system lifecycle.
	 */
	MultiXactState->nextOffset = 0;

	/*
	 * Because of the above, a shutdown and restart is likely to leave
	 * high-numbered MultiXactMember page files that would not get recycled
	 * for a long time (about as long as the system had been up in the
	 * previous cycle of life).  To clean out such page files, we issue an
	 * artificial truncation call that will zap any page files in the first
	 * half of the offset cycle.  Should there be any page files in the last
	 * half, they will get cleaned out by the first checkpoint.
	 *
	 * XXX it might be a good idea to disable this when debugging, since it
	 * will tend to destroy evidence after a crash.  To not be *too* ruthless,
	 * we arbitrarily spare the first 64 pages.  (Note this will get
	 * rounded off to a multiple of SLRU_PAGES_PER_SEGMENT ...)
	 */
	offset = ((~ (uint32) 0) >> 1) + 1;

	cutoffPage = MXOffsetToMemberPage(offset) + 64;

	/*
	 * Defeat safety interlock in SimpleLruTruncate; this hack will be
	 * cleaned up by ZeroMultiXactMemberPage call below.
	 */
	MultiXactMemberCtl->shared->latest_page_number = cutoffPage;

	SimpleLruTruncate(MultiXactMemberCtl, cutoffPage);

	/*
	 * Initialize lastTruncationPoint to invalid, ensuring that the first
	 * checkpoint will try to do truncation.
	 */
	MultiXactState->lastTruncationPoint = InvalidMultiXactId;

	/*
	 * Since we don't expect MultiXact to be valid across crashes, we
	 * initialize the currently-active pages to zeroes during startup.
	 * Whenever we advance into a new page, both ExtendMultiXact routines
	 * will likewise zero the new page without regard to whatever was
	 * previously on disk.
	 */
	LWLockAcquire(MultiXactOffsetControlLock, LW_EXCLUSIVE);

	startPage = MultiXactIdToOffsetPage(MultiXactState->nextMXact);
	(void) ZeroMultiXactOffsetPage(startPage);

	LWLockRelease(MultiXactOffsetControlLock);

	LWLockAcquire(MultiXactMemberControlLock, LW_EXCLUSIVE);

	startPage = MXOffsetToMemberPage(MultiXactState->nextOffset);
	(void) ZeroMultiXactMemberPage(startPage);

	LWLockRelease(MultiXactMemberControlLock);
}

/*
 * This must be called ONCE during postmaster or standalone-backend shutdown
 */
void
ShutdownMultiXact(void)
{
	/*
	 * Flush dirty MultiXact pages to disk
	 *
	 * This is not actually necessary from a correctness point of view. We do
	 * it merely as a debugging aid.
	 */
	SimpleLruFlush(MultiXactOffsetCtl, false);
	SimpleLruFlush(MultiXactMemberCtl, false);
}

/*
 * Get the next MultiXactId to save in a checkpoint record
 */
MultiXactId
MultiXactGetCheckptMulti(bool is_shutdown)
{
	MultiXactId	retval;

	LWLockAcquire(MultiXactGenLock, LW_SHARED);

	retval = MultiXactState->nextMXact;
	if (!is_shutdown)
		retval += MultiXactState->mXactCount;

	LWLockRelease(MultiXactGenLock);

	debug_elog3(DEBUG2, "MultiXact: MultiXact for checkpoint record is %u",
				retval);

	return retval;
}

/*
 * Perform a checkpoint --- either during shutdown, or on-the-fly
 */
void
CheckPointMultiXact(void)
{
	/*
	 * Flush dirty MultiXact pages to disk
	 *
	 * This is not actually necessary from a correctness point of view. We do
	 * it merely to improve the odds that writing of dirty pages is done
	 * by the checkpoint process and not by backends.
	 */
	SimpleLruFlush(MultiXactOffsetCtl, true);
	SimpleLruFlush(MultiXactMemberCtl, true);

	/*
	 * Truncate the SLRU files
	 */
	TruncateMultiXact();
}

/*
 * Set the next-to-be-assigned MultiXactId
 *
 * This is used when we can determine the correct next Id exactly
 * from an XLog record.  We need no locking since it is only called
 * during bootstrap and XLog replay.
 */
void
MultiXactSetNextMXact(MultiXactId nextMulti)
{
	debug_elog3(DEBUG2, "MultiXact: setting next multi to %u", nextMulti);
	MultiXactState->nextMXact = nextMulti;
	MultiXactState->mXactCount = 0;
}

/*
 * Ensure the next-to-be-assigned MultiXactId is at least minMulti
 *
 * This is used when we can determine a minimum safe value
 * from an XLog record.  We need no locking since it is only called
 * during XLog replay.
 */
void
MultiXactAdvanceNextMXact(MultiXactId minMulti)
{
	if (MultiXactIdPrecedes(MultiXactState->nextMXact, minMulti))
	{
		debug_elog3(DEBUG2, "MultiXact: setting next multi to %u", minMulti);
		MultiXactState->nextMXact = minMulti;
		MultiXactState->mXactCount = 0;
	}
}

/*
 * Make sure that MultiXactOffset has room for a newly-allocated MultiXactId.
 *
 * The MultiXactOffsetControlLock should be held at entry, and will
 * be held at exit.
 */
void
ExtendMultiXactOffset(MultiXactId multi)
{
	int			pageno;

	/*
	 * No work except at first MultiXactId of a page.  But beware: just after
	 * wraparound, the first MultiXactId of page zero is FirstMultiXactId.
	 */
	if (MultiXactIdToOffsetEntry(multi) != 0 &&
		multi != FirstMultiXactId)
		return;

	pageno = MultiXactIdToOffsetPage(multi);

	/* Zero the page */
	ZeroMultiXactOffsetPage(pageno);
}

/*
 * Make sure that MultiXactMember has room for the members of a newly-
 * allocated MultiXactId.
 *
 * The MultiXactMemberControlLock should be held at entry, and will be held
 * at exit.
 */
void
ExtendMultiXactMember(uint32 offset)
{
	int		pageno;

	/*
	 * No work except at first entry of a page.
	 */
	if (MXOffsetToMemberEntry(offset) != 0)
		return;

	pageno = MXOffsetToMemberPage(offset);

	/* Zero the page */
	ZeroMultiXactMemberPage(pageno);
}

/*
 * Remove all MultiXactOffset and MultiXactMember segments before the oldest
 * ones still of interest.
 *
 * This is called only during checkpoints.  We assume no more than one
 * backend does this at a time.
 */
static void
TruncateMultiXact(void)
{
	MultiXactId nextMXact;
	uint32		nextOffset;
	MultiXactId oldestMXact;
	uint32		oldestOffset;
	int			cutoffPage;
	int			i;

	/*
	 * First, compute where we can safely truncate.  Per notes above,
	 * this is the oldest valid value among all the OldestMemberMXactId[] and
	 * OldestVisibleMXactId[] entries, or nextMXact if none are valid.
	 */
	LWLockAcquire(MultiXactGenLock, LW_SHARED);

	/*
	 * We have to beware of the possibility that nextMXact is in the
	 * wrapped-around state.  We don't fix the counter itself here,
	 * but we must be sure to use a valid value in our calculation.
	 */
	nextMXact = MultiXactState->nextMXact;
	if (nextMXact < FirstMultiXactId)
		nextMXact = FirstMultiXactId;

	oldestMXact = nextMXact;
	for (i = 1; i <= MaxBackends; i++)
	{
		MultiXactId thisoldest;

		thisoldest = OldestMemberMXactId[i];
		if (MultiXactIdIsValid(thisoldest) &&
			MultiXactIdPrecedes(thisoldest, oldestMXact))
			oldestMXact = thisoldest;
		thisoldest = OldestVisibleMXactId[i];
		if (MultiXactIdIsValid(thisoldest) &&
			MultiXactIdPrecedes(thisoldest, oldestMXact))
			oldestMXact = thisoldest;
	}

	/* Save the current nextOffset too */
	nextOffset = MultiXactState->nextOffset;

	LWLockRelease(MultiXactGenLock);

	debug_elog3(DEBUG2, "MultiXact: truncation point = %u", oldestMXact);

	/*
	 * If we already truncated at this point, do nothing.  This saves time
	 * when no MultiXacts are getting used, which is probably not uncommon.
	 */
	if (MultiXactState->lastTruncationPoint == oldestMXact)
		return;

	/*
	 * We need to determine where to truncate MultiXactMember.  If we
	 * found a valid oldest MultiXactId, read its starting offset;
	 * otherwise we use the nextOffset value we saved above.
	 */
	if (oldestMXact == nextMXact)
		oldestOffset = nextOffset;
	else
	{
		int			pageno;
		int			slotno;
		int			entryno;
		uint32	   *offptr;

		LWLockAcquire(MultiXactOffsetControlLock, LW_EXCLUSIVE);

		pageno = MultiXactIdToOffsetPage(oldestMXact);
		entryno = MultiXactIdToOffsetEntry(oldestMXact);

		slotno = SimpleLruReadPage(MultiXactOffsetCtl, pageno, oldestMXact);
		offptr = (uint32 *) MultiXactOffsetCtl->shared->page_buffer[slotno];
		offptr += entryno;
		oldestOffset = *offptr;

		LWLockRelease(MultiXactOffsetControlLock);
	}

	/*
	 * The cutoff point is the start of the segment containing oldestMXact.
	 * We pass the *page* containing oldestMXact to SimpleLruTruncate.
	 */
	cutoffPage = MultiXactIdToOffsetPage(oldestMXact);

	SimpleLruTruncate(MultiXactOffsetCtl, cutoffPage);

	/*
	 * Also truncate MultiXactMember at the previously determined offset.
	 */
	cutoffPage = MXOffsetToMemberPage(oldestOffset);

	SimpleLruTruncate(MultiXactMemberCtl, cutoffPage);

	/*
	 * Set the last known truncation point.  We don't need a lock for this
	 * since only one backend does checkpoints at a time.
	 */
	MultiXactState->lastTruncationPoint = oldestMXact;
}

/*
 * Decide which of two MultiXactOffset page numbers is "older" for truncation
 * purposes.
 *
 * We need to use comparison of MultiXactId here in order to do the right
 * thing with wraparound.  However, if we are asked about page number zero, we
 * don't want to hand InvalidMultiXactId to MultiXactIdPrecedes: it'll get
 * weird.  So, offset both multis by FirstMultiXactId to avoid that.
 * (Actually, the current implementation doesn't do anything weird with
 * InvalidMultiXactId, but there's no harm in leaving this code like this.)
 */
static bool
MultiXactOffsetPagePrecedes(int page1, int page2)
{
	MultiXactId multi1;
	MultiXactId multi2;

	multi1 = ((MultiXactId) page1) * MULTIXACT_OFFSETS_PER_PAGE;
	multi1 += FirstMultiXactId;
	multi2 = ((MultiXactId) page2) * MULTIXACT_OFFSETS_PER_PAGE;
	multi2 += FirstMultiXactId;

	return MultiXactIdPrecedes(multi1, multi2);
}

/*
 * Decide which of two MultiXactMember page numbers is "older" for truncation
 * purposes.  There is no "invalid offset number" so use the numbers verbatim.
 */
static bool
MultiXactMemberPagePrecedes(int page1, int page2)
{
	uint32	offset1;
	uint32	offset2;

	offset1 = ((uint32) page1) * MULTIXACT_MEMBERS_PER_PAGE;
	offset2 = ((uint32) page2) * MULTIXACT_MEMBERS_PER_PAGE;

	return MultiXactOffsetPrecedes(offset1, offset2);
}

/*
 * Decide which of two MultiXactIds is earlier.
 *
 * XXX do we need to do something special for InvalidMultiXactId?
 * (Doesn't look like it.)
 */
static bool
MultiXactIdPrecedes(MultiXactId multi1, MultiXactId multi2)
{
	int32 diff = (int32) (multi1 - multi2);

	return (diff < 0);
}

/*
 * Decide which of two offsets is earlier.
 */
static bool
MultiXactOffsetPrecedes(uint32 offset1, uint32 offset2)
{
	int32 diff = (int32) (offset1 - offset2);

	return (diff < 0);
}
